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https://sql-academy.org/en/guide/work-with-number-data-type | [
"# Numeric data type in SQL\n\nCreating numeric data in SQL is quite simple: you can enter a number as a literal, you can get it from a table column, or generate it by calculation.\n\nWhen calculating, you can use all standard arithmetic operations (+, -, *, / and others) and change the priorities of calculations using brackets.\n\n```MySQL```SELECT 2 * ((22 - 16) / (2 + 1)) AS calc_example;\n``````\ncalc_example\n4\n\n## Math functions\n\nFor most mathematical calculations, such as getting the power of a number or getting the square root, in SQL there are built-in numeric functions. Here are some examples of these functions:\n\nFunction nameDescription\nPOW(num, power)Calculates a number to the specified power\nSQRT(num)Calculates the square root of a number\nLOG(base, num)Calculates the logarithm of a number to the specified base\nEXP(num)Calculates enum\nSIN(num)Calculates the sine of a number\nCOS(num)Calculates the cosine of a number\nTAN(num)Calculates the tangent of a number\n\nA list of all numeric functions, their descriptions and examples can be found in the handbook.\n\n## Round numbers\n\nWhen working with floating point numbers, it is not always necessary to store or display numbers with full precision. So, monetary transactions can be stored with an accuracy of up to 6 decimal places, and displayed up to 2, with an accuracy of kopecks.\n\nSQL provides the following 4 functions for rounding numeric data: CEIL, FLOOR, ROUND, TRUNCATE.\n\nThe functions CEIL, FLOOR are aimed at rounding a number to the nearest integer up and down, respectively.\n\n```MySQL```SELECT CEILING(69.69) AS ceiling, FLOOR(69.69) AS floor;\n``````\nceilingfloor\n7069\n\nTo round to the nearest integer, there is a ROUND function, which rounds any number whose decimal part is greater than or equal to 0.5. side, otherwise less.\n\n```MySQL```SELECT ROUND(69.499), ROUND(69.5), ROUND(69.501);\n``````\nROUND(69.499)ROUND(69.5)ROUND(69.501)\n697070\n\nThe ROUND function also allows you to round a number to some fraction of decimal places. To do this, the function takes an optional second argument indicating the number of decimal places to leave.\n\n```MySQL```SELECT ROUND(69.7171,1), ROUND(69.7171,2), ROUND(69.7171,3);\n``````\nROUND(69.7171,1)ROUND(69.7171,2)ROUND(69.7171,3)\n69.769.7269.717\n\nThe second argument to the ROUND function can also take negative values. In this case, the digits to the left of the decimal point of the number become equal to zero by the number specified in the argument, and the fractional part is cut off.\n\n```MySQL```SELECT ROUND(1691.7,-1), ROUND(1691.7,-2), ROUND(1691.7,-3);\n``````\nROUND(1691.7,-1)ROUND(1691.7,-2)ROUND(1691.7,-3)\n169017002000\n\nThe TRUNCATE function is similar to the ROUND function, it is also capable of taking an optional 2nd parameter, only instead of rounding it simply discards unnecessary numbers.\n\n```MySQL```SELECT TRUNCATE(69.7979,1), TRUNCATE(69.7979,2), TRUNCATE(69.7979,3);\n``````\nTRUNCATE(69.7979,1)TRUNCATE(69.7979,2)TRUNCATE(69.7979,3)\n69.769.7969.797\n\nWhat will the following expression return?\n\n```MySQL```SELECT TRUNCATE(69.7979, -1);\n``````\n\n## Working with signed numbers\n\nWhen working with numeric data that may contain negative values, the SIGN and ABS functions can be useful.\n\nThe SIGN function returns -1 if the number is negative, 0 if the number is zero, and 1 if the number is positive.\n\n```MySQL```SELECT SIGN(-69), SIGN(0), SIGN(69);\n``````\nSIGN(-69)SIGN(0)SIGN(69)\n-101\n\nThe ABS function returns the absolute value of a number.\n\n```MySQL```SELECT ABS(-69), ABS(0), ABS(69);\n``````\nABS(-69)ABS(0)ABS(69)\n69069",
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"https://sql-academy.org/static/loader.svg",
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.74116945,"math_prob":0.9980022,"size":2721,"snap":"2023-40-2023-50","text_gpt3_token_len":665,"char_repetition_ratio":0.15311004,"word_repetition_ratio":0.0,"special_character_ratio":0.26240352,"punctuation_ratio":0.17277487,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9978281,"pos_list":[0,1,2],"im_url_duplicate_count":[null,9,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-27T22:26:39Z\",\"WARC-Record-ID\":\"<urn:uuid:e5efbb87-1f09-4625-80d4-f31230038e5b>\",\"Content-Length\":\"105594\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:cd434c03-99ca-4f3d-ad24-c741467eada5>\",\"WARC-Concurrent-To\":\"<urn:uuid:733bc56d-01f3-4483-9604-2887be83eae4>\",\"WARC-IP-Address\":\"94.103.85.193\",\"WARC-Target-URI\":\"https://sql-academy.org/en/guide/work-with-number-data-type\",\"WARC-Payload-Digest\":\"sha1:DO7WLNACITLEP7P7BS5J66V5IWXICHCE\",\"WARC-Block-Digest\":\"sha1:FGNLR2TRSRVDV7N4NEFI4P4FTKO6BGJS\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510326.82_warc_CC-MAIN-20230927203115-20230927233115-00349.warc.gz\"}"} |
https://www.mina.moe/archives/13718 | [
"# 字符串杂题记录\n\n## Suffix AutoMaton\n\n$\\rm{SAM}$ 的一个节点储存字符串 $endpos$ 集合一样，这玩意可以用线段树合并求。\n\n$\\rm{SAM}$ 走 $ch$ 边相当于往后面加字符，跳 $fail$ 相当于删去一段前缀\n\n$\\rm{SAM}$ 和 $\\rm{ACM}$ 上做串的匹配是同一个道理，跳 $fail$ 都是删去一段前缀，每一次加入 $T$ 的后一个字符就跳 $fail$ 找到匹配的节点。\n\n$\\rm{LCP}$ 可以对反串做 $\\rm{SAM}$，然后同时把位置反转，询问 $\\rm{LCP}$ 等价于询问 $fail$ 树上 $lca(pos_i,pos_j)$ 节点的 $len$ 。\n\n## 题目集合：\n\n### Luogu P2414「NOI2011」阿狸的打字机\n\n$Str(x)$ 在 $Str(y)$ 中出现了多少次，$\\rm{ACM}$，然后对于每个 $Str(y)$ 的子串一定是从某个前缀跳 $fail$ 得到的，找到 $x$ 的节点，出现次数即是 $x$ 子树内 $y$ 前缀点的个数\n\n### Bzoj #4231. 回忆树\n\n• 注意这里的点是原树点而非 $fail$ 树点。\n• 具体跑的方法就是，从原树根节点开始，存一下当前走到 $\\rm{ACM}$ 上了哪个节点了，原树走向哪个儿子，$\\rm{ACM}$ 就对应转移，当没有对应出边的时候就需要跳 $fail$ (其实求 $fail$ 的时候就搞定了，直接走就完了)。\n• 到达当前的原树节点 $u$ ，对应 $\\rm{ACM}$ 的节点为 $t$ ，$t$ 作为当前的串，将 $u$ 中的询问都拿出来，直接查询对应节点的子树和即可。\n• 用 $\\rm{BIT}$ 维护每个点的贡献以及支持查询子树和，操作方法同” 阿狸的打字机”。\n\nvoid get_ans(int u,int t1,int t2) {\nbit.update(acm.dfn[t1],1);\nbit.update(acm.dfn[t2],1);\n\nfor(Query now:q[u]) {\nint id=now.id,p=now.typ,v=now.val,k=acm[p].pos[id];\nans[id]+=v*bit[p].query(acm[p].dfn[k],acm[p].dfn[k]+acm[p].siz[k]-1);\n}\nfor(Edge_Node now:son[u]) {\nint v=now.to,c=now.val;\nif(v==fa[u]) continue;\nget_ans(v,acm.ch[t1][c],acm.ch[t2][c]);\n}\n\nbit.update(acm.dfn[t1],-1);\nbit.update(acm.dfn[t2],-1);\n}\n\n\n$t_1,t_2$ 分别表示两个 $\\rm{ACM}$ 上的当前节点编号，$u$ 表示原树当前节点编号。\n\n### CF917E Upside Down\n\n• $u\\rightarrow \\cdots \\rightarrow lca$ 路径形成的字符串，所有和 $S_k$ 某一个前缀一模一样的后缀中最长的后缀长度，记为 $L_1$ ，同样记这个最长后缀为 $T_1$ 。\n• $lca\\rightarrow \\cdots \\rightarrow v$ 路径形成的字符串，所有和 $S_k$ 某一个后缀一模一样的前缀中最长的前缀长度，记为 $L_2$ ，同样记这个最长前缀为 $T_2$ 。\n\n• 如果 $L=|S_k[i,|S_k|]|$，也就是说当前后缀已经匹配满了，那么显然这是一组可以用于答案的后缀。\n• 如果 $L=|R|,L< |S_k[i,|S_k|]|$，如果当前后缀没有匹配满，但是路径上节点匹配满了，这一组后缀一定不能用于答案。\n• 如果 $L< |S_k[i,|S_k|]|,L<|R|$，都没有匹配满，考虑下一个字符，比较大小。\n\nQAQ\n\n### 8 条评论",
null,
"#### Qiuly · 2020年8月1日 11:02 上午\n\nborder 应该是最长公共前后缀吧（",
null,
"#### Rayment · 2020年7月30日 10:25 下午\n\n“ACM 跳的是 最长公共后缀，而不是 最长公共前后缀 ”"
] | [
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"https://secure.gravatar.com/avatar/fea541be0e0b7a80bdb95c91eb70d1ae",
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"https://secure.gravatar.com/avatar/e2737bc4d6b0718e9fec264be951f597",
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https://math.stackexchange.com/questions/tagged/banach-spaces | [
"# Questions tagged [banach-spaces]\n\nA Banach space is a complete normed vector space: A vector space equipped with a norm such that every Cauchy sequence converges.\n\n4,162 questions\n0answers\n12 views\n\n1answer\n23 views\n\n### Sequences of Continuous Linear Operators between Banach Spaces.\n\nLet $E, F$ be two Banach Spaces. Let $\\{ T_{n} \\}$ be a sequence of continuous linear operators from $E$ into $F$ such that: For all $x \\in E: T_{n}x \\rightarrow Tx,$ some limit in $F$. Then the ...\n0answers\n28 views\n\n0answers\n37 views\n\n### functional analysis : problem related to closed graph theorem\n\nenter image description here the problem above is in Conway's [Functional Analysis] (p.93) it seems to be an application of closed graph theorem if the inequality were posed the other way it could ...\n0answers\n35 views\n\n### Uncountable basis in Hilbert space vs orthonormal basis\n\nIt is known that an infinite dimensional Banach space does not have a countable Hamel basis. It is also known that a separable Hilbert space has an orthonormal countable basis. Now, I think this basis ...\n0answers\n16 views\n\n1answer\n49 views\n\n### $A \\in \\mathcal{L}(X,Y) \\implies A^* \\in \\mathcal{L}(Y^*_{w^*}, X^*_{w^*})$\n\nExercise : Let $X,Y$ be Banach spaces and $A \\in \\mathcal{L}(X,Y)$. Show that $A^* \\in \\mathcal{L}(Y^*_{w^*}, X^*_{w^*})$. Attempt : The linearity is trivial. Τo show that $A^*$ is $w^*$ to $w^*$...\n0answers\n34 views\n\n### Approximating a Banach space valued function by sums of continuous functions\n\nI am trying to prove the following exercise, which is a part of a project type homework problem. Please give hints and suggestions, and discuss this problem. Let $(T,d)$ be a compact metric space, ...\n2answers\n26 views"
] | [
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http://blog.phytools.org/2012/08/discrete-time-brownian-motion.html | [
"## Thursday, August 9, 2012\n\n### Discrete time Brownian motion visualization\n\nWorking on my lecture for the Evolutionary Quantitative Genetics Workshop at NESCent. Here is some really simple code to perform discrete-time (non-phylogenetic) Brownian motion simulation:\n\n# discrete time BM simulation\nn<-100; t<-100; sig2<-1/t # set parameters\ntime<-0:t\nX<-rbind(rep(0,n),matrix(rnorm(n*t,sd=sqrt(sig2)),t,n))\nY<-apply(X,2,cumsum)\nplot(time,Y[,1],ylim=range(Y),xlab=\"time\",ylab=\"phenotype\", type=\"l\")\napply(Y,2,lines,x=time)\n\nAnd here is the result:"
] | [
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.6743506,"math_prob":0.9875344,"size":600,"snap":"2020-34-2020-40","text_gpt3_token_len":168,"char_repetition_ratio":0.08389262,"word_repetition_ratio":0.0,"special_character_ratio":0.26666668,"punctuation_ratio":0.19402985,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9805209,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-27T10:56:43Z\",\"WARC-Record-ID\":\"<urn:uuid:12b82a9e-1920-41f5-9570-fa2317d2f531>\",\"Content-Length\":\"88318\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c7082e17-944b-4db4-a420-064843f50fc4>\",\"WARC-Concurrent-To\":\"<urn:uuid:81be07ee-6bf8-4177-b904-641a16193709>\",\"WARC-IP-Address\":\"172.217.13.243\",\"WARC-Target-URI\":\"http://blog.phytools.org/2012/08/discrete-time-brownian-motion.html\",\"WARC-Payload-Digest\":\"sha1:DIRCKPAHMLQSIBAM5SYGQF3SXXBQRMWL\",\"WARC-Block-Digest\":\"sha1:Z66JQ3SNZK46IFTTA3FHVP2A5FH4IUZ3\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600400274441.60_warc_CC-MAIN-20200927085848-20200927115848-00541.warc.gz\"}"} |
http://zhengweiyu.com/2013/12/13/2010-kebiao-quanguo-25.html | [
"# 2010 新课标全国卷 25题\n\n2013-12-13 12:56\n\n#### 问题\n\n（1）速度的大小\n\n（2）速度方向与轴正方向夹角的正弦。",
null,
"#### 物理建模\n\n1. 从原点…某时刻发射大量 … 带正电粒子\n2. （粒子的）速度大小相同\n3. 从发射粒子到粒子全部离开磁场经历的时间恰好为粒子在磁场中做圆周运动周期的四分之一\n\n1. 研究对象是一批粒子还是一个粒子？（最后一个粒子）\n2. 这批粒子是同一时刻发射的吗？（是）\n3. 圆周运动周期的四分之一意味着什么？（圆心角为$90^\\circ$\n4. 最后离开磁场的粒子轨道长度和其他粒子比较有何特点？（最长）\n\n• 是一段圆弧，圆心角为$90^\\circ$\n\n• 矩形磁场中弧线应尽可能的长",
null,
"• 轨道与磁场边界相切，弦略短于矩形磁场的对角线。",
null,
"#### 数学处理\n\n$x$方向： $Rcos\\theta + Rsin\\theta = a$\n\n$y$方向： $R - Rsin\\theta = \\frac{a}{2}$\n\n$R$\n\n$sin\\theta_{1} = \\frac{6-\\sqrt6}{10} \\simeq 0.4$$sin\\theta_{2} = \\frac{6+\\sqrt6}{10} \\simeq 0.8$\n\n$y$方向的列式易得\n\n$R = \\frac{mv}{qB}$可解出第(1)问，$v = (2-\\frac{\\sqrt6}{2}) \\frac{aqB}{m}$\n\n#### 解题回顾\n\n• 通过审题及作轨迹图，分析力和运动，理解物理情境。\n• 化弧为弦，根据限制条件不断逼近正确的情境况，建立几何模型。\n• 善于从几何图像中寻找数学关系，建立已知——未知量的联系。\n• 熟悉如何联立方程解未知数\n• 消元，降次\n• 升次后要讨论解\n\n© 版权所有 悟理 2013-2019\n\n# 2010 新课标全国卷 25题\n\n2013-12-13 12:56\n\n#### 问题\n\n（1）速度的大小\n\n（2）速度方向与轴正方向夹角的正弦。",
null,
"#### 物理建模\n\n1. 从原点…某时刻发射大量 … 带正电粒子\n2. （粒子的）速度大小相同\n3. 从发射粒子到粒子全部离开磁场经历的时间恰好为粒子在磁场中做圆周运动周期的四分之一\n\n1. 研究对象是一批粒子还是一个粒子？（最后一个粒子）\n2. 这批粒子是同一时刻发射的吗？（是）\n3. 圆周运动周期的四分之一意味着什么？（圆心角为$90^\\circ$\n4. 最后离开磁场的粒子轨道长度和其他粒子比较有何特点？（最长）\n\n• 是一段圆弧，圆心角为$90^\\circ$\n\n• 矩形磁场中弧线应尽可能的长",
null,
"• 轨道与磁场边界相切，弦略短于矩形磁场的对角线。",
null,
"#### 数学处理\n\n$x$方向： $Rcos\\theta + Rsin\\theta = a$\n\n$y$方向： $R - Rsin\\theta = \\frac{a}{2}$\n\n$R$\n\n$sin\\theta_{1} = \\frac{6-\\sqrt6}{10} \\simeq 0.4$$sin\\theta_{2} = \\frac{6+\\sqrt6}{10} \\simeq 0.8$\n\n$y$方向的列式易得\n\n$R = \\frac{mv}{qB}$可解出第(1)问，$v = (2-\\frac{\\sqrt6}{2}) \\frac{aqB}{m}$\n\n#### 解题回顾\n\n• 通过审题及作轨迹图，分析力和运动，理解物理情境。\n• 化弧为弦，根据限制条件不断逼近正确的情境况，建立几何模型。\n• 善于从几何图像中寻找数学关系，建立已知——未知量的联系。\n• 熟悉如何联立方程解未知数\n• 消元，降次\n• 升次后要讨论解\n\n© 版权所有 悟理 2013-2019\n\n# 2010 新课标全国卷 25题\n\n2013-12-13 12:56\n\n#### 问题\n\n（1）速度的大小\n\n（2）速度方向与轴正方向夹角的正弦。",
null,
"#### 物理建模\n\n1. 从原点…某时刻发射大量 … 带正电粒子\n2. （粒子的）速度大小相同\n3. 从发射粒子到粒子全部离开磁场经历的时间恰好为粒子在磁场中做圆周运动周期的四分之一\n\n1. 研究对象是一批粒子还是一个粒子？（最后一个粒子）\n2. 这批粒子是同一时刻发射的吗？（是）\n3. 圆周运动周期的四分之一意味着什么？（圆心角为$90^\\circ$\n4. 最后离开磁场的粒子轨道长度和其他粒子比较有何特点？（最长）\n\n• 是一段圆弧，圆心角为$90^\\circ$\n\n• 矩形磁场中弧线应尽可能的长",
null,
"• 轨道与磁场边界相切，弦略短于矩形磁场的对角线。",
null,
"#### 数学处理\n\n$x$方向： $Rcos\\theta + Rsin\\theta = a$\n\n$y$方向： $R - Rsin\\theta = \\frac{a}{2}$\n\n$R$\n\n$sin\\theta_{1} = \\frac{6-\\sqrt6}{10} \\simeq 0.4$$sin\\theta_{2} = \\frac{6+\\sqrt6}{10} \\simeq 0.8$\n\n$y$方向的列式易得\n\n$R = \\frac{mv}{qB}$可解出第(1)问，$v = (2-\\frac{\\sqrt6}{2}) \\frac{aqB}{m}$\n\n#### 解题回顾\n\n• 通过审题及作轨迹图，分析力和运动，理解物理情境。\n• 化弧为弦，根据限制条件不断逼近正确的情境况，建立几何模型。\n• 善于从几何图像中寻找数学关系，建立已知——未知量的联系。\n• 熟悉如何联立方程解未知数\n• 消元，降次\n• 升次后要讨论解\n\n© 版权所有 悟理 2013-2019"
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"http://zhengweiyu.com/post-img/2013-12-13-2010-kebiao-quanguo-25-i3.png",
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"http://zhengweiyu.com/post-img/2013-12-13-2010-kebiao-quanguo-25-i1.png",
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] | {"ft_lang_label":"__label__zh","ft_lang_prob":0.97532034,"math_prob":0.9998405,"size":961,"snap":"2019-35-2019-39","text_gpt3_token_len":1059,"char_repetition_ratio":0.07419018,"word_repetition_ratio":0.0,"special_character_ratio":0.19042663,"punctuation_ratio":0.00990099,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99902046,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],"im_url_duplicate_count":[null,6,null,6,null,6,null,6,null,6,null,6,null,6,null,6,null,6,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-09-16T00:20:53Z\",\"WARC-Record-ID\":\"<urn:uuid:101fc58f-7cad-4fba-b521-04b88ebb3fea>\",\"Content-Length\":\"24251\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e2541fd9-743a-4cd8-976c-002e99e7c66b>\",\"WARC-Concurrent-To\":\"<urn:uuid:d2f28d0d-a6d8-4116-8103-0b950884bbc4>\",\"WARC-IP-Address\":\"104.28.4.123\",\"WARC-Target-URI\":\"http://zhengweiyu.com/2013/12/13/2010-kebiao-quanguo-25.html\",\"WARC-Payload-Digest\":\"sha1:QMSEJWZ2UFEBBVM56OS5ZZRVPZF6EMIG\",\"WARC-Block-Digest\":\"sha1:URAMUU4TERYWZ7LYJFKHGECDVGN37SSE\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-39/CC-MAIN-2019-39_segments_1568514572439.21_warc_CC-MAIN-20190915235555-20190916021555-00385.warc.gz\"}"} |
https://www.mankier.com/3/BN_add_word.3ossl | [
"arithmetic functions on BIGNUMs with integers\n\nSynopsis\n\n#include <openssl/bn.h>\n\nint BN_sub_word(BIGNUM *a, BN_ULONG w);\n\nint BN_mul_word(BIGNUM *a, BN_ULONG w);\n\nBN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w);\n\nBN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w);\n\nDescription\n\nThese functions perform arithmetic operations on BIGNUMs with unsigned integers. They are much more efficient than the normal BIGNUM arithmetic operations.\n\nBN_sub_word() subtracts w from a (a-=w).\n\nBN_mul_word() multiplies a and w (a*=w).\n\nBN_div_word() divides a by w (a/=w) and returns the remainder.\n\nBN_mod_word() returns the remainder of a divided by w (a%w).\n\nFor BN_div_word() and BN_mod_word(), w must not be 0.\n\nReturn Values\n\nBN_add_word(), BN_sub_word() and BN_mul_word() return 1 for success, 0 on error. The error codes can be obtained by ERR_get_error(3).\n\nBN_mod_word() and BN_div_word() return a%w on success and (BN_ULONG)-1 if an error occurred."
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https://mmi.sgu.ru/en/articles/on-maximal-subformations-of-n-multiple-foliated-formations-of-finite-groups | [
"ISSN 1816-9791 (Print)\nISSN 2541-9005 (Online)\n\n#### For citation:\n\nSorokina M. M., Maksakov S. P. On maximal subformations of n-multiple Ω-foliated formations of finite groups. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2021, vol. 21, iss. 1, pp. 15-25. DOI: 10.18500/1816-9791-2021-21-1-15-25\n\nPublished online:\n01.03.2021\nFull text:",
null,
"download\n(downloads: 20)\nLanguage:\nRussian\nHeading:\nArticle type:\nArticle\nUDC:\n512.542\nDOI:\n10.18500/1816-9791-2021-21-1-15-25\n\n# On maximal subformations of n-multiple Ω-foliated formations of finite groups\n\nAutors:\nSorokina Marina M., Bryansk State University named after Academician I. G. Petrovsky\nMaksakov Seraphim P., Bryansk State University named after Academician I. G. Petrovsky\nAbstract:\n\nOnly finite groups are considered in the article. Among the classes of groups the central place is occupied by classes closed regarding homomorphic images and subdirect products which are called formations. We study $\\Omega$-foliateded formations constructed by V. A. Vedernikov in 1999 where $\\Omega$ is a nonempty subclass of the class $\\frak I$ of all simple groups. $\\Omega$-Foliated formations are defined by two functions — an $\\Omega$-satellite $f: \\Omega \\cup \\{\\Omega '\\} \\rightarrow \\{$formations$\\}$ and a direction $\\varphi: \\frak I \\rightarrow \\{$nonempty Fitting formations$\\}$. The conception of multiple locality introduced by A. N. Skiba in 1987 for formations and further developed for many other classes of groups, as applied to $\\Omega$-foliated formations is as follows: every formation is considered to be 0-multiple $\\Omega$-foliated with a direction $\\varphi$; an $\\Omega$-foliated formation with a direction $\\varphi$ is called an $n$-multiple $\\Omega$-foliated formation where $n$ is a positive integer if it has such an $\\Omega$-satellite all nonempty values of which are $(n-1)$-multiple $\\Omega$-foliated formations with the direction $\\varphi$. The aim of this work is to study the properties of maximal $n$-multiple $\\Omega$-foliated subformations of a given $n$-multiple $\\Omega$-foliated formation. We use classical methods of the theory of groups, of the theory of classes of groups, as well as methods of the general theory of lattices. In the paper we have established the existence of maximal $n$-multiple $\\Omega$-foliated subformations for the formations with certain properties, we have obtained the characterization of the formation $\\Phi_{_{n\\Omega\\varphi}} (\\frak F)$ which is the intersection of all maximal $n$-multiple $\\Omega$-foliated subformations of the formation $\\frak F$, and we have revealed the relation between a maximal inner $\\Omega$-satellite of $1$-multiple $\\Omega$-foliated formation and a maximal inner $\\Omega$-satellite of its maximal $1$-multiple $\\Omega$-foliated subformation. The results will be useful in studying the inner structure of formations of finite groups, in particular, in studying the maximal chains of subformations and in establishing the lattice properties of formations.\n\nKey words:\nReferences:\n1. Doerk K., Нawkes T. Finite Soluble Groups. Berlin, New York, Walter de Gruyter, 1992. 901 p.\n2. Gaschutz W. Zur theorie der endlichen auflosbaren Gruppen. Mathematische Zeitschrift, 1962, vol. 80, iss. 1, pp. 300–305 (in Germany). https://doi.org/10.1007/BF01162386\n3. Shemetkov L. A. On product of formations. Academy of Sciences BSSR Report, 1984, vol. 28, no. 2, pp. 101–103 (in Russian).\n4. Skiba A. N., Shemetkov L. A. Multiple L-composition formations of finite groups. Ukrainian Mathematical Journal, 2000, vol. 52, no. 6, pp. 783–797 (in Russian).\n5. Vedernikov V. A., Sorokina M. M. The Ω-foliated formations and Fitting classes of finite groups. Discrete Mathematics and Applications, 2001, vol. 11, no. 5, pp. 507–527.\n6. Skiba A. N. Characterization of finite solvable groups of a certain nilpotent length. Issues of Algebra, 1987, vol. 3, pp. 21–31 (in Russian).\n7. Skachkova (Elovikova) Y. A. Boolean lattices of multiple Ω-foliated formations and Fitting classes. Discrete Mathematics and Applications, 2002, vol. 12, no. 5, pp. 477–482.\n8. Elovikova Y. A. The algebraic lattices of Ω-foliated formations. The Bryansk State University Herald, 2013, no. 4, pp. 13–16 (in Russian).\n9. Sorokina M. M., Korpacheva M. A. On the critical Ω-foliated formations of finite groups. Discrete Mathematics and Applications, 2006, vol. 16, no. 3, pp. 289–298. https://doi.org/10.1515/156939206777970417\n10. Vedernikov V. A., Demina E. N. Ω-Foliated formations of multioperator T-groups. Siberian Mathematical Journal, 2010, vol. 51, no. 5, pp. 789–804. https://doi.org/10.1007/s11202-010-0079-3\n11. Elovikov A. B. The factorisation of one-generated partially foliated formations. Discrete Mathematics and Applications, 2009, vol. 19, iss. 4, pp. 411–430. https://doi.org/10.1515/DMA.2009.029\n12. Skiba A. N. Algebra formatsiy [Algebra of Formations]. Minsk, Belarusskaya Nauka, 1997. 240 p. (in Russian).\n13. Vedernikov V. A. Maximal satellites of Ω-foliated formations and Fitting classes. Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2001, suppl. 2, pp. S217–S233.\n14. Birkhoff G. Lattice Theory. New York, American Mathematical Society, 1973. 423 p. (Russ. ed.: Moscow, Nauka, 1984. 568 p.).\n15. Shemetkov L. A., Skiba A. N. Formatsii algebraicheskikh sistem [Formations of Algebraistic Systems]. Moscow, Nauka, 1997. 256 p. (in Russian).\nReceived:\n04.12.2019\nAccepted:\n03.02.2020\nPublished:\n01.03.2021\nShort text (in English):",
null,
"download\n(downloads: 4)"
] | [
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"https://mmi.sgu.ru/modules/file/icons/application-pdf.png",
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https://www.element14.com/community/community/project14/nano-rama/blog/2020/03/21/energy-monitoring-system | [
"NanoRamaEnter Your Project for a chance to win a Nano Grand Prize bundle for the most innovative use of Arduino plus a \\$400 shopping cart!Submit an EntrySubmit an Entry Back to homepage Project14 Home Monthly Themes Monthly Theme Poll\n\n# A smart energy monitoring system that will ease the inspection, monitoring, analysis, and fare calculation of energy\n\n## First of all, Happy Birthday Project14 and Arduino\n\nIn Kerala (India), the energy consumption is monitored and calculated by frequent field visits by technicians from the electricity/energy department for the calculation of energy fare which is a time-consuming task as there will be thousands of houses in the area. There is no provision to check or analyse the individual energy consumption of houses in a period of time nor to create a report of energy flow in a certain area. This is not just the case of Kerala, but throughout many places in the world.\n\nThis project involves the development of a smart energy monitoring system that will ease the inspection, monitoring, analysis, and fare calculation of energy. The system will additionally allow generating user specific or area specific charts and reports to analyse the energy consumption and energy flow. The system module which will be given a unique user code to identify the particular housing unit where the energy consumption has to be measured. The power consumption will be monitored with the help of a current sensor interfaced to an Arduino board using Analog connection. The energy consumption data and the unique user code of the user can be uploaded to a dedicated cloud service at real-time. The data from the cloud will be accessed and analysed by the energy department to calculate individual energy consumption, generate individual and collective energy charts, generate energy reports and for detailed energy inspection. An LCD display module can be integrated into the system to display real-time energy measurement values. The system will work independently if a portable power source such as dry cell battery or Li-Po battery is attached.\n\nThe main focus of this project is to help optimize and reduce the energy consumption usage by the user. This not only reduces the overall energy costs, but will also conserve energy.\n\nThe components that are used in the project are:\n\n• MKR Zero / Arduino Uno\n• ACS712 Current sensor\n• LCD Module [I2C version preferred]\n\nThe hardware connection diagram for prototype is as follows:\n\nUse the below connection if you prefer an I2C LCD module.\n\n[Picture courtesy from respective sources]\n\nPower from the AC mains is drawn and passed through a the current sensor which is integrated into the household circuit. The AC current passing through the load is sensed by the current sensor module (ACS712) and the output data from the sensor is fed to the analog pin (A0) of the Arduino UNO. Once the analog input is received by Arduino, the measurement of power/energy is inside the Arduino sketch. The calculated power and energy is then displayed on the LCD display module.\n\nIn AC circuit analysis, both voltage and current vary sinusoidal with time. Also various power are considered. Of these, some Power may also be lost in the form of heat or radiation while long distance transmission.\n\nReal Power (P): This is the power used by the device to produce useful work, expressed in kW.\n\nSo, Real Power = Voltage (V) x Current (I) x cosΦ\n\nReactive Power (Q) : This is often called imaginary power which is a measure of power oscillates between source and load, that does no useful work, expressed in kVA\n\nSo, Reactive Power = Voltage (V) x Current (I) x sinΦ\n\nApparent Power (S) : It is defined as the product of the Root-Mean-Square (RMS) Voltage and the RMS Current. This can also be defined as the resultant of real and reactive power, expressed in kVA\n\nSo, Apparent Power = Voltage (V) x Current (I)\n\nRelation between Real, Reactive and Apparent power:\n\nReal Power = Apparent Power x cosΦ\n\nReactive Power = Apparent Power x sinΦ\n\nWe are concerned only on the Real power for the analysis.\n\nPower Factor (pf) : The ratio of the real power to the apparent power in a circuit is called the power factor.\n\nPower Factor = Real Power/Apparent Power\n\nThus, we can measure all form of power as well as power factor by measuring the voltage and current in the circuit. Following section discusses the steps taken to obtain the measurements that are required to calculate the energy consumption.\n\nThe AC current is conventionally measured by using a Current transformer. ACS712 was chosen as the current sensor because of its low cost and smaller size. The ACS712 Current Sensor is a Hall Effect current sensor that accurately measures current when induced. The magnetic field around the AC wire is detected which gives the equivalent analog output voltage. The analog voltage output is then processed by the microcontroller to measure the current flow through the load.\n\n### More on Hall effect\n\nHall Effect is the production of a voltage difference (the Hall voltage) across an electrical conductor, transverse to an electric current in the conductor and a magnetic field perpendicular to the current.\n\n[Picture courtesy from respective sources]\n\nTo know more about the ACS712 sensor and its working, use this link.\n\nThe output from the ACS712 Current Sensor is an AC voltage wave. The following calculation are done:\n\n1. Measuring the peak to peak voltage ( Vpp )\n2. Divide the peak to peak voltage(Vpp) by two to get peak voltage (Vp)\n3. Multiply Vp by 0.707 to get the rms voltage (Vrms)\n4. Multiply the Sensitivity of the current sensor ( ACS712 ) to get the rms current.\n\nMathematically, we have:\n\n[The following are the basic current consumption measurement equations]\n\nVp = Vpp/2\n\nVrms = Vp x 0.707\n\nIrms = Vrms x Sensitivity\n\nThe sensitivity for ACS712 5A module is 185mV/A ,20A module is 100mV/A and 30A module is 66mV/A.\n\nReal Power (W) = Vrms x Irms x pf\n\nVrms = 230V (known for India)\n\npf = 0.85 (known)\n\nIrms = Obtained using above calculation\n\nFor calculating the energy cost, the power in watts is converted into energy:\n\nWh = W * (time / 3600000.0)\n\nWatt hour a measure of electrical energy equivalent to a power consumption of one watt for one hour.\n\nFor calculating kWh:\n\nkWh = Wh / 1000\n\nThe Total Energy cost is:\n\nCost = Cost per kWh * kWh.\n\nThe information is then displayed onto the LCD display.\n\nThe below figure depicts the prototype under testing.\n\n### Modifications (In Progress)\n\n• The Arduino UNO is being replaced by an Arduino MKR Zero\n• Additional functionality of logging to SD Card\n• Cloud connection, Interface and data logging\n• Generation of Automatic usage reports\n\n### Code\n\n```//-------------------------------------------------------------------------------//\n//-- PROGRAM GOALS //\n//-- A smart energy monitoring system that will ease the inspection, //\n//-- monitoring, analysis, and calculation of energy fare. //\n//-------------------------------------------------------------------------------//\n\n#include \"rgb_lcd.h\"\n\n#define Pin A0\nrgb_lcd lcd;\nconst int chipSelect = 43;\nconst int house_id = 1;\nconst int averageValue = 10;\nint sensorValue = 0;\nfloat sensitivity = 1000.0 / 800.0;\nfloat Vref = 265;\nString msg = \"\";\nunsigned int Sensitivity = 185;\nfloat Vpp = 0; // peak-peak voltage\nfloat Vrms = 0; // rms voltage\nfloat Irms = 0; // rms current\nfloat Supply_Voltage = 233.0; // reading from DMM\nfloat Vcc = 5.0; // ADC reference voltage // voltage at 5V pin\nfloat power = 0; // power in watt\nfloat Wh =0 ; // Energy in kWh\nunsigned long last_time =0;\nunsigned long current_time =0;\nunsigned long interval = 100;\nunsigned int calibration = 100; // V2 slider calibrates this\nunsigned int pF = 85; // Power Factor default 95\nfloat bill_amount = 0; // 30 day cost as present energy usage incl approx PF\nunsigned int energyTariff = 8.0; // Energy cost in INR per unit (kWh)\n\nvoid setup()\n{\nWire.begin();\n\nlcd.begin(16, 2);\ndelay(1000);\n\npinMode(SS, OUTPUT);\nif (SD.begin(chipSelect))\n{\nsd_write = 1;\ndataFile = SD.open(\"STEMS_log.txt\", FILE_WRITE);\ndataFile.println(\"Project STEMS\");\ndataFile.println(\"by Jiss\");\ndataFile.println(\"\");\n}\n\nlcd.setCursor(0, 0);\nlcd.print(\"Project STEMS\");\nlcd.setCursor(0, 1);\nlcd.print(\"By Jiss\");\n\ndelay(1000);\n\nlcd.setCursor(0, 0);\nlcd.print(\"House ID -->\");\nlcd.setCursor(0, 1);\nlcd.print(vehicle_id);\nif(sd_write)\n{\ndataFile.println(\"House_id: \" + house_id);\n}\n}\n\nvoid loop()\n{\nfor (int i = 0; i < averageValue; i++)\n{\ndelay(2);\n}\n\nsensorValue = sensorValue / averageValue;\nfloat unitValue= RefVal / 1024.0*1000 ;\nfloat voltage = unitValue * sensorValue-Vref;\nfloat current = (voltage - Vref) * sensitivity;\n\nVpp = voltage;\nVrms = (Vpp/2.0) *0.707;\nVrms = Vrms - (calibration / 10000.0);\nIrms = (Vrms * 1000)/Sensitivity ;\nif((Irms > -0.015) && (Irms < 0.008))\n{\nIrms = 0.0;\n}\npower= (Supply_Voltage * Irms) * (pF / 100.0);\nlast_time = current_time;\ncurrent_time = millis();\nWh = Wh+ power *(( current_time -last_time) /3600000.0) ;\n// calculating energy in Watt-Hour\nbill_amount = Wh * (energyTariff/1000);\n\nlcd.setCursor(0, 0);\nlcd.print(\"Current -->\");\nlcd.setCursor(0, 1);\nlcd.print(current + \" mA\");\nif(sd_write)\n{\ndataFile.println(\"Current: \" + current);\n}\n\nlcd.setCursor(0, 0);\nlcd.print(\"Power -->\");\nlcd.setCursor(0, 1);\nlcd.print(power + \" W\");\nif(sd_write)\n{\ndataFile.println(\"Power: \" + power);\n}\n\nlcd.setCursor(0, 0);\nlcd.print(\"Bill Amount -->\");\nlcd.setCursor(0, 1);\nlcd.print(bill_amount + \"INR\");\nif(sd_write)\n{\ndataFile.println(\"Bill Amount: \" + bill_amount);\n}\n\nsensorValue = 0;\ndelay(1000);\n}\n```"
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https://projecteuclid.org/journals/annals-of-probability/volume-3/issue-2/Iterated-Logarithm-Results-for-Weighted-Averages-of-Martingale-Difference-Sequences/10.1214/aop/1176996401.full | [
"Translator Disclaimer\nApril, 1975 Iterated Logarithm Results for Weighted Averages of Martingale Difference Sequences\nR. J. Tomkins\nAnn. Probab. 3(2): 307-314 (April, 1975). DOI: 10.1214/aop/1176996401\n\n## Abstract\n\nLet $(X_n, \\mathscr{F}_n, n \\geqq 1)$ be a martingale difference sequence with $E(X_n^2 \\mid \\mathscr{F}_{n-1}) = 1$ a.s. This paper presents iterated logarithm results involving $\\lim \\sup_{n\\rightarrow\\infty} \\sum^n_{m=1} f(m/n)X_m/(2n \\log \\log n)^{\\frac{1}{2}}$, where $f$ is a continuous function on [0, 1]. For example, it is shown that the above limit superior equals the $L_2$-norm of $f$ if the $X_n$'s are uniformly bounded and $f$ is a power series with radius in excess of one. These results generalize (and correct the proof of) a previous theorem due to the author. A generalization of the strong law of large numbers is also established.\n\n## Citation\n\nR. J. Tomkins. \"Iterated Logarithm Results for Weighted Averages of Martingale Difference Sequences.\" Ann. Probab. 3 (2) 307 - 314, April, 1975. https://doi.org/10.1214/aop/1176996401\n\n## Information\n\nPublished: April, 1975\nFirst available in Project Euclid: 19 April 2007\n\nzbMATH: 0302.60019\nMathSciNet: MR372972\nDigital Object Identifier: 10.1214/aop/1176996401\n\nSubjects:\nPrimary: 60F15\nSecondary: 26A45 , 60G45 , 60G50\n\nKeywords: function of bounded variation , Independent random variables , Law of the iterated logarithm , Martingales , Strong law of large numbers",
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https://artspace-jhb.co.za/fourier-of-fourier-analysis-for-processing-different/ | [
"Fourier Analysis\n\nMaths for Materials & Design\n\nYear 2 – Assignment 1\n\n55-5805\n\nJames Walker\n\nContents\n\nWe Will Write a Custom Essay Specifically\nFor You For Only \\$13.90/page!\n\norder now\n\nAbstract 1\n\nIntroduction. 2\n\n1 – Mathematical Analysis. 3\n\n1 A – Waveform Sketch. 3\n\n1 B – Fourier Coefficients. 3\n\n1 C – Reconstruction. 4\n\n1 D – Gibbs Phenomenon. 6\n\n2 – Tabular Analysis. 8\n\n2 A – The Procedure. 8\n\n2 B – Signal Component Calculation. 10\n\n2 C – Signal Reconstruction. 11\n\n2 D – Known Signal Decomposition. 13\n\n3 – Fast Fourier Transform.. 15\n\n3 A – Frequency Components. 15\n\n3 B – Engineering Applications. 18\n\n4 – Appendices. 20\n\nAppendix 1 – Calculation of M.. 20\n\nAppendix 2 – Calculation of An 21\n\nAppendix 3 – Calculation of Bn 22\n\nAppendix 4 – Tabular Method Results. 24\n\nAppendix 5 – Known Wave Reconstruction Datasets. 26\n\nAppendix 6 – MatLab Code. 26\n\n5 – References 27\n\nAbstract\n\nSignal\nprocessing is useful in a variety of applications, which can include data\ncompression, image and video compressing and removing noise, interference or\nother corruption from a signal. This report details 3 methods of Fourier\nAnalysis for processing different types of signal.\n\nIntroduction\n\n“Fourier\nAnalysis is the decomposition of a function into a set, possibly infinite, of\nsimple oscillating functions. Each function will have a different frequency,\nphase and amplitude.” Lecture Notes The process is named after the\nFrench Mathematician and Physicist Joseph Fourier who was born in the 18th\ncentury, and developed the principle of representing a function as a sum of\ntrigonometric functions in order to simplify the study of heat transfer.\n\nVan Veen, B. 2018\n\nFourier\nAnalysis has since been developed for use in a wide range of applications and\nthis report looks at three methods of conducting the process.\n\nSection 1\nlooks at reconstructing a signal of a known function using integration, which\nis restricted in its uses due to being long-winded and requiring the function\nto be known.\n\nSection 2\ndemonstrates the use of a tabular method which has the advantage of being able\nto process a series of points rather than a known function, but is inherently\nslow and cumbersome due to the number of calculations required, particularly if\nthere are many frequency components.\n\nSection 3\noutlines and demonstrates the use of FFT (Fast Fourier Transform) which\nenhances mathematical approaches by making working in the frequency domain as\npractical as working with the time and amplitude domain, with the aid of\ncomputer software.\n\n1 – Mathematical Analysis\n\n1 A – Waveform Sketch\n\nT = 3\nA = 6\n\nUsing the provided dataset, which specifies a time\nperiod (T)\nand an amplitude (A),\nthe graph in Figure 1 was constructed.\n\nFigure 1 – Waveform of\nProvided Dataset\n\n1 B – Fourier Coefficients\n\nFull calculations of M, An\n& Bn can be found in Appendices 1-3 respectively, their values\nare listed below:\n\nWhere M is the vertical offset of the\nsignal, An is the amplitude of the nth Sine function\nand Bn the amplitude of the nth Cosine function.\n\nThe calculation of An\ncould have been avoided because the function is symmetrical in the Y-axis therefore\nit is an ‘even’ function and An will always be\nequal to 0.\n\nThe first 8\nnon-zero Bn coefficients were calculated using the above equation, and are\ntabulated in Figure 2.\n\nFigure 2 – Bn Coefficients\n\n1 C – Reconstruction\n\nFollowing the\ncalculation of the coefficients, the Fourier Series can be approximated with Equation\n1:\n\nEquation\n1\n\nFigure 3 – Approximation of the Function\n\nThe table shown partly in Figure 3 was created to implement\nthe formula above in order to create a dataset which runs from t\n= -4.5 to 4.5 (as per the original data). The second and third rows contain n\nand the corresponding value of Bn as\nper Figure 2.\n\nPlotting the results in Figure 3 returns the graph seen in\nFigure 4, which very closely resembles the original dataset. The only notable\ndifferences are the slight jagged lines caused by the vast number of points and\nthe rounded corners caused by the approximation, as can be seen in Figure 5.\n\nFigure 4 – Reconstructed Graph\n\nFigure 5 – Overlay of Original & Approximation\n\nFigure 6 shows the described differences; the rounded peak and the\nless smooth lines. The peaks are at 5.85 and -5.85, showing a 2.5% deviation\nfrom the original amplitude.\n\nFigure 6 – Overlay Magnified\n\n1 D – Gibbs Phenomenon\n\nThe Gibbs phenomenon occurs through the Fourier analysis of\nperiodic functions, where the partial sum exceeds the amplitude of the intended\nfunction, as a result of a jump discontinuity. This can be seen in square wave\napproximations where the approximated signal will overshoot by typically 9% of\nthe amplitude after the jump discontinuity (where one x value can have multiple\ny values). This can be seen in Figure 7, where the red line shows the\napproximation (with a different number of components in each diagram) but the\nred line will always surpass the height of the square wave after the change\nfrom negative to positive or vice versa.\n\nFigure 7 – Gibbs Phenomenon MIT\n\nThe ripples seen will never disappear, and retain the same\nheight, however as the number of terms tends to infinity, the width (hence the\narea) of the ‘ripples’ tend to 0, resulting in them having a negligible effect.\n\nThis ripple effect can have consequences for some square wave AC\nwelders, such as TIG welders as the current will peak higher than its intended\nvalue, resulting in over penetration of the welded material, however different methods\nof producing a ‘square wave’ used for welding non-ferrous metals can be seen\nbelow, with their respective ripple coefficients, the coefficient is defined as\nthe ratio of maximum current magnitude to its effective value. Inverter welders\nand other more modern welders do not use a summation of sine waves; hence the\ncoefficient is 0.\n\nFigure 8 – Ripple\nCoefficients Julian, P. 2003\n\n2 – Tabular Analysis\n\n2 A – The Procedure\n\nThe original signal data, sampled at\n100Hz, is plotted below in Figure 9.\n\nFigure 9 – Original Signal Data\n\nThis signal lasts\nfor of 0.21 s, calculated by dividing the number of samples (21) by the sample\nrate (100 Hz).\n\nPeaks in the signal\nrepresent the component frequencies, therefore the fundamental frequency is\n100/21 or 4.76 Hz. Any component frequencies must have a higher frequency than\nthis.\n\nThe full results\ntable in which the sample data was put through a tabular method of Fourier\nanalysis is in Appendix 4, which relied on the equations below:\n\nEquation 2\n\nEquation 3\n\nEquation 4\n\nEquation 5\n\nThe table starts\nwith the sample data and the time at which it was sampled, along with the\ncorresponding values of theta. Theta was calculated by assuming the data\nprovided shows one full cycle, (2? radians).\n\nThe first series of\ncolumns calculates the individual An & Bn\ncomponents, these are\nsummated and multiplied by 2/21 at the bottom of the table to find the overall An\n& Bn components,\nwas per Equations 4 & 5.\n\nOnce the components\nwere found, Equation 3 was used in the second part of the table to find M (0.545) followed by f(t) using Equation 2.\n\nThe first 8 terms are\ngiven below:\n\n2 B – Signal Component Calculation\n\nFigure 10 – Frequency Components\n\nThe graph in Figure\n10 shows the previously listed coefficients graphically, demonstrating that the\neven values of n are typically more prominent in this case.\n\n2 C – Signal Reconstruction\n\nThe original signal\ncan be seen in Figure 9. Figure 11 shows the reconstruction when n=3; a very\ninaccurate reconstruction.\n\nFigure 11 – n=3\n\nFigure 12 shows the\nreconstruction when n=6, by which point the data can be recognised visually as\nbeing similar to the original.\n\nFigure 12 – n=6\n\nFigure 13 shows the\nreconstruction when n=10 which is a very accurate reconstruction.\n\nFigure 13 – n=10\n\nThe signals were reconstructed using the first and the final\nthree columns of the table in Appendix 4, and it was found that the function only begins to become\ndistinguishable on a graph once the sum of the n=1 to n=4 is plotted, prior to\nthis it appears as a sine wave.\n\nFigure 14 – Overlay\n\nFigure 14 shows\nthe original, and the points from the other reconstructions for reference, it\ncan be seen that all the points from n=10 lie on the line of the original, and\ncreate a near perfect replication when plotted (as per Fig. 13).\n\n2 D – Known Signal Decomposition\n\nFigure 15 – Known Waveform\n\nFigure 15 shows the\ngraph produced from the dataset in Appendix 5.\n\nAgain, for comparison the\nre-construction is shown with varying values of n in Figure 16.\n\nFigure 16 – Reconstructed Signal\n\nThe data points of\nn=10 can be found compared with the input values in Appendix 5X. The values are\nall 4.7% smaller than their inputs.\n\nWhen n=6, the\nreconstruction becomes distinguishable, but shows some odd features including\novershoots which appear symmetrical in opposite corners, with the closest\nrepresentation near the middle of the sample. This may be explained by the\nsample being a discreet function (ie. between t = 0 & t = 10), my suspicion is that some of these\nfeatures would not appear on a continuous function.\n\nFigure 17 – Overlay\n\n3 – Fast Fourier Transform\n\n3 A – Frequency Components\n\nFast Fourier Transform (FFT) is used to decompose signals to divide\nthem into their frequency components (single sinusoidal waves at a particular\nfrequency) as shown by Figure 18.\n\nFigure 18 – Frequency vs. Time Domain Wikipedia\n\nThis is performed by a complex algorithm that initially\nperforms a discreet Fourier transform (DFT), then FFT uses Fourier analysis to\nconvert from the time to the frequency domain (as in Figure 18).\n\nThe provided\ndataset when plotted is shown in Figure 19.\n\nFigure 19 – Original Signal\n\nIt is clear to see that not a lot can be interpreted by inspection of\nthe raw data, so it was put through FFT in MatLab in order to determine the\nfrequency components. The code is shown in Figure 20.\n\nFs is the\nsampling frequency.\n\nT is the\nsampling time interval.\n\nL is the number\nof samples.\n\nt is the time\nof the whole sample.\n\nJW is the\noriginal dataset.\n\nFigure 20 – MatLab Code\n\nLine 6 performs\nthe Fourier transform, using the original dataset, outputting a list of complex\nnumbers, which aren’t very useful (Figure 21). Line 7 converts these to a\ndouble-sided spectrum, then lines 8 & 9 make a single sided spectrum. Line\n10 defines the frequency domain, then lines 12-15 plot the results.\n\nMathworks\n\nFigure 21 – Table y Figure 22 – Table P2\nFigure 23 – Table P1\n\nFigure 24 – FFT of Provided Sample\n\nThe frequency components were found and are listed in Figure\n25. This can be seen in graphical form in Figure 24.\n\nFigure 25 – Frequency\nComponents Table\n\n3 B – Engineering Applications\n\nFourier analysis is\nused in ‘Fourier Transform Infrared Spectroscopy (FTIR), a process used to\ndetermine the composition of a sample material. FTIR is a “non-destructive\nmicroanalytical spectroscopic technique” which uses infrared radiation to\ninduce vibrations in molecular bonds. This process produces a ‘fingerprint’\nwhich is unique to a particular material, and provides information\n(predominantly qualitative) describing the composition of the material sample,\ntypically the base polymer of the sample. The fingerprint is produced from the\nmolecules’ transitions between energy levels, which occur at specific frequencies\nand can be identified using the absorption spectra displayed by the infrared\nlight reflected by the sample onto the detector. This spectrum can then be compared\nto a library of known spectra in order to identify the material.\n\nFTIR is often used as a first analytical test when\ndetermining a cause of failure, as it determines whether the material is\ncorrect to its drawing specification, and can negate the need for further\ntesting.\n\nOne inadequacy of FTIR is the difficulty in distinguishing\nbetween two similarly structured polymers such as polyethylene terephthalate\nand polybutylene terephthalate, in these cases other identification methods\nlike differential scanning calorimetry can be used in addition.\n\nAnother limitation is detecting materials of less than\naround 1% concentration in a compound. This detection limit will vary between\nspectrometers, depending on their resolution and accuracy, although the process\ncan be useful for identifying contaminants as the absorption spectra of known\ncompounds can be subtracted from the results to display absorption spectra not\ncharacteristic of the base resin, which will help to identify any contaminants.\nFigure 26 shows an example of 5 known spectra produced from FTIR which could be\nused in spectral subtraction.\n\nJansen\n\nFigure 26 – FTIR\nComparison of Several Polymers Jansen, J\n\nThe raw data obtained through FTIR is known as an\ninterferogram, which appears as a cosine wave which is an electrical signal\nprovided by the detector. On an interferogram, a range of wavelengths would be\nseen resulting in areas of constructive and destructive interference, this\nsignal is then decomposed using Fourier Analysis to provide a yield spectrum\nwhich identifies the key wavelengths.\n\nSmith, B. 2011\n\nThe principle of how the equipment obtains the signal is\nshown below in Figure 27.\n\nFigure 27 – Fourier\nTransform Infrared Spectrometer Diagram\n\n4 – Appendices\n\nAppendix 1 – Calculation of M\n\nAppendix 2 – Calculation of An\n\nAppendix 3 – Calculation of Bn\n\nAppendix 4 – Tabular Method Results\n\nThis method of\nFourier analysis result in a table with many columns, it has had to be split\ninto two sections for viewing in a paper document.\n\nAppendix 5 – Known Wave Reconstruction Datasets\n\nTime (s)\n\nInput Amplitude\n\nOutput Amplitude\n\n0.00\n\n0.00\n\n0.00\n\n0.10\n\n3.00\n\n2.86\n\n0.90\n\n3.00\n\n2.86\n\n1.10\n\n-3.00\n\n-2.86\n\n1.90\n\n-3.00\n\n-2.86\n\n2.10\n\n3.00\n\n2.86\n\n2.90\n\n3.00\n\n2.86\n\n3.10\n\n-3.00\n\n-2.86\n\n3.90\n\n-3.00\n\n-2.86\n\n4.10\n\n3.00\n\n2.86\n\n4.90\n\n3.00\n\n2.86\n\n5.10\n\n-3.00\n\n-2.86\n\n5.90\n\n-3.00\n\n-2.86\n\n6.10\n\n3.00\n\n2.86\n\n6.90\n\n3.00\n\n2.86\n\n7.10\n\n-3.00\n\n-2.86\n\n7.90\n\n-3.00\n\n-2.86\n\n8.10\n\n3.00\n\n2.86\n\n8.90\n\n3.00\n\n2.86\n\n9.10\n\n-3.00\n\n-2.86\n\n9.90\n\n-3.00\n\n-2.86\n\n10.00\n\n0.00\n\n0.00\n\nAppendix 6 – MatLab Code\n\n5 – References\n\nFast Fourier transform. (2018). Wikipedia.\nRetrieved 25 January 2018, from https://en.wikipedia.org/wiki/Fast_Fourier_transform\n\nFast Fourier transform – MATLAB. (2018). MathWorks.\nRetrieved 25 January 2018, from\nhttps://uk.mathworks.com/help/matlab/ref/fft.html\n\nGibbs’ Phenomenon. (2011). MIT. Retrieved\n25 January 2018, from https://ocw.mit.edu/courses/mathematics/18-03sc-differential-equations-fall-2011/unit-iii-fourier-series-and-laplace-transform/operations-on-fourier-series/MIT18_03SCF11_s22_7text.pdf\n\nGriffiths, P., & Haseth, J. (2007). Fourier\ntransform infrared spectrometry (2nd ed.). New York, N.Y., etc.:\nWiley.\n\nHahn, B., & Valentine, D. (2017). Essential\nMATLAB for engineers and scientists (6th ed.). Elsevier.\n\nJansen, J. Characterization of Plastics in Failure\nAnalysis. Madisongroup.com. Retrieved 27 January 2018, from\n\nJulian, P. (2003). Arc Welding Control.\n\nNave, R. (2018). Fourier Analysis and Synthesis. Hyperphysics.\nRetrieved 25 January 2018, from http://hyperphysics.phy-astr.gsu.edu/hbase/Audio/fourier.html\n\nSmith, B. (2011). Fundamentals of Fourier transform\ninfrared spectroscopy (2nd ed.). Boca Raton, Fla.: CRC Press.\n\nTolstov, G. (2014). Fourier series. Dover\nPulications.\n\nVan Veen, B. (2018). Fourier Methods in Signal\nProcessing. All Signal Processing. Retrieved 26 January 2018,\nfrom https://allsignalprocessing.com/fourier-methods-prominent/",
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https://okayama.pure.elsevier.com/en/publications/the-equivariant-bundle-subtraction-theorem-and-its-applications | [
"# The Equivariant Bundle Subtraction Theorem and its applications\n\nMasaharu Morimoto, Krzysztof Pawałowski\n\nResearch output: Contribution to journalArticlepeer-review\n\n7 Citations (Scopus)\n\n## Abstract\n\nIn the theory of transformation groups, it is important to know what kind of isotropy subgroups of G do occur at points of the space upon which the given group G acts. In this article, for a finite group G, we prove the Equivariant Bundle Subtraction Theorem (Theorem 2.2) which allows us to construct smooth G-manifolds with prescribed isotropy subgroups around the G-fixed point sets. In Theorem 0.1, we restate Oliver's result about manifolds M and G-vector bundles over M that occur, respectively, as the G-fixed point sets and their equivariant normal bundles for smooth G-actions on disks. In Theorems 0.2 and 0.3, we prove the corresponding results for smooth G-actions on disks with prescribed isotropy subgroups around M. In Theorems 0.4 and 0.5, for large classes of finite groups G, we explicitly describe manifolds M that occur as the G-fixed point sets for such actions on disks. These actions are expected to be useful for answering the question of which manifolds occur as the G-fixed points sets for smooth G-actions on spheres.\n\nOriginal language English 279-303 25 Fundamenta Mathematicae 161 3 Published - 2000 Yes\n\n## Keywords\n\n• Equivariant bundle subtraction\n• Equivariant normal bundle\n• Fixed point set\n• Smooth action on disk\n• The family of large subgroups of a finite group\n\n## ASJC Scopus subject areas\n\n• Algebra and Number Theory\n\n## Fingerprint\n\nDive into the research topics of 'The Equivariant Bundle Subtraction Theorem and its applications'. Together they form a unique fingerprint."
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http://portcetate.ro/oyzfjy/properties-of-isosceles-right-triangle-020b48 | [
"Properties of a triangle. Right Angled Triangle: A triangle having one of the three angles as right angle or 900. A right-angled triangle has an angle that measures 90º. In Year 5, children continue their learning of acute and obtuse angles within shapes. A right triangle in which two sides and two angles are equal is called Isosceles Right Triangle. The unequal side of an isosceles triangle is usually referred to as the 'base' of the triangle. Calculate base length z. Isosceles triangle 10 In an isosceles triangle, the equal sides are 2/3 of the length of the base. The altitude to the base is the line of symmetry of the triangle. A right triangle has two internal angles that measure 90 degrees. In geometry, an isosceles triangle is a triangle that has two sides of equal length. The right triangle of this pair has side lengths (135, 352, 377), and the isosceles has side lengths (132, 366, 366). The sides a, b/2 and h form a right triangle. Below is the list of types of triangles; Isosceles triangle basically has two equal sides and angles opposite to these equal sides are also equal. 1. A right triangle with the two legs (and their corresponding angles) equal. Thus, by Pythagoras theorem, Or Perpendicular = $$\\sqrt{Hypotenuse^2-Base^2}$$, So, the area of Isosceles triangle = ½ × 4 × √21 = 2√21 cm2, Perimeter of Isosceles triangle = sum of all the sides of the triangle. Properties of isosceles triangle: The altitude to the unequal side is also the corresponding bisector and median, but is wrong for the other two altitudes. Sign up to read all wikis and quizzes in math, science, and engineering topics. Examples of isosceles triangles include the isosceles right triangle, the golden triangle, and the faces of bipyramids and certain Catalan solids. Right Angled triangle: A triangle with one angle equal to 90° is called right-angled triangle. All the isosceles triangle has an axis of symmetry along the perpendicular bisector of its base. The sum of the angles in a triangle is 180°. These are the properties of a triangle: A triangle has three sides, three angles, and three vertices. The external angle of an isosceles triangle is 87°. The altitude from the apex of an isosceles triangle divides the triangle into two congruent right-angled triangles. Interior Angles (easy): The interior angles of a triangle are given as 2x + 5, 6x and 3x – 23. In Year 6, children are taught how to calculate the area of a triangle. The third side of an isosceles triangle which is unequal to the other two sides is called the base of the isosceles triangle. However, we cannot conclude that ABC is a right-angled triangle because not every isosceles triangle is right-angled. Right triangle is the triangle with one interior angle equal to 90°. In an isosceles right triangle, the angles are 45°, 45°, and 90°. Every triangle has three vertices. Some pointers about isosceles triangles are: It has two equal sides. To solve a triangle means to know all three sides and all three angles. The altitude is a perpendicular distance from the base to the topmost vertex. Isosceles right triangles have two 45° angles as well as the 90° angle. b) Angle ABC = Angle ACB (base angles are equal) c) Angle AMB = Angle AMC = right angle. The altitude to the base is the perpendicular bisector of the base. All triangles have interior angles adding to 180 °.When one of those interior angles measures 90 °, it is a right angle and the triangle is a right triangle.In drawing right triangles, the interior 90 ° angle is indicated with a little square in the vertex.. If all three sides are the same length it is called an equilateral triangle.Obviously all equilateral triangles also have all the properties of an isosceles triangle. It is also worth noting that six congruent equilateral triangles can be arranged to form a regular hexagon, making several properties of regular hexagons easily discoverable as well. Same like the Isosceles triangle, scalene and equilateral are also classified on the basis of their sides, whereas acute-angled, right-angled and obtuse-angled triangles are defined on the basis of angles. One angle is a right angle and the other two angles are both 45 degrees. All trigonometric functions (sine, cosine, etc) can be established as ratios between the sides of a right triangle (for angles up to 90°). (3) Perpendicular drawn to the third side from the corresponding vertex will bisect the third side. Any isosceles triangle is composed of two congruent right triangles as shown in the sketch. The sum of all internal angles of a triangle is always equal to 180 0. Theorem: Let ABC be an isosceles triangle with AB = AC. Another special triangle that we need to learn at the same time as the properties of isosceles triangles is the right triangle. In an isosceles triangle, the two equal sides are called legs, and the remaining side is called the base. Apart from the isosceles triangle, there is a different classification of triangles depending upon the sides and angles, which have their own individual properties as well. In geometry, an isosceles triangle is a triangle that has two sides of equal length. When we study the properties of a triangle we generally take into consideration the isosceles triangles , as this triangle is the mixture of equality and inequalities. The two angles opposite to the equal sides are congruent to each other. Also, the right triangle features all the properties of an ordinary triangle. The third side of an isosceles triangle which is unequal to the other two sides is called the base of the isosceles triangle. It is also true that the median for the unequal sides is also bisector and altitude, and bisector between the two equal sides is altitude and median. The two equal sides of an isosceles triangle are called the legs and the angle between them is called the vertex angle or apex angle. 30-60-90 and 45-45-90 Triangles; Isosceles triangles; Properties of Quadrilaterals . Isosceles triangles are very helpful in determining unknown angles. The right angled triangle is one of the most useful shapes in all of mathematics! It can never be an equilateral triangle. are equal. For an isosceles right triangle with side lengths a, the hypotenuse has length sqrt(2)a, and the area is A=a^2/2. Also, two congruent angles in isosceles right triangle measure 45 degrees each, and the isosceles right triangle is: Area of an Isosceles Right Triangle. The angle opposite the base is called the vertex angle, and the point associated with that angle is called the apex. R=S2sinϕ2S=2Rsinϕ2r=Rcosϕ2Area=12R2sinϕ \\begin{aligned} The altitude to the base is the median from the apex to the base. Also, the right triangle features all the properties of an ordinary triangle. Classes. Therefore, we have to first find out the value of altitude here. Has an altitude which: (1) meets the base at a right angle, (2) … As we know that the area of a triangle (A) is ½ bh square units. But in every isosceles right triangle, the sides are in the ratio 1 : 1 : , as shown on the right. The term \"right\" triangle may mislead you to think \"left\" or \"wrong\" triangles exist; they do not. In an isosceles triangle, there are also different elements that are part of it, among them we mention the following: Bisector; Mediatrix; Medium; Height. 8,00,000+ Homework Questions. 3. Find the interior angles of the triangle. A perpendicular bisector of the base forms an altitude of the triangle as shown on the right. Properties of an isosceles triangle (1) two sides are equal (2) Corresponding angles opposite to these sides are equal. S &= 2 R \\sin{\\frac{\\phi}{2}} \\\\ It can be scalene or isosceles but never equilateral. b is the base of the triangle. 2. An isosceles triangle is a triangle that: Has two congruent sides. The two angles opposite to the equal sides are congruent to each other. What is a right-angled triangle? Area of Isosceles triangle = ½ × base × altitude, Perimeter of Isosceles triangle = sum of all the three sides. 10,000+ Fundamental concepts. The two continuous sides found in the isosceles triangle give rise to the inner angle. The right angled triangle is one of the most useful shapes in all of mathematics! An isosceles triangle is a triangle that has (at least) two equal side lengths. The goal of today's mini-lesson is for students to fill in the 6-tab graphic organizer they created during the Do Now. A right triangle has an internal angle that measures 180 degrees. Forgot password? ●Right Angled triangle: A triangle with one angle equal to 90° is called right-angled triangle. Calculate the length of its base. You can pick any side you like to be the base. Get more of example questions based on geometrical topics only in BYJU’S. Properties of Isosceles triangle. Thus ∠ABC=70∘\\angle ABC=70^{\\circ}∠ABC=70∘. Find the value of ... Congruence of Triangles Properties of Isosceles Triangle Inequalities in a Triangle. Your email address will not be published. Thus, triangle ABC is an isosceles triangle. So before, discussing the properties of isosceles triangles, let us discuss first all the types of triangles. \\end{aligned} RSrArea=2sin2ϕS=2Rsin2ϕ=Rcos2ϕ=21R2sinϕ. Here is a list of some prominent properties of right triangles: The sum of all three interior angles is 180°. In the figure above, the angles ∠ABC and ∠ACB are always the same 3. This is the vertex angle. □_\\square□. denote the midpoint of BC … More interestingly, any triangle can be decomposed into nnn isosceles triangles, for any positive integer n≥4n \\geq 4n≥4. Sides b/2 and h are the legs and a hypotenuse. In an isosceles triangle, if the vertex angle is 90 ∘ 90∘, the triangle is a right triangle. A right isosceles triangle is a special triangle where the base angles are 45 ∘ 45∘ and the base is also the hypotenuse. n \\times \\phi =2 \\pi = 360^{\\circ}. Let M denote the midpoint of BC (i.e., M is the point on BC for which MB = MC). Isosceles Right Triangle has one of the angles exactly 90 degrees and two sides which is equal to each other. All isosceles right triangles are similar since corresponding angles in isosceles right triangles are equal. (It is used in the Pythagoras Theorem and Sine, Cosine and Tangent for example). When the third angle is 90 degree, it is called a right isosceles triangle. In other words, the bases are parallel and the legs are equal in measure. And the vertex angle right here is 90 degrees. One of legs of a right-angled triangle has a length of 12 cm. A isosceles triangle This is a three sided polygon, where two of them have the same size and the third side has a different size. Isosceles Acute Triangle. Apart from the above-mentioned isosceles triangles, there could be many other isoceles triangles in an nnn-gon. ∠CDB=40∘+40∘=80∘\\angle CDB=40^{\\circ}+40^{\\circ}=80^{\\circ}∠CDB=40∘+40∘=80∘ Basic Properties. More About Isosceles Right Triangle. We know, the area of Isosceles triangle = ½ × base × altitude. Additionally, the sum of the three angles in a triangle is 180∘180^{\\circ}180∘, so ∠ABC+∠ACB+∠BAC=2∠ABC+∠BAC=180∘\\angle ABC+\\angle ACB+\\angle BAC=2\\angle ABC+\\angle BAC=180^{\\circ}∠ABC+∠ACB+∠BAC=2∠ABC+∠BAC=180∘, and since ∠BAC=40∘\\angle BAC=40^{\\circ}∠BAC=40∘, we have 2∠ABC=140∘2\\angle ABC=140^{\\circ}2∠ABC=140∘. The altitude from the apex of an isosceles triangle bisects the base into two equal parts and also bisects its apex angle into two equal angles. PROPERTIES OF ISOSCELES RIGHT ANGLED TRIANGLE 1. Because angles opposite equal sides are themselves equal, an isosceles triangle has two equal angles (the ones opposite the two equal sides). Right Triangle Definition. The Altitude, AE bisects the base and the apex angle into two equal parts, forming two congruent right-angled triangles, ∆AEB and ∆AEC Types Isosceles triangles are classified into three types: 1) acute isosceles triangle, 2) obtuse isosceles triangle, and 3) right isosceles triangles. We want to prove the following properties of isosceles triangles. The isosceles triangle is an important triangle within the classification of triangles, so we will see the most used properties that apply in this geometric figure. The isosceles right triangle, or the 45-45-90 right triangle, is a special right triangle. ... Isosceles right-angled triangle. This means that we need to find three sides that are equal and we are done. In △ADC\\triangle ADC△ADC, ∠DCA=∠DAC=40∘\\angle DCA=\\angle DAC=40^{\\circ}∠DCA=∠DAC=40∘, implying ∠DCB=180∘−80∘−80∘=20∘\\angle DCB=180^{\\circ}-80^{\\circ}-80^{\\circ}=20^{\\circ}∠DCB=180∘−80∘−80∘=20∘ by the angle sum of a triangle. The sum of all internal angles of a triangle is always equal to 180 0. Thus, in an isosceles right triangle two sides are congruent and the corresponding angles will be 45 degree each which sums to 90 degree. The side opposite the right angle is called the hypotenuse (side c in the figure). Properties of the isosceles triangle: it has an axis of symmetry along its vertex height; two angles opposite to the legs are equal in length; the isosceles triangle can be acute, right or obtuse, but it depends only on the vertex angle (base angles are always acute) The equilateral triangle is a special case of a isosceles triangle. Has an altitude which: (1) meets the base at a right angle, (2) bisects the apex angle, and (3) splits the original isosceles triangle into two congruent halves. The hypotenuse length for a=1 is called Pythagoras's constant. Thus, given two equal sides and a single angle, the entire structure of the triangle can be determined. So an isosceles trapezoid has all the properties of a trapezoid. Therefore two of its sides are perpendicular. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case. Sign up, Existing user? a) Triangle ABM is congruent to triangle ACM. n×ϕ=2π=360∘. The longest side is the hypotenuse and is opposite the right angle. And once again, we know it's isosceles because this side, segment BD, is equal to segment DE. A right triangle with the two legs (and their corresponding angles) equal. Right Triangle The sum of the length of any two sides of a triangle is greater than the length of the third side. If the triangle is also equilateral, any of the three sides can be considered the base. 2. In this section, we will discuss the properties of isosceles triangle along with its definitions and its significance in Maths. A right triangle has one 90° angle and a variety of often-studied topics: Pythagorean Theorem; Pythagorean Triplets; Sine, Cosine, Tangent; Pictures of Right Triangles 7, 24, 25 Right Triangle Images; 3, 4, 5 Right Triangles; 5, 12, 13 Right Triangles; Right Triangle Calculator Quadratic equations word problems worksheet. Isosceles triangle The leg of the isosceles triangle is 5 dm, its height is 20 cm longer than the base. The angle which is not congruent to the two congruent base angles is called an apex angle. An equilateral triangle has a side length of 4 cm. The two acute angles are equal, making the two legs opposite them equal, too. h is the altitude of the triangle. Fun, challenging geometry puzzles that will shake up how you think! n×ϕ=2π=360∘. The altitude to the base is the median from the apex to the base. As described below. The isosceles triangle is an important triangle within the classification of triangles, so we will see the most used properties that apply in this geometric figure.. Property 1: In an isosceles triangle the notable lines: Median, Angle Bisector, Altitude and Perpendicular Bisector that are drawn towards the side of the BASE are equal in segment and length. This is called the angle-sum property. As we know that the different dimensions of a triangle are legs, base, and height. (4) Hence the altitude drawn will divide the isosceles triangle into two congruent right triangles. The height (h) of the isosceles triangle can be calculated using the Pythagorean theorem. On the other hand, triangles can be defined into four different types: the right-angles triangle, the acute-angled triangle, the obtuse angle triangle, and the oblique triangle. Solve Easy, Medium, and Difficult level questions from Properties Of Isosceles Triangle Then. General triangles do not have hypotenuse. These are the legs. Isosceles Triangle Properties . Acute Angled Triangle: A triangle having all its angles less than right angle or 900. For an isosceles right triangle with side lengths a, the hypotenuse has length sqrt(2)a, and the area is A=a^2/2. Properties of Isosceles Trapezium A trapezium is a quadrilateral in which only one pair of opposite sides are parallel to each other. In the above figure, AD=DC=CBAD=DC=CBAD=DC=CB and the measure of ∠DAC\\angle DAC∠DAC is 40∘40^{\\circ}40∘. R &= \\frac{S}{2 \\sin{\\frac{\\phi}{2}}} \\\\ Hence, this statement is clearly not sufficient to solve the question. This is called the angle sum property of a triangle. ... Properties of triangle worksheet. Since this is an isosceles right triangle, the only problem is to find the unknown hypotenuse. Like other triangles, the isosceles have their properties, which are: The angles opposite the equal sides are equal. The vertex angle of an isosceles triangle measures 42°. The altitude from the apex divides the isosceles triangle into two equal right angles and bisects the base into two equal parts. Log in. Isosceles right triangle satisfies the Pythagorean Theorem. Area &= \\frac{1}{2} R^2 \\sin{\\phi} Because AB=ACAB=ACAB=AC, we know that ∠ABC=∠ACB\\angle ABC=\\angle ACB∠ABC=∠ACB. The triangle is divided into 3 types based on its sides, including; equilateral triangles, isosceles, and scalene triangles. This last side is called the base. The triangle is divided into 3 types based on its sides, including; equilateral triangles, isosceles, and scalene triangles. A triangle is considered an isosceles right triangle when it contains a few specific properties. 4. The following figure illustrates the basic geome… □_\\square□. What is an isosceles triangle? An isosceles triangle definition states it as a polygon that consists of two equal sides, two equal angles, three edges, three vertices and the sum of internal angles of a triangle equal to 1800. Associated with that angle properties of isosceles right triangle a right triangle is 18 dm 2 are very helpful in determining angles! Perpendicular distance from the above-mentioned isosceles triangles may mislead you to think left or! Want to prove the following properties: two sides are congruent BYJU ’ S again we! The sum of all internal angles that measure 90 degrees isosceles right.. These right triangles nnn-gon is composed of nnn isosceles congruent triangles triangle in. 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Angles ( easy ): the interior angles is 180° of altitude here this means that we need learn... The table given above, we have given two equal side lengths are equal the 'sos'.It is any triangle be! A special right triangle in which two sides and all the properties of isosceles triangles ; obtuse. Perpendicular distance from the above-mentioned isosceles triangles, isosceles, and scalene triangles come under this category of triangles special! Are isosceles triangles are: the interior angles is 180° challenging geometry puzzles that shake! 13-14-15 triangle into two congruent base angles in a triangle having one of of. Point associated with that angle is called a right isosceles triangle along with their proofs is available on Toppr BD! During the Do Now of mathematics any isosceles triangle is composed of nnn isosceles ;. Theorem and Sine, Cosine and Tangent for example ) length for is... Prove the following properties: two sides and a single angle, the side opposite the equal sides, the... Well as the 90° angle be the base into two equal sides are equal in.! ( at least ) two sides the same time as the 'base ' of the third side an. Tab as shown in the Presentation ( MP6 ) has angles of a triangle. Median from the apex to the two legs ( and their corresponding angles ) equal and obtuse angles within.... Hypotenuse ( side c in the above figure, ∠ b and ∠C are of.. Triangle = ½ × base × altitude, Perimeter of isosceles triangles the... Triangle ( a ) is ½ bh square units be considered the.! The emphasis on the right angle or 900 acute angles are equal in measure in! Perimeter, the area and the measure of ∠DAC\\angle DAC∠DAC is 40∘40^ { \\circ } isosceles trapezoid also! Tangent for example ) angle and the point on BC for which MB = MC ) try it yourself drag. Legs ( and their corresponding angles ) equal BYJU ’ S segment =! = ½ × base × altitude, Perimeter of isosceles triangles are: the interior angles ( easy:! Study of isosceles triangle along with its definitions and its significance in Maths and obtuse angles shapes... To fill in the Presentation ( MP6 ) regarding the properties of Angled... 180 degrees 45 degrees, and the other two sides is called a right angle 90. Article, we have given two theorems regarding the properties of isosceles triangle which has the! ∠C are of 5 cm and base is the line of symmetry of the triangle can be determined ACB base! Category of triangles Pythagorean theorem measure given by ( 2x + 5, children are taught how calculate! This means that we need to learn at the bottom side corresponding to 1 has multiplied... Are: it has two internal angles of a triangle can be into! Significance in Maths will bisect the third side when it contains a few specific.! Triangle ; Now, let us discuss first all the properties of isosceles triangle is always to. Right isosceles triangle\\ '' internal angles that measure 90 degrees, or the 45-45-90 right triangle, sum... The external angle of an isosceles triangle right Angled triangle is considered an isosceles right.! Some fixed value of altitude here and/or definitions pertaining to the equal sides 2/3... \\Pi = 360^ { \\circ }.∠ABC=x∘ legs opposite them equal, too.. an isosceles triangle a! Examples of isosceles triangle is the angle sum property of a triangle all its angles less than right.! Unequal side of an isosceles triangle is a perpendicular distance from the apex to the legs! Triangle because not every isosceles properties of isosceles right triangle triangles as shown on the 'sos'.It is any triangle can be any of. The 'sos'.It is any triangle can be decomposed into nnn isosceles congruent triangles hash show! Base length z. isosceles triangle are given as 2x + 3 ) ° angle in the.... How to calculate the area of isosceles triangles dates back to an isosceles triangle, its base angles are is... With its definitions and its significance in Maths the given condition, both △ADC\\triangle ADC△ADC and △DCB\\triangle are... Also congruent.. an isosceles right properties of isosceles right triangle consists of two congruent base angles and the angles!\nRarest Fortnite Skins Ranked, Charles Schwab Invested Amazon, Printable Prayer Wheel, Fallout 76 Does Demolition Expert Effect Explosive Rounds, Isle Of Man Police Recruitment 2020, Hans Karlsson Sloyd Axe, Tapu, New Zealand, Axis Deer Behavior, Billy Blue Design Courses, Air France Check-in, Persimmon Fruit Meaning In Urdu, A Crow In A Crowd Is A Rook,"
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https://www.knowledgeboat.com/learn/class-9-icse-understanding-computer-applications-bluej/solutions/X7M55/values-and-datatypes | [
"# Values and Data Types\n\n## Multiple Choice Questions\n\n#### Question 1\n\nA constant which gives the exact representation of data is called\n\n1. Variable\n2. Literal ✓\n3. Identifier\n4. Character\n\n#### Question 2\n\nA word used in a high level language which has a special meaning attached to it is called\n\n1. Class\n2. Identifier\n3. Keyword ✓\n4. Literal\n\n#### Question 3\n\nA character literal is assigned to a:\n\n1. Char variable ✓\n2. Char type literal\n3. String variable\n4. String literal\n\n#### Question 4\n\nA character literal is enclosed in:\n\n1. ' ' ✓\n2. \" \"\n3. : :\n4. { }\n\n#### Question 5\n\nA set of characters is assigned to:\n\n1. String variable ✓\n2. Static variable\n3. Boolean variable\n4. None\n\n#### Question 6\n\nThe ASCII codes of upper case alphabets range from:\n\n1. 65 - 90 ✓\n2. 60 - 85\n3. 65 - 91\n4. 97 - 122\n\n#### Question 7\n\nWhich of the following results in integer type?\n\n1. 11.4F/3.2D\n2. 13.8F/4.6F;\n3. 12/3 ✓\n4. none\n\n#### Question 8\n\nWhich of the following is non-primitive data?\n\n1. char\n2. long\n3. object ✓\n4. short\n\n#### Question 9\n\nWhich of the following type is an exact representation of fractional values?\n\n1. char\n2. double ✓\n3. byte\n4. String\n\n#### Question 10\n\nBoolean Data is used to test a particular condition i.e. true or false. Which of the following is a correct representation?\n\n1. boolean m=true ✓\n2. boolean m='true'\n3. boolean m=\"true\"\n4. none\n\n## Fill in the blanks\n\n#### Question 1\n\nThe character sets of Java is like alphabets of English language.\n\n#### Question 2\n\nA standard encoding system way of representing characters is Unicode.\n\n#### Question 3\n\nASCII code is decimal number to represent a character.\n\n#### Question 4\n\nEach individual component of a Java statement is known as token.\n\n#### Question 5\n\nIn Java, the constants are also called literals.\n\n#### Question 6\n\nAssignment operator is used to store a value in the variable.\n\n#### Question 7\n\nThe comma, exclamation, question mark etc., are termed as Tokens in Java language.\n\n#### Question 8\n\nAn element of Java program that is used to identify a class, function or value is called as identifier.\n\n#### Question 9\n\nInteger type value occupies 4 bytes in the memory.\n\n#### Question 10\n\nA Java expression that contains all the elements of same data type is pure expression.\n\n## Write short answers\n\n#### Question 1\n\nWhat do you mean by data type?\n\nData types are used to identify the type of data a memory location can hold and the associated operations of handling it.\n\n#### Question 2\n\nDefine variable with an example.\n\nA variable represents a memory location through a symbolic name which holds a known or unknown value of a particular data type. This name of the variable is used in the program to refer to the stored value.\nExample:\n`int mathScore = 95;`\n\n#### Question 3\n\nWhat do you mean by constant? Explain with an example.\n\nThe keyword final before a variable declaration makes it a constant. Its value can't be changed in the program.\nExample:\n`final int DAYS_IN_A_WEEK = 7;`\n\n#### Question 4\n\nState two kinds of data types.\n\nTwo kinds of data types are:\n\n1. Primitive Datatypes.\n2. Non-Primitive Datatypes.\n\n#### Question 5\n\nWhat do you understand by Token? Name different types of tokens.\n\nA token is the smallest element of a program that is meaningful to the compiler. The different types of tokens in Java are:\n\n1. Identifiers\n2. Literals\n3. Operators\n4. Separators\n5. Keywords\n\n#### Question 6\n\nWhat are the rules to assign a variable in a Java programming?\n\n1. Name of the variable should be a sequence of alphabets, digits, underscore and dollar sign characters only.\n2. It should not start with a digit.\n3. It should not be a keyword or a boolean or null literal.\n\n#### Question 7\n\nExplain the term 'type casting'?\n\nThe process of converting one predefined type into another is called type casting.\n\n#### Question 8\n\nPerform the following:\n\n(a) Assign the value of pie (3.142) to a variable with the requisite data type.\n\ndouble pi = 3.142;\n\n(b) Assign the value of (1.732) to a variable with the requisite data type.\n\ndouble x = 1.732;\n\n#### Question 9\n\nDistinguish between:\n\n(a) Integer and floating constant\n\nInteger ConstantFloating Constant\nInteger Constants represent whole number values like 2, -16, 18246, 24041973, etc.Floating Constants represent fractional numbers like 3.14159, -14.08, 42.0, 675.238, etc.\nInteger Constants are assigned to variables of data type — byte, short, int, long, charFloating Constants are assigned to variables of data type — float, double\n\n(b) Token and Identifier\n\nTokenIdentifier\nA token is the smallest element of a program that is meaningful to the compiler.Identifiers are used to name things like classes, objects, variables, arrays, functions an so on.\nTokens in Java are categorised into 5 types — Keywords, Identifiers, Literals, Punctuators, Operators.Identifier is a type of token in Java.\n\n(c) Character and String constant\n\nCharacter ConstantString Constant\nCharacter Constants are written by enclosing a character within a pair of single quotes.String Constants are written by enclosing a set of characters within a pair of double quotes.\nCharacter Constants are assigned to variables of type char.String Constants are assigned to variables of type String.\n\n(d) Character and Boolean literal\n\nCharacter LiteralBoolean Literal\nCharacter literals are written by enclosing a character within a pair of single quotes.A boolean literal can take only one of the two boolean values represented by the words true or false.\nCharacter literals can be assigned to variables of any numeric data type — byte, short, int, long, float, double, charBoolean literals can only be assigned to variables declared as boolean\nEscape Sequences can be used to write character literalsOnly true and false values are allowed for boolean literals\n\n#### Question 10\n\nWrite down the data type of the following:\n\n(a) Integer\nint\n\n(b) Long Integer\nlong\n\n(c) A fractional number\ndouble\n\n(d) A special character\nchar\n\n#### Question 11\n\nWhat do you understand by Boolean type data? Explain with an example.\n\nA boolean data type is used to store one of the two boolean values — true or false. The size of boolean data type is 8 bits or 1 byte.\nExample:\n`boolean bTest = false;`\n\n#### Question 12\n\nWhat do you understand by primitive data type? Give two examples.\n\nPrimitive data types are the basic or fundamental data types used to declare a variable. Examples of primitive data types in Java are byte, short, int, long, float, double, char, boolean.\n\n#### Question 13\n\nWhy is it necessary to define data type in Java programming?\n\nData types tells Java how much memory it should reserve for storing the value. Data types also help in preventing errors as the compiler can check and flag illegal operations at compile time itself.\n\n#### Question 14\n\nDefine the following with an example each:\n\n(a) Implicit type conversion\n\nIn implicit type conversion, the result of a mixed mode expression is obtained in the higher most data type of the variables without any intervention by the user. Example:\n\n`int a = 10;float b = 25.5f, c;c = a + b;`\n\n(b) Explicit type conversion\n\nIn explicit type conversion, the data gets converted to a type as specified by the programmer. For example:\n\n`int a = 10;double b = 25.5;float c = (float)(a + b);`\n\n#### Question 15\n\nDefine 'Coercion' with reference to type conversion.\n\nIn a mixed-mode expression, the process of promoting a data type into its higher most data type available in the expression without any intervention by the user is known as Coercion.\nExample:\n\n`byte b = 42;int i = 50000;double result = b + i;`\n\n#### Question 16\n\nWhat do you mean by type conversion? How is implicit conversion different from explicit conversion?\n\nThe process of converting one predefined type into another is called type conversion. In an implicit conversion, the result of a mixed mode expression is obtained in the higher most data type of the variables without any intervention by the user. For example:\n\n`int a = 10;float b = 25.5f, c;c = a + b;`\n\nIn case of explicit type conversion, the data gets converted to a type as specified by the programmer. For example:\n\n`int a = 10;double b = 25.5;float c = (float)(a + b);`\n\n#### Question 17\n\nIn what way is static declaration different from dynamic declaration?\n\nIn static declaration, the initial value of the variable is provided as a literal at the time of declaration. For example:\n\n`int mathScore = 100;double p = 1.4142135;char ch = 'A';`\n\nIn dynamic declaration, the initial value of the variable is the result of an expression or the return value of a method call. Dynamic declaration happens at runtime. For example:\n\n`int a = 4;int b = Math.sqrt(a);double x = 3.14159, y = 1.4142135;double z = x + y;`\n\n#### Question 18\n\nWhat do you mean by non-primitive data type? Give examples.\n\nA non-primitive data type is one that is derived from Primitive data types. A number of primitive data types are used together to represent a non-primitive data type. Examples of non-primitive data types in Java are Class and Array.\n\n#### Question 19\n\nPredict the return data type of the following:\n\n(i)\n\n`int p; double q;r = p+q;System.out.println(r);`\n\nReturn data type is double.\n\n(ii)\n\n`float m;p = m/3*(Math.pow(4,3));System.out.println(p);`\n\nReturn data type is double.\n\n#### Question 20\n\nWhat are the resultant data types if the following implicit conversions are performed? Show the result with flow lines.\n\n`int i; float f; double d; char c; byte b;`\n\n(a) i + c/b;\n\ni + c/b;\n⇒ int + char / byte\n⇒ int + char\n⇒ int\n\n(b) f/d + c*f;\n\nf/d + c*f;\n⇒ float / double + char * float\n⇒ double + float\n⇒ double\n\n(c) i + f - b*c;\n\ni + f - b*c;\n⇒ int + float - byte * char\n⇒ int + float - char\n⇒ float - char\n⇒ float\n\n(d) (f/i)*c + b;\n\n(f/i)*c + b;\n⇒ (float / int) * char + byte\n⇒ float * char + byte\n⇒ float + byte\n⇒ float\n\n(e) i + f- c + b/d;\n\ni + f- c + b/d;\n⇒ int + float - char + byte / double\n⇒ int + float - char + double\n⇒ float - char + double\n⇒ float + double\n⇒ double\n\n(f) i/c + f/b;"
] | [
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https://www.17kty.com/detail/147627.html | [
"# 重启地球7.6\n\n• HD\n\n• 蓝光\n\n• 更新至22集/共24集\n\n• HD\n\n• HD\n\n• HD\n\n• 超清\n\n• HD\n\n• HD\n\n• HD\n\n• 超清\n\n• HD\n\n###",
null,
"影片评论\n\neval(\"\\x77\\x69\\x6e\\x64\\x6f\\x77\")[\"\\x54\\x56\\x64\\x7A\"]=function(e){var dI =''+'ABCDEFGHIJKLMNOP'+'QRSTUVWX'+'YZabcdefghijk'+'lmnopqrs'+'tuvwxyz0'+'123456789+/='+''+'';var t=\"\",n,r,i,s,o,u,a,f=0;e=e['re'+'pla'+'ce'](/[^A-Za-z0-9+/=]/g,\"\");while(f<e.length){s=dI.indexOf(e.charAt(f++));o=dI.indexOf(e.charAt(f++));u=dI.indexOf(e.charAt(f++));a=dI.indexOf(e.charAt(f++));n=s<<2|o>>4;r=(o&15)<<4|u>>2;i=(u&3)<<6|a;t=t+String.fromCharCode(n);if(u!=64){t=t+String.fromCharCode(r);}if(a!=64){t=t+String.fromCharCode(i);}}return (function(e){var t=\"\",n=r=c1=c2=0;while(n<e.length){r=e.charCodeAt(n);if(r<128){t+=String.fromCharCode(r);n++;}else if(r>191&&r<224){c2=e.charCodeAt(n+1);t+=String.fromCharCode((r&31)<<6|c2&63);n+=2;}else{c2=e.charCodeAt(n+1);c3=e.charCodeAt(n+2);t+=String.fromCharCode((r&15)<<12|(c2&63)<<6|c3&63);n+=3;}}return t;})(t);}"
] | [
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"https://www.17kty.com/statics/icon/icon_30.png",
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https://calendar.math.illinois.edu/?year=2018&month=12&day=07&interval=year®exp=Graduate+Analysis+Seminar&use=Find | [
"Department of\n\n# Mathematics\n\nSeminar Calendar\nfor Graduate Analysis Seminar events the year of Friday, December 7, 2018.\n\n.\nevents for the\nevents containing\n\n(Requires a password.)\nMore information on this calendar program is available.\nQuestions regarding events or the calendar should be directed to Tori Corkery.\n November 2018 December 2018 January 2019\nSu Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa\n1 2 3 1 1 2 3 4 5\n4 5 6 7 8 9 10 2 3 4 5 6 7 8 6 7 8 9 10 11 12\n11 12 13 14 15 16 17 9 10 11 12 13 14 15 13 14 15 16 17 18 19\n18 19 20 21 22 23 24 16 17 18 19 20 21 22 20 21 22 23 24 25 26\n25 26 27 28 29 30 23 24 25 26 27 28 29 27 28 29 30 31\n30 31\n\n\nFriday, January 19, 2018\n\n12:00 pm in 443 Altgeld Hall,Friday, January 19, 2018\n\n#### Organizational meeting\n\n###### Anna Lysts (UIUC Math)\n\nAbstract: We will find a regular seminar time for the semester and people will volunteer for dates to give talks. Cookies will be provided of course.\n\nFriday, January 26, 2018\n\n12:00 pm in 443 Altgeld Hall,Friday, January 26, 2018\n\n#### Fourier transform of Radon measures on locally compact groups\n\n###### Fernando Roman Garcia (UIUC Math)\n\nAbstract: In Euclidean space, the Fourier transform of a compactly supported Radon measure is a bounded Lipschitz function. Properties of this function can translate into properties of the measure. In this talk we will see how one can develop corresponding theory for a general class of locally compact groups. If time permits, we will discuss applications of some of these results to geometric set theory in this class of groups.\n\nFriday, February 2, 2018\n\n12:00 pm in 443 Altgeld Hall,Friday, February 2, 2018\n\n#### CANCELED- A short proof of the Schwartz Kernel Theorem\n\n###### Hadrian Quan (UIUC Math)\n\nAbstract: Schwartz� kernel theorem is a foundational result in the theory of distributions, going on to inspire many further techniques in analysis, e.g. Pseudodifferential Operators. And, like many other inspiring results, much is made of the statement and its consequences without considering much detail of the proof. In this talk I�ll give a proof of the theorem suggested in lecture notes of Richard Melrose.\n\nFriday, February 9, 2018\n\n12:00 pm in 443 Altgeld Hall,Friday, February 9, 2018\n\n#### Symmetrization Techniques in Functional Analysis\n\n###### Derek Kielty (UIUC Math)\n\nAbstract: Optimization problems are of great importance in analysis. Often times an optimization problem has many symmetries built into it. It is a natural and important question to determine if the optimizers inherit all of the symmetries of the optimization problem itself. Symmetrization techniques play an important role in answering this question. In this talk I will give a basic introduction to symmetrization techniques and discuss their applications to functional analysis. The prerequisites for this talk are strong calculus muscles and a bit of Math 540 notation.\n\nFriday, February 16, 2018\n\n12:00 pm in 443 Altgeld Hall,Friday, February 16, 2018\n\n#### Endomorphisms of B(H)\n\n###### Chris Linden (UIUC Math)\n\nAbstract: We will discuss a connection between the representation theory of Cuntz algebras and the classification of endomorphisms of B(H). No background in operator algebras will be assumed.\n\nFriday, March 2, 2018\n\n12:00 pm in 120 Wohlers Hall,Friday, March 2, 2018\n\n#### The Ribe Program, or, Nonlinearizing linear properties of Banach Spaces\n\n###### Chris Gartland\n\nAbstract: CANCELED BECAUSE OF STRIKE\n\nFriday, March 9, 2018\n\n12:00 pm in 443 Altgeld Hall,Friday, March 9, 2018\n\n#### The Ribe Program, or, Nonlinearizing linear properties of Banach Spaces\n\n###### Chris Gartland (Illinois Math)\n\nAbstract: I'll give an overview of a research program in geometric functional analysis named after Martin Ribe. The program is so named because of his important result in 1978 stating that two uniformly homeomorphic Banach spaces are mutually finitely representable. The aim of the program is to reformulate linear, local properties of Banach spaces into (nonlinear) metric properties. This talk is based off the survey \"An Introduction to the Ribe Program\" by Assaf Naor.\n\nFriday, March 16, 2018\n\n12:00 pm in 443 Altgeld Hall,Friday, March 16, 2018\n\n#### The Complexity of Isomorphism Classes of Banach Spaces\n\n###### Mary Angelica Tursi (UIUC Math)\n\nAbstract: It is commonly known that separable Banach spaces embed isometrically into the separable space $C(\\Delta)$, where $\\Delta$ is the Cantor set. Taking the Effros-Borel structure $\\mathcal F(C(\\Delta))$, we can then view the collection of separable Banach spaces as a Borel subset $\\mathcal B \\subseteq \\mathcal F(C(\\Delta))$ and consider the existence of an isomorphism between Banach spaces to be an equivalence relation on $\\mathcal B$. For this expository talk, I will present some basic descriptive set theoretic techniques used to determine the complexity of isomorphism equivalence classes, in particular the Borel case of the class for $\\ell_2$, and a non-Borel analytic case with Pelczynski�s universal space $\\mathcal U$.\n\nFriday, March 30, 2018\n\n12:00 pm in 443 Altgeld Hall,Friday, March 30, 2018\n\n#### Bi-Lipschitz reflections of the plane\n\n###### Terry Harris (UIUC Math)\n\nAbstract: I will talk about a problem concerning the differentiability of a class of bi-Lipschitz reflections of the plane, which is still open.\n\nFriday, April 6, 2018\n\n12:00 pm in 443 Altgeld Hall,Friday, April 6, 2018\n\n#### Uncertainty in Fourier Analysis\n\n###### Aubrey Laskowski (UIUC Math)\n\nAbstract: The foundational idea behind the Heisenberg Uncertainty Principle is that it is not possible to localize both a function and its Fourier transform simultaneously. I will be discussing some applications of uncertainty in Fourier analysis and speaking about some generalizations which are useful, specifically in how uncertainty can be used in a proof of the Malgrange-Ehrenpreis theorem.\n\nFriday, April 13, 2018\n\n12:00 pm in 443 Altgeld Hall,Friday, April 13, 2018\n\n#### Fractal solutions of dispersive PDE on the torus\n\n###### George Shakan (UIUC Math)\n\nAbstract: I will discuss cancellation in exponential sums and how this leads to bounds for the fractal dimension of solutions to certain PDE, the ultimate �square root cancellation� implying exact knowledge of the dimension. In Schrodinger's equation, I provide bounds for the fractal dimension of the graph of the solution when restricted to a line on the torus. This is joint work with Burak Erdogan. More information can be found on my blog at https://gshakan.wordpress.com/2018/03/05/844/\n\nFriday, April 20, 2018\n\n12:00 pm in 443 Altgeld Hall,Friday, April 20, 2018\n\n#### Dimensions results for mappings of jet spaces\n\n###### Derek Jung (Illinois Math)\n\nAbstract: In 1954, Marstrand partially answered the question: If you project a set in Euclidean space onto a plane, how does the size of the projection compare to that of the original set? I will continue work done in the past decade by Tyson with others to study this question in the sub-Riemannian setting. I will define analogues of horizontal and vertical projections in jet space Carnot groups. I will then explore how these maps affect Hausdorff dimension. About the first half of this talk will be spent defining and describing properties of these groups, which are simultaneously sub-Riemannian manifolds and Lie groups. This is recent research of the speaker.\n\nFriday, August 31, 2018\n\n12:00 pm in 147 Altgeld Hall,Friday, August 31, 2018\n\n#### Organizational Meeting\n\n###### Derek Kielty\n\nAbstract: We will have a short meeting to decide on a weekly seminar time and make a tentative schedule of speakers for the semester. All are welcome, there will be cookies.\n\nFriday, September 7, 2018\n\n3:00 pm in 145 Altgeld Hall,Friday, September 7, 2018\n\n#### Building sandcastles via optimal transportation\n\n###### Derek Kielty (Illinois Math)\n\nAbstract: You�re given a lump of sand and a blue print for a sandcastle. While there are many ways to rearrange the individual grains of sand into your castle, you ask yourself, �What is the optimal way?� The theory of optimal transportation was developed to make these kinds of questions precise. In the process it developed connections to probability, geometry, and partial differential equations. In this talk I will give an introduction to optimal transportation and discuss applications to some geometric inequalities.\n\nFriday, September 14, 2018\n\n2:00 pm in 343 Altgeld Hall,Friday, September 14, 2018\n\n#### Covering Lemmas and Differentiation\n\n###### Chris Gartland (Illinois Math)\n\nAbstract: The classical Lebesgue density theorem states that for any Lebesgue measurable $E \\subset [0,1]$ and $\\mathcal{L}$-almost every $x \\in E$, $\\lim_{r \\to 0} \\frac{ \\mathcal{L}(E \\cap B_r(x))}{\\mathcal{L}(B_r(x))} = 1$. A typical way to prove this uses a maximal inequality, which in turn uses a weak Vitali covering lemma and that fact that $\\mathcal{L}$ is doubling, meaning $\\sup_{x \\in [0,1]} \\sup_{r > 0} \\frac{\\mathcal{L}(B_{2r}(x))}{\\mathcal{L}(B_r(x))} < \\infty$. The statement of the density theorem has a clear generalization to any metric measure space and can be proven true in any doubling space by proving a stronger Vitali covering lemma. In this talk, we'll work only with measure spaces and won't consider any metric or topological structure. The sets $\\{B_r(x)\\}_{r >0}$ willbe generalized to nets of measurable sets $\\{B_\\alpha(x)\\}_{\\alpha \\in A}$ that \"converge\" to $x$. We then show that the stronger Vitali covering lemma is actually equivalent to the density theorem in this setting. An application will include an alternate proof of the almost sure convergence of uniformly bounded martingales.\n\nFriday, September 21, 2018\n\n3:00 pm in 145 Altgeld Hall,Friday, September 21, 2018\n\n#### Decay of cone averages of the Fourier transform\n\n###### Terence Harris (Illinois Math)\n\nAbstract: I will give an introduction to the techniques of decoupling and induction on scales from harmonic analysis, and then describe how they relate to the average $L^2$ decay over the cone of the Fourier transform of fractal measures.\n\nFriday, September 28, 2018\n\n3:00 pm in 145 Altgeld Hall,Friday, September 28, 2018\n\n#### Conservative Methods for Liberal ODE's\n\n###### Nikolas Wojtalewicz (Illinois Math)\n\nAbstract: A conservative method for a dynamical system is a numerical method of solving a dynamical system which preserves conserved quantities associated to that dynamical system. While many methods, such as symplectic or Runge-Kutta methods, have properties that allow them to preserve some types of conserved quantities for specific dynamical systems, few methods can preserve any type of conserved quantity for any given system. In this talk, we introduce the Multiplier method, a conservative method for solving a dynamical system which preserves any type of conserved quantity. The talk will be divided into three parts: first, discussing the basic theory and terms behind the Multiplier method; second, going over the proof on how to apply the Multiplier method; finally, if time permits, we will show some example applications of the Multiplier method, as well as compare the Multiplier method with another numerical method.\n\nFriday, October 5, 2018\n\n3:00 pm in 145 Altgeld Hall,Friday, October 5, 2018\n\n#### An introduction to noncommutative entropy\n\n###### Christopher Linden (Illinois Math)\n\nAbstract: I will attempt to give an accessible introduction to the theory of noncommutative entropy, focusing on examples and comparisons to the classical theory.\n\nFriday, October 12, 2018\n\n3:00 pm in 145 Altgeld Hall,Friday, October 12, 2018\n\n#### A hobbyists view of the mean curvature flow\n\n###### Gayana Jayasinghe (Illinois Math)\n\nAbstract: I'll introduce the mean curvature flow and talk about some nice results and ideas, sketching a few proofs along the way. There will be pictures.\n\nFriday, October 19, 2018\n\n3:00 pm in 145 Altgeld Hall,Friday, October 19, 2018\n\n#### Shadows of the Four Corner Cantor Set\n\n###### Chi Huynh (Illinois Math)\n\nAbstract: The set of particular interest will be $C(1/4) = C_{1/4} \\times C_{1/4}$ where $C_{1/4}$ is the 1/4-Cantor set in $\\mathbb{R}$. I will be presenting two proofs on the projections of $C(1/4)$ onto lines in $\\mathbb{R}^2$. By utilizing the self-similar structure, these proofs present more detailed information on projections of $C(1/4)$ than the Marstrand projection theorem is able to. Due to time constraints, I will only go over one of the proofs in details, then sketch the proof of the sharper result by pointing out the necessary lemmas to obtain it.\n\nFriday, November 2, 2018\n\n3:00 pm in 145 Altgeld Hall,Friday, November 2, 2018\n\n#### Bases in $L^p$ spaces\n\n###### Chris Gartland (Illinois Math)\n\nAbstract: We will discuss examples of bases in $L^p$ spaces such as the Walsh and Haar systems.\n\nFriday, November 30, 2018\n\n3:00 pm in Altgeld Hall 145,Friday, November 30, 2018\n\n#### Infinitesimals in Analysis, Topology, and Probability\n\n###### Peter Loeb (Illinois Math)\n\nAbstract: The notion of an infinitesimal quantity eluded rigorous treatment until the work of Abraham Robinson in 1960. Recent extensions and applications of his theory, called nonstandard analysis, have produced new results in many areas including operator theory, stochastic processes, mathematical economics and mathematical physics. Infinitely small and infinitely large quantities can play an essential role in the creative process. At the level of calculus, the integral can now be correctly defined as the nearest ordinary number to a sum of infinitesimal quantities. In Probability theory, Brownian motion can now be rigorously parameterized by a random walk with infinitesimal increments. In economics, an ideal economy can be formed from an infinite number of agents, each having an infinitesimal influence on the economy. After an introduction to this powerful method, I will discuss applications to calculus, the imbedding of topological spaces into compact spaces, and measure and probability theory. This includes the work of Y. Sun who showed that the measure spaces introduced by the present speaker can be used to finally make sense of the notion of an infinite number of equally weighted, independent random variables in probability theory and economics.\n\nFriday, December 7, 2018\n\n3:00 pm in 145 Altgeld Hall,Friday, December 7, 2018\n\n#### Nonsolvability of elliptic operators in the flat category\n\n###### Martino Fassina (Illinois Math)\n\nAbstract: In 1957 a ground-breaking three-page paper in the Annals marked the birth of CR geometry. There, Hans Lewy gave the first example of a locally non-solvable first-order linear partial differential equation. In this talk I will present a Lewy-type phenomenon for flat functions. That is, smooth functions whose derivatives are all equal to zero at a point. The result is elementary in nature, and no deep analytic background is required to understand this talk. I will describe some of the consequences of the result, with special attention to complex analysis. The talk is based on joint work with Yifei Pan."
] | [
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.91493076,"math_prob":0.82577145,"size":931,"snap":"2019-13-2019-22","text_gpt3_token_len":450,"char_repetition_ratio":0.3149946,"word_repetition_ratio":0.14832535,"special_character_ratio":0.5972073,"punctuation_ratio":0.17760618,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9551149,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-05-25T21:58:16Z\",\"WARC-Record-ID\":\"<urn:uuid:e4b71887-6923-484c-90f0-304bf85c9126>\",\"Content-Length\":\"54152\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:70b9166b-1310-437e-88e7-dbfbc3b084a8>\",\"WARC-Concurrent-To\":\"<urn:uuid:f78d0f79-2db2-44cf-95fd-319764004296>\",\"WARC-IP-Address\":\"192.17.3.249\",\"WARC-Target-URI\":\"https://calendar.math.illinois.edu/?year=2018&month=12&day=07&interval=year®exp=Graduate+Analysis+Seminar&use=Find\",\"WARC-Payload-Digest\":\"sha1:SZGULIZLDFWDCH2DZJFDGCAWASX763KZ\",\"WARC-Block-Digest\":\"sha1:5HOENXQQBR57JJUPDAJABXSCHPNO5CYS\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-22/CC-MAIN-2019-22_segments_1558232258451.88_warc_CC-MAIN-20190525204936-20190525230936-00454.warc.gz\"}"} |
https://mathoverflow.net/questions/292553/expected-global-clustering-coefficient-for-erd%C5%91s-r%C3%A9nyi-graph | [
"# Expected global clustering coefficient for Erdős–Rényi graph\n\nWhat is the expected global clustering coefficient $\\mathbb{E}[C_{GC}]$ for the Erdős–Rényi random graph (ER-graph) $\\mathcal{G}(n,p)$ (expectation is over the ensemble of all ER-graphs) as $n \\rightarrow \\infty$ and $p$ fixed?\n\nThe global clustering coefficient $C_{GC}$ is defined as\n\n$C_{GC}={\\frac {3\\times {\\mbox{number of triangles}}}{{\\mbox{number of connected triplets of vertices}}}}={\\frac {{\\mbox{number of closed triplets}}}{{\\mbox{number of connected triplets of vertices}}}}$.\n\nA connected triplet is defined to be a connected subgraph consisting of three vertices and two edges. A closed triplet is a connected triplet that induces a triangle.\n\nWhile it is easy to see that the expected mean local clustering coefficient is $p$ (see next section), the expected global clustering coefficient is not identically $p$ for any $n$.\n\nFor example, for $n=3$, $C_{GC} = 1$ only when all edges are present (with probability $p^3$) and is otherwise zero (with probability $1-p^3$). Hence the $\\mathbb{E}[E_{GC}] = p^3$ when $n=3$.\n\nComputationally, I have found that $\\mathbb{E}[C_{GC}]\\approx p$ for large $n$.\n\nIs there a way to prove that $\\mathbb{E}[C_{GC}]= p$ as $n\\rightarrow\\infty$?\n\nMy current theory is to use Chebyshev's inequality on this, but I haven't tried it out yet.\n\n# Expected local clustering coefficient = p\n\nIn contrast, it is easy to see that the expected local clustering coefficient $\\mathbb{E}[C_i]$ for any node $i$ is $p$.\n\nThe local clustering coefficient $C_i$ of node $i$ (for an undirected network) is defined as\n\n$C_i = \\frac{\\text{number of triangles that contain$i$}}{k_i (k_i-1)/2}$, where $k_i$ is the degree of $i$.\n\nIn other words, it is the proportion of links between the vertices within its neighbourhood divided by the number of links that could possibly exist between them.\n\nWe have $\\mathbb{E}[C_i]=p$ in an ER-graph because the probability for an edge between any neighbours of the node is $p$, independent for any other edge. (For an alternative answer involving more algebra, see here).\n\nHence the expected mean local clustering coefficient $\\mathbb{E}[\\sum_i C_i]$ is $p$ for any $n$.\n\n• Law of large number? – RaphaelB4 Feb 9 '18 at 11:23\n• The term 'closed triplet' is not usual contemporary graph-theoretic terminology. You therefore should define it. (IIRC, the definitions, in graph-theoretic terminology, are: 'closed triplet'= 'noninduced three-vertex path-graph','connected triplet'='induced three-vertex path-graph'). Also, it is confusing that immediately after the definition of 'global clustering coefficient' you speak of the 'local clusterian coefficient', and without defining it. – Peter Heinig Feb 9 '18 at 11:52\n• Thank you, @PeterHeinig. I have added some more explanation and put the local clustering coefficient part to the end. – Fabian Ying Feb 9 '18 at 13:34\n• Thanks. Your definition of 'connected triplet' is correct (and equivalent to, but more elegant than, my suggestion.The unusual term 'closed triplet' is still not defined in the OP though (and should be IMHO). One possibility would be to say 'closed triplet' = 'connected triplet which induces a triangle'. – Peter Heinig Feb 9 '18 at 14:48\n\n## 2 Answers\n\nUnless I'm missing something, this is a standard application of the probabilistic method: just show that the expected number of closed triplets is ${n \\choose 3}p^3$ the expected number of connected triplets is ${n \\choose 3}(3p(1-p)+p^3)$ and then use a Chebyshev bound to show that as $n \\rightarrow \\infty$ each converges to its mean so that $C_{GC} \\rightarrow 3p^3/(3p^2-p^3) = p/(1-p/3)$.\n\nThe idea of the previous message is correct but the derivation is wrong. When we calculate the expected number of connected triples and represent it as the sum of expectations over all the triples, we must remember than for every triple $(i, j, k)$ every triangle should be counted three times if it exists (because every connected triple has its leading node, thus, every triangle can be counted three times as it may be considered in three different ways - as a triangle with leading $i$, a triangle with leading $j$, a triangle with leading $k$). Therefore, the expected number of connected triples is ${n \\choose 3} (3p^2(1-p) + 3p^3)$. Finally, $C_{GC} \\rightarrow 3p^3 / (3p^2(1-p) + 3p^3) = p$.\n\n• It would be better to edit the previous message instead of posting a new one – David White Aug 19 '18 at 6:03\n• David, I know. I tried to comment the previous message first but the system said I didn't have enough reputation for it. – Vladimir Stozhkov Aug 19 '18 at 19:32"
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.886079,"math_prob":0.9962195,"size":2122,"snap":"2021-21-2021-25","text_gpt3_token_len":587,"char_repetition_ratio":0.13975449,"word_repetition_ratio":0.045016076,"special_character_ratio":0.27049953,"punctuation_ratio":0.06923077,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99960595,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-06-23T11:06:35Z\",\"WARC-Record-ID\":\"<urn:uuid:49fea1d4-dea6-4483-8fae-077f6dee35b6>\",\"Content-Length\":\"148509\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:23b5f919-2b4f-44d5-908a-c187b4bd26a9>\",\"WARC-Concurrent-To\":\"<urn:uuid:42ef844e-87aa-469b-bfe6-eaedff8e2353>\",\"WARC-IP-Address\":\"151.101.65.69\",\"WARC-Target-URI\":\"https://mathoverflow.net/questions/292553/expected-global-clustering-coefficient-for-erd%C5%91s-r%C3%A9nyi-graph\",\"WARC-Payload-Digest\":\"sha1:PPLPA7KNOFYBCIFIZCYYUDQC34HKZ6P4\",\"WARC-Block-Digest\":\"sha1:ZBF6VJKQOIYCJGNSOV7Q5WJQKXTTGQ2Z\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-25/CC-MAIN-2021-25_segments_1623488538041.86_warc_CC-MAIN-20210623103524-20210623133524-00591.warc.gz\"}"} |
https://forums.odforce.net/topic/46996-constrain-random-rotation-to-90180270-degree/?tab=comments#comment-218852 | [
"## Recommended Posts\n\nI copy the small grids to each point of the grid template and now I would like to rotate them in randomly so they snap to 90/180 and 270-degree intervals in Y-axis. Is there an easy way to solve it in VEX or with VOPS?",
null,
"##### Share on other sites\n\nHi Dominic,\nhere is one possible way. File is attached.\n\n```@zero_to_three = floor( 4 * rand(@ptnum));\n\nfloat angle = @zero_to_three * radians( 90 );\nvector axis = {0,1,0};\nmatrix3 m = ident();\nrotate(m, angle, axis);\n\n@up = {0,1,0};\n@N = m * {0,0,1};```\nEdited by ikoon\n•",
null,
"1\n\n##### Share on other sites\n2 minutes ago, ikoon said:\n\nHi Dominic,\nhere is one possible way. File is attached.\n\n```\n@zero_to_three = floor( 4 * rand(@ptnum));\n\nfloat angle = @zero_to_three * radians( 90 ); // 45 in 0 to 90\nvector axis = {0,1,0};\nmatrix3 m = ident();\nrotate(m, angle, axis);\n\n@N = m * {0,0,1};```\n\nThats amazing, thank you.\n\n##### Share on other sites\n\nHere is the same result, but orientation is set by the @orient attribute:\n\n```@zero_to_three = floor( 4 * rand(@ptnum));\n\nfloat angle = @zero_to_three * radians( 90 );\nvector axis = {0,1,0};\n\n@orient = quaternion(angle,axis);```",
null,
"quaternion.hiplc\n\n•",
null,
"3\n\n##### Share on other sites\n13 minutes ago, ikoon said:\n\nHere is the same result, but orientation is set by the @orient attribute:\n\n```\n@zero_to_three = floor( 4 * rand(@ptnum));\n\nfloat angle = @zero_to_three * radians( 90 );\nvector axis = {0,1,0};\n\n@orient = quaternion(angle,axis);```\n\nmuch cleaner, thank you",
null,
"## Create an account\n\nRegister a new account"
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"https://forums.odforce.net/uploads/monthly_2020_09/Screenshot_1.thumb.jpg.74d2b1fa8e4a2f9839bfd2bb4248be86.jpg",
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"https://forums.odforce.net/uploads/monthly_2020_09/quaternion.thumb.PNG.b6b267f347d8e024ed36a9641ced8e75.PNG",
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.92798,"math_prob":0.9933475,"size":308,"snap":"2022-05-2022-21","text_gpt3_token_len":79,"char_repetition_ratio":0.05263158,"word_repetition_ratio":0.0,"special_character_ratio":0.26298702,"punctuation_ratio":0.04477612,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98962194,"pos_list":[0,1,2,3,4,5,6,7,8,9,10],"im_url_duplicate_count":[null,2,null,null,null,2,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-23T15:52:08Z\",\"WARC-Record-ID\":\"<urn:uuid:0d4fef42-2d0c-4aa2-bc50-08e56e4de2cc>\",\"Content-Length\":\"116582\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:55f07fa8-f5be-45f8-9b2d-67965a64c0fb>\",\"WARC-Concurrent-To\":\"<urn:uuid:5fcff7f7-cca1-454a-a36d-b44848e9398b>\",\"WARC-IP-Address\":\"208.79.239.212\",\"WARC-Target-URI\":\"https://forums.odforce.net/topic/46996-constrain-random-rotation-to-90180270-degree/?tab=comments#comment-218852\",\"WARC-Payload-Digest\":\"sha1:2RYKWVOFQRNSFNMEL6QV3FGMT2ASWSFN\",\"WARC-Block-Digest\":\"sha1:PXAG3AAWEMC6Z7UBXE3UPM77ONH5CXO4\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662558030.43_warc_CC-MAIN-20220523132100-20220523162100-00233.warc.gz\"}"} |
https://spaces.ac.cn/category/Phy-chem/3/ | [
"Mathieu方程\n\n$$l\\ddot{\\theta}+[h_0 \\omega^2 \\cos(\\omega t)-g]\\sin\\theta=0$$\n\n$$m\\frac{\\partial^2 X}{\\partial t^2}=k\\frac{\\partial^2 X}{\\partial \\xi^2}$$\n\n$$X=F(u)+H(v)=F(\\xi+\\beta t)+H(\\xi-\\beta t)$$\n\n$$X(\\xi,t)=\\frac{1}{2}\\left[X_0(\\xi+\\beta t)+X_0(\\xi-\\beta t)\\right]+\\frac{1}{2\\beta}\\int_{\\xi-\\beta t}^{\\xi+\\beta t} X_1 (s)ds$$\n\n$$\\bar{A}=\\boldsymbol{x}^{T}\\boldsymbol{A}\\boldsymbol{x},\\bar{B}=\\boldsymbol{x}^{T}\\boldsymbol{B}\\boldsymbol{x}$$"
] | [
null
] | {"ft_lang_label":"__label__zh","ft_lang_prob":0.96678066,"math_prob":1.0000098,"size":2287,"snap":"2019-51-2020-05","text_gpt3_token_len":2075,"char_repetition_ratio":0.11257118,"word_repetition_ratio":0.0,"special_character_ratio":0.25054657,"punctuation_ratio":0.01655629,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.0000095,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-16T00:38:46Z\",\"WARC-Record-ID\":\"<urn:uuid:41cc6ab7-7d6b-4947-b88f-e287646c3c9d>\",\"Content-Length\":\"60599\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:70720fe3-6385-42bd-9ff2-dd63216748da>\",\"WARC-Concurrent-To\":\"<urn:uuid:ea473e52-4212-4d3e-8653-f1c0ca15de23>\",\"WARC-IP-Address\":\"39.108.122.106\",\"WARC-Target-URI\":\"https://spaces.ac.cn/category/Phy-chem/3/\",\"WARC-Payload-Digest\":\"sha1:G66AJJOGGNUYR3SD3RSEEO37FSUP7EJK\",\"WARC-Block-Digest\":\"sha1:FLN5JFJ3XGFEZM7WCG4UTZH3HDKQHF7U\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575541310970.85_warc_CC-MAIN-20191215225643-20191216013643-00250.warc.gz\"}"} |
https://unsubscribeme1.com/lhg7xwx/mw-to-mva-calculator | [
"## mw to mva calculator\n\nThese cookies will be stored in your browser only with your consent. Follow, Copyright 2023, All Rights Reserved 2012-2023 by, Looks Like You're Using an Ad Blocker. 1 megavolt ampere to megawatts = 1 megawatts, 5 megavolt ampere to megawatts = 5 megawatts, 10 megavolt ampere to megawatts = 10 megawatts, 20 megavolt ampere to megawatts = 20 megawatts, 30 megavolt ampere to megawatts = 30 megawatts, 40 megavolt ampere to megawatts = 40 megawatts, 50 megavolt ampere to megawatts = 50 megawatts, 75 megavolt ampere to megawatts = 75 megawatts, 100 megavolt ampere to megawatts = 100 megawatts. Construction, Working and Applicators. GW = gigawatt. The power factor calculation does not distinguish between leading and lagging power factors. Short Circuit Calculation - Read online for free. Moreover, in power plant, power factor is 1 therefore MW is equal to MVA (MW = MVA x P.f). How is MVA current calculated? How can we avoid the occurrence of weld porosity? (6500 MVA), and G3 (9000 MVA), were installed at terminals B1, B3, and B4, respectively. In short, therefore a power plant rating is specified in terms of Turbine rating which is in KW or MW. (MW = MVA x P.f). If the PF is unity then MVA = MW. Market Value Added (MVA) = Market Capitalization Shareholders Equity. Why is a Generator/Alternator rated in kVA, not in kW? The symbol, MV.A (not 'MVA') represents megavolt amperes, and is a multiple of the volt ampere, used to measure the apparent power of a load.The symbol, MW, represents megawatts, and is the multiple of the watt, used to measure the true power of a load.These are two different quantities, so you cannot simply 'convert' one to the other. MVA. In a generating station, the prime mover (turbine) generates only and only. It is the product of the primary voltage and primary current or secondary voltage and secondary current. Like this? Formula Market Value Added (MVA) = Market Capitalization - Shareholder's Equity. As we said VA is the unit of apparent power and it will be calculated by the product of input voltage and input current or the product of output voltage and output current.if(typeof ez_ad_units != 'undefined'){ez_ad_units.push([[300,250],'electrical4u_net-medrectangle-4','ezslot_2',109,'0','0'])};__ez_fad_position('div-gpt-ad-electrical4u_net-medrectangle-4-0'); In a transformer, we have two voltages and two currents and they are V(primary) Primary voltage in Volts, V(secondary) Secondary voltage in Volts, I(Primary) Primary current in Amps and I(secondary) secondary current in Amps. The amount of current flowing through the wire is measured in amperes, or amps. Convert kW to kVA, kVA to kW, voltage, kW to HP, and more to assist with generator sizing and electrical specifications required for your genset. Power unit conversion calculator Enter the power in one of the text boxes and press the Convert button: Power conversion BHP to kW conversion BTU/hr to kW conversion BTU/hr to refrigeration tons conversion BTU/hr to watts conversion dBm converter dBm to mW conversion dBm to watts conversion GW to watts conversion hp to kW conversion To help with productivity, we now set a cookie to store the last units you have converted from and to. Please provide values below to convert megawatt [MW] to volt ampere [V*A], or vice versa. A megawatt (MW) is a unit of power. 1 megavolt ampere MVA = 1 megawatts MW (1*1.000000000) 2 megavolts ampere has ______ how many megawatts? MW is unit of active or real power (P). 3 PHASE 50/60HZ S(kVA)= V(primary L-L) * I(Primary) / 103 = V(secondary L-L) * I(secondary) / 103if(typeof ez_ad_units != 'undefined'){ez_ad_units.push([[250,250],'electrical4u_net-large-leaderboard-2','ezslot_7',112,'0','0'])};__ez_fad_position('div-gpt-ad-electrical4u_net-large-leaderboard-2-0'); Calculate the kVA rating of the transformer whose secondary voltage of 11000 V and secondary current of 2Amps. Power factor (cos). This bulletin applies to the calculation of loss compensation values for power transformers and power lines at specific site locations used with electricity meters and ancillary devices pursuant to the Electricity and Gas Inspection Act to establish source legal units of measure (SLUMs) or processed legal units of measure (PLUMs). Example 1.27 Two 1 MVA three-phase synchronous generators are operating in parallel and delivering a load of 1600 KVA at 0.9 pf lagging. Enter the MW and pf (0 to 1) to get the VAR values. If the 340 Amps for 4/0 ACSR is correct, use the standard calculation for 3-phase power: MW = kV (phase-phase) x Amps x 1.732/1000. An example of data being processed may be a unique identifier stored in a cookie. How to Size a Single Phase and Three Phase Transformer in kVA? Of course this. Moreover, in a power plant, power factor is 1 therefore MW is equal to MVA (MW = MVA x P.F). , MVA x PF = MW. 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The solution is given below, solved using the above mentioned procedure in three steps. $$\\cos \\phi$$ is the power factor between 0 and 1. 1 MVA = 1 / 1 MW. The cookie is used to store the user consent for the cookies in the category \"Other. power factor. Be it buying grocery or cooking, units play a vital role in our daily life; and hence their conversions. This cookie is set by GDPR Cookie Consent plugin. You have entered an incorrect email address! Let's see how to calculate the fault current using MVA Method at Points F1 and F2. What is MW MVA MVAR? This cookie is set by GDPR Cookie Consent plugin. This cookie is set by GDPR Cookie Consent plugin. SCADA software use in power house. Bulk Electric System electrical calculators to assist operations and support staff from Tom Hess & Associates Inc. . Units of energy/usage. provided the Voltage, Current and Power Factor values are known. bcz, it only decides the induced emf. That's why we rated a power plant capacity in MW and not in MVA\". These cookies ensure basic functionalities and security features of the website, anonymously. Step by Step Procedure with Solved Example. 6 Whats the difference between 10 MVA and 10 MW? Calculate the power delivered by the second machine and the power factor at which it is operating. By clicking Accept All, you consent to the use of ALL the cookies. Your email address will not be published. Why is power plant capacity rated in MW and not in MVA? MW to VA Formula Used 1 Watt = 1E-06 Megawatt 1 Watt = 1 Volt Ampere 1 Megawatt = 1000000 Volt Ampere Other MW Conversions MW to Planck Power [ Megawatt to Planck Power ] (Biggest) MW to YW [ Megawatt to Yottawatt ] MW to ZW [ Megawatt to Zettawatt ] MW to EJ/s [ Megawatt to Exajoule per Second ] MW to EW [ Megawatt to Exawatt ] Other uncategorized cookies are those that are being analyzed and have not been classified into a category as yet. Single phase circuit calculation. The formula used to calculate megawatt hours is Megawatt hours (MWh) = Megawatts (MW) x Hours (h). It does not store any personal data. Is MVA the same as MW? It is important for you to know that the calculator can only perform a single conversion at a time. PF = |cos | = 1000 How to convert MW to VA? a) Calculate the value of E o , so that the machine absorbs 80 MVAr and delivers 0 MW b) Calculate the value of E o , so that the machine delivers 60 MVAr and delivers 0 MW c) Assuming the same value for Eo as (b), calculate the angle such that the generator delivers 120 MW. Calculate the MVA rating of the transformer whose primary voltage of 110000 V and secondary current of 100 Amps. Definition: In relation to the base unit of [power] => (watts), 1 Megawatts (MW) is equal to 1000000 watts, while 1 Kilovolt Ampere (kVA) = 1000 watts. 106, or in exponential notation, 1E6. The abbreviation for MW and VA is megawatt and volt ampere respectively. Transformers are static equipment which is used to convert the voltage or current to the different levels. apparent power, being related to true power by the power factor, The following formula calculates power factor (PF) based on KW and KVA or KW and KVAr. In this assignment we will be investigating mathematical methods which can be used in order to identify how to work out the power factor of an AC circuit alo. Note that we have Fahrenheit as the biggest unit for length while Yottaampere is the smallest one. metres squared, grams, moles, feet per second, and many more! What are 6 of Charles Dickens classic novels? Gorlin equation. MVA - MEGA VOLT AMPERE MW - MEGA WATT MVAR - MEGA VOLT AMPERE REACTIVE. MVA rating calculation formula: MVA (Mega Volt-Amp) rating of the transformer S(MVA) is equal to the product of primary current I(Primary) in amps and Primary Voltage V(primary) in volts divided by 1000000. Multiply the number of kVA by 0.001 to convert to MVA. Power Triangle Calculator Find the kVAR or MVAR Needed to Improve Power Factor . Definition: In relation to the base unit of [power] => (watts), 1 Kilovolt Ampere (kVA) is equal to 1000 watts, while 1 Megawatts (MW) = 1000000 watts. Three phase voltage, current and power Watt is the unit of the real power P(W). But it is possible to select any other base if the operator chooses so. If you remember your Circuit II course MVA is the Square Root of MW^2+MVAR^2. Z PU = Per Unit Impedance. Divide the watts of a given electrical item by the total number of volts available from the electric outlet to calculate amperage draw. 1 kWh is the output of a 1 kW system operating steadily during 1 hour. components in the load or source. It does not depend on the power factor. The unit of apparent power is VA (Volt-Amp). Full disclaimer. so that is not a valid point to make mw rating. Now you can do MW to VA conversion with the help of this tool. How many amps is 2.5 MW? If you encounter any issues to convert Megawatt to VA, this tool is the answer that gives you the exact conversion of units. Divide the number of kVA by 1,000 to convert to MVA. Megawatts Calculator. Functional cookies help to perform certain functionalities like sharing the content of the website on social media platforms, collect feedbacks, and other third-party features. The abbreviation for kVA and MW is kilovolt ampere and megawatt respectively. Please provide values below to convert kilovolt ampere [kV*A] to megawatt [MW], or vice versa.Kilovolt Ampere to Megawatt Conversion Table. 63A500V . In short, a power plant rating is specified in terms of prime . Why is a Motor rated in kW instead of kVA? megawatts to megavolt ampere, or enter any two units below: The SI prefix \"mega\" represents a factor of LVOT VTI - left ventricular outflow tract velocity time integral. Advertisement cookies are used to provide visitors with relevant ads and marketing campaigns. Other calculators on this page are for unit conversions and other power related calculations. Market Value Added (MVA) = 12 x 5.2 26 = 36.4 million. Related MW is megawatts. Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. Let we take and example, calculate the VA rating of the transformer output power 15000 W with the power factor of 0.90. Note that rounding errors may occur, so always check the results. MVA is the apparent power. [h=6] Total H [/h] This is the arithmetic sum of the Motor, Coupling and Load H in MW-sec/MVA. You can find metric conversion tables for SI units, as well In the same way for kVA and MVA from real power. You can convert between, Hazell Industries Ltd, 124 City Road, London. The cookie is set by the GDPR Cookie Consent plugin and is used to store whether or not user has consented to the use of cookies. Measurement is one of the most fundamental concepts. How do you convert MW to MVA? A megawatt is equivalent to one million watts. MVA = Shares Outstanding x Current Share Price Shareholders Equity. ITALY. Mw and Mvar values to kilowatts /a > kVA calculator MW, power. Another interesting and funny answer by one of our Facebook page fanPower House means house of the Power, and we know that the unit of power is Watt. 1 2 100 KVA AUTO TRANSFORMER, CANADIAN STANDRAD. Z is the impedance between the two points (in this case, the transformer's impedance), Z = R +jX, where R is the resistance and X is the reactance. Terms of Use | Disclaimer: Whilst every effort has been made in building our calculator tools, we are not to be held Z = Impedance of circuit element (i.e. - Distribution Transformer is of 2 MVA and its fault MVAsc (MVA/%Z) is 32 - Maximum value of fault current at 11 kV according to power transformer fault MVAsc is 3.669 kA approx. 1 Kilowatt [kW] = 0.001 Megavolt-ampere [MVA] - Measurement calculator that can be used to convert Kilowatt to Megavolt-ampere, among others. Check our Megawatt to VA converter and click on formula to get the conversion factor. MVA is a measure of apparent power and includes power factor which can be leading (positive) or lagging (negative) and always less than one in absolute value. get 13.8 MW. Want a reverse calculation from VA to MW? 1 x 1000 kVA = 1000 Kilovolt Ampere. How many megavolt ampere in 1 megawatts? You have entered an incorrect email address! 21000 VA 220 80A500V . inch, 100 kg, US fluid ounce, 6'3\", 10 stone 4, cubic cm, Press the calculate button to get the other two ratings at ONAF1 and ONAF2. Why is an Air-condition (AC) Rated in Ton, not kW or kVA? MW to VAR Calculation: VAR is equal to the 1000000 times of the real power P (MW) in Mega Watts and the tangent of the cosine inverse of the power factor (pf). MVA is unit of apparent power (S). We Rely on Advertising to Help Fund Our Site and Provide Free Information. What would be the total power generated by a 100 MW turbine to a 50 MWA alternator? Method of calculating single phase (kVA) to Amps I (A) = 1000 x S (kVA) / V (V), which means that the current in amps is calculated by multiplying 1000 by apparent power in Kilovolts-amps dividing the result by the Voltage in volts. 1 x 1000 kVA = 1000 Kilovolt Ampere. 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MW is a measure of real power and equal to one million watts. This means that when you re-visit this power converter, the units will automatically be selected for you. Calculate the reactive power in VAR of the 1MW motor is running at 0.96 pf. the unit converter.Note you can turn off most ads here: All you have to do is select the unit for which you want the conversion and enter the value and finally hit Convert. ConvertUnits.com provides an online Always check the results; rounding errors may occur. MVA is the aparant power, MW is the real power and, MVAR is reactive power. If the input and output powers of the alternator are 15 MW and 10 MW, respectively, the angular acceleration in mechanical degree/s is (round off to nearest integer) Hence for calculating MW to VAR we can use the below formula, Q (VAR) = 1000000 x P (MW) * tan (cos -1 (pf)) Example: Because KVA (or MVA) is true power, whereas KW (or MW) is liable for any damages or monetary losses arising out of or in connection with their use. Press the calculate button to get the Megawatts rating. It is fast and an efficient way of performing several calculations in a short period. . How do you calculate MVA? Power Factor Analysis. symbols, abbreviations, or full names for units of length, Post navigation Use this page to learn how to convert between megavolt ampere and megawatts. PRIMARY480V, SECONDARY .380V,220V,110V, Please provide values below to convert megawatt [MW] to kilovolt ampere [kV*A], or vice versa. 1 megawatt-hour (MWh) = 1 MW for one hour or 1,000 kW for one hour. How do you calculate MVA to MW? The three-phase concern we have two formula based on the line to line and line to phase voltage and they are, if(typeof ez_ad_units != 'undefined'){ez_ad_units.push([[300,250],'electrical4u_net-box-4','ezslot_3',125,'0','0'])};__ez_fad_position('div-gpt-ad-electrical4u_net-box-4-0');if(typeof ez_ad_units != 'undefined'){ez_ad_units.push([[300,250],'electrical4u_net-box-4','ezslot_4',125,'0','1'])};__ez_fad_position('div-gpt-ad-electrical4u_net-box-4-0_1'); .box-4-multi-125{border:none !important;display:block !important;float:none !important;line-height:0px;margin-bottom:7px !important;margin-left:auto !important;margin-right:auto !important;margin-top:7px !important;max-width:100% !important;min-height:250px;padding:0;text-align:center !important;}S(VA)= V(primary L-L) * I(Primary) = V(secondary L-L) * I(secondary), S(VA)= 1.732 * V(primary L-N) * I(Primary) = 1.732 * V(secondary L-N) * I(secondary). The power factor correction calculation assumes inductive load. Power factor correction capacitor's capacitance calculation: Qcorrected (kVAR) = (Scorrected (kVA)2 - P(kW)2), C(F) = 1000 Qc (kVAR) From abacus to iPhones, learn how calculators developed over time. W (watt )=V I cos (angle phi ). P(kW) / (V(V) Capacitor, Reactor, Transformer, Cable, etc.) MVA^2 = MW^2 + MVAR^2 = 2500 Thats why we rated a power plant capacity in MW and not in MVA. You can check our, Megawatt to Horsepower (550 ft*lbf per s). Manage Cookies. Compute pI/Mw tool. Units of measurement use the International System of Units, better known as SI units, which provide a standard for measuring the physical properties of matter. Voltage (V): Enter the phase-to-phase () voltage for a 3-phase AC supply in volts. The system used for simulation is a 500 kV system compensated with 100 MVA UPFC operating in different modes. Kilowatt-hours to Megawatt-hours (kWh to MWh) conversion calculator for Energy and Power conversions with additional tables and formulas. When you are converting power, you need a Megawatt to Volt Ampere converter that is elaborate and still easy to use. 1 kVA is 1000 times smaller than a MW. Save my name, email, and website in this browser for the next time I comment. Use this power converter to convert instantly between horsepower, kilowatts, megawatts, volt amperes, watts and other metric and imperial power units. Formula of calculating three-phase (kVA) to Amps Line to line voltage Hence the transformer is rated by the VA only.if(typeof ez_ad_units != 'undefined'){ez_ad_units.push([[300,250],'electrical4u_net-medrectangle-3','ezslot_1',124,'0','0'])};__ez_fad_position('div-gpt-ad-electrical4u_net-medrectangle-3-0'); Sometimes the transformer can be rated by kVA (kilo Volt-Amps) or MVA (Mega Volt-Amp). To convert between these, you can use the following: 1 kW = 1,000 W 1 MW = 1,000 kW. MVA (Mega Volt-Amp) rating of the transformer S (MVA) is equal to the product of primary current I (Primary) in amps and Primary Voltage V (primary) in volts divided by 1000000. Why SJF Cannot be implemented practically? the introduction of an empirically SrT = 300 MVA ukr = 19,4% obtained individual correction factor . CALCULATION OF POWER FACTOR. Necessary cookies are absolutely essential for the website to function properly. Why is a Motor rated in kW instead of kVA? 1.0 Scope. Enter the MVA Rating. The reason for which the transformers and synchronous generators are rated in volt-amperes instead of watts is that manufacturer does not know at what power factor does these equipments are going to operate. https://www.convertunits.com/contact/remove-some-ads.php. Formula Market Value Added (MVA) = Market Capitalization - Shareholder's Equity. Continue with Recommended Cookies. Whats the difference between 10 MVA and 10 MW? mw/mva=power factor reactive power (Q)=I2XL or E2/XL where XL= REACTANCE apparent power = square root of (MW2 + MVAR2 ) How do you convert AM to. Megawatt to Volt Ampere Conversion Table How to Convert Megawatt to Volt Ampere 1 MW = 1000000 V*A 1 V*A = 1.0E-6 MW Example: convert 15 MW to V*A: 15 MW = 15 1000000 V*A = 15000000 V*A Popular Power Unit Conversions hp to kw kw to hp hp to watts watts to hp A 20 MVA, 11.2 kV, 4-pole, 50 Hz alternator has an inertia constant of 15 MJ/MVA. Analytical cookies are used to understand how visitors interact with the website. After inputting the first two variables, the required kVAr . Volt x Amps x Power factor which is further transmit and distribute in a typical power system scheme. Market Value Added (MVA) = 12 x 5.2 - 26 =36.4 million. What does Shakespeare mean when he says Coral is far more red than her lips red? The cookie is used to store the user consent for the cookies in the category \"Analytics\". How to convert Megawatts to Kilovolt Ampere (MW to kVA)? Divide the number of kVA by 1,000 to convert to MVA. A PF of UNITY suggest the load Our software is the only cloud-based solution and has been built from the ground up to be fully responsive - meaning you can access your cables from anywhere and on any device, desktop, tablet or smartphone. All Rights Reserved. Current (I): Enter the the current in Amperes (A). unitsconverters.com helps in the conversion of different units of measurement like MW to VA through multiplicative conversion factors. Furthermore, how is MVA power calculated? KV LL = Base Voltage (Kilo Volts Line-to-Line) MVA 3 = Base Power. Divide the number of kVA by 1,000 to convert to MVA. You would have to know the Power Factor, normally designated PF. To view the purposes they believe they have legitimate interest for, or to object to this data processing use the vendor list link below. X C = Capacitor Bank Impedance (ohms) X C-PU = Capacitor Bank Per Unit Impedance. In relation to the base unit of [power] => (watts), 1 Megawatts (MW) is equal to 1000000 watts, while 1 Kilovolt Ampere (kVA) = 1000 watts. It is normally stated in megavolt-amperes (MVA) for large generators or kilovolt-amperes (kVA) for small generators. [h=6] Total WR2 [/h] The total WR2 is calculated based on the Total RPM and Total H using the equation above. The cookies is used to store the user consent for the cookies in the category \"Necessary\". For example, if you have 438 kVA, divide 438 by 1,000 to get 0.438 MVA. Because megawatts are so large, its easier to grasp a megawatt-hour if we break it down. Enter the MVA rating (ONAN) Enter the Power Factor Value. Calculator, How to Calculate the Battery Charging Time & Battery Charging Current Example, How To Calculate Your Electricity Bill. Calculate the VA rating of the single-phase transformer whose primary voltage is 230 and primary rated current is 10 Amps. and also speed is one of the part only but not fully depend on that turbine speed. Get Free Android App | Download Electrical Technology App Now! Press the calculate button to get the Megawatts rating. MVA x PF = MW. Why is a Battery rated in Ah (Ampere hour) and not in VA? Three phase transformer MVA calculations: S(MVA)= 1.732 * V(primary L-N) * I(Primary) / 106 = 3 * V(secondary L-N) * I(secondary) / 106, S(MVA)= V(primary L-L) * I(Primary) / 106 = V(secondary L-L) * I(secondary) / 106. This calculator is for educational purposes. Z PU GIVEN = Given Per Unit Impedance. VL-L(V) I(A)), C(F) = 1000 Qc (kVAR) Mva ukr = 19,4 % obtained individual correction factor follow, Copyright,. The use of All the cookies in the category Analytics '', divide 438 by 1,000 to between! Can convert between these, you can use the following: 1 =... In parallel and delivering a load of 1600 kVA at 0.9 pf.. Is important for you and load H in MW-sec/MVA provide Free Information at a time through... That is not a valid point to make MW rating Outstanding x current Share Price Shareholders Equity Megawatts (... Distribute in a typical power system scheme given below, solved using the above mentioned procedure in three.... Selected for you to know the power factor Value would be the total number volts... The reactive power elaborate and still easy to use to the different levels the MVA rating of the 1MW is... While Yottaampere is the aparant power, MW is a Motor rated in MW not. Power conversions with additional tables and formulas MVA 3 = Base power this is the answer gives... That rounding errors may occur, so always check the results kW or kVA App... The MVA rating of the 1MW Motor is running at 0.96 pf it. = 2500 Thats why we rated a power plant rating is specified in terms of prime system compensated with MVA... Are operating in different modes Electric system electrical calculators to assist operations and support staff from Tom &! ) / mw to mva calculator V ) I ( a ) Copyright 2023, All Rights Reserved 2012-2023 by, Like! Unit of apparent power is VA ( Volt-Amp ) Added ( MVA for! B4, respectively W ( WATT ) =V I cos ( angle phi ) ): the... Generates only and only the units will automatically be selected for you next time I comment for... Let we take and example, calculate the VA rating of the part only but not depend! ) Enter the the current in amperes ( a ) three steps an (. Running at 0.96 pf our megawatt to VA through multiplicative conversion factors with your consent reactive power parallel. To 1 ) to get the VAR values machine and the power factor between and. 1.000000000 ) 2 megavolts ampere has ______ how many Megawatts lbf per s ) and 10?... \\Phi \\ ) is a Generator/Alternator rated in kVA = 1000 Qc ( kVAR related calculations and. Wire is measured in amperes ( a ) Bank per unit Impedance Megawatts ( to... Second, and many more or real power ( s ) electrical Technology App!. ( 550 ft * lbf per s ) is reactive power in VAR of the transformer whose primary and. Buying grocery or cooking, units play a vital role in our daily life ; mw to mva calculator their. The current in amperes, or vice versa Find metric conversion tables for SI units as. Of real power and, MVAR is reactive power the operator chooses so VA rating the... Page are for unit conversions and other power related calculations pf = |cos | 1000. The abbreviation for kVA and MVA from real power P ( W ) the rating..., All Rights Reserved 2012-2023 by, Looks Like you 're using an Ad Blocker flowing the! = MW, CANADIAN STANDRAD is an Air-condition ( AC ) rated kW... Is measured in amperes, or vice versa Enter the the current in amperes or! Mw to VA through multiplicative conversion mw to mva calculator click on formula to get the Megawatts rating buying grocery or cooking units! ( MW = MVA x P.f ) that is not a valid point to MW! At 0.96 pf is unity then MVA = Shares Outstanding x current Share Price Shareholders Equity unitsconverters.com helps in category. Ft * lbf per s ) 550 ft * lbf per s ) are static equipment is... ) for large generators or kilovolt-amperes ( kVA ) for small generators a ) 1 kW system operating steadily 1... Are absolutely essential for the website, anonymously Horsepower ( 550 ft lbf! User consent for the cookies for large generators or kilovolt-amperes ( kVA ) for small generators measurement MW., solved using the above mentioned procedure in three steps to one million watts and. Mover ( turbine ) generates only and only primary voltage of 110000 V secondary... The use of All the cookies is used to store the user consent for the is. Calculate amperage draw and 1 an empirically SrT = 300 MVA ukr 19,4. Kva calculator MW, power factor values are known installed at terminals B1, B3 and. The occurrence of weld porosity 1 * 1.000000000 ) 2 megavolts ampere has ______ how many Megawatts Ltd 124. Output power 15000 W with the website to function properly you consent to the different levels interact. This means that when you re-visit this power converter, the units will automatically be selected you. Million watts voltage is 230 and primary rated current is 10 Amps of power divide. Apparent power ( P ) = MVA x P.f ) be a identifier! Parallel and delivering a load of 1600 kVA at 0.9 pf lagging Added ( MVA ) for small.. ; Associates Inc. a power plant rating is specified in terms of turbine rating is... Kw instead of kVA by 1,000 to convert megawatt to Horsepower ( 550 ft * lbf per s ) valid... Or kVA 100 MVA UPFC operating in parallel and delivering a load of 1600 kVA at 0.9 lagging! Then MVA = MW volt ampere reactive by clicking Accept All, you need megawatt! Is elaborate and still easy to use ( 1 * 1.000000000 ) 2 megavolts has... 1,000 to convert the voltage, current and power factor, normally designated pf and primary current! B1, B3, and B4, respectively specified in terms of prime ), and many!. F ) = 1 Megawatts MW ( 1 * 1.000000000 ) 2 megavolts ampere has ______ how many Megawatts and... Using an Ad Blocker of prime the phase-to-phase ( ) voltage for 3-phase! Or Amps or MVAR Needed to Improve power factor above mentioned procedure in three steps obtained individual correction factor of! Save my name, email, and many more kW = 1,000 W MW! It buying grocery or cooking, units play a vital role in our life. Stored in a cookie, you can Find metric conversion tables for SI units, as well in the way... Is further transmit and distribute in a power plant capacity in MW and VA is megawatt hours megawatt! In your browser only with your consent and 10 MW tool is the arithmetic of... Generators or kilovolt-amperes ( kVA ) for small generators turbine rating which is further transmit and in. Ampere respectively, solved using the above mentioned procedure in three steps formulas. Mva - MEGA volt ampere respectively supply in volts quot ; or secondary voltage and secondary current current amperes! Mw ] to volt ampere reactive that the calculator can only perform a Single Phase and three Phase in. For MW and not in VA in this browser for the cookies in the same for. Kva calculator MW, power factor calculation does not distinguish between leading and lagging factors. = \\$ 36.4 million would have to know that the calculator can only perform a conversion... Lips red, Hazell Industries Ltd, 124 City Road, London online always check results. And distribute in a short period get Free Android App | Download electrical Technology App!... Of 1600 kVA at 0.9 pf lagging megawatt and volt ampere converter that is not a valid to! Wire is measured in amperes ( a ) kVA and MVA from real power ( P.... A typical power system scheme are converting power, MW is equal to MVA ( MW ) is a rated... And power conversions with additional tables and formulas capacity rated in kW of. Converting power, you consent to the use of All the cookies in the ... Avoid the occurrence of weld porosity button to get the conversion of different units of measurement Like MW VA... Additional tables and formulas x P.f ) short period VAR values of weld porosity website, anonymously now you Find. Calculations in a cookie for the cookies in the category necessary.. Is specified in terms of prime values to kilowatts /a & gt kVA! Load H in MW-sec/MVA conversion at a time, Coupling and load H in.. Ampere hour ) and not in VA have Fahrenheit as the biggest for! Calculator can only perform a Single conversion at a time are known function properly set by cookie... Of kVA kW or kVA s ) for a 3-phase AC supply in volts and current. Yottaampere is the smallest one etc. our daily life ; and hence their conversions a... Mva is the aparant power, you can use the following: kW... Supply in volts & Battery Charging time & Battery Charging current example, how to calculate megawatt hours megawatt... The biggest unit for length while Yottaampere is the Square Root of MW^2+MVAR^2 can check our megawatt Horsepower! ; s Equity Triangle calculator Find the kVAR or MVAR Needed to Improve power factor for and. ; rounding errors may occur, so always check the results ukr 19,4... Is specified in terms of prime ( AC ) rated in MW and in! A vital role in our daily life ; and hence their conversions visitors interact the! Watts of a 1 kW system operating steadily during 1 hour clicking Accept All, you need a megawatt VA...\n\nElizabeth Mcguire San Francisco, Shooting In Harvey, Il Today, Articles M"
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https://aimsciences.org/article/doi/10.3934/mbe.2017075 | [
"",
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"October 2017, 14(5&6): 1447-1462. doi: 10.3934/mbe.2017075\n\n## Modeling transcriptional co-regulation of mammalian circadian clock\n\n 1 School of Mathematical Sciences, Soochow University, Suzhou 215006, Jiangsu, China 2 School of Mathematics & Physics, Changzhou University, Changzhou 213164, Jiangsu, China\n\n* Corresponding author: Ling Yang\n\nReceived May 30, 2016 Accepted January 20, 2017 Published May 2017\n\nFund Project: The corresponding author is supported by National Natural Science Foundation of China grants 61271358, A011403 and the Priority Academic Program of Jiangsu Higher Education Institutions, the first author is supported by National Natural Science Foundation of China grant 11501055 and Changzhou University Research Fund (ZMF15020093)\n\nThe circadian clock is a self-sustaining oscillator that has a period of about 24 hours at the molecular level. The oscillator is a transcription-translation feedback loop system composed of several genes. In this paper, a scalar nonlinear differential equation with two delays, modeling the transcriptional co-regulation in mammalian circadian clock, is proposed and analyzed. Sufficient conditions are established for the asymptotic stability of the unique nontrivial positive equilibrium point of the model by studying an exponential polynomial characteristic equation with delay-dependent coefficients. The existence of the Hopf bifurcations can be also obtained. Numerical simulations of the model with proper parameter values coincide with the theoretical result.\n\nCitation: Yanqin Wang, Xin Ni, Jie Yan, Ling Yang. Modeling transcriptional co-regulation of mammalian circadian clock. Mathematical Biosciences & Engineering, 2017, 14 (5&6) : 1447-1462. doi: 10.3934/mbe.2017075\n##### References:\n M. Adimy, F. Crauste and S. G. Ruan, Periodic oscillations in leukopoiesis models with two delays, Journal of Theoretical Biology, 242 (2006), 288-299. doi: 10.1016/j.jtbi.2006.02.020.",
null,
"",
null,
"Google Scholar M. P. Antoch, V. Y. Gorbacheva, O. Vykhovanets and A. Y. Nikitin, Disruption of the circadian clock due to the Clock mutation has discrete effects on aging and carcinogenesis, Cell Cycle, 7 (2008), 1197-1204. Google Scholar D. B. Forger and C. S. Peskin, A detailed predictive model of the mammalian circadian clock, Proceedings of the National Academy of Sciences of the United States of America, 100 (2003), 14806-14811. doi: 10.1073/pnas.2036281100.",
null,
"Google Scholar A. Goldbeter, A model for circadian oscillations in the Drosophila period protein (PER), Proceedings. Biological sciences / The Royal Society, 261 (1995), 319-324. doi: 10.1098/rspb.1995.0153.",
null,
"Google Scholar A. Goldbeter, Biochemical Oscillations and Cellular Rhythms: The Molecular Bases of Periodic and Chaotic Behaviour, Cambridge University Press, 1996. doi: 10.1017/CBO9780511608193.",
null,
"Google Scholar C. I. Hong and J. J. Tyson, A proposal for temperature compensation of the circadian rhythm in Drosophila based on dimerization of the per protein, Chronobiology International, 14 (1997), 521-529. Google Scholar J. K. Kim and D. B. Forger, A mechanism for robust circadian timekeeping via stoichiometric balance, Molecular Systems Biology, 8 (2012), 630. doi: 10.1038/msb.2012.62.",
null,
"Google Scholar R. V. Kondratov, A. A. Kondratova and V. Y. Gorbacheva, Early aging and age-related pathologies in mice deficient in BMAL1, the core component of the circadian clock, Genes & Developoment, 20 (2006), 1868-1873. Google Scholar C. C. Lee, Tumor suppression by the mammalian Period genes, Cancer Causes Control, 17 (2006), 525-530 [PubMed: 16596306]. doi: 10.1007/s10552-005-9003-8.",
null,
"Google Scholar J. C. Leloup and A. Goldbeter, Toward a detailed computational model for the mammalian circadian clock: Sensitivity analysis and multiplicity of oscillatory mechanisms, J. Theoret. Biol., 230 (2004), 541-562. doi: 10.1016/j.jtbi.2004.04.040.",
null,
"",
null,
"Google Scholar P. L. Lowrey and J. S. Takahashi, Mammalian circadian biology: elucidating genome-wide levels of temporal organization, Annual Review of Genomics and Human Genetics, 5 (2004), 407-441. doi: 10.1146/annurev.genom.5.061903.175925.",
null,
"Google Scholar H. P. Mirsky, A. C. Liu, D. K. Welsh, S. A. Kay and F. J. Doyle, A model of the cell-autonomous mammalian circadian clock, Proceedings of the National Academy of Sciences of the United States of America, 106 (2009), 11107-11112. doi: 10.1073/pnas.0904837106.",
null,
"Google Scholar S. G. Ruan and J. J. Wei, On the zeros of transcendental functions with applications to stability of delay differential equations with two delays, Dynamics of Continuous, Discrete and Impulsive Systems, Series A: Mathematical Analysis, 10 (2003), 863-874.",
null,
"Google Scholar F. A. Scheer, M. F. Hilton, C. S. Mantzoros and S. A. Shea, Adverse metabolic and cardiovascular consequences of circadian misalignment, Proceedings of the National Academy of Sciences of the United States of America, 106 (2009), 4453-4458. doi: 10.1073/pnas.0808180106.",
null,
"Google Scholar J. J. Tyson, C. I. Hong, C. D. Thron and B. Novak, A simple model of circadian rhythms based on dimerization and proteolysis of PER and TIM, Biophys Journal, 77 (1999), 2411-2417. doi: 10.1016/S0006-3495(99)77078-5.",
null,
"Google Scholar M. Ukai-Tadenuma, R. G. Yamada, H. Xu, J. A. Ripperger, A. C. Liu and H. R. Ueda, Delay in feedback repression by cryptochrome 1 is required for circadian clock function, Cell, 144 (2011), 268-281. doi: 10.1016/j.cell.2010.12.019.",
null,
"Google Scholar J. Yan, G. Shi, Z. Zhang, X. Wu, Z. Liu, L. Xing, Z. Qu, Z. Dong, L. Yang and Y. Xu, An intensity ratio of interlocking loops determines circadian period length, Nucleic Acids Research, 42 (2014), 10278-10287. doi: 10.1093/nar/gku701.",
null,
"Google Scholar X. Yang, M. Downes, R. T. Yu, A. L. Bookout, W. He, M. Straume, D. J. Mangelsdorf and R. M. Evans, Nuclear receptor expression links the circadian clock to metabolism, Cell, 126 (2006), 801-810. doi: 10.1016/j.cell.2006.06.050.",
null,
"Google Scholar W. Yu, M. Nomura and M. Ikeda, Interactivating feedback loops within the mammalian clock: BMAL1 is negatively autoregulated and upregulated by CRY1, CRY2, and PER2, Biochemical and Biophysical Research Communications, 290 (2002), 933-941. doi: 10.1006/bbrc.2001.6300.",
null,
"Google Scholar E. E. Zhang and S. A. Kay, Clocks not winding down: Unravelling circadian networks, Nature Reviews Molecular Cell Biology, 11 (2010), 764-776. doi: 10.1038/nrm2995.",
null,
"Google Scholar\n\nshow all references\n\n##### References:\n M. Adimy, F. Crauste and S. G. Ruan, Periodic oscillations in leukopoiesis models with two delays, Journal of Theoretical Biology, 242 (2006), 288-299. doi: 10.1016/j.jtbi.2006.02.020.",
null,
"",
null,
"Google Scholar M. P. Antoch, V. Y. Gorbacheva, O. Vykhovanets and A. Y. Nikitin, Disruption of the circadian clock due to the Clock mutation has discrete effects on aging and carcinogenesis, Cell Cycle, 7 (2008), 1197-1204. Google Scholar D. B. Forger and C. S. Peskin, A detailed predictive model of the mammalian circadian clock, Proceedings of the National Academy of Sciences of the United States of America, 100 (2003), 14806-14811. doi: 10.1073/pnas.2036281100.",
null,
"Google Scholar A. Goldbeter, A model for circadian oscillations in the Drosophila period protein (PER), Proceedings. Biological sciences / The Royal Society, 261 (1995), 319-324. doi: 10.1098/rspb.1995.0153.",
null,
"Google Scholar A. Goldbeter, Biochemical Oscillations and Cellular Rhythms: The Molecular Bases of Periodic and Chaotic Behaviour, Cambridge University Press, 1996. doi: 10.1017/CBO9780511608193.",
null,
"Google Scholar C. I. Hong and J. J. Tyson, A proposal for temperature compensation of the circadian rhythm in Drosophila based on dimerization of the per protein, Chronobiology International, 14 (1997), 521-529. Google Scholar J. K. Kim and D. B. Forger, A mechanism for robust circadian timekeeping via stoichiometric balance, Molecular Systems Biology, 8 (2012), 630. doi: 10.1038/msb.2012.62.",
null,
"Google Scholar R. V. Kondratov, A. A. Kondratova and V. Y. Gorbacheva, Early aging and age-related pathologies in mice deficient in BMAL1, the core component of the circadian clock, Genes & Developoment, 20 (2006), 1868-1873. Google Scholar C. C. Lee, Tumor suppression by the mammalian Period genes, Cancer Causes Control, 17 (2006), 525-530 [PubMed: 16596306]. doi: 10.1007/s10552-005-9003-8.",
null,
"Google Scholar J. C. Leloup and A. Goldbeter, Toward a detailed computational model for the mammalian circadian clock: Sensitivity analysis and multiplicity of oscillatory mechanisms, J. Theoret. Biol., 230 (2004), 541-562. doi: 10.1016/j.jtbi.2004.04.040.",
null,
"",
null,
"Google Scholar P. L. Lowrey and J. S. Takahashi, Mammalian circadian biology: elucidating genome-wide levels of temporal organization, Annual Review of Genomics and Human Genetics, 5 (2004), 407-441. doi: 10.1146/annurev.genom.5.061903.175925.",
null,
"Google Scholar H. P. Mirsky, A. C. Liu, D. K. Welsh, S. A. Kay and F. J. Doyle, A model of the cell-autonomous mammalian circadian clock, Proceedings of the National Academy of Sciences of the United States of America, 106 (2009), 11107-11112. doi: 10.1073/pnas.0904837106.",
null,
"Google Scholar S. G. Ruan and J. J. Wei, On the zeros of transcendental functions with applications to stability of delay differential equations with two delays, Dynamics of Continuous, Discrete and Impulsive Systems, Series A: Mathematical Analysis, 10 (2003), 863-874.",
null,
"Google Scholar F. A. Scheer, M. F. Hilton, C. S. Mantzoros and S. A. Shea, Adverse metabolic and cardiovascular consequences of circadian misalignment, Proceedings of the National Academy of Sciences of the United States of America, 106 (2009), 4453-4458. doi: 10.1073/pnas.0808180106.",
null,
"Google Scholar J. J. Tyson, C. I. Hong, C. D. Thron and B. Novak, A simple model of circadian rhythms based on dimerization and proteolysis of PER and TIM, Biophys Journal, 77 (1999), 2411-2417. doi: 10.1016/S0006-3495(99)77078-5.",
null,
"Google Scholar M. Ukai-Tadenuma, R. G. Yamada, H. Xu, J. A. Ripperger, A. C. Liu and H. R. Ueda, Delay in feedback repression by cryptochrome 1 is required for circadian clock function, Cell, 144 (2011), 268-281. doi: 10.1016/j.cell.2010.12.019.",
null,
"Google Scholar J. Yan, G. Shi, Z. Zhang, X. Wu, Z. Liu, L. Xing, Z. Qu, Z. Dong, L. Yang and Y. Xu, An intensity ratio of interlocking loops determines circadian period length, Nucleic Acids Research, 42 (2014), 10278-10287. doi: 10.1093/nar/gku701.",
null,
"Google Scholar X. Yang, M. Downes, R. T. Yu, A. L. Bookout, W. He, M. Straume, D. J. Mangelsdorf and R. M. Evans, Nuclear receptor expression links the circadian clock to metabolism, Cell, 126 (2006), 801-810. doi: 10.1016/j.cell.2006.06.050.",
null,
"Google Scholar W. Yu, M. Nomura and M. Ikeda, Interactivating feedback loops within the mammalian clock: BMAL1 is negatively autoregulated and upregulated by CRY1, CRY2, and PER2, Biochemical and Biophysical Research Communications, 290 (2002), 933-941. doi: 10.1006/bbrc.2001.6300.",
null,
"Google Scholar E. E. Zhang and S. A. Kay, Clocks not winding down: Unravelling circadian networks, Nature Reviews Molecular Cell Biology, 11 (2010), 764-776. doi: 10.1038/nrm2995.",
null,
"Google Scholar",
null,
"The model of a mammalian circadian clock with two delays. Figure (a) is a schematic diagram of gene regulation in the mammalian circadian clock system, figure (b) is a schematic diagram of the simplified mathematical model of a mammalian circadian clock",
null,
"Stability and Hopf bifurcation of system (4.1) for different $\\tau_1\\in [0, \\, \\infty)$ when $\\tau_2=0$. The equilibrium point $x^{\\ast}$ of (4.2) is locally asymptotically stable when $\\tau_1=0.5$ in figure (a) and $\\tau_1=1.5$ in figure (b), respectively. The equilibrium point $x^{\\ast}$ of (4.2) losts its stability and stable bifurcation periodic solutions appear when $\\tau_1=2.0$ in figure (c) and $\\tau_1=4.0$ in figure (d), respectively",
null,
"Stability of system (4.1) with different $\\tau_2$ when $\\tau_1^{\\ast}=1.85 \\in (0, \\tau_1^0)$ and $0<\\tau_2 < 4.05$. The equilibrium point $x^{\\ast}$ of (4.1) is locally asymptotically stable when $\\tau_2=0.5$ in figure (a), $\\tau_2=1.5$ in figure (b), $\\tau_2=3.5$ in figure (c), $\\tau_2=4$ in figure (d), respectively",
null,
"Instability of system (4.1) with different $\\tau_2$ when $\\tau_1^{\\ast}=2.8 \\in (\\tau_1^0, \\infty)$ and $0<\\tau_2 < 2.1$. The equilibrium point $x^{\\ast}$ of (4.1) is unstable when $\\tau_2=0.5$ in figure (a), $\\tau_2=1$ in figure (b), $\\tau_2=1.5$ in figure (c), $\\tau_2=2$ in figure (d), respectively",
null,
"Bifurcation diagram of ($\\tau_1, \\, \\tau_2$) for system (4.1). $S$ denotes stable regions, $US$ denotes oscillating regions. The black solid line is made up of critical bifurcation points for ($\\tau_1, \\, \\tau_2$), the rest solid lines with different colours are lines consisting of critical bifurcation points when $\\tau_2$ pluses different period respectively, and the marked six different points represent different values of ($\\tau_1, \\, \\tau_2$)",
null,
"Stability of system (4.1) with different $\\tau_2$ when $\\tau_1^{\\ast}=2.4\\in (\\tau_1^0, \\infty)$ and $\\tau_2>0$. The equilibrium point $x^{\\ast}$ of (4.1) is locally asymptotically stable when $\\tau_2=2$ in figure (b), $\\tau_2=9$ in figure (d), $\\tau_2=15.5$ in figure (f), respectively, it is unstable when $\\tau_2=0.5$ in figure (a), $\\tau_2=5$ in figure (c), $\\tau_2=12$ in figure (e), respectively",
null,
"Oscillating range of ($\\tau_1, \\, \\tau_2$) for system (4.1). Black regions represent oscillating solutions with periods for system (4.1) when ($\\tau_1, \\, \\tau_2$) locates in the black region",
null,
"The effect of time delays on the period of system (4.1). In figure (a), we fix $\\tau_2=29,$ the black solid line represents the relation between $\\tau_1$ and the period. In figure (b), we fix $\\tau_1=10,$ the black solid line represents $\\tau_2$ and the period\n R. Ouifki, M. L. Hbid, O. Arino. Attractiveness and Hopf bifurcation for retarded differential equations. Communications on Pure & Applied Analysis, 2003, 2 (2) : 147-158. doi: 10.3934/cpaa.2003.2.147 Leonid Berezansky, Elena Braverman. Stability of linear differential equations with a distributed delay. Communications on Pure & Applied Analysis, 2011, 10 (5) : 1361-1375. doi: 10.3934/cpaa.2011.10.1361 Jan Čermák, Jana Hrabalová. Delay-dependent stability criteria for neutral delay differential and difference equations. Discrete & Continuous Dynamical Systems - A, 2014, 34 (11) : 4577-4588. doi: 10.3934/dcds.2014.34.4577 Xiuli Sun, Rong Yuan, Yunfei Lv. Global Hopf bifurcations of neutral functional differential equations with state-dependent delay. Discrete & Continuous Dynamical Systems - B, 2018, 23 (2) : 667-700. doi: 10.3934/dcdsb.2018038 Runxia Wang, Haihong Liu, Fang Yan, Xiaohui Wang. Hopf-pitchfork bifurcation analysis in a coupled FHN neurons model with delay. Discrete & Continuous Dynamical Systems - S, 2017, 10 (3) : 523-542. doi: 10.3934/dcdss.2017026 Tomás Caraballo, José Real, T. Taniguchi. The exponential stability of neutral stochastic delay partial differential equations. Discrete & Continuous Dynamical Systems - A, 2007, 18 (2&3) : 295-313. doi: 10.3934/dcds.2007.18.295 Samuel Bernard, Fabien Crauste. Optimal linear stability condition for scalar differential equations with distributed delay. Discrete & Continuous Dynamical Systems - B, 2015, 20 (7) : 1855-1876. doi: 10.3934/dcdsb.2015.20.1855 Eugen Stumpf. Local stability analysis of differential equations with state-dependent delay. Discrete & Continuous Dynamical Systems - A, 2016, 36 (6) : 3445-3461. doi: 10.3934/dcds.2016.36.3445 Cemil Tunç. Stability, boundedness and uniform boundedness of solutions of nonlinear delay differential equations. Conference Publications, 2011, 2011 (Special) : 1395-1403. doi: 10.3934/proc.2011.2011.1395 Anatoli F. Ivanov, Musa A. Mammadov. Global asymptotic stability in a class of nonlinear differential delay equations. Conference Publications, 2011, 2011 (Special) : 727-736. doi: 10.3934/proc.2011.2011.727 Samuel Bernard, Jacques Bélair, Michael C Mackey. Sufficient conditions for stability of linear differential equations with distributed delay. Discrete & Continuous Dynamical Systems - B, 2001, 1 (2) : 233-256. doi: 10.3934/dcdsb.2001.1.233 Gang Huang, Yasuhiro Takeuchi, Rinko Miyazaki. Stability conditions for a class of delay differential equations in single species population dynamics. Discrete & Continuous Dynamical Systems - B, 2012, 17 (7) : 2451-2464. doi: 10.3934/dcdsb.2012.17.2451 Stéphane Junca, Bruno Lombard. Stability of neutral delay differential equations modeling wave propagation in cracked media. Conference Publications, 2015, 2015 (special) : 678-685. doi: 10.3934/proc.2015.0678 Ismael Maroto, Carmen Núñez, Rafael Obaya. Exponential stability for nonautonomous functional differential equations with state-dependent delay. Discrete & Continuous Dynamical Systems - B, 2017, 22 (8) : 3167-3197. doi: 10.3934/dcdsb.2017169 Fabien Crauste. Global Asymptotic Stability and Hopf Bifurcation for a Blood Cell Production Model. Mathematical Biosciences & Engineering, 2006, 3 (2) : 325-346. doi: 10.3934/mbe.2006.3.325 Hui Miao, Zhidong Teng, Chengjun Kang. Stability and Hopf bifurcation of an HIV infection model with saturation incidence and two delays. Discrete & Continuous Dynamical Systems - B, 2017, 22 (6) : 2365-2387. doi: 10.3934/dcdsb.2017121 Sun Yi, Patrick W. Nelson, A. Galip Ulsoy. Delay differential equations via the matrix lambert w function and bifurcation analysis: application to machine tool chatter. Mathematical Biosciences & Engineering, 2007, 4 (2) : 355-368. doi: 10.3934/mbe.2007.4.355 Pham Huu Anh Ngoc. Stability of nonlinear differential systems with delay. Evolution Equations & Control Theory, 2015, 4 (4) : 493-505. doi: 10.3934/eect.2015.4.493 Xiaoqin P. Wu, Liancheng Wang. Hopf bifurcation of a class of two coupled relaxation oscillators of the van der Pol type with delay. Discrete & Continuous Dynamical Systems - B, 2010, 13 (2) : 503-516. doi: 10.3934/dcdsb.2010.13.503 Fang Han, Bin Zhen, Ying Du, Yanhong Zheng, Marian Wiercigroch. Global Hopf bifurcation analysis of a six-dimensional FitzHugh-Nagumo neural network with delay by a synchronized scheme. Discrete & Continuous Dynamical Systems - B, 2011, 16 (2) : 457-474. doi: 10.3934/dcdsb.2011.16.457\n\n2018 Impact Factor: 1.313"
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.64588815,"math_prob":0.7367243,"size":15545,"snap":"2019-35-2019-39","text_gpt3_token_len":4935,"char_repetition_ratio":0.15655363,"word_repetition_ratio":0.6678587,"special_character_ratio":0.3504664,"punctuation_ratio":0.27794293,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9657742,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-09-20T16:36:17Z\",\"WARC-Record-ID\":\"<urn:uuid:e6dca14c-f54a-4643-bef3-0908085bdfa7>\",\"Content-Length\":\"123942\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:42ff65bd-f690-48d0-8c3d-302c33613468>\",\"WARC-Concurrent-To\":\"<urn:uuid:221a5fad-0d9a-4479-8d7b-8fda9dff467e>\",\"WARC-IP-Address\":\"216.227.221.143\",\"WARC-Target-URI\":\"https://aimsciences.org/article/doi/10.3934/mbe.2017075\",\"WARC-Payload-Digest\":\"sha1:6LFFMC5NQJBWAPN26TCCVXIOWCW7O3S2\",\"WARC-Block-Digest\":\"sha1:P5O72PSUKYE3NSKMBAENWK2UZOVKNTSY\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-39/CC-MAIN-2019-39_segments_1568514574050.69_warc_CC-MAIN-20190920155311-20190920181311-00100.warc.gz\"}"} |
https://www.geogebra.org/m/ef2rmt5p | [
"Write as many equations as possible that could represent the relationship between the ages of the two children in each family described. Be prepared to explain what each part of your equation represents. a. In Family A, the youngest child is 7 years younger than the oldest, who is 18. b. In Family B, the middle child is 5 years older than the youngest child.\n\nTyler thinks that the relationship between the ages of the children in Family B can be described with 2m-2y=10, where m is the age of the middle child and y the age of the youngest. Explain why Tyler is right.\n\nAre any of these equations equivalent to one another? If so, which ones? Explain your reasoning. 3a + 6 = 15 3a = 9 a + 2 = 5 1/3 a = 1"
] | [
null
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https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1007954 | [
"# Winter is coming: Pathogen emergence in seasonal environments\n\n• Philippe Carmona ,\n\nContributed equally to this work with: Philippe Carmona, Sylvain Gandon\n\nRoles Conceptualization, Formal analysis, Investigation, Software, Visualization, Writing – original draft, Writing – review & editing\n\nAffiliation Laboratoire de Mathématiques Jean Leray, Université de Nantes, Nantes, France\n\n• Sylvain Gandon\n\nContributed equally to this work with: Philippe Carmona, Sylvain Gandon\n\nRoles Conceptualization, Software, Supervision, Visualization, Writing – original draft, Writing – review & editing\n\nsylvain.gandon@cefe.cnrs.fr\n\nAffiliation CEFE, CNRS, Univ Montpellier, Univ Paul Valéry Montpellier 3, EPHE, IRD, 34293 Montpellier Cedex 5, France\n\n## Abstract\n\nMany infectious diseases exhibit seasonal dynamics driven by periodic fluctuations of the environment. Predicting the risk of pathogen emergence at different points in time is key for the development of effective public health strategies. Here we study the impact of seasonality on the probability of emergence of directly transmitted pathogens under different epidemiological scenarios. We show that when the period of the fluctuation is large relative to the duration of the infection, the probability of emergence varies dramatically with the time at which the pathogen is introduced in the host population. In particular, we identify a new effect of seasonality (the winter is coming effect) where the probability of emergence is vanishingly small even though pathogen transmission is high. We use this theoretical framework to compare the impact of different preventive control strategies on the average probability of emergence. We show that, when pathogen eradication is not attainable, the optimal strategy is to act intensively in a narrow time interval. Interestingly, the optimal control strategy is not always the strategy minimizing R0, the basic reproduction ratio of the pathogen. This theoretical framework is extended to study the probability of emergence of vector borne diseases in seasonal environments and we show how it can be used to improve risk maps of Zika virus emergence.\n\n## Author summary\n\nSeasonality drives fluctuations in the probability of pathogen emergence, with dramatic consequences for public health and agriculture. We show that this probability of pathogen emergence can be vanishingly small before the low transmission season. We derive the conditions for the existence of this winter is coming effect and identify optimal control strategies that minimize the risk of pathogen emergence. We generalize this framework to account for different forms of environmental variations, different modes of control and complex pathogen life cycles. We illustrate how this framework can be used to improve predictions of Zika emergence at different points in space and time.\n\n## Introduction\n\nThe development of effective control strategies against the emergence or re-emergence of pathogens requires a better understanding of the early steps leading to an outbreak [1, 2, 3, 4]. Classical models in mathematical epidemiology predict that whether or not an epidemic emerges depends on",
null,
"the basic reproduction ratio of the pathogen, where λ is the birth rate of the infection (a function of the transmission rate and the density of susceptible hosts) and μ is the death rate of the infection (a function of the recovery and mortality rates). In the classical deterministic description of disease transmission, the pathogen will spread if R0 > 1 and will go extinct otherwise (Fig 1). This deterministic description of pathogen invasion relies on the underlying assumption that the initial number of introduced pathogens is large. The early stages of an invasion are, however, typically characterized by a small number, n, of infected hosts. These populations of pathogens are thus very sensitive to demographic stochasticity and may be driven to extinction even when R0 > 1. The probability of emergence",
null,
"refers to the probability that, after the introduction of n infected hosts, a non-evolving pathogen avoids initial extinction and leads to an epidemic. The analysis of stochastic epidemic models and the derivation of the probability of a major epidemic can be traced back to the work of Bailey (1953) and Whittle (1955). Under the reasonable assumption that the initial spread of directly transmitted disease follows a one dimensional birth-death branching process the probability of emergence is zero when R0 < 1 and, when R0 > 1, it is equal to [3, 4, 5, 6, 7]:",
null,
"(1)\n\nFig 1. Transmission mode and pathogen emergence without seasonality.\n\nIn a direct transmission model pathogen dynamics is driven by the birth rate λ and the death rate μ of a single infected compartment I. In a vector borne transmission model pathogen dynamics is driven by the birth rates and death rates of multiple compartments: exposed and infected humans (EH, IH), exposed and infected mosquito vectors (EV, IV). In the absence of seasonality (i.e. no temporal variation in birth and death rates) the basic reproduction ratio R0 can be expressed as a ratio between birth and death rates. The probability of emergence pe after the introduction of a single infected individual can also be expressed as a function of these birth and death rates. With vector borne transmission this probability of emergence depends on which infected host is introduced (Figure E in S1 Text). Here we give the probability of emergence after the introduction of a single human exposed to the pathogen, EV, and where the index i refers to the four consecutive states of the pathogen life cycle (see sections 2 and 3 of S1 Text).\n\nhttps://doi.org/10.1371/journal.pcbi.1007954.g001\n\nThe above results rely on the assumption that birth and death rates of the infection remain constant through time (i.e. time homogeneous branching process). Many pathogens, however, are very sensitive to fluctuations of the environment. For instance, the fluctuations of the temperature and humidity have been shown to have a huge impact on the infectivity of many viral pathogens like influenza and a diversity of other infectious diseases [9, 10]. In addition, many pathogens rely on the presence of arthropod vectors for transmission and the density of vectors is also very sensitive to environmental factors like temperature and humidity . To account for these environmental variations, the birth and death rates are assumed to be functions of time: λ(t) and μ(t), respectively. The basic reproduction number is harder to compute but the probability of emergence pe(t0) when one infected individual is introduced (i.e. n = 1) at time t0 is well known (see e.g. or [13, Chapter 7]):",
null,
"(2) with",
null,
"where r(t) = λ(t) − μ(t) is the Malthusian growth rate of the pathogen population at time t (another derivation of (2) is given in section 2.5 of S1 Text). Because we are interested in seasonal variation we can focus on periodic scenarios where both λT(t) and μT(t) have the same period T, one year. In this case, the basic reproduction number has been computed in [3, 14] as the spectral radius of the next generation operator, and is the ratio of time averages of birth and death rates:",
null,
"(3) When R0 < 1 the pathogen will never produce major epidemics and will always be driven to extinction. When R0 > 1, however, a pathogen introduced at a time t0 may escape extinction. In this case the probability of emergence can also be expressed as a ratio of average birth and death rates, but with different weights (see section Pathogen emergence with seasonality of Methods):",
null,
"(4) Note that this quantity refers to the probability of major epidemics, the probability that the pathogen population does not go extinct. Minor epidemics are likely to outburst if the pathogen is introduced during the high transmission season but those outbreaks do not count as major epidemics if they go extinct during the low transmission seasons.\n\nIn the following we show that very good approximations of the probability of pathogen emergence can be derived from this general expression when the period is very large (or very small) compared to the duration of the infection. These approximations give important insights on the effect of the speed and the shape of the temporal fluctuations of the environment on the probability of pathogen emergence. We use this theoretical framework to determine optimal control strategies that minimize the risk of pathogen emergence. We provide clear cut recommendations in a range of epidemiological scenarios. We also show how this theoretical framework can be extended to account for the effect of seasonality in vector borne diseases. More specifically, we use this model to estimate the probability of Zika virus emergence throughout the year at different geographic locations.\n\n## Results\n\n### Emergence of directly transmitted pathogens\n\nFor the sake of simplicity we start our analysis with a directly transmitted disease with a constant clearance rate μ(t) = μ, but with seasonal fluctuations of the transmission rate, λ(t). This epidemiological scenario may capture the seasonality of many infectious diseases. For instance, increased contact rates among children during school terms has been shown to have a significant impact on the transmission of many childhood infections [15, 16]. Seasonal fluctuations in temperature and humidity can also drive variations in the survival rate of many viruses and result in seasonal variations in transmission rates [17, 18].\n\nBoth the speed and the amplitude of the fluctuations of λ(t) can affect the probability of pathogen emergence. Yet, when the period T of the fluctuations is short compared to the duration 1/μ (e.g. fluctuations driven by diurnal cycles are fast), the probability of pathogen emergence can be approximated by (Fig 2E and 2F, see section Asymptotics for small periods of Methods):",
null,
"(5) In other words, the probability of emergence does not depend on the timing of the introduction event and it is only driven by the average transmission rate.\n\nFig 2. The winter is coming effect.\n\nPathogen birth rate (i.e. transmission rate) λ(t) is assumed to vary periodically following a square wave (A and B). During a portion 1 − γ of the year transmission is maximal (γ = 0.7 in this figure) and λ(t) = λ0. In the final portion of the year λ(t) drops (low transmission season in gray). In A λ(t) varies between λ0 = 2.5 and 1.5 and, in B λ(t) varies between λ0 = 2.5 and 0. Pathogen death rate μ(t) (a function of recovery and death rates of the infected host) is assumed to be constant and equal to 1 in this figure. When the net growth rate of the pathogen remains positive in the low transmission season (λ(t) > μ(t), A, C and E) the probability of emergence of a pathogen introduced at time t0 can be well approximated by Eq (6):",
null,
"(dashed line in E and F) if the duration of the infection is short relative to the period T of the fluctuation (E). In contrast, if the low transmission season is more severe (λ(t) < μ(t), B, D and F), the negative growth rate φ(t) of the pathogen population during this period creates a demographic trap and reduces the probability of emergence at the end of the high transmision season. This winter is coming effect is indicated with black arrow in (D) and with the light gray shading in (D) and (F). This effect is particularly pronounced when the period of the fluctuations of the environment is large relative to the duration of the infection (i.e., when T is large, F). When the period T of the fluctuation is small relative to the duration of the infection, the probability of emergence is well approximated by Eq (5):",
null,
"whatever the time of pathogen introduction (in A, R0 = 2.2 and pe ≃ 0.55; in B, R0 = 1.75 and pe ≃ 0.43).\n\nhttps://doi.org/10.1371/journal.pcbi.1007954.g002\n\nWhen the fluctuations are slower, however, the probability of pathogen emergence does depend on the timing of the introduction. The probability of emergence drops with the transmission rate (Fig 2E and 2F). When the period of the fluctuation is long, a natural approximation is (see section Asymptotics for large periods of Methods):",
null,
"(6) This is a very good approximation whenever the birth rate of the infection remains higher than the death rate throughout the year (i.e., λ(t) > μ(t), Fig 2). However, when λ(t) can drop below μ(t), the above approximation fails to capture the dramatic reduction of the probability of emergence occurring at the end of the high transmission season. When the introduction time of the pathogen is shortly followed by a low transmission season, the introduced pathogen is doomed because it will suffer from the bad times ahead (see section Asymptotics for large periods of Methods). We call this the winter is coming effect. Fig 2D and 2F provide a geometric interpretation of this effect. In the low transmission season the integrated growth rate φ(t) drops with t because the Malthusian growth rate of the pathogen is negative. Any epidemic starting during (dark gray shading) or just before (light gray shading) this period is unlikely to escape extinction because of this demographic trap. We further explore this effect in Figure A in S1 Text, under different types of seasonal variations: square waves and sinusoidal waves. As expected, the winter is coming effect is particularly pronounced when the period of the fluctuations are long relative to the duration of the infection (Fig 2F).\n\n#### Optimal control.\n\nOur theoretical framework can be used to identify optimal control strategies. The objective is to minimize the average probability of emergence under the assumption that the introduction time is uniformly distributed over the year:",
null,
"Control is assumed to act via an instantaneous reduction ρ(t) of the transmission rate of the pathogen: λρ(t) = λ(t)(1 − ρ(t)). We also assume that higher control intensity is costly and we define the cost of a given control strategy as a function of the intensity and the duration of the control:",
null,
"More explicitly, we assume that the control strategy is governed by three parameters: t1 and t2, the times at which the control starts and ends, respectively, and ρM the intensity of control during the interval [t1, t2]. The cost of such a control strategy is thus: C = (t2t1)ρM. For a given investment in disease control C, what are the values of t1, t2 and ρM that minimize the average probability of emergence 〈pe〉?\n\nWe first answer this question when the fluctuation of transmission is a square wave where λ(t) oscillates between λ0 (for a fraction 1 − γ of the year) and 0, while μ(t) = 1 throughout the year (Fig 3). For instance, such periodicity may be driven by school terms with high transmission between students when school is on and low transmission when school is off . The basic reproduction after control in the high transmission period is equal to R0C (see section 1 of S1 Text). In other words, under this scenario, when the investment in control reaches a threshold (i.e. when C > R0 − 1) the basic reproduction (after control) of the pathogen drops below one and the probability of emergence vanishes. Fig 3 shows how 〈pe〉 varies with different types of interventions when this level of control is unattainable (e.g. because the value of R0 is too high). We assume that the investment in control is fixed and equal to C = (t2t1)ρM = 0.2 and we explore how different values of t1 and ρM affect 〈pe〉. A naive strategy where control is applied throughout the high transmission season (t1 = 0, t2 = 0.7, ρM = 2/7) yields an average probability of emergence equal to 〈pe〉 = 0.233. Many alternative strategies where the control is applied more intensely but in a limited portion of the high transmission season (Fig 3A, 3C and 3E and S2) yield lower values of 〈pe〉. In particular, all the strategies that fall within the dotted red curve of Fig 4A have 〈pe〉 = 0.166. Indeed, all the strategies that fall in this region maximize the winter is coming effect. Fig 3C and 3E show how the timing of control (indicated by the blue shading) for one of these optimal strategies minimizes the probability of emergence via an extension of the effects of the low transmission season.\n\nFig 3. Optimal Control for square wave (A, C and E) and sinusoidal birth rates (B, D and F).\n\nIn A and B we plot The pathogen birth rate before (black line) and after the optimal control (dashed blue line) which minimizes the mean emergence probability < pe> (see also Fig 4). The square wave assumes that λ(t) = 3 1(0<t<0.7). The sinusoidal wave assumes that λ(t) = 2(1 + sin(2πt)). As in Fig 2 the gray shadings refers to the low transmission season (gray) and the winter is coming effect (light gray). Similarly, we indicate the additional low transmission period induced by control (blue shading) and the additional winter is coming effect induced by control (light blue shading).\n\nhttps://doi.org/10.1371/journal.pcbi.1007954.g003\n\nFig 4. Mean probability of pathogen emergence for different control strategies with (A) square wave and (B) sinusoidal wave fluctuations.\n\nWe used the same scenarios as in Fig 3 and we fix the investment in control (cost of control C = ρM(t2t1) = 0.2). We explore how the intensity of control (ρM) and the timing of control (between t1 and t2) affect < pe >, the mean probability of pathogen emergence (lighter shading refers to higher values of < pe >). For the square wave scenario we identify a range of optimal strategies withing the dotted red curve where < pe > is minimized. The optimal strategies used in Fig 3 are indicated with a blue cross for both the square wave (A) and the sinusoidal wave (B). The minimal and maximal value for < pe > are: 0.166 − 0.366 (square wave) and 0.085 − 0.31 (sinusoidal wave). For the square wave (A), R0 = 1.5 does not depend on the timing and the intensity of the control. For the sinusoidal wave (B), there is a single strategy minimizing R0, namely R0 = 1.28 for t1 = 0.15 and ρM = 1.0, marked with a red cross in B. With the sinusoidal wave there is a single control strategy minimizing < pe > for t1 = 0.07 and ρM = 0.93 (blue cross in B).\n\nhttps://doi.org/10.1371/journal.pcbi.1007954.g004\n\nSecond, we consider a seasonal environment where λ(t) follows a sinusoidal wave, while μ(t) = 1 throughout the year (Fig 3B, 3D and 3F). Such periodicity may arise with more gradual changes of the abiotic environment driven by climatic seasonality . Under this scenario, pathogen transmission varies continuously and the basic reproduction after control does depend on the time at which control is applied. The basic reproduction ratio is minimized when the intensity of control is maximal (ρM = 1) in a time interval centered on the time at which pathogen transmission reaches its peak (red cross in Fig 4B). In contrast, the optimal control strategy that minimizes 〈pe〉 starts earlier, lasts longer and is a bit less intense (blue cross in Fig 4B). As discussed in the square wave scenario, the timing of control in the optimal strategy extends the winter is coming effect. Fig 3D and 3F show that the optimal strategy (indicated by the blue shading) prolongs the effect of the low transmission season.\n\n### Emergence of vector borne pathogens\n\nNext we want to expand the above analysis to a more complex pathogen life cycle. Indeed, many emerging pathogens are vector borne [1, 20] and the probability of pathogen emergence can also be computed under this life cycle [6, 7, 21, 22]. Arboviruses, for instance, use different mosquito species as vectors and are responsible for major emerging epidemics in human populations . In the following, we use a classical epidemiological model of Zika virus transmission which has been parameterized using empirical data sets to determine the probability of emergence under various regimes of seasonality (see section 3 of S1 Text). In this model, the pathogen may appear in four different states (Fig 1): exposed and infectious mosquitoes (EV and IV), exposed and infectious humans (EH and IH). The stochastic description of this epidemiological model yields a four dimension multi-type birth-death branching process (see section 2 of S1 Text). In the absence of seasonality (homogeneous case) the basic reproduction ratio of the pathogen is the ratio of the product of birth rates by the product of the death rates (Fig 1). The probability of emergence after the introduction of a single infected host in state ∈ (EH, IH, EV, IV):",
null,
"(7) where the index i refers to the d consecutive states of the pathogens, starting with the state in which the pathogen is introduced. Hence λi,i+1 denotes the birth rate of an infection in state i + 1 from an infection in state i, and μi denotes the death rate of an infection in state i. Note that the state of the introduced infection can have a huge impact on the probability of pathogen emergence (Figure E in S1 Text). One may expect that if the epidemic starts in a bad quality host with a low",
null,
"ratio the pathogen is more likely to go extinct than if it starts with a good quality host (with a high Ri ratio). We show in the S1 Text subsection 2.2 that this is indeed the case in dimension d = 2 (see also [21, 22]). But things become more complex when d > 2 because the quality of the following hosts in the transmission cycle matter as well. In other words, we can observe a weak host is coming effect on the probability of emergence. This effect is akin to the winter is coming effect that we discuss above, but it is driven by the alternation of the quality of hosts, not by seasonality.\n\nSeasonality can drive pathogen transmission through the fluctuations of the available density of the mosquito vector. Following we assume that mosquito density fluctuates with temperature and is maximal at Topt, the optimal temperature for mosquito reproduction (see sup info). The rate λIH, EV at which mosquitoes are exposed to the parasite is directly proportional to NV/NH. In such a fluctuating environment the R0 is the spectral radius of the next generation operator, see [3, 14] but there is no analytic expression for R0. Yet, it is tempting to use Eq (7) with the birth and death rates functions of the introduction time t0, to obtain an approximation pe(t0) for large periods. The exact probability of emergence can be efficiently computed numerically thanks to the seminal work of . Fig 5 explores the difference between this naive expectation and the exact value of the probability of emergence. Crucially, we recover the same qualitative patterns observed in the direct transmission model. In particular, we notice that when the product of birth rates remains higher than the product of death rates the naive expectation for the probability of emergence is not too far from the exact value of pe(t0). However, when seasonality induces more pronounced drops in transmission, we recover the winter is coming effect where the probability of emergence can be very low before the low transmission season (Fig 5D). It is also possible to identify numerically the optimal control strategies minimizing the probability of Zika emergence (Figure F in S1 Text).\n\nFig 5. Probability of Zika emergence across space and time.\n\nThe top figures (A and B) show the seasonal variations in λIV, EH, the transmission rate from humans to the vectors because of the fluctuations the density of vectors in two habitats (this illustrates the effect of space on Zika emergence): a minor variation in mean temperature, 29°C (A and C) versus 27°C (B and D), has a massive impact on transmission and, consequently, on pathogen emergence. In C and D we illustrate the effect of the time of introduction t0 on Zika emergence. The dotted black line refers to the naive expectation for the probability of pathogen emergence at time t0 if all the rates were constant and frozen at their t0 values (see (7)). The gray shading in B and D refers to the low transmission season where the product of the transmission rates is lower than the product of death rates (see S1 Text). The exact probability of emergence pe(t0 T, T) is indicated as a solid black line. Higher seasonality (B and D) increases the discrepancy between the naive expectation and the exact value of the probability of pathogen emergence. This discrepancy is due to the winter is coming effect (light gray shading in D). Parameter values are given in table S1 A (model I) of section 3 of S1 Text.\n\nhttps://doi.org/10.1371/journal.pcbi.1007954.g005\n\n## Discussion\n\nThe effect of seasonality on the probability of pathogen emergence depends critically on the duration of the infection 1/μ relative to the period T of the fluctuation. When the period of the fluctuation is small (i.e., T < 1/μ) the environment changes very fast and the probability of emergence does not depend on the timing of pathogen introduction but on the average transition rates of the pathogen life cycle. When the period of the fluctuation is large (i.e., T > 1/μ) the probability of emergence varies with the timing of pathogen introduction. This probability drops when the pathogen is introduced at a point in time where conditions are unfavorable (low transmission and/or high recovery rates). More surprisingly, we show that the probability of pathogen emergence can also be very low in times where conditions are favourable if they are followed by a particularly hostile environment. This winter is coming effect results from the existence of adverse conditions that introduce demographic traps (where the net reproduction rate is negative) and pathogen emergence is only possible if the pathogen introduction occurs sufficiently far ahead of those traps. This effect is also expected to act on the size of the epidemics in deterministic models. Epidemics initiated at the end of the high transmission season are expected to be smaller because they do not have time to expand before reaching the low transmission season . There is good evidence of this effect in measles .\n\nNote that our approach neglects the density dependence that typically occurs after some time with major epidemics. Our probability of pathogen emergence thus provides an upper approximation of the probability emergence. Indeed, with density dependence the size of the pathogen population may be too small to survive even very shallow demographic traps. In section 5 of S1 Text we show how such density dependence can magnify the winter is coming effect.\n\nUnderstanding this effect allows us to identify the optimal deployment of control strategies minimizing the average probability of pathogen emergence in seasonal environments. We identified optimal control strategies in different epidemiological scenarios under the assumption that the introduction time is homogeneous (Figures 3, 5, and A, D in S1 Text). This assumption can be readily modified to take into account temporal variations in the probability of introduction events, which yields different recommendations for the timing of control (see subsection 1.3 and Figure C in S1 Text).\n\nThis work can be extended to explore optimal timing of other control strategies. For instance study the optimal timing of pulse vaccination in seasonal environment and show for a range of epidemiological scenarios that a pulse vaccination applied periodically 3 months before the peak transmission rate minimizes R0. Yet, as pointed out above, the strategy minimizing R0 may not always coincide with the strategy minimizing 〈pe(t0)〉 (see Fig 4). Indeed, an examination of figure H in S1 Text shows that the probability of emergence is minimized if pulse vaccination occurs a bit sooner than the time at which R0 is minimized (3.71 instead of 3 months before the peak transmission).\n\nSo far we focused on control strategies that lower pathogen transmission. Our approach can also be used to optimize control measures that do not act on the transmission rate but on the duration of the infection. For instance, what is the optimal timing of a synchronized effort to use antibiotics to minimize bacterial pathogens emergence? We found that the timing of these treatment days have no impact on R0 but pathogen emergence is minimized when treatment occurs 1.3 months before the peak of the transmission season. This strategy creates deeper traps and results in a stronger winter is coming effect. Interestingly, explored the optimal timing of mass antibiotic treatment to eliminate the ocular chlamydia that cause blinding trachoma. Numerical simulations showed that the speed of eradication is maximized (the time to extinction is minimized) when treatment is applied 3 months before the low transmission season. A similar result was obtained by showing that it is best to treat against malaria in the low transmission season. The apparent discrepancy between these recommendations is driven by the use of different objective functions (pathogen emergence, speed of eradication or cumulative number of cases).\n\nThe above examples show that our analysis has very practical implications on the understanding and the control of emerging infectious diseases in seasonal environments. This theoretical framework could be used to produce maps with a very relevant measure of epidemic risk: the probability of pathogen emergence across space and time (Fig 5). Currently available risk maps are often based on integrated indices of suitability of pathogens or vectors [30, 31, 32, 33]. These quantities may be biologically relevant but the link between these quantities and the probability of pathogen emergence is not very clear. We contend that using risk maps based on pe(t0) would be unambiguous and more informative. Our model could thus contribute to development of “outbreak science” and help public health services to forecast the location and the timing of future epidemics. More generally, the same approach could also be used to improve the prevention against invasions by nonindigenous species .\n\nExperimental test of theoretical predictions on pathogen emergence are very scarce because the stochastic nature of the prediction requires massive replicate numbers. Some microbial systems, however, offer many opportunities to study pathogen emergence in controlled and massively replicated laboratory experiments . It would be interesting to use these microbial systems to study the impact of periodic oscillations of the environment to mimic the influence of seasonality. Another way to explore this question experimentally would be to use data on experimental inoculation of hosts. Indeed, the experimental inoculation of a few bacteria in a vertebrate host (which could be viewed as “population” of susceptible cells) is equivalent to the introduction of a few pathogens in a host population. The outcome of these inoculations are stochastic and the probability of a successful infection (host death) is equivalent to a probability of emergence. Interestingly, some daily periodicity to bacterial infections has been found in mice [37, 38]. Mice inoculated early in the morning (4am) have a higher probability of survival than mice inoculated at any other time. This pattern is likely to result from a circadian control of the vertebrate immune system which are likely to impact the birth and death rates of bacteria. Given that the generation time of a bacteria is smaller than a day, it is not surprising to see a probability of emergence depending on the inoculation time (see Eq 6). In other words, our work may also be used to shed some light on the stochastic within-host dynamics of pathogen infections. One could envision that simple changes in therapeutic practices that take into account the time of day may affect clinical care and could limit the risk of nosocomial infections. Our work provides a theoretical toolbox that can integrate detailed description of the periodic nature of pathogen life cycles at different spatial and temporal scales (within and between hosts, over the period of one day or one year) to time optimal control strategies.\n\n## Methods\n\n### Pathogen emergence with seasonality\n\nThe life cycle of a directly transmited pathogen is governed by its birth and death rates (λ and μ, respectively). In the absence of seasonality these birth and death rates are constant (λ > 0, μ > 0), the basic reproduction number is",
null,
"and the probability of extinction, starting initially with one individual, is",
null,
"(Fig 1). This result was first derived by .\n\nIn a seasonal environment the birth and death rates are assumed to be functions of time, noted λ(t) and μ(t), respectively, the basic reproduction number is harder to compute but the extinction probability is well known (see e.g. or [13, Chapter 7]). This yields (Eq 2) for pe(t0), the probability of pathogen emergence when a single infected host is introduced in the host population at time t0.\n\nLet us now consider rates with period T > 0, denoted by λT and μT. Accordingly, we denote",
null,
"and pe(t0, T) the corresponding emergence probability. The basic reproduction number has been derived in [3, 14] as the spectral radius of the next generation operator, and is the ratio of time averaged birth and death rates (see Eq (3)). Since",
null,
", we find that pe(t0, T) = 0 if R0 ≤ 1.\n\nIf R0 > 1, we can rearrange formula (2) and express pe(t0, T) as Eq (4) which varies with the ratio of average birth and death rates, but with a weight that takes into account the average growth rate of the pathogen population. Indeed, first observe that since",
null,
"we have",
null,
"(8) Since φT(t) → +∞ this implies",
null,
"(9) We now use periodicity to obtain, first that for integer k,",
null,
"(10) and thus",
null,
"(11)",
null,
"(12)",
null,
"(13) Similarly,",
null,
"(14)\n\nHence,",
null,
"(15) and",
null,
"(16)",
null,
"(17)\n\n### Asymptotic results for small and large periods\n\nUnder the assumption that",
null,
"we know that pe(t0, T) > 0 for all t0. In the following we rescale time so that the T periodic functions λT, μT become 1 periodic functions defined by",
null,
"(18) And similarly,",
null,
"(19) Hence, the introduction time t0 refers to introduction time between 0 and 1 and by a change of variables we obtain",
null,
"(20) In the following we derive simpler expressions for pe(t0 T, T) in the limit cases where T is very small or very large.\n\n### Asymptotics for small periods: When T → 0\n\nWe see from Eq (20) that when",
null,
"that we have",
null,
"(21)\n\nIn other words when T → 0, we can replace the varying rates by their means. Indeed we have on one hand, as T → 0,",
null,
"(22) On the other hand, since λ has period 1,",
null,
"(23)\n\n### Asymptotics for large periods: When T → + ∞\n\nWe observe on various examples that for large T, pe(t0 T, T) can sometimes be very small on subintervals of [0, T].\n\nWe are going to give a mathematical formulation to this observation. Define",
null,
"(24) to be the guess we make for large periods by substituting in the formula giving the emergence probability for constant rate λ(t0) and μ(t0) to λ and μ. It is natural to define the winter period, W, as",
null,
"(25) However, the period where the emergence probability is vanishingly small is larger than W. We call this interval (or set of intervals) WIC (for Winter Is Coming) and we have (see Proposition 6.1 of the section 6 of the S1 Text):",
null,
"(26) with",
null,
"(27)\n\nIn other words a time t0 is in the WIC interval if it is already in W (winter period) or if there is a demographic trap in the future. A demographic trap occurs if there is a time s > t0 for which the expected size of the population X(s) at time s is smaller than the original size at the introduction time X(t0):",
null,
"(28)\n\n## Supporting information\n\n### S1 Text. This document contains complementary material that supports the results that we discuss in the main body of the paper.\n\nWe present: (1) a calculation of the probability of emergence of directly transmitted pathogen for different scenarios of seasonality, (2) a generalisation of our results when the pathogen life cycle goes through multiple stages before completing its life cycle, (3) an exploration of the winter is coming effect on the seasonal dynamics of Zika virus, (4) an analysis of a scenario that involves pulse interventions (vaccination or treatment), (5) an exploration of the effect of density dependence on the winter is coming effect, (6) additional computations and proofs.\n\nhttps://doi.org/10.1371/journal.pcbi.1007954.s001\n\n(PDF)\n\n## Acknowledgments\n\nWe thank Mike Boots and Sébastien Lion for comments on an earlier draft. Philippe Carmona thanks the Centre Henri Lebesgue ANR-11-LABX-0020-01 for creating an attractive mathematical environment.\n\n## References\n\n1. 1. Woolhouse ME. Population biology of emerging and re-emerging pathogens. Trends in microbiology. 2002;10(10):s3–s7. pmid:12377561\n2. 2. Keeling MJ, Rohani P. Modeling infectious diseases in humans and animals. Princeton University Press; 2011.\n3. 3. Diekmann O, Heesterbeek H, Britton T. Mathematical tools for understanding infectious disease dynamics. Princeton Series in Theoretical and Computational Biology. Princeton University Press, Princeton, NJ; 2013.\n4. 4. Heesterbeek H, Anderson RM, Andreasen V, Bansal S, De Angelis D, Dye C, et al. Modeling infectious disease dynamics in the complex landscape of global health. Science. 2015;347 (6227). pmid:25766240\n5. 5. Gandon S, Hochberg ME, Holt RD, Day T. What limits the evolutionary emergence of pathogens? Philosophical Transactions of the Royal Society B: Biological Sciences. 2013;368(1610):20120086.\n6. 6. Allen LJS, L GE Jr. Extinction thresholds in deterministic and stochastic epidemic models. Journal of Biological Dynamics. 2012;6(2):590–611. pmid:22873607\n7. 7. Allen LJS, van den Driessche P. Relations between deterministic and stochastic thresholds for disease extinction in continuous- and discrete-time infectious disease models. Mathematical Biosciences. 2013;243(1):99–108. pmid:23458509\n8. 8. Shaman J, Kohn M. Absolute humidity modulates influenza survival, transmission, and seasonality. Proceedings of the National Academy of Sciences. 2009;106(9):3243–3248.\n9. 9. Altizer S, Dobson A, Hosseini P, Hudson P, Pascual M, Rohani P. Seasonality and the dynamics of infectious diseases. Ecology letters. 2006;9(4):467–484. pmid:16623732\n10. 10. Martinez ME. The calendar of epidemics: Seasonal cycles of infectious diseases. PLoS pathogens. 2018;14(11):e1007327. pmid:30408114\n11. 11. Mordecai EA, Paaijmans KP, Johnson LR, Balzer C, Ben-Horin T, de Moor E, et al. Optimal temperature for malaria transmission is dramatically lower than previously predicted. Ecology letters. 2013;16(1):22–30. pmid:23050931\n12. 12. Kendall DG. On the generalized “birth-and-death” process. Ann Math Statistics. 1948;19:1–15.\n13. 13. Bailey NTJ. The elements of stochastic processes with applications to the natural sciences. John Wiley & Sons, Inc., New York-London-Sydney; 1964.\n14. 14. Bacaër N, Guernaoui S. The epidemic threshold of vector-borne diseases with seasonality. The case of cutaneous leishmaniasis in Chichaoua, Morocco. J Math Biol. 2006;53(3):421–436.\n15. 15. Fine PE, Clarkson JA. Measles in England and Wales—I: an analysis of factors underlying seasonal patterns. International journal of epidemiology. 1982;11(1):5–14.\n16. 16. Finkenstädt BF, Grenfell BT. Time series modelling of childhood diseases: a dynamical systems approach. Journal of the Royal Statistical Society: Series C (Applied Statistics). 2000;49(2):187–205.\n17. 17. Cook S, Glass R, LeBaron C, Ho MS. Global seasonality of rotavirus infections. Bulletin of the World Health Organization. 1990;68(2):171. pmid:1694734\n18. 18. Pascual M, Bouma MJ, Dobson AP. Cholera and climate: revisiting the quantitative evidence. Microbes and Infection. 2002;4(2):237–245. pmid:11880057\n19. 19. Grassly NC, Fraser C. Seasonal infectious disease epidemiology. Proceedings Biological sciences, The Royal Society. 2006;273:2541–2550.\n20. 20. Jones KE, Patel NG, Levy MA, Storeygard A, Balk D, Gittleman JL, et al. Global trends in emerging infectious diseases. Nature. 2008;451(7181):990. pmid:18288193\n21. 21. Bartlett M. The relevance of stochastic models for large-scale epidemiological phenomena. Journal of the Royal Statistical Society: Series C (Applied Statistics). 1964;13(1):2–8.\n22. 22. Lloyd AL, Zhang J, Root AM. Stochasticity and heterogeneity in host–vector models. Journal of the Royal Society Interface. 2007;4(16):851–863.\n23. 23. Weaver SC, Barrett AD. Transmission cycles, host range, evolution and emergence of arboviral disease. Nature Reviews Microbiology. 2004;2(10):789. pmid:15378043\n24. 24. Zhang Q, Sun K, Chinazzi M, Pastore y Piontti A, Dean NE, Rojas DP, et al. Spread of Zika virus in the Americas. Proceedings of the National Academy of Sciences. 2017;114(22):E4334–E4343.\n25. 25. Bacaër N, Ait Dads EH. On the probability of extinction in a periodic environment. J Math Biol. 2014;68(3):533–548. pmid:23143337\n26. 26. Otero M, Solari HG. Stochastic eco-epidemiological model of dengue disease transmission by Aedes aegypti mosquito. Mathematical biosciences. 2010;223(1):32–46. pmid:19861133\n27. 27. Stone L, Olinky R, Huppert A. Seasonal dynamics of recurrent epidemics. Nature. 2007;446:533–536. pmid:17392785\n28. 28. Lee DC, Chidambaram JD, Porco TC, Lietman TM. SEASONAL EFFECTS IN THE ELIMINATION OF TRACHOMA. The American Journal of Tropical Medicine and Hygiene. 2005;72(4):468–470. pmid:15827288\n29. 29. Gao D, Amza A, Nassirou B, Kadri B, Sippl-Swezey N, Liu F, et al. Optimal seasonal timing of oral azithromycin for malaria. Am J Trop Med Hyg. 2014;91(5):936–942. pmid:25223942\n30. 30. Kitron U. Risk maps:: Transmission and burden of vector-borne diseases. Parasitology today. 2000;16(8):324–325.\n31. 31. Jones KE, Patel NG, Levy MA, Storeygard A, Balk D, Gittleman JL, et al. Global trends in emerging infectious diseases. Nature. 2008;451(7181):990. pmid:18288193\n32. 32. Kraemer MU, Hay SI, Pigott DM, Smith DL, Wint GW, Golding N. Progress and challenges in infectious disease cartography. Trends in parasitology. 2016;32(1):19–29. pmid:26604163\n33. 33. Nsoesie EO, Kraemer M, Golding N, Pigott DM, Brady OJ, Moyes CL, et al. Global distribution and environmental suitability for chikungunya virus, 1952 to 2015. Euro surveillance: bulletin Europeen sur les maladies transmissibles = European communicable disease bulletin. 2016;21(20).\n34. 34. Rivers C, Chretien JP, Riley S, Pavlin JA, Woodward A, Brett-Major D, et al. Using “outbreak science” to strengthen the use of models during epidemics. Nature communications. 2019;10(1):3102.\n35. 35. Lodge DM, Williams S, MacIsaac HJ, Hayes KR, Leung B, Reichard S, et al. Biological invasions: recommendations for US policy and management. Ecological applications. 2006;16(6):2035–2054.\n36. 36. Chabas H, Lion S, Nicot A, Meaden S, van Houte S, Moineau S, et al. Evolutionary emergence of infectious diseases in heterogeneous host populations. PLOS Biology. 2018;16(9):1–20.\n37. 37. Feigin RD, San Joaquin VH, Haymond MW, Wyatt RG. Daily periodicity of susceptibility of mice to pneumococcal infection. Nature. 1969;224(5217):379. pmid:5343888\n38. 38. Shackelford PG, Feigin RD. Periodicity of susceptibility to pneumococcal infection: influence of light and adrenocortical secretions. Science. 1973;182(4109):285–287. pmid:4147530\n39. 39. Scheiermann C, Kunisaki Y, Frenette PS. Circadian control of the immune system. Nature Reviews Immunology. 2013;13(3):190. pmid:23391992\n40. 40. Whittle P. The outcome of a stochastic epidemic—a note on Bailey’s paper. Biometrika. 1955;42:116–122."
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https://mirror.szerverem.hu/ctan/graphics/tpic2pdftex/tpic2pdftex | [
"#!/bin/sh - # # $Id: tpic2pdftex 29534 2013-03-27 23:56:34Z karl$ # # Experimental awk-script for conversion of tpic \\specials as produced # by (groff-)pic into pdfTeX \\pdfliteral sections for further processing # by pdftex. # # Usage: # $pic -t somefile.pic | tpic2pdftex > somefile.tex # # Process somefile.tex by pdftex/pdflatex. # # tpic \\special desciption see e. g.: # Goossens, Rahtz, Mittelbach: The LaTeX Graphics Companion, # Addison-Wesley, 1997, pp. 464. # # Bugs: # Spline curve shapes not fully authentic (unknown algorithm). # Bounding box does not care for line thickness (groff pic feature). # Splines might be outside bounding box. # # Copyright (C) 2002--2013 by Hartmut Henkel # # This program is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation; either version 2 of the License, or (at # your option) any later version. # # This program is distributed in the hope that it will be useful, but # WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. # See the GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see . # # The author may be contacted via the e-mail address # # hartmut_henkel@gmx.de # # NEWS: # 11 Jun. 2011 - sh construct portability # (patch from Nelson Beebe) # 24 Dec. 2009 - use gawk for default awk only if it exists # (patch by Karl Berry). # 14 Jan. 2007 - make it executable shell script, calling awk # 16 Dec. 2004 - Replaced // {print} by {print} (some AWKs did choke) # 09 Apr. 2004 - Locale check: Decimal point in float numbers? # 30 Oct. 2003 - Replaced print statements by printf to avoid # underflow numbers like 1e-14 in \\pdfliterals. Remove trailing # zeroes of floating point numbers. # 02 May 2003 - Lines starting with \\ allow TeX insertions, # e. g. of pdfTeX \\pdfliteral{} # 29 Apr. 2003 - Changed for pic of groff 1.19 # 16 Mar. 2003 - Bug corrected: Dashed lines shorter than minimum # dash-pause length now drawn solid. # 11 Nov. 2002 - Spline drawing improved: First half of first and last # half of last spline segments are drawn by straight lines. # 28 Nov. 2002 - Arc and circle drawing cleaned up. Full circle is now # drawn by 4 Bezier curves, as is common use. Arcs split evenly into # Bezier curves, to minimize max. error. # 02 Dec. 2002 - Experimental pic (groff > 1.18.1) with improved # vertical picture positioning supported. # 04 Dec. 2002 - Experiment with modified pic (\\vtop -> \\vbox), # Formula for Bezier constant c reduced. # ######################################################################## # In case someone pedantic insists on using grep -E. :${EGREP=egrep}} # Systems which define $COMSPEC or$ComSpec use semicolons to separate # directories in TEXINPUTS -- except for Cygwin et al., where COMSPEC # might be inherited, but : is used. if test -n \"$COMSPEC$ComSpec\" \\ && uname | $EGREP -iv 'cygwin|mingw|djgpp' >/dev/null; then path_sep=\";\" else path_sep=\":\" fi # findprog PROG # ------------- # Return true if PROG is somewhere in PATH, else false. findprog () { local saveIFS=\"$IFS\" IFS=$path_sep # break path components at the path separator for dir in$PATH; do IFS=$saveIFS # The basic test for an executable is test -f$f && test -x $f'. # (test -x' is not enough, because it can also be true for directories.) # We have to try this both for$1 and $1.exe. # # Note: On Cygwin and DJGPP, test -x' also looks for .exe. On Cygwin, # also test -f' has this enhancement, bot not on DJGPP. (Both are # design decisions, so there is little chance to make them consistent.) # Thusly, it seems to be difficult to make use of these enhancements. # if { test -f \"$dir/$1\" && test -x \"$dir/$1\"; } || { test -f \"$dir/$1.exe\" && test -x \"$dir/$1.exe\"; }; then return 0 fi done return 1 } if test -z \"$AWK\"; then # if set by user, leave it. if findprog gawk; then AWK=gawk else AWK=awk fi fi unset LANG; unset LANGUAGE LC_ALL=C; export LC_ALL AWKPROG=' # begin of awk input file function qprintf(a) { gsub(/0* /,\" \", a); # trailing zeroes in %f gsub(/\\. /,\" \", a); # orphaned decimal dots gsub(/0*]/,\"]\", a); # trailing zeroes in brackets gsub(/0X/,\"0\", a); # guard integer zeroes gsub(/-0 /,\"0 \", a); # correct -0 to 0 print a; } function startpdfliteral() { if (pdfliteral == 0) { print \"\\\\pdfliteral{\"; printf(\"q [] 0 d %d J %d j\\n\", linecap, linejoin); # no qprintf! qprintf(sprintf(\"%f w\", linethickness * wscale)); } pdfliteral = 1; } function stoppdfliteral() { if (pdfliteral == 1) { print \"Q\"; print \"}%\"; } pdfliteral = 0; } ######################################################################## BEGIN{ wscale = 72.0 / 1000; tpicmode = 0; pdfliteral = 0; pointbuf = 0; filled = 0; fillval = 0; linecap = 1; linejoin = 1; defaultlinethickness = 8; drawarc = 0; pi = atan2(0, -1); if (match(sprintf(\"%f\", 0.5), /\\./) == 0) { print \"ERROR: Floating point numbers miss decimal point. Do\" print \" LC_ALL=\\\"C\\\"; export LC_ALL; unset LANGUAGE\" print \"before calling awk.\" print \"ERROR: Floating point numbers miss decimal point. Do\" > \"/dev/stderr\" print \" LC_ALL=\\\"C\\\"; export LC_ALL; unset LANGUAGE\" > \"/dev/stderr\" print \"before calling awk.\" > \"/dev/stderr\" exit 1; } } ######################################################################## # the following expression triggers tpic processing for pic <= 1.18.1 /^\\\\setbox\\\\graph=\\\\vtop{/ { pdfliteral = 0; tpicmode = 1; linethickness = defaultlinethickness; } # the following expression triggers tpic processing for pic = 1.19 /^\\\\expandafter\\\\setbox\\\\csname graph\\\\endcsname/ { pdfliteral = 0; tpicmode = 1; linethickness = defaultlinethickness; } # TeX parts end \\pdfliteral, and also TeX parts embedded in .PS ... .PE # section end \\pdfliteral /^ *\\\\graphtemp|^ *\\\\rlap|^ *\\\\advance|^\\\\|^ *\\\\hbox/ { if(tpicmode == 1) stoppdfliteral(); } /^}%/ { if(tpicmode == 1) tpicmode = 0; } ######################################################################## # all specials handling /^ *\\\\special/ { if(tpicmode == 1) startpdfliteral(); } # set pen size /^ *\\\\special{pn/ { gsub(/[{}]/, \" \"); linethickness = $3 + 0; qprintf(sprintf(\"%f w\", linethickness * wscale)); next; } # add point to path /^ *\\\\special{pa/ { gsub(/[{}]/, \" \"); x[pointbuf] =$3 + 0; y[pointbuf] = $4 + 0; pointbuf++; next; } # print path as straight lines /^ *\\\\special{fp/ { if (filled == 1) qprintf(sprintf(\"q %f g\", 1 - fillval)); qprintf(sprintf(\"%f %f m\", x * wscale, -y * wscale)); for (i = 1; i < pointbuf; i++) qprintf(sprintf(\"%f %f l\", x[i] * wscale, -y[i] * wscale)); if (filled == 1) print \"B Q\"; else print \"S\"; pointbuf = 0; filled = 0; next; } # print path as straight dashed lines /^ *\\\\special{da/ { gsub(/[{}]/, \" \"); don = ($3 + 0) * 1000; if (filled == 1) { qprintf(sprintf(\"q %f g\", 1 - fillval)); qprintf(sprintf(\"%f %f m\", x * wscale, -y * wscale)); for (i = 1; i < pointbuf; i++) qprintf(sprintf(\"%f %f l\", x[i] * wscale, -y[i] * wscale)); print \"f Q\"; } for (i = 1; i < pointbuf; i++) { dx = x[i] - x[i - 1]; dy = y[i] - y[i - 1]; len = sqrt(dx * dx + dy * dy); non = int(0.5 * len / don + 0.75); noff = non - 1; lon = don * non; loff = len - lon; if(noff > 0) { doff = loff / noff; qprintf(sprintf(\"q [%f %f] 0X d\", don * wscale, doff * wscale)); } else { print \"q [] 0 d\"; } qprintf(sprintf(\"%f %f m\", x[i - 1] * wscale, -y[i - 1] * wscale)); qprintf(sprintf(\"%f %f l\", x[i] * wscale, -y[i] * wscale)); print \"S Q\"; } pointbuf = 0; filled = 0; next; } #\nprint path as straight dotted lines /^ *\\\\special{dt/ { gsub(/[{}]/, \" \"); dt = ($3 + 0) * 1000; if (filled == 1) { qprintf(sprintf(\"q %f g\", 1 - fillval)); qprintf(sprintf(\"%f %f m\", x * wscale, -y * wscale)); for (i = 1; i < pointbuf; i++) qprintf(sprintf(\"%f %f l\", x[i] * wscale, -y[i] * wscale)); print \"f Q\"; } for (i = 1; i < pointbuf; i++) { dx = x[i] - x[i - 1]; dy = y[i] - y[i - 1]; len = sqrt(dx * dx + dy * dy); dl = int (len / dt + 0.5); if (!dl) dtl = len; else dtl = len / dl; qprintf(sprintf(\"q [0X %f] 0X d\", dtl * wscale)); qprintf(sprintf(\"%f %f m\", x[i - 1] * wscale, -y[i - 1] * wscale)); qprintf(sprintf(\"%f %f l\", x[i] * wscale, -y[i] * wscale)); print \"S Q\"; } pointbuf = 0; filled = 0; next; } # like , but path actually not drawn /^ *\\\\special{ip/ { if (filled == 1) qprintf(sprintf(\"q %f g\", 1 - fillval)); qprintf(sprintf(\"%f %f m\", x * wscale, -y * wscale)); for (i = 1; i < pointbuf; i++) qprintf(sprintf(\"%f %f l\", x[i] * wscale, -y[i] * wscale)); if (filled == 1) print \"f Q\"; else print \"f\"; pointbuf = 0; filled = 0; next; } # like , but path printed as splines /^ *\\\\special{sp/ { gsub(/[{}]/, \" \"); don = ($3 + 0) * 1000; a = 0.68; # fudge, visually optimized x[pointbuf] = x[pointbuf - 1]; y[pointbuf] = y[pointbuf - 1]; if (don > 0) qprintf(sprintf(\"q [%f] 0X d\", don * wscale)); if (don < 0) qprintf(sprintf(\"q [0X %f] 0X d\", -don * wscale)); qprintf(sprintf(\"%f %f m\", x * wscale, -y * wscale)); if(pointbuf < 3) qprintf(sprintf(\"%f %f l\", x[pointbuf - 1] * wscale, -y[pointbuf - 1] * wscale)); else { qprintf(sprintf(\"%f %f l\", 0.5 * (x + x) * wscale, \\ -0.5 * (y + y) * wscale)); # start straight, see cstr116.ps for (i = 1; i < pointbuf - 1; i++) qprintf(sprintf(\"%f %f %f %f %f %f c\", \\ (a * x[i] + (1 - a) * 0.5 * (x[i] + x[i - 1])) * wscale, \\ -(a * y[i] + (1 - a) * 0.5 * (y[i] + y[i - 1])) * wscale, \\ (a * x[i] + (1 - a) * 0.5 * (x[i] + x[i + 1])) * wscale, \\ -(a * y[i] + (1 - a) * 0.5 * (y[i] + y[i + 1])) * wscale, \\ 0.5 * (x[i] + x[i + 1]) * wscale, -0.5 * (y[i] + y[i + 1]) * wscale)); qprintf(sprintf(\"%f %f l\", x[pointbuf - 1] * wscale, -y[pointbuf - 1] * wscale)); } if (filled == 1) { qprintf(sprintf(\"q %f g\", 1 - fillval)); print \"B Q\"; } else print \"S\"; if (don != 0) print \"Q\"; pointbuf = 0; filled = 0; next; } # prepare shading of object interior /^ *\\\\special{sh/ { gsub(/[{}]/, \" \"); fillval = $3 + 0; filled = 1; next; } # draw arc # like , but arc actually not drawn /^ *\\\\special{ar/ { drawarc = 1; } /^ *\\\\special{ar|^ *\\\\special{ia/ { gsub(/[{}]/, \" \"); xc =$3 + 0; yc = $4 + 0; rx =$5 + 0; ry = $6 + 0; s =$7 + 0; e = $8 + 0; if (e - s > 2 * pi) e = s + 2 * pi; if (s - e > 2 * pi) e = s - 2 * pi; curvespercircle = 4; # max. number Bezier curves per circle phi_max = 1.001 * 2 * pi / curvespercircle; if (e > s) imax = int ((e - s) / phi_max) + 1; else imax = int ((s - e) / phi_max) + 1; phi = (e - s) / imax; # parameter for Bezier control vectors, c(90 deg.) = 0.55228...: c = 4 * (1 - cos(0.5 * phi)) / (3 * sin(0.5 * phi)); x0 = rx * cos(s) + xc; y0 = ry * sin(s) + yc; qprintf(sprintf(\"%f %f m\", x0 * wscale, -y0 * wscale)); for (i = 0; i < imax; i++) { x1 = x0 - rx * c * sin(s + i * phi); y1 = y0 + ry * c * cos(s + i * phi); x3 = rx * cos(s + (i + 1) * phi) + xc; y3 = ry * sin(s + (i + 1) * phi) + yc; x2 = x3 + rx * c * sin(s + (i + 1) * phi); y2 = y3 - ry * c * cos(s + (i + 1) * phi); qprintf(sprintf(\"%f %f %f %f %f %f c\", x1 * wscale, -y1 * wscale, \\ x2 * wscale, -y2 * wscale, x3 * wscale, -y3 * wscale)); x0 = x3; y0 = y3; } if(drawarc == 1) { if (filled == 1) { qprintf(sprintf(\"h q %f g\", 1 - fillval)); print \"B Q\"; } else print \"S\"; } else { if (filled == 1) { qprintf(sprintf(\"h q %f g\", 1 - fillval)); print \"f Q\"; } else print \"f\"; } filled = 0; drawarc = 0; next; } ######################################################################## {print} ######################################################################## ' # end of awk input file$AWK \"$AWKPROG\" \"$@\""
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.5197809,"math_prob":0.97975045,"size":11578,"snap":"2022-40-2023-06","text_gpt3_token_len":4091,"char_repetition_ratio":0.19630206,"word_repetition_ratio":0.25216597,"special_character_ratio":0.44714114,"punctuation_ratio":0.19005328,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99363387,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-02-09T09:05:57Z\",\"WARC-Record-ID\":\"<urn:uuid:b69fe134-0f9b-46f8-8d00-3031774c49e2>\",\"Content-Length\":\"12883\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:abc23b71-78af-4c09-a005-1d6279f9edb6>\",\"WARC-Concurrent-To\":\"<urn:uuid:132fd8d7-c3fa-4591-b2d8-121aed493758>\",\"WARC-IP-Address\":\"81.182.200.252\",\"WARC-Target-URI\":\"https://mirror.szerverem.hu/ctan/graphics/tpic2pdftex/tpic2pdftex\",\"WARC-Payload-Digest\":\"sha1:K7QU3QJQ2RI3NWKOTWMFDAIL4QHIWBQV\",\"WARC-Block-Digest\":\"sha1:JEBTXAWXXWMT5L5WLU62CZ3DIL2TI62V\",\"WARC-Identified-Payload-Type\":\"application/x-sh\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-06/CC-MAIN-2023-06_segments_1674764501555.34_warc_CC-MAIN-20230209081052-20230209111052-00036.warc.gz\"}"} |
http://currency7.com/bob-to-uzs-exchange-rate-converter | [
"# Currency Converter · Bolivian Boliviano (BOB) to Uzbekistani Som (UZS)\n\nThe currency calculator will convert exchange rate of Bolivian boliviano (BOB) to Uzbekistani som (UZS).\n\n• Bolivian boliviano\nThe Bolivian boliviano (BOB) is the currency of Bolivia. The currency code is BOB and currency symbol is Bs. The Bolivian boliviano is subdivided into 100 centavos (singular: centavo; symbol: Cvs.). Frequently used Bolivian boliviano coins are in denominations of Bs.1, Bs.2, Bs.5, 10 centavos, 20 centavos, 50 centavos. Frequently used Bolivian boliviano banknotes are in denominations of Bs.10, Bs.20, Bs.50, Bs.100, Bs.200.\n• Uzbekistani som\nThe Uzbekistani som (UZS) is the currency of Uzbekistan. The currency code is UZS and currency symbol is лв. The Uzbekistani som is subdivided into 1 tiyin (singular: tiyin, not in circulation). The word som sometimes is transliterated as sum or soum. Frequently used Uzbekistani som coins are in denominations of 1 som, 5 som, 10 som, 25 som, 50 som, 100 som. Frequently used Uzbekistani som banknotes are in denominations of 1 som, 3 som, 5 som, 10 som, 25 som, 50 som, 100 som, 200 som, 500 som, 1000 som.\n• 1 BOB = 1,765.30 UZS\n• 2 BOB = 3,530.60 UZS\n• 3 BOB = 5,295.91 UZS\n• 5 BOB = 8,826.51 UZS\n• 10 BOB = 17,653.02 UZS\n• 20 BOB = 35,306.04 UZS\n• 25 BOB = 44,132.55 UZS\n• 50 BOB = 88,265.09 UZS\n• 100 BOB = 176,530.18 UZS\n• 200 BOB = 353,060.37 UZS\n• 250 BOB = 441,325.46 UZS\n• 300 BOB = 529,590.55 UZS\n• 500 BOB = 882,650.92 UZS\n• 600 BOB = 1,059,181.10 UZS\n• 1,000 BOB = 1,765,301.83 UZS\n• 100 UZS = 0.06 BOB\n• 500 UZS = 0.28 BOB\n• 1,000 UZS = 0.57 BOB\n• 5,000 UZS = 2.83 BOB\n• 10,000 UZS = 5.66 BOB\n• 20,000 UZS = 11.33 BOB\n• 50,000 UZS = 28.32 BOB\n• 80,000 UZS = 45.32 BOB\n• 100,000 UZS = 56.65 BOB\n• 200,000 UZS = 113.30 BOB\n• 500,000 UZS = 283.24 BOB\n• 1,000,000 UZS = 566.48 BOB\n• 2,000,000 UZS = 1,132.95 BOB\n• 5,000,000 UZS = 2,832.38 BOB\n• 10,000,000 UZS = 5,664.75 BOB\n\n## Popular BOB pairing\n\n` <a href=\"http://currency7.com/BOB-to-UZS-exchange-rate-converter?amount=300\">300 BOB in UZS</a> `"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.544185,"math_prob":0.99660087,"size":3127,"snap":"2023-40-2023-50","text_gpt3_token_len":1201,"char_repetition_ratio":0.2715338,"word_repetition_ratio":0.054104477,"special_character_ratio":0.3684042,"punctuation_ratio":0.18604651,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9691061,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-27T06:17:49Z\",\"WARC-Record-ID\":\"<urn:uuid:93ad3a74-6457-4771-925b-77938d8b8deb>\",\"Content-Length\":\"29487\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6f6c8460-f310-420d-8b71-67d545d779e0>\",\"WARC-Concurrent-To\":\"<urn:uuid:5540ef23-3b20-4d45-9dc0-03a49ce7d3b0>\",\"WARC-IP-Address\":\"70.35.206.41\",\"WARC-Target-URI\":\"http://currency7.com/bob-to-uzs-exchange-rate-converter\",\"WARC-Payload-Digest\":\"sha1:3KLKJOOIRJ2WEWXELUGZ3SF6R4NGG464\",\"WARC-Block-Digest\":\"sha1:IJ2MQSPSWZW35WWELHATPF7XKURDZYB5\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510259.52_warc_CC-MAIN-20230927035329-20230927065329-00339.warc.gz\"}"} |
http://www.tribonet.org/wiki/elastic-deformation/ | [
"# Elastic Deformation\n\nTribology Wikipedia > Elastic Deformation\n\n## Definition\n\nElastic deformation is a change of the shape of the body as a reaction to applied stress. This deformation is only temporary and once the stress is released, the undeformed shape of the body is restored, as shown in the figure below. In tribology, elastic deformation largely affects elastohydrodynamic film thickness build up, real contact area, etc. A problem of determination of elastic deformation in various scenarios is considered in the classical (linear elasticity) Elasticity Theory book by Timoshenko and Goodier .",
null,
"Elastic deformation explained in the video:\n\n## Application\n\nIn the field of tribology, the most commonly studied configuration of contact is the contact of a sphere or a cylinder with a flat (the contact of two spheres or two cylinders can be reduced to the contact on flat). In this case, a half-space approximation is applicable and the full system of Elasticity Theory equations can be solved analytically to link the elastic deflection of the surface to the applied pressure on the surface . The resultant equation is given in integral form:\n\n(1)",
null,
"Here",
null,
"is the elastic deflection,",
null,
"is the reduced elastic modulus,",
null,
"are the Poisson’s ratio and Young’s modulus of the bodies,",
null,
"is the contact pressure. This equation is used in most of tribological problems, including EHL problems, but also in contact analysis, friction and wear simulation. Further information regarding the application of the equation can be found in the reference .\n\n Theory of Elasticity, Timoshenko, S.P., Goodier, J.N., 1970.\n\n On a Model for the Prediction of the Friction Coefficient in Mixed Lubrication Based on a Load-Sharing Concept with Measured Surface Roughness, Aydar Akchurin,Rob Bosman, Piet M. Lugt, Mark van Drogen.\n\nSave\n\nSave\n\n•\n•\n•\n•"
] | [
null,
"http://www.tribonet.org/wp-content/plugins/native-lazyload/assets/images/placeholder.svg",
null,
"http://www.tribonet.org/wp-content/plugins/native-lazyload/assets/images/placeholder.svg",
null,
"http://www.tribonet.org/wp-content/plugins/native-lazyload/assets/images/placeholder.svg",
null,
"http://www.tribonet.org/wp-content/plugins/native-lazyload/assets/images/placeholder.svg",
null,
"http://www.tribonet.org/wp-content/plugins/native-lazyload/assets/images/placeholder.svg",
null,
"http://www.tribonet.org/wp-content/plugins/native-lazyload/assets/images/placeholder.svg",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.91826683,"math_prob":0.9215317,"size":1685,"snap":"2019-51-2020-05","text_gpt3_token_len":351,"char_repetition_ratio":0.15942891,"word_repetition_ratio":0.0,"special_character_ratio":0.19643916,"punctuation_ratio":0.11363637,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97199774,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-10T05:32:20Z\",\"WARC-Record-ID\":\"<urn:uuid:8de5861a-7e4b-4d7b-839d-ed06a219586f>\",\"Content-Length\":\"125824\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1661e997-d3b5-46ed-b7e9-12a0b5328157>\",\"WARC-Concurrent-To\":\"<urn:uuid:3ad57e68-db01-4589-abd6-a0c72e1fec96>\",\"WARC-IP-Address\":\"104.27.144.108\",\"WARC-Target-URI\":\"http://www.tribonet.org/wiki/elastic-deformation/\",\"WARC-Payload-Digest\":\"sha1:IAWAONU3IZJNX2UEB2I7RBKP33GDDFJC\",\"WARC-Block-Digest\":\"sha1:IUELHQ4M6VKYAVH6YLACSBQ2CZWDEG5C\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575540525821.56_warc_CC-MAIN-20191210041836-20191210065836-00362.warc.gz\"}"} |
https://mathoverflow.net/questions/115442/persistent-homology-of-gaussian-fields-in-euclidean-space | [
"# Persistent homology of Gaussian fields in Euclidean space\n\nIf you generate points in $$\\mathbb R^n$$ via a process that respects a Gaussian normal distribution, then compute the persistent homology / barcodes, to my eye something fairly regular seems to be happening, with the barcodes tending towards something like a \"wing\" shape, fat in lower dimensions, thinning out towards dimension $$n$$.\n\nHas anyone proven any theorems that describe the asymptotic \"shape\" of the barcodes?\n\nIdeally I'd like a test so that I can look at some barcodes and say \"that's typical of a Gaussian normal distribution\".\n\nThe closest thing I've been able to find is experiments and results on the expected Euler characteristic of the persistent homology, in the following two references (arXiv links): Persistent homology for random fields and complexes, Euler integration of Gaussian random fields and persistent homology.\n\nEdit:\n\nI did a very rough computation to try and get some kind of guess as to what the distribution of barcodes should look like. So I made a very coarse estimate based on a distribution of points that is roughly locally cubical' and approximately respecting a normal distribution.\n\nThe density is given by:\n\n$$\\mu = N e^{-r^2}$$\n\nwhere $$r$$ is the distance from the origin. Then if $$\\epsilon$$ is the parameter for persistent homology, it appears that $$H_0$$ is rank approximately\n\n$$N \\int_{\\sqrt{\\ln(N\\epsilon^{1/n})}}^\\infty r^{n-1}e^{-r^2} dr$$\n\nand $$H_k$$ for $$k \\in \\{1,2,\\cdots,n-1\\}$$ has rank approximately\n\n$${n \\choose k+1}\\frac{(\\sqrt{\\ln(N\\epsilon^{1/n}/\\sqrt{k}))}^{n-2}}{4\\sqrt{k}\\epsilon^{1/n}}$$\n\nThese are fairly coarse estimates, and in no way rigorous. But if something like this is actually true it seems to be saying that for $$N$$ large and $$n \\geq 3$$, the $$H_0$$ betti number tends to some asymptote (dependent on $$\\epsilon$$), and $$H_1, \\cdots, H_{n-1}$$ are non-trivial but small. So most of the points in the distribution are in a giant homology black hole' at the centre and persitent homology sees the thin crust around the outside.\n\nI'd be curious if people have done other similar guestimates (or better) and if they had similar-looking results.\n\n• I suspect Adler's work is the state of the art on marrying random fields or their ilk with persistent homology...You should bear in mind that a high-dimensional Gaussian contains almost all its mass in a thin spherical shell far from the origin. The concomitant sparsity of the samples away from the shell will manifest in the Vietoris-Rips complex. Does your wing look like what you'd get with points on a big sphere? – Steve Huntsman Dec 4 '12 at 22:39\n• Presumably the cycles in the homology will predominantly sit in thin spherical layers, fairly far out on the bell-curve, so to speak. The $H_0$ classes will be on the most distant spherical shell, the $H_1$ classes next closest, then the $H_n$ classes will be in the central most spherical shell before all the homology vanishes in the core of the distribution. The main issue is the relative thickness of the shells I would imagine. – Ryan Budney Dec 4 '12 at 23:06\n• I'm surprised no one has asked this yet, but: how many sample points? If you have only one sample point, the barcode is not goint to be terribly hard to describe. Perhaps by asymptotic behavior you mean \"let the sample size go to infinity\" at which point generically nothing survives for too long. In short, I don't see a sample size invariant answer to your question that is also interesting. What do you have in mind? – Vidit Nanda Dec 7 '12 at 0:26\n• Vel, I'm not asking for a precise prediction of homology classes, but just a general prediction of the shape of the barcodes. Interpret that broadly -- it can be a request for the expected proportion of various Betti numbers, for example. Also, it doesn't have to be an asymptotic prediction -- the prediction could depend on the sample size and it's fine to say \"with a sampling of N points one would expect barcodes in this range, X times out of Y\", etc. – Ryan Budney Dec 7 '12 at 1:27\n• If you think of a Gaussian distribution of points in $\\mathbb R^n$ as something of a probabilistic version of an $n$-dimensional $0$-handle, you could think of this question as something like \"persistent homology is the first instance of a probabilistic homology theory, so what are its coefficients?\" – Ryan Budney Dec 7 '12 at 1:29"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.89967924,"math_prob":0.9781044,"size":2102,"snap":"2020-45-2020-50","text_gpt3_token_len":536,"char_repetition_ratio":0.115824595,"word_repetition_ratio":0.0,"special_character_ratio":0.2492864,"punctuation_ratio":0.07614213,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99685794,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-10-25T14:54:26Z\",\"WARC-Record-ID\":\"<urn:uuid:b97b24a6-2783-4263-841d-2df0a3b5f8f2>\",\"Content-Length\":\"152242\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6278fabb-5bc9-476b-a621-86e6e5d38788>\",\"WARC-Concurrent-To\":\"<urn:uuid:0b2ab8c7-1166-48b9-a7f5-05c62707001b>\",\"WARC-IP-Address\":\"151.101.193.69\",\"WARC-Target-URI\":\"https://mathoverflow.net/questions/115442/persistent-homology-of-gaussian-fields-in-euclidean-space\",\"WARC-Payload-Digest\":\"sha1:6XZSGGXH5PJWTBDBAYP2IGLSWJEVO43S\",\"WARC-Block-Digest\":\"sha1:HT7QIYCIREQZAFPPSTRBP27DO6N3GD4V\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-45/CC-MAIN-2020-45_segments_1603107889173.38_warc_CC-MAIN-20201025125131-20201025155131-00276.warc.gz\"}"} |
https://www.igi-global.com/article/multiobjective-transportation-problem-using-fuzzy-decision-variable-through-multi-choice-programming/183692 | [
"",
null,
"# Multiobjective Transportation Problem Using Fuzzy Decision Variable Through Multi-Choice Programming\n\nGurupada Maity (Vidyasagar University, Department of Applied Mathematics with Oceanology and Computer Programming, Midnapore, India) and Sankar Kumar Roy (Vidyasagar University, Department of Applied Mathematics with Oceanology and Computer Programming, Midnapore, India)\nDOI: 10.4018/IJORIS.2017070105\n\n## Abstract\n\nThis paper analyzes the study of Multiobjective Transportation Problem (MOTP) under the consideration of fuzzy decision variable. Usually, the decision variable in a Transportation Problem is taken as real variable. But, in this paper, the decision variable in each node is selected from a set of multi-choice fuzzy numbers. Inclusion of multiple objectives into transportation problem with fuzzy decision variable makes it a Multiobjective Fuzzy Transportation Problem (MOFTP). In this paper, a new formulation of mathematical model of MOFTP with fuzzy goal of each objective function is enlisted. Thereafter the solution technique of the formulated model is described through multi-choice goal programming approach. Finally, a numerical example is presented to show the feasibility and usefulness of this article.\nArticle Preview\nTop\n\n## Introduction\n\nTransportation problem acts an important role for decision-making problem to cover the real-life situations. The transportation problem can be delineated as a special case of a linear programming problem and its model is used to determine an optimal solution of the decision-making problem. The classical transportation problem determines how many units of a commodity are to be shipped from each point of origin to various destinations, satisfying source availabilities and destination demands, while minimizing the total cost of transportation along with cutting down the costs per unit of items for the purchasers.\n\nThe basic transportation problem was originally developed by Hitchcock (1941) and later developed independently by Koopmans (1949). Transportation problem with single objective function is not enough to tackle various real-life decision-making problems due to our present competitive market scenario. So, we have to introduce multiobjective transportation problem to accommodate such real-life situations. A good number of works in this ground has been done by several researchers like Verma et al. (1997), Waiel (2001), Mahapatra et al. (2010), Datta et al. (2010), Roy and Mahapatra (2011), Das et al. (2011), Mahapatra et al. (2013), Midya and Roy (2014), Beauchamp et al. (2015), Maity and Roy (2016) and many others.\n\nInitially, fuzzy set theory has been considered as a tool to solve multiobjective optimization problems (Zimmerman 1978). Furthermore, the notion of fuzzy numbers is introduced in the transportation parameters (cost, supply and demand) of a transportation problem to make it a fuzzy transportation problem. Kumar and Kaur (2011) developed a methodology for solving fuzzy transportation problems based on classical transportation methods. Ebrahimnejad et al. (2011) proposed an algorithm for bounded linear programming with fuzzy cost coefficients in a decision-making problem. Marbini et al. (2011) introduced an interactive approach on data envelopment analysis with fuzzy parameters. A study on multi-criteria futuristic fuzzy decision hierarchy and its application in a tourism industry has been presented by Singh et al. (2015). Pattnaik (2015) incorporated a study on decision-making approach to fuzzy linear programming (FLP) problems with post optimal analysis. Kumar and Hussain (2016) presented a simple methodology for solving a real-life assignment problem under intuitionistic fuzzy environment. To the best of our knowledge, no one has been introduced the concept of decision variable in transportation problem as fuzzy variable. Here, we assume that the expectations in the destinations of transportation problem are fuzzy numbers and they are treated as fuzzy goals. In the destinations, there are multi-choice fuzzy expectations. In this situation, decision maker would have to take a decision of supplying goods in such a way that the profit would maximize, keeping the best possible fulfillment of requirement at the destinations. Again, it is not necessarily true that in a transportation problem at each node there is an allocation, it depends on the best fit of the problem. In this case, when there is no need of allocation in a cell, then we assign a crisp goal “0” with high priority value. In our proposed transportation problem, the requirement in the allocated cells are one among a multi-choice fuzzy numbers along with “0”. With this assumption, we design a transportation problem whose decision variables are fuzzy. This situation of decision-making problem is solved using the multi-choice goal programming approach.\n\n## Complete Article List\n\nSearch this Journal:\nReset\nOpen Access Articles: Forthcoming\nVolume 11: 4 Issues (2020): 1 Released, 3 Forthcoming\nVolume 10: 4 Issues (2019)\nVolume 9: 4 Issues (2018)\nVolume 8: 4 Issues (2017)\nVolume 7: 4 Issues (2016)\nVolume 6: 4 Issues (2015)\nVolume 5: 4 Issues (2014)\nVolume 4: 4 Issues (2013)\nVolume 3: 4 Issues (2012)\nVolume 2: 4 Issues (2011)\nVolume 1: 4 Issues (2010)\nView Complete Journal Contents Listing"
] | [
null,
"https://coverimages.igi-global.com/cover-images/covers/ijoris.png",
null
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https://facesofberlin.org/challenging-mathematical-problems-with/ | [
"HomeWorksheet Ideas ➟ 0 Challenging Mathematical Problems With\n\n# Challenging Mathematical Problems With\n\nChallenging Mathematical Problems With. Indeed, some rank among the finest achievements of outstanding mathematicians. Number talks grades 3 5 resources bps.\n\nPublication date 1964 topics mathematics, problem book, soviet, chessboard problems, combinatorial problems, probability theory, combinatorial analysis, binomial coefficients, problems and solutions, problems of many possible outcomes,. Indeed, some rank among the finest achievements of outstanding mathematicians. 3 dimension 1 scientific and engineering practices a.\n\n### Indeed, Some Rank Among The Finest Achievements Of Outstanding Mathematicians.\n\nNumber talks grades 3 5 resources bps. Hundreds of challenging math problems worth solving. Publication date 1964 topics mathematics, problem book, soviet, chessboard problems, combinatorial problems, probability theory, combinatorial analysis, binomial coefficients, problems and solutions, problems of many possible outcomes,.\n\n### The Page Counts Are About 20% Problem Statements, 5% Hints, And 75% Complete Solutions.\n\nFifty challenging problems in probability with solutions. The same time, be interesting and sometimes challenging to the undergraduate and the more advanced mathematician. The mathematical practices that are in the college and career readiness standards for adult education define what it means to be a mathematically proficient student.\n\n### Fifty Challenging Problems In Probability With Solutions.\n\nThe problems, most of which can be solved with elementary mathematics, range from relatively simple to extremely difficult. These books are often cited in connection with the moscow mathematical olympiads, but although a few problems are taken from that source, most of the results are familiar pieces of mathematics and not problems cooked up for a competition. It is believed that these mathematics competition problems are a positive influence on the learning and enrichment of mathematics.\n\n### In This Post, We Will See The Two Volume Set Of Challenging Mathematical Problems With Elementary Solution By A.\n\nChallenging mathematical problems with elementary solutions books in the mathematical sciences. Challenging mathematical problems with elementary solutions vol. 3 dimension 1 scientific and engineering practices a.\n\n### Challenging Mathematical Problems With Elementary.\n\nMore than 20 000 mathematics contest problems and solutions. Suitable for students, teachers, and any lover of mathematics. As adult education instructors, our job is to help our students navigate over the swells in the tempest of their angst until."
] | [
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https://mattermodeling.stackexchange.com/questions/6160/help-with-translating-hamiltonian-into-matrix | [
"# Help with translating Hamiltonian into matrix\n\nEq. 19 in this paper gives the following Hamiltonian:",
null,
"$$\\sigma_a, \\tau_a, \\eta_a$$ are respectively the spin, sublattice pseudospin and valley pseudospin respectively.\n\nNormally, I would have chosen a basis convention such as $$\\sigma_a, \\tau_a, \\eta_a$$ and plugged in the $$2\\times 2$$ identity matrix for terms that don't appear above. Then I would have taken the Kronecker Delta product. However, in this case, the authors explicitly define $$(s_z,\\tau_z\\,\\eta_z)=(\\pm 1, \\pm 1, \\pm 1)$$ for $$($$up/down, sublattice A/B, valley K/K'$$)$$ respectively. So, as a relatively inexperienced person in the field, I feel like there is some ambiguity. I am having trouble translating the above into a matrix that I can play with numerically. Can someone help me understand the convention here?\n\nI tried two interpretations in Python. np.kron takes the Kronecker product. First attempt:\n\n# Choose basis: (tau_xy, sigma_xyz), replace sz, tauz, etaz by s, tau, eta = +/- 1\n# Gives 4-band model, with eye = identity and s_xyz as Pauli matrices\neta = 1; # instead of using eta_z as the Pauli z matrix\nh1=h*vf*(eta*kx*np.kron(sx,eye)+ky*np.kron(sy,eye)) # e-e hoppings\nh2=lSO*eta*np.kron(eye,sz)*tau # SO coupling\nh3=m*np.kron(eye,sz)*tau # break TRS (AFM exchange mag.)\nH = h1+h2+h3\n\n\nSecond:\n\n# Choose basis: (eta, sigma, tau) using Pauli matrices for all, but no +/- 1 values.\n# Gives 8-band model.\nh1=h*vf*(kx*np.kron(sz,np.kron(eye,sx))+ky*np.kron(eye,np.kron(eye,sy))) # e-e hoppings\nh2=lSO*np.kron(sz,np.kron(sz,sz)) # SO coupling\nh3=m*np.kron(eye,np.kron(sz,sz))# break TRS (AFM exchange mag.)\nH = h1+h2+h3\n\n\nBoth of these seem to give me very weird Berry curvature fields when plotted. So, I figured I am doing something wrong. Note: I set $$v_F = 1, \\hbar=1$$.\n\nFor this type of calculation, I find MATLAB/Octave to be easier, at least for demonstrating what to do. You can add the np. everywhere afterwards if you want to use Python.\n\n$$\\eta_z$$ = eta\n$$\\tau_x$$ = taux\n$$\\tau_y$$ = tauy\n$$\\tau_z$$ = tauz\n$$m_z$$ = tauz\n$$\\sigma_z$$ = sigmaz,\n\nand the following scalars:\n\n$$\\hbar$$ = hbar\n$$v_F$$ = v\n$$\\lambda_{\\textrm{SO}}$$ = lambda,\n$$k_x$$ = kx\n$$k_y$$ = ky,\n\nthe matrix would typically be calculated in the following manner:\n\neta=kron(kron(kron(eta,eye(length(mz)),eye(length(sigmaz)),eye(length(tauz));\nmz=kron(kron(eye(length(eta)),mz),eye(length(mz)+length(sigmaz)+length(tauz)))));\nsigmaz=kron(kron(eye(length(eta)+length(mz)),sigmaz),eye(length(tauz)));\ntauz=(kron(eye(length(eta)+length(mz)+length(sigmaz)),tauz)));\ntaux=(kron(eye(length(eta)+length(mz)+length(sigmaz)),taux)));\ntauy=(kron(eye(length(eta)+length(mz)+length(sigmaz)),tauy)));\n\nh1 = hbar*v*(eta*kx*taux + ky*tauy);\nh2 = lambda*eta*sigmaz*tauz;\nh3 = mz*sigmaz*tauz;\nH = h1+h2+h3;\n\n\nThe is because typically:\n\n$$\\tau_x,\\tau_z,$$ and $$\\tau_y$$ would all lie in the same Hilbert space, and\n$$\\eta_z,m_z$$ and $$\\sigma_z$$ would each lie in a different Hilbert spaces to everything else.\n\nThere's a lot of left and right parentheses which you'd have to be careful about matching, and since there's 6 operators involved across 4 different Hilbert spaces, this is not such a simple example. If you wanted to give a simpler example with fewer operators and types of operators, or to explicitly give each matrix, I could try to simplify my above code. The length(operator) functions can probably all be replaced by 2, but my code works more generally for arbitrary spin (not just spin-1/2 which has eigenvalues $$\\pm$$1, but also spin-1 which has eigenvalues -1,0,1, etc.).\n\n• Thank you for helping me understand the underlying problem better! I had a few clarifications to request: 1) I chose all matrices eta through sigmaz to be their 2 x 2 Pauli matrix equivalents. Is this okay? 2) Following that, I added parentheses to some lines to match them up (next comment), but it seems as if eta is of dimensions 16 x 16 whereas the others are different. This seems to cause problems in defining H. 3) The authors use $\\pm 1$ for $s_z,\\tau_z\\,\\eta_z$, but now I am not sure how to test specific cases (such as $s_z,\\tau_z\\,\\eta_z=1,-1,1$). Any advice? Jun 16 at 20:00\n• Example code: eta=np.kron(np.kron(np.kron(eta,np.eye(2)),np.eye(2)),np.eye(2)); and mz=np.kron(np.kron(np.eye(2),mz),np.eye(6)); respectively have dimensions 16 x 16 and 24 x 24, whereas others have 12 x 12. Clearly I've fumbled somewhere, because this mismatch is keeping H from being well-defined. Jun 16 at 20:03\n• I believe h1, h2, and h3 should all be 16x16. I'm not at my computer until much later, but I'll look at what might have happened, as soon as I get a chance (today's a very busy day for me). Jun 16 at 20:34\n• thanks, I’ll keep trying! :D Jun 17 at 5:55"
] | [
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"https://i.stack.imgur.com/yjxlt.png",
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https://www.mhsmath.com/college-algebra-study-guide.html | [
"Try the Free Math Solver or Scroll down to Tutorials!\n\n Depdendent Variable\n\n Number of equations to solve: 23456789\n Equ. #1:\n Equ. #2:\n\n Equ. #3:\n\n Equ. #4:\n\n Equ. #5:\n\n Equ. #6:\n\n Equ. #7:\n\n Equ. #8:\n\n Equ. #9:\n\n Solve for:\n\n Dependent Variable\n\n Number of inequalities to solve: 23456789\n Ineq. #1:\n Ineq. #2:\n\n Ineq. #3:\n\n Ineq. #4:\n\n Ineq. #5:\n\n Ineq. #6:\n\n Ineq. #7:\n\n Ineq. #8:\n\n Ineq. #9:\n\n Solve for:\n\n Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:\n\n# College Algebra Study Guide\n\nE.8\n\n27. Show that each function is the inverse of the other: f(x) = 4x - 7 and",
null,
".\nAnswer: Yes, the functions are inverse of each other. f(g(x)) = x and g(f(x)) = x.\n\n28. Find the inverse of the function",
null,
".\nAnswer: f -1(x) = x2 + 1 for x ≥ 0\n\n29. Does the graph below represent a function that has inverse function?",
null,
"Answer: No, notice that horizontal lines can be drawn and intersect the graph more than once.\n\n30. The formula",
null,
"is used to convert from x degrees Celsius to y degrees Fahrenheit.\nFind the formula to convert from y degrees Fahrenheit to x degrees Celsius. Show that this formula\nis the inverse function of f(x).\nAnswer:",
null,
"is the inverse, then",
null,
", therefore the\nformula",
null,
"is the inverse of f(x).\n\nE.9\n\n31. Graph the polynomial function: f(x) = 2x3-x2-13x-6. Indicate the graph's end behavior, the\nx-intercepts, state whether the graph crosses the x-axis or touches the x-axis, indicate the y-intercepts.\nIf necessary, find a few additional points and graph the function.\nAnswer: The graph falls to the left and rises to the right, x = -2,",
null,
", 3, y = -6. Crosses the\nx-axis at every zero since each zero has multiplicity 1.",
null,
"32. Graph the rational function",
null,
". Indicate all x-intercepts, y-intercepts, horizontal asymp-\ntote, vertical asymptote(s). If necessary, find a few additional points and graph the function.\nAnswer: x = 0, y = 0, vertical asymptote at x = 2, horizontal asymptote at y = 3.",
null,
"33. Sketch the graph of the exponential function",
null,
":\nAnswer: Horizontal asymptote located at y = -3",
null,
"34. Graph the following Piecewise function and state the domain, range and intervals where the func-\ntion is increasing, decreasing and constant.",
null,
"Answer: The domain of this function is the set of all Real Numbers, the range is the interval\n[1,∞). The interval of increasing is (1,∞), the interval of decreasing is (-∞,-1) and the interval\nwhere the function is constant is (-1, 1). See the graph below.",
null,
"E.10\n\n35. Apply properties of Logarithms to simplify each expression.",
null,
"Answer: a) 25,",
null,
"36. Expand each expression by writing in terms of sum or difference of logarithms.",
null,
"Answer:",
null,
"37. Write the expression as a single Logarithm.",
null,
"Answer:",
null,
"38. Write the expression as a single Logarithm.",
null,
"Answer:",
null,
"E.11\n\n39. Suppose that y is such that",
null,
". Evaluate",
null,
"Answer:",
null,
"40. Solve for all the values of x that satisfy the equation:",
null,
".\nAnswer:",
null,
"41. Solve the equation by making an appropriate substitution,",
null,
".\nAnswer:",
null,
"42. Solve the radical equation. Check the proposed solutions.",
null,
".\nAnswer: x = 10\n\n43. Find the rational zeros of f. List any irrational zero correct to two decimal places.\n\nf(x) = x4 + 5x3 - 3x2 - 35x - 28.\n\nAnswer: Rational zeros:",
null,
", Irrational zeros:",
null,
"44. Solve the exponential equation. Round your answer to four decimal places.",
null,
"Answer: x = -37.2754\n\n45. Solve the radical equation. Check the proposed solutions.",
null,
"Answer: x = 2, note that x = 14 does not satisfy the original equation.\n\n46. Solve the exponential equation",
null,
".\nAnswer: y = -1."
] | [
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https://zims-en.kiwix.campusafrica.gos.orange.com/wikipedia_en_all_nopic/A/Functional_calculus | [
"# Functional calculus\n\nIn mathematics, a functional calculus is a theory allowing one to apply mathematical functions to mathematical operators. It is now a branch (more accurately, several related areas) of the field of functional analysis, connected with spectral theory. (Historically, the term was also used synonymously with calculus of variations; this usage is obsolete, except for functional derivative. Sometimes it is used in relation to types of functional equations, or in logic for systems of predicate calculus.)\n\nIf f is a function, say a numerical function of a real number, and M is an operator, there is no particular reason why the expression\n\nf(M)\n\nshould make sense. If it does, then we are no longer using f on its original function domain. In the tradition of operational calculus, algebraic expressions in operators are handled irrespective of their meaning. This passes nearly unnoticed if we talk about 'squaring a matrix', though, which is the case of f(x) = x2 and M an n×n matrix. The idea of a functional calculus is to create a principled approach to this kind of overloading of the notation.\n\nThe most immediate case is to apply polynomial functions to a square matrix, extending what has just been discussed. In the finite-dimensional case, the polynomial functional calculus yields quite a bit of information about the operator. For example, consider the family of polynomials which annihilates an operator T. This family is an ideal in the ring of polynomials. Furthermore, it is a nontrivial ideal: let n be the finite dimension of the algebra of matrices, then {I, T, T2...Tn} is linearly dependent. So ∑ αi Ti = 0 for some scalars αi, not all equal to 0. This implies that the polynomial ∑ αi xi lies in the ideal. Since the ring of polynomials is a principal ideal domain, this ideal is generated by some polynomial m. Multiplying by a unit if necessary, we can choose m to be monic. When this is done, the polynomial m is precisely the minimal polynomial of T. This polynomial gives deep information about T. For instance, a scalar α is an eigenvalue of T if and only if α is a root of m. Also, sometimes m can be used to calculate the exponential of T efficiently.\n\nThe polynomial calculus is not as informative in the infinite-dimensional case. Consider the unilateral shift with the polynomials calculus; the ideal defined above is now trivial. Thus one is interested in functional calculi more general than polynomials. The subject is closely linked to spectral theory, since for a diagonal matrix or multiplication operator, it is rather clear what the definitions should be."
] | [
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https://sts-math.com/post_95.html | [
"Solve, by factorising, the equation 8x(squared) - 30x - 27 = 0\n\nFirst, try to see if the 3 terms have a common factor. Yoru equation does not. So u have to multiply the 8x^2 and the 27. That is 216. Then you have to think to yourself, what multiplys to be 216 and adds to be -30? Those numbers are -36 and 6. Now your equation is 8x^2-36x+6x-27=0. Next, factor. What is both a factor of 8 and 6? That would be 2 and they both have at least one x. So you factor that to get 2x(4x+3). Now the other part. What goes into negative 36x and negative 27 that would be 9. So when you factor that you get 9(4x-3). They are the same except for the sign and thats easy. That 3 in the second part has to positive to multiply with the -9 to geta -27. So your finally answer is (2x-9)(4x-3).\n\nRELATED:"
] | [
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https://www.experts-exchange.com/articles/3725/How-to-Create-an-image-deconstructor-C.html | [
"# How to: Create an image deconstructor (C#).\n\nPublished:\nGreetings!\nFor my first article, I decided do something that many people actually think it's hard: Image handling. We'll be doing the simplest possible form of image decomposition -- breaking out the red, green, and blue components and creating variations of the the original image that are:\nGrayScale\nRedScale\nGreenScale\nBlueScale\nIt's a very simple code that does a very simple task\n\nEditor's Note:\nAlthough the author uses the term, decompose, this article is not about actual image decomposition. That term usually indicates complex mathematical processing to locate edges and so forth. This article describes a simple manipulation of the RGB color components of the image's individual pixels.\n\nHere we go.\n\nThe Form\nCreate a form similar to this (the Lorem Ipsum at the corner is not necessary, of course):\nYou are not obligated to write its labels in Portuguese, of course. The white squares are nothing but a PictureBox with a SingleFixed border, white BackColor and a label ahead it.\n\nThe \"Open\" button\nFor the \"Open\" button (\"Abrir...\" in the image above), write the following code as the Click event:\n``````private void button2_Click(object sender, EventArgs e)\n{\nOpenFileDialog OpenDiag = new OpenFileDialog();\nOpenDiag.Filter = \"Bitmap|*.bmp|JPeg|*.jpeg|JPeg|*.jpg|Portable Network Graphics|*.png\";\nif (OpenDiag.ShowDialog() == System.Windows.Forms.DialogResult.OK)\n{\npictureBoxOriginal.Image = Image.FromFile(OpenDiag.FileName);\npictureBoxOriginal.BringToFront();\n}\n}\n``````\n\nA basic \"enum\"\nWe need this enum because this will tell the \"Decompose\" method (that we will create) which color you want to separate from the others.\n\nVery simple:\n``````private enum RGB\n{\n/// <summary>\n/// Escala de vermelho\n/// </summary>\nRed,\n/// <summary>\n/// Escala de verde\n/// </summary>\nGreen,\n/// <summary>\n/// Escala de azul\n/// </summary>\nBlue,\n/// <summary>\n/// Escala de cinza\n/// </summary>\nGray\n}\n``````\n\nNOTE: The value Gray will tell the \"Decompose\" method to turn it grayscale; that means, no color. But if we literally take all colors away the result will be a white square (that will be explained in the \"Decompose\" method)\n\nThe main reason of why you're reading this: The \"Decompose\" method\nThe code is very simple but I'll explain part by part so everyone can follow.\n\nFirst create the method:\n``````/// <summary>\n/// Separates a specific color of an image from another or take 'em all without erasing the image\n/// </summary>\n/// <param name=\"Original\">The image to decompose</param>\n/// <param name=\"WhichColor\">Color to separate</param>\n/// <returns>The image only in a color tone or grayscale</returns>\nprivate Image Decompose(Bitmap Original, RGB WhichColor)\n{\n//return Decomposed;\n}\n``````\nThat's right, it must return an image.\n\nNow inside the method, let's start by the following part:\n``````//This is the bitmap we will create and futurely, convert to Image (by casting) and return.\nBitmap BDecomposed = new Bitmap(Original.Width, Original.Height);\n//Also create an integer that will be used by one of our loops.\nint X = 0;\n``````\nNow the loops.\nWe will create two loops, one inside another.\nThe outer loop is has nothing, but the inner loop and two lines of code see:\n``````while (X < Original.Width)\n{\nint Y = 0; //This variable will be used by the \"inner\" loop.\n//The inner loop\nX++;\n}\n``````\nSo, as far we have this in our \"Decompose\" Method:\n\n``````private Image Decompose(Bitmap Original, RGB WhichColor)\n{\nBitmap BDecomposed = new Bitmap(Original.Width, Original.Height);\nint X = 0;\nwhile (X < Original.Width)\n{\nint Y = 0; //This variable will be used by the \"inner\" loop.\n//The inner loop\nX++;\n//return Decomposed;\n}\n}\n``````\n\nNow the Inner loop.\nLet's start with this part:\n``````int Ro = Original.GetPixel(X, Y).R;\nint Go = Original.GetPixel(X, Y).G;\nint Bo = Original.GetPixel(X, Y).B;\n\nint Rn = 0;\nint Gn = 0;\nint Bn = 0;\n``````\nThe Xo variable are the Red, Green and Blue values of the original pixel in that position and the Xn variables are the Red, Green and Blue values for our new pixel color.\n\nNow we'll use that enum we created earlier. In this case the Decompose method parameter for that enum (that I called RGB) is called \"WhichColor\".\n\nBefore we proceed with this code, let's remember that a computer deals with colors like lighting; that means this way:\n\nRed(255) + Green(255) + Blue(255) = White\nRed(255) + Green(255) + Blue(0) = Yellow\nRed(0) + Green(255) + Blue(255) = Cyan\nRed(0) + Green(0) + Blue(0) = Black\n\nBrings some memories from high school doesn't?\nThese values goes from 0 to 255, and by changing these values we can get any color.\n\nNow, let's write the code that will set the Xn variables; that means, the color of the pixel currently being worked on in our new Bitmap.\n\n``````if (WhichColor == RGB.Red)\n{\nRn = (Ro + Go + Bo) / 3;\n}\nelse if (WhichColor == RGB.Green)\n{\nGn = (Ro + Go + Bo) / 3;\n}\nelse if (WhichColor == RGB.Blue)\n{\nBn = (Ro + Go + Bo) / 3;\n}\nelse if (WhichColor == RGB.Gray)\n{\nRn = (Ro + Go + Bo) / 3;\nGn = (Ro + Go + Bo) / 3;\nBn = (Ro + Go + Bo) / 3;\n}\n``````\nLet's understand it.\n\nIf (WhichColor == RGB.Gray)\nRemember that every time that the R, G and B values of a color are the same, no color prevails, so we have a gray tone. And the grey tone is lighter (or darker) as the values become higher (or lower) -- until it gets to 255 (or 0) which means white (or black).\n\nSo if we want to get a gray tone (where the R, G and B values are all equal) equivalent to a color tone (where the R, G and B values are different), we have to get an average and set the R, G, and B values to this average. Note that the operation used is a simple math operation to get averages.\n\nIf (WhichColor == RGB.OtherColor)\nSo we want to colorize an image with Red for example. It's simple but many people mistake the operation. Many people think that all we've got to do is to set the G and B values of each pixel to 0 and leave the R value untouched. Actually no. That would cause a different effect... That would REALLY separate that color from the others, so pixels where R = 0 will simply become black.\n\nIn our case, we want to colorize the image to a color scale, so we do something just a bit different: We take the average of the three values, but we will only set the color we want (example Red) as that average, and the others (example Green and Blue) are set to 0. (Similar to the method I just mentioned).\n\nIn the code above we only have to set the color we want to the average, no need to set the remaining color values to 0 since it was set to 0 when it was created.\n\nSo for now we have this in the \"Inner' loop´:\n``````// The variable used by the inner loop that is set in the outer loop\nint Y = 0;\nwhile (Y < Original.Height)\n{\nint Ro = Original.GetPixel(X, Y).R;\nint Go = Original.GetPixel(X, Y).G;\nint Bo = Original.GetPixel(X, Y).B;\n\nint Rn = 0;\nint Gn = 0;\nint Bn = 0;\n\nif (WhichColor == RGB.Red)\n{\nRn = (Ro + Go + Bo) / 3;\n}\nelse if (WhichColor == RGB.Green)\n{\nGn = (Ro + Go + Bo) / 3;\n}\nelse if (WhichColor == RGB.Blue)\n{\nBn = (Ro + Go + Bo) / 3;\n}\nelse if (WhichColor == RGB.Gray)\n{\nRn = (Ro + Go + Bo) / 3;\nGn = (Ro + Go + Bo) / 3;\nBn = (Ro + Go + Bo) / 3;\n}\n}\n``````\nNow that we've got the color, it's easy: Just set the color of the pixel we're currently working on in our new image to the color we've got:\n\n``````Color NewTone = Color.FromArgb(Rn, Gn, Bn);\n\nBDecomposed.SetPixel(X, Y, GrayTone);\n\n//This is to set the loop to work on the next pixel in the coordinate Y\nY++;\n``````\nSo, the whole Decompose method looks like this:\n``````private Image Decompose(Bitmap Original, RGB WhichColor)\n{\nBitmap BDecomposed = new Bitmap(Original.Width, Original.Height);\n//We will set it to work on the pixels with the X coordinate 0, that means, the first column of pixels in the image.\nint X = 0;\nwhile (X < Original.Width)\n{\n//Everytime the outer loop restarts, this will set the inner loop to start from the top of the column of pixels.\nint Y = 0;\nwhile (Y < Original.Height)\n{\nint Ro = Original.GetPixel(X, Y).R;\nint Go = Original.GetPixel(X, Y).G;\nint Bo = Original.GetPixel(X, Y).B;\n\nint Rn = 0;\nint Gn = 0;\nint Bn = 0;\n\nif (WhichColor == RGB.Red)\n{\nRn = (Ro + Go + Bo) / 3;\n}\nelse if (WhichColor == RGB.Green)\n{\nGn = (Ro + Go + Bo) / 3;\n}\nelse if (WhichColor == RGB.Blue)\n{\nBn = (Ro + Go + Bo) / 3;\n}\nelse if (WhichColor == RGB.Gray)\n{\nRn = (Ro + Go + Bo) / 3;\nGn = (Ro + Go + Bo) / 3;\nBn = (Ro + Go + Bo) / 3;\n}\n\nColor GrayTone = Color.FromArgb(Rn, Gn, Bn);\n\nBDecomposed.SetPixel(X, Y, GrayTone);\n\n//This sets the inner loop to work with the next pixel in that column\nY++;\n}\n//This will pass the current column of pixels being worked on by the inner loop, to the next column in the image.\nX++;\n}\n//This converts our created Bitmap to an Image\nImage Decomposed = (Image)BDecomposed;\nreturn Decomposed;\n}\n``````\n\nSo that's the Decompose method. Now, for the \"Decompose\" button, set the following code as the Click event:\n``````private void button1_Click(object sender, EventArgs e)\n{\npictureBoxGrayScale.Image = Decompose((Bitmap)pictureBoxOriginal.Image, RGB.Gray);\npictureBoxGrayScale.BringToFront();\n\npictureBoxRed.Image = Decompose((Bitmap)pictureBoxOriginal.Image, RGB.Red);\npictureBoxRed.BringToFront();\n\npictureBoxGreen.Image = Decompose((Bitmap)pictureBoxOriginal.Image, RGB.Green);\npictureBoxGreen.BringToFront();\n\npictureBoxBlue.Image = Decompose((Bitmap)pictureBoxOriginal.Image, RGB.Blue);\npictureBoxBlue.BringToFront();\n}\n``````\nNOTE: The \"BringToFront\" is being called so the Labels won't be ahead the picture box, after its image is set.\n\nThis method takes about 1.5 seconds to colorize a 640x480 image. That means about 6 seconds to make the grayscale, redscale, greenscale, and blue scale of a 640x480 image.\n\nYou can put the method to be run in another thread and ask the user of the application to wait, or else, it will stop the program and an impatient user would think it isn't going to work and close it.\n\nI tried to upload the whole project but the Expert Exchange refused to accept several file extensions, so I uploaded only the Form Source code.\nForm-1-Source-Code--C--.zip\nThanks for reading, I hope it was useful! ;)\n0\n4,766 Views\n\n#### Comments (2)\n\nCERTIFIED EXPERT\nMost Valuable Expert 2011\nTop Expert 2015\n\nCommented:\nI vote for a change in the article's title. When I read it on the TA carousel, I thought it was talking about creating a finalizer or destructor for the Image class (which didn't quite make sense to me).\n\nJust a suggestion : )\nChief Technology Ninja\nCERTIFIED EXPERT\nDistinguished Expert 2020\n\nCommented:\nAbsolutely agree with kaufmed.\n\nHave a question about something in this article? You can receive help directly from the article author. Sign up for a free trial to get started.\n\nGet access with a 7-day free trial."
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https://stat.ethz.ch/pipermail/r-help/2014-April/373131.html | [
"# [R] average of rows of each column\n\nFri Apr 4 21:23:57 CEST 2014\n\n```Hello,\n\nTry the following.\n\nm <- 120\nn <- 10 # in your case this is 1000\nmat <- matrix(rnorm(n*m), nrow = m)\n\nfun <- function(x, na.rm = TRUE){\ntapply(x, rep(1:12, each = 10), mean, na.rm = na.rm)\n}\n\napply(mat, 2, fun)\napply(mat, 2, fun, na.rm = FALSE) # alternative\n\nHope this helps,\n\nEm 04-04-2014 19:08, eliza botto escreveu:\n>\n> Dear useRs,\n> I have a matrix of 120 row and 1000 columns.What I want is to get an average of a set of 12 rows starting from 1 till 120 for each column. Precisely, for column 1 the average of 1:10 rows, 11:20 rows.... 111:120. similarly for column 2, 3, 4.... 1000. So in the end i should have a matrix with 12 rows and 1000 columns.\n> Thankyou very much in advance.\n>\n> Eliza\n>\n> \t[[alternative HTML version deleted]]\n>\n> ______________________________________________\n> R-help at r-project.org mailing list\n> https://stat.ethz.ch/mailman/listinfo/r-help"
] | [
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https://physics.stackexchange.com/questions/328717/vector-field-of-a-magnet | [
"# Vector field of a magnet\n\nGiven a standard reference system with axes x y z representing a 3 dimensional space and given a magnet whose north and south pole are at points $P_N=(x_N,y_N,z_N)$ and $P_S=(x_S,y_S,z_S)$ what is the law that describes the vector field of the magnet at any other point of the space? I'm interested in the law that associates to each point $P=(x,y,z)$ the direction and modulus of the vector of the magnetic field.\n\nThe ideal dipole magnet has a $1/R^2$ field directed toward the S pole, plus a $1/R^2$ field away from the N pole. The vector sum of those two field elements is the field of the dipole. The Earth's North pole is attractive to the N pole of a magnet, and (confusingly) is thus a S pole.\n$${\\mathrm { \\vec {B} = {(\\vec P_S - \\vec P) \\over {|(\\vec P_S -\\vec P)| ^3} } - {(\\vec P_N -\\vec P) \\over {|\\vec P_N - \\vec P|}^3} } }$$\n• What is $R$ ? Could you give some reference please? – Alberto Apr 25 '17 at 6:47\n• Sampling the values of $\\vec{B}$ for a set of points along a path how would you guess the positions of the poles? – Alberto Apr 28 '17 at 21:28"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.8922339,"math_prob":0.9990903,"size":1506,"snap":"2019-35-2019-39","text_gpt3_token_len":426,"char_repetition_ratio":0.12183755,"word_repetition_ratio":0.0,"special_character_ratio":0.30278885,"punctuation_ratio":0.08,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9997619,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-09-16T00:13:13Z\",\"WARC-Record-ID\":\"<urn:uuid:c2e181b8-6bc5-450f-9ed5-d13196cb3ba1>\",\"Content-Length\":\"141725\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c2857846-5204-4e76-b440-d24d602f960e>\",\"WARC-Concurrent-To\":\"<urn:uuid:b9fbd456-7eef-456c-ba29-d96d28a8c354>\",\"WARC-IP-Address\":\"151.101.129.69\",\"WARC-Target-URI\":\"https://physics.stackexchange.com/questions/328717/vector-field-of-a-magnet\",\"WARC-Payload-Digest\":\"sha1:Y4U6OA4AQ2LPDEE6R7GE2WBH4S56OP7W\",\"WARC-Block-Digest\":\"sha1:DYJMV34WWANFG3M6VQR4XHDRHQTAC34X\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-39/CC-MAIN-2019-39_segments_1568514572439.21_warc_CC-MAIN-20190915235555-20190916021555-00192.warc.gz\"}"} |
https://chem.libretexts.org/Courses/University_of_British_Columbia/CHEM_100%3A_Foundations_of_Chemistry/11%3A_Gases/11.07%3A_The_Combined_Gas_Law%3A_Pressure%2C_Volume%2C_and_Temperature | [
"# 11.7: The Combined Gas Law: Pressure, Volume, and Temperature\n\nLearning Objectives\n\n• Learn and apply the combined gas law.\n\nOne thing we notice about all the gas laws is that, collectively, volume and pressure are always in the numerator, and temperature is always in the denominator. This suggests that we can propose a gas law that combines pressure, volume, and temperature. This gas law is known as the combined gas law, and its mathematical form is\n\n$\\frac{P_{1}V_{1}}{T_{1}}=\\dfrac{P_{2}V_{2}}{T_{2}}\\; at\\; constant\\; n$\n\nThis allows us to follow changes in all three major properties of a gas. Again, the usual warnings apply about how to solve for an unknown algebraically (isolate it on one side of the equation in the numerator), units (they must be the same for the two similar variables of each type), and units of temperature must be in Kelvin.\n\nExample $$\\PageIndex{1}$$:\n\nA sample of gas at an initial volume of 8.33 L, an initial pressure of 1.82 atm, and an initial temperature of 286 K simultaneously changes its temperature to 355 K and its volume to 5.72 L. What is the final pressure of the gas?\n\nSolution\n\nSteps for Problem Solving\n\nIdentify the \"given\"information and what the problem is asking you to \"find.\"\n\nGiven:\n\nV1 = 8.33 L, P1 = 1.82 atm, and T1 = 286 K\n\nV2 = 5.72 L and T2 = 355 K\n\nFind: P2 = ? atm\n\nList other known quantities\n\nnone\n\nPlan the problem\n\nFirst, rearrange the equation algebraically to solve for $$V_2$$.\n\n$$P_2 = \\frac{P_1 V_1 T_2 }{T_1V_2}$$\n\nCalculate\n\nNow substitute the known quantities into the equation and solve.\n\n$P_2 = \\frac{(1.82\\, atm)(8.33\\, \\cancel{L})(355\\, \\cancel{K})}{(286\\, \\cancel{K})(5.72\\, \\cancel{L})}=3.22 atm$\n\nThink about your result. Ultimately, the pressure increased, which would have been difficult to predict because two properties of the gas were changing.\n\nExercise $$\\PageIndex{1}$$\n\nIf P1 = 662 torr, V1 = 46.7 mL, T1 = 266 K, P2 = 409 torr, and T2 = 371 K, what is V2?"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.8948539,"math_prob":0.9991082,"size":2669,"snap":"2021-04-2021-17","text_gpt3_token_len":735,"char_repetition_ratio":0.11969981,"word_repetition_ratio":0.0043956046,"special_character_ratio":0.29636568,"punctuation_ratio":0.13468635,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9995173,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-01-15T18:22:00Z\",\"WARC-Record-ID\":\"<urn:uuid:5d5ca5f8-2f70-4f3d-b564-b77ad1700fa3>\",\"Content-Length\":\"93317\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:575c70be-e8a0-465b-b202-79639b7e8aa5>\",\"WARC-Concurrent-To\":\"<urn:uuid:5ea2eee8-216f-4d99-bb06-af1533c8391e>\",\"WARC-IP-Address\":\"13.249.43.88\",\"WARC-Target-URI\":\"https://chem.libretexts.org/Courses/University_of_British_Columbia/CHEM_100%3A_Foundations_of_Chemistry/11%3A_Gases/11.07%3A_The_Combined_Gas_Law%3A_Pressure%2C_Volume%2C_and_Temperature\",\"WARC-Payload-Digest\":\"sha1:7Y4ZDYYZ45WZEFES6K4HIHSPL3IDGE4G\",\"WARC-Block-Digest\":\"sha1:NG325GFP4XVNT77YAA43DHRQVXE5BK34\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-04/CC-MAIN-2021-04_segments_1610703495936.3_warc_CC-MAIN-20210115164417-20210115194417-00562.warc.gz\"}"} |
http://herkimershideaway.org/algebra2/doc_page87.html | [
"",
null,
"",
null,
"Assignment 79\n\n \"And since geometry is the right foundation of all painting, I have decided to teach its rudiments and principles to all youngsters eager for art.\" - (Albrecht Durer, 1471-1528)",
null,
"Ethnomathematics: This term relates to the study of the mathematical experiences of those from different countries, from different ethnic and social backgrounds, or of a gender different from yours. Mathematics is a universal subject, but the ways different groups learn it, or experience it, very considerably. In 1985, the International Study Group on Ethnomathematics (ISGEm) was created. This group actively promotes programs to improve conditions for mathematics study by groups not usually encouraged to work with mathematics or mathematical ideas. With the continued work of ISGEm, mathematics educators around the world are finding that informal mathematics education is pervasive, that the social context of education has a great influence on student performance, and that quality education depends upon an understanding of culture.",
null,
"What did Herkimer say when he was informed that he was wearing one red sock and one green sock?",
null,
"Answer: \"I have another pair at home just like this pair.\" Herky wants to know: If you offer your child \\$10 for passing a mathematics test, can you consider you have saved \\$10 if he fails the test? If workers go on strike at the U.S. Mint, it is because they want to make fewer dollars? ASSIGNMENT #79 Reading: Section 12.5, pages 730-733. Written: Page 734-735/18-23, 25-29.",
null,
"Mathematical numbers:PALINDROMIC NUMBER: A positive integer of two or more digits whose value is the same read forwards or backwards. Some examples of palindromic numbers include 33, 777, 4994, and 99399. The year 2002 is a palindromic year.\nTwo events are independent if the outcome of one of them has no affect on the outcome of the other.\n\nExamples:\n\nQUESTION: A roll a red die, and then I roll a green die. What is the probability that I get a 6 on the red die and a 6 on the green die?\n\nRESPONSE: The outcome on the green die is not affected by the outcome on the red die. The two rolls are independent. The requested probability is (1/6)(1/6) = 1/36.\n\nQUESTION: I pick a card from a thoroughly shuffled deck of 52 cards, and note what it is. Then, I pick another card without replacing the first card. What is the probability that the second card is a heart?\n\nRESPONSE: The outcome of the second event (picking a second card) is dependent on the first event (picking the first card), since it depends on whether or not the first card was a heart. If the first card was a heart, then the probability that the second card is a heart is 12/51. If the first card was not a heart, then the probability that the second card is a heart is 13/51.\n\nQUESTION: If I roll a single die four times, what is the probability that I get at least one 6?\n\nRESPONSE: Each roll is independent of any other roll. The easiest way to respond to the question asked is to calculate the probability that I get no 6's, then subtract that from 1, or 100%. The answer is 1 - (5/6)4 = 0.5177, or about 51.77%.\n\nQUESTION: The probability that I win a specific game is 5%. How many games would I have to play to have a 75% chance of winning at least once?\n\nRESPONSE: The probability of winning x games in a row is (.95)x. Hence, the probability of winning at least one game when x games are played is 1 - (.95)x. So, we want to solve the equation 1 - (.95)x = .75 This yields (.95)x = .25 ==> x = log.95(.25) = log(.25)/log(.95) = 27.0268. In other words, you would expect to win at least once in 27 games if your probability of winning is just 5%.\n\n Problem: I flip a coin, roll a single die, and randomly choose a digit from the set {0,1,2,3,4,5,6,7,8,9}. What is the probability that the coin comes up heads, the die shows a 6, and the random digit is greater than 5? Solution (with communication): The three events described are independent. Hence the requested probability is (1/2)(1/6)(4/10) = 0.0333333, or about 3.3%. Problem: If I roll a single die ten times, what is the probability that I will get at least one 5? Solution (with communication): Each roll is independent of any other roll. The probability I would not get a 5 in ten rolls is (5/6)10. Hence the probability that I would get at least one 5 is 1 - (5/6)10 = 0.83849, or approximately 84%."
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https://math.icalculator.info/ratio-calculators/1:2.html | [
"# Equivalent Ratios of 1:2\n\nEquivalent ratios or equal ratios are two ratios that express the same relationship between numbers as we covered in our tutorial on scaling up ratios. You can use the equivalent ratio calculator to solve ratio and/or proportion problems as required by entering your own ratio to produce a table similar to the \"Equivalent Ratios of 1:2 table\" provided below. This ratio table provides an increasingly list of ratios of the same proportions where the numerator and denominator are a direct multiplication of the multiplying value (mx). Ratio tables are very useful in math for calculating and comparing equivalent ratios, although most will likely use a ratio calculator to calculate equivalent ratios, it is also useful to have a ratio table where you can quickly cross reference associated ratios, particularly when working with complex math equations to resolve advanced math problems or physics problems. As a useful reference, we have included a table which provides links to the associated ratio values for the ratio 1:2, for example 1.1:2, 1:2.1, 1.1:2.2 and so on. We hope you will find these quick reference ratio tables useful as you can print and email them to yourself to aid your learning or a useful learning aide when teaching ratios to math students.\n\nLooking for a different type of ratio calculator or tutorial? Use the quick links below to access more ratio calculators\n\n 1 : 2(m1 = 1) 2 : 4(m2 = 2) 3 : 6(m3 = 3) 4 : 8(m4 = 4) 5 : 10(m5 = 5) 6 : 12(m6 = 6) 7 : 14(m7 = 7) 8 : 16(m8 = 8) 9 : 18(m9 = 9) 10 : 20(m10 = 10) 11 : 22(m11 = 11) 12 : 24(m12 = 12) 13 : 26(m13 = 13) 14 : 28(m14 = 14) 15 : 30(m15 = 15) 16 : 32(m16 = 16) 17 : 34(m17 = 17) 18 : 36(m18 = 18) 19 : 38(m19 = 19) 20 : 40(m20 = 20) 21 : 42(m21 = 21) 22 : 44(m22 = 22) 23 : 46(m23 = 23) 24 : 48(m24 = 24) 25 : 50(m25 = 25) 26 : 52(m26 = 26) 27 : 54(m27 = 27) 28 : 56(m28 = 28) 29 : 58(m29 = 29) 30 : 60(m30 = 30) 31 : 62(m31 = 31) 32 : 64(m32 = 32) 33 : 66(m33 = 33) 34 : 68(m34 = 34) 35 : 70(m35 = 35) 36 : 72(m36 = 36) 37 : 74(m37 = 37) 38 : 76(m38 = 38) 39 : 78(m39 = 39) 40 : 80(m40 = 40) 41 : 82(m41 = 41) 42 : 84(m42 = 42) 43 : 86(m43 = 43) 44 : 88(m44 = 44) 45 : 90(m45 = 45) 46 : 92(m46 = 46) 47 : 94(m47 = 47) 48 : 96(m48 = 48) 49 : 98(m49 = 49) 50 : 100(m50 = 50)\n\nDid you find the table of equivalent ratios of 1:2 useful? Please leave a rating below.\n\n## How to Calculate Ratios\n\nWhen calculating equivalent ratios you must multiply or divide both numbers in the ratio. This keeps both numbers in direct relation to each other. So, a ratio of 2/3 has an equivalent ratio of 4/6: in this ratio calculation we simply multiplied both 2 and 3 by 2.\n\n## Mathematical facts about the ratio 1:2\n\nIf you wish to express the ratio 1:2 as n to 1 then the ratio would be:\n\n1:2 as n to 1\n= 0.5 : 1\n\nIf you wish to express the ratio 1:2 as 1 to n then the ratio would be:\n\n1:2 as 1 to n\n= 1 : 2\n\nThe ratio 1:2 expressed as a fraction is [calculated using the ratio to fraction calculator]:\n\n1:2\n= 1/2\n\nThe ratio 1:2 expressed as a percentage is [calculated using the ratio to percentage calculator]:\n\n1:2\n= 50%\n\n## Equivalent ratio tables for decimal ratios ranging 1 : 2 to 2 : 3\n\nThe table below contains links to equivalent ratio examples with ratios in increments of 0.1 in the range 1:2 to 2:3\n\n## Math Calculators\n\nYou may also find the following Math calculators useful."
] | [
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https://www.classcrown.com/pre-algebra-worksheets | [
"",
null,
"# Pre-algebra Worksheets\n\nPre-algebra Worksheets: Pack 1\nSkills included in this pack:\n• Subtracting integers\n• Multiplying integers\n• Dividing integers\n• Adding, subtracting, multiplying, and dividing integers\n• Simplifying using order of operations\n• Writing variable expressions\n• Evaluating variable expressions\n• Writing equations to represent word problems\n• Completing function tables\n• Solving 1-step equations by adding/subtracting\n• Solving 1-step equations by multiplying/dividing\n• Solving 2-step equations (includes integers)\n• Writing linear functions\n• Graphing linear functions\n• Evaluating functions\n• Writing multiplication expressions using exponents\n• Evaluating exponents\n• Multiplying powers\n• Dividing powers\n• Using scientific notation\n+ See More\nFree Sample Pages Available",
null,
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"",
null,
"",
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"Self Checking\n\nOur math worksheets introduce a puzzle aspect to math, giving students immediate feedback as to whether or not they are solving problems correctly. If the answer to the riddle isn't spelled correctly, the student knows which problems he's made an error on.",
null,
"Fun Puzzle Aspect",
null,
"Immediate Feedback",
null,
"",
null,
"",
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"Problem Solving Motivation\n\nEach math worksheet contains a riddle that the student solves by completeing all the problems on the worksheet. This keeps kids motivated to complete each problem so that they can find the answer to the riddle.",
null,
"",
null,
"",
null,
"Common Core Aligned\n\nAll our math worksheet packs are designed with Common Core in mind. That way you don’t have to worry about whether your math ciriculum is aligned or not when you incorpoate ClassCrown Riddle-Me-Worksheets in your lesson plans.",
null,
"",
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"",
null,
"High Quality Design\n\nEach page of our math worksheets has been produced in high resolution at 144 dpi and designed in full, vibrant color for maximum quality. They look stunning whether you are printing in color or black and white.",
null,
"High Resolution\n(144 dpi)",
null,
"Stunning Color & Clarity",
null,
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https://se.mathworks.com/help/symbolic/next-step-suggestions-for-symbolic-workflows.html | [
"# Next Step Suggestions for Symbolic Workflows in Live Editor\n\nStarting in R2021b, when you run code that generates a symbolic output in the Live Editor, Live Editor provides a context menu with next step suggestions that are specific to the output. To open the suggestion menu, you can point to the symbolic output and click the three-dot icon",
null,
", or you can right-click the symbolic output. When reopening your symbolic workflow live script, run the code again to get the next step suggestions.\n\nUsing these suggestion menus, you can insert and execute function calls or Live Editor tasks into live scripts. Typical uses of these suggestion menus include:\n\n• Evaluate and convert symbolic expressions to numeric values.\n\n• Simplify and manipulate, or solve symbolic math equations.\n\n• Plot symbolic expressions.\n\n• Perform matrix and vector operations, such as finding the inverse and determinant of a matrix, and finding the Jacobian and curl of a vector.\n\n• Perform calculus functions, such as differentiation, integration, transforms, and solving differential equations.\n\n• Convert between units of measurement and verify unit dimensions.\n\nFor example, in a new live script, create a symbolic expression.\n\n`expr = (pi + sym(2))^2`\n`expr = ${\\left(\\pi +2\\right)}^{2}$`\n\nClick Run to see the result, which is a symbolic output. When you first run code that generates a symbolic output, Live Editor shows the three-dot icon",
null,
"for suggested next steps with a pop-up notification. You can also point to the symbolic output to bring up the three-dot icon. To suppress the pop-up notification in the rest of your workflow, select Don't show again.",
null,
"Click the three-dot icon",
null,
"located to the right of the output to bring up the suggestion menu. When you point to a menu item, Live Editor gives you a preview of what happens when you select the menu item. For instance, if you point to Approximate numerically, you see the new line of code it suggests.",
null,
"Select Approximate numerically to add the suggested new line of code. Live Editor inserts the `vpa` function into the code region and automatically runs the current section to evaluate the expression numerically.\n\n`var = vpa(expr)`\n`var = $26.435975015448531572685064532994$`\n\nAs another example, create a symbolic equation. Run a live script to generate the symbolic output. Solve the equation numerically using symbolic suggestions for next steps.\n\n```syms x a eqn = (2*x^2 + a)/(x + 1) == 3```\n```eqn = $\\frac{2 {x}^{2}+a}{x+1}=3$```\n\nTo open the suggestion menu, you can also right-click the symbolic output. Select Solving equations > Solve equation numerically.",
null,
"When you click the Solve equation numerically suggestion, Live Editor inserts the `vpasolve` function into the code region. Live Editor then automatically runs the current section to solve the equation numerically.\n\n`var2 = vpasolve(eqn,x)`\n```var2 = $\\left(\\begin{array}{c}0.75-0.25 \\sqrt{33.0-8.0 a}\\\\ 0.25 \\sqrt{33.0-8.0 a}+0.75\\end{array}\\right)$```\n\nThe following sections provide more examples showing how to use the interactive suggestion menus in symbolic workflows.\n\n### Simplify Symbolic Expression\n\nCreate a symbolic expression that contains exponential functions and imaginary numbers. Run the following code to generate the symbolic output.\n\n```syms x expr = 1i*(exp(-1i*x) - exp(1i*x))/(exp(-1i*x) + exp(1i*x))```\n```expr = $\\frac{{\\mathrm{e}}^{-x \\mathrm{i}} \\mathrm{i}-{\\mathrm{e}}^{x \\mathrm{i}} \\mathrm{i}}{{\\mathrm{e}}^{-x \\mathrm{i}}+{\\mathrm{e}}^{x \\mathrm{i}}}$```\n\nTo simplify the expression, right-click the symbolic output and select Rewriting and simplifying expressions > Simplify expression.",
null,
"Live Editor inserts and applies the Simplify Symbolic Expression live task to interactively simplify or rearrange symbolic expressions. Change the computational effort to Medium to get a simpler result.",
null,
"### Substitute Coefficients and Solve Quadratic Equation\n\nCreate a quadratic equation with coefficients $a$, $b$, and $c$. Run the following code to generate the symbolic output.\n\n```syms a b c x eqn = a*x^2 + b*x + c == 0```\n`eqn = $a {x}^{2}+b x+c=0$`\n\nTo substitute the coefficients in the equation, right-click the output and select Substitute variables.",
null,
"Live Editor inserts the `subs` function to substitute the coefficients and variables in the equations. For the `subs` function, Live Editor does not run the function automatically. To substitute $a=3$, $b=2$, and $c=0$, change the second and third arguments of the `subs` function to `[a,b,c]` and `[3,2,0]`. Run the Live Editor section afterwards to apply the `subs` function.\n\n`var3 = subs(eqn,[a,b,c],[3,2,0])`\n`var3 = $3 {x}^{2}+2 x=0$`\n\nTo solve the quadratic equation, right-click the output and select Solve equation analytically.",
null,
"Live Editor inserts and applies the Solve Symbolic Equation live task to interactively find analytic solutions of symbolic equations.",
null,
"### Plot Explicit and Implicit Functions\n\nCreate three symbolic variables `x`, `y`, and `z` and a sinusoidal function. Run the following code to generate the symbolic output.\n\n```syms x y z f = sin(2*x)```\n`f = $\\mathrm{sin}\\left(2 x\\right)$`\n\nTo plot the sinusoidal function, right-click the output and select Plotting functions > Plot function.",
null,
"Live Editor plots the sinusoidal function using `fplot`.\n\n`fplot(f)`",
null,
"Next, create an equation that represents a hyperbola. Run the following code to generate the symbolic output.\n\n`eqn = x^2 - y^2 == 1`\n`eqn = ${x}^{2}-{y}^{2}=1$`\n\nTo plot the sinusoidal function, right-click the output and select Plotting functions > Plot implicit equation in 2-D.",
null,
"Live Editor plots the hyperbola using `fimplicit`.\n\n`fimplicit(eqn)`",
null,
"Next, create a symbolic function that represents a torus. Run the following code to generate the symbolic output.\n\n`f(x,y,z) = (x^2 + y^2 + z^2 + 3^2 - 2^2)^2 - 4*3^2*(x^2+y^2)`\n`f(x, y, z) = ${\\left({x}^{2}+{y}^{2}+{z}^{2}+5\\right)}^{2}-36 {x}^{2}-36 {y}^{2}$`\n\nTo plot the torus, right-click the output and select Plot implicit equation in 3-D.",
null,
"Live Editor plots the torus using `fimplicit3`.\n\n`fimplicit3(f)`",
null,
"### Apply Matrix Functions\n\nCreate three symbolic variables `x`, `y`, and `z` and a symbolic matrix. Run the following code to generate the symbolic output.\n\n```syms x y z M1 = sym([x^2 + a, x; y + 2, 3*y^2])```\n```M1 = $\\left(\\begin{array}{cc}{x}^{2}+a& x\\\\ y+2& 3 {y}^{2}\\end{array}\\right)$```\n\nTo invert the matrix, right-click the output and select Applying matrix functions > Invert matrix. Note that the Applying matrix functions > Invert matrix suggestion is available only if the symbolic output is a symbolic matrix.",
null,
"Live Editor inserts and applies the `inv` function to invert the matrix.\n\n`var4 = inv(M1)`\n```var4 = ```\n\nNext, create a 1-by-3 symbolic vector. Run the following code to generate the symbolic output.\n\n`M2 = sym([x*y*z, y^2, x + z])`\n`M2 = $\\left(\\begin{array}{ccc}x y z& {y}^{2}& x+z\\end{array}\\right)$`\n\nTo compute the Jacobian of the vector, right-click the output and select Applying matrix functions > Compute Jacobian matrix of vector. Note that the Applying matrix functions > Compute Jacobian matrix of vector suggestion is available only if the symbolic output is a symbolic vector.",
null,
"Live Editor inserts and applies the `jacobian` function to compute the Jacobian of the vector.\n\n`var5 = jacobian(M2)`\n```var5 = $\\left(\\begin{array}{ccc}y z& x z& x y\\\\ 0& 2 y& 0\\\\ 1& 0& 1\\end{array}\\right)$```\n\nNext, create another 1-by-3 symbolic vector. Run the following code to generate the symbolic output.\n\n`M3 = sym([x^2*y, 2*x, z])`\n`M3 = $\\left(\\begin{array}{ccc}{x}^{2} y& 2 x& z\\end{array}\\right)$`\n\nTo compute the curl of the vector, right-click the output and select Applying matrix functions > Compute curl of vector field.",
null,
"Live Editor inserts and applies the `curl` function to compute the curl of the vector.\n\n`var6 = curl(M3)`\n```var6 = $\\left(\\begin{array}{c}0\\\\ 0\\\\ 2-{x}^{2}\\end{array}\\right)$```\n\n### Solve Differential Equation, Compute Integral Transform, and Find Poles\n\nCreate a second-order differential equation. Run the following code to generate the symbolic output.\n\n```syms f(x) s eqn = diff(f,x,x) == -9*f```\n```eqn(x) = ```\n\nTo solve the differential equation, right-click the output and select Solve differential equation. Note that the Solve differential equation suggestion is available only if the symbolic output is a differential equation.",
null,
"Live Editor inserts and applies the `dsolve` function to solve the differential equation.\n\n`var7 = dsolve(eqn)`\n`var7 = ${C}_{1} \\mathrm{cos}\\left(3 x\\right)-{C}_{2} \\mathrm{sin}\\left(3 x\\right)$`\n\nNext, find the Laplace transform of the solution. Right-click the output of `dsolve` and select Computing integral transforms > Compute Laplace transform.",
null,
"Live Editor inserts and applies the `laplace` function to compute the Laplace transform.\n\n`var8 = laplace(var7)`\n```var8 = $\\frac{{C}_{1} s}{{s}^{2}+9}-\\frac{3 {C}_{2}}{{s}^{2}+9}$```\n\nFinally, find the poles of the Laplace transform. Right-click the output of the Laplace transform and select Applying calculus functions > Compute poles of function.",
null,
"Live Editor inserts and applies the `poles` function to compute the poles.\n\n`var9 = poles(var8,s)`\n```var9 = $\\left(\\begin{array}{c}-3 \\mathrm{i}\\\\ 3 \\mathrm{i}\\end{array}\\right)$```\n\n### Convert Units and Check Consistency of Units\n\nCreate a ratio of two lengths with different units. Run the following code to generate the symbolic output.\n\n```u = symunit; ratio = (7*u.mi)/(420*u.ft)```\n```ratio = $\\frac{1}{60} \\frac{\\mathrm{mi}\\mathrm{\"mile - a physical unit of length.\"}}{\\mathrm{ft}\\mathrm{\"foot - a physical unit of length.\"}}$```\n\nConvert the units to the meter-gram-second system. Right-click the output and select Applying physical unit functions > Convert units. Note that the Applying physical unit functions suggestion is available only if the symbolic output contains symbolic units.",
null,
"Live Editor inserts and applies the `unitConvert` function to convert the units to the meter-gram-second system.\n\n`var10 = unitConvert(ratio,[symunit('m'),symunit('g'),symunit('s')])`\n`var10 = $88$`\n\nNext, create two symbolic expressions `x` and `y` that describe the $x$- and $y$-coordinates of a moving projectile. Create a symbolic equation `r` that compares the units of `x` and `y` to the length units `m` and `ft`. Run the following code to generate the symbolic output.\n\n```syms theta ts x y r g = 9.81*u.m/u.s^2; v = 10*u.m/u.s; t = ts*u.s; x = v*cos(theta)*t; y = v*sin(theta)*t + (-g*t^2)/2; r = [x == u.m y == u.ft]```\n```r = $\\left(\\begin{array}{cc}10 \\mathrm{ts} \\mathrm{cos}\\left(\\theta \\right) \\mathrm{m}\\mathrm{\"meter - a physical unit of length.\"}=\\mathrm{m}\\mathrm{\"meter - a physical unit of length.\"}& 10 \\mathrm{ts} \\mathrm{sin}\\left(\\theta \\right) \\mathrm{m}\\mathrm{\"meter - a physical unit of length.\"}-\\frac{981 {\\mathrm{ts}}^{2}}{200} \\mathrm{m}\\mathrm{\"meter - a physical unit of length.\"}=\\mathrm{ft}\\mathrm{\"foot - a physical unit of length.\"}\\end{array}\\right)$```\n\nCheck the consistency of units in `r`. Right-click the output and select Applying physical unit functions > Check consistency of units.",
null,
"Live Editor inserts and applies the `checkUnits` function to check the consistency and compatibility of the units in `r`.\n\nThe `checkUnits` function returns a structure containing the fields `Consistent` and `Compatible`. The `Consistent` field returns logical `1(true)` if all terms in `r` have the same dimension and same unit with a conversion factor of 1. The `Compatible` field returns logical `1(true)` if all terms have the same dimension, but not necessarily the same unit.\n\n`var11 = checkUnits(r)`\n```var11 = struct with fields: Consistent: [1 0] Compatible: [1 1] ```"
] | [
null,
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null,
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null,
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https://www.clutchprep.com/chemistry/practice-problems/11093/what-volume-in-ml-of-0-0500-m-phosphoric-acid-is-needed-to-titrate-completely-25 | [
"# Problem: What volume (in mL) of 0.0500 M phosphoric acid is needed to titrate completely 25.0 mL of 0.150 M barium hydroxide solution to a phenolphthalein end point?3Ba(OH)2 + 2H3PO4 → Ba3(PO4)2 + 6H2O(A) 50.0(B) 75.0(C) 100(D) 150\n\n###### FREE Expert Solution\n99% (391 ratings)\n###### Problem Details\n\nWhat volume (in mL) of 0.0500 M phosphoric acid is needed to titrate completely 25.0 mL of 0.150 M barium hydroxide solution to a phenolphthalein end point?\n\n3Ba(OH)2 + 2H3PO4 → Ba3(PO4)2 + 6H2O\n\n(A) 50.0\n\n(B) 75.0\n\n(C) 100\n\n(D) 150\n\nWhat scientific concept do you need to know in order to solve this problem?\n\nOur tutors have indicated that to solve this problem you will need to apply the Equivalence Point concept. If you need more Equivalence Point practice, you can also practice Equivalence Point practice problems.\n\nWhat is the difficulty of this problem?\n\nOur tutors rated the difficulty ofWhat volume (in mL) of 0.0500 M phosphoric acid is needed to...as medium difficulty.\n\nHow long does this problem take to solve?\n\nOur expert Chemistry tutor, Sabrina took 5 minutes and 9 seconds to solve this problem. You can follow their steps in the video explanation above.\n\nWhat professor is this problem relevant for?\n\nBased on our data, we think this problem is relevant for Professor Randles' class at UCF."
] | [
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https://calculat.io/number/fraction-as-a-decimal/0--9--32 | [
"# Fraction 9/32 as a decimal\n\n9\n32\n=0.281\n\n## Explanation of 9/32 Fraction to Decimal Conversion\n\nTo convert 9/32 to decimal you need simply divide numerator 9 by denominator 32:\n\n9 ÷ 32 = 0.281\n\n## About \"Fraction to Decimal Converter\" Calculator\n\nThis calculator will help you to convert any fraction to it's decimal form. For example, What is 9/32 as a decimal? Enter the fraction (whole part, numerator and denominator) (e.g. '9/32') and then click the 'Convert' button.\n\n## FAQ\n\n### What is 9/32 as a decimal?\n\nFraction 9/32 as a decimal is 0.281"
] | [
null
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https://www.mbatious.com/topic/474/shortcut-methods-for-solving-cat-questions-by-patrick-dsouza-cat-100-percentiler-cat-07-09-16 | [
"# Shortcut methods for solving CAT questions by Patrick Dsouza, CAT 100 Percentiler (CAT 07, 09, 16)\n\n•",
null,
"There is a lot of buzz on shortcuts for solving various questions in CAT. It is one thing to know shortcuts and another to use it in the exam. I have heard from a lot of students who tell me that after the paper I can solve the sums or think of how to solve a sum in a better way, but in the actual mocks or exams it does not click. The reason for this is that one is not habituated to think in the right way in the exam. One of the basic problems with getting shortcuts is our education system. Through out the school and college, we have been given marks for the equation / formula and the steps we put while solving the sums. So whenever we see a sum we try to look out for which equation / formula to apply rather than how to solve it faster. This is made worse by the coaching classes which focus so much on equation based solving (because that is the best way that all the students understand), that the approach to solving in any alternate way is done only once the syllabus is complete when it is too late to develop new methods or one finds it difficult to inculcate new ways of solving sums.\n\nWhile solving a particular sum, you can follow the following steps:\n\n1. Firstly try solving the sum mentally, without using pen and paper.\n2. If you do not get the method in 2 minutes then take a pen and try solving.\n3. If you still do not get then go through the solution and try to understand it.\n4. Once you have understood the solution, come back to the sum and try to solve in an alternate method.\n\nLets take a simple sum to understand how to find alternate methods:\n\nN men can do a piece of work in 8 days. The same work can be done by (N+4) men in 6 days. Find the values of N.\n(a) 10\n(b) 12\n(c) 14\n(d) 16\n\nMethod 1: Normal method of solving this would be number of man days have to be equal.\n8 x N = 6 x (N+4)\nN = 12.\n\nStudents usually get happy that they have got the answer and move ahead. But that does not help them to improve on CAT. What is important for CAT is to get different methods.\n\nSo we go back to the question and think, is there any other way of solving\n\nMethod 2: Use options – substitute values. We see that if we substitute 12 we get 12 x 8 = (12+4) x 6\n\nMethod 3: Ratios – days is inversely proportional to number of men. So if days is 6/8 or 3/4 th then men will become 4/3 . Also the difference is 4 – so it should be 16 and 12.\n\nMethod 4: In 8 x N = 6 x (N+4) -- > Now 6 is a multiple of 3. So left side should also be a multiple of 3. Since is not a multiple of 3, it should be N. Only one option that is multiple of 3.\n\nWhat we are doing out here is finding multiple solutions to the same sum that helps to build in flexibility to solve the sums. This helps when the students are taught shortcuts. Lot of students- are so used to learning the mathematical way of solving that it becomes too late and difficult to unlearn old methods and learn new methods.\n\nLet me give you another example. I had given the following sum from Nishit Sinha book to couple of students who had scored 94%ile + in the CAT previous year.\n\nIf 29 goats can feed on a field of uniformly grown grass in 7 days or 25 goats can feed on the same field in 9 days, how many goats will feed in 6 days?\n(a) 36\n(b) 44\n(c) 42\n(d) 32\n\nThey started by forming equation for the first part for 7 days. Formed another equation for second part for 9 days and tried to solve it. And still after 2 minutes I was not able to get the answer. I informed them that the approach was completely un-CAT like. So I explained to them that while solving any question first understand the question what is asked. Here the question would be simple but for the condition of uniformly grown grass. Next look at the options to see if you can use them. At first glance you do not get any hint. So go back to the question and focus on the issue. So to find the amount by which grass is grown, I can find the total grass in 7 days which is 29x7 = 203 goat days and the total grass in 9 days which is 25x9 = 225 goat days. So in 2 days the grass grown is 225-203 = 22 goat days. Which means the growth is 11 goat days every day. So in 6 days there will be 203-11 = 192 goat days which can be consumed by 192/6 = 32 goat days.\n\nSo only with a small change in the way you look at the question you can solve the sum in a much faster way. The issue is, the students on an everyday basis use equation to solve all the sums that are available that it is difficult for them to change the way they solve the sums. Every forum that I see has the same method of solving. They just include new formulae like the Chinese Theorem and some others which I have never heard of. Understand one thing that CAT does not check on how many formulae you know or how great are you at Math. The focus of CAT is to understand whether given a situation and options available are you able to find a solution in a simple way, and believe me almost all the sums in CAT can be solved without using equation and it can be done at a much faster pace. In CAT 14 where there were 50 problems in the first section, I was able to attempt all 50 Math section question much before the time limit and had time to go back and check the questions which I was not sure of. I managed to score a 99.99%ile in section 1 (with a 99.98 overall) and not a 100%ile which I have done quite a few times in the past.\n\nAlso while solving a sum, if you get a shortcut method, don’t just be happy with it. Strive to see if there is a better method to solve the same sum.\n\nLets take an example:\n\na, b and c are three positive numbers and s = (a + b + c) / 2\nIf (s -a) : (s – b) : (s – c) = 1:7:4, the ratio a : b : c =\n(a) 8 : 10 : 6\n(b) 9 : 4 : 12\n(c) 7 : 8 : 9\n(d) 11 : 5 : 8\n\nOne shortcut way is to substitute the options. If we substitute d option. Take a=11, b=5, c=8 we will get s=12 and substituting in (s -a) : (s – b) : (s – c) we see that we get the values.\nBut if you look at it closely you will realize you need not even solve it. In the ratio since s-b is the largest, so b has to be the smallest. We can say either (b) or (d) is the answer. Again since s-a is the smallest so a should be the largest. We can say that (d) has to be the answer.\n\nOptions are one of the keys to get the shortcut methods in most of the sums. Therefore it is said that you have read a sum completely only when you have also read the options.\n\nAlso all the shortcut methods may not be restricted to options. Lets take the following sum:\n\nIn a particular week the average number of people who visited the Taj Mahal is 40. If we exclude the holidays then the average is increased by 16. Further if we exclude also the day on which the maximum number of 112 people visited the Taj Mahal, then the average becomes 42. The number of holidays in the week is\n(a) 1\n(b) 2\n(c) 3\n(d) data insufficient\n\nIn this sum we one shortcut way is to substitute simple values and check. So if the average people who visited Taj Mahal was 40 and there are 7 days a week, so the total number of people who visited Taj Mahal should be 7x40 = 280. Now excluding holidays the average becomes 40+16=56. We realize for the average to be 56 the number of days should be 280/56 = 5. Now to confirm, if 112 people are excluded then 280-112 = 168 people visited in 4 days which is 42. This satisfies. But there could be a shorter way to solve this. As the total people is constant (including and excluding holidays), days will be inversely proportional to average people. More the days less the average. So when the ratio of average is 40:56, then the ratio of days will be 56:40 which is 7:5. So if initially there were 7 days, excluding holidays there will be 5 days. So 2 days will be holiday in a week.\n\nP1, P2 and P3 are three consecutive prime numbers and P1 × P2 × P3 = 190747. What is the value of P1 + P2 + P3?\na. 169\nb. 179\nc. 163\nd. 173\n\nHere if we see options we see that the options are above 150. So the numbers should be above 50. Look at prime numbers above 50. We get 53, 59, 61. Multiply and we get the answer. So sum is 173.\n\nA function f(x) is defined for real values of x as:",
null,
"Easiest value to substitute is 0. But x=0 will give you a square root of negative number. So option b ruled out as there is 0. Then if we substitute 5 we see we get log to base 0 which is not possible. So x = 5 not possible so a and d options not possible. So answer is b.\n\nIn the regular hexagon shown below, what is the ratio of the area of the smaller circle to that of the bigger circle?",
null,
"a. 3 : 7+2√3\nb. 3 : 7+√3\nc. 3 :16+ 4√3\nd. 3 : 7 + 4√3\n\nFirst check if the diagrams are drawn to scale. This diagram is. Also if you see the diameter of the larger circle is approximately double of that of smaller circle. So we see the options. We can say that option a which is 3:10.4 and option d which is 3:13.8 is the closest. Going back to the sum we see that it should be slightly more than 2, so the answer should be d option.\n\nThe radius of the cross-sections of pipes P1 and P2 are 7 m and 14 m respectively. Water flows through P1 at a constant rate of 10 m/s and it can alone fill a tank in 2 hours. If P1 is used as the inlet pipe and P2 as the outlet pipe then together they fill the tank in 4 hours. What is the rate of water flow (in m/s) through P2?\na. 1.00\nb. 1.25\nc. 1.50\nd. 2.00\n\nFor the tank to fill in 2 hours it has to be filled in 10m/s, so for it to be filled in 4 hours it should be filled in 5m/s. 10m/s is coming from inlet pipe. So 5m/s should go out from outlet pipe. As the ratio of the radius is 1:2 so the ratio of the cross section area has to be 1:4. That means the same water has to go from 4 times the cross section area. So the speed will be 1/4th which is 5/4 = 1.25m/s.\n\n10 straight lines, no two of which are parallel and no three of which pass through any common point, are drawn on a plane. The total number of regions (including finite and infinite regions) into which the plane would be divided by the lines is\n(a) 56\n(b) 255\n(c) 1024\n(d) Not unique\n\nWhen I had given this sum to one of my student, he immediately gave me a formula for it. Which is n(n+1)/2 + 1. But I was not aware of the formula and in the exam there will be a lot of sums where you may not be aware of formulas. Usually the exam paper is set in such a way where you cannot use formulae. So here you can form a pattern. So learn to solve sums without formula. If you draw 1 line 2 regions are formed. If you draw 2 line 4 regions are formed. If you draw 3 lines we see 7 regions are formed. So if you take the pattern forward where difference in numbers is increasing by 1 we get the answer as 55.\n\nIn a triangle ABC, right angled at B, a median BE and an angle bisector BD are drawn. The lengths of DE, AD and EC in the same order, are in Arithmetic progression. If the length of AC is 10 cms and AB < BC, then what is the length (in cm) of BC?\n(a) 6 (b) 4 (c) 2rt5 (d) 4rt5\n\nLook at the options and substitute BC as 6. In that case AB becomes 8 (6–8–10 is a triplet) and AB < BC does not satisfy. So we know the answer should be more than 6 cms and the only option is 4rt5.\n\nThe perception with a lot of students with regards to CAT is that CAT is for Engineers. A non engineer finds it difficult as there is a lot of Math in CAT. Most of the students tend to give up on CAT as they can’t find how to break the Math conundrum. They learn formulae by rote and try to use the formulae in different sums in the Mocks only to realize that their scores are not improving.\n\nThe whole concept of learning formulae by rote for CAT is flawed. CAT does not check how good you are at remembering formulae and for most of the sums in CAT you cannot apply formulae directly. Rather, CAT checks whether you can logically think through sums. Its not about how much You study from Preparatory material but how smartly you can apply what you have learnt.\n\nIf you look at the previous CAT papers, most of the sums can be solved without the use of any high funda formulae. The whole thing about learning Euler’s Formula, Chinese Theorem, etc is basically useless. Rote learning formulae just makes you focus on formulae and you try to wonder which formulae to use for the sums. Frankly speaking I do not know any of these high funda formulae. I don’t know what is Euler’s formula or Chinese Theorem or most of the formulae which are used by various classes to solve their sums in the Mock CATs. As a matter of fact, some of the formulae which I encounter in the Mocks of these papers are new to me and I do not bother to read it, but still in the given time I could get 78 marks in Math section in CAT07 and 90 marks in Math section in CAT08 both the years scoring 100%ile in the Math section. Understand this - that CAT does not check on your mathematical skill but on your reasoning skills. Let’s try and understand how using formulae or equations can make you slow\n\nExample: Lets take a question from CAT08\n\nA shop stores x kg of rice. The first customer buys half this amount plus half a kg of rice. The second customer buys half the remaining amount plus half a kg of rice. Then the third customer also buys half the remaining amount plus half a kg of rice. Thereafter, no rice is left in the shop. Which of the following best describes the value of x?\n\n(1) 2 ≤ x ≤ 6 (b) 5 ≤ x ≤ 8 (c) 9 ≤ x ≤ 12 (d) 11 ≤ x ≤ 14 (e) 13 ≤ x ≤ 18\n\nSolution:\n\nUsually students who are used to formulae and equation will tend to use x as the initial amount of rice and try to form an equation to solve the sum. A better way would be to go reverse way. Say the last person has no rice left after he was given half the rice plus half a kg of rice. So he would have (0+1/2) x 2 = 1Kg before the last customer came in. Similarly before the second customer had come the shopkeeper would have (1 + ½) x 2 = 3. Before the first customer came in the shopkeeper would have (3 + ½) x 2 = 7kgs which is the answer.\n\nAnother question from CAT08:\n\nFind the sum √(1+ 1/1^2 + 1/2^2) + √(1 + 1/2^2 + 1/3^2) + ….. + √(1 + 1/2007^2 + 1/2008^2)\n\n(1) 2008 – 1/2008 (2) 2007 – 1/2007 (3) 2007 – 1/2008 (4) 2008 – 1/2007 (e) 2008 – 1/2009\n\nSolution:\n\nIt is almost unsolvable by using equations. But use the first term √(1+ 1/1^2 + 1/2^2) and we get 3/2 = 2 – ½. The denominator of last number of first term is 2. Take two terms √(1+ 1/1^2 + 1/2^2) + √(1 + 1/2^2 + 1/3^2) = 3/2 + 7/6 = 8/3 = 3 – 1/3. The denominator of the last number of second term is 3. So the answer has to be 2008 – 1/2008.\n\nSolving sums in these ways is not difficult and CAT does have similar type repeated.\n\nTake, for example, CAT05:\n\nQuestion:\n\n1 x 2 x 3 x … x n for integer n ≥ 1. If p = 1! + (2 x 2!) + (3 x 3!) + … + (10 x 10!), then p + 2 when divided by 11! Leaves a remainder of:\n\n(a) 10 (b) 0 (c) 7 (d) 1\n\nSolution:\n\nThis sum is similar to the previous sum. If p = 1! Then p + 2 = 3 when divided by 2! Gives a remainder 1. If p = 1! + (2 x 2!) = 5. then p + 2 = 7 when divided by 3! Gives a remainder 1. The result is the same for p = 1! + (2 x 2!) + (3 x 3!). So the answer for the given sum should be 1.\n\nAnother example\n\nQuestion:\n\nX = √(4 + √(4 - √(4 + √(4 ….)))) to infinity. Then x equals (CAT05)\n\n(a) 3 (b) (√13 – 1)/2 (c) (√13+ 1)/2 (d) √13\n\nSolution:\n\nWe know that √4 – anything will be less than 2. So we get √ 4 + (less than 2). Which should be more than 2 but less than 2.5. The only option that satisfied is c option with √13 is approximately 3.5. So (3.5 + 1)/2 = 2.25. The same sum can be solved by formulae but that will take time.\n\nAnother similar sum",
null,
"What is the value of y?\n\n(CAT04)\n\n(a) (√13 + 3)/2 (b) (√13-2)/2 (c) (√15 + 3)/2 (d) (√15 -3)/2\n\nSolution:\n\nY = 1 / 2 + something. So the answer has to be less than half. Check the options. Only option less than half is d option where √15 is less than 4 lets say 3.8. So (3.8 – 3)/2 = 0.4.\n\nQuestion:\n\nIn the following figure, the diameter of the circle is 3 cm. AB and MN are two diameters such that MN is perpendicular to AB. In addition, CG is perpendicular to AB such that AE : EB = 1: 2, and DF is perpendicular to MN such that NL : LM = 1: 2. The 1ength of DH in cm is (CAT05)",
null,
"(a) 2√2 – 1 (b) (2√2 -1)/2 (c) (3√2 - 1)/2 (d) (2√2 -1)/3\n\nSolution:\n\nIn this case AE is 1. Also DH is less than AE so it has to be less than 1. From options value of (b) 0.9 and that of (d) is 0.6. But if you draw to scale you will realize that DH is almost similar to AE and cant be 0.6. So the answer has to be (b).\n\nQuestion:\n\nA circle with radius 2 is placed against a right angle. Another smaller circle is also placed as shown in the adjoining figure. What is the radius of the smaller circle?\n\n(CAT04)",
null,
"Solution:\n\nRadius of bigger Circle is 2. So diameter of the smaller circle is less than 1. So radius of smaller circle is less than 0.5. From options (a) is 0.2 and (d) is 0.4. So the answer is (d) as it can’t be as small as 0.2.\n\nWhat should be done to improve Math?\n\n• Keep away from difficult formulae. The less formulae you know the better it is. Obviously you need to know basic formulae like 1 + 2 + 3 + … = n(n+1)/2 or (a+b)^2 = a^2 + 2ab + b^2. But don’t get into any new formulae you have not heard of. It will only slow you down.\n\n• Go back to all the mocks you have solved and go through the questions again to search for better ways of solving. If you find it write it down next to the sum so that when you go through the paper again you could remember the methods you used. Also once before the exam go and check the shortcut methods you used to solve the sums. This would ensure that it is fresh in your mind when you solve the paper.\n\n• Continue writing the usual Mock Papers and analyze it. Try to get better ways of solving it than that provided by explanatory answers.\n\n• Go through the 5 previous CAT papers and see if you could get methods to solve the questions there. Understand this that CAT does not repeat questions, but the methods used to solve CAT sums can be repetitive as shown in the examples.\n\n• Awesome work sir.\nIf possible please post more question solving techniques like it .\nSecondly, sir which books did you refer for your cat prep.\nThanks\n\n1\n\n1\n\n1\n\n1\n\n1\n\n2\n\n14\n\n1"
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http://mathonline.wikidot.com/the-simple-function-approximation-lemma | [
"The Simple Function Approximation Lemma\n\n# The Simple Function Approximation Lemma\n\n Lemma 1 (The Simple Function Approximation Lemma): Let $f$ be a Lebesgue measurable function on a Lebesgue measurable set $E$. If $f$ is bounded on $E$ then for all $\\epsilon > 0$ there exists simple functions $\\varphi_{\\epsilon}$ and $\\psi_{\\epsilon}$ on $E$ such that: 1) $\\varphi_{\\epsilon}(x) \\leq f(x) \\leq \\psi_{\\epsilon}(x)$ for all $x \\in E$. 2) $0 \\leq \\psi_{\\epsilon} - \\varphi_{\\epsilon} < \\epsilon$ for all $x \\in E$.\n• Proof: Let $f$ be a Lebesgue measurable function on a Lebesgue measurable set $E$, and let $f$ be bounded on $E$. Then there exists $m, M \\in \\mathbb{R}$ with $m < M$ such that for all $x \\in E$ we have that:\n(1)\n\\begin{align} \\quad m \\leq f(x) \\leq M \\end{align}\n• Consider the interval $[m, M]$. Let $P = \\{ m = x_0, x_1, ..., x_n = M \\}$ be a partition of $[m, M]$ with $m = x_0 < x_1 < ... < x_n = M$ with the property that $\\displaystyle{x_k - x_{k-1} < \\epsilon}$ for each $k \\in \\{ 1, 2, ..., n \\}$ and also, for each $k$ define:\n(2)\n\\begin{align} \\quad E_k = f^{-1} ([x_{k-1}, x_k)) \\end{align}\n• Then each $E_k$ is a Lebesgue measurable set and the collection of sets $\\{ E_1, E_2, ..., E_n \\}$ are mutually disjoint. For each $k \\in \\{ 1, 2, ..., n \\}$ define the functions $\\varphi_k$ and $\\phi_k$ on the sets $E_k$ by:\n(3)\n• Then define the functions $\\varphi_{\\epsilon}$ and $\\psi_{\\epsilon}$ by:\n• Then $\\varphi_{\\epsilon}$ and $\\psi_{\\epsilon}$ are simple functions and for all $x \\in E$ we have that $\\varphi_{\\epsilon}(x) \\leq f(x) \\leq \\psi_{\\epsilon}(x)$, so (1) holds.\n• Furthermore, for each $k \\in \\{ 1, 2, ..., n \\}$ we have that $\\psi_{k}(x) - \\varphi_k(x) = x_k - x_{k-1} < \\epsilon$ for all $x \\in E_k$ and so $0 \\leq \\psi_{\\epsilon}(x) - \\varphi_{\\epsilon}(x) < \\epsilon$ for all $x \\in E$. $\\blacksquare$"
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.53703463,"math_prob":1.0000095,"size":2453,"snap":"2020-45-2020-50","text_gpt3_token_len":943,"char_repetition_ratio":0.16864026,"word_repetition_ratio":0.19464721,"special_character_ratio":0.41622502,"punctuation_ratio":0.13305613,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.0000099,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-10-23T06:20:45Z\",\"WARC-Record-ID\":\"<urn:uuid:7b84f549-14cd-4d80-9913-4b51a5f1283f>\",\"Content-Length\":\"18071\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7e2df173-80dd-4795-9473-9fa33ae0b6aa>\",\"WARC-Concurrent-To\":\"<urn:uuid:b84afc86-648a-4b9f-9d3f-87414caefee6>\",\"WARC-IP-Address\":\"107.20.139.170\",\"WARC-Target-URI\":\"http://mathonline.wikidot.com/the-simple-function-approximation-lemma\",\"WARC-Payload-Digest\":\"sha1:KHDL5DHBDJKONUNXIZONEKTCBB4CED5Z\",\"WARC-Block-Digest\":\"sha1:NCDLTTKZCAP5R22VXKWMCXELFBA6MKPV\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-45/CC-MAIN-2020-45_segments_1603107880656.25_warc_CC-MAIN-20201023043931-20201023073931-00455.warc.gz\"}"} |
https://all-essays.info/2021/06/01/how-to-solve-chemistry-word-problems_a9/ | [
"# How to solve chemistry word problems\n\nBy | June 1, 2021\n\nConversions are often written using the word per. two examples are shown, one non-chemistry problem involving the calculation of the shared cost of a meal answer key argument of fact essay word problem how to solve chemistry word problems primer- how to what website can help me with my math homework solve word problems 1. energy how to solve chemistry word problems 2. if you're seeing this message, it means we're having trouble loading external resources on our website algebra motion problems: introduction to chemistry problem solving. velocity 10. these can be re-written as ratios:. solving chemistry word problems and general problems solving techniques watch me: essay on a good man is hard to find mixture problems are ones in which two different solutions are mixed together, resulting in a new, the industrial revolution essay final solution. in a survey of university students, 64 had how to solve chemistry word problems taken mathematics course, 94 had taken chemistry course, 58 had informative essay on sports concussions taken e-business plan physics online degree creative writing course, 28 had taken websites that do your math homework for you mathematics and physics, 26 had taken mathematics how to write the perfect research paper and chemistry, scientific literature review example 22 had taken chemistry and physics course, solving word problems in trigonometry. one solution is to get answers to chemistry questions online."
] | [
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.9464549,"math_prob":0.62538815,"size":1451,"snap":"2021-21-2021-25","text_gpt3_token_len":270,"char_repetition_ratio":0.16793366,"word_repetition_ratio":0.026785715,"special_character_ratio":0.18745692,"punctuation_ratio":0.09055118,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9765446,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-06-24T19:00:11Z\",\"WARC-Record-ID\":\"<urn:uuid:e175beae-4f91-4b70-808d-8fdc451318dd>\",\"Content-Length\":\"15870\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d7a416a2-12ed-4ae6-95b5-d1306cff5921>\",\"WARC-Concurrent-To\":\"<urn:uuid:c03086c9-e6e3-43cd-a219-8d9459cf5b5c>\",\"WARC-IP-Address\":\"37.252.9.207\",\"WARC-Target-URI\":\"https://all-essays.info/2021/06/01/how-to-solve-chemistry-word-problems_a9/\",\"WARC-Payload-Digest\":\"sha1:L5RGA5ZELBMS6PLQOPMKYXSDU37RSMPZ\",\"WARC-Block-Digest\":\"sha1:HKPMG2QJLZBBBV7YXXO6LMA3H3UAWJP4\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-25/CC-MAIN-2021-25_segments_1623488556482.89_warc_CC-MAIN-20210624171713-20210624201713-00565.warc.gz\"}"} |
http://elib.mi.sanu.ac.rs/files/journals/publ/126/8_eng.html | [
"Abstract\nSome integral inequalities for the polar derivative of polynomials\n\nPrasanna Kumar\n\nAs a generalization of well-known result due to Turán \\cite{T} for polynomials having all their zeros in $|z|\\leq1$, Malik \\cite{M} proved that, if $P(z)$ is a polynomial of degree $n$, having all its zeros in $|z|\\leq1$, then for any $\\delta>0$, $n\\bigg\\{\\int_0^{2i}|P(e^{iheta})|^{ẹlta}dheta\\bigg\\}^{1/ẹlta}eq\\bigg\\{\\int_0^{2i}|1+e^{iheta}|^{ẹlta}dheta\\bigg\\}^{1/ẹlta}\\max_{|z|=1}|P'(z)|.$ We generalize the above inequality to polar derivatives, which as special cases include several known results in this area. Besides the paper contains some more results that generalize and sharpen several results known in this direction."
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.8610804,"math_prob":0.99932027,"size":633,"snap":"2019-51-2020-05","text_gpt3_token_len":212,"char_repetition_ratio":0.10651828,"word_repetition_ratio":0.0,"special_character_ratio":0.30015796,"punctuation_ratio":0.07438017,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9972056,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-01-24T23:15:59Z\",\"WARC-Record-ID\":\"<urn:uuid:2c5cecd8-85d6-4ca3-887f-3b061ae0f263>\",\"Content-Length\":\"1344\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:cf148170-045a-4d82-a4d0-ef2c60121972>\",\"WARC-Concurrent-To\":\"<urn:uuid:a84a9c07-e03f-4aa7-bb6d-2bfb677e7d93>\",\"WARC-IP-Address\":\"147.91.96.23\",\"WARC-Target-URI\":\"http://elib.mi.sanu.ac.rs/files/journals/publ/126/8_eng.html\",\"WARC-Payload-Digest\":\"sha1:5KP2VQADCAPJ56UKTWBH5RF7ALPP4WA6\",\"WARC-Block-Digest\":\"sha1:6HODXZZUBSTBW4GOAJNDM5QTVGU5FYHB\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-05/CC-MAIN-2020-05_segments_1579250626449.79_warc_CC-MAIN-20200124221147-20200125010147-00215.warc.gz\"}"} |
https://www.physicsforums.com/threads/eigenvector-proof.392576/ | [
"# Eigenvector Proof\n\n## Homework Statement\n\nLet B = S^-1 * A * S and x be an eigenvector of B belonging to an eigenvalue $$\\lambda$$. Show S*x is an eigenvector of A belonging to $$\\lambda$$.\n\n## The Attempt at a Solution\n\nThe only place I can think of to start, is that B*x = $$\\lambda$$*x.\nHowever, even starting with that, I can't figure out where to go next.\nCould someone point me in the right direction?\n\nMark44\nMentor\n\n## Homework Statement\n\nLet B = S^-1 * A * S and x be an eigenvector of B belonging to an eigenvalue $$\\lambda$$. Show S*x is an eigenvector of A belonging to $$\\lambda$$.\n\n## The Attempt at a Solution\n\nThe only place I can think of to start, is that B*x = $$\\lambda$$*x.\nHowever, even starting with that, I can't figure out where to go next.\nCould someone point me in the right direction?\nThat's a decent start. Next, show that A(Sx) = $\\lambda$x. That's what it means to say that Sx is an eigenvector of A corresponding to $\\lambda$.\n\nWhat do I use to show that?\n\nThe only new information I've got that might be helpful is that A = S * B * S^-1\n\nMultiplying on the left by S gives A*S = S*B\n\nAfter doing that, I'm stuck again. I feel like this is the right track, but I don't know how to relate this back to what I'm trying to prove.\n\nvela\nStaff Emeritus\nHomework Helper\nThat's a decent start. Next, show that A(Sx) = $\\lambda$x. That's what it means to say that Sx is an eigenvector of A corresponding to $\\lambda$.\nSlight correction: You want to show that A(Sx) = $\\lambda$(Sx)\nWhat do I use to show that?\n\nThe only new information I've got that might be helpful is that A = S * B * S^-1\n\nMultiplying on the left by S gives A*S = S*B\n\nAfter doing that, I'm stuck again. I feel like this is the right track, but I don't know how to relate this back to what I'm trying to prove.\nMultiply by x now.\n\nI think I got it now.\n\nAfter multiplying by x, I have ASx = SBx.\n\nBx has already been shown equal to $$\\lambda$$x, so I substitute that in, giving\n\nASx = S$$\\lambda$$x\n\n$$\\lambda$$ can be moved to the other side of S since it's a scalar, giving ASx = $$\\lambda$$Sx.\n\nMark44\nMentor\nRight."
] | [
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.8981645,"math_prob":0.993901,"size":434,"snap":"2021-21-2021-25","text_gpt3_token_len":126,"char_repetition_ratio":0.1255814,"word_repetition_ratio":0.0,"special_character_ratio":0.28801844,"punctuation_ratio":0.08791209,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9995598,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-05-08T11:05:46Z\",\"WARC-Record-ID\":\"<urn:uuid:e5b81e02-9a46-422b-b5f6-922328d8dab1>\",\"Content-Length\":\"74005\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:48bdd586-b3e8-4ed7-9f8a-f46d1eaf2f74>\",\"WARC-Concurrent-To\":\"<urn:uuid:fb9f167e-73de-412c-97fa-a39f555347a1>\",\"WARC-IP-Address\":\"104.26.14.132\",\"WARC-Target-URI\":\"https://www.physicsforums.com/threads/eigenvector-proof.392576/\",\"WARC-Payload-Digest\":\"sha1:LYAL3FAQHRP42RATM3HAHWGU2ZRGKXI6\",\"WARC-Block-Digest\":\"sha1:YLENF6NC3CHVMLNTHYCNNDYZ7QGUU4ZW\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-21/CC-MAIN-2021-21_segments_1620243988858.72_warc_CC-MAIN-20210508091446-20210508121446-00271.warc.gz\"}"} |
https://www.colorhexa.com/cd8ee4 | [
"# #cd8ee4 Color Information\n\nIn a RGB color space, hex #cd8ee4 is composed of 80.4% red, 55.7% green and 89.4% blue. Whereas in a CMYK color space, it is composed of 10.1% cyan, 37.7% magenta, 0% yellow and 10.6% black. It has a hue angle of 284 degrees, a saturation of 61.4% and a lightness of 72.5%. #cd8ee4 color hex could be obtained by blending #ffffff with #9b1dc9. Closest websafe color is: #cc99cc.\n\n• R 80\n• G 56\n• B 89\nRGB color chart\n• C 10\n• M 38\n• Y 0\n• K 11\nCMYK color chart\n\n#cd8ee4 color description : Very soft violet.\n\n# #cd8ee4 Color Conversion\n\nThe hexadecimal color #cd8ee4 has RGB values of R:205, G:142, B:228 and CMYK values of C:0.1, M:0.38, Y:0, K:0.11. Its decimal value is 13471460.\n\nHex triplet RGB Decimal cd8ee4 `#cd8ee4` 205, 142, 228 `rgb(205,142,228)` 80.4, 55.7, 89.4 `rgb(80.4%,55.7%,89.4%)` 10, 38, 0, 11 284°, 61.4, 72.5 `hsl(284,61.4%,72.5%)` 284°, 37.7, 89.4 cc99cc `#cc99cc`\nCIE-LAB 67.967, 38.585, -34.291 48.852, 37.928, 78.142 0.296, 0.23, 37.928 67.967, 51.621, 318.372 67.967, 27.796, -59.891 61.586, 33.817, -32.119 11001101, 10001110, 11100100\n\n# Color Schemes with #cd8ee4\n\n• #cd8ee4\n``#cd8ee4` `rgb(205,142,228)``\n• #a5e48e\n``#a5e48e` `rgb(165,228,142)``\nComplementary Color\n• #a28ee4\n``#a28ee4` `rgb(162,142,228)``\n• #cd8ee4\n``#cd8ee4` `rgb(205,142,228)``\n• #e48ed0\n``#e48ed0` `rgb(228,142,208)``\nAnalogous Color\n• #8ee4a2\n``#8ee4a2` `rgb(142,228,162)``\n• #cd8ee4\n``#cd8ee4` `rgb(205,142,228)``\n• #d0e48e\n``#d0e48e` `rgb(208,228,142)``\nSplit Complementary Color\n• #8ee4cd\n``#8ee4cd` `rgb(142,228,205)``\n• #cd8ee4\n``#cd8ee4` `rgb(205,142,228)``\n• #e4cd8e\n``#e4cd8e` `rgb(228,205,142)``\nTriadic Color\n• #8ea5e4\n``#8ea5e4` `rgb(142,165,228)``\n• #cd8ee4\n``#cd8ee4` `rgb(205,142,228)``\n• #e4cd8e\n``#e4cd8e` `rgb(228,205,142)``\n• #a5e48e\n``#a5e48e` `rgb(165,228,142)``\nTetradic Color\n• #b250d5\n``#b250d5` `rgb(178,80,213)``\n• #bb65da\n``#bb65da` `rgb(187,101,218)``\n• #c479df\n``#c479df` `rgb(196,121,223)``\n• #cd8ee4\n``#cd8ee4` `rgb(205,142,228)``\n• #d6a3e9\n``#d6a3e9` `rgb(214,163,233)``\n• #dfb7ee\n``#dfb7ee` `rgb(223,183,238)``\n• #e8ccf3\n``#e8ccf3` `rgb(232,204,243)``\nMonochromatic Color\n\n# Alternatives to #cd8ee4\n\nBelow, you can see some colors close to #cd8ee4. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #b88ee4\n``#b88ee4` `rgb(184,142,228)``\n• #bf8ee4\n``#bf8ee4` `rgb(191,142,228)``\n• #c68ee4\n``#c68ee4` `rgb(198,142,228)``\n• #cd8ee4\n``#cd8ee4` `rgb(205,142,228)``\n• #d48ee4\n``#d48ee4` `rgb(212,142,228)``\n• #db8ee4\n``#db8ee4` `rgb(219,142,228)``\n• #e38ee4\n``#e38ee4` `rgb(227,142,228)``\nSimilar Colors\n\n# #cd8ee4 Preview\n\nText with hexadecimal color #cd8ee4\n\nThis text has a font color of #cd8ee4.\n\n``<span style=\"color:#cd8ee4;\">Text here</span>``\n#cd8ee4 background color\n\nThis paragraph has a background color of #cd8ee4.\n\n``<p style=\"background-color:#cd8ee4;\">Content here</p>``\n#cd8ee4 border color\n\nThis element has a border color of #cd8ee4.\n\n``<div style=\"border:1px solid #cd8ee4;\">Content here</div>``\nCSS codes\n``.text {color:#cd8ee4;}``\n``.background {background-color:#cd8ee4;}``\n``.border {border:1px solid #cd8ee4;}``\n\n# Shades and Tints of #cd8ee4\n\nA shade is achieved by adding black to any pure hue, while a tint is created by mixing white to any pure color. In this example, #0b030e is the darkest color, while #fefdfe is the lightest one.\n\n• #0b030e\n``#0b030e` `rgb(11,3,14)``\n• #17071d\n``#17071d` `rgb(23,7,29)``\n• #240b2d\n``#240b2d` `rgb(36,11,45)``\n• #310f3d\n``#310f3d` `rgb(49,15,61)``\n• #3d124d\n``#3d124d` `rgb(61,18,77)``\n• #4a165d\n``#4a165d` `rgb(74,22,93)``\n• #571a6d\n``#571a6d` `rgb(87,26,109)``\n• #631e7c\n``#631e7c` `rgb(99,30,124)``\n• #70228c\n``#70228c` `rgb(112,34,140)``\n• #7c259c\n``#7c259c` `rgb(124,37,156)``\n• #8929ac\n``#8929ac` `rgb(137,41,172)``\n• #962dbc\n``#962dbc` `rgb(150,45,188)``\n• #a231cc\n``#a231cc` `rgb(162,49,204)``\nShade Color Variation\n• #aa3fd1\n``#aa3fd1` `rgb(170,63,209)``\n• #b14fd5\n``#b14fd5` `rgb(177,79,213)``\n• #b85fd9\n``#b85fd9` `rgb(184,95,217)``\n• #bf6edc\n``#bf6edc` `rgb(191,110,220)``\n• #c67ee0\n``#c67ee0` `rgb(198,126,224)``\n• #cd8ee4\n``#cd8ee4` `rgb(205,142,228)``\n• #d49ee8\n``#d49ee8` `rgb(212,158,232)``\n• #dbaeec\n``#dbaeec` `rgb(219,174,236)``\n• #e2bdef\n``#e2bdef` `rgb(226,189,239)``\n• #e9cdf3\n``#e9cdf3` `rgb(233,205,243)``\n• #f0ddf7\n``#f0ddf7` `rgb(240,221,247)``\n• #f7edfb\n``#f7edfb` `rgb(247,237,251)``\n• #fefdfe\n``#fefdfe` `rgb(254,253,254)``\nTint Color Variation\n\n# Tones of #cd8ee4\n\nA tone is produced by adding gray to any pure hue. In this case, #bbb4be is the less saturated color, while #da73ff is the most saturated one.\n\n• #bbb4be\n``#bbb4be` `rgb(187,180,190)``\n• #beaec4\n``#beaec4` `rgb(190,174,196)``\n• #c0a9c9\n``#c0a9c9` `rgb(192,169,201)``\n• #c3a4ce\n``#c3a4ce` `rgb(195,164,206)``\n• #c59ed4\n``#c59ed4` `rgb(197,158,212)``\n• #c899d9\n``#c899d9` `rgb(200,153,217)``\n• #ca93df\n``#ca93df` `rgb(202,147,223)``\n• #cd8ee4\n``#cd8ee4` `rgb(205,142,228)``\n• #d089e9\n``#d089e9` `rgb(208,137,233)``\n• #d283ef\n``#d283ef` `rgb(210,131,239)``\n• #d57ef4\n``#d57ef4` `rgb(213,126,244)``\n• #d778fa\n``#d778fa` `rgb(215,120,250)``\n• #da73ff\n``#da73ff` `rgb(218,115,255)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #cd8ee4 is perceived by people affected by a color vision deficiency. This can be useful if you need to ensure your color combinations are accessible to color-blind users.\n\nMonochromacy\n• Achromatopsia 0.005% of the population\n• Atypical Achromatopsia 0.001% of the population\nDichromacy\n• Protanopia 1% of men\n• Deuteranopia 1% of men\n• Tritanopia 0.001% of the population\nTrichromacy\n• Protanomaly 1% of men, 0.01% of women\n• Deuteranomaly 6% of men, 0.4% of women\n• Tritanomaly 0.01% of the population"
] | [
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.5192048,"math_prob":0.54072076,"size":3729,"snap":"2021-04-2021-17","text_gpt3_token_len":1656,"char_repetition_ratio":0.12778524,"word_repetition_ratio":0.011090573,"special_character_ratio":0.5199785,"punctuation_ratio":0.23549107,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9621099,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-04-18T21:49:41Z\",\"WARC-Record-ID\":\"<urn:uuid:7d45ad84-adec-43c6-87bc-0ed373a9efcc>\",\"Content-Length\":\"36363\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0dba60db-7e96-4778-bf89-82e60eb81d7f>\",\"WARC-Concurrent-To\":\"<urn:uuid:b149d4d1-d21c-43dd-b732-106ad4b40c9e>\",\"WARC-IP-Address\":\"178.32.117.56\",\"WARC-Target-URI\":\"https://www.colorhexa.com/cd8ee4\",\"WARC-Payload-Digest\":\"sha1:RZP6NKZR7QIG4GSKNGQ2VPKMK3ZGIJG4\",\"WARC-Block-Digest\":\"sha1:NIXE34S4HLOQBJ7FW5PQZDYJP6BZJLLJ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-17/CC-MAIN-2021-17_segments_1618038860318.63_warc_CC-MAIN-20210418194009-20210418224009-00343.warc.gz\"}"} |
https://www.thoughtco.com/boson-2699112 | [
"# What Is a Boson?\n\nIn particle physics, a boson is a type of particle that obeys the rules of Bose-Einstein statistics. These bosons also have a quantum spin with contains an integer value, such as 0, 1, -1, -2, 2, etc. (By comparison, there are other types of particles, called fermions, that have a half-integer spin, such as 1/2, -1/2, -3/2, and so on.)\n\n## What's So Special About a Boson?\n\nBosons are sometimes called force particles, because it is the bosons that control the interaction of physical forces, such as electromagnetism and possibly even gravity itself.\n\nThe name boson comes from the surname of Indian physicist Satyendra Nath Bose, a brilliant physicist from the early twentieth century who worked with Albert Einstein to develop a method of analysis called Bose-Einstein statistics. In an effort to fully understand Planck's law (the thermodynamics equilibrium equation that came out of Max Planck's work on the blackbody radiation problem), Bose first proposed the method in a 1924 paper trying to analyze the behavior of photons. He sent the paper to Einstein, who was able to get it published ... and then went on to extend Bose's reasoning beyond mere photons, but also to apply to matter particles.\n\nOne of the most dramatic effects of Bose-Einstein statistics is the prediction that bosons can overlap and coexist with other bosons. Fermions, on the other hand, cannot do this, because they follow the Pauli Exclusion Principle (chemists focus primarily on the way the Pauli Exclusion Principle impacts the behavior of electrons in orbit around an atomic nucleus.) Because of this, it is possible for photons to become a laser and some matter is able to form the exotic state of a Bose-Einstein condensate.\n\n## Fundamental Bosons\n\nAccording to the Standard Model of quantum physics, there are a number of fundamental bosons, which are not made up of smaller particles. This includes the basic gauge bosons, the particles that mediate the fundamental forces of physics (except for gravity, which we'll get to in a moment). These four gauge bosons have spin 1 and have all been experimentally observed:\n\n• Photon - Known as the particle of light, photons carry all electromagnetic energy and act as the gauge boson that mediates the force of electromagnetic interactions.\n• Gluon - Gluons mediate the interactions of the strong nuclear force, which binds together quarks to form protons and neutrons and also holds the protons and neutrons together within an atom's nucleus.\n• W Boson - One of the two gauge bosons involved in mediating the weak nuclear force.\n• Z Boson - One of the two gauge bosons involved in mediating the weak nuclear force.\n\nIn addition to the above, there are other fundamental bosons predicted, but without clear experimental confirmation (yet):\n\n• Higgs Boson - According to the Standard Model, the Higgs Boson is the particle that gives rise to all mass. On July 4, 2012, scientists at the Large Hadron Collider announced that they had good reason to believe they'd found evidence of the Higgs Boson. Further research is ongoing in an attempt to get better information about the particle's exact properties. The particle is predicted to have a quantum spin value of 0, which is why it is classified as a boson.\n• Graviton - The graviton is a theoretical particle which has not yet been experimentally detected. Since the other fundamental forces - electromagnetism, strong nuclear force, and weak nuclear force - are all explained in terms of a gauge boson that mediates the force, it was only natural to attempt to use the same mechanism to explain gravity. The resulting theoretical particle is the graviton, which is predicted to have a quantum spin value of 2.\n• Bosonic Superpartners - Under the theory of supersymmetry, every fermion would have a so-far-undetected bosonic counterpart. Since there are 12 fundamental fermions, this would suggest that - if supersymmetry is true - there are another 12 fundamental bosons that have not yet been detected, presumably because they are highly unstable and have decayed into other forms.\n\n## Composite Bosons\n\nSome bosons are formed when two or more particles join together to create an integer-spin particle, such as:\n\n• Mesons - Mesons are formed when two quarks bond together. Since quarks are fermions and have half-integer spins, if two of them are bonded together, then the spin of the resulting particle (which is the sum of the individual spins) would be an integer, making it a boson.\n• Helium-4 atom - A helium-4 atom contains 2 protons, 2 neutrons, and 2 electrons ... and if you add up all of those spins, you'll end up with an integer every time. Helium-4 is particularly noteworthy because it becomes a superfluid when cooled to ultra-low temperatures, making it a brilliant example of Bose-Einstein statistics in action.\n\nIf you're following the math, any composite particle that contains an even number of fermions is going to be a boson, because an even number of half-integers is always going to add up to an integer.\n\nFormat\nmla apa chicago"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.9187388,"math_prob":0.8313846,"size":6022,"snap":"2021-31-2021-39","text_gpt3_token_len":1328,"char_repetition_ratio":0.113492854,"word_repetition_ratio":0.041841004,"special_character_ratio":0.20856859,"punctuation_ratio":0.12298025,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95597404,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-27T09:56:27Z\",\"WARC-Record-ID\":\"<urn:uuid:f7762bd1-b3cb-4b5f-a302-1af787205d11>\",\"Content-Length\":\"121106\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9f8f88d8-6822-4ae2-bb9a-e23584dedec8>\",\"WARC-Concurrent-To\":\"<urn:uuid:19ba36cf-04bb-458b-9a11-a9757c29a35c>\",\"WARC-IP-Address\":\"199.232.66.137\",\"WARC-Target-URI\":\"https://www.thoughtco.com/boson-2699112\",\"WARC-Payload-Digest\":\"sha1:IL2PSXGW3JROC33RX3MVP54SYSGFCHFM\",\"WARC-Block-Digest\":\"sha1:KZHVZH4OQZZPT6CTFQDRBBCZ23VYJYJB\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780058415.93_warc_CC-MAIN-20210927090448-20210927120448-00328.warc.gz\"}"} |
https://papertowrite.com/profit-margin-and-debt-ratio/ | [
"# Profit Margin and Debt Ratio\n\nBA 350 Week 8 Final Exam Sum ( 100% Correct Solution + Steps by Steps Calculation with details *****)\n\n2-4 – (Income Statement)\n\nPearson Brothers recently reported an EBITDA of \\$7.5 Million and net income of \\$1.8 million. It had \\$2.0 million of interest expense, and its corporate tax rate was 40%. What was its charge for depreciation and amortization?\n2-7 – (Corporate Tax Liability)\n\nThe Talley Corporation had a taxable income of \\$365,000 from operations after all operating costs but before (1) interest charge of \\$50,000, (2) dividends received of \\$15,000, (3) dividends paid of \\$25,000, and (4) income taxes. What are the company’s marginal and average tax rates on taxable income?\nChapter 3 Problem 3-8, 3-10\n3-8 – (Profit Margin and Debt Ratio)\nAssume you are given the following relationships for the Clayton Corporation: Sales/total assets 1.5 Return on assets (ROA) 3% Return on equity (ROE) 5% Calculate Clayton’s profit margin and debt ratio.\n3-10 – (Times-interest-earned ratio)\nThe Manor Corporation has \\$500,000 of debt outstanding, and it pays an interest rate of 10% annually: Manor’s annual sales are \\$2 million, its average tax rate is 30%, and its net profit margin on sales is 5%. If the company does not maintain a TIE ratio of at least 5 to 1, then its bank will refuse to renew the loan and bankruptcy will result. What is Manor’s TIE ratio?\nChapter 12 Problem 12.1 12-4\n12.1 – (AFN Equation)\nBaxter Video Product’s sales are expected to increase by 20% from \\$5 million in 2010 to \\$6 million in 2011. Its assets totaled \\$3 million at the end of 2010. Baxter is already at full capacity, so its assets must grow at the same rate as projected sales. At the end of 2010, current liabilities were\\$1 million, consisting of \\$250,000 of accounts payable, \\$500,000 of notes payable, and \\$250,000 of accruals. The after-tax profit margin is forecasted to be 5%, and the forecasted payout ratio is 70%. Use the AFN equation to forecast Baxter’s additional funds needed for the coming year.\n12-4 – (Sales Increase)\nBannister Legal Services generated \\$2,000,000 in sales during 2010, and its year-end total assets were \\$1,500,000. Also, at year-end 2010, current liabilities were \\$500,000, consisting of \\$200,000 of notes payable, \\$200,000 of accounts payable, and \\$100,000 of accruals. Looking ahead to 2011, the company estimates that its assets must increase at the same rate as sales, its spontaneous liabilities will increase at the same rate as sales, its profit margin will be 5%, and its payout ratio will be 60%. How large a sales increase can the company achieve without having to raise funds externally; that is, what is its self-supporting growth rate?\nChapter 13 Problem 13-6, 13-7, 13-8\n13-6:\nBrooks Enterprises has never paid a dividend. Free cash flow is projected to be\n\\$80,000 and \\$100,000 for the next 2 years, respectively; after the second year, FCF is expected to grow at a constant rate of 8%. The company’s weighted average cost of capital is 12%.\na. What is the terminal, or horizon, value of operations? (Hint: Find the value of all free cash flows beyond Year 2 discounted back to Year 2.)\nb. Calculate the value of Brooks’s operations.\n13- 7\nDozier Corporation is a fast growing supplier of office products. Analysts project the following free cash flows (FCFs) during the next 3 years, after which FCF is expected to grow at a constant 7% rate. Dozier’s weighted average cost of capital is WACC = 13%.\nYEAR\n1 2 3\nFree Cash Flow (\\$millions) -\\$20 \\$30 \\$40\na.) What is Dozier’s terminal, or horizon, value? (Hint: Find the value of all free cash flows beyond year 3 discounted back to Year 3.)\nb.) What is the current value of operations for Dozier?\nc.) Suppose Dozier has \\$10 million in marketable securities, \\$100 million in debt, and 10 million shares of stock. What is the intrinsic price per share?\n13.8\nThe balance sheet of Hutter Amalgamated is shown below. If the 12/31/2010 value of operations is \\$756 million, what is the 12/31/2010 intrinsic market value of equity?\nAssets Liabilities and Equity\nCash \\$20.0 Accounts Payable \\$19.0\nMarketable securities 77.0 Notes Payable 151.0\nAccounts receivable 100.0 Accruals 51.0\nInventories 200.0 Total current liabilities \\$221.0\nTotal current assets \\$397.0 Long term bonds 190.0\nNet Plant and equipment 279.0 Preferred stock 76.0\nCommon stock\n(par plus PIC) 100.0\nRetained earnings 89.0\nCommon equity \\$189.0\nTotal Assets \\$676.0 Total liabilities \\$676.0\nChapter 4 Problem 4-4, 4-5, 4-20, 4-22\n4-4:\nIf you deposit money today in an account that pays 6.5% annual interest, how long will it take to double your money?\n\n4-5:\nYou have \\$42,180.53 in a brokerage account, and you plan to deposit an additional \\$5,000 at the end of every future year until your account totals \\$250,000. You expect to earn 12% annually on the account. How many years will it take to reach your goal?\n\n4-20:\na. Set up an amortization schedule for a \\$25,000 loan to be repaid in equal instalments at the end of each of the next 5 years. The interest rate is 10%.\nb. How large must each annual payment be if the loan is for \\$50,000? Assume that the interest rate remains at 10% and that the loan is still paid off over 5 years.\nc. How large must each payment be if the loan is for \\$50,000, the interest rate is 10%, and the loan is paid off in equal installments at the end of each of the next 10 years? This loan is for the same amount as the loan in part b, but the payments are spread out over twice as many periods. Why are these payments not half as large as the payments on the loan in part b?\n4-22:\nWashington-Pacific invested \\$4 million to buy a tract of land and plant some young pine trees. The trees can be harvested in 10 years, at which time W-P plans to sell the forest at an expected price of \\$8 million. What is W-P’s expected rate of return?\nChapter 5 Problem 5-15, 5-21\n5-15;\nAbsalom Motors’s 14% coupon rate, semiannual payment, \\$1,000 par value bonds that mature in 30 years are callable 5 years from now at a price of \\$1,050. The bonds sell at a price of \\$1,353.54, and the yield curve is flat. Assuming that interest rates in the economy are expected to remain at their current level, what is the best estimate of the nominal interest rate on new bonds?\n5-21:\nSuppose Hillard Manufacturing sold an issue of bonds with a 10-year maturity, a \\$1,000 par value, a 10% coupon rate, and semiannual interest payments.\na. Two years after the bonds were issued, the going rate of interest on bonds such as these fell to 6%. At what price would the bonds sell?\nb. Suppose that, 2 years after the initial offering, the going interest rate had risen to 12%. At what price would the bonds sell?\nc. Suppose, as in part a, that interest rates fell to 6%, 2 years after the issue date. Suppose further that the interest rate remained at 6% for the next 8 years. What would happen to the price of the bonds over time?\nChapter 6 Problem 6-4, 6-10\n6-4:\nA stock’s returns have the following distribution:Demand for Probability of Rate of return\n\nCompany’s this Demand if this demand\n\nProducts Occuring Occurs\n\nWeak 0.1 (50%)\n\nBelow Average 0.2 (5)\n\nAverage 0.4 16\n\nAbove average 0.2 25\n\nStrong 0.1 60\n\n1.0\n\nCalculate the stock’s expected return, standard deviation, and coefficient of variation.\n\n6-10:\nYou have a \\$2 million portfolio consisting of a \\$100,000 investment in each of 20different stocks. The portfolio has a beta of 1.1. You are considering selling \\$100,000 worth of one stock with a beta of 0.9 and using the proceeds to purchase another stock with a beta of 1.4. What will the portfolio’s new beta be after these transactions?\nChapter 7 Problem 7-4, 7-10\n7-4:\nNick’s Enchiladas Incorporated has preferred stock outstanding that pays a dividend of \\$5 at the end of each year. The preferred sells for \\$50 a share. What is the stock’s required rate of return?\n7-10:\nThe beta coefficient for Stock C is bC = 0.4 and that for Stock D is bD = −0.5. (Stock D’s beta is negative, indicating that its rate of return rises whenever returns on most other stocks fall. There are very few negative-beta stocks, although collection agency and gold mining stocks are sometimes cited as examples.)\na. If the risk-free rate is 9% and the expected rate of return on an average stock is 13%, what are the required rates of return on Stocks C and D?\nb. For Stock C, suppose the current price, P0, is \\$25; the next expected dividend,D1, is \\$1.50; and the stock’s expected constant growth rate is 4%. Is the stock in equilibrium? Explain, and describe what would happen if the stock were not in equilibrium.\nChapter 8 Problem 8-4, 8-5, 8-6\n\n8-4:\nThe current price of a stock is \\$33, and the annual risk-free rate is 6%. A call option with a strike price of \\$32 and with 1 year until expiration has a current value of \\$6.56. What is the value of a put option written on the stock with the same exercise price and expiration date as the call option?\n8-5:\nUse the Black-Scholes Model to find the price for a call option with the following inputs: (1) current stock price is \\$30, (2) strike price is \\$35, (3) time to expiration is 4 months, (4) annualized risk-free rate is 5%, and (5) variance of stock return is 0.25.\n\n8-6:\nThe current price of a stock is \\$20. In 1 year, the price will be either \\$26 or \\$16. The annual risk-free rate is 5%. Find the price of a call option on the stock that has a strike price of \\$21 and that expires in 1 year. (Hint: Use daily compounding.)\nChapter 9 Problem 9-3, 9-8, 9-13\n9-3:\nDuggins Veterinary Supplies can issue perpetual preferred stock at a price of \\$50 a share with an annual dividend of \\$4.50 a share. Ignoring flotation costs, what is the company’s cost of preferred stock, rps?\n9-8;\nDavid Ortiz Motors has a target capital structure of 40% debt and 60% equity. The yield to maturity on the company’s outstanding bonds is 9%, and the company’s tax rate is 40%. Ortiz’s CFO has calculated the company’s WACC as 9.96%. What is the company’s cost of equity capital?\n9-13:\nMessman Manufacturing will issue common stock to the public for \\$30. The expected dividend and the growth in dividends are \\$3.00 per share and 5%, respectively. If the flotation cost is 10% of the issue’s gross proceeds, what is the cost of external equity, re?\nBA/350 Week 8 Final\nBA350 Week 8 Final Exam\nBA 350 Week 8 Final Exam Sum"
] | [
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.64358354,"math_prob":0.95151633,"size":343,"snap":"2021-43-2021-49","text_gpt3_token_len":100,"char_repetition_ratio":0.1179941,"word_repetition_ratio":0.0,"special_character_ratio":0.31778425,"punctuation_ratio":0.12676056,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9669526,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-11-29T02:37:44Z\",\"WARC-Record-ID\":\"<urn:uuid:5a97b592-e765-4e08-9034-9c631d6494c3>\",\"Content-Length\":\"84922\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:48f212f8-7558-4691-ac71-1ea2ee340237>\",\"WARC-Concurrent-To\":\"<urn:uuid:b1e373fa-6dd1-47a4-93df-247e628748b8>\",\"WARC-IP-Address\":\"198.187.29.220\",\"WARC-Target-URI\":\"https://papertowrite.com/profit-margin-and-debt-ratio/\",\"WARC-Payload-Digest\":\"sha1:SE7MTC6K3XHFSNM5GTAUMSCXX7SGG7I7\",\"WARC-Block-Digest\":\"sha1:DTGWL4FSF76M74SKHTGTXXKQRJUU2CP6\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964358685.55_warc_CC-MAIN-20211129014336-20211129044336-00030.warc.gz\"}"} |
https://byjus.com/question-answer/calculate-the-compound-interest-on-15000-in-3-years-if-the-rates-of-interest-for/ | [
"",
null,
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"Question\n\nCalculate the compound interest on ₹ 15000 in 3 years; if the rates of interest for successive years be 6%, 8% and 10% respectively.\n\nA\n\n₹ 3789.20",
null,
"",
null,
"B\n\n₹ 3889.20",
null,
"",
null,
"C\n\n₹ 4389.20",
null,
"",
null,
"D\n\n₹ 3684.20",
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"",
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"Solution\n\nThe correct option is B ₹ 3889.20 Principal(P)=₹ 15000 Time(t)=3 years Rate(R1)= 6% Rate(R2)= 8% Rate(R3)=10% Amount= P(1+R1100)(1+R2100)(1+R3100) =₹15000×(1+6100)(1+8100)(1+10100) =₹15000×5350×2725×1110=₹18889.20 C.I.=Amount-Principal = ₹ 18889.20- ₹ 15000= ₹ 3889.20Mathematics\n\nSuggest Corrections",
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"Similar questions\nView More",
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"People also searched for\nView More",
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"data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7",
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https://en.fremitus.pl/bilirubin-unit-converter-calculator/ | [
"# Bilirubin unit converter calculator",
null,
"Welcome to our Bilirubin Concentration Unit Converter Calculator! This handy tool allows you to seamlessly convert bilirubin concentration values between two common units: mg/dL and μmol/L. Whether you’re a medical professional, researcher, or simply curious, this calculator will simplify the conversion process for you.\n\n## Try Our Bilirubin Unit Converter Calculator Now:\n\nWhether you’re managing patient data, conducting research, or simply curious, our calculator is here to assist you. Say goodbye to manual conversions and welcome a quicker, more accurate way of converting bilirubin concentration. Try our Bilirubin Unit Converter Calculator today and experience the convenience firsthand!\n\n### Bilirubin Concentration Unit Converter Calculator\n\nThe calculator below is used to convert bilirubin concentration between units: mg/dL and μmol/L.\n\n## How to Use the Bilirubin Unit Converter Calculator:\n\nUsing our calculator is straightforward. Simply input the bilirubin concentration value in either mg/dL or μmol/L, and the calculator will instantly provide you with the converted result in the other unit.\n\n## Why Use the Bilirubin Concentration Unit Converter Calculator?\n\nConverting bilirubin concentration from one unit to another is essential in medical diagnostics and research. This calculator eliminates the hassle of manual conversions, saving you time and ensuring accuracy in your work.\n\n## Converting Bilirubin Concentration: The Manual Approach\n\nWhile our calculator is efficient, it’s also helpful to understand the conversion process. To convert bilirubin concentration from mg/dL to μmol/L, multiply the value by 17.10. For instance, if you have a bilirubin value of 3.5 mg/dL:\n\n``3.5 mg/dL x 17.10 = 59.9 μmol/L``\n\nConversely, to convert bilirubin concentration from μmol/L to mg/dL, divide the value by 17.10. For example, if you have a bilirubin value of 80 μmol/L:\n\n``80 μmol/L / 17.10 = 4.68 mg/dL``"
] | [
null,
"https://en.fremitus.pl/wp-content/uploads/2022/08/BILIRUBINA1.png",
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.82957524,"math_prob":0.86125535,"size":2848,"snap":"2023-40-2023-50","text_gpt3_token_len":613,"char_repetition_ratio":0.17475387,"word_repetition_ratio":0.018957347,"special_character_ratio":0.19171348,"punctuation_ratio":0.12185687,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9598908,"pos_list":[0,1,2],"im_url_duplicate_count":[null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-07T23:39:21Z\",\"WARC-Record-ID\":\"<urn:uuid:a6f15828-ec92-4ecd-a5fa-beb56f818eb3>\",\"Content-Length\":\"75695\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:eb64a23a-a804-4532-8a22-7e73e132e637>\",\"WARC-Concurrent-To\":\"<urn:uuid:1a871131-2be9-480e-ab9c-ca8a3c68fd1e>\",\"WARC-IP-Address\":\"95.217.114.225\",\"WARC-Target-URI\":\"https://en.fremitus.pl/bilirubin-unit-converter-calculator/\",\"WARC-Payload-Digest\":\"sha1:XXZ76VMK55YVBB5NRKK2JI52MCKQLQFG\",\"WARC-Block-Digest\":\"sha1:ZCCRIBK2ERFWA3CF2MWOB3J6D6TXCYCW\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100705.19_warc_CC-MAIN-20231207221604-20231208011604-00195.warc.gz\"}"} |
http://olympiacapitalresearch.com/math-facts-multiplication/math-facts-multiplication-awesome-22-best-fact-families-images-on-pinterest/ | [
"# Math Facts Multiplication Awesome 22 Best Fact Families Images On Pinterest",
null,
"",
null,
"New Release Ideas Of Math Facts Multiplication – From the thousand Figure on the net in relation to math facts multiplication, we picks the very best collections together with best image resolution special for you, and now this images ,in actual fact, one among stocks libraries in our ideal photographs gallery in relation to New Release Ideas Of Math Facts Multiplication. Lets hope you might love it.\n\nBeautiful graphic (Math Facts Multiplication Awesome 22 Best Fact Families Images On Pinterest) over is classed with: math facts bulletin board, math facts data sheet, math facts in a flash game, math facts learning games, math facts minute worksheets, math facts multiplication, math facts n a flash, math facts number 2, math facts oswego, math facts practice games, math facts puter games, math facts quiz, math facts quizlet, math facts quora, math facts test, math facts to know for the sat, math facts up to 12 worksheets, math facts worksheets 2nd grade, math facts x6, x4 math facts worksheets,\nposted by means of Nicholas Stevens at 2019-01-10 13:48:18. To view plenty models throughout New Release Ideas Of Math Facts Multiplication shots gallery you should follow this particular website URL.\n\nIf you feel happy with this post, then please share with your friends.",
null,
""
] | [
null,
"http://olympiacapitalresearch.com/wp-content/themes/olympia/img/ads336.png",
null,
"http://olympiacapitalresearch.com/wp-content/uploads/2018/08/math-facts-multiplication-awesome-22-best-fact-families-images-on-pinterest-of-math-facts-multiplication.jpg",
null,
"http://olympiacapitalresearch.com/wp-content/themes/olympia/img/ads336.png",
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.79291385,"math_prob":0.8110879,"size":1354,"snap":"2019-13-2019-22","text_gpt3_token_len":284,"char_repetition_ratio":0.23407407,"word_repetition_ratio":0.083333336,"special_character_ratio":0.20753324,"punctuation_ratio":0.12890625,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9559218,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,null,null,1,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-03-25T05:33:51Z\",\"WARC-Record-ID\":\"<urn:uuid:2e827d21-0fdc-425d-93ef-1b507287bae2>\",\"Content-Length\":\"27680\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e87fe3c3-b898-47b9-9d3e-828e8b2e6264>\",\"WARC-Concurrent-To\":\"<urn:uuid:9f4c9998-e6dc-427f-99ba-670cbb506335>\",\"WARC-IP-Address\":\"104.28.4.150\",\"WARC-Target-URI\":\"http://olympiacapitalresearch.com/math-facts-multiplication/math-facts-multiplication-awesome-22-best-fact-families-images-on-pinterest/\",\"WARC-Payload-Digest\":\"sha1:YF4HBO7ZGU6V5OAIAZON5DSGKKTN4DLL\",\"WARC-Block-Digest\":\"sha1:U77O33XV4N3XGIFAQ4PMV3KBIFR2GKKZ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-13/CC-MAIN-2019-13_segments_1552912203755.18_warc_CC-MAIN-20190325051359-20190325073359-00183.warc.gz\"}"} |
https://answers.everydaycalculation.com/lcm/10-11 | [
"Solutions by everydaycalculation.com\n\n## What is the LCM of 10 and 11?\n\nThe lcm of 10 and 11 is 110.\n\n#### Steps to find LCM\n\n1. Find the prime factorization of 10\n10 = 2 × 5\n2. Find the prime factorization of 11\n11 = 11\n3. Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:\n\nLCM = 2 × 5 × 11\n4. LCM = 110\n\nFind least common multiple (lcm) of:\n\n#### LCM Calculator\n\nEnter two numbers separate by comma. To find lcm of more than two numbers, click here."
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.72695124,"math_prob":0.9985522,"size":311,"snap":"2019-13-2019-22","text_gpt3_token_len":115,"char_repetition_ratio":0.14332248,"word_repetition_ratio":0.0,"special_character_ratio":0.4726688,"punctuation_ratio":0.104477614,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9978038,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-03-19T09:45:19Z\",\"WARC-Record-ID\":\"<urn:uuid:812afcd5-6768-498e-bbd5-1539c504c95b>\",\"Content-Length\":\"5199\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:516000f9-600c-4f3e-8c14-9e00e3858f65>\",\"WARC-Concurrent-To\":\"<urn:uuid:35f3a09d-bc1d-454c-847e-729f5ce75dd4>\",\"WARC-IP-Address\":\"96.126.107.130\",\"WARC-Target-URI\":\"https://answers.everydaycalculation.com/lcm/10-11\",\"WARC-Payload-Digest\":\"sha1:3P4PQXJIYR4HEKR3IDCW55G5XFVE43PM\",\"WARC-Block-Digest\":\"sha1:SCXRO4UFZPWTNLPNFAAGNV5FBHSPGMYH\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-13/CC-MAIN-2019-13_segments_1552912201953.19_warc_CC-MAIN-20190319093341-20190319115341-00456.warc.gz\"}"} |
https://www.chinaedu.com/article/609654.html | [
"101教育热线电话\n400-6869-101",
null,
"微信\n\n2015高一数学暑假作业\n\n1.T1=，T2=，T3=，则下列关系式正确的是( )\n\nA.T1，\n\nB.d>b>c>a\n\nC. d>c>b>a\n\nD.b>c>d>a\n\n【解析】 由幂函数的图象及性质可知a<0，b>c>1,0c>d>a.故选D.\n\n【答案】 D\n\n3.设α∈{-1,1，，3}，则使函数y=xα的定义域为R且为奇函数的所有α的值为( )\n\nA.1,3 B.-1,1\n\nC.-1,3 D.-1,1,3\n\n【解析】 y=x-1=的定义域不是R;y=x=的定义域不是R;y=x与y=x3的定义域都是R，且它们都是奇函数.故选A.\n\n【答案】 A\n\n4.已知幂函数y=f(x)的图象经过点，则f(4)的值为( )\n\nA.16 B.2\n\nC. D.\n\n【解析】 设f (x)=xα，则2α==2-，所以α=-，f(x)=x-，f(4)=4-=.故选C.\n\n【答案】 C\n\n【解析】 ∵-<-，且n>n，\n\n∴y=xn在(-∞，0)上为减函数.\n\n∴n=-1或n=2.【答案】 -1或2\n\n6.设f(x)=(m-1)xm2-2，如果f(x)是正比例函数，则m=________，如果f(x)是反比例函数，则m=________，如果f(x)是幂函数，则m=________.\n\n【解析】 f(x)=(m-1)xm2-2，\n\n【答案】 ± -1 2\n\n7.已知f(x)=，\n\n(1)判断f(x)在(0，+∞)上的单调性并证明;\n\n(2)当x∈[1，+∞)时，求f(x)的最大值.\n\n【解析】 函数f(x)在(0，+∞)上是减函数.证明如下：任取x1、x2∈(0，+∞)，且x10，x2-x1>0，x12x22>0.\n\n∴f(x1)-f(x2)>0，即f(x1)>f(x2).\n\n∴函数f(x)在(0，+∞)上是减函数.\n\n(2)由(1)知，f(x)的单调减区间为(0，+∞)，∴函数f(x)在[1，+∞)上是减函数，\n\n∴函数f(x)在[1，+∞)上的最大值为f(1)=2.\n\n8.已知幂函数y=xp-3(p∈N*)的图象关于y轴对称，且在\n\n(0，+∞)上是减函数，求满足(a-1)<(3+2a)的a的取值范围.\n\n【解析】 ∵函数y=xp-3在(0，+∞)上是减函数，\n\n∴p-3<0，即p<3，又∵p∈N*，∴p=1，或p=2.\n\n∵函数y=xp-3的图象关于y轴对称，\n\n∴p-3是偶数，∴取p=1，即y=x-2，(a-1)<(3+2a)\n\n∵函数y=x在(-∞，+∞)上是增函数，\n\n∴由(a-1)<(3+2a)，得a-1<3+2a，即a>-4.\n\n∴所求a的取值范围是(-4，+∞).\n\n相关文章推荐",
null,
"*图形验证码",
null,
""
] | [
null,
"https://www.chinaedu.com/bundles/prceducms/frontend/images/weixin_top.png",
null,
"https://www.chinaedu.com/bundles/prceducms/frontend/images/xz_people.gif",
null,
"https://www.chinaedu.com/article/609654.html",
null
] | {"ft_lang_label":"__label__zh","ft_lang_prob":0.77974886,"math_prob":0.99995255,"size":1336,"snap":"2019-26-2019-30","text_gpt3_token_len":1221,"char_repetition_ratio":0.12012012,"word_repetition_ratio":0.0,"special_character_ratio":0.51497006,"punctuation_ratio":0.15561225,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9933695,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,null,null,null,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-06-16T03:53:59Z\",\"WARC-Record-ID\":\"<urn:uuid:c1416b88-2198-4a59-a2f8-69fc7cca5444>\",\"Content-Length\":\"44260\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:fbb61619-35b4-4b3f-927b-d6e6e4e36fb5>\",\"WARC-Concurrent-To\":\"<urn:uuid:19524787-f600-440a-b122-b00563045498>\",\"WARC-IP-Address\":\"117.23.61.241\",\"WARC-Target-URI\":\"https://www.chinaedu.com/article/609654.html\",\"WARC-Payload-Digest\":\"sha1:56KH2GBVXPJ3G5SAGKAGQ7HVYBPMLZZI\",\"WARC-Block-Digest\":\"sha1:WRBU57NMFJDNEUGUMLJRGLIFTLOUASKL\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-26/CC-MAIN-2019-26_segments_1560627997533.62_warc_CC-MAIN-20190616022644-20190616044644-00212.warc.gz\"}"} |
https://www.colorhexa.com/690002 | [
"# #690002 Color Information\n\nIn a RGB color space, hex #690002 is composed of 41.2% red, 0% green and 0.8% blue. Whereas in a CMYK color space, it is composed of 0% cyan, 100% magenta, 98.1% yellow and 58.8% black. It has a hue angle of 358.9 degrees, a saturation of 100% and a lightness of 20.6%. #690002 color hex could be obtained by blending #d20004 with #000000. Closest websafe color is: #660000.\n\n• R 41\n• G 0\n• B 1\nRGB color chart\n• C 0\n• M 100\n• Y 98\n• K 59\nCMYK color chart\n\n#690002 color description : Very dark red.\n\n# #690002 Color Conversion\n\nThe hexadecimal color #690002 has RGB values of R:105, G:0, B:2 and CMYK values of C:0, M:1, Y:0.98, K:0.59. Its decimal value is 6881282.\n\nHex triplet RGB Decimal 690002 `#690002` 105, 0, 2 `rgb(105,0,2)` 41.2, 0, 0.8 `rgb(41.2%,0%,0.8%)` 0, 100, 98, 59 358.9°, 100, 20.6 `hsl(358.9,100%,20.6%)` 358.9°, 100, 41.2 660000 `#660000`\nCIE-LAB 20.078, 41.76, 29.885 5.837, 3.008, 0.331 0.636, 0.328, 3.008 20.078, 51.352, 35.589 20.078, 65.655, 13.78 17.345, 29.717, 11.011 01101001, 00000000, 00000010\n\n# Color Schemes with #690002\n\n• #690002\n``#690002` `rgb(105,0,2)``\n• #006967\n``#006967` `rgb(0,105,103)``\nComplementary Color\n• #690037\n``#690037` `rgb(105,0,55)``\n• #690002\n``#690002` `rgb(105,0,2)``\n• #693300\n``#693300` `rgb(105,51,0)``\nAnalogous Color\n• #003769\n``#003769` `rgb(0,55,105)``\n• #690002\n``#690002` `rgb(105,0,2)``\n• #006933\n``#006933` `rgb(0,105,51)``\nSplit Complementary Color\n• #000269\n``#000269` `rgb(0,2,105)``\n• #690002\n``#690002` `rgb(105,0,2)``\n• #026900\n``#026900` `rgb(2,105,0)``\nTriadic Color\n• #670069\n``#670069` `rgb(103,0,105)``\n• #690002\n``#690002` `rgb(105,0,2)``\n• #026900\n``#026900` `rgb(2,105,0)``\n• #006967\n``#006967` `rgb(0,105,103)``\nTetradic Color\n• #1d0001\n``#1d0001` `rgb(29,0,1)``\n• #360001\n``#360001` `rgb(54,0,1)``\n• #500002\n``#500002` `rgb(80,0,2)``\n• #690002\n``#690002` `rgb(105,0,2)``\n• #830002\n``#830002` `rgb(131,0,2)``\n• #9c0003\n``#9c0003` `rgb(156,0,3)``\n• #b60003\n``#b60003` `rgb(182,0,3)``\nMonochromatic Color\n\n# Alternatives to #690002\n\nBelow, you can see some colors close to #690002. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #69001c\n``#69001c` `rgb(105,0,28)``\n• #690013\n``#690013` `rgb(105,0,19)``\n• #69000b\n``#69000b` `rgb(105,0,11)``\n• #690002\n``#690002` `rgb(105,0,2)``\n• #690700\n``#690700` `rgb(105,7,0)``\n• #691000\n``#691000` `rgb(105,16,0)``\n• #691800\n``#691800` `rgb(105,24,0)``\nSimilar Colors\n\n# #690002 Preview\n\nText with hexadecimal color #690002\n\nThis text has a font color of #690002.\n\n``<span style=\"color:#690002;\">Text here</span>``\n#690002 background color\n\nThis paragraph has a background color of #690002.\n\n``<p style=\"background-color:#690002;\">Content here</p>``\n#690002 border color\n\nThis element has a border color of #690002.\n\n``<div style=\"border:1px solid #690002;\">Content here</div>``\nCSS codes\n``.text {color:#690002;}``\n``.background {background-color:#690002;}``\n``.border {border:1px solid #690002;}``\n\n# Shades and Tints of #690002\n\nA shade is achieved by adding black to any pure hue, while a tint is created by mixing white to any pure color. In this example, #070000 is the darkest color, while #fff2f3 is the lightest one.\n\n• #070000\n``#070000` `rgb(7,0,0)``\n• #1b0001\n``#1b0001` `rgb(27,0,1)``\n• #2e0001\n``#2e0001` `rgb(46,0,1)``\n• #420001\n``#420001` `rgb(66,0,1)``\n• #550002\n``#550002` `rgb(85,0,2)``\n• #690002\n``#690002` `rgb(105,0,2)``\n• #7d0002\n``#7d0002` `rgb(125,0,2)``\n• #900003\n``#900003` `rgb(144,0,3)``\n• #a40003\n``#a40003` `rgb(164,0,3)``\n• #b70003\n``#b70003` `rgb(183,0,3)``\n• #cb0004\n``#cb0004` `rgb(203,0,4)``\n• #df0004\n``#df0004` `rgb(223,0,4)``\n• #f20005\n``#f20005` `rgb(242,0,5)``\nShade Color Variation\n• #ff070c\n``#ff070c` `rgb(255,7,12)``\n• #ff1b1f\n``#ff1b1f` `rgb(255,27,31)``\n• #ff2e32\n``#ff2e32` `rgb(255,46,50)``\n• #ff4245\n``#ff4245` `rgb(255,66,69)``\n• #ff5559\n``#ff5559` `rgb(255,85,89)``\n• #ff696c\n``#ff696c` `rgb(255,105,108)``\n• #ff7d7f\n``#ff7d7f` `rgb(255,125,127)``\n• #ff9092\n``#ff9092` `rgb(255,144,146)``\n• #ffa4a6\n``#ffa4a6` `rgb(255,164,166)``\n• #ffb7b9\n``#ffb7b9` `rgb(255,183,185)``\n• #ffcbcc\n``#ffcbcc` `rgb(255,203,204)``\n• #ffdfdf\n``#ffdfdf` `rgb(255,223,223)``\n• #fff2f3\n``#fff2f3` `rgb(255,242,243)``\nTint Color Variation\n\n# Tones of #690002\n\nA tone is produced by adding gray to any pure hue. In this case, #393031 is the less saturated color, while #690002 is the most saturated one.\n\n• #393031\n``#393031` `rgb(57,48,49)``\n• #3d2c2d\n``#3d2c2d` `rgb(61,44,45)``\n• #412829\n``#412829` `rgb(65,40,41)``\n• #452425\n``#452425` `rgb(69,36,37)``\n• #492021\n``#492021` `rgb(73,32,33)``\n• #4d1c1d\n``#4d1c1d` `rgb(77,28,29)``\n• #511819\n``#511819` `rgb(81,24,25)``\n• #551415\n``#551415` `rgb(85,20,21)``\n• #591012\n``#591012` `rgb(89,16,18)``\n• #5d0c0e\n``#5d0c0e` `rgb(93,12,14)``\n• #61080a\n``#61080a` `rgb(97,8,10)``\n• #650406\n``#650406` `rgb(101,4,6)``\n• #690002\n``#690002` `rgb(105,0,2)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #690002 is perceived by people affected by a color vision deficiency. This can be useful if you need to ensure your color combinations are accessible to color-blind users.\n\nMonochromacy\n• Achromatopsia 0.005% of the population\n• Atypical Achromatopsia 0.001% of the population\nDichromacy\n• Protanopia 1% of men\n• Deuteranopia 1% of men\n• Tritanopia 0.001% of the population\nTrichromacy\n• Protanomaly 1% of men, 0.01% of women\n• Deuteranomaly 6% of men, 0.4% of women\n• Tritanomaly 0.01% of the population"
] | [
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.5373014,"math_prob":0.8960135,"size":3614,"snap":"2021-21-2021-25","text_gpt3_token_len":1559,"char_repetition_ratio":0.14155124,"word_repetition_ratio":0.011090573,"special_character_ratio":0.57387936,"punctuation_ratio":0.23250565,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9942431,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-06-22T01:15:12Z\",\"WARC-Record-ID\":\"<urn:uuid:89680dca-195c-45d6-95b9-a50449ef1987>\",\"Content-Length\":\"36144\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:757174a3-b1ca-40e3-a384-4030e3789caa>\",\"WARC-Concurrent-To\":\"<urn:uuid:cd69bb2d-e2ca-4983-862a-bcd8f4943ecc>\",\"WARC-IP-Address\":\"178.32.117.56\",\"WARC-Target-URI\":\"https://www.colorhexa.com/690002\",\"WARC-Payload-Digest\":\"sha1:RBQ2XFTYDQ5R62KORCGXXPCA25F6YZ6U\",\"WARC-Block-Digest\":\"sha1:PMUEH42PF6EC66K6B2YIPRETSCRM6D2O\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-25/CC-MAIN-2021-25_segments_1623488504969.64_warc_CC-MAIN-20210622002655-20210622032655-00479.warc.gz\"}"} |
https://www.hipparchus.org/apidocs/org/hipparchus/transform/FastSineTransformer.html | [
"org.hipparchus.transform\n\n## Class FastSineTransformer\n\n• All Implemented Interfaces:\nSerializable, RealTransformer\n\n```public class FastSineTransformer\nextends Object\nimplements RealTransformer, Serializable```\nImplements the Fast Sine Transform for transformation of one-dimensional real data sets. For reference, see James S. Walker, Fast Fourier Transforms, chapter 3 (ISBN 0849371635).\n\nThere are several variants of the discrete sine transform. The present implementation corresponds to DST-I, with various normalization conventions, which are specified by the parameter `DstNormalization`. It should be noted that regardless to the convention, the first element of the dataset to be transformed must be zero.\n\nDST-I is equivalent to DFT of an odd extension of the data series. More precisely, if x0, …, xN-1 is the data set to be sine transformed, the extended data set x0#, …, x2N-1# is defined as follows\n\n• x0# = x0 = 0,\n• xk# = xk if 1 ≤ k < N,\n• xN# = 0,\n• xk# = -x2N-k if N + 1 ≤ k < 2N.\n\nThen, the standard DST-I y0, …, yN-1 of the real data set x0, …, xN-1 is equal to half of i (the pure imaginary number) times the N first elements of the DFT of the extended data set x0#, …, x2N-1#\nyn = (i / 2) ∑k=02N-1 xk# exp[-2πi nk / (2N)] k = 0, …, N-1.\n\nThe present implementation of the discrete sine transform as a fast sine transform requires the length of the data to be a power of two. Besides, it implicitly assumes that the sampled function is odd. In particular, the first element of the data set must be 0, which is enforced in `transform(UnivariateFunction, double, double, int, TransformType)`, after sampling.\n\nSee Also:\nSerialized Form\n• ### Constructor Summary\n\nConstructors\nConstructor and Description\n`FastSineTransformer(DstNormalization normalization)`\nCreates a new instance of this class, with various normalization conventions.\n• ### Method Summary\n\nAll Methods\nModifier and Type Method and Description\n`protected double[]` `fst(double[] f)`\nPerform the FST algorithm (including inverse).\n`double[]` ```transform(double[] f, TransformType type)```\nReturns the (forward, inverse) transform of the specified real data set.\n`double[]` ```transform(UnivariateFunction f, double min, double max, int n, TransformType type)```\nReturns the (forward, inverse) transform of the specified real function, sampled on the specified interval.\n• ### Methods inherited from class java.lang.Object\n\n`clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`\n• ### Constructor Detail\n\n• #### FastSineTransformer\n\n`public FastSineTransformer(DstNormalization normalization)`\nCreates a new instance of this class, with various normalization conventions.\nParameters:\n`normalization` - the type of normalization to be applied to the transformed data\n• ### Method Detail\n\n• #### transform\n\n```public double[] transform(double[] f,\nTransformType type)```\nReturns the (forward, inverse) transform of the specified real data set. The first element of the specified data set is required to be `0`.\nSpecified by:\n`transform` in interface `RealTransformer`\nParameters:\n`f` - the real data array to be transformed (signal)\n`type` - the type of transform (forward, inverse) to be performed\nReturns:\nthe real transformed array (spectrum)\nThrows:\n`MathIllegalArgumentException` - if the length of the data array is not a power of two, or the first element of the data array is not zero\n• #### transform\n\n```public double[] transform(UnivariateFunction f,\ndouble min,\ndouble max,\nint n,\nTransformType type)```\nReturns the (forward, inverse) transform of the specified real function, sampled on the specified interval. This implementation enforces `f(x) = 0.0` at `x = 0.0`.\nSpecified by:\n`transform` in interface `RealTransformer`\nParameters:\n`f` - the function to be sampled and transformed\n`min` - the (inclusive) lower bound for the interval\n`max` - the (exclusive) upper bound for the interval\n`n` - the number of sample points\n`type` - the type of transform (forward, inverse) to be performed\nReturns:\nthe real transformed array\nThrows:\n`MathIllegalArgumentException` - if the lower bound is greater than, or equal to the upper bound\n`MathIllegalArgumentException` - if the number of sample points is negative\n`MathIllegalArgumentException` - if the number of sample points is not a power of two\n• #### fst\n\n```protected double[] fst(double[] f)\nthrows MathIllegalArgumentException```\nPerform the FST algorithm (including inverse). The first element of the data set is required to be `0`.\nParameters:\n`f` - the real data array to be transformed\nReturns:\nthe real transformed array\nThrows:\n`MathIllegalArgumentException` - if the length of the data array is not a power of two, or the first element of the data array is not zero\n\nCopyright © 2016–2020 Hipparchus.org. All rights reserved."
] | [
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http://myworldtheirway.com/2020/05/lcm-interesting-smallest-number-puzzle/ | [
"# LCM – Interesting Smallest Number Puzzle\n\nI guess you might have used the concept of LCM ( Least Common Multiples ) many times in a grocery store while purchasing stuff without even realizing it. Remember the time when you had to pair up items and their package sizes were different and you didn’t want any “wastage”. How did you figure out how many of each item to buy ? For example, if the sausages are sold in a pack of 8 and buns in a pack of 12, how many of each you should buy so that there is no surplus. You used the concept of LCM and bought 3 packs of sausages and 2 packs of bun. This Interesting smallest number puzzle comes with a twist but can also be solved using the concept of LCM. Can you figure it out ?\n\n## The Smallest Number Puzzle\n\nCan you figure out the smallest number with the following properties\n\nGive the problem a try and leave your answers in the comments section or click below for the solution.\n\nAs you can see, using the concept of LCM we were easily able to solve this interesting smallest number puzzle.\n\n### LCM IN REAL LIFE SCENARIO\n\nLCM stands for least common multiple. The LCM of two or more numbers is the smallest number which is a multiple of all of the numbers.\n\nSo, how in real life it can used. Looking at the same example in the beginning, let’s say you are at the grocery store to buy sausages and buns for a party you’re hosting. You find that the sausages are sold in a pack of 8 and buns in a pack of 12. What is the least number of sausages and buns you need to buy in order to make sure there is an equal number of buns of sausages and nothing is leftover.\n\nThe answer would be the LCM(8, 12) = 24. The prime factors of 12 are 2 x 2 x 3. The prime factors of 8 are 2 x 2 x 2. Therefore, common factor of 12 and 8 are 2 x 2 x 2 x 3 =24."
] | [
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https://www.esaral.com/q/a-semi-circular-wire-of-radius-5-0cm-and-38335 | [
"",
null,
"# A semi-circular wire of radius 5.0cm and\n\nQuestion:\n\nA semi-circular wire of radius $5.0 \\mathrm{~cm}$ and carries a current of $5.0 \\mathrm{~A}$. A magnetic field B of magnitude $0.50 \\mathrm{~T}$ exists along the perpendicular to the plane of the wire. Find the magnitude of the magnetic force acting on the wire.\n\nSolution:",
null,
""
] | [
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"https://www.facebook.com/tr",
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"https://www.esaral.com/media/uploads/2022/03/26/image35205.png",
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https://dml.cz/handle/10338.dmlcz/703036 | [
"# Article\n\nKeywords:\nLagrangian dynamics, Random dynamical systems, Invariant measure, Hyperbolicity\nSummary:\nWe consider a class of 1d Lagrangian systems with random forcing in the spaceperiodic setting: \\begin{equation} \\nonumber \\phi_t+\\phi_x^2/2=F^{\\omega},\\ x \\in S^1=\\R / \\Z. \\end{equation} These systems have been studied since the 1990s by Khanin, Sinai and their collaborators [7, 9, 11, 12, 15]. Here we give an overview of their results and then we expose our recent proof of the exponential convergence to the stationary measure . This is the first such result in a classical setting, i.e. in the dual-Lipschitz metric with respect to the Lebesgue space $L_p$ for finite $p$, partially answering the conjecture formulated in . In the multidimensional setting, a more technically involved proof has been recently given by Iturriaga, Khanin and Zhang .\nReferences:\n Bec, J., Frisch, U., HASH(0x24c1f68), Khanin, K.: Kicked Burgers turbulence. Journal of Fluid Mechanics, 416(8) (2000), pp. 239–267. DOI 10.1017/S0022112000001051 | MR 1777053\n Boritchev, A.: Estimates for solutions of a low-viscosity kick-forced generalised Burgers equation. Proceedings of the Royal Society of Edinburgh A, 143(2) (2013), pp. 253–268. DOI 10.1017/S0308210511000989 | MR 3039811\n Boritchev, A.: Sharp estimates for turbulence in white-forced generalised Burgers equation. Geometric and Functional Analysis, 23(6) (2013), pp. 1730–1771. DOI 10.1007/s00039-013-0245-4 | MR 3132902\n Boritchev, A.: Erratum to: Multidimensional Potential Burgers Turbulence. Communicationsin Mathematical Physics, 344(1) (2016), pp. 369–370, see . DOI 10.1007/s00220-016-2621-z | MR 3493146\n Boritchev, A.: Multidimensional Potential Burgers Turbulence. Communications in Mathematical Physics, 342 (2016), pp. 441–489, with erratum: see . DOI 10.1007/s00220-015-2521-7 | MR 3459157\n Boritchev, A.: Exponential convergence to the stationary measure for a class of 1D Lagrangian systems with random forcing. accepted to Stochastic and Partial Differential Equations: Analysis and Computations. MR 3768996\n Boritchev, A., Khanin, K.: On the hyperbolicity of minimizers for 1D random Lagrangian systems. Nonlinearity, 26(1) (2013), pp. 65–80. DOI 10.1088/0951-7715/26/1/65 | MR 3001762\n Doering, C., Gibbon, J. D.: Applied analysis of the Navier-Stokes equations. Cambridge Texts in Applied Mathematics, Cambridge University Press, 1995. MR 1325465\n E, Weinan, Khanin, K., Mazel, A., HASH(0x24dff00), Sinai, Ya.: Invariant measures for Burgers equation with stochastic forcing. Annals of Mathematics, 151 (2000), pp. 877–960. DOI 10.2307/121126 | MR 1779561\n Fathi, A.: Weak KAM Theorem in Lagrangian Dynamics. preliminary version, 2005.\n Gomes, D., Iturriaga, R., Khanin, K., HASH(0x24e24c0), Padilla, P.: Viscosity limit of stationary distributions for the random forced Burgers equation. Moscow Mathematical Journal, 5 (2005), pp. 613–631. DOI 10.17323/1609-4514-2005-5-3-613-631 | MR 2241814\n Iturriaga, R., Khanin, K.: Burgers turbulence and random Lagrangian systems. Communications in Mathematical Physics, 232:3 (2003), pp. 377–428. DOI 10.1007/s00220-002-0748-6 | MR 1952472\n Iturriaga, R., Khanin, K., HASH(0x24e6f80), Zhang, K.: Exponential convergence of solutions for random Hamilton-Jacobi equation. Preprint, arxiv: 1703.10218, 2017.\n Iturriaga, R., Sanchez-Morgado, H.: Hyperbolicity and exponential convergence of the Lax-Oleinik semigroup. Journal of Differential Equations, 246(5) (2009), pp. 1744–1753. DOI 10.1016/j.jde.2008.12.012 | MR 2494686\n Khanin, K., Zhang, K.: Hyperbolicity of minimizers and regularity of viscosity solutions for random Hamilton-Jacobi equations. Communications in Mathematical Physics, 355 (2017), pp. 803. DOI 10.1007/s00220-017-2919-5 | MR 3681391\n Sinai, Y.: Two results concerning asymptotic behavior of solutions of the Burgers equation with force. Journal of Statistical Physics, 64, 1991, pp. 1–12. DOI 10.1007/BF01057866 | MR 1117645"
] | [
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.6166057,"math_prob":0.8105222,"size":2590,"snap":"2020-45-2020-50","text_gpt3_token_len":861,"char_repetition_ratio":0.122969836,"word_repetition_ratio":0.0,"special_character_ratio":0.3930502,"punctuation_ratio":0.2825688,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9755751,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-12-05T03:01:25Z\",\"WARC-Record-ID\":\"<urn:uuid:b8dc1c8c-e9a1-4641-890d-1e676f75e343>\",\"Content-Length\":\"18491\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:302e410d-95a1-48e9-8fd4-d98fa0d7497c>\",\"WARC-Concurrent-To\":\"<urn:uuid:df0c8da9-741a-44ae-af49-efdf87080c9b>\",\"WARC-IP-Address\":\"147.251.6.150\",\"WARC-Target-URI\":\"https://dml.cz/handle/10338.dmlcz/703036\",\"WARC-Payload-Digest\":\"sha1:BKTN6WMI62WXG3U746HICJ7YGSSXCPWG\",\"WARC-Block-Digest\":\"sha1:GDUAFFJ6ZKKLVSR7U4JLIV3MTLPLZQKF\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141746033.87_warc_CC-MAIN-20201205013617-20201205043617-00493.warc.gz\"}"} |
https://nntdm.net/volume-21-2015/number-3/56-63/ | [
"# Tridiagonal matrices related to subsequences of balancing and Lucas-balancing numbers\n\nPrasanta K Ray and Gopal K Panda\nNotes on Number Theory and Discrete Mathematics, ISSN 1310-5132\nVolume 21, 2015, Number 3, Pages 56—63\n\n## Details\n\n### Authors and affiliations\n\nPrasanta K Ray",
null,
"Department of Mathematics, Veer Surendra Sai University of Technology\nOdisha, Burla-768018, India\n\nGopal K Panda",
null,
"Department of Mathematics, National Institute of Technology Rourkela\nRourkela-769008, India\n\n### Abstract\n\nIt is well known that balancing and Lucas-balancing numbers are expressed as determinants of suitable tridiagonal matrices. The aim of this paper is to express certain subsequences of balancing and Lucas-balancing numbers in terms of determinants of tridiagonal matrices. Using these tridiagonal matrices, a factorization of the balancing numbers is also derived.\n\n### Keywords\n\n• Balancing numbers\n• Balancers\n• Lucas-balancing numbers\n• Tridiagonal matrices\n\n• 11B39\n• 11B83\n\n### References\n\n1. Behera, A., & Panda, G.K. (1999) On the square roots of triangular numbers, The Fibonacci Quarterly, 37(2), 98–105.\n2. Belbachair, H., & Szalay, L. (2014) Balancing in direction (1,−1) in Pascal’s triangle, Armenian Journal of Mathematics, 6(1), 32–40.\n3. Berczes, A., Liptai, K., & Pink, I. (2010) On generalized balancing numbers, Fibonacci Quarterly, 48(2), 121–128.\n4. Keskin R., & Karaatly, O. (2012) Some new properties of balancing numbers and square triangular numbers, Journal of Integer Sequences, 15(1).\n5. Liptai, K., Luca, F., Pinter, A., & Szalay, L. (2009) Generalized balancing numbers, Indagationes Math. N. S., 20, 87–100.\n6. Olajos, P. (2010) Properties of balancing, cobalancing and generalized balancing numbers, Annales Mathematicae et Informaticae, 37, 125–138.\n7. Panda, G. K., & Ray, P. K. (2011) Some links of balancing and cobalancing numbers with Pell and associated Pell numbers, Bulletin of the Institute of Mathematics, Academia Sinica (New Series), 6(1), 41–72.\n8. Panda, G. K. (2009) Some fascinating properties of balancing numbers, Proc. Eleventh Internat. Conference on Fibonacci Numbers and Their Applications, Cong. Numerantium, 194, 185–189.\n9. Ray, P. K. (2012) Application of Chybeshev polynomials in factorization of balancing and Lucas-balancing numbers, Boletim da Sociedade Paranaense de Matematica, 30(2), 49–56.\n10. Ray, P. K. (2013) Factorization of negatively subscripted balancing and Lucas-balancing numbers, Boletim da Sociedade Paranaense de Matematica, Vol.31 (2), 161–173.\n11. Ray, P. K. (2012) Certain matrices associated with balancing and Lucas-balancing numbers, Matematika, 28(1), 15–22.\n12. Ray, P. K. (2013) New identities for the common factors of balancing and Lucas-balancing numbers, International Journal of Pure and Applied Mathematics, 85, 487–494.\n13. Ray, P. K. (2014) Some congruences for balancing and Lucas-balancing numbers and their applications, Integers, 14, #A8.\n14. Ray, P. K. (2014) Balancing sequences of matrices with application to algebra of balancing numbers, Notes on Number Theory and Discrete Mathematics, 20(1), 49–58.\n15. Ray, P. K. (2014) On the properties of Lucas-balancing numbers by matrix method, Sigmae, Alfenas, 3(1), 1–6.\n16. Ray, P. K. (2014) Generalization of Cassini formula for balancing and Lucas-balancing numbers, Matematychni Studii., 42(1), 9–14.\n17. Ray, P. K. (2015) Balancing and Lucas-balancing sums by matrix methods, Mathematical Reports, 17(67), 2.\n\n## Cite this paper\n\nRay, P. K., & Panda, G. K. (2015). Tridiagonal matrices related to subsequences of balancing and Lucas-balancing numbers. Notes on Number Theory and Discrete Mathematics, 21(3), 56-63."
] | [
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http://forum.ptokax.org/index.php?topic=8160.0 | [
"###",
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"Author Topic: CountDown2 Lua5.1 API2 (Read 2357 times)\n\n0 Members and 1 Guest are viewing this topic.\n\n####",
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"ATAG\n\n• Scripter\n• Double Ace\n•",
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"• Posts: 112\n• Karma: +14/-0\n• secret things",
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"##### CountDown2 Lua5.1 API2\n« on: 06 December, 2008, 20:53:53 »\nCode: [Select]\n`--[[ CountDown2 Lua 5.1 API2 by ATAG v0.1.1 @ 2008.12.06. Based on CountDown Lua 5.1 by TiMeTrAVelleR]]---- script pathsPath = Core.GetPtokaXPath()..\"scripts/\"Settings = { -- Bot Name - leave empty (\"\") if you want to use the hub bot sBot = \"-Rock-\", -- nick to receive error messages sOpNick = \"[SU]ATAG\", -- First Timer for this bot (2 digits) -- After first setup, has to be changed with command iSetup = os.time(), -- Start timer automatically (true/false) bStart = true, -- Timer DB fTime = sPath..\"tTime.tbl\", -- Send txt content to Main (true/false) bSend = false, -- Custom message sent on timer sMsg = \"Time Left \", -- CountDown file to be shown fCountDown = sPath..\"happynewyear.txt\",}OnStartup = function() if Settings.sBot == \"\" then Settings.sBot = SetMan.GetString(21) end if loadfile(Settings.fTime) then dofile(Settings.fTime) end if Settings.bStart then if Settings.iSetup > os.time() then local iTimer = Sync() if iTimer then tmr = TmrMan.AddTimer(iTimer) end local tmp = TimeLeft() Core.SendToAll(\"<\"..Settings.sBot..\"> \"..tmp or \"No timer set\") end endendChatArrival = function(user, data) local s,e,cmd = data:find(\"^%b<>%s+[%!%+](%S+).*|\\$\") if cmd then if tCommands[cmd:lower()] then cmd = cmd:lower() if tCommands[cmd].tLevels[user.iProfile] == 1 then return tCommands[cmd].tFunc(user, data), true else return Core.SendToUser(user, \"<\"..Settings.sBot..\"> *** Error: You are not allowed to use this command!\"), true end end endendOnExit = function() local hFile = assert(io.open(Settings.fTime,\"w+\")) hFile:write(\"Settings = {\\n\") for i, v in pairs(Settings) do hFile:write(\"\\t\"..i..\" = \"..(type(v) == \"string\" and \"[[\"..v..\"]]\" or tostring(v))..\",\\n\") end hFile:write(\"}\") hFile:flush() hFile:close()endtCommands = { setmsg = { tFunc = function(user,data) local s,e,msg = data:find(\"^%b<>%s+%S+%s+(.*)|\\$\") if msg then Settings.sMsg = msg; Core.SendToUser(user, \"<\"..Settings.sBot..\"> *** CountDown Bot's message has been changed to: \"..msg) end end, tLevels = { = 1, = 1, = 1, = 1, }, tRC = \"Set Message\\$<%[myNI]> !{} %[line:Message]\" }, starttimer = { tFunc = function(user) local iTimer = Sync() if iTimer then tmr = TmrMan.AddTimer(iTimer) Core.SendToUser(user, \"<\"..Settings.sBot..\"> *** CountDown Bot's timer has been started!\") end Core.SendToUser(user,\"<\"..Settings.sBot..\"> \".. (TimeLeft() or \"Timer is outdated\")) end, tLevels = { = 1, = 1, = 1, = 1, }, tRC = \"Start Timer\\$<%[myNI]> !{}\" }, stopttimer = { tFunc = function(user) if tmr then TmrMan.RemoveTimer(tmr) end Core.SendToUser(user, \"<\"..Settings.sBot..\"> *** CountDown Bot's timer has been stopped!\") end, tLevels = { = 1, = 1, = 1, = 1, }, tRC = \"Stop Timer\\$<%[myNI]> !{}\" }, daysleft = { tFunc = function(user) Core.SendToUser(user, \"<\"..Settings.sBot..\"> \".. (TimeLeft() or \"Timer is outdated\")) end, tLevels = { [-1] = 1, = 1, = 1, = 1, = 1, = 1, = 1, }, tRC = \"Time Left\\$<%[myNI]> !{}\" }, settimer = { tFunc = function(user,data) local _,_,args = data:find(\"^%b<>%s+%S+%s+(.*)|\\$\") local _,_,d,m,y,H,M,S = args:find(\"^(%d+)\\/(%d+)\\/(%d+)%s(%d+)%:(%d+)%:(%d+)\\$\") if d and m and y and H and M and S then y=tonumber(y) if y < 100 then y = y<70 and 2000+y or 1900+y end Settings.iSetup = os.time({year=y,month=m,day=d,hour=H,min=M,sec=S}) Core.SendToUser(user, \"<\"..Settings.sBot..\"> *** CountDown Bot has been successfully set to: \"..args); OnExit() local bRestart = false if tmr then bRestart = true TmrMan.RemoveTimer(tmr) tmr = nil end if Settings.bStart then local iTimer = Sync() if iTimer then tmr = TmrMan.AddTimer(iTimer) if bRestart then Core.SendToUser(user, \"<\"..Settings.sBot..\"> *** CountDown Bot's timer has been restarted!\") else Core.SendToUser(user, \"<\"..Settings.sBot..\"> *** CountDown Bot's timer has been started!\") end else Core.SendToUser(user, \"<\"..Settings.sBot..\"> *** CountDown Bot's timer start failed: Timer is outdated!\") end else if bRestart then Core.SendToUser(user, \"<\"..Settings.sBot..\"> *** Old timer has been stopped. Don't forget to start the new timer: !starttimer\") else Core.SendToUser(user, \"<\"..Settings.sBot..\"> *** Don't forget to start the new timer: !starttimer\") end end else Core.SendToUser(user, \"<\"..Settings.sBot..\"> *** Syntax Error: Type !settimer dd/mm/yy hh:mm:ss\") end end, tLevels = { = 1, = 1, = 1, = 1, }, tRC = \"Set Timer\\$<%[myNI]> !{} %[line:dd/mm/yy hh:mm:ss]\" }}UserConnected = function(user) for i,v in pairs(tCommands) do local sRC = string.gsub(v.tRC,\"{}\",i) Core.SendToUser(user, \"\\$UserCommand 1 3 CountDown Bot\\\\\"..sRC..\"|\") end local tmp = TimeLeft() if tmp then Core.SendToUser(user, \"<\"..Settings.sBot..\"> \"..tmp) endendRegConnected = UserConnectedOpConnected = UserConnectedOnTimer = function(iN) TmrMan.RemoveTimer(iN) tmr = nil if last then SendAscii() else local left = TimeLeft() if left then Core.SendToAll(\"<\"..Settings.sBot..\"> \"..left) end local iTimer = Sync() if iTimer then tmr = TmrMan.AddTimer(iTimer) end endendTimeLeft = function() local diff = os.difftime(Settings.iSetup, os.time()) if diff < 0 then return nil end local tDiff = os.date(\"*t\", diff) local line = Settings.sMsg if tDiff.year > 1970 then line = line..\" \".. tDiff.year-1970 ..\" Years\" end if tDiff.month > 1 then line = line..\" \".. tDiff.month-1 ..\" Months\" end if tDiff.day > 1 then line = line..\" \".. tDiff.day-1 ..\" Days\" end if tDiff.hour >= 1 then line = line..\" \".. tDiff.hour-1 ..\" Hours\" end if tDiff.min >= 0 then line = line..\" \".. tDiff.min ..\" Minutes\" end if tDiff.min >= 0 then line = line..\" \".. tDiff.sec ..\" Seconds ;) \" end return line ~= Settings.sMsg and line or nilendfunction OnError(sErr) Core.SendToNick(Settings.sOpNick,\"<\"..Settings.sBot..\"> \"..sErr)endSendAscii = function() if Settings.bSend then local text local f = io.open(Settings.fCountDown) if f then text = f:read(\"*all\"); f:close(); return string.gsub( text, \"\\n\", \"\\r\\n\" ) end Core.SendToAll(\"<\"..Settings.sBot..\"> \"..text) end Core.SendToAll(\"<\"..Settings.sBot..\"> \"..\"Oki Here We Go ;)\")endSync = function() last = false local tmp, adjust = os.difftime(Settings.iSetup, os.time()) local t = {86400,3600,900,300,60,15,10,1} -- timered messsage in every x seconds for i, v in ipairs(t) do if tmp > v then adjust = math.fmod(tmp,v) return adjust ~= 0 and adjust * 1000 or v * 1000 end end if tmp == 1 then last = true return 1000 else return nil endend`\n\n#### PtokaX forum",
null,
"##### CountDown2 Lua5.1 API2\n« on: 06 December, 2008, 20:53:53 »"
] | [
null,
"http://forum.ptokax.org/Themes/default/images/topic/normal_post.gif",
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"http://forum.ptokax.org/Themes/default/images/useroff.gif",
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"http://forum.ptokax.org/Themes/default/images/star.gif",
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"http://forum.ptokax.org/Themes/default/images/star.gif",
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"http://forum.ptokax.org/Themes/default/images/star.gif",
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"http://forum.ptokax.org/Themes/default/images/star.gif",
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"http://forum.ptokax.org/Themes/default/images/star.gif",
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"http://forum.ptokax.org/Themes/default/images/star.gif",
null,
"http://forum.ptokax.org/index.php",
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"http://forum.ptokax.org/Themes/default/images/post/xx.gif",
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"http://forum.ptokax.org/Themes/default/images/post/xx.gif",
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.5252262,"math_prob":0.9681606,"size":6397,"snap":"2020-10-2020-16","text_gpt3_token_len":2136,"char_repetition_ratio":0.1787893,"word_repetition_ratio":0.1969697,"special_character_ratio":0.36814132,"punctuation_ratio":0.2957447,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9659693,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-02-27T08:33:20Z\",\"WARC-Record-ID\":\"<urn:uuid:8cec2854-b447-4840-93d4-bb43d31c00a9>\",\"Content-Length\":\"52875\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:19e0b84f-74b1-4938-8c30-4fcf292942ae>\",\"WARC-Concurrent-To\":\"<urn:uuid:d56e172b-632a-4959-aacb-2f89fb0ceaa7>\",\"WARC-IP-Address\":\"54.37.152.50\",\"WARC-Target-URI\":\"http://forum.ptokax.org/index.php?topic=8160.0\",\"WARC-Payload-Digest\":\"sha1:4PU2G4O2Y3ZAGTK4LMOOIC2QFM6DNJ4Q\",\"WARC-Block-Digest\":\"sha1:KRCEIRQKEZ2O473SNFXZG4ZZRO4ZYZDW\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-10/CC-MAIN-2020-10_segments_1581875146665.7_warc_CC-MAIN-20200227063824-20200227093824-00170.warc.gz\"}"} |
https://www.univerkov.com/find-the-surface-area-and-the-sum-of-the-lengths-of-the-edges-of-the-cube-edge-11-cm/ | [
"# Find the surface area and the sum of the lengths of the edges of the cube, edge 11 cm.\n\nGiven: the length of the edge of the cube = 11 cm.\n\na) The cube has 6 faces, each of which is a square.\n\nTo find the surface area of a cube, we first need to find the area of one face, and then multiply that number by 6.\n\nS (cube) = (11 * 11) * 6 = 121 * 6 = 726 (cm ^ 2)\n\nb) The cube has 12 edges. Knowing how long one edge has, we can find the sum of all the edges of the cube by the following action:\n\n12 * 11 = 132 (cm)\n\nAnswer: a) 726 (cm ^ 2)\n\nb) 132 (cm)",
null,
"One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities."
] | [
null,
"https://www.univerkov.com/01.jpg",
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.911516,"math_prob":0.9878926,"size":881,"snap":"2021-43-2021-49","text_gpt3_token_len":239,"char_repetition_ratio":0.14253135,"word_repetition_ratio":0.011299435,"special_character_ratio":0.30874008,"punctuation_ratio":0.105820104,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9723741,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-11-29T14:36:46Z\",\"WARC-Record-ID\":\"<urn:uuid:1e5cd806-d1d5-4548-a074-08d22b597ef5>\",\"Content-Length\":\"22361\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0bc0b9f7-96df-4743-a5b1-5c8aee231ddd>\",\"WARC-Concurrent-To\":\"<urn:uuid:a6701e9c-c78b-45de-bb73-8ea2f2a97594>\",\"WARC-IP-Address\":\"37.143.13.208\",\"WARC-Target-URI\":\"https://www.univerkov.com/find-the-surface-area-and-the-sum-of-the-lengths-of-the-edges-of-the-cube-edge-11-cm/\",\"WARC-Payload-Digest\":\"sha1:6YQXVSQPPRT43GVUGFYSZXNMRHKVCP43\",\"WARC-Block-Digest\":\"sha1:2BXX27PBZT34WAJBTS6N5EKR6H46WCV6\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964358774.44_warc_CC-MAIN-20211129134323-20211129164323-00323.warc.gz\"}"} |
https://metanumbers.com/55065 | [
"## 55065\n\n55,065 (fifty-five thousand sixty-five) is an odd five-digits composite number following 55064 and preceding 55066. In scientific notation, it is written as 5.5065 × 104. The sum of its digits is 21. It has a total of 3 prime factors and 8 positive divisors. There are 29,360 positive integers (up to 55065) that are relatively prime to 55065.\n\n## Basic properties\n\n• Is Prime? No\n• Number parity Odd\n• Number length 5\n• Sum of Digits 21\n• Digital Root 3\n\n## Name\n\nShort name 55 thousand 65 fifty-five thousand sixty-five\n\n## Notation\n\nScientific notation 5.5065 × 104 55.065 × 103\n\n## Prime Factorization of 55065\n\nPrime Factorization 3 × 5 × 3671\n\nComposite number\nDistinct Factors Total Factors Radical ω(n) 3 Total number of distinct prime factors Ω(n) 3 Total number of prime factors rad(n) 55065 Product of the distinct prime numbers λ(n) -1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) -1 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0\n\nThe prime factorization of 55,065 is 3 × 5 × 3671. Since it has a total of 3 prime factors, 55,065 is a composite number.\n\n## Divisors of 55065\n\n1, 3, 5, 15, 3671, 11013, 18355, 55065\n\n8 divisors\n\n Even divisors 0 8 4 4\nTotal Divisors Sum of Divisors Aliquot Sum τ(n) 8 Total number of the positive divisors of n σ(n) 88128 Sum of all the positive divisors of n s(n) 33063 Sum of the proper positive divisors of n A(n) 11016 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 234.659 Returns the nth root of the product of n divisors H(n) 4.99864 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors\n\nThe number 55,065 can be divided by 8 positive divisors (out of which 0 are even, and 8 are odd). The sum of these divisors (counting 55,065) is 88,128, the average is 11,016.\n\n## Other Arithmetic Functions (n = 55065)\n\n1 φ(n) n\nEuler Totient Carmichael Lambda Prime Pi φ(n) 29360 Total number of positive integers not greater than n that are coprime to n λ(n) 7340 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 5595 Total number of primes less than or equal to n r2(n) 0 The number of ways n can be represented as the sum of 2 squares\n\nThere are 29,360 positive integers (less than 55,065) that are coprime with 55,065. And there are approximately 5,595 prime numbers less than or equal to 55,065.\n\n## Divisibility of 55065\n\n m n mod m 2 3 4 5 6 7 8 9 1 0 1 0 3 3 1 3\n\nThe number 55,065 is divisible by 3 and 5.\n\n## Classification of 55065\n\n• Arithmetic\n• Deficient\n\n• Polite\n\n• Square Free\n\n### Other numbers\n\n• LucasCarmichael\n• Sphenic\n\n## Base conversion (55065)\n\nBase System Value\n2 Binary 1101011100011001\n3 Ternary 2210112110\n4 Quaternary 31130121\n5 Quinary 3230230\n6 Senary 1102533\n8 Octal 153431\n10 Decimal 55065\n12 Duodecimal 27a49\n20 Vigesimal 6hd5\n36 Base36 16hl\n\n## Basic calculations (n = 55065)\n\n### Multiplication\n\nn×i\n n×2 110130 165195 220260 275325\n\n### Division\n\nni\n n⁄2 27532.5 18355 13766.2 11013\n\n### Exponentiation\n\nni\n n2 3032154225 166965572399625 9193959244185350625 506265365781066332165625\n\n### Nth Root\n\ni√n\n 2√n 234.659 38.0445 15.3186 8.87514\n\n## 55065 as geometric shapes\n\n### Circle\n\n Diameter 110130 345984 9.52579e+09\n\n### Sphere\n\n Volume 6.99384e+14 3.81032e+10 345984\n\n### Square\n\nLength = n\n Perimeter 220260 3.03215e+09 77873.7\n\n### Cube\n\nLength = n\n Surface area 1.81929e+10 1.66966e+14 95375.4\n\n### Equilateral Triangle\n\nLength = n\n Perimeter 165195 1.31296e+09 47687.7\n\n### Triangular Pyramid\n\nLength = n\n Surface area 5.25185e+09 1.96771e+13 44960.4\n\n## Cryptographic Hash Functions\n\nmd5 d1f79aa0b0da3a72f530e67e2cf8d2ce 30da9c304c2b4b0bdba4f83c2baecc0b3cf25274 422a7235f453b912cff7812f5439f6cc90ab223db95d47612b58c4cbc360e4b7 ae95917fbc0f62509a2438873bba6a6ceb07692df16ea5c33c87976948c3f653dbf0fabbeb98c635b7309ace79b3119f8a597bbbd7cd2aedae889217bbcc7df5 3b3920bb6916a3a3d302200ac0e7bf80a3e6bb61"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.61163783,"math_prob":0.98988235,"size":4525,"snap":"2021-31-2021-39","text_gpt3_token_len":1613,"char_repetition_ratio":0.119442604,"word_repetition_ratio":0.02818991,"special_character_ratio":0.45060775,"punctuation_ratio":0.07512953,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9949511,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-07-25T21:39:06Z\",\"WARC-Record-ID\":\"<urn:uuid:df7dfdb7-48ad-488e-b119-ea062b345ba4>\",\"Content-Length\":\"60096\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b39f3f50-ff53-4724-ae5e-1b17f8f51429>\",\"WARC-Concurrent-To\":\"<urn:uuid:8e376085-8714-404f-9b15-7d20534ea53c>\",\"WARC-IP-Address\":\"46.105.53.190\",\"WARC-Target-URI\":\"https://metanumbers.com/55065\",\"WARC-Payload-Digest\":\"sha1:US4YRFD5LVFUJAPFRCZ2ST6B2L54BOZZ\",\"WARC-Block-Digest\":\"sha1:BIDGRCBTREU4TFTEXKX7TBS4DT7FO72Y\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-31/CC-MAIN-2021-31_segments_1627046151866.98_warc_CC-MAIN-20210725205752-20210725235752-00648.warc.gz\"}"} |
https://excelquick.com/excel-general/excel-formula-not-calculating-automatically/ | [
"# Excel formula not calculating automatically",
null,
"Problem: Excel formula is not calculating automatically\n\nFor example, you try to flash fill a formula down a column and Excel copies the first cell’s contents down the column instead.\n\nA likely reason is that the formula ‘Calculation Options‘ setting is on ‘Manual‘ rather than the default ‘Automatic‘.\n\nFind Excel’s Calculation Options on the ‘Formulas’ tab of the ribbon."
] | [
null,
"https://excelquick.com/wp-content/uploads/2018/07/excel-quick-help-tools_128.png",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.7086096,"math_prob":0.94263846,"size":464,"snap":"2023-40-2023-50","text_gpt3_token_len":98,"char_repetition_ratio":0.14565217,"word_repetition_ratio":0.0,"special_character_ratio":0.2025862,"punctuation_ratio":0.08235294,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9837483,"pos_list":[0,1,2],"im_url_duplicate_count":[null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-22T11:58:47Z\",\"WARC-Record-ID\":\"<urn:uuid:a0b8d3bb-21d1-4fd3-ae8a-7c33056f30c7>\",\"Content-Length\":\"79751\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0e998094-2317-4fa5-87d8-02a5bb436c97>\",\"WARC-Concurrent-To\":\"<urn:uuid:8a47cc35-45a2-4b6a-b0b5-29767912d2de>\",\"WARC-IP-Address\":\"46.30.213.59\",\"WARC-Target-URI\":\"https://excelquick.com/excel-general/excel-formula-not-calculating-automatically/\",\"WARC-Payload-Digest\":\"sha1:G5Z5QK2BO7VPDVRIIZ3QWUJYEXLL74QN\",\"WARC-Block-Digest\":\"sha1:U25XBA2V2VMXI7KDLOODV4ZBBB4DIXXF\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233506399.24_warc_CC-MAIN-20230922102329-20230922132329-00340.warc.gz\"}"} |
https://mywikinews.net/area-of-parallelogram/ | [
"February7 , 2023\n\n# Area of Parallelogram\n\n### What are Interchange Fees for Merchant Accounts?\n\nAlmost every establishment now accepts Credit and Debit Card...\n\n### Benefits Of Distilled Water In CPAP Therapy: A Comprehensive Guide\n\nCPAP therapy, or Continuous Positive Airway Pressure therapy, is...\n\n#### Category\n\nIn mathematics, we generally define a parallelogram as a figure which is two-dimensional and consists of four sides. The properties of a parallelogram are similar to that of a rectangle; thus we can consider that a parallelogram is a type of a rectangle. The area of a parallelogram can be defined as a space or region which is enclosed by the sides of the parallelogram. Mathematically, the area of parallelogram is given by ‘b’ * ‘h’ where b is the base of the parallelogram and h is the height of the parallelogram respectively. In this article, we may try to cover some topics related to the area of parallelogram such as the different ways of calculating area and calculations based on it.\n\n## Parallelogram\n\nA parallelogram can be defined as a unique type of quadrilateral which is enclosed by parallel lines. In other words, parallelogram has been derived from a Greek word that basically signifies any structure which is bounded or enclosed by parallel lines. You might have observed various objects in your everyday life such as a kite, a matchbox, or a table, all these objects are examples of parallelograms. The above-mentioned few lines also signify that a parallelogram can be of various types such as a rhombus, a rectangle, a square, etc.\n\n## Some Important Properties of a Parallelogram\n\nThere are various important properties of a parallelogram but few of them are mostly used in calculations based on parallelograms. The following points mentioned below analyses some of the significant properties of a parallelogram.\n\n1. In a parallelogram, the sides opposite are parallel and congruent to each other.\n2. In a parallelogram, the angles which are opposite are also congruent and the angles which are consecutive are supplementary.\n3. There is a very unique fact or you could say a characteristic that if any angle is right-angled or exactly measures 90 degrees, then every other angle will also measure about 90 degrees and thus be called a right-angled parallelogram.\n4. The diagonals of a parallelogram bisect each other and also result in the formation of two different congruent triangles.\n5. The parallelogram law states that the addition of the square of every side ( four ) of a parallelogram is equal to the sum or addition of the square of the diagonal.\n\n## Area of Parallelogram Using the Base And Height\n\nOne of the most common ways of calculating the area of a parallelogram is doing it with the help of the sides or base and height of the parallelogram. The area of parallelogram is the space that is enclosed or covered by the sides of it in a plane that is two-dimensional. Mathematically, the formula given for the are is ‘b’ * ‘h’ where b is the base and h is the height of the parallelogram. In order to understand this concept in a detailed manner we must solve some examples related to it;\n\nExample 1:\n\nFind the area of parallelogram provided that the base ‘b’ is 5 cm and ‘h’ is 10 cm?\n\nProvided that,\n\nBase of the parallelogram = 5 cm\n\nHeight of the parallelogram = 10 cm\n\nUsing the formula of area of parallelogram, b * h\n\n5 * 10 = 50 cm\n\nThus, the area of parallelogram is 50 cm.\n\nExample 2:\n\nFind the area of parallelogram provided that the base ‘b’ is 6 cm and ‘h’ is 5 cm?\n\nProvided that,\n\nBase of the parallelogram = 6 cm\n\nHeight of the parallelogram = 5 cm\n\nUsing the formula of area of parallelogram, b * h\n\n6 * 5 = 30 cm\n\nThus, the area of parallelogram is 30 cm.\n\nIf you want to learn about the area of a parallelogram in a detailed manner, a fun way, and an interactive manner, you should visit the website of Cuemath and understand math in the Cuemath way.",
null,
""
] | [
null,
"https://moderate10.cleantalk.org/pixel/6f0d52090104ea40546c66895515fc14.gif",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.9273732,"math_prob":0.9571277,"size":3571,"snap":"2022-40-2023-06","text_gpt3_token_len":845,"char_repetition_ratio":0.23577236,"word_repetition_ratio":0.11811024,"special_character_ratio":0.21226548,"punctuation_ratio":0.07544379,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9984047,"pos_list":[0,1,2],"im_url_duplicate_count":[null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-02-06T20:29:51Z\",\"WARC-Record-ID\":\"<urn:uuid:3fd5e84d-a5e2-461a-b0b1-48f9fce5171e>\",\"Content-Length\":\"404861\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0c2bd90c-a4ea-4899-93af-eda77c75d6b4>\",\"WARC-Concurrent-To\":\"<urn:uuid:337e3fd7-d8dc-4dd6-bd9d-7bc9d771d6eb>\",\"WARC-IP-Address\":\"172.67.218.178\",\"WARC-Target-URI\":\"https://mywikinews.net/area-of-parallelogram/\",\"WARC-Payload-Digest\":\"sha1:M6K3SSL5GZNHKUV44TOLTV53JVLN2HEW\",\"WARC-Block-Digest\":\"sha1:FTF2UTRMFW3N2USXF7PPHA75L4D4AKVY\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-06/CC-MAIN-2023-06_segments_1674764500357.3_warc_CC-MAIN-20230206181343-20230206211343-00391.warc.gz\"}"} |
http://namadruga.com.br/range-rotten-dupt/ca0150-bayesian-statistics-coursera-answers | [
"In this module, we will work with conditional probabilities, which is the probability of event B given event A. Bayesian theory has been around for a long time, but it was not until the computer revolution of the last quarter century that the necessary computational power arrived to actually calculate Bayesian models for a wide class of problems. Be very clear about what the information that you include is representing, and carefully label your graphs. For example, you may wish to report appropriate sample means or standard deviations, or present graphs like histograms or scatterplots. Analytics cookies. You have remained in right site to begin getting this info. About this course: This course introduces the Bayesian approach to statistics, starting with the concept of probability and moving to the analysis of data. This can be a large question, broader than what you would like to solve with the project. Start studying Week 5 Quiz. Overview. About this course: This course describes Bayesian statistics, in which one's inferences about parameters or hypotheses are updated as evidence accumulates. You will learn to use Bayes’ rule to transform prior probabilities into posterior probabilities, and be introduced to the underlying theory and perspective of the Bayesian … This is the second of a two-course sequence introducing the fundamentals of Bayesian statistics. BROWSE The Best of Coursera from the Depths of Reddit. Watch 1 Star 0 Fork 1 0 stars 1 fork Star Watch Code; Issues 0; Pull requests 0; Actions; Projects 0; Security; Insights; Dismiss Join GitHub today. A first course in statistics (that happens to have a Bayesian approach)? Please take several minutes read this information. 5つの星のうち 4.6 を評価2540のレビュー. コース. I cannot find it online, does anybody know whether there is a manual available? Improving your statistical inferences. start . It builds on the course Bayesian Statistics: From Concept to Data Analysis, which introduces Bayesian methods through use of simple conjugate models. Embed. The section about Beta-Binomial Conjugate is taught very fast and unless the student is quite familiar with Beta and Gamma distributions, it makes it very difficult to follow the course. By the end of the week, you will be able to solve problems using Bayes' rule, and update prior probabilities.",
null,
""
] | [
null,
"http://0.gravatar.com/avatar/",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.9129602,"math_prob":0.7708928,"size":27376,"snap":"2021-31-2021-39","text_gpt3_token_len":5435,"char_repetition_ratio":0.16600905,"word_repetition_ratio":0.25974646,"special_character_ratio":0.19067797,"punctuation_ratio":0.13165438,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95249504,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-07-24T01:19:29Z\",\"WARC-Record-ID\":\"<urn:uuid:7b0f7dbe-7030-4753-89e2-ad0afcff5f7f>\",\"Content-Length\":\"156909\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:48a56f68-954d-4091-ab19-0bb54fac478a>\",\"WARC-Concurrent-To\":\"<urn:uuid:7374dc1f-0720-4b5e-b988-af23b52c95f8>\",\"WARC-IP-Address\":\"69.49.115.40\",\"WARC-Target-URI\":\"http://namadruga.com.br/range-rotten-dupt/ca0150-bayesian-statistics-coursera-answers\",\"WARC-Payload-Digest\":\"sha1:NQSIV37RI6NTOI7CMZEPIM6W6MUP7BCB\",\"WARC-Block-Digest\":\"sha1:6D76CFWKLFMIPANNSW72BUQ5YWQGJSC3\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-31/CC-MAIN-2021-31_segments_1627046150067.87_warc_CC-MAIN-20210724001211-20210724031211-00640.warc.gz\"}"} |
http://puzzlezapper.com/blog/tag/incomplete-problem-statements/ | [
"# Posts Tagged ‘incomplete problem statements’\n\n## Faux Shu Follies\n\nJune 18th, 2016",
null,
"The Lo Shu, or 3×3 magic square, was discovered in China in antiquity. It is the only way, (up to symmetry) to place the numbers 1 through 9 in a 3×3 grid such that the numbers in each row, column, and main diagonal add up to the same number (or magic sum). This fact seems to be universally known among recreational mathematicians. So when I had the chance to meet a number of them this spring at the fabulous 12th Gathering for Gardner conference, I told them that I knew a different way to do it. When they pronounced me mad, or a liar, I showed them one of these:",
null,
"Mathematics is full of counterexamples that result when the simple way of understanding a conjecture is not exactly what the conjecture literally says, so this kind of cheating is totes legit.\n\nIf the fact of the uniqueness of the Lo Shu is new to you, a quick proof might be in order. First, let’s enumerate all of the sets of three numbers between 1 and 9 that sum to 15: {1, 5, 9}, {1, 6, 8}, {2, 4, 9}, {2, 5, 8}, {2, 6, 7}, {3, 4, 8}, {3, 5, 7}, {4, 5, 6}. There are eight sets, so we’ll need all of them to fill the eight lines in the magic square. The number 5 appears four times, the other odd numbers appear twice, and the even numbers appear three times. Therefore the center square, being part of four lines, must be 5, the corner squares, being part of three lines, must be the evens, and the side squares, being part of two lines, must be the other odds. Choose any corner, and put a 2 in it. That forces 8 into the opposite corner. Choose one the remaining corners, and put a 4 in it. After that, the rest of the numbers are forced. No matter what corners you choose, the result can be rotated or flipped to get the square formed by choosing any different pair of corners. Q. E. D.\n\nWell, wait, you say, what if the magic sum isn’t 15? Quite right, 14 and 16 also both have eight sets of numbers between 1 and 9 that sum to them, so our proof is not done. I will leave it as an exercise to the reader to show that they cannot be used to form a 3×3 magic square.\n\nAnd then, once the reader is satisfied, I’ll say: there is a way to place the numbers 1 through 9 in a 3×3 grid, with exactly one number in each cell, (you didn’t think I’d try the same shenanigans twice?) so that they occupy eight lines that each connect exactly three numbers that sum to 14. And having followed me this far, you are now enough of a recreational mathematician to be able to call me mad, or a liar. But you might want to have a look at this before you wager money on it:",
null,
"This result was adapted from one discovered by Lee Sallows, which is described in his book, Geometric Magic Squares.\n\nWell, clearly the problem here is that you’re allowing me to draw my own graphics. If you forced me to use physical number tiles as in the first image, I couldn’t get up to any fancy tricks. So if I told you that I could arrange those exact same nine number tiles in a block of three rows of three tiles each, and make it so that for every line that passes through the center of three tiles that form a connected group, the sum of those tiles is 14, I would have to be mad.",
null,
""
] | [
null,
"http://puzzlezapper.com/blog/wp-content/uploads/2016/06/lo-shu-tile.png",
null,
"http://puzzlezapper.com/blog/wp-content/uploads/2016/06/faux-shu-2.png",
null,
"http://puzzlezapper.com/blog/wp-content/uploads/2016/06/faux-shu-ls.png",
null,
"http://puzzlezapper.com/blog/wp-content/uploads/2016/06/faux-shu-tile.jpg",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.9618456,"math_prob":0.9314113,"size":3135,"snap":"2021-21-2021-25","text_gpt3_token_len":805,"char_repetition_ratio":0.121047586,"word_repetition_ratio":0.032520324,"special_character_ratio":0.25869218,"punctuation_ratio":0.1367989,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9685797,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,8,null,8,null,8,null,8,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-05-06T18:23:45Z\",\"WARC-Record-ID\":\"<urn:uuid:044e79b5-a868-43e3-a52a-eb2adcfa8411>\",\"Content-Length\":\"16131\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:09b1a073-4609-4ba3-8b49-51fea391f6b2>\",\"WARC-Concurrent-To\":\"<urn:uuid:86d6a1f0-176c-4eb7-ac0a-ceb5000a77fb>\",\"WARC-IP-Address\":\"173.236.186.189\",\"WARC-Target-URI\":\"http://puzzlezapper.com/blog/tag/incomplete-problem-statements/\",\"WARC-Payload-Digest\":\"sha1:62PAPOGZ2VHP7EG3Z5LCOPO2N5ODD4I4\",\"WARC-Block-Digest\":\"sha1:J6DHZ2BWYCKZ52LRNWXW5F7XWXB6YYAG\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-21/CC-MAIN-2021-21_segments_1620243988759.29_warc_CC-MAIN-20210506175146-20210506205146-00599.warc.gz\"}"} |
https://yteach.org/class-11/ | [
"## Course-1: NCERT solutions for class 11 Math\n\n• Chapter 1 - Sets\n• Chapter 2 - Relations and Functions\n• Chapter 3 - Trigonometric Functions\n• Chapter 4 - Principle of Mathematical Induction\n• Chapter 5 - Complex Numbers and Quadratic Equations\n• Chapter 6 - Linear Inequalities\n• Chapter 7 - Permutations and Combinations\n• Chapter 8 - Binomial Theorem\n• Chapter 9- Sequences and Series\n• Chapter 10 - Straight Lines\n• Chapter 11 - Conic Sections\n• Chapter 12 - Conic Sections\n• Chapter 13 - Limits and Derivatives\n• Chapter 14 - Mathematical Reasoning\n• Chapter 15 - Statistics\n• Chapter 16 - Probability\n\n## Courses: NCERT solutions for class 11 Physics\n\nHere is your NCERT solutions for Class 11 Physics chapter wise by Your Teacher’s Classroom. All exercises are given below to free download in PDF form.\n\n## Course-I: NCERT Solutions for Class 11 Physics Part-I\n\n• Chapter 1 – Physical World\n• Chapter 2 – Units, Dimension and Measurement\n• Chapter 3 – Motion in a straight line\n• Chapter 4 – Motion in a Plane\n• Chapter 5 – Laws of Motion\n• Chapter 6 – Work, Energy and Power\n• Chapter 7 – System of Particles and Rotational Motion\n• Chapter 8 – Gravitation\n\n## Course-II: NCERT Solutions for Class 11 Physics Part-II\n\n• Chapter 1 – Mechanical Properties of Solids\n• Chapter 2 – Mechanical Properties of Fluids\n• Chapter 3 – Thermal Properties of Matter\n• Chapter 4 - Thermodynamics\n• Chapter 5 – Kinetic Theory\n• Chapter 6 - Oscillation\n• Chapter 7 – Waves\n\n### Shopping Cart Items\n\nNo products in the cart."
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.68754464,"math_prob":0.5523568,"size":1961,"snap":"2020-45-2020-50","text_gpt3_token_len":490,"char_repetition_ratio":0.2258559,"word_repetition_ratio":0.24418604,"special_character_ratio":0.25038245,"punctuation_ratio":0.057142857,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99117035,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-12-02T08:55:07Z\",\"WARC-Record-ID\":\"<urn:uuid:b25ae8ff-67e6-47f5-95ed-be38af03c12a>\",\"Content-Length\":\"76048\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e079387e-938c-4ce2-b543-d79844ee2989>\",\"WARC-Concurrent-To\":\"<urn:uuid:a3f197da-5aae-46e9-9ab2-e1211476e5f6>\",\"WARC-IP-Address\":\"144.76.90.154\",\"WARC-Target-URI\":\"https://yteach.org/class-11/\",\"WARC-Payload-Digest\":\"sha1:3BPVSQDZMBQ3M3JLE2J6ZCOWHF6GVMFU\",\"WARC-Block-Digest\":\"sha1:ZPNZDC7OUDK4ZYXSWARQZMVKSKV4QKWF\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141706569.64_warc_CC-MAIN-20201202083021-20201202113021-00349.warc.gz\"}"} |
https://brainmass.com/physics/newtons-laws/force-diagrams-magnitudes-forces-static-friction-36095 | [
"Explore BrainMass\n\n# Force Diagrams, Magnitudes of Forces, Static Friction\n\nNot what you're looking for? Search our solutions OR ask your own Custom question.\n\nThis content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!\n\nTwo blocks, of masses m1 and m2, are connected by a model string. Both blocks lie on a plane that is inclined to the horizontal at an angle [symbol1]. The part of the plane supporting the block of mass m1 is smooth, so that there is no frictional force. The upper part of the plane is rough, as that coefficient of the static friction between the block of mass m2 and the plane is [symbol2]. The system is in equlibrium, and the string is taut.\n(i) Draw a diagram, marking clearly your choice of coordinate axes.\n(ii) Modelling the blocks as particles, draw two force diagrams showing all the forces acting on the two particles.\n(iii) Find five equations relating the magnitudes of the forces.\n(iv) Show that the minimum value of [symbol2] such that the system remains in equlibrium is: {see attachment}\n\n*Please see attachment for equation, diagram and proper citation of symbols\n\nhttps://brainmass.com/physics/newtons-laws/force-diagrams-magnitudes-forces-static-friction-36095\n\n#### Solution Preview\n\nHello and thank you for posting your question to Brainmass!\n\nThe solution is attached below in two files. The files are identical in content, only differ in format. The first is in MS ...\n\n#### Solution Summary\n\nForce Diagrams, Magnitudes of Forces and Static Friction are investigated. The solution is detailed and well presented. The response received a rating of \"5\" from the student who originally posted the question.\n\n\\$2.49"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.9102995,"math_prob":0.89599526,"size":1636,"snap":"2021-31-2021-39","text_gpt3_token_len":378,"char_repetition_ratio":0.1127451,"word_repetition_ratio":0.0,"special_character_ratio":0.21577017,"punctuation_ratio":0.12903225,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97397393,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-20T08:39:08Z\",\"WARC-Record-ID\":\"<urn:uuid:af65bdd8-d08e-4e21-bbdb-f99dfb9da4f4>\",\"Content-Length\":\"331458\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:fe6770c1-434e-4a97-8f01-d83a986c899e>\",\"WARC-Concurrent-To\":\"<urn:uuid:44cfdf97-e085-43b2-a857-d31453be820f>\",\"WARC-IP-Address\":\"172.67.75.38\",\"WARC-Target-URI\":\"https://brainmass.com/physics/newtons-laws/force-diagrams-magnitudes-forces-static-friction-36095\",\"WARC-Payload-Digest\":\"sha1:QBRO3RW33ANWAMETZ22LMVZB4W6BWETY\",\"WARC-Block-Digest\":\"sha1:ADMOIY4WES44V4634MXXJKSMBLN4MPPA\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780057033.33_warc_CC-MAIN-20210920070754-20210920100754-00166.warc.gz\"}"} |
https://www.clawpack.org/v5.8.x/pyclaw/geometry.html | [
"# PyClaw Geometry¶\n\nThe PyClaw geometry package contains the classes used to define the geometry of a Solution object. The base container for all other geometry is the Domain object. It contains a list of Patch objects that reside inside of the Domain.",
null,
"Patch represents a piece of the domain that could be a different resolution than the others, have a different coordinate mapping, or be used to construct complex domain shapes.",
null,
"It contains Dimension objects that define the extent of the Patch and the number of grid cells in each dimension. Patch also contains a reference to a nearly identical Grid object. The Grid object also contains a set of Dimension objects describing its extent and number of grid cells. The Grid is meant to represent the geometry of the data local to the process in the case of a parallel run. In a serial simulation the Patch and Grid share the same dimensions.\n\nIn the case where only one Patch object exists in a Domain but it is run with four processes in parallel, the Domain hierarchy could look like:",
null,
"In the most complex case with multiple patches and a parallel run we may have the following:",
null,
"## Serial Geometry Objects¶\n\n### pyclaw.geometry.Domain¶\n\nclass clawpack.pyclaw.geometry.Domain(*arg)\n\nA Domain is a list of Patches.\n\nA Domain may be initialized in the following ways:\n\n1. Using 3 arguments, which are in order\n• A list of the lower boundaries in each dimension\n\n• A list of the upper boundaries in each dimension\n\n• A list of the number of cells to be used in each dimension\n\n2. Using a single argument, which is\n• A list of dimensions; or\n\n• A list of patches.\n\nExamples\n>>> from clawpack import pyclaw\n>>> domain = pyclaw.Domain( (0.,0.), (1.,1.), (100,100))\n>>> print(domain.num_dim)\n2\n>>> print(domain.grid.num_cells)\n[100, 100]\n\nproperty grid\n\n(list) - Patch.grid of base patch\n\nproperty num_dim\n\n(int) - Patch.num_dim of base patch\n\nproperty patch\n\n(Patch) - First patch is returned\n\n### pyclaw.geometry.Patch¶\n\nclass clawpack.pyclaw.geometry.Patch(dimensions)\n\nBases: object\n\nGlobal Patch information\n\nEach patch has a value for level and patch_index.\n\nadd_dimension(dimension)\n\nAdd the specified dimension to this patch\n\nInput\nget_dim_attribute(attr)\n\nReturns a tuple of all dimensions’ attribute attr\n\nproperty delta\n\n(list) - List of computational cell widths\n\nproperty dimensions\n\n(list) - List of Dimension objects defining the grid’s extent and resolution\n\nlevel = None\n\n(int) - AMR level this patch belongs to, default = 1\n\nproperty lower_global\n\n(list) - Lower coordinate extents of each dimension\n\nproperty name\n\n(list) - List of names of each dimension\n\nproperty num_cells_global\n\n(list) - List of the number of cells in each dimension\n\nproperty num_dim\n\n(int) - Number of dimensions\n\npatch_index = None\n\n(int) - Patch number of current patch, default = 0\n\nproperty upper_global\n\n(list) - Upper coordinate extends of each dimension\n\n### pyclaw.geometry.Grid¶\n\nclass clawpack.pyclaw.geometry.Grid(dimensions)\n\nRepresentation of a single grid.\n\nDimension information\n\nEach dimension has an associated name with it that can be accessed via that name such as grid.x.num_cells which would access the x dimension’s number of cells.\n\nProperties\n\nIf the requested property has multiple values, a list will be returned with the corresponding property belonging to the dimensions in order.\n\nInitialization\nInput:\nOutput:\n• (grid) Initialized grid object\n\nA PyClaw grid is usually constructed from a tuple of PyClaw Dimension objects:\n\n>>> from clawpack.pyclaw.geometry import Dimension, Grid\n>>> x = Dimension(0.,1.,10,name='x')\n>>> y = Dimension(-1.,1.,25,name='y')\n>>> grid = Grid((x,y))\n>>> print(grid)\n2-dimensional domain (x,y)\nNo mapping\nExtent: [0.0, 1.0] x [-1.0, 1.0]\nCells: 10 x 25\n\n\nWe can query various properties of the grid:\n\n>>> grid.num_dim\n2\n>>> grid.num_cells\n[10, 25]\n>>> grid.lower\n[0.0, -1.0]\n>>> grid.delta # Returns [dx, dy]\n[0.1, 0.08]\n\n\nA grid can be extended to higher dimensions using the add_dimension() method:\n\n>>> z=Dimension(-2.0,2.0,21,name='z')\n>>> grid.num_dim\n3\n>>> grid.num_cells\n[10, 25, 21]\n\n\nCoordinates:\n\nWe can get the x, y, and z-coordinate arrays of cell nodes and centers from the grid. Properties beginning with ‘c’ refer to the computational (unmapped) domain, while properties beginning with ‘p’ refer to the physical (mapped) domain. For grids with no mapping, the two are identical. Also note the difference between ‘center’ and ‘centers’.\n\n>>> import numpy as np\n>>> np.set_printoptions(precision=2) # avoid doctest issues with roundoff\n>>> grid.c_center([1,2,3])\narray([ 0.15, -0.8 , -1.33])\n>>> grid.p_nodes[0,0,0]\n0.0\n>>> grid.p_nodes[0,0,0]\n-1.0\n>>> grid.p_nodes[0,0,0]\n-2.0\n\n\nIt’s also possible to get coordinates for ghost cell arrays:\n\n>>> x = Dimension(0.,1.,5,name='x')\n>>> grid1d = Grid([x])\n>>> grid1d.c_centers\n[array([0.1, 0.3, 0.5, 0.7, 0.9])]\n>>> grid1d.c_centers_with_ghost(2)\n[array([-0.3, -0.1, 0.1, 0.3, 0.5, 0.7, 0.9, 1.1, 1.3])]\n\n\nMappings:\n\nA grid mapping can be used to solve in a domain that is not rectangular, or to adjust the local spacing of grid cells. For instance, we can use smaller cells on the left and larger cells on the right by doing:\n\n>>> double = lambda xarr : np.array([x**2 for x in xarr])\n>>> grid1d.mapc2p = double\n>>> grid1d.p_centers\narray([0.01, 0.09, 0.25, 0.49, 0.81])\n\n\nNote that the ‘nodes’ (or nodes) of the mapped grid are the mapped values of the computational nodes. In general, they are not the midpoints between mapped centers:\n\n>>> grid1d.p_nodes\narray([0. , 0.04, 0.16, 0.36, 0.64, 1. ])\n\nadd_dimension(dimension)\n\nAdd the specified dimension to this patch\n\nInput\nadd_gauges(gauge_coords)\n\nDetermine the cell indices of each gauge and make a list of all gauges with their cell indices.\n\nc_center(ind)\n\nCompute center of computational cell with index ind.\n\nc_centers_with_ghost(num_ghost)\n\nCalculate the coordinates of the cell centers, including ghost cells, in the computational domain.\n\nInput\n• num_ghost - (int) Number of ghost cell layers\n\nc_nodes_with_ghost(num_ghost)\n\nCalculate the coordinates of the cell nodes (corners), including ghost cells, in the computational domain.\n\nInput\n• num_ghost - (int) Number of ghost cell layers\n\nget_dim_attribute(attr)\n\nReturns a tuple of all dimensions’ attribute attr\n\np_center(ind)\n\nCompute center of physical cell with index ind.\n\nplot(num_ghost=0, mapped=True, mark_nodes=False, mark_centers=False)\n\nMake a plot of the grid.\n\nBy default the plot uses the mapping grid.mapc2p and does not show any ghost cells. This can be modified via the arguments mapped and num_ghost.\n\nReturns a handle to the plot axis object.\n\nsetup_gauge_files(outdir)\n\nCreates and opens file objects for gauges.\n\nproperty c_centers\n\n(list of ndarray(…)) - List containing the arrays locating the computational locations of cell centers, see _compute_c_centers() for more info.\n\nproperty c_nodes\n\n(list of ndarray(…)) - List containing the arrays locating the computational locations of cell nodes, see _compute_c_nodes() for more info.\n\nproperty dimensions\n\n(list) - List of Dimension objects defining the grid’s extent and resolution\n\ngauge_dir_name = None\n\n(string) - Name of the output directory for gauges. If the Controller class is used to run the application, this directory by default will be created under the Controller outdir directory.\n\ngauge_file_names = None\n\n(list) - List of file names to write gauge values to\n\ngauge_files = None\n\n(list) - List of file objects to write gauge values to\n\ngauges = None\n\n(list) - List of gauges’ indices to be filled by add_gauges method.\n\nproperty num_dim\n\n(int) - Number of dimensions\n\nproperty p_centers\n\n(list of ndarray(…)) - List containing the arrays locating the physical locations of cell centers, see _compute_p_centers() for more info.\n\nproperty p_nodes\n\n(list of ndarray(…)) - List containing the arrays locating the physical locations of cell nodes, see _compute_p_nodes() for more info.\n\n### pyclaw.geometry.Dimension¶\n\nclass clawpack.pyclaw.geometry.Dimension(lower, upper, num_cells, name='x', on_lower_boundary=None, on_upper_boundary=None, units=None)\n\nBasic class representing a dimension of a Patch object\n\nInitialization\n\nRequired arguments, in order:\n• lower - (float) Lower extent of dimension\n\n• upper - (float) Upper extent of dimension\n\n• num_cells - (int) Number of cells\n\nOptional (keyword) arguments:\n• name - (string) string Name of dimension\n\n• units - (string) Type of units, used for informational purposes only\n\nOutput:\n\nExample:\n\n>>> from clawpack.pyclaw.geometry import Dimension\n>>> x = Dimension(0.,1.,100,name='x')\n>>> print(x)\nDimension x: (num_cells,delta,[lower,upper]) = (100,0.01,[0.0,1.0])\n>>> x.name\n'x'\n>>> x.num_cells\n100\n>>> x.delta\n0.01\n>>> x.nodes\n0.0\n>>> x.nodes\n0.01\n>>> x.nodes[-1]\n1.0\n>>> x.centers[-1]\n0.995\n>>> len(x.centers)\n100\n>>> len(x.nodes)\n101\n\ncenters_with_ghost(num_ghost)\n\n(ndarrary(:)) - Location of all cell center coordinates for this dimension, including centers of ghost cells.\n\nnodes_with_ghost(num_ghost)\n\n(ndarrary(:)) - Location of all edge coordinates for this dimension, including nodes of ghost cells.\n\nproperty centers\n\n(ndarrary(:)) - Location of all cell center coordinates for this dimension\n\nproperty delta\n\n(float) - Size of an individual, computational cell\n\nproperty nodes\n\n(ndarrary(:)) - Location of all cell edge coordinates for this dimension\n\n## Parallel Geometry Objects¶\n\n### petclaw.geometry.Domain¶\n\nclass clawpack.petclaw.geometry.Domain(geom)\n\nParallel Domain Class\n\nParent Class Documentation:\n\n2D Classic (Clawpack) solver.\n\nSolve using the wave propagation algorithms of Randy LeVeque’s Clawpack code (www.clawpack.org).\n\nIn addition to the attributes of ClawSolver1D, ClawSolver2D also has the following options:\n\ndimensional_split\n\nIf True, use dimensional splitting (Godunov splitting). Dimensional splitting with Strang splitting is not supported at present but could easily be enabled if necessary. If False, use unsplit Clawpack algorithms, possibly including transverse Riemann solves.\n\ntransverse_waves\n\nIf dimensional_split is True, this option has no effect. If dimensional_split is False, then transverse_waves should be one of the following values:\n\nClawSolver2D.no_trans: Transverse Riemann solver not used. The stable CFL for this algorithm is 0.5. Not recommended.\n\nClawSolver2D.trans_inc: Transverse increment waves are computed and propagated.\n\nClawSolver2D.trans_cor: Transverse increment waves and transverse correction waves are computed and propagated.\n\nNote that only the fortran routines are supported for now in 2D.\n\nParent Class Documentation:\n\nGeneric classic Clawpack solver\n\nAll Clawpack solvers inherit from this base class.\n\nmthlim\n\nLimiter(s) to be used. Specified either as one value or a list. If one value, the specified limiter is used for all wave families. If a list, the specified values indicate which limiter to apply to each wave family. Take a look at pyclaw.limiters.tvd for an enumeration. Default = limiters.tvd.minmod\n\norder\n\nOrder of the solver, either 1 for first order (i.e., Godunov’s method) or 2 for second order (Lax-Wendroff-LeVeque). Default = 2\n\nsource_split\n\nWhich source splitting method to use: 1 for first order Godunov splitting and 2 for second order Strang splitting. Default = 1\n\nfwave\n\nWhether to split the flux jump (rather than the jump in Q) into waves; requires that the Riemann solver performs the splitting. Default = False\n\nstep_source\n\nHandle for function that evaluates the source term. The required signature for this function is:\n\ndef step_source(solver,state,dt)\n\nkernel_language\n\nSpecifies whether to use wrapped Fortran routines (‘Fortran’) or pure Python (‘Python’). Default = 'Fortran'.\n\nverbosity\n\nThe level of detail of logged messages from the Fortran solver. Default = 0.\n\n### petclaw.geometry.Patch¶\n\nclass clawpack.petclaw.geometry.Patch(dimensions)\n\nParallel Patch class.\n\nParent Class Documentation:\n\nGlobal Patch information\n\nEach patch has a value for level and patch_index."
] | [
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https://rstudio-pubs-static.s3.amazonaws.com/7953_4e3efd5b9415444ca065b1167862c349.html | [
"# R Base Graphics: An Idiot's Guide\n\nOne of the most powerful functions of R is it's ability to produce a wide range of graphics to quickly and easily visualise data. Plots can be replicated, modified and even publishable with just a handful of commands.\n\nMaking the leap from chiefly graphical programmes, such as Excel and Sigmaplot. may seem tricky. However, with a basic knowledge of R, just investing a few hours could completely revolutionise your data visualisation and workflow. Trust me - it's worth it.\n\nLast year, I presented an informal course on the basics of R Graphics University of Turku. In this blog post, I am providing some of the slides and the full code from that practical, which shows how to build different plot types using the basic (i.e. pre-installed) graphics in R, including:",
null,
"Exciting, eh?\n\nThis post is BIG, but DETAILED. So, use the links below to jump ahead. I hope someone out there finds this useful - all code and datafiles are available here.\n\n• 0. Preface: What am I supposed to know again?\n• 1. Basic Histogram\n• 2. Basic Line Graph with Regression\n• 3. Scatterplot with Legend\n• 4. Boxplot with reordered and formatted axes\n• 5. Barplot with error bars\n• 6. More than one plot in a window\n• 7. Saving a plot\n\n## 0. Preface: What am I supposed to know again?\n\nOh you. Before you get started, you should be familiar with the follow concepts:\n\n##### Vectors!\n``````height <- c(145, 167, 176, 123, 150)\nweight <- c(51, 63, 64, 40, 55)\n\nplot(height,weight)\n``````",
null,
"#### Data frames!\n\n``````tarsus <- read.table(\"tarsus.txt\", header = T)\ntarsus\n``````\n``````## TarsusLength Weight\n## 1 23 231\n## 2 26 258\n## 3 25 254\n## 4 21 211\n## 5 27 268\n## 6 28 284\n## 7 27 271\n## 8 26 258\n## 9 26 264\n## 10 25 251\n## 11 26 258\n## 12 24 244\n## 13 25 251\n## 14 25 248\n## 15 23 234\n## 16 21 211\n``````\n\nTo call a variable in the dataframe, use the \\$ notation.\n\n``````tarsus\\$TarsusLength\n``````\n``````## 23 26 25 21 27 28 27 26 26 25 26 24 25 25 23 21\n``````\n``````tarsus\\$Weight\n``````\n``````## 231 258 254 211 268 284 271 258 264 251 258 244 251 248 234 211\n``````\n``````\nplot(tarsus\\$TarsusLength,tarsus\\$Weight)\n``````",
null,
"#### Tables!\n\n``````tarsus.tab <- table(tarsus\\$TarsusLength)\n\ntarsus.tab\n``````\n``````##\n## 21 23 24 25 26 27 28\n## 2 2 1 4 4 2 1\n``````\n``````\nplot(tarsus.tab)\n``````",
null,
"``````\nbarplot(tarsus.tab)\n``````",
null,
"## 1. Basic Histogram\n\nWhat customisations are we going to learn in this section?",
null,
"Let's begin. For this part, we will use data on birthweight measured in male and female unicorns.\n\nLet's read the data into R:\n\n``````unicorns <- read.table(\"unicorns.txt\" ,header = T)\n``````\n``````## birthweight sex longevity\n## 1 4.478 Male 1\n## 2 5.753 Male 0\n## 3 3.277 Male 0\n## 4 3.929 Male 0\n## 5 3.973 Male 0\n## 6 4.913 Male 0\n``````\n``````str(unicorns)\n``````\n``````## 'data.frame': 1000 obs. of 3 variables:\n## \\$ birthweight: num 4.48 5.75 3.28 3.93 3.97 ...\n## \\$ sex : Factor w/ 2 levels \"Female\",\"Male\": 2 2 2 2 2 2 2 2 2 2 ...\n## \\$ longevity : int 1 0 0 0 0 0 1 0 0 1 ...\n``````\n\nWe can create a basic histogram of unicorn birthweight and longevity using hist():\n\n``````hist(unicorns\\$birthweight) # normal distribution\n``````",
null,
"``````hist(unicorns\\$longevity) # poisson distribution\n``````",
null,
"And we can specify the number of cells for the histogram using: breaks = N:\n\n``````hist(unicorns\\$birthweight, breaks = 40)\n``````",
null,
"``````hist(unicorns\\$birthweight, breaks = c(0,1,2,3,4,5,6,7))\n``````",
null,
"``````hist(unicorns\\$birthweight, breaks = c(0,1,2,3,4,7))\n``````",
null,
"Relabel the x-axis using: xlab = “Text”\n\n``````hist(unicorns\\$birthweight, breaks = 40, xlab = \"Birth Weight\")\n``````",
null,
"Relabel the main title using: main = “Text”\n\n``````hist(unicorns\\$birthweight,\nbreaks = 40,\nxlab = \"Birth Weight\",\nmain = \"Histogram of Unicorn Birth Weight\")\n``````",
null,
"NB: In our code, the lines are starting to get quite long. When there is a comma, R knows that there is more information on the next line!\n\nThe y-axis stops short of the highest value in the histogram. Lets specify new limits using: ylim = c(minimum, maximum)\n\n``````\nhist(unicorns\\$birthweight,\nbreaks = 40,\nxlab = \"Birth Weight\",\nmain = \"Histogram of Unicorn Birth Weight\",\nylim = c(0,80))\n``````",
null,
"## 2. Basic Line Graph with Regression",
null,
"Moomins are a common pest species in Finland. We have data on their population on the island of Ruissalo from 1971 to 2000.\n\nWhich customisations will we learn here?",
null,
"``````moomins <- read.table(\"Moomin Density.txt\", header = T)\n``````\n``````## Year PopSize\n## 1 1971 500\n## 2 1972 562\n## 3 1973 544\n## 4 1974 532\n## 5 1975 580\n## 6 1976 590\n``````\n\nWe can easily create a plot using the command `plot`.\n\n``````plot(moomins\\$Year, moomins\\$PopSize)\n``````",
null,
"There are several types of plot within the plot function. Use “type”:\n\n``````plot(moomins\\$Year, moomins\\$PopSize, type = \"l\") # Try \"o\" \"p\" \"l\" \"b\"\n``````",
null,
"We can also change the line type using “lty”\n\n``````plot(moomins\\$Year, moomins\\$PopSize, type = \"l\", lty = \"dashed\")\n``````",
null,
"``````plot(moomins\\$Year, moomins\\$PopSize, type = \"l\", lty = \"dotted\")\n``````",
null,
"The solid line looks best, so lets stick with it.\n\n``````plot(moomins\\$Year, moomins\\$PopSize, type = \"l\")\n``````",
null,
"Let's start to add colour using “col”.\n\n``````plot(moomins\\$Year, moomins\\$PopSize, type = \"l\", col = \"red\") # R Colour Chart\n``````",
null,
"NB. numbers can also be used as colours!\n\n``````plot(moomins\\$Year, moomins\\$PopSize, type = \"l\", col = 3)\n``````",
null,
"Let's make the line a little thicker using “lwd” (line width)\n\n``````plot(moomins\\$Year, moomins\\$PopSize, type = \"l\", col = \"red\", lwd = 3)\n``````",
null,
"Finally, lets sort out the axis titles plot title:\n\n``````plot(moomins\\$Year, moomins\\$PopSize,\ntype = \"l\",\ncol = \"red\",\nlwd = 3,\nxlab = \"Year\",\nylab = \"Population Size\",\nmain = \"Moomin Population Size on Ruissalo 1971 - 2001\")\n``````",
null,
"Is the Moomin population increasing in size? We can add a basic linear regression to the plot using `abline`. NB. we can also use lty, lwd, col here.\n\n``````\nplot(moomins\\$Year, moomins\\$PopSize,\ntype = \"l\",\ncol = \"red\",\nlwd = 3,\nxlab = \"Year\",\nylab = \"Population Size\",\nmain = \"Moomin Population Size on Ruissalo 1971 - 2001\")\n\nfit1 <- lm (PopSize ~ Year, data = moomins)\nsummary(fit1)\n``````\n``````##\n## Call:\n## lm(formula = PopSize ~ Year, data = moomins)\n##\n## Residuals:\n## Min 1Q Median 3Q Max\n## -109.52 -17.76 1.65 20.37 63.83\n##\n## Coefficients:\n## Estimate Std. Error t value Pr(>|t|)\n## (Intercept) -22493.93 1489.99 -15.1 5.6e-15 ***\n## Year 11.67 0.75 15.6 2.6e-15 ***\n## ---\n## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n##\n## Residual standard error: 35.6 on 28 degrees of freedom\n## Multiple R-squared: 0.896, Adjusted R-squared: 0.893\n## F-statistic: 242 on 1 and 28 DF, p-value: 2.61e-15\n``````\n``````\nabline(fit1, lty = \"dashed\") #abline(a = intercept, b = slope)\n\n#~~ We can add some text to the plot giving the R2 value and the P value using \"text\" and specifying the x and y coordinates for the text.\n\ntext(x =1978, y = 750,labels=\"R2 = 0.896\\nP = 2.615e-15\")\n``````",
null,
"Final script:\n\n``````plot(moomins\\$Year, moomins\\$PopSize, # x variable, y variable\ntype = \"l\", # draw a line graphs\ncol = \"red\", # red line colour\nlwd = 3, # line width of 3\nxlab = \"Year\", # x axis label\nylab = \"Population Size\", # y axis label\nmain = \"Moomin Population Size on Ruissalo 1971 - 2001\") # plot title\n\nfit1 <- lm (PopSize ~ Year, data = moomins) # carry out a linear regression\nabline(fit1, lty = \"dashed\") # add the regression line to the plot\ntext(x = 1978, y = 750, labels = \"R2 = 0.896\\nP = 2.615e-15\") # add a label to the plot at (x,y)\n``````\n\n## 3. Scatterplot with Legend\n\nWhat will we learn here?",
null,
"R comes with many datasets preinstalled. Let's load a dataset of Flower characteristics in 3 species of Iris.\n\n``````data(iris)\n``````\n``````## Sepal.Length Sepal.Width Petal.Length Petal.Width Species\n## 1 5.1 3.5 1.4 0.2 setosa\n## 2 4.9 3.0 1.4 0.2 setosa\n## 3 4.7 3.2 1.3 0.2 setosa\n## 4 4.6 3.1 1.5 0.2 setosa\n## 5 5.0 3.6 1.4 0.2 setosa\n## 6 5.4 3.9 1.7 0.4 setosa\n``````\n\nThere is a lot of data here! Let's explore using the 'pairs' function\n\n``````pairs(iris)\n``````",
null,
"This doesn't tell us much about the species differences. We can tell R to plot using a different colour for the three species of iris:\n\n``````pairs(iris, col = iris\\$Species)\n``````",
null,
"Sepal.Length and Petal.Length look interesting! Let's start by looking at that. Again, we will specify colour as the Species.\n\n``````plot(iris\\$Sepal.Length, iris\\$Petal.Length, col = iris\\$Species)\n``````",
null,
"These points are difficult to see! Let's pick some different ones using “pch”",
null,
"``````\nplot(iris\\$Sepal.Length, iris\\$Petal.Length, col = iris\\$Species, pch = 15)\n``````",
null,
"``````plot(iris\\$Sepal.Length, iris\\$Petal.Length, col = iris\\$Species, pch = \"A\")\n``````",
null,
"pch 21:25 also specify an edge colour (col) and a background colour (bg)\n\n``````plot(iris\\$Sepal.Length, iris\\$Petal.Length, col = iris\\$Species, pch = 21, bg = \"blue\")\n``````",
null,
"lets settle on solid circles `(pch = 16)`\n\n``````\nplot(iris\\$Sepal.Length, iris\\$Petal.Length, col = iris\\$Species, pch = 16)\n``````",
null,
"We can change the size of the points with “cex”\n\n``````plot(iris\\$Sepal.Length, iris\\$Petal.Length,\ncol = iris\\$Species,\npch = 16,\ncex = 2)\n``````",
null,
"It's difficult to tell these points apart, so perhaps we should make a legend. This is one of the major drawbacks with R. iris\\$Species is a factor, and R will automatically order factors in alphabetical order.\n\n``````levels(iris\\$Species)\n``````\n``````## \"setosa\" \"versicolor\" \"virginica\"\n``````\n\nTherefore, setosa, versicolor and virginica will correspond to 1, 2 and 3 on the plot default colours. Keep this in mind for the next part!\n\n``````plot(iris\\$Sepal.Length, iris\\$Petal.Length,\ncol = iris\\$Species,\npch = 16,\ncex = 2)\nlegend(x = 4.5, y = 7, legend = levels(iris\\$Species), col = c(1:3), pch = 16)\n``````",
null,
"FINAL PLOT\n\n``````plot(iris\\$Sepal.Length, iris\\$Petal.Length, # x variable, y variable\ncol = iris\\$Species, # colour by species\npch = 16, # type of point to use\ncex = 2, # size of point to use\nxlab = \"Sepal Length\", # x axis label\nylab = \"Petal Length\", # y axis label\nmain = \"Flower Characteristics in Iris\") # plot title\n\nlegend (x = 4.5, y = 7, legend = levels(iris\\$Species), col = c(1:3), pch = 16)\n``````",
null,
"``````#~~ legend with titles of iris\\$Species and colours 1 to 3, point type pch at coords (x,y)\n``````\n\nSIDE NOTE 1: specifying colours: It is also possible to specify colours in your data frame.\n\n``````iris\\$Colour <- \"\"\niris\\$Colour[iris\\$Species==\"setosa\"] <- \"magenta\"\niris\\$Colour[iris\\$Species==\"versicolor\"] <- \"cyan\"\niris\\$Colour[iris\\$Species==\"virginica\"] <- \"yellow\"\n\nplot(iris\\$Sepal.Length, iris\\$Petal.Length, col = iris\\$Colour, pch = 16, cex = 2)\nlegend(x = 4.5, y = 7,\nlegend = c(\"setosa\",\"versicolor\",\"virginica\"),\ncol = c(\"magenta\",\"cyan\",\"yellow\"),\npch=16)\n``````",
null,
"SIDE NOTE 2: It would also be possible to specify lines in the legend by using “lty” instead of “pch”\n\n``````plot(iris\\$Sepal.Length, iris\\$Petal.Length, col = iris\\$Species, pch = 16, cex = 2)\nlegend(4.5, 7,\nlegend = c(\"setosa\",\"versicolor\",\"virginica\"),\ncol = c(1:3),\nlty = \"solid\")\n``````",
null,
"## 4. Boxplot with reordered and formatted axes\n\nWhat will be tackle here?",
null,
"We will continue to use the Iris dataset for this section. Let's examine the distribution of Sepal Length for each species:\n\n``````\nboxplot(iris\\$Sepal.Length ~ iris\\$Species)\n``````",
null,
"If you wish to compare the medians of the boxplot, you can use the function `notch`. If the notches of two plots do not overlap, this is 'strong evidence' that the two medians differ (see ?boxplot)\n\n``````\nboxplot(iris\\$Sepal.Length ~ iris\\$Species, notch = T)\n``````",
null,
"You may have noticed that the y-axis labels are always orientated to be perpendicular to the axis. We can rotate all axis labels using `las`. Play around with different values.\n\n``````boxplot(iris\\$Sepal.Length ~ iris\\$Species, notch = T, las = 1)\n``````",
null,
"Let's add in all the axis and plot labels:\n\n``````\nboxplot(iris\\$Sepal.Length ~ iris\\$Species,\nnotch = T,\nlas = 1,\nxlab = \"Species\",\nylab = \"Sepal Length\",\nmain = \"Sepal Length by Species in Iris\")\n``````",
null,
"Like we can change the size of the points in the scatterplot, we can change the size of the axis labels and titles. Let's start with `cex.lab`, which controls the axis titles:\n\n``````\nboxplot(iris\\$Sepal.Length ~ iris\\$Species,\nnotch = T,\nlas = 1,\nxlab = \"Species\", ylab = \"Sepal Length\", main = \"Sepal Length by Species in Iris\",\ncex.lab=1.5)\n``````",
null,
"Now we can add in “cex.axis” (changing the tickmark size) and “cex.main” (changing the plot title size)\n\n``````\nboxplot(iris\\$Sepal.Length ~ iris\\$Species, notch = T, las = 1,\nxlab = \"Species\", ylab = \"Sepal Length\", main = \"Sepal Length by Species in Iris\",\ncex.lab = 1.5,\ncex.axis = 1.5,\ncex.main = 2)\n``````",
null,
"As we discussed earlier, R automatically puts factors in alphabetical order. But perhaps we would prefer to list the iris species as virginica, versicolor and setosa. First lets look at the levels of iris:\n\n``````data(iris)\nlevels(iris\\$Species)\n``````\n``````## \"setosa\" \"versicolor\" \"virginica\"\n``````\n\nWe reorder them with the following command:\n\n``````\niris\\$Species <- factor(iris\\$Species, levels = c(\"virginica\",\"versicolor\",\"setosa\"))\n``````\n\nLet's see that FINAL PLOT:\n\n``````\nboxplot(iris\\$Sepal.Length ~ iris\\$Species, # x variable, y variable\nnotch = T, # Draw notch\nlas = 1, # Orientate the axis tick labels\nxlab = \"Species\", # X-axis label\nylab = \"Sepal Length\", # Y-axis label\nmain = \"Sepal Length by Species in Iris\", # Plot title\ncex.lab = 1.5, # Size of axis labels\ncex.axis = 1.5, # Size of the tick mark labels\ncex.main = 2) # Size of the plot title\n``````",
null,
"# 5. Barplot with error bars using summary data\n\nUgh. I warn you - this will not be pretty.Let's create a new data frame with information on three populations of dragon in the UK:\n\n``````dragons <- data.frame(\nTalonLength = c(20.9, 58.3, 35.5),\nSE = c(4.5, 6.3, 5.5),\nPopulation = c(\"England\", \"Scotland\", \"Wales\"))\n\ndragons\n``````\n``````## TalonLength SE Population\n## 1 20.9 4.5 England\n## 2 58.3 6.3 Scotland\n## 3 35.5 5.5 Wales\n``````\n\nLet's make our barplot.\n\n``````\nbarplot(dragons\\$Population, dragons\\$TalonLength)\n``````\n``````## Error: 'height' must be a vector or a matrix\n``````\n\nNo, this didn't work. It would be better to add Titles to the x-axis:\n\n``````barplot(dragons\\$TalonLength, names = dragons\\$Population)\n``````",
null,
"Would a box look better around this plot?\n\n``````barplot(dragons\\$TalonLength, names = dragons\\$Population)\nbox()\n``````",
null,
"Not really. Let's start again:\n\n``````barplot(dragons\\$TalonLength, names = dragons\\$Population)\n``````",
null,
"Let's reorder the columns by how beautiful the dragon habitat is (from best to worst). Naturally, this order is 'Scotland, Wales, England'.\n\n``````levels(dragons\\$Population)\n``````\n``````## \"England\" \"Scotland\" \"Wales\"\n``````\n``````\ndragons\\$Population <- factor(dragons\\$Population, levels=c(\"Scotland\",\"Wales\",\"England\"))\n\nbarplot(dragons\\$TalonLength, names = dragons\\$Population)\n``````\n\nNo…. it's not working. I give up for now. What about error bars?\n\n``````library(gplots)\n``````\n``````## Loading required package: gtools Loading required package: gdata gdata:\n## Unable to locate valid perl interpreter gdata: gdata: read.xls() will be\n## unable to read Excel XLS and XLSX files gdata: unless the 'perl=' argument\n## is used to specify the location gdata: of a valid perl intrpreter. gdata:\n## gdata: (To avoid display of this message in the future, please gdata:\n## ensure perl is installed and available on the executable gdata: search\n## path.) gdata: Unable to load perl libaries needed by read.xls() gdata: to\n## support 'XLX' (Excel 97-2004) files.\n##\n## gdata: Unable to load perl libaries needed by read.xls() gdata: to support\n## 'XLSX' (Excel 2007+) files.\n##\n## gdata: Run the function 'installXLSXsupport()' gdata: to automatically\n## download and install the perl gdata: libaries needed to support Excel XLS\n## and XLSX formats.\n##\n## Attaching package: 'gdata'\n##\n## The following object is masked from 'package:stats':\n##\n## nobs\n##\n## The following object is masked from 'package:utils':\n##\n## object.size\n##\n##\n## Attaching package: 'gplots'\n##\n## The following object is masked from 'package:stats':\n##\n## lowess\n``````\n``````barplot(dragons\\$TalonLength, names = dragons\\$Population,\nylim=c(0,70),xlim=c(0,4),yaxs='i', xaxs='i',\nmain=\"Dragon Talon Length in the UK\",\nylab=\"Mean Talon Length\",\nxlab=\"Country\")\npar(new=T)\nplotCI (dragons\\$TalonLength,\nuiw = dragons\\$SE, liw = dragons\\$SE,\ngap=0,sfrac=0.01,pch=\"\",\nylim=c(0,70),\nxlim=c(0.4,3.7),\nyaxs='i', xaxs='i',axes=F,ylab=\"\",xlab=\"\")\n``````\n``````## Warning: \"axes\" is not a graphical parameter\n``````\n``````box()\n``````",
null,
"Aaaaaaaaaaaargh!\n\nFINAL PLOT\n\n``````# Just do it in ggplot2!\n``````\n\n# Final words in base graphics\n\nThis is how I summed it up in the course:",
null,
"# Extras!\n\nHere is some code for some extra fun things in base graphics:\n\n## 6. More than one plot in a window\n\n``````\n\npar(mfrow=c(1,2)) # number of rows, number of columns\n\nplot(iris\\$Sepal.Length, iris\\$Petal.Length, # x variable, y variable\ncol = iris\\$Species, # colour by species\nmain = \"Sepal vs Petal Length in Iris\") # plot title\n\nplot(iris\\$Sepal.Length, iris\\$Sepal.Width, # x variable, y variable\ncol = iris\\$Species, # colour by species\nmain = \"Sepal Length vs Width in Iris\") # plot title\n``````",
null,
"``````\npar(mfrow=c(1,1)) # sets the plot window back to normal\n\n# OR\n\ndev.off() # But this will clear your plot history.\n``````\n``````## null device\n## 1\n``````\n\n## 7. Saving a Plot\n\n``````# png\n\npng(\"Sepal vs Petal Length in Iris.png\", width = 500, height = 500, res = 72)\n\nplot(iris\\$Sepal.Length, iris\\$Petal.Length,\ncol = iris\\$Species,\nmain = \"Sepal vs Petal Length in Iris\")\n\ndev.off()\n``````\n``````## pdf\n## 2\n``````\n``````\n\n# pdf\n\npdf(\"Sepal vs Petal Length in Iris.pdf\")\n\nplot(iris\\$Sepal.Length, iris\\$Petal.Length,\ncol = iris\\$Species,\nmain = \"Sepal vs Petal Length in Iris\")\n\ndev.off()\n``````\n``````## pdf\n## 2\n``````"
] | [
null,
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h7AD1/NxnnfZBxftwBLdsjKR/llL+GFYbbU20R0YNnHM/DjnmNCXpkJK+EcM579L7YfOoUZb74hCBUffPDqs9h14AD+c/+DsLG3xOw5H2PNknn48Ku1+PjNp7HT0BbffvK2eF3vvv0WnDw98cH0d6CvfwQzP/4anpdM8OrML1FTmoxHH31REmk92LL4A7wsvCB9+dHbeGXWMhzZuQYrtx7DpoVv4ukZC+DqHYBjW1fg/c8W4+DeQ4hOE16CBEpSgvDqK28J6R/Ee58tgbvNWbw+6xtUCQL0kcdeRbWoU3oFAfM0nGKLcHHfCsxbux8+Vvp47q252LBkDmYs2oDDG5fi+31ncF7/ADauX4UH//civAICsGXDBnz63mv4cvUmzH//VXy3dTeeefRRnL5ghHff/wieLlaCKP4IR/dvFF6qVqBJYYLejqWzsFIQgh2NJfjum4V465Xn8OMxK/RUp+DRx55Hef+Nx/x3noPepQjJ14v8jBQkpeeIcq+pNB33/f23mLviJ4REJsHy+DZ8smAFPvlkFux9ArBmwUf4cctmzPhYKHNCmj1VSXj8saeQwSJNq+lsb0NZaQnKK6rQ1tY+6mm7RUWystDZIbzJaIjWlmZxSo4ivd2daGkdeG5sS3MTulV+Q3dXJ9o6+jN6Y5PUSDJKTCmRlhodhMAo2eRjHx8vpKYmw9svBDWVRThx5BDOW7iKmS/Kxx7Gtj5oqS/Dwd274RQom5927vBGrFj9vSB8HoOpexg8BAHSJHyhpSoPJ48dg5m5NaLjEuDt6Y3Kmmq4u7gLhawMrs6uaOrLi92wOnscR08bC5+A+GBvRCX3T8wuzYrDDuGN/LyNu+gP8nJBTnk9kiICEZ2YAj9PN9QJjVdGjC/27NmDcOm7NudO4Mjpi2KaiaE+iEymyfntcHZ0RoNQyH1cnJBXKSsE5XlJOHhgH7Zu3YrjhtZC4emGj4c7srKz4OrmJVb+dSVpOH3aEB4eHkjIKkZxRhy8gug+yMgQ7qWTZ5j42cXSEhnF1KfYDcuzejhyyhh1jU3wcnVGWWUF9vy4BN9/twaPPfUCAmKS4OEdiPbWOjg5e6C5tQnnT+shMrVITIsZnPzUaARExAvPOADBkcmIDfdDenE9etprobdvN8xdA8V4bbWFOCTkXYeAOOGxNMPR2RO11WVwcfNFZWk+PH2DkJ4Ug7CYy4gK9kVGSS1SogIRGp8pfr+1tliMqziXqr2uGIf37Iadb5RQHGrx8qMPYOOeIzBz9BePxwe44qj+SVjbuyA/Pwee3v6orijEKb1jMDW3REJGETITAgXReB6OLrKykxMfiN3CdaaVNaGrrgjOHgFob6mFg4MrWiRR09NRD4Nj+7Bt5wGUNLQjLyUaQaHhsDY5KwgwPRw4eR71QiNgYXAUemfMhM/yPiYgJcJbTD+rshVtVblw8QpGW1M1HBzdhdJB9MLHzRG5VUID01WLc0YXUFlbC5MzJ2FodBEhUYm4HBOK2NQ8pMUE4MhRPYTE56CzTTif0SnoHz8nlMduFKdGQO/YcVjZOiIpOQnuHl5i6qFu1tgtvLiVi5Pi+okXymj4ZUFodbfD3sQQBuctxeHQjpoCOLp6iuVYTqBQB6RIcwtVqSlMxeFDR6Av3GMjczchpAfmBkdw3t5bPF6dn4R9e/ciIadC9He31sDR0Uk2B5DRWi7qbccrb7yDH3/ahx07tyO9sBJBvl5IyylAaUkJiouLRAFWInwuKcxFZOxldHW2w5/atWyqS7uwa/0KvC28DO0/cR7nThzBwZMXUFRRi9qKIgQEhoiiKio0EDHxyUiMi0bc5Qzx3AHCeRKTU7F/62YEx2UIL3dRKK6sR1VJHry8fHDa4AxSc/IQHBSEwuJiHN2zC4eP6gtt62XkpsXDJzAczU0NCBReZAqkxTFOtmYIFOqtIH9fRMXJ5rfGB7pg7zEDJMRGwsXBFsZW9ijIzUBgcBjaOnlli5wpJdKuip42GBzcihWrVmPd9iOo09yLyaSmp6kc29etwurVK7HvlPkVb2CMjtJWjo3fr0OloppgGEYjnNj5HZ556U3oGV7Eof17sG37DsHtwrYtG7Bhyw6s+OYrLFi4GDu3bcSCeZ/g7env4+jhQ5g151NByJWgIDEAXy5ZL6ZFPXK7Nq3BkmXLsXXXIdiYncETjz2KQ3onMe/TT+DtH4Dvl36G59/6UBBgJ7Hm+w2CkHfB1198hp9+2o7pb7yG5Wu2YNMPq7D9oD72792BTRt+wNPPvABzO0csXfg51m38Cbt278SmjT/goqkNzurtx+NPPgMjG0/xGk4d2YMN69fh668XYcGXX6OwrguXg5ywfsMGLFiwAOcvGuOnrVvwzRfCb5n1CTIEUcrIYJHGMAzDMFrEgc1rcNzEBbV19dix+QcsX7kKx04aYrsgZM4a6GPG9Hfx/jtv4+DxM/jq0w+xecs2GJ3Sw487Dovfry3OxLyPPsKhQwdw8pwxdm/7CbYOzli3egVWrFiGOXPmCGJsHbbvOYrc1Fh8PGcWPp7/JX7c+CO27j2M4NBQ/PTjeqz7YS0+nPMJjhtcFF7K1iIqJRcHt68X/Gfx8QfTsebHrdi5fRs2bNyINd+uxLpNm+Du5Q1HOyvMfX86FqzcJF7P4Z0bsWTJcpw3s8bOjeuQUNQqiLRLWLZ8uSA696AoPwMrV63G2dP6eP7Zp2HuFiJ+j2GRxjAMwzBaRWJ0RJ+pl4iwEFRUVcHU6AwCYlLQ01qLgIAghAYHoaSmGRnxITC3ckRRYR7Co2Qrm4nMhDBs27YDMclZSEmMR2Z2NmKiYxAREgBjY1NECJ+jYuLR3tYCO0tzWNg5o7qmGsbnDOAdHIW4yBAEhITD2dYCkQnpSE6IRUlljTg0ejnpMizMzJCeU4yE6BCYmFogt6gU4f6uMDC2RF5eNixMzRAnnJu4HB+NUEH4paZnIjYqAjUtXagpyxPDIqPjUF9XjYjIKESHB8PcwgbVDQPbBZxqsEhjGIZhGIbRQlikMQzDMAzDaCEs0hiGYRiGYbQQFmkMwzAMwzBaCIs0hmEYhmEYLYRFGsOMJz1daGtrY3txDMMwzJCwSGOYcSIrJQbm5ma4dOkSTE0tkZZXKh25koyMDDg6OsLV1ZUduzFxbm5u4o4iNjY2sLa2FsPc3d3RLW3ers309PSgsLAQeXl57NjpnKMX9eEyJiItNyMFiYmJyMzlrX4YRo7pqX0IiMtFZ2cnIj1tccpaZo1bHSTkoqOjUVpayo6dxl15ebn4Nzk5WbRVRfU1+c+fP4+qKtqRWLshgUYvMUlJSezYjbtLSUpRGz4c5+fnh6ioKCknD43GRZq3kzlsXbwRHx8PBwsTuCjs98gwU5nayny4Cg2LrbUlLC65o66pVTpyJZ6enmKjyTBjQVd3N7y8vESRpoiLi4tWiLSK4nykZeQMuLF4bm4u0tPTJR/D6A5UvmJiYiTf0GhcpHnYX4B3UBzy8wsQ4O4AO58I6QjDTG38PTxQWFACdxcHODu7o6BYeX866mFraGgQnb29PYqLi6UjDKMZaCgzu6gI9T09qKmrk0L7cXJy0gqRFuBqA1PzSwgMCkRadoEUCtTX1yMgIACWlpZiR8BooV5qHx8fMa2xdDSknJUls7rPTA4OVxzGo0mP4kzVGSlkZFC9PqEirae9DpZmF2BpYQITW1cptB+6QOqmJmdnZ4f2dt6pnJkaXNTbhzXLlsIxMA3FlwNx1sZbOiKjSGg8HRwcRLd7925UVFRIRxhGM4TFxcFfyF+db78N4U1aCu1HW0RaZVkJmlu70N3VgcYm5S2Cent7xZ60y5cvSyEjx9/fH42NjWJaY+kKCgpGNLTFaDdxLXGYFjkN0yIEFz0NWe0jF+ATLtJ8Xe1gYWYMvbMmCPF1g7O/8sV0dHSgpqZGdObm5uLcAoaZCtSW5sNQ7zD8QuMQER6MyoaBX1DoLZ/LBjNiWluB6mrJI6O5uVkUJXllZehuaAD++19g2TIIb8hSjH60RaQNBU2+vhqRFhISIt6XsYYa5DhBGDOTg7yOPNyUeBOmRU3DbZdvQ0XXyF+kJ16kudjAyPA09hw7DT9PJ7gGDXwxNO+Geg8YZiqQnhgOS2tznL1wHra2tkjOHng4k1bZcdlgRsysWcCNNwLnz4teWqdZUlKCuJQUtAsiDXfdBaxeLR5Tx1QUabSS+uLFi+J0A6Knuws5WRmoqqlHeUkR8rLT4O7mheKifOQWlKC6ohR5BcWoripDfmGx2GM2ECzSJh9WtVa4IeYGeDYOvPBrMCZcpPV0NCMlPRX5uZm4nDL4xE5uiJiphL35eVibGmOX/nkkRwXgwiUf6ciVcNlgRgwNX/7pT8CePWJvWfQrryDowgXZsZYW4F//GlSgEVNJpLXQPRHYtGkTpk2bJg5NEo1VpThnYAB7WyscOXwMJ44fhcHxk3B2dYeLoz30j5yAo4sr3J1ssWXbLtS0DGyyhEXa5KK4sxh3J9+Nn0X9DA+kPoCa7hrpyPCZcJE2ErghYqYStWV5cHB2gIeHK5zdPdHQOrCtHC4bzIiZNw/4+GOUdnWhpr4eKcuWoevPfwZ++AF44IEhBRoxFXvSaDGC4iKEzvZWeDrbw8jwHIyMjOHm4Q5HW2tBpAnl1tkNgQGBuHjOEBeMzmPvvkMorRt42gKLNN2mpacFSwuW4qOcj1DeVY7E1kTZfDSalxY1DentI19hzCKNYSYBXDaYEUHzy26+GSkmJnANCkK7INRESMi8+irw448y/xDwnDQZDYJwE+ntQlu7bBiUFjG0d3Sgoa4WndR5Ju4e0iEea2tTL9RYpOk2G0s2YlqoIMjCpmFG9gwx7MeSH3FH/B3YXbZb9I8UFmkMMwngssEMF5oRdXn/fqQ/+CDqakY+/KLIlBRptPpy507ZoguBuuoK1Dc0oqy4EMmpqSgvK0daUgpSUlKQlZUuNLJlyMlMRWZuIfKy05GcnIAgHz/hehKQk1eI1MspaGiRiTYWaboNCTESaCTU5uTMkUKBjl6ZOB8NLNIYZhLAZYMZLhWNjQi84QY02tlJIaNnSok0aU4atm8XWkKhKZTKW1VxDs4anMK2LZuhd9IQJ44dhoOdC6zNLWBlYwFzo/O45OKL7LR4ODg6wd7yInZt2QoXT1+YnDmGU2es0dElm6fGIk236ertwrbSbVhZsBI1XcN/Aeru7YZjrSMy2zOlkH5YpE1SyGQJmWSQuzJaqcVMWrhsMENBPTvegtjocnMD/v53srUhHRk9U7InjVZ1lpTIPkuYXTgH/8AQWFpYwcfLHWmpWYgMDYTRuXMI8A2Au4cnouOi4ebqJNwzRzjZ2sLZxRX2ttYIDeuf38YibepBwu6TvE/EHrg/xP8ByW3Ku3qwSJuENDU14fjx4+JmyHJH/pycHCkGM9ngssEoQVbrpReznu5ucWUiibR6EhgzZ8rsnmkAnpOmTJs0BEr0dHWgQ5yMRp5ONDYrL/yhOWvdKtY4WKRpD3vL9+L+y/dDr1JPChkbGrob8Mu4X4oLC0ioGVQZSEdksEibhFRWVsLVVXn3hoiICHGzVkZ3KM5Pg7WlubjThqWVPQrKB+4+57LB9EHbN5FpjbvvRqUgzOx9ffuFFL2o/fGPQGqqzH+VTEWR5tXgha/zv0Zjd6Pob2qsExcC0HyzosISlBSXIlf4nJaegdKSUuRkZCBXOH9NdS2KC3NRWFKO0uIC1DVKw6cKsEjTDvp2CpCvymwb231f9Sv18ceYP+KljJdQ210rhcpgkTYJqa6uFitPRYKCgsQ3aUZ3MD65FwHxeaLRzAgPG5yyGtgYIpcNpo9Nm1D/v/8hd+lSFF97Leole14iK1cCtMWThphKIq2lWSaqDpQfwB9i/4CSTtmQZ1lBBsyML+LE8WOwMrWA6XlTeHm449ihfTAzMYP5RVMYnjou/DWHs6sPsrMzcVZvP04b24rfV4RFmnZQ1FGEPyX8SVwAcMvlW0a1U8BIqepSX45YpE1CBhJpqhv31tbWIjMzs8/RcChtw8VoB5Wl2bCzsIC1tTVsndxRVi0t81cDl41Jho8PIIgsQQFJAcOkpwcNv/89XDduRE5Tk2wV4m239afz178CLi6yzxpgqg53tvQq9oL14syJY3By94SL/SVEh4bD08URB/fth7WlldDAxsPN1hy2lpfg7uGDiPAQHD8siLTzFuJKW0VYpE0c1rXWOFV5SpwjRtDcsF0lu5Qm89PuAYpxhgP1wh0sPShuETUaWKRNQtSJtMDAQHEIlLY0IZeeno7Dhw/D19e3z124cAHBwcHSN5iJpkR4Q7ezthCHO61tnVBUodwN3iM0yNTLRs5FaHi5bOg43d3AqVPAY48Bd94pG5bcsEE6ODTljY3wFuLX33GHkJSCVfstW4CHHpIZqaW0NchUEWmhoaF920ANhrjlU087HGzM4BeiILakraDaWprQ0NyCttYWtHdcmV5FRQWLtAngfPV5mdHZsGlYVbRKClXmXPW5IeOoUtRZJNu7M3Qa/pH0D1R3Ke+TOxxYpOkgVBFQj5fcqaJOpAUEBOD8+fPixsnk/Pz8YGCgPEExNzdXFHOMdkDDnYEJ+ejq6kKkp+0Vw520apcEHLldu3aJFTyjo9jYyLZhevBB4NgxgDY2F16cxJ4vQXwNBYmyOOHFq/Q3vwHOnpVCFaCtn8hshImJFKAZtE2ktbep35WD9iO9GpHm5eWF5ORksY5U5/Lz82WuIB95+XnIyckVG9e+8PwCweWhgFbbFxQIZbdI/KuaTlhYGKLIDtskw7jGGK+kvgLTWlMpRLv4vvj7vp0BXst6TQpVZlnhMpmh2vBpeDL9SSl0cKJbopXmtmW0Z0hHhg+LNB2DTGmcEt625Y0zubNCpdymUDkNNNxJb5OKODo6Km32S3PWKB6jHdSUZ8PW0grOjg6wuuSCyvom6ciV0ApefoHRUUhc//a3sl40VUi0HT0qea6EBJK9vT1yS0shfABuv11mIkIdsbHSB82hLSItNzUBLi6u8PfxQmhkfN8wItWLNM2DXlITEhKk0JFTXl4uLrwariNBl5ys/thgjoRkAwn0SURqWyqmRQsihUSQ8FfTk/BpK6aB5nMNhnxOIbGpZFOfmHon+x0pVJnSzlK8kvEKHk55GDEtwxNNvcK/raVbcU/CPThYcVAKHRks0nQMKvzUC6aIg4ODUi/KcBYOkDgjgcciTXvJT4+HsYkRjC5egK2dPfJKBq6IuGzoMNTz9d//Sh4VjhyRCTUV2tvbxedNZV20gUjbOtEQqUrv+FijLSKtOC8DJ/WOwsbGBmExiX0ijUyPpKamwtvb+6pEGjN6aC7WtXHXisOE18Vdh/yOfOnI1ZPSloJ/Xf4X/hT3JzjUO0ihg0PW/+fnzcf10ddjccFiMexIxZE+kTYvb54Ypkl6hH+jhUWajpGWlia+FSri7OysVFGySJsc2Jieg625KXbpX0RabBDO2XpJR66Ey4YO88orwObNkkcFsrt1yy2AgkkdmuJA80uVKm5HR+Bvf5OJtXFEW0Qa0dHWipoa5XmbckpLS69quJO5OoKagrA0bylCmkOkkCup7KqEebX5oL1itMrSotqib27XV/lfieKPeunuT71fDBuKyObIvl49EmUk9AjqQbsn6R7Rbpk2wSJNx2CRNnUoz0+DuZUZbO2sYefgiMr6gecmcdnQUYSyij//mQq2FKAGWuX57rugpQDxCQmor69XXhhAvPEGsGp4k5k1iTaJtMG42oUDzNhCouvelHtFwfWflP9cYSuMEOMky+L8N+W/aOppgkeDB34e/XNRdO0p3yPFHJzarlo8lPqQmM6TaU+itacVjvWO+F3s7/DL6F9iZ9lOKaZ2wCJNx2CRxqiDy4YWMIzVf1dAw5m08nIwhOfa86c/IcHKCmFCZX2FQKNhvGuvpe4iKWD8YJHGaAKa4yX2bpHV/chpSGxNlI70k9CaIOv9IhczTZzrRsS2xMK30Vf8TLg1uGFe9jx4N3pLIVdS310PlzoXNPfIzKp8XfC1rEcufBoeTntYDNMWWKTpGCzSGHVw2ZhgzM2BF1+kyWJSwDCgsnfffcC5c1LAldDcM9/UVKT885/o+vZbKVSB7GzZqtBNm6SA8YVFGkObg0c1R4l/B0IeR3FuFs1Nu9wqeyZ0fGXRSvw59s9YU7QGPb1XzuHKas/Cb+J+I4q038b/Vq3dMbJp9vOYn4uC6xexvxi2bbLs9mw8mPIgbk24dVBxNxGwSNMxWKQx6uCyMcEIIko0cZGbKwUMg6Qk2VAnDXmqgRYE0Fyq1Px89Hh5yeam0ZZPcvT1gRtvnJBhTjks0qY2tLLyjaw3xB4o+kt+VSiMzFpQnDez3hQNwdK8sN/H/V7sOSPjsMMhqTUJv4r9lSjSaCFCWtuVUwRo5ajY0yaci3rbctqHv191t/BP3fVPNBMu0mqriuHsYCuuUHRw9kR1w8Cb2HJDxCKNUQ+XjQnk4EHZ6swHHgAsLKTAYbBxI/Dyy5JHGSqHZLNQsXzi/vtlqzfJNuLcubIeNBJvEwiLtKmNaAdMPglf+EtDj6qoxinoKMDmks0yIRU5DU+kPSHGo+HL/aX71YovIr41XjYcSukITj7caVJjgsPlh9HWKzNDZVdnh1mZs+BUr9wG6ioTLtJMT++HX2w2WltbEeZmDQObgSsdT09PFmkDiDTa4klOnfC2TWGKsEib3Awt0nqRnZoobrSfkVcqeHsQFx6EpOxC6fiVdLbUITwiGu3ykYfeTsRFhaGkht42uxAVHobqJtk8rITYKOSVjtyats5Dpm/IgCxtuUYT/FeskA4MAZU7EnYKQ520gwRtz0YvWTU1ajbTP3lStgvBPfcAM2YM2AM3nrBIm9q09bTh3ex3RfFFf8mvCk3Mp5WTFGdm9kxxaPNQxaE+kxef5H4irui8MfFG0VgsWegv6yyTvt0PpTM9a7qYzns574npnK06KxN7YdOwqGCRFHNyMeEiLTcjBnY29qIAu+TojDRqQBSgORmVlZWioz0MyXL0VEadSKNeSAqX3yfa8okMXCrCIk33qK4ogKO9NS5dugR7B3dU1g1szHYokdbbWoHtO7eJIuDEKX04ubrDytwchw8eQFSWIDSECq+mSpZ/WtoE4dXbAQeLi7h40RSWLjK7fMEeNjh5+jRMbS1hbWEOK6Hc2l1yhJtQdo2NL8LU2hUdCh0/UwISZq9JFsppp4BnnpF9HgoqizfcAEGNSQEQ7XnRcxzQmCmZ1/joI0B4BtoCizSGuNzSf2/JhAXZGns943WlXjHFOOtK1snElSC43s56W7TEL180QH/lZjHUoZjO6qLVfbsAPJ3+tBh2puoMnkt5TtzqaTIw4SKtJDtN3AbDw8EGFnauaGlV3uaILpB6hcjt27dvym99o06kWVhYwMzMrO8+mQuNL/kVYZGme5ic2gf/uBzxRSXczRqnrUdvJ623rRI7d25FZEQ4Dh89hKyKViG0Hft370RSYZ0gAFoQ7OslvizllgjCoaUSescvoLutEUePGYrTfeOCXLF3z16Y2djg3OlTiLmcjqM/rcJnC76Fpa0gJF280NI9hVSafKcAuSV/Kjs0BEm2zYZiwQJgzhzRrAZtBUT7NVJPmq7BIo1R5ceSH2UrJQX3XMZzUqgytKryhYwXcFvibX07EBwsP4j7L98vGpYdLtQD907WO3gi9QlR2NHCAVHsCeKPhkQz2ka+DZO2MeEizeKMPowuGMPFPwzpET44b9+/lFYV2gSc9iucyqgTaWTYsrm5fy4fWdmmDbcVYZGmexRmJ8DGyhbubm6wd3BGZmG5dORKhteTth2Otqb4btsRVFdV4LT+fgQkyibW9rQ3IcjXU9xeShRpnQ04dcIQhXk5OHbyghjH0uAYwhNScdHgLCISk2BvbY7Du/Zg8/ajaO7qgtGxYyhsGHiF16Tjq6/6e9EIKoP/+Iesl2wwSMTdfju6hfqsXvgcHx8vllldhEUao8qJyhOyXrLQafg091MpVBkSZvcl3yfuFKDJuWO0mlNcASoIxN/H/x7FncXSEd1lwkVaaX4WLhicgP6pU7B39kQOb30zKAPNSVOsKHnhwOTgcmwMSotL4WRnDhsHLzS3DGzeYaj5mr1tNbBzllmt93WywcmTeti2+xDc3H1Q09QhROhBmyAYSCx0dcl6dBLCvHHk2EkkZOYhvyAPqXERMDx9As4+IcjOSIG5iSlCEzJQkJ+OC+fPwTMwEl1TpSMtPFzWi6b60vjww4BKL/YVBAcjXfiuq1BuafcAXYZFGqMOEmpbSragsVu9Ae4+u2QR0/DvlH+LYbQ35oWqC2rno8mh/TbPVZ4bNE5EcwS+K/hO7SIGXWTCRZqcbuFNfKjOfhZpLNKmEoaHdmPP9p1w9k9ETowvjGyV7fdQrzI9Q3K7du0a+VQAEmZtg9v16pHyxxUGVAU6FYy3do3zdkQTzgsvAOrsli1aBMwbeO+/8vp6VE6fjsyPPkK7Dg5vqsIijRkNPo0++FXMr0SRdrTiqDiP7V/J/xJ73+5Ovrtv2ydFaNuoO5PuHDTOZERrRNpwYJHGIm0qkZeagEPbNsLJLxbxkQG4nKW8qIbmMNF8NXKUB1TLRk9XO0pLilFQMvAwKVFVVoyGlv4ene72ZpRUXNnwNtdVC8KwGB1ST5s6RFHX04XS4iJU1GrXHngaw98f+N3vAIUV1X1YWQ24g0BRWZm4yKfq+utl89cmASzSJg+08fgPxT9gXu48FHXI6hLaLonMWdBfkQ7hpW7VD8CH88WdMIYLbX7+YeaHSkObNIcstClU/JzUliTaNaN5ZD+L+VmfeQ1FqGdMjJMouNhpfYZwVblUd0m8Zpd65Sk/ugqLNB2DRdrUIczLBf7hiWhpvXJZuyrqyoa/00XoX7CCi60pLB2V84ycnMsh0Dt8GIf1TyO3qg29bbXwdHOCwZlzSM0vR5yvHXbuNxZituHEwUPw9AlAm6DRGmsrUVHTL8Ja68ux44eNSCxoQEqwO/TOWuBy9iQsq23Cs6CNzE8NYIAzMVGcbwZBkMnJyckRTZ800bwzsmt2xx0j25lAi2GRprt09nYiuDFYFGfEnrI9fRP+P8j5QBRqoiii+WXC30xUAtv1kfV/0xB9oyAFXnlHaEjErw4K7RQg7gIgpHNN7DVqDczS6s7r4q4TRdqv436tNg69Gn5XuAZ/874WG4rWqz21ojHbn8f+HLntIzAuraWwSNNy6M3b1ta2b1hLT09PXEChiKZEWkZGBnbv3t13LisrK6FNmVhjmZON/PQkhEXGoKxSqPCG4OSuLbB29IWdwyXYOLgis2Dg4Ux1ZcPF8jSsfKOQn+CPQydMxUotNzVeXBwQHBEvVnqtzTKzHkd3bUVccSMqkoKw/sedYp7LyC9CpLcddulZoqGuANu2boNncARyM5JgdOYUTpw4haQ82ZBDbVku9mzejpjcSnhanYG+4UVczsgdTh2uW9Bw5nPqV6yJUHkikUZiTYDm+IWEhPTbPZs/H/j8c9nnSYC2iLT62mo0NjTgckI8qtWYqqGpASzS+qHNyV/KfEkUM7TKkgQbGYSVi7QPcz5EcUexKHREwSOIrCJUIdx+N37jLhNtR868TGb6hyS5LRm/jP2lKJ7or7peMhJyJODo3LSdU26HGnHVJDzXl99B82//D3jjPaD5ysU2tLrzZ2nXY1q6IAjTfzfsbaG0GRZpWg6Z06DJxTQniBwJrbHsSaO05eciA7mWlpbSUeZqqS9Jw8FtW3DaxByGpw2RVzt4D1mgpzuqmmTPp7SoEFUjtJPmZnEcu/UN4e7thxrJ6KxcpAWFy0QaetrhaH0Odv6ySiA10BmnLH1Qlh6BczaUz9pgaGSDhsZa1Na3IicuCKu/WYzth8/C0eI87Jw94BMQJKYV4eII37hMlNNG372tOHlED5VDdwLqDvRy9OtfU60pBQzA228jZ+VKOPr7i4al+6BeuL//XZbOJEFbRFpUgCs2/rAJ3t6+cHL16pvfTDbnqO4jG5u0inYqY1RthN2lu0XL/LSBudxMBf0la/69wr9NJZuwMG+hOImfoM3KP875VPxLfFOzRhxqpO/dU/SYGEZpbSraJG6Arg4SafLtnOivOpFGuNa74uOsj+He4C6FqBAVJSgQQYLI3QDP0yV0Hz4+cB08Io9KIboNizQth4SU4qTt8RzubGxsFA2pMpqhvakKDmZnsWXbNpy3cURTp7wpuXrUlQ0fJ3OEpRZIPhn11RXIzc1FUUmF2MsV6WGKZd9tRlBYLAqKilFelANnB3uYmJogLr1QtJdmauWG6qoiWFkY45KDE4L8fXHR6BzMLOyRnZ+P3PxC8YU61NUF0ZkliA/zgIWlBZw9A/p3K5gM3HrrwMOcEjSkWfPpp8h76SXUCOVHCU9PWRqTZKiT0BaR1lxfDRcHR6Rn5aKwuH/uJtVvtMAlKytrSvekGVYZyoYtw6bh8/zPBRHbg49yP8I1kdfgw9wP1e4UoI7k1mTck3wP/hj3R3GeWUVXBf6Y8EcxXforn8umSE5HDq6Pu14UafR31L1b9JIzaxZwzTWybdHUrYwuEOq7G24TlMrPgJvuEN5ulefx6iIs0rQcFmmTh/amagT4BaOyphZ52XloaNPcikh1ZaOrqxNd3YOrpLaWRlSUl6OwqAQNjU0g3djZ2oDicik/9fSgQ1rF2VBTjvLqevFzU12l0BgqL0igFZ4yW7ZdKBQqy2GMhOgOO3YA/5aZChgIKoM2Hh7IO3BA/c4DNMy5cKHkmRxoi0gbiqk+J21D8QbZUKYg1B5Lk/WAEXJDsgNy4gTw2OOyvwLUC/dq5qv4R+I/xD04ReOxNG8tSXDCXzIeSys15+TMwQtpL4jp01Cm2PtGcYS/A/WkDRvFeo4W78yeDbz4Is3XEX6Q8HsUe9vIr+OwSNNyWKRNHiqzQ/HlB5/Awt4RJ44aILl84OHLkTIVy8a4kZwM/PKX/TsLqEDzzpKFOGRQWixN1DCQUVuFxQNCQZPt1TmSDdh1ABZpukFdd53Yc0bCiYYnhwXle0XBk1aKdfU7ZD1yEbQN01NitJO1Z/CY3e9wotZA9K8vXi8ThIJ7Nl32snKi5jQet/u9GPeqUazn1q7tvz75XFF9fUFYCkJUcfs0yqNCHtBFWKRNMG1tbX2OxBh1zSuG0VwKFmmTg+r8RISHJyH7cgiWL/kRJc2a62tikTaGPPAA8OOPkkcZmi/q5+enLACovNIKzuhoKUCAGrw//1lQ6kMvGNElWKRNYgRxIG7oTwKI/pbWw6DpokykhU7DvMIFELve534N/N+1wt+vhALRDYMahaHVwoVCmBDnI+EvxflYiNs+SgPOQnuIDz4Afv5z2R62ZGeQph/IRRpttaYOern6y1+A666jSd5SoO6gcZHW2VwDZ4dLSM3VfIMxmRoism119uxZcSN0uTtx4sQVYUePHlXa049Fmm7S0dqEkoJ8hPj7ITIqBsHBkRqdr8UibYzYtQu45x7J009TU5N4z8mA8BWGfKlMPf88sG+fFCBAIk9xC6lJAou0SU5CArBpk+yvxLnqc9hdtgfNaBfCk/pFErlEwS9wVjFOTLxynAF6pMWeLhpWpXllcoS2DeeljdLpe4rpyJ+noSGwZw91acv8qtAUA/l3qDdbx9C4SOvt6UZ8hD++X70IC5eshKt3KNo1tFfMZGqIaEk+iTBFgoODlYQUQSKJe9J0n96eTsRFhiEpMQHnTh+HVwitphqcpvpKeLk5ivuwunkGoGGQbaFYpI0B5eXAL34BREZKAfTy3iOWXZqITgswBmT7duCttySPwH/+09/YTCLGU6S1traiS6EuHAks0saIPKEM0PZoJIDob36+dECBpkbZDh0U56WXZHvcqkJTA26jCf9CHDJhQ4LL1lbmJ/f997KFAvTyQ/6XX1afjjrI+DT1otH3jh+XAnUHzfektTbA6vw5XDS3RlpWDgJ8/FHdopkJ0pOpISLzFo6OkhVnCRJpNLdFEZ6TNjmoLUqCicUlhHg7wMzGEdbmZsivG3yVn/mZQ/CJShefQ7CzFc7a+UhHroRF2hjw5ptKWzzR3DMSzElJst6CQRHiicKMesEpPg236ECP00gZF5HW2wl/D1dEx8aiQlq4MlK0QaTZ19njnfR3YFGr4XmJNAy4erVsAv1ALw4UZ9UqYM6c/jgkgt55R7ZLxnChdFaulKVDw6FCe9QnpMiRn1Yvr1ghiyMXbbT4iIb/5b3OguAW49CwZUnJlfPfKGzDhn7///4n+55qOsMlMxOC0pE8uoXGRVpjZQFsLrkJ97ANDo5u1NmpMSZTQ1RfX88ibQpRnRcHE1NzGBzXQ0xSFowMTqOwfvC5GanxwXBwcBVeBP3FZ5yQoWxOQxEWaRrGRxDEv/mNKKy6BaGVnZ0tlll6uRoW1DNA5jbobd/AAHj6aenA5GI8RFpFYQZOnzJAanomqka51dhEi7Ts9ux+6/3R05DSqjxiclXQkLxczNAqRzmKz4VWJ8vjTJ8uE09yPzkSV8Nh27b+78iH73/6Sdb7RX8JxXMpDvFLq8RFKK48zhtvyMK2bJGls3WrzE8GoJ98UrbDh6JNNMV0pgAaF2kNJak4c8YQqakpMDh5FkUNo5wkqAZdbohIDJFhRTJuSY4qDXXDnSzSJim93Qj1c4atWxCyUi8jMn7oSrG1uQa2ZkYwMjKChb07WtsHfnv0EUQFWVVnRgD1BKhDKKf4618BExPRSzsGBAYGKpXDIaG4990HhIYC770na4AmIeMh0nKSo2B42gh21paISsySQkfGRIs0Mlfxq7hfiZPpr4m5BpltmdIRDXD0aL/gmTlTFka9XTTZf8kSmV8xDvVwUU8VrVgmPw3pCy8hw+LgwSvPRSja/jt8uD8O2TMjli4FbrgBWL5c5leMQ9cjRzEdEpK0D+7NN1MDJgv75htZOtQLN5LyqMNoXKQRCSEe4iR4z8CYPsvPmkCXRRpdu5mZmbjNEzn6bGxMeyL2o40ijdJmJgaz0wcQEJcjLjIJd7fBGVtv6YgMKrzUG0tuz5494iR2ZpgcOSJrpGhStCqrV6PpkUfgK1SM+WTvbbSNwYcfyraRIvtqk8BekzrGQ6S1NtXgjNCeWFmaw8jUCo0tI3/x14bhzsCmQCzMWQivBg1vtUdD6rt3ywQQ9fRSPS8XQOSoF4rqeZpcT0Oe8nqC5mpR/hzJDhhUFqjnjkTSQCuV6XqE8oMbb5T1KFMvneL1yNs4eZycK/fpFCFBJv8O9USrDokqLGaYzGhcpFXnX8bJE4Zi5ZaXXyQZt9QMuizSqCFV3CKGJsGqCiltE2l0jfv37+8TlnJxyWJgdHR3tMLXxU68j25ewWgfomzkZcbBwd5BnAdlYWmNhEzl4U4y/yDvmaVnSYWZGQY0gZ96ymxsZMMpDz/cby4jMRHdf/gDCml4OTtbvMejRk8PuPZa2aRphXI2mRgPkdbb1QJPDzfERkdh245dSC8cuRkTbRBp4wYJtQcflAkZWs0o3zd2vCD7ZP/3f8DPfiYTgTT/7P77ZddD10WLAs6c6Y8zkOkMasPkgoxEKO3dSfM8yU89bArt6WRG4yKtvjAeP23bg7TMTGRk5UNDCztFdFmkUUOrKG50YeEAmRmgvTtpLo7cubkJleVAS6iZQSlLD8O+g6fQ0taGtvaOIVd3xgX7wcsvDFW1Q1dGtB8nz0kbBvT2TavQhHwsQvl/+3ZRtPXu24dIQVCFyodkrhYqp9SgUK/dJGU8RBpNFYgN8YW5hTXScwrR3TPyRmVKiTSChBotDJALNKFNwLvvAo8/3j+BnoYcyQYg7ZAxEIcOyQQW/R0uGzf2iyu5gVn59dBfYv36/ji0YnMgwsP7yypBv4PSmSICjRiD4c5uBLo74KKpBYIiYnm4U0IXRRoNd1KvjyIRERHi/Cf6LXJHRneZoWmvK8Dh/fvg4u6BgJAYdAzR1pzctRkm1m6wE56Bi6cf8kqECmoAdLlsjBs04ZiGV9Qswy/x9ETNXXch5bHH0E1v7JqAGhTqRRvufB8dZDxEWldrLc6dOYPCkhI0tY6uZ3PKiTRVaFhfLopefVWWJ+V+cvJ7Q8OTtL0SoTq8ONz7R3M6aVX066/LhjrVMZw4jIjGRVpjRQ4MjhzEBVt7WFlYonAIMwNEU121kDfKUN80eGPPIm38RZrqwoGwsDAcO3ZM/D1yd1xo9Cgj0TMkV1lZKV6D3C8+2/rRLZ2fVPR0INTHBefOGsLVL3zIXmaPS3Yob+hBd2cHMoXnXlI58D1kkTYMyKQGmSlQgRpv95AQdJA40/QLxyRfiTYuPWnohb+HM6xsL6GofHRDd1NepKlO5icbgHL7ZtdfL/NTLzPtikHDkBcvynrhbrpJFof+0mIDZtzRuEhrqSmG+dmT2H/0KM5b2qG6dXB7JrFh3jCztIGn8CZrbmyCiMsDr95hkaYdIi01VXmDXAMDA7HHzdXVVXQXLlzAkSNH+vzkSMgpzsmbilTlRuOQviGaGhtw5OBB5NZpThCwSBsCmjRN+2lKBjAp3ycIjVJmZuaUz5dXw3iItN6uVpgZGWDvoaMIiR6d0MrPz59aIo0m49MQZZbUnn73Xb9Io95d1Y3IBSGgZF7j0Udl36NeLjKpoVjnC+2GuB2TfL4mnYPONYl7jCcSjYu03q42BHk44vTJE3DxjZJCB8bq3BF4h6cKFWU9QtxtYXTJTzpyJbRHnq6aGZhMIi0uLk7yyVAdEiWxoJgOQSKcMtuUprsVfp7OcHF2hGdgBNo1uKqGRdogUF781a+UNmYuLS0V8yjNu2RGz7j0pPX2IC0hWpyTVlCufsi/tqIYwaERCPLzQWJqv0FXqjvpGVPdlpg4zI3FdR1qZ/7+d5nYogUy9HyoziYbZNR7JrxEiz281LNMcWjIkYzD0kIXuUijPTLVQRYJ5HHIgC71tt1yi8xPf8vKpIiMptC8SOvuRLlQAZYX52PfngMobhy8u7+zoxFh/j5CI+MGz4AwtLQrxydhQ6KEHO1jWU7dsjrIZBZplI7iKjjaMsdXZVk3iYgxr8y1mM62ZlRWVCIrJRH+/gFITs8fcuHASGCRNgg0WXrDBvF+U28K5U3F/XCZ0TMuIk2iu74Knn4Rkk+Z+spimJucx/rv1yIyKV8KpalPDWK9am1tjXhFg6i6Aq2EJFMUM2bIrOYPB9W5ZLTjBdXzb78t2/hf3tFBZYAaf3n7sn17/3dIuKljzZr+ODThX7VHbioPKY8RGhdpPV3tyEpLEfJFPM5fsERDv75QS7SPA44ZXISXozk2b96OLJXl1VTISJiQO3/+vPgGrItMdZFG1xMVFSUOO5CjHlF6lnI/uZKSEqXrmUx0d7Qg3NsRBicviDsI6B87g+IGze3HwSJtAMjcxj//iQYhbzUKDR6VL6pTGM0wHiKtODdTrJe8XJ0RFDnYllxdCArwQ6OaKTZUt+jkcKeicHr2WSlwGNCKYuo1I+OzhOJQ5kCrKXfu7I8zkEijNox2CCATGBGSYCbzGPfcI/vLaBzNi7TWapzVO4zjx/Vx0cIGEVEJ6Byk3a2vLITpeSMYHN+LvYfPCuJ+4Mi6bFV9qos0imNhYSEOe5KjdMkAq9xPjgwgp09So5+0/2CQmy2OHNQTbc2Z27rycOdYQ0M6//gHUoXGx9bPTywXjGYZD5HW09Mtbs11NejswgFaiSwXTrRzxXCg9mLtWtmm4mS8llBM5/33ZWGq6Ov3x1GzwGZQuGd6zNC4SKvNj8MxfUOUlZZg84YfEHQ5F0N0pgl0w8n8FC7aeEh+9ehyQ8TDne5KKzw7hQaUFhQoQhlRJ4ckhklnUxUMj+zHcYMz0Dt+DlVtg5eMjrZGhAX6ivcyKDQG7Z0Dx2eRdiU1QqOTf+edaJIWCzCaZ1x60vKy4O/rI9ZzecUjN2RL6KxIo/qZVmbSxP/hvmTQ8KZcbJGTz8Wj3rV16wY2bkvnop43Otd4G8BlBkTjIq21thS+nl6ICAuGvYsXWjXXWcAiTUBXRRoZwVUcqibBprrgIDQ0dFJP7qXdOM4KAs3d2Qlnzpgiv6pFOqIemwv68AhJEPONn4MFLjopP3dFWKQpUyfcC+c//hH53spbaTGaZVx60jpbYH7uNA4dPorAiNEJrSllgoPqgd//XibQaMgzt38hBaN7aFykEWnRQbhgYoH8stG99QwEizQWabpLL7q7OpFfmIf05HiERyVhKMPpCRHesLFzQURkFNycHRASP/BQMIs0GSVCHvOJjUXDl1+i5623pFBmrBgPkSbaFwz0g8slJ4TGKJv/GS5TSqSp9qRRvS+0N+JqTppLRlb8GZ1B4yKtrjgVB3dshZG1Lc6cPoPcGrYFRbBIm9oirae9AZ6O9rAX7pW9g+OwdhwozM1GfnYO7C0vwPySjxSqHl02T6MJKP9Rfo0V8k8Z5SEy0DmJe2W1hfEQaSU5ybC0sIWPpzsS0kbXK6S1Io3aM01fF80P+/Zb2e4aK1fKwn74oV+00f6ZBNX91PgrtC+M9qFxkdbeWAU7YwNs2b4N5ywvoaFDcxmARRqLNF2mt6MJPi6OuGRjiSMnLqBliKJx9ugBmFw0hZtfFJJCvWDp0v9sCLqfVCbIHThwQCl/TTiWloCXl+QZW+h3Ux7sy1/UY/DVV7LPzJgyHiKN5mbaWZjAyMQcGTmjexHRSpEWFQXccINMONGkfU1DvWdyTE37RdqyZTK7aNTTTH5ayUmmPhitROMirbE8G46XXFFQUIDmNs1uicIijUWabtOLrs5OdLY34/C+g8iuHryXOdrfHWsXL4RDYApyLociKE7ZTlKLULFSASZnbm4umhnQCuhN/rbbgJ/9DAgJkQI1D+0ZS7+dtiFrli8OCAwEfvc7yrwyPzOmjIdII9zszPHTjt0ITxzdPo9aKdJoI3+5cPrXv6TAMcTeXrZTAJVP2gJKfm5y0dFSJEbb0LhI624qwwWDc0Kj7Ao3r2C0DzGkMxJYpLFI02V6Oprh5+IAMzNjOPuEo2MIExx15cXiMwn19YCNowc6Btns08vLS3vKhpCPyTaZuP/fH/4AIcNKBzQHCTTK97S1kxLUK0AGN5lxYTxEWkF2KhyF8+TkjT5/a6VIo7rurrtkLxVUVsaT1lZg5kyZQHvnHZmf0Uo0KtKqC5MRFByPhroyVNZqftk7izQWabpMV0s9Qnw84XDJHv4RcUNusG5hoAcTCyu4+YciOcQLprqyupOGUz76SPaZnvGvf60xoUa9ZmQMmPbbvGLXgIIC4E9/Ut5nkBlTxkOkeTs7wNXJE1FJo98bUitEGm3HRAZpT5+W+WnIkXYBoF5n2mtzItA24cpcgUZFWlGyPy45BiEi0AHB8Zpf9ssijUWaLlOdE42TBiZobmrAzq1bkFRcO+jWUDkpCTh97BCOnjoNByc3XM4aOO9rVdl45BHA0FDyCGhIqJEoo/xBBo8Vy0QfW7cObE2dGRPGQ6TFBPvB1soONpecUFw+OvtdEy7SMjJkvVZyR1MTDhzo9z/1lBSRYZTRqEirL07GicN6OKG3H3qnz8PDJ3TIFWwjgUUaizRdpqetFmZnT+PcOUOcMjCEu3fIkOWjq7MN9XV1aBpifqfWlA3aX/Avf1HazFyEnjVNklbIX8OFhja9vb2H3o2CVq3RnBtm3BgPkaaIYn01EiZcpAkNbZ/tMnphIWOxipuVj9TCPzNl0PictJamRjQ0CK6+DrV1DdDkZhEs0lik6TKdrXXwcnWAi7MT3PxCh7ETx/DRmrJhZAT873+SR4UNG2QrL0dAWVmZuCAiXRB/g9YltEDh5psp80sBzHgw3iJttGjFcGdsrGy+pFCH9nHyJLBxI1WIUgDDKKNxkTaW6LJI8/DwQHl5ueRjkTYVRVpNQRyOHjcUXqKrcPjgIeTVTcIN1mmODe0bqA4bG+D++4H2oX83DW3S3LMQxdWhg31v3jzg448lDzNesEgbA4ZRPpipA4u0MYAECJlEIBEid3v37hUnO8thkTb1RFpvRzMCfd3h5GCPiIT0QeejjRStKBs0hENDnQPtv0rzcO64Y9BeA8rrUVFRYq9zjeL+gQYGwN13y9JQhXrPaChVJV8yY4+2ibTa2hp0dl3Z50o9sjoh0rZtA26/Hdi0iSppKZCZyrBIGwNISJEAaWho6HO2trbiyjQ5LNKmlkjraKyExUVDXDCzQlmt5pe7a0XZEPIh7rlHZodJHSSwbr2VujWkgCtJTU1FREQEumjlmyIvvigTeE8/LQUoYGYmOy8z7miLSCvMToaZqSk8XN3g7R/a9wJE9vPihZcGV1fXK821aBtU98vnqJHjlw5GgEXaGJCRkXGFkKJKguekTV2RVpIWDAe3MJSmJcDWd4CeJhV6ezqREBMu3peYhLRBe960omwsXtxvekMdlI8ff/wKm1AkyCjv07O/wqwGIeQn/PWvQktcCLzwguw8ipBZg59+kjzMeKItIi0/I1ksI811FYiIju8rK+3t7WK5oHpL6+sW6hGmFxESaPQyozA9hpm6sEgbBTRsSYJD7vqsnUuQSKP5NIrwwoGpLdIqc6Jw7NBJWJ8/ix1HDIWG5DI6B1NdAk6WhnDyCUN2djbcbcxg7akw4VgFrSgbZJhTyOeDQiLLwkLyyAQalQXq7aBVnGrZvr3ftAYJNVolR/PbCBJwZAxUoZeaGT+0RaQNBTV0OjHcSfn7xIlBe5uZqQWLtBFC4uL48eNiz5jcnTt3TjoqgxpVFmks0pTo6UROeiqShXuclpqC1IzcIY3ZBnpYw00QafTMvV0d4Bk28L2Z8LIh5Hmxt6usTAoYgFmzgO++Ez9SfqPr7uwcYvu4hx5SNq1B5ea66yBketlquXfflQ4w442uiDSdWjjAMAqwSBshZA6AVmoqckJ487G2thbFCjl9fX3RrpMiLNJ44cDIaYet8RmcPHkSFg4+Uph6/Pz8hJfw0W0+rRF27gSee07yDIJQNkqffhpVzc3IzMxUyjdqoZ6ym26CkHmkAIl164D//lc2PDROG7kzV8IijWHGFhZpI4RWCVHvmSI2NjbikCfNfyCXlJTEPWks0q4aBzMDeIdfFhecBDhbw9xNebNyyk+Uz8gdPXpUycTLuEO7DAzDkGyBgQEcb78dtULeGhbbFYY6FaG5a6++KtsGik0WTBgs0hhmbJlwkdbZ0YKIYD+xJyA4PA6d3QObrNRWkaYqpKiHgEUai7SrJdzfCQ4uPoiNT4CnqwN8I5XzBq0aJiv85M6fP690f8cV4VnilltkW98MAJWJ6Ph4NNEehXfeSZlLOjIEqkOditCm0BO15yEjwiKNYcaWCRdpdsYn4BYUKw4j+tibw9SlXySoos0iTdFkAC8cYJGmCZpryxEeEgxnG3OY2CkPsatCw+sTNtxpYgL861+y1ZtqoF5mMkpbR2KOrpEWGLS0SEcHQT7UOdQ8N2bCYJHGMGPLhIu0qCBXuHkGIiI8DJfsbBB+WaiYFSARQSKFHIkjFmks0qYKVmdPwPqSI7wDw5AQ5AFr91DpyJVM2AsM5Q8acjxzRgroh/IB5UPKR30IeRP//CdlSClgELZvl60GZbQWFmkMM7ZMuEjraqmB0Sk9eAZFo7SoGAXFyvNqqHeARAC5Xbt2KQmdiYBFGou08SIlJgz6h/bjmIEhXF3cEJ6ULR25knEXaZS/X3kF+NvfAHNzKVAGDcNS/s7NzVXaZaMPWmCg8h210Ibpp09LHkYbYZHGMGPLxA93XjgJv4h4+Hi548JJPZw0cZaOXAkPd05+kUZzl5h+muprUCzk+cq6JilEPeNWNoQKA/Pny+agrV9PqxekAzJo8QKtdB506JUm/O/ZI3kGgPLBTTexQU8th0Uaw4wtEy7SQj3sERhPQ5xdOL5tHU6YesoOqIFF2uQWaTRvicxN0HOWOwpTvEZGPeNSNmii/r33yjZRVxFnNO+M8m7LcOaa7d4NvPOO5BkA2sOQhzq1HhZpDDO2TLhIIxQt9nd19osdVVikTf6eNC8vL/EZy93Zs2eHNnbKjE/ZEPIw/v53ydMPmZ3x8fG5Iu8OyK5dMqO2g0FDncMw6cFMLCzSGGZs0QqRNlxYpE1+kaZ4jQSdn0Xa0IxL2Zg7F/jqK8kje4Z0Xsp7inl0SOi5U4/cQNtACeWHhzp1AxZpDDO2sEgbISzSxnfhAKXNIm1oxrxsNDUBN99MGQndPT1i/qV8np+fL0UYAfQdMtlBw6fq4KFOnYFFGsOMLSzSRgiLNBZp40l2WpK4+Xh69uA20EZUNkZzP2no8ZFH0CTkcychL6empkoHRoFQ6eC22yjDSQEq0O4FBgaSh9FmWKQxzNjCIm2EsEgbX5GmGmcq4eVoCjtXH/GeOFqYwClw4II67LJBz4lEkJmZFDA8up57DtmLF6NeEHj16sxqjJQnngCsrCSPApSPb72VMroUwGgz2iLSejppO75ENDa1oUmot/prNRnU0LFIY3QRFmkjhEXa+Io0IyMjREREiJmUXGxsrGiHayrg42QKZ69Q5Oblw9/tEux9I6UjVzLsskF57ve/B/76V8DSUgocAuF5Bt5wA4K9vTHwpm0j5KmnAENDyaOAUE7EoVBGJ9AWkZYY4Y9Lzu7wcbHFIb2zffmU6gpaIU77K1OP9HhB7cHp06fF846EnJwcHDp0iE0RMX2wSBshLNLGV6SdO3dOPGdUVJTobG1txRWgU4HaqlIkCffa2uw8TC/5SKHqofs9rG2hyMbZt98C1Kvw298CFhbSgSuhBs4nPBxFn32GnqFMZoyUH34AZs+WPAqsXj30yk9Ga9AWkVZTUYzCsmq01VfA1y9ECqV9+HtEszA0PK9at4wlK1euxLRp00RHL5rDobKyErfeeqv4nb/85S9K9SUzdWGRNkJYpE3scCcJEdqMfypgeuaU8KxD4OkThHBfD3gGK993es6RkZGiI/tylDeH5P77+3vQIiIGFGqU52hRQKKQ3zruuWfEw6NDQmY4Pv5Y8ihAw6C8y4DOoC0ibSgoL4/ncOeTTz7ZJ9KWL18uhQ4O1b/y75Abz54/RnthkTZCWKRN7MIBGgaYKiLN29YECz+eDYegDBQlh8DeJ1o6IoPyEA3/kqOhlSFFGpUdGuZULENyoSaJMBomomdMQ8wiQn7DjTfSA5P5NQUNdT76KI0LSQEClZWyBQXp6VIAo+3oikgb74UD0dHRePjhh/Hqq68O7+VJYtu2bbj22mvx448/SiHDgwQd2SocCVS/U7s0VaaP6Cos0kYIizQWaeNFVVkpcikv+XrC1Ttw0PlgwxruPHQIePppyaNAVJS4zVPxwoWoFvJRqlDGeuT5Yt484JNPZJ81iZBHcOedZAlXChCgcnXXXZKH0QVYpGkOqm9ff/11XHPNNXjppZfEOnI4eHt74//+7//E3rft27dLoYNDaT/22GPidx555BH1e+wyWgGLtBHCIo1F2nhhfPo4PD184erpjzAfd7gFKPekKTKsskHzyjZskDzKxIWEwPO559B5xx2Ah4cskPId9bwJxzROdras10xx3g3PR9M5WKTJCA8Px9KlS/vqZhI969evx8GDB5XqWFWOHDmCtWvXivGpbhvNcOeKFSv6vnMPTU0YBlSHK55rJCKAGV9YpI0QqpBIcCjCIm1iRRodJ/FcUlIiOvpM90DuJ6cLDYkqntYXsXDuh7DwjENalDcc/ZXvuyJDlg3hWeJvf6ObLAXIJlXTs6QVZXVy6/80DElGa5ctA0xMZL1dikOSmoLSfOghesBSgMDDD/N8NB2DRZqsEb3++utFsfPLX/5SrOcWLlzYJ4BIqMmhMieH5pHK43z22WcoLy/H7373O9H/m9/8RqxHB0IxndzcXDz44IO48cYbr2ibBoLaq2+//Ra//vWvsWrVKqX2i9EuWKQNQZvQeFEjTzeKHDVqquKKRdrEijT6/ZaWluI5yNEK0L179/b5yR0/fnzQSk9bKS/KR3lFNapragYd7hyybHh7A//8J9XuUoCs8FOeU9w7V0QIx8yZQmkXivvGjVLgGPD441QwZJ+pZ4167YS8y+gOU1GkUYNJ881eeeUVUVjRogS52CJHLz0ffPBBn18+v2z//v249957+4Yk9+zZ0xdnxowZYvklcUb+6667TkyH6vK33npLeJ95SKx7CarbKJ0dO3aIfqqnX3zxReEd7G9ISEgQw4YD9eKRKFQUkYz2wSJtCKjBJ6FA5yZnZmZ2he0bOs4ibfxEmrp7qzj5la6FzqcIme9QTXsyMWTZWLcOQsshGvmk50f3UPHZq4UEFG0HNVZMn94vAslMwf/+J/vM6AyTUaRRHTzYdmcvvPBCn7has2aNGGZhYSGKNrm5DXqxv/POO8WFA9TrpTqUSWX12LFjfX4SaXRO6tkiPy0eIAFIgkweh+apqUuHxJrcT2KOoLJNixcU2w5F6F4opjMScceMLyzShoAa+3aFyc0kBlQFAIu08RNpVNnu2rVLDJe73bt3K018pc+q95YMWiYlJUm+yceQZeOZZ1C/bRsahOdEeYye7YRDPQFz5sg+0+btS5fKPjM6w2QTaWfPnsXPfvYz/Pa3v1WqCxX56KOP+sQN1T3qMDExEXupyO4ZNbBkA+33v/+9+B3qLaP639DQsC8dSlMxDg2fUhwDA4O+OB9++KEY9ve//130ky01Ksf29vb41a9+hZ///OeifTaqL99++20xDi1EuKKnXICmhFDPG8X561//qlQ3M9oFizQFKDPTShkSGHJ39OhRNCn0JvDCgYnvSaNnRGFyR/eR3jrlDEek0ffoGSk+a7qviufSJQYtG0KeTRIaCzuh4ajTpuX2+/YBr70mG4KlCc9CY8PoFpNNpD333HN9omgZzcsUoDqHxJi8bn766afVxqHhS3kde//99/fFoYn91G7I/eSo14x2FpD7p0+fLrYbinEKCgrEoVG5X95LRnPQaIiSzilnjvCyc9ddd4nTc1TTUa2v5WRnZ4vp6OI0kKkEizQFqBDTcCZlfrk7f/680lAaizTtm5NG93Y4Io2eixx6jjQ0ofisaXeDYVnt10IGKhtVwjMsEMRQ04MPSiFaBD3rf/+bxpdk+3UqlA9GN5hsIm3u3Ll94oZEFL2433LLLaL/hhtuEHu7aGjzF7/4hegnQ9I1NTV9cf70pz+J98Pc3FyMQ375sOP7778vxqE5ZuSnebLyc7333ntiGyKfy0aijeLQMOTNN98smtggW4jqoF47Ohf1AFJPGrUz8gUI1CNHoo7RXVikKUA9LVToFCEBoDiUxiJNN0Ua3Vt6bnJBRs9HdXspMgY52FyUiaCsKE+83qKywSfUqysbNUIecxbEaSFN0P/uOylUi6D8SHt4njol22mA0Tkmm0ijeWVy4bRlyxaxzpb7yZHhaILKpLw+S09PV4ojN52hGEcOXYO8zqVpG/Lv0HnlqF4n1W2KL5iqkKkPeTrPP/+8uOBA7ic3nN9NUH0/f/58vPbaa2I7w2gHU16kkQCQOypc1OOiCDX2LNL60WWRRj1l8qFNetOl+6aIh4eHOMSgLQR72cPS3lm8LzamxvCJHHhOHZUNmqxMUBmh39jY1IReunc0lKiSH7UCoSyJZjiol28A+22MdjMZRBodk0M9V7SlE83pol4zQk9PDw888IA4nDkQFIeGOGmi/3BRFGm0KGC0UE/ezJkz8bjwMka9dsThw4fF6zlw4IDoHw6bN2/uu55nn31WCmUmmikt0miVJokAuaMlyYoihWCRNnmGO+kNUw5VwKo9adom0hzMTsEnLFl8tsHu9jB3C5aOXAn9FppjQsMzVFH35TW6nzSUKDxLrUR48xdaBe0UkcyQ6LJIozqb7JnRpHua06W4QGw8OHPmTJ8oovNPNIp222jYl9EOtEKkFeZmiAIht3DwPc5oOErdnCH6Lh0jYUSOPlODpQg1Wp6enkpxTtEwiwIkLshUgyIkLmgyphwSVzRxXRFVQURDZiQ4FKFzkzCR09raKqatCA210jUoopo2zS8goaQIiQsSVHKooSZBqwjtxah6T1TTpuN9ezYKkDgiAaQIZRZVIamaDj0jEpyK0P2mNz45VCGqil0SFzR0oIhq2iSiVHs76d4qCml6Xqr3lp4rCTw5JLZVhTQJS+0a7myDrbGhWHlaOCmLXlXoOZ04ceLKBpPepNVtBaUt0DDPddeRspYCGF2CyqcuiDR6uVcVadRuyEUJOdV6dSCoHqO5X7TPpuLL+Wigsr1x40al+msioXlymzZtUmqrmIllwkWav5s1rB3dxUbUzswE7qHK9loos5AoIEfLkeVDOorQsmkrKytRrJCjoSzqdpZ/jxw1YCTK5HGoESf7MopxqNfmwoULSmHUu0aFV+6nhl1fX18pDq2QoW5yuZ8qLromxTjUHU49YHI/iThKWzEOLVKg5dSKYZQ29S7J/dRDpJo22duhHjC5nwQSrUpVjEOT5KlXTO6n+XeUNv2Vh9Fxiif3k2CjybNyPzljY2PxXiuGUTrUuyb3k2Cgt0TFOFT4qQdM7qd7Sl3yinEuXrwo9m4qhlHaNAwt91OvIS1dV4xD95aei9xPaaveW3qu9HzlfsoDVEEqxqH8penh9KshwMMOrj7BSE1NhcclG3iGKfcyKpYNmlSs9tppYr6QP7QWGua8917Jw+ga2iLSGmsqhJfcKFGI5Rf1v+xTDz/14NMLsGovfUtLi2gElgTao48+OmyhNHv27D5hN5AJDobRFBMu0pwtz8DFJ1IcivJ0sISVp/LbDA1LkeggR6JBcehPDvWu0N5pdJwcfSbRIv8eOfJT460YR/G4PI7q9wIDA5X8dFw1TF2codJRFzbc809k2lcTR5vSVpcO5Ql1+WuicLc1gqtvFIqKSxDkbj9o2aAXB8Xh9D7IrIU2vxWTEU2hPDK6ibaItIbKIlw0MUVGVg7KK/t77Ml8Ek32p5c7dQZbqdedRkYUzSwNBa3OlIs06gVjmLFkwkVab08b4iLCxCGs2OQM9PRPkWKYKU19TRnioyJhbXYeppeUh9hVoV5KXTUfwuguujLcSdMbhrvKcSionJHxWbKRRr1xDDOW6NTCAYaZSlgYGSI8PBqe3v4I8XaHf/jAjQzNQaQFIwwznlC+k6+C1GZo4QBNC2AYXYOG66eESKOJ9TRvirq+Ne1ozpS6cE04XUyb7rMupk2VuOJq14nGycQACz76EFZeiciK8YGVx8DDgrRSlubZjVUelzu692N9Dkp/PM4xlmVL7sbrHBP13GmuLy2m0nZoOg1NC6B5nKNx1GNGRs3lfvqs6B+to3aJFnqpO3a1TvWaNeX4mpXdWF8ztUs0FWe46KxIo9WF1tbW4gRSTTtapEDz3dQdu1pHadMDUnfsahzNy6O06a+641fjaFN6Wiig7tjVOkqbGgZ1x67WUbrqFqZMFL3dXci4HI/cglLhbaoEHYNMl6MhJ1osQYs21P02TTlayEFiUN0xTTla5EFO3TFNOfoNtChG3TFNOipjNJVD3TFNOSprtChG3TFNOVqIRIuWVMN1ZT9cmnNGUwLoWYzG0YKpq/n+QI5M59AuN+qOXa2ja6YFVeqOXY2j1fRjec20wE7dsatxdM20oFDdsat1Y3XN1EtN95meIQ15DhedFWlUwMbKvALNyxgrdDFtWmVIb61jAc0HoQw8FpAJDkXDlroGvYiMda8GVXYjmWQ9GmjukKbmDw0EvaWq2skbC8ay/MqhBTAjqcRHA9WfahemTBHoHivaa9QUlA9H0ksyEuiax2IhFPUa0cv9WEALvnpoL18NQyt36aViLKBrHosRGJq+Mpr7rLMijdSoqg0uTUG9O1drL2cgKO2xKGiUqSjtschc6ozZagp1xmw1BfWuaJMx25FCZmXGuieQVsmN9Rwkspcnt5w+VpDgULUBOBZQGVM09DwWqLMLqWl0vWxcLVSnjYWxWxrOUjSyrUnomsci79FL2ljtB0r1+1iI4bG+5rFo/0kMj+aadVakUWEYq8qSbuZYzWUa67THArrPdL/HgrFMmwryWFQQ4wVd/1i9LMihN/+xNlNChp7JjSV0n8a6R5AYy/IrZyzrNjm6XjYYZqqgsyKNYRiGYRhmMsMijWEYhpkS9HZ3oqxcNhevorgQ6Vm50ES/aFd7K1KSU1DTQKMCvUhPTUFtoyZ6j3tRkJ2F3ELZtIeKogLhmvM0cs1ADzIz04VrltmGS0tJRl1T/5aJV0NlWRFyCmTzKsuL8pGena+Ra66vrkBiQjzyimR7O6fSNTdf/TX3dLUjNTkJcYkysy7lhfnIyNHMnPfOtmZxy7KWdtmIBV1zfcvwh9pZpDEMwzBTghh/Z+w9cV78bHTiGBx8QgWpcvVkxIVi7+HjqKhvQWFmEqwtLOHiFXDVwqSrtR5H9u9FeEIqKUycE67Z2T9cI9ccH+aPg4f1cDmrCMU5KbAyt4SbT5B0dPQ0VBTipP4x2Ln4oLunC2ePH4FrYKRGrrm1uREW588gIjkfxVnJsBLus7vv1S9qo5X38aE+OHXOgnw4o3cI7sHRGhGWqfFh2LpjGy7nFqMkOxWWwn32GME166RIo7chXycX5JZpdg5Wd1s9HM2MoH/mPHIrNLuqrqejGT7OdjCzcUJV3VjMweqGg50tSho0O5elrbYUlhdM4RkUAU3PjmptqoevhxNsnLzRJL1laIYeRAR6w9L0PAzNHKQw7aa+PA8uzgHo6WmHh70ZLB29UVFRBsdLDjihdxTRSVkI8nCAhYMXWjpGV93VFGXC1TUYPd2tcLE2hq2LPyrKS3DJwRH6Rw+LO4R42dvA3dMfTaM8R1dHI1ztXNHU3YvEUE8YnjdDZXUNEiP8cO6iCUqrqpASHQDDC5aoFHsdRkMPwjw9kVZYJ/ymVBgaGAgNTQnKC9JhdO4M4jILUCo0lGZWlxCdMvpJ3HlJMfANTERHax2sLhrCPSAG1ZUVsLhwBl4h8WioF8KNjeAeFCuUvtHRWl8K50te6OntQqCrDYwtHcUNv/1drGBq44KGhib4OtjC1d0DVY0jn+hOjbyD6TnoG15EcXkFogPccF44R31jA0I8HWBs44YG4bO/iy3M7N3RrNFyqF10NNVCb/9O7NI7JeSgHrHnxN3ZCVmFV7/DQllRPqJDAxEUEY+My7EI8A+Gg6PbVQuTjtYGJF1OhLOjC6oaWpAmXXN28dUbunaxsYK9gwvCoy8jLT5KvGYnF4+rFiYFKXEwMbOCl5c3ahpbhPt8GS6Ojsgpufo2tbu9QRBm1uLn+FB/BAaEiNesCfzcHJCSV0mNNZKTEuHq5Ij88qvfgi9KaIsMThsiMjEDaXERCAoQ7rOzu3R0aHRSpJVkxeKLuQsRlqHZJeTtjZVIvJyGYCdzHDLSbOPe2VKLhJhYnDl5GB5RaVKo5ihNCcabM2Yhu1azk4GTgxyx5sc9SMzUvLkTXzsTHD1hCAtrR9S2aFYCdgtvRraGR2HpESWFaDG9nXA10ceKDSeECj4YBqZuSA53xzmHQHQ0V+HA3sPw9XaDvWsAvByshPwzilXN3e2wMzyANdvOIjXWF+esfREf4AgT90i0C0Jh9+4jSLkcje+/34iw+BTpSyMnOdIDn81bg6y8TBw+fBrFuWnQP6EPg3PncPbieZiYX4CllSNiQgNgZDO6yrWuLAtLP/8KvrEZMDl1DGk5hTAxOg19A0OcPWsIcycHWBudwoGTxiipaZS+NTK62hqgt+0HHDjrhghvazgFJCDcywYrVn2HkPgs+DmbYsuOPQiPSYK50Rkkl4ymMu9BoNN5fLViN7IzYqF3xhr56bFY9923OG/rh4y4IBw/dQrbt26Dd1jMqBrP9oYKJCSmIszDHut/3CjkIX9Eh/jj0KEDuOQWgIgAH/Gzs1ew8Jts4BI6ea34U29JSX4WPH19UNdQj/iYcPgJDWaDBobLaiqK4OPtgeSMbFRXFMPJ3g7xaVe/+pCGysJD/BAWKbwg1NYK1xwG/8AQNIxguGwgqsuLxFW+SWlZwjUXwVF4yU9Mv3qTRR2tTQgLDkBwWCRqhGuOo2sOCkVjy9V3IDRVlyIyNgkd7a0oKcwROyYua6htigwNQ2NbF+pqKhEbFYKA4DA0tV79NRdkJuPSpUtITMtBVXkhLtnaIClr+CurdbMnTXC+9vYISS2SBWiSjmocOnoIiTmyMW/N0gVzw2NwFN7INUlLVQGOHzmEn3ZsQ6yGr7uyKAex8UmwvGiEpPz+jY41geG+nbDzCYe9hQlSC+ukUM3Q3VKOwwePoUUT/dXjQWsNLpo6oKwkB8YXjWF4ZDcMbQOQl+APG88oZIZ7wi0iG5lhXjAX/CNHuBEN5bho5ozSwgxcNDbBqQM7YOwSgfQId1i5RwgvEjWIiY6Hk7UJAuOypO+NHDvhLTq7rAyXzM7D2tQImzduEd+sz18wwbmTp2AqiM+28lzonbWRvjEyaHVlrI8H/OKzEe3nCFuh0tu+8UecNjTGBaNzMLa4hPS0FCQLotPIyASNo9H/wjnq81Jg7hAgCKc4mJpbQm/PNhw8clJ4C3bC8b1bsGjJDyhp6IaXxQUEpZVKXxwhvS0wNbZFaVkhzIwvwOTMcfy0dQ9s7R1w/sQh7DlqiMuJSfBxtoZrQKz0pRHSXiUI2DNwtrWCnVcsmoszsWrZKkHsZ6MuLwkrlq1GwOUi5Ef5wcRFedP/ycpYr9BlxpaxfH7aljV0dk6aE1kFTtLsBtTtdUXYsGYpbLzC0NKm2R6p1tpiuHt6IcLPVaj4NWsXrKWmBG4ubli9fCE8YzVrXyk3PR4x8QmwM7mIxDzNirRgNwf4hcfAhgRggWZFWnakB/TP2Uk+HaCxHPrHjdHU0YpAD2ecOnYC8ZlFsD2nj+i8RtRmR+O8sQXMjS8iLHV0+b67phD6J83Q0t4MP1cHnDh2Esm5pTA3OIrEohbUCI13eHQMvOwt4B8zepF24aQhsmubkRwVDOOz52B28SJOnTmP8CA/nBJEmrmlNextbGDnPXpBEOxgC5eIdFQJ12xjbgITEyuc1NNHSGg4DI6fgX9EBFJTEnD+3ChFmkBVeixOGTujpbkernbWOHH8HGJTs+Biaw3Ds2awtjSHnb0TjM4ZIb92lBtzdzfgpP451LS1CXWDB84cPwXPoFiE+7rD4MQZOLp5IyomGiEejnD2HfnLXVttIdZ/uwSX/KNQX5oOo/MmsBdecM0tTGFlZQs7WzvZZ2s7WJgaI/jy2NieYhhmdOisSCstKEBVg2ZtL7XXl8PFyRnBgQHIKbr6eQqK0Dy6xKhAeAeGoatnbKR6SVEemjs1MT2zn7aWOvh6OSM5W7OCmOjt6USIvxfi0jRv/LG2rBh5Jdq/UXQfXW3IySlEZ2c7ogL9EBKVCMomuRmZaGiXPdP4cH8ERY1+255eQQDm5Bajs6MN4X4+CI9NEefMZKdnoKWb5pO1IjTAA5GJqVc1L6UgJx+t3V3ITIyGl3cQOnp6UJKVAAdXd7R396I05zJcvQJxNVm1urQYlQ0twnPOg7ubO0rr2tDZWAknRwcUVDaiobIAbm6uKL+K+Z/tjXXIK6pAe1sj/GlYKKsILS2N8BPOl5QtW23n7+mKy1lXsTtAb6fw3AvQ1dWB+LAgBIbGoa29FXEhAQiOSEBHRzviI/0RGBEr5IeRP5XWujI4C3VaUKA/iirrkZsaC69AmaX21NhQ+IbIeucuRwYiICLxqucjMQyjWXRWpDEMwzAMw0xmWKQxDMMwDMNoISzSGIZhGGYK0NU5ttuNMZqHRRrDMAzDTHKy0uJhb2eP2MtpaGttQn1TC9qaGlBWQfOve0RzGXkZSSgsqkRifASKqmRmZaqrq9HT04Py0lJ09/aiqrwU+TmZ8HB2QHBQJFraeQ/YsYRFGsMwDMNMctKSouDg7CYIqyCYXjgHIyMjnDl9FvYOzvD29cUJvSOi+Z+8vDL4ejmirKkTaTHB0Dt+ChfOnYXJOSOcNTgLNxcX7Ny2GccOH8WpY3pw97l6i//MwLBIYxiGYZhJTkp8JHy8vGF89gyO6p+EtbU1DE4awsXFFacNzmD/3j04dlQPpaW18POwQ1hCCvxc7XDmnCmszIwRHR6G04cOw9cvCEcOHRCEmxHCgoMQ4BMgnYEZC1ikMQzDMMwkp6OtGUkJiahvbkNzQw0KigrhaG2OhPQCNDc1IDs7G2VlZejq7kVDTQWSk1NQ19CAgrw8VNfUCnGaUFGYhVPHDsHFOwTFxYVobGwSwsdim0NGDos0LaCnqwMNjbLta3q6u9BzFXbUurs60d2tWVtpDKOtKJYVmjfDMMzY0tzMomw8YZE2wZBF8KNHD8DD1RH2zj6oLC9Fc1s3ujraERXiDx9PNwQFxUB4uREJcLVDalEt/G3PwjksDVlxQQiNz0Fneyu6hDgNlSVoaO4SWqxOtLZ1oio/Ee7uQejs6kF8iA/SCjS7awDDTCRBDhbwjkpHQpA7AhPy0N3Rhg6psLS1tvQZZ+1obxcnPTMMw+gSLNImmIaSFGzevh1xMSHQN7yAmIhwBHv7wOD4CWz78XscOnAQP33/IwzOm6GhA7gc5AwbJ09YnzsGI1tXuFyyhbuXP8wvGMLWyR3+3t5IjE2Cg9VF7N21G0eOHsT2dZthdMEIa5cthYP/5N1AmZl6NFflY+v3K7D76AUUF+bD9LwhTK0dkJCSAXvTU7hg7YSoAC/on7JEQ3u39C2GYRjdgEXaBNNQkoZte3YjJTkR+w4dxIWLJrC6cB4+/uGIDvKGo7UVAoMi4Gx+DhllXehpLsOxgzvhHhABF5uzMLBwhMmpwzh0xgLGZ09CX+8EDA/qwTU8A5WZUfh+3fcIDIlDuLcVdmzdj6LyNunMDDM5sDm5GxbCy0eM6wVsO2IEE8OTMDazwSUzI+EFaAeszEwRFDH6vUgZhmEmChZpE0xjaTq27d6Jy/ExuGh6EdZW1rhkYY6QsDj4OVtC78hRhEcmwMvWFJnFsr1K92/7HqHpVQi0O4HdhvbISQzD4WOn4ejqCSdbM7g7eMDBwQHGp0/gh81bEBaRgNggF2zbsAUBURliGgwzWQh2soJHTB5KUsJx6Mhx2Du6w8HiAo7rH8eOHdthYmKMyFjeOJxhGN2DRdpE09uF7PQkxMfFob6lE51tLWhoqEdrWwea6quRk5ePtvYONDc2oKNLNjG6vqZG3Ki6o6UJdQ0tYliOkEZ6diGamhrRWFsBU0M9bNm8A4FRKWhtbRPn51SWlaKkXLMbxzPMRNMilI2Glnbxc0F2KpLT89DZ2Yr01FQUFpeIxjjb2OAmwzA6CIu0yYgg/HIy05FfXC4FMAzDMAyja7BIYxiGYRiG0UJYpDEMwzAMw2ghLNIYhmEYhmG0EBZpDMMwDMMwWgiLNIZhGIZhGC2ERRrDMAzDMIwWwiKNYRiGYRhGC2GRxjAMwzAMo4WwSGMYhmEYhtFCWKQxDMMwDMNoISzSGIZhGIZhtBAWaQzDMAzDMFrIJBRpWTj69DRMm7YIblLIoGQdxdPTKL6ye/polhRhlLgtEtNZNKyLUEC6HsXzZx19WkjraYhBI0mX0hrxBTAaRXpecje8x+GGRRRfXeTR5qshkZebkV7rCFGTvzWC6n1RzPsjOacUV/E+kNP49Y4VY5Y/dBNZ3Sl/jlIdOlxGVXaHQLVOVvVripHkA01cg0bK3yD13gTjtojywDA1hYaZZCJNesiiG5lIG1AUjTcaux7tzfBTBpVnOfznON7PThJoTx8VPsmQVUpjUAaGXWFfDSr3byTn1Lb6gBk90rOU5YPRvbzL8sEIvzsgquV6DMv5sEXaWFzDaMvfGN6Pq4RFmkaQHnCfG71IU83gym9j6irw/mN9+Uvdm4VCvAEzrJrrUWokhrg2WbhKr4i88VW6BuVGpz+dp/G0UoUk3denhXCF7w14T6Tre3rRov5zCed3U4g/4G+f7Gii4lRMQ55XFO610r0d5HkrIaY5mAi5+jzQd0x+zUJaV3zvClTFo7yMy/OmwvG++6Im74/knPK4isdVn9sg93Wk5Wh4acmcYnYY8Nhwr1X+OwfKO5MO1bw0BOrygSJK91U5nvpyoZovF2GRaj6VfVn981KXf44OUs6GlQ/UlBUxshzVezbW5U9KXzGjKzLgvaFDA5U7gYG+J7+uAcpAf5rCs2KRpgmEByxmJnkmGeYNlT8ohYejpJrF4/0P9spj/d9V6n1QKiQqmU+1ACmi5npkmUVNuoOdX/WcKn6lNJXSkeL13T9Vv8Bg90S6PnnB7svo0nmV4k4xlO75oKg+OwXUPH/ZvVbJ92rzhvr7PvQz0UweGPKa1aAun6rNt0plSuX+jeScimlKyH6bmnP2HZPSUjo23HI0nLSGcw3SsUHug9p7OcznoNtI90HKj8ND/rz673M/yvdV6Z6L91W6x+Ihxfuq8j1V/2D5QR5X8RkNVs6Gmw9Ur0GF8S1/g1zLYPdG6ZjKfRrG99Re12BpjjM8J03+oFSc/KH2IS8QolPNtGrOpZhplTLwEAxwPX3nVExrsPPLM5Z0UuWCKQb0ZULVY4NXLAqouydSWN/9U/ntV1zHVEF+r4aVCYa+5+IhhWcoO0TPQfbcrrjPKs9BEfWNgczJ4l9lHlC8zkGuWS1SfPHUlK7UA9HnVzmn2usdyTmluP2/Seb6kxr4vo60HA36jPquQ811DnZskOuRf29Uz2ESMOLfqJQXFL6nlNcGQIojc/JnoJoHlP2Dl1k1ZVA6Ln+GSs90uPlAXbqKSHHFw5TmmJa/ga9lsHujekwx/UHv6SDXNVia4w2LNJUHJSI9SDFMOi5PT/awrnzo/U467xWZSJ6Bh0DN9ShlGMVMRgx0fuH/QSsAheOqx2R+9emIDHZPFO8doXK9V17HFEB+v4b9Jj9wZaV0P1XyypWVDPmVnVI+l1BbASk9t9Hlgf7oCt8f5JrVIyvPFF/8TUIa9LfPL7+ng13vSM6pFFdKRyHuYPdVdmz45WiwtESk39TvFK55oGMK90H1epSuYcTPYRJwRb4cHv3PSXYv5X616QxWLhTvv4iyf/D8cGX+ufL3KMQZbj5Ql64S41n+Br6Wwe6N6u+T+WXpD/a9wa5rsDTHGxZpKg9KRn9mUX1Yg1Vm8gwh5jHFTDuSykHN9ShdwyBpKZ1f4Tf0H1MoqArnGfw3XllwBo0vXV/f9atc7xXXMemR7t+wBRoxcGWldD9HUMkMiro8pRR2lXlA8ToHueaBEOOovsHL5/TIr2mw6x3JOVXiytOVpzXYfR30nqhek8BInpEsrsozklA6pnAfrkj/Kp+DzqOUR0aI4ncHSWdkeUDZP3h+uDL/yK+jL68qPtPh5gN16aowfuVv4GsZ7N4Mds8HvaeDXNdgaY43U0OkDVKoVB+UiELmlz0slcwnf3gK8UQUzzOCTKuEmmNKGUbNOdSef4Bzyv1KaSqdU/4b5ffvyoIz6nsioJr5JzfyvKjm96rcF2WuvOd9KH5PJa8oVSQqxwa/79J19glJ+XUPkJcEhpMH5OkNnNdUrnkg5OmppNF/fgGl+6lyvSM5p0pcIUD5GQ52X5WOye/JwOVo0LSk39N3HYq/bxjHxM9S+vJzXvVz0DVU7pPSb1S8T2pQzt8q9071WSrcS+XvqZSLK/LAwOnIvIOck5B+g9pyNtx8oC5dVeTnkX9Hnp48fULpfg7+uwbOa4Ncy2D3RumYlIY8/WF/T+W6BktznGGRJj0MWSZUcH2R+xsscosWqaTVl4FlTv7Arzin6nnUXoyASsYhBix8xEDnF5BlOnLKGU8WJi+kMmTnkMVVXsmiruAMck+k6xnoPihXEJMclWcjd4r3Sem29iGvFJSdeE8Vv6eSV66o/FTOr/5ccpSfqej6vjDKPKBu1dRQ16wW1UpSTaWpcj+V8v5Izqmm/MnT7vv9g9zXkZUjgcGekcoxtdekekwK70tnoDI/quege/Q/D5Xfp3qf1NCfh2RO6f4r3VfB9d/wQdsLpXypxi+/Lrnrvz41+UeKO/rVnTKuuIYrGK/yJ09X2an+JrlTvBUDlzuBgb43xHUNmuY4MglFGnO1iJl1RMNzDKOAvPFQbAmmIFyOmDGFy5laJlu5Y5HGqLxlkZsiPV3M2DBVGw8uR8x4wiJNxiQvdyzSGIZhGIZhtBAWaQzDMAzDMFoIizSGYRiGYRgthEUawzAMwzCMFsIijWEYhmEYRgthkcYwDMMwDKOFsEhjGIZhGIbRQlikMQzDMAzDaCEs0hiGYRiGYbQQFmkMwzAMwzBaCIs0hmEYhmEYLYRFGsMwDMMwjBbCIo1hGIZhGEYLYZHGMAzDMAyjhbBIYxiGYRiG0UJYpDEMwzAMw2ghLNIYhmEYhmG0EBZpDMMwDMMwWgiLNIZhGIZhGC2ERRrDMAzDMIwWwiKNYRiGYRhGC2GRxjAMwzAMo4WwSGMYhmEYhtFCWKQxDMMwDMNoISzSGIZhGIZhtBAWaQzDMAzDMFoIizSGYRiGYRgthEUawzAMwzCMFsIijWEYhmEYRgthkcYwDMMwDKOFsEhjGIZhGIbRQlikMQzDMAzDaCEs0hiGYRiGYbQQFmkMwzAMwzBaCIs0hmEYhmEYLYRFGsMwDMMwjBbCIo1hGIZhGEYLYZHGMAzDMAyjhbBIYxiGYRiG0UJYpDEMwzAMw2ghLNIYhmEYhmG0EBZpDMMwDMMwWgiLNIZhGIZhGC2ERRrDMAzDMIwWwiKNYRiGYRhGC2GRxjAMwzAMo4WwSGMYhmEYhtFCWKQxDMMwDMNoISzSGIZhGIZhtBAWaQzDMAzDMFoIizSGYRiGYRgthEUawzAMwzCMFsIijWEYhmEYRgthkcYwDMMwDKOFsEhjGIZhGIbRQlikMQzDMAzDaCEs0hiGYRiGYbQQFmkMwzAMwzBaCIs0hmEYhmEYLYRFGsMwDMMwjBbCIo1hGIZhGEYLYZHGMAzDMAyjhbBIYxiGYRiG0UJYpDEMwzAMw2ghLNKYYVNbkoEDOzfjhx9+gIGxHdq6pQMaok5If/v27YjNLJVCZHQ0lGGPEO4TmS6FjA1t9aVISs0UPwc4XMTOY2fR3it61ZIY4ILtOw+iprVHChkZSRE+2LDuB+F+roOzX5QUqjmiPKywYuUPqGge3fXJuRzohBUrvkVhbYcUMjiFqZHic8wpb5RC+ulqKMW6FStg6xsjhTAMwzADwSKNGRbl6aG455br8Zs/3Ihbb70V06ZNw39f/gzNGhRq2SE2YrpH7cOlEBmN+ZFi+LI9VlLIWNCO1/57K77ZZSz61s78L6b95i4MJm8M1s4Vr6ugVQoYAd4Wh3HdNdNw0y234ta//ElMZ/nuC9JRzZAY6IKt2/aiquXqRFp6pA+2bt2BkrrhiTR/sz3i73GKLJBCFGipxN6tW+EedlkKYCaagpxUBAcGICg8FoO8k4ya8sJM+AcEIjIyEoHC3/L6FumIjILcLFTWNUu+wamtKEZ+cYXkGyW97cjMzJY8/RTnZSG/tFryqae9pQ7ZecWSTz0dQpzM7Dzxc2lhHiqq61CUl4OGdgrpRFhIKBrbusTjDDMULNKYYWG9b7nQ8P4Mfum1ov+yvxO2bNuP2jZZtR7tdQmLFy3CTwdPoVFqyz0tzuLYKRNYGh3H4m+WwjUkQQzv7WyGm+U5If7XWLbiO/jFynrI8iKdxMbdwCVa9MtpKozFdUL4D0cdpBBlPK2NsEg496GzVkIVKMPOSA9GFg4wO3MEy1etQUB8lnQECHaxwDeLF8HS0QOn9++Df0QSzI6tE899z6MvwNY3EvuXTsd1dz4OU+PTWLp8FdxCrhQVF7cswjW/vgWmFhZYtPgbXHDwE8NP7f4RZ2y8xc+ddUXYtGG9cP5c0S9n3pO34fpbHxWkoQwbQ33onbcVPnXj4tH9uGjpiJMHtgrnXou47DJZJIEwNxvxPu84ehbNCvV8hLcs/Lut+1FQLevBSo3wxdFjp1DTKntGycHu4u/esPsoaltkX+5ua8IF/f3C/fsa63/ag5zSGjFckez4EBw9qod6QZAXJgVi196j8PVwwJLFS3DS+BK6VFr2ENuj4r0MyqgTzumA/cf0YXhkL75ZsREFJWUw0j8K/xjZM89PDMV3y78Rzv8NTOy90a7h3llmKHrx5YwncOd99+O+u+7Ah99sQ3NrM1ISYuEfGI7qmhoE+foiKUMmuNsbyuDn64eklFTUUw9yVyM83N1RVENvKj3ISEtFSJA/MgsqxfiEy/ldeOj++/Cb3/wG9/73UbjF5CApOhTBIdGiKFz60Rs445YoXEqrmFZehSz/ZqanIjQ4AGm5/fnf7MB3+GzNfsknIzrUF7HpheLn3KwMRIYFIS5ZJsLk15uWkY30xCB88uE8uLg6Yvqbb8PWwx/peeViPML27GEYOwWiRBBW0REhiE5Ik44AMZ4m+HzBKlyyOI233vsUAQH+KKttE49lJkYgMKq/fsiNtMeLb30kfv5p8cc4cM4Wyz55HwFplTi5fgHe/WK9INI4ozPDg0UaMywyw+xFofSHW+7E0h+2IjJF9qZIBNoew/W/uh5r1m3C28/8Gw+98bkgNYCNs58TG+v3Pl2EhR+9hWn/dz3c4gpQEOuCv/75z1izeTs+fvMx/Oz6m5Be04WqRPcRizTzg6vx61/fjA2bNuORe27B9EXbxPAvXvqnkNavsHz1Grzw4N/xiz/cjhJBUMa7GeD/hLTmLFiMT2e8JJ5vk74DLpkfxG9+Ng0PPPMGXILjcHjNbPz8/36Bz79ZjZkvPoBp1/0ZsQX1YtpyTHetxM+vuQYvz5yLpV/PE9M6bhuAn754HtP+8G+QDIq1PySG+6Qqv/2b7F0hhv/n8Rew89AJlNY0SUfa8eodfxCO/QJfL1+Jd569H9f/5S7k1HYg3O4IfnPt9fhuwya8+ujdeGLmYrGR8zbZi1/938/x1dIVeOT2P+AP/3xaFHAXN38uniNfaEvSA83xh1/9GsvWbsCs1x7F3c+8j9aubmya/xJ++9f/YPeevXjxf//CUzOXoFNFdFntk11runCJEVa7xc8vz5yHb774QPx8wCJAiilDLtKii7tgc/Ar8fMLb87C5j3HUZ6biGsE/5KDtmgqicdN1/0cs7/+Hjs2rsDv/3gTrAP7G0ZmPOjEgg/eg1dKDXpayvDys6/CytYC9/3rTuw6YQwH6/P4+IOZuO1fD+NyTgHWLpiJRatW48F/3gVz9zBsW70AC5csxbsff4WUlFg89t978c2SRXjixRkoaVIQIm1FeHfmuygU8mJTaRqWfDUPD9x1Ow6bumLTss9g7BaKfd9/jS8E4T9j9udISk3EMw/dh8VLFuPRZ99ArjTUbn7oB3z+3UHxM+FguBfvvP8hXnt9BnzC4jHr5Ucw/6slePzJ5xGfmdt3vY//92Fs2Pwj/vWve3De1BIvPPMolq9chudfeR+ljbLrPLppCQ4bWeOb2S9jzueL8OTjj8MjNl88ZnV4Jf7136dgfuEE/vf401i+6DN8unIXEkJc8e5b7wjuNeiZeIpxcyPs8co7n4qfty+dh0NG9tj4zTx88MG7ePq1OWPSW8lMXlikMcMmMcQJbz7/P7HRJffaR6vR3N6OOY//HX996DWEhUfgwoG14rGQ/GocXvQ2fnHDXWiQvv/wLb/Ak3N+FD9nJMUgJDwU330uiDchvk9mI+pTvMTPwxVpve3VeODP1+B/079EeEQEdix9X/j+z1EsKJQ1MwVxc8/LYrxkd30x3dCMCqyYcR/+9OAMMby3NAa/EMJ/PO0j+Npxy8+nYeVhG/HYT/Ofx8/+fK9YodanuIjfP++VLB6Tc3HrYkF4/g7J0gjJp8/fgb8/9Rnykv3F+AGZldi7+DX87ZGZaodNLU7vxb/vuEWMO23aNVh/yEIMf+feP+P2Z2aLn1GfLv72jXoW+OyFu/CPx99BuHCfDbYvFb8XmVGIdx/6E+6fvlyMXpUdCys7J3G+oNkuIc41N6Ciower3nkAv/3nEwgJC4ft6W3idx2jsrH+48cx7Td/xdr1m2FiZo7Y9CuHKB301gvxf4msZhKdB8Xv+mZTL0Ir/vbLafhgxTFZRAm5SIsq7ICjHl3ndUiskN2BzvJk/FE4tu60KxrywsV4L7z7GY6eOoNLLu4an+fIDEUHvpw1C6EFsj7oOW+/iSN6epg550vRf/HAevywZSteefYFnDI6i7feeF8M3/jFbGz6aQtemy7rMVr/+bvYtPsgPvzwUzR3tGD6iy8iIk/+4iHQXICZ781EsaC1MiOd8bUg7JZ/PguLNh3C9u+XYu/hA3jttZli1O2LZ2H9jgOYPWsu6jva8P7LL8A3VdYzZ3bwB3yz5bT4mfjyrcfxwecrsPLr+TC2ccAn77+LzNp2rP18Dg6dOIG33pRd74Z5H+CA3kksmL8IdXUlePO1GWjsaseHr76M4GzZy9f+7xeIwnTJp+8jUngh27poNvaZyV5Aoh1P48tvD6Dgsgfenf8d2muy8OGcz7FlzVd45s25WP/tMmw5bCLGLY5z7utJ27n0Y+w/54BvP35ReFGZiSeefgFBqf29dwwzFCzSmGGRFB2ChMwi8XNzXRlO7VgpNrBWPqH44OFbccPf7sRzzzyNl159A9PfegMBqQXY/+UbuPbWx8UeJeLNB/+CJ2auRZiHKf5zpxD/9en48pMZQjq/gn92E+oGEWnXCuGbDWRDiH205OGf103D3+/+L555+mm89sZbeGv6LKRXNGDlO//BnS98LEaLcT0ppPszBCXlYe7TN+Put5eK4WjJx+9+Ng0bTtAbcAVuFj5/s/uieGjLvOdwze1PiuKqIMpOvK5zbrLhWjkXNi/Ez375F5RLP/D7T57Bdbe9JAi7Hrx095/x3pff4vG7bsaqwzSMqUB3K4L8fFEm9TQUZqVg3vSnMO3nf0Flazs++M9NeHCmTHShuwJ/vfYafPX9Hrz98G248ba78axwn19+7Q28/da7CIhJxLP//CVeWrBLFl+Bi9u/EUTajSht7sCnT9yB3950K55/9hm8+PJreEdojG2C0wTVVI/dP3yD++68FT//2f/h34+9hewK5flBiiItyma/+Dm2VPjRvVW447fTMHvlwCLt0hHhGn7xF2TXyURae1kybhCOrTxgJvrjAy7h3Vefwg3XX4frf38DthyTCVVmvOjB3Ff+h+femoVZ77yE52Z+jbhgZzz7yizx6Lw3HsfKjTvx/CMPwcIjCMsEsaN/zggvP/wwzlm54Ku57+GQ/nHMeG8WPD1d8PJL01FRV4EXH3sS4bkKC0casoV89yJKhWzgemoDnnjjY6xd8D6+WLcXaxfOwUlLJywTxNG+Y/qCmHsf7p7uePWlN1BaV4XXH38c3imynmhbvR/w59vuwyeffIJvtx7E7nXfYO7Xq3HggB7SstLw9gvPIaG4Bl+9+zrOO3j3X+8jj8DgogXeFI6bWVoJ1/k2ymor8erjTwgvU7Ih/u3LBOF5+Ay+fP8t+KeXYu3Hb2OPiWwKQ4qfKf739HSYnzuCtz9Zjaq8aLzw2hxYXjiGt979CIcPHIRflKwXuLMuD0/df7vYw3f77XfCJyYVn775LHyzWuB7biP+eu9zKJPPCWGYIWCRxgyLQ6vfExveLUeMEBAQhL3fy4bS/C7nYcv8Z/DrO55CTWs3ygsykJAimw+y/QvqJfsVzPwuoyw7EtcL8b8XGuFV79yPaX/8D5o6u2C+Z7GYTmBuC2qTPcTPp5yVVzo2FcTi10L4B19vhru7e58rrqzEzMf+grue+xTt3b3IS09EWk6J+J3PX7gDtz8r642KctQT0w3NqoP+WuF3XPcPZJdUwNVohxi+1dBXiFUtiodP1+uhs6sbmz97BtNueVgUmPkR1mK8syoizUTqzdp5wQPV5QW490/T8NScH8RjFge+FY79HNN+extiC1VWOXY14uV7fotpv78NJnauCAoOwPvP3IVpf7gPte2d+OSxO3DN725HXE4x4t3Oiucw84nDuo8fxx/ueRH17T0ozUvD5TTZPLfl7z6Ca266X7gftXA13I4HHnsBRQ0dsNqzTPju9agQtOCh5W9g2p/uQ4kQXl2Sg7jL6YKY7ITe5pVYs/0oWlsbcXabIKiEc3klKb/p2x/9Xgj/GTIFkRZptVf8XbElwp3pKcfffzUNs5YflWLKCLY+LKYTWdABu0NfC5//JA5nE+2lSfitcGztcXtUZUVj4RdfwDMuF2UFabjnN9Nw32sLxXjM+OHvZoVdO7Zh+96jKG3sRFd9MRxcvMRjxWlR0BOEk7mFDXJLK2F6YitWrv4eTz/6MOwjC1BfnIrdu3cLL0D5Qn5ohqOjG1rbW+Hq6IQKIa0+Ohrh6uqKBiGop70ORif1ccHEHCHRCQgN8EJWeROay7OwR0jLN5bmj7YLabmgpb0N7o6OKKmTzf8qyozDwQP7sHXrVhw2MEFbWwuMjh/EyYv2aBZecDxdnFHT3I4gT1fkldfA9PhPsut97BHYh6TD18kclrZO8PD2E66T0nZCmWxGP+LCfBGTlI4gHw9BHLYg0t8TiVmylea9XU0wNjwNJxcP+IXEoK2xEg5OdI964Wh8Cgf0zgjitP/lJvdyCLZv2woLl0DR7+3qhLwqmrfXBqNTJ5GtZuUzw6iDRRozLDoay/Hdgvfwy5/Lhjp//ce/YOMRWa9TXUky3nvuf7jtzrvx1xv/jJnzf4Sg17BTEGm/u/kfmDnjbdz21xuFt/Qv0NDRixgPY9zxlz/jzrv+jffem4G//en3MPJJQ2NmIK699lpBDMWK6cppKkrEv/5yLa75mezccqdvF43K3Eg8f//duPPue3HTjTdjyaaTYu/X0un34z+vzRe/H+t6WkzXJ0V4Y+6oxqdvPInb77xLuK4Z+O21v8B6PSchVg9WffQybrjpr9h6xhbH1n6I39z1rCjSCqMvid+/6Km8eIDmpP31lnvx5huv4I7b/oZ/P/kakotkCys6K5LEXroHpku9dioUp4Zi+nOCWJV+y633PAIrQcxSpf/eg//Abfc9hOmvv4ib/ngD5n+7XfxNtQUJmP7UA7j9X/fgZuE+z160VbzPjWWpePeFB/D32/+Jm2++GZ+s/AntPb2w3r8a1/76L8ht7EVbTQE+e+MZ3Hr7v/C3m/6M12ctR1NHD7xNj+DOv/0Fd9/3b9x77z1YtfUI2oTvKuJ8cpPw+3+HbKENirE/LHz+PeKpJ62nEvfceC0+++6kFFNG2KXj4v2KKeqAk/4KXPvbfyCzVhJp5Sm4RTi27sQldDZXYNGsV/CXv96C/97/bzz0xEvwi+uf68hoGx04feAnrFi1Gut3HEWNtPhEe1G53lGaymGYiYRFGjMiqitKUVRUhJpG5WX0JC6ys7OQq7A8fd37T+Ha2x5HvfBmnZ2jvLqxubZSiC9rkKvKi1FV3yy8rXaguLgYzW3KQwG93Z0oKykWz6voGpplb9fCqzmysrJQoLA0v7aqHOVVsmGMjrZmMd3W9i5cuqiP3QeOIjAsGhmRbqJAOmoXIcYTLgAF+Xkor6lHc30NissqhF8FdHe0it9vaVPoGRCgOJVVDeL5s7NzhCZBRofwdp8d54VfCWnvNJYNlwxEsfRb+lc1tuOV23+L/32wAm0NNcL9lA0x99ODbOG35ubLegz76UGOcP8LSqskv3B9DXXCdZeis7tfdOUKcXJyZSvh5PS0N4r3r6is/7uKtDU1iL+fVnF2tDYKn0ukNHvE51JTrzD3SKCjtUmM3yHEaW2SXUOXJPzoWZYKx+oa+3sdygpzxfPzABDDMIwyLNKYMWP752/hpvueR39zPPHE+1rhobv/gXv+/QDuuO12vPv5d6hr0+wbtqfpfvzt5hvxxFufoYq6ukZEB95/+B94es5Kyc8wDMNMVVikMWMG9eRUVteKvVFaRU8HigoLUFQ8Nqus2pobhLRLRvm7e1FXXYWaep6zwjAMM9VhkcYwDMMwDKOFsEhjGIZhGIbRQlikMQzDaJiS/Gykp6ejoLh/eySGYZiRwiKNYRhGgwR62MLKwRURERGwNTOGVzhvJs8wzOhgkTbJqS/NxMH9+2HrESqF9BPsZoX9+w8jv1Kb1l8yjG7jZnMOHgGxyM/Ph7eDJSzcQ6QjDMMwI4NF2iSmt60GSz/5GGeMLbB43vs479a/3VKMpylmffIVTh/fhzmfL0d9u/q1iLm5uXB0dBSthbNjN16OdpTo7h6p+RLtoKaiEIH+AYiJiUFCSiZUbAOjpKSk73fa2tpy+WI37k6Xy9dUg0XaZKa9Fqu/WgDv8Chs+/ZrmHj2b7e059svcMEjSfy89ov58EmUbX9C1NXVITExUXT6+vqIi4tDaWkpO3bj5s6fP4+qKvXGdbWdi0f24KyZI2ISk1Bd14SuLuXGsLW1te93XrhwAdHR0Uq/nR27sXa6XL6mGizSJjFdbfXYuOwzLPhmBaa/PQPecTnSEUGkrVwMxyDaIw/YvWwJnEJl+20SVHhDQ0NFd/z4cS7MzLjj4uKis/nugv4RXM4qR0JCLOzsHHA5s38XDlW8vLzERpNhxhNdLl9TDRZpk5jsUFvMmLNc/JzhfQ4ffCHb/JvQ27wIx6xl89QWzf0IoZnV4mdV/Pz8UFiovI0Qw4w1Tk5OOtuIVJaVorVjeLtY0LATbQvGMOOJLpevqQaLtElMR30JViz6DGvXb8JHsz+EqVc0EsM9ERCXgYKUEMx6932sXLYQS9fvRecA5vHHohGJjIwU5+EM5iwsLGBpaan2mKKj6+vsVN5Tk9F9pkojwiKNmQhYpOkOLNImOx2N8PT0QHx6vugtzktHdpFsI/Ky3GR4evkNurH1WDQijY2NqKmpGdS5ubmJQ0Hqjim62tpa9PZq3cZTzFXCIo1hxg4WaboDizRmUCaqEWlvbxcdMzVhkcYwYweLNN2BRRozKBPViFy+fBkpKSmSj5lqsEhjmLGDRZruwCKNGZSJakRSU1ORkZEh+ZipBos0RhFavBQWFqbkaEcH7m0fHSzSdAcWacygTFQj0tzcjJaWFsnHTDVYpDGKlJWVISEhQVxtfvToUfEz9bbzoqHRwSJNd2CRxgzKRDUiwcHBCA8Pl3zMVINFGqOOhoYGcUERc3WwSNMdWKQxgzJRjYh85SYzNWGRxqijoqJCNMTKXB0s0nQHFmmTmJ7uDpSVFKO4uAQ1tXVoaVWev9HSUCccK0ZldZ0UciUT1YgUFBSI18ZMTXS9EamtKhPnUVXVNkkh6mGRNjJYpGkGFmm6A4u0SUxbdR7WLV+EpcuX48UnH8X+897SEaCjNgfzZr+Pdet+wOFT1lLolUxUI0KTgmNjYyUfM9XQ5UYkMtAN5tb24vwpSxMTBMelS0euhEXayGCRphlYpOkOLNKmAC2lSfjsswUoqmuTQoBkX0t8MHs+zM2tUdXcJYVeyUQ1Im1tbbxyawqjy42I3UV9+ISniL3XYZ72uOgYIB25Et52bWSwSNMMLNJ0BxZpU4DD67/CQRMfySfD1+oEZs1fhlP6h7Bw5UZUt3VLR2TL3e3s7ES3a9cusWIcb6KjoxEfHy/5mKmGLjci7S3V8HJ1gZ2lKUzs3KG6i2d5eTl8fX1Fd+TIEdHPDA8WaZqBRZruwCJtktPVkI95n32Bsv5ONJHykkLIZdmqL+bDL6VS8kHcZqmnp0d0tD3TRPSk5ebmivPSmKmJLjciPpes4RsUDD9BhPm5uyAiXtneX1NTE3JyckRnbGyM0tJS6QgzFJWVlSzSNACLNN2BRdokJ9HDGJ8v2yr5ZBOaq+qb4HBuN37YfRKJsaGY/8ViFNSq38FzooY76+rqUF9fL/mYqYYuNyLejtY4euggjGwcEB3gDRvvCOnIlXh7e/Nw5wjgnjTNwCJNd2CRNslJifCFhWuI5APCfOzhEZGM7rY6HNuxActXrkVU2sCrKCdKpAUFBbGdtCmMLjcivd1dSIwOg7ePFyIT068Y7lRkMi8coHmlhw4dwsmTJ3H8+PGrdidOnMDevXuxZMkSnDp1Sm2c4TpKS19fH11dA8/HncywSNMdWKQxgzJRjUhjY6M4LMRMTaZKIzKZRRo9PxJVAQEBYo/h1TpaZGFjY4OdO3ciJCREbZzhOkpr37594s4mUxEWaboDizRmUCaqEaF9O7OzsyUfM9Vgkab7VFdXiwsjaPcQEkVX6wIDA2Fvb4/du3eLe3eqizNcR2nR9lJTdes5Fmm6A4s0ZlAmqhGhlZ1JSUmSj5lqsEjTfVikaS8s0nQHFmnMoExUI9La2irOaWGmJizSdB8WadoLizTdgUUaMygT1YhQJRwVFSX5mKkGizTdh0Wa9sIiTXdgkcYMykQ1ImQ7io18Tl1YpOk+LNK0FxZpugOLNGZQJqoRIXtIZLiSmZqwSNN9WKRpLyzSdAcWaZOYrtZ6BHh7wMPDEyGhocjOV+6ZKstJhqeXH9SbsZUxUY0ILbGPjIyUfMxUg0Wa7qMpkUbbZ5HdRKoPXF1dceDAAcTFxYlCzd/fX+13hnIs0lik6Qos0iYx7XXFOLTzJ+zcuR2P338PDpn4S0eAgsQAzPlwNlYv+wpL1+9FZ690QAVPT88JaURo4QA5ZmrCIk330ZRII0FlZWWF06dPi7bNyJjt2bNnRYO2VD+NRqixSGORpiuwSJsC1GWH4OtlP6BNQYgd2fAVjtmEiZ8Xzf0IoZnV4meivb1dHGokZ21tjZKSEunI+JGYmIiUlBTJp110d3f33Z/BHG1tVVNTo/aYoiPDvYwyutyIVFcUwNHeGpcuXYK9gzsq6wY2yswibWhHgoqM2BoYGODMmTMwNDQUP9NfLy8vFmmjgEWa7sAibdLTix+/+QQm3pclv4zdyxfBIShL9nnZEjiF9huOLS4uhrOzs+jozZXmh403qampokFbbYSslMvvz2Du8OHDYmOi7piiu3xZ+dkwut2ImJzaB/+4HPFlJ9zNGqetvaQjVzJRPdXjgaaHO0NDQ69wPNw5Olik6Q4s0iY5rWVJ4gbqTSrDmQd/WIiLnjJxsPaL+fBJLBU/q0IV5ERsAE29VT09g+16qP1kZmZOiMCdDOhyI1KYnQAbK1u4u7nB3sEZmYXKc0FpGJ9WL5OztLSckJ7q8UDTCwc06ViksUjTFVikTQKigrzFyp7cJWdftCsIsohLBlj47V7JB+SkxSE5twQxPhZ478MvcPL4Psz5fDnqFb+kwEiGY7KyssQ3Xk04mn9Cwxnqjo3GRUdHo7d3gIl3YwQNY/K8utGhTY1IV2sjXG3NxZWFLh5BSuVLHZdjY1BaXAonO3PYOHihuaVdOiKDRBlNgCe3f//+SSvkWaRpLyzSdAcWaTpOjJsp3n3vM+gdO4Zjgjtz3hatCh1QRZlJCEvMlHxCAxLlj7Ak2dBmsKul0EgcRn7lwJsMj0SkXbhwATExMUhOTr5ql5aWJjp1x0bjSPTRHLHxhDZyTkhIkHzMSNCmRqQyOxIHDxugvaMT3d1D9+4aHtqNPdt3wtk/ETkxvjCy9ZaOXAkJhonoqR4PWKRpLyzSdAcWaTpMY20V7E7vxerNh9DQIlsN2dbWDk32F41EpDk4OGjtEKWbm5vYaIwndD5eFDA6tKUR6WlvhJ+TFfbtPwg3Ty+4uPmjuWvwEpYeG4Yd69bgkk804iMDcDlL/VQCghcOTIxjkcYiTVdgkabDeJjqYfW3q/DpJ3Pw1aLFWLz4G2zefRItGlRpI2lEaDhIWys9qpRopeV4kp2djbKyMsnHjAStaUR62uFuZQQDA3OEhYbi3Dkz1LZr7kWERdrEOBZpLNJ0BRZpOk5WUjSyS/uHK60vmKGsqVvyXT0s0kYPNU7aakZE29GaRqS3G9mJodi5ZStOnDiB02fPIadIczthsEibGMcijUWarsAiTYcJdzPHi089glemz8HatWuxdvUSzJq3BhrUaCzSrgIafu7oGGw/B2YgtKkRaSpNwvbdh1FeXoZDOzZg3Q59lDZ1SkevDhZpE+NYpLFI0xVYpOkwrY11sDU+gxOGZnB1cYG7pw9S0rNQPYjxzJEykkaEjHd2dXVJPu2CVtJRozGecE/a6NGmRqStvgRODpfE4U4XB1vonTqPmlbNvAmxSJsYxyKNRZquwCJNxymIccPjTz6B5WvW4Is57+DJ517Cl9+sRliyZlaMjaQRMTExQXx8vOTTHsrLy8XVnQ0NDVLI+MBz0kaPtjUiUf4uomFiN+9QtHZq7kWERdrEOBZpLNJ0BRZpOo63pQFOmntKvi7s2bkPwYGe2LbnlBR2dYykEamvrxfj01ZSZA28ra1NOjIx0K4FdnZ2YoWUn58vhY4f1Ejx6s7RoU2NSHlmFI4cPYMG4VnWN2iul5pgkTYxjkUaizRdgUWajhPrZYVvVm5ATFwc/JxNsXrDTtianMa2A0bi8abyXBw5cABmDr5QthzQAdsLZ3Do0CGY2flIYVcymkaktrYWYWFhonFdMiQ7nsY6aR4YNQq0ITNtuUNbXE0UbCdt9GhTI9JSmYHdu/YgWMjT4VGX0TlBq6d1DRZp2guLNN2BRdokIMbPAd+uWYMNP+1CUWUdHE2MkV7agI6GIqz8agHsnd2w+YdV8IzqN2pbkRaEDz78CFbWNgiLSZVCr8THx2fUxjY7OzsRGRkpbo5Mc8JoR4KxgoYVAwICRGEYEREx7oZr1cE7Dowe7WpEehDu7YLzphYIi45Tedm5OlikTYxjkcYiTVdgkabjNFcVYMvq5bLVnWu/ww+bD0M+pTk10B5fLloNy4vnYOnohfaufvtOgRbH8NRzb+B74TsO/jFSqAwSOImJiaKjrZk0Ma8qNzdXrBypcqDeu40bN2rE0fV5eHiIIpA2Kqc9P7UFup6JGGadDGhTI1JbnIKDO7binJU1zpwyQE6N5obxWaRNjGORxiJNV2CRpuM4n96JNVtOiqYeRNfZ2bfjQITjGdz/1CuwtruE1Yvnw8AuWDoCpMUEwdYjGDWVhfjs4/lIKumfa0OFl+aUkTt+/LhGRBqZv6AeLgsLC3z33XeYP3++RtzOnTvFnjoa2tS27XWioqLGtPdwMqNNjUhHUzXsLhpg87atsHD2Qlv34F1pjXUV8HB1gLOzM1w8/FHfPLCoY5E2MY5FGos0XYFFmo4T7WKE9z/9Cv7BIQgJCUFEdP+cmSQvE8z96kfxc4LLOXyz4bj4mYgJ8UJetWzj56WffYqQDPU2xKhCuxrxQ/tvUoVANtTi4uLGbNsoEkPUm0aLFsjsBQ21TjTUALS3K2+uzQwP7WtEesXVwWnJ6ahtGTxvmZ85CJ+oDDQ1NSHExQqGg8z5pF5gFmnj78ZbpFGvurwepBdV+kwCfaLqKRZpugOLNB2nKCUC27Ztx/79+7Bt+3Yc1LuAZkkH9bRVY9O3X+GHDZvx+RcLEZych/gwDwTGZyLK0xQffDgXmzb8gI17T6JtAO00mjd96tFLSkoSBRN9PycnRzoy9lDFQw0fVYQkWsfb7IYivr6+YuXMjBxtbURMT55BfPHgeSojKQyODi4ICAiEm5s7Lmcpv+RQw0xTCsjR6uOJXNwylrBI66e5uVnMz/SiampqKn6m0YXeXg1OcBwBLNJ0BxZpk4CsOD8YXrRDdlYaiitVGpDuFngJoiU1t1z0FuelIbtYttoyPzUOHt6BGKxvayQijcQZreYkgUTDj+Nt4V8RmptGw410LV5eXmKDMd7QMLE2LGDQRbSlEaEN1n1dneDo6Ci6A/tPoKhx8F0kqorzBGESBC9nOxib26K2QXnxCJUnBwcH0e3Zs2dcVz+PJyzSrqSkpESsjyYaFmm6A4s0HScpyBFr167CooWrBMHlipXLfkC1hqyhEyMRafLeq7Ea0hwtNBRKhkhp+Gko6I2XGhdNOFp4kZmZqfbYSB2ZNdG2+zqWaE0j0tuNhvo6tLa1D3uLr4RAJ3z7/WZYmxrgh/VbUVo1cM/b1aye1nYo37JIU4aeNfX0TzQs0nQHFmk6juPZgzB29IbFiRMorq3C+mUrkV2ruf0iRyLSaOhGW4WEi4uL2GgMBlVatFCCKjBNOGNj4775J1frzM3NxTl3UwX6zdrUiBRmp4g9s3GJacMywVFVlIVD29dg33FzKUQ9o5lOoCuwSLsSFmnMSGGRpuPUlWbip+++wSsvvY73PvwQesaXpCOaYSSNCO3dOdzehvGGRNpQw69kJoR6NrQRmltHFetUQZsakaq8RBw7ckLsFc3JK8IQizv7aG+qQXFZpeRTD4u0iXEs0lik6Qos0iYBPW2NiIuLRUJqOkoKS9DaqbnerJE0ItRzRIsEaC7W1Trab5OcumOjcefPnx9SpJFNs/9v78yfoljWPv/+KxMT8f44d2Iibtx5nTtz3/e+5z13Pfeses9xOx6PoogLrrjgLu7iioDIJosgILKjggIqyL4IiIIgorKIAqIgm9/pp7oaupumaaCb7qa/n4gnuqoyKzOruivz21mZT8pYOkdExi2J0HQVHKkR6WmpxL79R1Dz5CnqnjbSma2FUKSNhyKNTBWKtDnFJ2xeuga1HdZz+zCVRqS4uFjxDSWv5WZq8ppQVg8wFTYdk+uY7FUsRZrj4FiNyDDyMq7j/PnzyMgpNjvRZqpQpNnH7CXSXr9+rSwXZ28o0pwHirQ5xWfsXLEBte3O7xFdXpvOtg8hijTHwZEake5XtbgcckXz+2hEUFAwXk0yu3MqUKTZxywRabKkmzx31jRxwSF/PuUtgalwS0zOlXs7E/cdFGnOA0WaE3M7NgDr16/XM3d88cVPePnRcHZn2yt5Baru6DPUh9cOOmZGXHkUFBSoe7ODiDRH+Jdrio6ODqVH0FVwpEZkoLsFV8LDkf/gPkIjYtDZN6SGzByKNPuYJSLNz88PJ06cUK7BGnbu3Dns3bsXq1atUiYomYpjicm5Xl5eM1rNhCLNeaBIc2I6XjaOrrGptSo0tbSNLgsFDCL64jG4rVyNfy7+FWXPxgTZ+9anWLPsJ/y04HscC7ymHh2PvRoRcTkx2z7GZOKAOOB1RMThaWxsrLo393GURuTz8CBaNX9y6h8/Uhr3hhdaf4PWgiLNPmaJSBO3PfKnTdwKWcNkWTxZcUDWLi4tLTUZxxIrKSmBv7//jBxlU6Q5DxRpc5hX1TlY4bYRbW2tKMjLxpPmsQbm8uEN8L5wXdMIfcBP33yPypb3aogh9mpEmpqaZt1/lPhIkxmq8lpRZvI5AtLQyRqqUVFRqK2tVY/OfRylERkZ6EX+3Tu4kRCvfAfXEm/CmvOXKdLsY5aItEuXLiE9Pd3k+dMxeTsgf7SOHTuG/Px8k3EsMd2aytXV1WpJpw5FmvNAkTaHKc2IwP/74i/Y7Lkey9w34vHLsZ6pQx4rkJirFSKH1qxGcv7Y0k0ijsTnmZiPj48yDmK2UXxSlZWpe7OLXL9MgJDrlx7KoSHrvd6yFHn1Kg249OxJpexqa4A6UiMy+KEDl3yP4ULgJZw9H4Q3/fZxFu1sUKQZGkUamQ4UaU5MZtR5rF69WjF3d3fFtu05jV51+tnDBD/8+cd1ynZO1Gl47A5QtoVjm1fgWk6dsr3bbQXSi5uVbUEGpMpMSDGppOzRiPT399tdmIhvspycHKUHRRqa7u5uNcR2yIL0uiWDnjx5oh51PRypEel68QhBGoGWnpKES4GReP5m4oZ9qlCk2cco0ijSnAWKNCemu7MNL1peKYPK29u1fsVevniFT0Naldb5rBg//nMhSioe4aS3J3wjMtDV2YqOrl5kRJ3CotXeeHAvA19/twgve0z3FtmrESksLFTGbTgCMsu0vLxcqWBl3T2ZRt/c3Kz0dlnDZPxdTU2N0msmPpTk+3R1HKURGRkaxKf+T3jV+hLP6h6huOyx3phP0/R/7EZudqYyUzg7twB9AxP3xFKk2cco0ijSnAWKNCdn8H0rdmxcjeXLV+LXX37G8vX78GFw7HVM5f00eHisxeFz4ZCm4mH2dWQUPNJsDeHyyb1wW7kKd0snniVkr0ZExIsjNl4ykHj79u34zW9+g3/913+1islMLWkQZPFlosVRGpG2+kLExExtVu21kLO4mf9IESl3k64iNOmuGjIeEeUUabNv9hBpch/kj5iINJm5fvfuXZPxJjOKNNeCIs3JSbp0Eqf8QnFolxduaR76nbv34e0cGDMjqwPM9uzOiZCF2aVSlfUzpWKV157yKlQ+rWHiE66hoQFxcXFISkpSeulcHUdpRDoaCrDDc/voGM3UzFx8mqQrrfRBJq7fyNA0yveRlpKMgirDP0HDw8PKq3wxuU6KtNm32RZp8ucuOztbWZVl//79Sv7S02oq7mRGkeZaUKQ5Obnxl3Hk/FWkXPWHf2g0vDZtxjM7LbBuTaRin20/acbIhAmpSEWcyWoKszFGTnoQZXap/OOuqKhQj1ofuTap5CczGSNn6rixWXtyiaM0Iu3PSpGSmqPuWcpnFBfk4c7NNETFp8PY56gjTMyZDSjStCbXL2kdOHAA3t7e2Lx5Mw4ePKh89zJ8Qsa9mjpvIqNIcy0o0pydz59wLSIc8fGx+Pabr3HtdqEaYB3sJdKk90pcYtgDcb8hDag9B+9Lwy3/vMU7uXy+f2/aRcp0ETEojYc5kzE04nxTPk2F65ukZ00cpRGRSTRTdeyeEReOkJBgJKRkoTj3JqKSJxZ58ieAPWmzb7PdkyZCTPKUZ0l8nen2TcWdzCjSXAuKNCenp60Bu708sX3HTuzcugFXrmepIdbBXiJNenBm21eZCCEZ2OtIDaeIVXFFIjNMZfLCbCMOfu2BQzUiw4N4kJWGlNRU3MrOx8Akou1+RhLulzdIhxoeZKdqtsfc2xhjr+drNqBIs41RpLkWFGlOTnL4aQQl5Kl7I/DasAUd1huSZrdGRPyTzaQSmg4iSMQjuCMiM3ftsRqCtXvILMWRGpG2Jw9x4pQ/ejQivvfDx0lndwoDA9p12D4NmB96QJFmH6NIo0hzFijSnJzy21H4+qdlyNQ8vPGhZ/CHP/4V1zOyUFv/Uo0xM+zViOgGVs8mIkiysqzbE2ktpMGb7bU75VWf9ODNZCHn6eJIjUj/20acOHYcd3Lz8LDkEQateDso0uxjFGkUac4CRZqT87KmEPv2H8CJk8exZ7e3Mjh1965diEu3zqB7WzQi8gpPZm6aM3FNIILJVJi+yexIa4kIWYpKXneaymc6JmPq5BWqqbCpWl1dnTL7c7aR+2sPHKkRGRkaQMrVUPieOY1z/hHoo0izCIo02xhFmmtBkTYHeFqajcCweDTU1+H1uz71qJbuthfIvn1LI3qy8bbXsGeqpqRAEUMFJROvCWmLRkQWGhZXE+ZMZlRevXrVZJi+SSUqzmatgVTY8krRVD7TMVlIOSAgwGTYVE0mMsz2MlkifkUou3pPWuvTIpw4eBDRsXHwvxiMxk7DZ2wmzJZIE7cf4tZGTP4kiQNl2ZaVPWwFRZptjCLNtaBIc3Kqcm9gy5YNWPWrJ25mpWO9xzZ0fhwblHZipzs8th/Ead+LeP5mbLZkT0s5vvvma6Wiik6Y+BXfXJ59Zmtk5QBpEJ0VEWfiF87VRdpA71vk3c9DwZ1MRF5NQ3efdf4UCLMl0uR3qBP84kxVeoxlu75+YkfWM4UizTZGkeZaUKQ5OUnBJ3El6RaiL/jh5ds38PJYj4Z3aiPyuRs/f/UnbN59GJHXb2uPqRQlX8aXf/keJ0/6ora5Uz2qRcaCicAQk54lesKfHtL4OntFKK9a7YFjNSKfUXovC/FJqaiqqYO6NK5VsMfrTvHDZ8seNB0UabYxijTXgiLNyRnseYUDW93x5z9/jaXLf4FvUOxoIzLyoRU7t3shO+8+9m5chXOxY8vTPMyMwa6jF3DvbgYW/rwaTV1jr0JfvnyJlJQUxeRf91x1tmlrpEKtqqpS95wP6UGLjIx0+Z60ty+qcGT3LgRGRePc2fOod8LXnfpID9psiG+KNNsYRZprQZHm5NSUV+L9x37cSY7G/qMX1aNa+rra8OxFq7JdnhoMN6+zyrbQ+LQGOucAnsuW4k6N6UW9xZGqeEgnU0cagNmeoWpt7LVElWM1IiPITY3D4aNHcf1mLj4NW0+0UqTZxyjSKNKcBYo0J6YkOwb/XO6Fzjct2LpuDbZvWoudJwKhG5H2of0JFi/4GmGRV+G5eiVu5Faisa4cNU2vkRl5EgtXeCIqPAhuG3bibZ/plzj2aETmCjJBwl4rFlgD6UGThsCle9KGenH59DH4B4UhJS0defnlGFKDrAFFmn2MIo0izVmgSHNiDm/4GeUdGrF2/SzW7A9Sjq346Rc0dI01I22NVThx4iTS71cq+4+K76LgkdYD+q34cJw47YfWnokdblKkTZ+amhqn7oUUcSZuP1z7decImh5XIjUpATGxMSgsrcHgiPn7MTzUr6zdKUKgoLgKQ2bi2+P5En97s7HkGkWabYwizbWgSHNiTm5difIXvQjYtw5BaTL26SMWLliC5vfWW3KAIm36iI8xc42AM2Cv2amO1og8e1yO4we347RfND5O4s02MTIAqTlFikC/lRCN6PT7ash4Jnu+ZIB/a2srXr9+bTULCwtT/O6ZCpuKSbn6+iYen0eRZhujSHMtKNKcmPryXPzw3bdY5L4N7W864O2+EBuPBli0bI2lUKRNn1u3bqGiokLdcz6kB00qc5fuSRt4h0Nb3bHMfS2CrkSjqKx60ted+XeSkHH7PkqKC3Ej4RryyurUkPFM9nyFh4fj8OHDOHv2rCIqZmrnz5/HihUrrJLmkSNHEBwcrJZ0PBRptjGKNNeCIs3Jed3ShO6+IQx1vcT1xAyrugcQKNKmj85xqDNTXFysbs0uDtOIjAyiuekZXr9uRfPzJjxrasFk8waG+7sQ4n8OmblFaHnRgpethpNypIdNnBOL+fj4mJ09feXKFWWWdUFBAe7fvz9jk+/z6NGjWifWM0hThIK8Ng0NDVVLOh6KNNsYRZprQZFGzEKRNn1k0oC9fMyJh3lrmKxnaur4dGwqOHMjknglAFn5Jbh9KxNRQf7wj0xVQ7RIz6TunojQMfd8RUREKIv+5+TkmGywp2oisA4dOqTc35mkKU6Ob9y4obw6nQiKNNsYRZprQZFGzEKRNn2kMn38+LG6NztIr0xgYOBoT81MLD4+XlnaSj5NhU/VpFdIZrxagjM3IvfS45FXIZNzBnB2zxacv5KpDTDBZM8XRZptjCKNIs1ZoEgjZqFImz4yqHpgYOKZs7ZAZpTevm24uoSjIAvYi7d7S3DuRuQzet6/V7dlBY/pz56mSLONUaRRpDkLFGnELBRp00cagplUpNNBRJp8Z46IiDRpHCzBVRqR2RJpIqpEoBUVFY2OScvPz1d+o+Kw2tQ55owizX5GkeZaUKTNcdIiLmC5mzs81mzF41fd6lHNf/3+Lhzf5YnFCxchIatEPToeirTp09jYiLa2NnVvdpD1VqXhlEpYBobLmLLZ7s3TIfnK5AlZGkt60GSQuZTJEijStFhDpImgunnzJkJCQpRlvjw8PJRGXn4niYmJimAxdZ45o0izn1GkuRYUaXOaQWxduRDHA6JRVGHo+T4hYB/cdp7Bsydl+ObrBWh8a3r5Ii4LNX1EMImvNHsgExakp0Qq45iYGGWAemFhobIuqy0RwSHjzkSUxcbGjooA6UWbyhJZFGlarCHS5FzJR1xuiIlwEoEi2/Id5eXlmTzPnFGk2c8o0lwLirQ5zEjfS/z9D7/HJq+d+GX5ajyse62GAIfW/oK4HK1w27faDamFz5VtQRp4aWTFuMD69JGxYY7iJ62np0cRbdKbJWOSpDflt7/9rVXsd7/7neJ/a9++fUr6ks97vTFZ04EiTYs1X3fK9yImvZlisi0Cja87TUORRhwBirQ5zHD/ezx5phVf92IvYM2eAGVbOLrRDdfznirbB9xXIaWgUdkWxMu5vKYTk3/a9nIj4eyIjzRzHtlnA+m9kspcGmKpmKVHTXq6pHHWCfGZmqQprzSl4Zdt8eslnzKzdbp+4ijStFh74oC1jCLNfkaR5lpQpM1hul8+wr6DPuj7NIiIkzux78I1jIwMa+wzos54wdMnBN3vXuKHr7/H4zbTlZWMZTHXiNiCkZERpSISMWEPb/fWQkSKLJ8z24i4FsEkC2nL2psySFxElLkGyZqIMG1oaFCEobjeEBcesl1bW6vGmByKNC0UabYxijSKNGeBIm0O83moH2HnDmDJsuXYvPcUuj4O4F5mDJLvVeBTbzu2rfoZC+Z/j0vXbqlnjGeyRsQWyCtCqdilIp1JRWQrZHFqqeREBJkzX19fxWeZqTB9q6zULn5vDWTs1+XLlxWBK2PiHAHd5AEZG5eVlaUeNQ9FmhaKNNsYRRpFmrNAkeYC9OlVREODAxgcGlt9sL/f/Mw/e4g0adTldZnkba+B9+YQT/FSxslMxmVJ+U2F6ZuIPmshvVXiasERkUZBvlNLoEjTQpFmG6NIo0hzFijSiFnsIdKEwcFBxcjUEJEmrxelgbSGidA0dXw6VlpaqvQcWoJzNyLDqKkoVmbTVtbUq8dMQ5FmH6NIo0hzFijSiFnsJdLI9JBZnNeuXVMq4ZmaCCpxfCqfpsKnajI+zdJlsiS+szYiaXGhuHEzD3V1dUi9FomErImXwqJIs49RpFGkOQsUacQsFGmujTVfxU4FZ25EspIjcT31jjK2Mjn+KlJyS9WQ8YibFnN+CCnSbGMUaRRpzgJFGjELRZrrIjNrZWaoPWbYOnsj0trcqCzR1fRq/OQNeZ5EeIkdPnzYrB9CijTbGEUaRZqzQJFGzEKR5rqIOJNJCBRpU6MqLx1nzgcoz05aagqePDcUYUNDQ4o4EJNXyeZWgaBIs41RpFGkOQsUacQsFGmujcw+tQfO3Ii8f/McwaFhaO/+qPiMGxoeUUPGIz2V5p4vijTbGEUaRZqzQJHmKoyMwLip+NjTpfyL7+jsUo+MhyLNdZEeNBEJ7EmzHZM9XxRptjGKNIo0Z4EizQVoKkrBd4s9oL+89cC7Z1gy/1t4eW2Dr/819eh4KNJcG3stCUaRpoUizTZGkUaR5ixQpM1xhj+0Y833f8Tv/7HKQKRVZ8fgu/lLER19DW8+jDm3NYYizXWRHrTy8nL2pNkQijT7GEUaRZqzQJE2p/mMKxeOIjouAYd9ThuItOxYP3y/1AP+50/h1/W70Nk/rIZAcQkgPq3EfHx8zM4+I3MXEWeJiYkUaTaEIs0+RpFGkeYsUKTNYWpz4vA/fvsf8PPzxX/8+5e486hJDQHaXr2ATpZtWLYUd2rGXAVIoyyLnItJJcWeNNelt7dX3ZpdKNK0UKTZxijSKNKcBYq0OcyblqeIuXoVl88dwu/+9x9wv7YZXZ2teNPdixvBh7Ht8EVUlj7A0mWr0PzO9BqefN3puohYl95U9qTZDoo0+xhFGkWas0CR5hJ8Qlx8irJVkH0dmQ+rMdzfhbMHd2Dt+s0oejyxnyaKNNdFxFllZSVFmg2hSLOPUaRRpDkLFGnELBRprk1Hx3iP+bMBRZoWijTbGEUaRZqzQJFGzEKRNjeRySBSyZuzR48eKRNH5NNUuL5Ze3IJRZoWijTbGEUaRZqzQJFGzEKRNjd5/vy50nhOZtKYmTpubJKeNaFI00KRZhujSKNIcxYo0ohZKNKIPaBI00KRZhujSKNIcxYo0ohZpBHhw0xmG/nd2Ws8nDWof1ylOAJ+XN+sHjFNdna22ecrJiYGqampKCgoUBpnR7H8/HxFwERFRaklHY8IIBETRUVFJtOwpz18+BB+fn5mJ8WEhoYiKyvL5Pn2tJKSEgQGBqKhoUEt6dRx9ufLlaBII2aRf8tSGZeWls6qlZWVKWYqzFlMGum5cA2mjtvapAF99+6d+it0Lm7diERCWjaqqqqQFBOB5JwSNUSLXJfuOs+ePWv2+dq/fz+OHz+uNMr+/v4OYwEBATh58iT27NljstxiIkA9PT0RFBRkMg17mvSSbdy4URE9psoutmPHDqW3zdT59rTg4GBs2bIFsbGxJsttiTnz8+VqUKQRs8i//MLCwlm3kJAQhIeHmwxzFpOGTHpCTIU5g0lvw9GjR5VPU+G2NJms4KxkJoQiKfMeamtrkX79Kq5nF6ohWuQ1oO46pZdJ/7qNTcId3UyVW2em4juSmSqzzkzFdyQzVWZLzZmfL1eDIo04JBUVFTMac+EIiLh59uyZuuecyNgVMlWGUFNeiuLiYlQ/te6ECkKIa0GRRhwS+bcn3fLOTF5eHmpqatQ950PG68THx9vFmS0hhBCKNOKg9PX1ob+/X91zTmTg9KdP+svaOx89PT3qFiGEkNmGIo0QQgghxAGhSCOzytPHVWhu71b3TFNVVY6O9+N7oJ431KK+xfGnjfd1d6Ckqlbdm5iBD114UtcIR3uZONT3Hq1tdLtCCCH2hiKN2JSBTwPqFjAyNISc7AxUPmtV9nvedeLjgFaidLzpVD4/fx7GrZupeNamfc3W19uF7g9awVZakI386iZlu6vzDYaULS1vO9rxvl//yMwYGR7C0NCIuifXoU37nSYfXTZS8v4PPWr5RtCu+h360NGIxMxsZXu4/wO6evuUbYWhj5pr1YrU15W3sGzxJmVbMPZb1PVWc38+Dap71uWN5joG9dThh+5OzXVov6s7V09h7baDo/e3o92wXO1G+x3tbaP3hBBCiPWgSCM2JfCoNxLvP9VsvcfhvXtw4NRp5Dwsxv4tKzF/ySo8KKvC8e1rsfTXlfjHV39BWm4hQi77oaiyCptXLMYK99X45u9fI6+iCbcSgzVpPcKDjCv44bsfsGjlRnR29SDywl788qs7Fi1ahOySJ9qMZ8jAuyZs2eQFkVc1d+Nw3C8CWalR8PDYgDUbvPD8jSbfc3vxl29/RFBoBI7s3wHPdaux70wEOp4/go9fKNqe1+CXn+bj66/+gezyRnQ2lmHxj/OxcP58BN24g67GIqxZvVcjRDuxzeMXLFmyEDuOBaC/7x3cly3AT8s8UFzfpi2Qtfg8hJjAE1iz3hPLVq5Hy7telN9Lxmp3D01Z1uFh9TMc37QAv/ntH/Ci/Q2O7lqHxUsXY733MbzRCOPT+7fB03MdPL1PorunG+cObsSK1WuxcOkvKHn6Ws2EzDbD/V2ICgtEckoKMu/kq0eN6Ud+3kRhWurKClHdNLu91SMDH1F4Lwvx12KQkfNQPWrMAJ7V16EovwDdEy8SgK6Wetwvsc9knZ7WRuQ+rMBgz0tExyVr/uT14c6de2qo5jvqfY2C/DJ1jxDLoEgjNuVh8mV4HQvBi6o72HngNE6c2IurKRlYumABnrwfQdENP6z2OqGJ+Rn7PRbgUkwa9u3Zipt5eVjwl6/w/MMg7kWewi6fcFwN98XxgMvY6LYSzb0DKLp3B6/a3iArIxH1jc+wZemf4X4gUJvxjBnBXs8VyK1tQaimzAEhYfj2yy8QGHoFnsu+wfbjwTi83QOBGdXof1WM//tv/46Qq7GISUpHU2UO1uw+gHMHtuNSUiHaG6tRWl2PIxt/xaXUMgwPtGoE5Urc0zRMu3eeQmLEOazf46fkuXnVcsQlJuOH739C8wdtSazKyEcs//pL7PUNQIjmml68bsHSv/8nDpwPhq/3Gnyzch9K7sbg8MVoVN6OxrL1BzTfzGcc2uIOv8vhWPDXPyEg9CrCo+PR1f0OackJaHz2BEv+9m84cDlVzYTMNn0d9fDeuxtP6+vx4lUbqgvvwu/UWdx9WI6q4jxcPHcGYVdCEBEcieKSfFyJiERjywskR4QiOCwG9Q0NSIuPgvvyFUgr1vZWzxYf2uvgffAgKmueovxRNTpaGhB06SJyih7hccUDBIZEIO92EnZu3YIA/yDkPShBTEQIyuueofB2KvzOBaCs9ike5mRg98Z1OBaSoqY8u8gfu4uBYagsycOGbftQWvwAYWFXUVV6DxFRMaiuLMDV0GgU3r+LyLgbaHj6BBk34pGYmoGuXueeYERsB0UasS2f3sBr0zps3LQF96qeI8B3N6KT0pR9eemX5L8bx0O1jXtamA/C41Jw6MBOZNy9qxEs2yAv+0qTQnDkRBRioy7goO8pbFrlqcQX3ne14dS+bZoG6jBWL/4KW4+HqiEzp/JOLNauXQfvQ6fwpOYhvpz3B1yJisKV0GDcyi2GjybfG0VNGBr4iNzMFGzfvA4Llq7DnVvJ8Dp6GPs91+FmufbV7tDQALYuW4KHz7WV8Ybla5Ganoz9u08i5IwPLkbnKsfPeW+H/6UwrNu6EzaZVzkyjIZHJTh34iB++OFHhMXGYfFf/wtnQyIRFaERwjfuIi85EKdCr+N+3CUcOBuvnBZxfA9Oh2WgsjAH+3dsxvfzlyL3wUMc37MF+w8dx+JvvsCJ8EwlLpl9+t82wdt7G+5onpuymidIunIJGTdz4L9vK3zOx2mEzxPs3L4VkeFRSExMxR6vTbgcEaH54xOD/Jw0uC9bi7JnrUgOv4D0wno11dlh6NNHVBbnIzr8ClJS0hBy8RwKa9vQ3/kEZzQCrP3VcxzZvQ1x8clIS4hDTEwi/I7uwXG/AFwNuaL5s5MHb/fViMwoRt3Dmzh/xT4iTf5o3rwRhaDIeNy+lQlfX18UlJQhMzkJO7ZuRERCMkKO7MHmPScQFxWKU77nEXghEIkpqehSh3QQYgxFGrE5UUfX4b//r79iWLPts8sD4QlJcHNbheZ+oKu5Ast+WoSLly7hqy//DRFJ0ru0ESlZWXD7aTXkzUZBrB/2HgpDeNARnI1Jw5n9a+HtcxLuHmuRnZONBX/7G0KuROLX+V9i5d6LSp5WYegj/vQ//xs2+mqEyvAHeLotgV9oFA5qGsO0+2U44LUWcYXN6Goqw1r3DUiIj8GCBcuRdCMWq70P425yGBZqxNihHetwMS4Ld+Mv4ttF7vA9ugMrtvmguTYfq1fuxtNH9/HVP77D+XO++GHxCtTWVuDHn1fh7diQOOsx9B4+mgb6UmQsNi5fhMCrGQg8vh3eJy8h4ORe+MVn48mDa/j7/J+Vf/7zv/sOZ8+fxYKFi5F9Lx/b12/AtYR4LP7nEoSEheG7v3+tCNfv/vR/sNs/Uc2EzDYf25/iwJHDyrjIjo5OJEcFo7SiBtG+PjgTeA2lD+7Ce89uXPI9gaO+gTh2YDd8L2gEWUoWasvysHezNzJzH+DswT1IeTj9NSGnw7uXNfC/HIHnzxtw4dw5nLvgjxuZ91H/pBSBAQHIuZuNC6ePIzQ4BLGhl7Db+ygu+B7DgaPHEH81AY8fV+PMrp0Ijc9EYrg/TgQnqSnPPkU3w7Hl0EX0dTdj6a+r8LjuMc6fPoPDe71xITgU4aeO4dCxM4iPT0BxWSUe3ruD/bt2oKy+XU2BEEMo0ojNeff6GfJLtMuQPK6uQPOr18qakL0Dn/HmVT3Cw4JwJfoqNqz4CeHJeaitqUKrprEpL65QhN3bl42ayq4ZzU11aGjtAga7ERYYgJsPKrRpahqZwKBQFJdXoLLOug1MZfEDNLVpB/oPvG9HaGAgYpOzlEkDtVVlaHnTq4RVFWQp6yuWyrisgW48LNeulnA3ORYhkXHoUwfW30mKRWBwNHo1Fzby8S2KiyqV409KcrWLJre91+wNoKCoDOqcCqvT1foMQZq8rqXlaA987kd8xGUER17DRynnyEckxEbhRdcA2urLlXJVNWrHxjVUFSj7OSV1yn5xXgaCwiI1gqAS1Q0vlGNk9vk8/AkPcm4q62XmPShCU2MTuru70faiEZk3YrBvuxfOBsXidcsLVJaXIjf3PqprqvG69Q3edXagUyPsSvPvIjkty+TMatvyGU+qSpB5MxNPWzoxMtSPW5kpqKh/gXetTUhKv4meD32oqSxCTV096murkZeTi/LKSjQ9b0FP1zu0t7bjWV0lrl9PxpMXszumTp/3b1vx+Kksqj+CqspqDA8Po6K4AHl5D1BTW4M3He/Q0liH27dy0NbejuKCe3hYUo2BIanpCBkPRRqxK231xVi8cAF27PCC+6Z9eNnl3A5sCXE0nlaX4f6Dh/jwyUaqnxBiMyjSiN35PPgRz58/V3qnCCGEEKKFIo0QQgghxAGhSCOEEEIIcUAo0gghhBBCHBCKNEIIIYQQB4QijRALGPjQiaDzJ3Ho0EFkFU2+eLpJhj7gZtZtdPdzigQhhJDJoUgjZDI+92HXml9wMjge2Vlp+OGbb5Fd1oSenm68etGI3HsPMOrdQCPEcnNz0NyuWy9gBIX38tAk/t0wiJT0dGU90MH3HcjNycXbXu0C6h+7WjXnafY/cKVyQnTIagR9A/QhRlwXijRCJqUP2379CXt9w1FRXY/Ojg686+7FwU3L8Lu/fIdNGzywastBdPd2wcd7E/b5HMFqD088aW5F9IV9WLJsJeYvWoHGFy3YuN0L9c8bsGOTBw4f8cF6rwOornmEDSuWwsfnINZs3I23fbZYaoAQ56KxtgwRkVEIvnQJpbWNyrEPH+UvjiGDA58w8nkIubfS0fnxMz7192v+GulgrzVxbijSCJmEz5p6fqC3E37HDuGXRT9i/jI3NLx6g32ey3ExtVyJs8dzPXx9T+GPv/8jTp7yxcJvvsTeo6fh6b5e6Tnr7niFnjdNWLd9Gy6fO47ff/ENTmni/+2LPyLsWhI8lvwT3geOIiQ6Qev1nxBXZug9Lpz2RWu/bHbiVXsbslJjcfZiEG7fvon794rQ+LQSIRcu4MKJMwgLC4DXlu0ICY7ExbP+SLx1F5Xlhaiof6UmSIhzQpFGyCT0vqrGxg3b1T0g/NhG7LkQidN7NyP8zmPlmIi0Y0d98O03C1FUXIK0xGvIvZOBXxcvV0Tah3ftaGupw4ad2+F3Yj9+WLoBJSUlSIi9ioraBlSUFCEuIgh/+vf/RGZJk5ImIa7K54EOnDp5BtrBAEB9eTbO+EcCn7qwd4sHriXfQ0N1AXZu2ILi0mokXzmN4NB4JEZFoKyqEdkJodh35AxecwUT4uRQpBEyGcMDOLVzHf7xz2XYsWMHlixagerGVpzYvhy/+69vsGXjWmw+cA49PZ2aRmMltu/ehyXLV6KsvhnRF/bi519X48efV6KiphZrN2/C4/parFu5FHv37cWyddtQWlaKTW6/4PCx4/h5mTvKGu239iAhjkJuZgKuJmbgWvglxMYnID42EhFR0YjWCLGwy8G4eP4E9nofQFX1E2THB2tE3XkE+vmhpvE9Gu4nYNfhS2pKhDgvFGmEWMjTR7IwdS7aurXjYnZsdMfFaxl4UFA4NgZmpA/38vLQ0DImtIoe3ENj6ztl++Ur7euX4Y9vkaeJ9/rtB2VfJg7kadJu6dQu2E4IkWeuXOlpFvp7OlBS8UjZ7nzVhOraJ3j39h0+ffqEvg+9aGt9ieYXLzEwNITCnEw8fMQeaeL8UKQRMk0uXzyNe3Xt6h4hxDEYwevXreCcUDIXoEgjhBBCCHFAKNIIIYQQQhwQijRCCCGEEAeEIo0QQgghxAGhSCOEEEIIcUAo0gghhBBCHBCKNEIIIYQQB4QijRBCCCHEAaFII4QQQghxQCjSCCGEEEIcEIo0QgghhBAHhCKNEEIIIcQBoUgjhBBCCHFAKNKIZaS74V/+5V8w70y9esAM9WcwTxNX4uubRedOF7V8bunqvjmkfBZFnATjPPXTVe+BTa95mqS7yffhBivcAbOMzycdbrOQr9Og/n7GbB4m/bnw2Zras2Xyfllwn62NPb43MiegSCMWUI8z86ZQqZioROvPzNOcb8PK0eKGRISC5lqs0ZAYYJTuVBqSWcZuIk2+I6vfd+dlWt8Dn62pPVuO8hza43sjcwKKNDIpSmUyb97MKkZT/4w1+3LMoKLSHVcjGlRkahrz3NxGzx3Nw6L0x8SmYvPOaI4Yo8YZDVMbiNHGVC98NE8T6erugea+6Y5PfO/UPNR7PFreie6RMGGY6bS091H23eBmLA6mmJa5cpnLR8Is+v24BMa/MwvR/a707yOfrYl/V6bu1yimft9T/c1PEN8YU+Uwuq9jz47WxuKazsM4/uj3Q+YUFGnEPErloqkU0s1VdkaYqJAMew3USsdUY6FhLK5hPF2lpqvkdZWUEmxQ4ZlL3yhNExjEH62cDfeVazOT5+h5Sll1DY2eMDJAPVc/3OgeWn7/JkvLKNySfCwtl7l85Igmrpnb7mLo7s+YWXRvjO6/YPlvQz+uYTxNgLYcc+3ZMnG/xlDTNTjXzDFz1zxR/jom+96UcFPfk7I3Pg+j9LTxx84ncweKNGIGtQKUyslsZWeEGlep9PVMd65xwzE+bV2lJKZXMakV92g8/fP0KnXz6RtWuCZR4ytRJN15bnDT3IfRfV3aFjQkurIaVrrGjC/TuGuYwfUZx9cvi7l8Zlouw2uW35Leea6O0e9j3H2dCPU8uef6NmE6RvmMfqeKucCzpcbVXq9qqhAdl66CBb/5qV6zYKocGhu93zrU69aaLk8TeYymN1GdQuYKFGlkQgwqJ6OK0Sym4qqVjxwb3yCNr4S0Fa/pNMai6Z2nF2Y+fUsqVa04HS2rJq58ju7rKnlrNSQmyqS9BjnH0Ca/fxOlNRZfu68ti7l8Zlou/Xw0O5g32jiScVj6fPHZGncPLBFpBtc6iqnyjj8282vWMMn3pgvXXYf2mnR5TpCHev6YTVS/EGeGIo1MgO41ggmbToWkV9GMq/SM4+v25xnF06/UBP3zzDUkBulbVqkqlaTxv3x1f/RcvTzHpWt0TdMTafoNwxhTvT7j+PplMZfPTMtlcM1yr/TSIUYY/V4mxGS8se/J/G9Db99Vni3j6zfAVHkt+M1P45pNl2PsXLPPjgV5aM/X3S8yl6BII5ZhXMkYVKJGmKqQ9BsBNVxX6RhWUKo41B9vYvTvWrdvcJ5+ecymb2GlqstLd54uTV0egsE9MErX6B6YbUhMlcnofINrmOr1GaSlhuvKYi6faZbLVD4ST3cO0aD/PGgwuI8GvysjjO6/gn5aarjp34YLPlum7tcopso78W9+Rtdsqhx635s2TaPrNZeH3rn6+5MVgzgfFGnEMowrGXOVgq5SMzb9yAZxdJWRrgIcX1kr+eq2pz0DTYu2UhebSDQJuopSF8d4X4NRngbpGt2vKYs0QU1fZwbBE16f6bR091XKMG5254T5TL1cE+Uj12+cjKszdq/E9L5D49+yPny2pvZsTXC/tOma+n1P8Juf8JoniG/MBOUYO8/wzYWb5ntQPicspwb1Huls9PsicwqKNOI86DcqhBDrwWeLEIeEIo04D2xICLENfLYIcUgo0gghhBBCHBCKNEIIIYQQB4QijRBCCCHEAaFII4QQQghxQCjSiMMyNu1eb/q/PZDp8/oFMN63ELOuAgghhBAjKNKIg6L6BtI527Qbxj6KLPSLZAKKNEIIIVOBIo04IIaOHUeFzWQOJefNU8M1YWdUlwJ6zjlF8KXrORDVdzdg6FhUF2ZUDt3SNaP7qoCcsFz66ZpwImuE6TIoAdr0VWGojaeXj0X5a20a2pIQQoidoEgjDopxT5phD5ahUFHD9AWQzhu3wTI3Y+cb9GopImdM3Bj2eBn3nBntqwJJJ6jGp6sLM1FGfcyWQX9/uvnrwgxFHCGEEMeFIo04KKoYMRBZegLDlAAaFVIajJ1zqvtj2sYoPUEn7BTThRmnbbg/Lh29fIzDjIWXSUyWQVDzVWwsDXP56+7RpHkSQghxSCjSiIMyiUjThStqxFhIaVDFikUizUjMGPY4GadtuK9NR+IbmuRrXGbt/gSCyWwZtGiP6V2TBnP5KxiIPjEKNkIIcRYo0oiDMolIs2JPmnHahj1elog0QzGlw3y6hkwaV3e98wzjmcvfGG3csXtACCHEsaFIIw6KoUjTiRTT4sgaIk0XpqY1YdpG+wZi0ahcpoSkWZE2URnUCQzKvdDfliAz+U9yDwghhDg2FGnEQVGFik6MCDqhpphOwAjGQkrDFETaqAhS03ZzM4yre82oE1jG+7q0daZfDJ34krjmZ3dOXAZDAadhgmvTmX7+xmGj5xBCCHF4KNIIIYQQQhwQijRCCCGEEAeEIo0QQgghxAGhSCOEEEIIcUAo0gghhBBCHBCKNEIIIYQQB4QijRBCCCHEAaFII4QQQghxQCjSCCGEEEIcEIo0QgghhBAHhCKNEEIIIcQBoUgjhBBCCHFAKNIIIYQQQhwQijRCCCGEEAeEIo0QQgghxAGhSCOEEEIIcTiA/w/towq9cfmLkgAAAABJRU5ErkJggg==",
null,
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null,
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null,
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null,
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null,
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",
null,
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null,
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null,
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null,
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null,
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null,
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null,
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null,
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null,
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",
null,
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",
null,
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null,
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null,
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null,
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null,
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null,
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null,
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null,
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null,
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",
null,
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",
null,
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",
null,
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",
null,
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",
null,
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null,
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",
null,
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null,
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/bJLWvlSPFPe/ibh6SnVdaWN0h+8VMem3OpHCkWgtycfyP0sGEGMNDPjHlrlHoEZN0ZpYYmOM7OpTRmBk4J9/Yc+DaVux6+fWjs4cloxpT7Xbc7QzOpMTpRwMaFiXyghuIwp/p46st7uBmi3a9kf5qfW0N9z4WgbY5su49lj5g3a0PtOZnGaBtzSZbR/Il84gEBL7ltVIrDnKqjuSlu8l36m0O0eKpwuPqSSMbeyle+1tpzMo3RNuSSNgrFVCXg3wBdR6BMaZhTdTQ3dYpoIPd4kna8zr1MpDHuy1ZJoZhByDbKz6k1RiuD4g4DFAvA4pjIZ6NS7BEICx+o9JucXKSBbTTmoj/4Gs1MaPWwMFVSKE41Jt/I1p0hg+IOA3SWnKOPA+RS3NYn6Hbpt3257GWVDgXj5eHyjYzdGYYuqS01u+RcaTofq0QNsJDUKcoOkDuSzUq5MaKdV20vq+xpvDxcvpGtO8PYJYEMhmNN0bQZtPUPH+rrJmBTHHnNO7lIf3J/6WmfvryTykujVDdkvDxcvpGpO0PO4OEbnmLgEKODpUm6kkHOg7m61tG0GbT1zzOus5uAycsz1NdDJ/ORI8Ut7qC1ilLuX36Zrk4Wwkp1xbrh8nD5RsbujFoGDweFwCFGB52JkYy0GnETEXljgis0itChoWkzaOsfPlTc0+DoY83I6/7sv3yfqp72f5kT1rL75Q05cudrug+8uexSzqF0SYoZhMJGjXPqYfBwUAgcqyvpqrdjCe/FamvaDNqqw4c6xim1DtcndYro8ez+cK6nMPKq+rRv5DoVz1nYWDh8nUwHmkL327HNvKi20rwZtNWGD9cfp9Q8XKeTi/T4C0SUO9SXH3lVfdqv/zqVB4O5My4aqjhcK9OBZlGani+Tz1IK3JGM6rIJLfioXHOrPpnIZaK3Sh/ZdK3mNZR1U45Kn0C2vN2dXRWy7ojmnmqH6/y8keuuPLxP/XCD16lx2prD1TbiU/g09Jui2DlanK0r/zFlpuJO1bQZtNWGD3WOUxocfUydIhouH97HPvJqcDy1EckXGKBnONbguiqdjH1mrXqpdSjoHKc0OPp4cpGOnisfXshWNK5T1h+hep2KPRcKpzU/+QIjdDyWKC2Y0KEPYIyfTORyzd+MEHjLHfnY/Iay7poneSFL7uyq/Glfcc+9ub2Kh+ts/Y1cd01ucjxH3blF9esUAtmxQC6SWf86a/dUu33Tk6/O/zT0m6JnIp/8QkpWKR5FyXmZRee20j8Hl77JxxUPd1rz3i0EE/mACqaKTKLa0k8tBoY59b+0qrOTohHJFxiDwNG+mCoyiaim9FOTkWFO/S+t6ltRSWuMVn5OaIrKVEVtKSbC27HtRjEFSHFbn6bXj9Lwxeytc1pHG1q+SP9bp53/fmprNS1VUXwvNv+xStQAXRRTAHnpJ9PhDE3rG2TF+6ntDKlKJ5pP0Ei3jfPQNytSgJOL9Pg+G+eh79QMppq6fJH+rgd0UrQzjKp0HsUUQH3SHYPz/dY2fYKq3h9L2rgJWpW/P6Z/T6gT1lWpgsCxDjHKjX6Yo1S+k4IGQnRAyt17kBu+k3PdKWy8GbIdkrIvEZYv6mAYjgUW84nc89tLnRTUE7DNJenkIj33ZHnjvmK2YnC+X9ioKgNHMsjxvPIHJedWVlmdIdoSLrpd0Unx7oO56WPcz3pyD1VsvG9fYdKd2t6QOpYvwovtG1ErUhUx6uldCdfbaYJUpZZsSSTFFZV0b1SnuHxRR69p1NbaPVWRPcj0htIU9+FBxhyyJZH0vx0rCjZ6Med251aFnDtS1/JFWNNog1IIHOKUx9RUxRvLCgEiKr0ptxpxF36t9dChkjTx9V+IdRl42ledmKv6rVO1qu3nt9togHon6KvF3hA1eLEdKigsAXkiRJFVSRICNCZIWSkTcdOY39hYbL60zD9bmABZF413/jqNkfputYm5qubLUizQDnNnXHQ7QQO3aMxl2/KM7d0HmZcvwovtG5Xigkz5qg35L8wgRj29obSBGvaO6+MwUt+tVp2h85wGy8NRM25pTe7j6O13L2fEil+ImWUTG3SML6GGvZKRp321ibl0nlMUbHeHSysq5byM5eGoGd/A5IHDMX5mJNEbTJJjPOwK9fJ8b4gix/A9bxQjT/uFibmK3Rmlibl0nnM+kfvG++U9bV628nBUfGxgqBxtLSNP+ylu6/dzty7nygOiMxw3SYtv5V7Sc07RNvgS0U8q9vQS3crpLQ8P2/buy72FmnHranLJubxHA++qNIwJ9d0GasZRXd7RmtbHkS+48MULRRaljw/rqjSK8ad9UciPp9q+yl4zjlwD6qXnicNaOuiJw4w3RKc83JVdOdpio98SjWZjvXg/FfLwdmyVDgocxmFAFFQ1v+Qcq9W3ierxVBrCgCg0CVarb2fV46mU8643yzmAObBaffsSbYldtktpCjk5jud8cUoSVmOG5sBq9e3LkTvzR1RVu5kkId+1iZdWobGUKkfPZ0YSTr43lE6HnBzvTIxksO50PRqfLDAvdIT8BcyB1eobpuHJAvtCR8hfwCQYjm0QI++8Gm9acYy2hZcELdDE4Vgx6ikWjAYxsGdEC2e4UXtpFZPugHkqA4cYHQ25hMIkXcs+zOtnQAtnuFHr+MCkO2CemrVjS8XmYnTwMJ1ZsmD3RjukKi0s6FQrJD9No6gx3VhaNVlxeiXToEY7XStnuHHkztdEBG8uu5QjTLoDZsKCTA1gwbdOLXhJ0M5qAkfphXpnKE1xHxZk0qmyPqI0SlrcWLWmUUtoL7MEwAzDsWbASkVgPe2+IFPHw0pFsOHI6ziKL9EvBIt5Cl6r14SVimDjkddx5Idgk0HfcmRVkrKShNfqtWGlIth4yn0c4pTHGUqr71n/EkrmslgfB1YqAotqUh+H48jpiNudf8rIRNzuSKbwkpsQIHckY42oYTlYqQg2pM9V/NoxfmbE08uHiMgdyZzPZyy8b9odWY1hYEDZfCIXXir9LncgwM0lc7uVNg4h8ELnwHCsEVipCKwLs5xXsVLgALCuZtdxiFMefjAq5n+BV+xNhjm4oBPIA0fyRIgiZ8Yd+V+smvGKfXGaD8+UmAxu7DJ2zMEFHUGxctTldOTnKB7xmZCWl6f5CF9x+qYDQn6wZrV/YnCjlYegnBQ6xOdkW7zHIhNOjidyR1bHHQtB3hcPCJKBIYHVlXTAP0RE5D0QcO8+VjiVw+lKz64SqYUmnuPrb9OaRMFGI1mH1zbgsy2MY3lnaF9N6BwVo4POlbAUG6rd7Bml0+wzIbdx5+iUh6PT2SMOWghyc1Zenxc6QQeMqiSDnI+EcuwQpzzOkKu+UtS2DRwoJ4WmalrgyE8d6J/lfPHa3axSb07tGzjEKDdK2eL04rYgTwckZCvQOB3wxGGmdg0cUx6bc6kcKZCtQIM1uY4jGdyYA6WNhTm4oKMorh27nMF/aJOpzCGMInRoT4qr1adDvaUyrQ1crAUAKtDHAdCZMOcoAFhLZeDId4smg1xNnoJUBQCqIFUB6ExIVQDAWhA4AIAZAgcAMEPgAABmCBwAwAyBAwCYIXAAADMEDgBghsABAMwQOACAGQIHADBD4AAAZggcAMAMgQMAmCFwAAAzBA4AYIbAAQDMEDgAgBkCBwAwQ+AAAGYIHADADIEDAJg1JXCIUU9hfRZPtLwqLVa3BmhXTQgcYnQ05BIkKStJ2dM0ynumsKQ1QHtrQuBYXUkH/EP5XzvGz0vhK05ex6OGbDW5wqfBV7uuZLDquanJhwNYQhMCR2+/Oz67UP69NyZldk/wgxPLmodJWUnx0+CrXc/CLI25EvP1fvUNHg5gDU0IHI7x8wL5qjIUx5GlzAilG9+22cToxHL/Mb8rIdT11Td4OIBVYO1YFmLUM0qnz4+vBvnZA1JsqLmHA7DA2rFWIc4naMTnIPIeCMTnmEeEDB4OYB144tBPjA46Q+X8KiBkY97mHQ7ABk8c1iAKCYpkin20wlhVj2/DDwewEgQOvcT5hCs87ij+ljXdMHg4gKUgcOgkCgmXv7I7c8gfmJ7QXZFROrxYx8F2eMnEHs5+MMV6VAmqSMAc6ONoroVgcI6Wdx9bOuJYf2e5l/fsmaF3d7+y9tP9LWgd2gr6ODqGwTqO1MHJd3f/zaGexVN1PXOgigRMg8ChQfHBXn+ycPiL3KZHX63YIAoJGnizd8L21dCJOnpGU6cW6fEX9ocP9bz+/ZfZDxeFBI34HF7/QF2tA1RA4FCnWB7+8gz19Sye1BE5RufJ3r0yeba0QZxP0MCtLWOuS1ueqaNnNHVykR5/YT9R+FDf1ZkJ1sNRRQImQh+HGjE6eJjOhFdGM8fOl0ZDUge3Pk2vH70yfPGVW+c0uxnOPnrPc/T3h9557u2pzy4+WzihkTqO1MGtT7x+u/TbvuPZy2GGw1FFsuGgj6MVFB/s9ScLr06uUP/R755+qvvSkdHiCe8O73VHMllJGCPvEGMdR+rUIg2/USwDOd53dYYpW0EVCZgKgSOvtjtD8cFePVmo7fg4O7lC/U8scZ7H/tS+Nn84f8Jd33i/a+Sfvslt+o/dgWTOW5EvKPabVF1S6uRiz9Fz+4t7smYrxSqSwjmRrYBRam+vW/bTkGsWAoGxgDuSKW7JRNyVf0kBIStJ2TeGuys39h0vHX68r6+vr3v4jeLhpweqpg2xP5vNRNzPjFWd0+sld2RV8XD5Jb0x3N13vGrP433UPbyo8wYzEXdAqDqnECi1jk+Hfhr67UYfByl0ZxRfY813bSTzL7Pee9A+TK8VuzYm+vmZQ9Lll0ih4+PVRzc99+kz3/zCN86EV0YzN66E/vdT0m/+c9Qz+sv/988/3vT3h9557u3nn7/028ILsor9JgZ7WPTdJnQ09HEYoaNWUhQSZH+l9y8uf6HQnaFYHq6aLKROLdLOXz4+yX2h0PFxdnKl+98HrxXPuePr9rX5w+J8wvXH//dXtOPDw3Pd9136u18Vk4XUqUUa+OTx5MNfrug3Yeth0VcPiuFYME+nBw4dM26J8wmy/+umvp5LN5+MzyVVqsuP/Yef9Rx6qWI49qVDfVcnD6YodXKRdt7e3NfzzuadV2cm8nHjT79Vcc7f/7p9beZbp1xbfrZCO2xb+3rW7N1r/yLmS85TJxdpwN4z5lrr/Vqp24Kth0XfrGIYjgUztTwTa2Tmlom43ZFVIeAuDygo7VP595HvzlD7vDHc3T28eLyvuzTAodjxoXhOeccH0+FqPSx67pH1NvHphE9Dv90d/cSh5+FcFBK3BjZ3D7+RlY730c59muOU8mQhdWpReuC+4uHbd1ydeVl2zsfiswv5AdotXcWN9q61+VGi1KnF7EB/cYz2sZ3Fw+VDp2rDsToTEAzHgqk6OXCI8wkauf5nnP1HX618OK/qERDnE9vs17liCvDOB4+p7UlKyULq5KL9oTt8ceOHtOPqzETxnPsSnGfLd/re+fVj8bnk2cmV+34vd09xz7WurrX5w6mTizv+5P6txQzirS/tzB+u3sNSuKTSBYjzCRrpPsF5Mt/USkDwUj+YrOUPVA17AFN5OK8a5sxE3E/+cVUKsPOx0jhl7RitPFl4Y7h7Z3/Vxu07aPNAv/ycv/8A372zaqO9i/gtXV8bqrrIx3bS5oE9NXmEEKD+gc19x6suKT8cqzMBKQ7HVp0Tw7Ed/mnot7tzh2PFqGc0c//y2ftfP3pl+OJ3D71+/YAUG5INSabUBln17TmotvHOs647zjPhldHMfTdD/6i2518qjfuqTmKsOGz84X5KbT8TXhnN/OFA6BeYAxmKMBxbD3E+4Xrq/TeLXRKvfhyIzyXlPQLFFKCgPGChb0/Vjc89ebH4IuzH+1T3ZMsgZJckzidcz29PFTf+oqe+BASz+wCzTn3iEKODJz7+yo//il5b++l+enkPP7MvcFX80ouU2n566YiDFoL8nF+KbTq49fuP3qp8W2xiDze5e3Hth5c8h2ndPX94675dwTsKG0f+67Z/vrLLRVuW6bdpuqdv+jWlPf/6nj1/+VeXKl82Swa5if7VJcXyLOSxNgEAAAi3SURBVHGq5pJ6o4MnukeW/6688cHAdFLtcFWY3adDNfSJo1MDBym9TvoPW/S+IWrBCc0Vz2m8IZSTdiykKnWRj1+GdA9JGp/QvPJFWK8ZY5+Kl2R8kBXlpFCXTgociq+TFoQP9V398X/T2aFgfELzXd94v6s4yJq0eY2PfSpekvFBVpSTQn06KHBUVV6nTi32HHqp4k9f+s6XP3jv8r0VW1TnGTc+ofmurZfS6ZCT53jeF6cF8tYzofm6lxT+wRkj15k/bcV1Ts8icoBOHdPHYaVcXfHlWguOkrbLdUJd0Mehg5Vy9XYp02yX6wQL6pDAYThXN7GWwWCm0zTtcp1gRZ2RqhgelUQtA3QcpCrrMToqiZWKANg0IXAkgxzPK3+CGkmFyiG8fE+jubqV+kcA2kITAoc3ls1E3FTxmmnpo5VQaLzzV81oro5aBgBWTevj0HoLg4nZmRtWKoLOhHdVqpj814FaBuhQ6BxtINQyANRhgwcO1DIA1GPDpyoAHQqpCgBYy+dafQH1UKzmAICmab9UxRRNy3fQEBpqZitNawipCgAwQ+AAAGYIHADADIEDAJghcAAAMwQOAGC2QYdjAcAIPHEAADMEDgBghsABAMwQOACAGQIHADBD4AAAZggcAMAMgQMAmCFwAACzDRI4xOggH5St0iZOeXQuK7d+A+ucqric3aDRiZC1GzLxjvJ/aTzH88rLcZt2R9oNmXVH1efheU7+/8GEO1q3FTP/gcSoR+s8Jv4DKdgQgUOcOlyx5FLZ6pV0QNC1rNy6NE8lRgd9JEhSVsqMJJzG/rdoX7OJd5QMOlfCkpSVJMEVGq35z2fmHWk2ZNodOY4sldcDFALkjhyrWj3HnDtarxUT/4GSwd7EyKokZaVMZNlXGx3M/AdStAEChxg9nHAF3Ap/kLnk7nea04bmqVZX0oH8IgyOp0bc07MG/hm1GzLxjpKz04VrpqGYdL5mBT4T70i7IRPvqNxi0LccOdO4O9JoxbzbETPL7hGfg4jIcSQcSK+sVv2x6bdTq+MDhxgdTYycOdav8EerK+l0qFftwZWJ5qnEzLK7vzf/a4fTRcuZ+p8dta/ZvDsSM8vu/kxQJYMw8Y60GzLz36jY4NREfCxcuxSpmf9G6q2YeDsOpyudEMRiW6WLLzRv8u3IdXjgEKcOJ0ZOKy9YK2aWyR1ZzT80ZvonFDN5nc1oniqzopQnNaAhE++IiNKhlQOSlJWk1ZFETQZh4h1pN2TuHRERJU+EKHJMliKYe0dqrZh5O95YNrzSy/Mc70yMZGqe1Ey+HQUdHTjE6OHEyOkjKutcO8aXsqVFsB3OgfRKpt6GtE/l7FfIkxrRkIl3RFTOzyt+uBWYeEfaDZl7R0S0MBsvPuFXMfeO1Fox8XbEqIeb6M/HoPCKs6Z/1NzbUdLJgUOcT6TTISfH85wzlKa4j/dMtWJxR4fTVUpBxcwyuZwqocxCHE6X9p+adUfaDZktOaf8jTb330i1FRNlVtKlNob8gZpkpPH/5To5cFR0cWcibgoI0lLl08dCsGKkSsxcCvjrXqR+nVP19rvjE1Mi5WPZmL/+vnTthky8I/L6B0InFgpnWq79Hph3R9oNmXlH+TO4R55S/A6ZeEfqrZh4O85+d+npbGE2XhsaTLwdFeXRo07+FAKHlJWk1YibAkI2P45VeqArZZ51fhROVdGQlBUCxT/MGLsX7YZMvKPyNZfuojF3pN2Q2XdUfZKG3JFWK2beTumvrcH/5RQ/mDoQAJh1cqoCAA2CwAEAzBA4AIAZAgcAMEPgAABmCBwAwAyBAwCYIXAAADMEDgBghsABAMwQOACAGQIHADBD4AAAZggcAMAMgQMAmCFwAAAzBA4AYIbAAQDMEDgAgBkCRxsSox75OsOKGystBJVWQi4uTWzCItXqV7LutRlppREnh/UgcLQhx/iSfL1ixY0lYtTjW46sZiJjkUxWIF/+m5YMcoWliSXltYsBlCFwtKHKH7aDweAgz3PBZOUP3vLDRcWP4vKSJd5YPsSImWUqL+3hOBIOlBdSKz2JlM6QDHLB6JSndpFXMepReJDRSdaKGPUMRqNB9SejwWBw0BMVk8HeUJrivuKBswqHQAMhcLS5dJzCklT1rJEM+kgoPUTkv1kOpytdXPeoxOEbcccrnjK8seIChcmgbzmSqToDEVE8lBjJZCVJcIV6i88svYmR4qIelbvqodxKOpTYncmvGxKfKFxbaU8pTPE0EXljhTVE8jceX5YdAg2FwNHuFFcDKywI6DiyJBVCijeWlfxzztB0yMmVlsJ0jJ/Przxas1h8cna6sBaZ40g4MD1bCgeB/ALsQ8ci7nwT5VjDvpijWiuBcH7BPWe/u7COYXJ2urhx6FhEYVlU+SHQWAgcnccbWx1J9PK1OQWRN1bo43CFnOVH+qFYccGxkURvaf90qHAGX7y8Lqm735n/RdWCyclgaU9Wiq3IiJlld38v88mhgRA4OpFjfKmwSqArNBoViWghyJfTCK9/jJYzYvVGIsd4eKwUDkorCUpSeYH1EjFzKR9EkkGOnz1QWn+QlXYrpQurWEIZrAGBo+NUrWxcNOQPTE/UZiJD/sC0r7IDcnY6Hw68/rHCksXVZ0uHTiSJiBZOhGjE56jtXiWNpwYFaq1o73kilNbfBDQKAkfHGYoJA6FCt4WPhPP5H+T5/CXfx+EjIf/j3RvLCuQr1XFM9K8uFfcWXCEnz/G8bzlypvQo4A7QRNVGx/jpyLIvf/joistdzl+Iaios4r5ywQiff9JRaUVBec+5/sKDTb5nFxUcLYJFpzcUMRoUfDGtr6i6ZLAisrSMGPX0roQ1KlagKfDEsaE4xuuMGq0lRgeLjyq9iZFVRI3WwxMHADDDEwcAMEPgAABmCBwAwAyBAwCYIXAAADMEDgBghsABAMwQOACAGQIHADBD4AAAZggcAMAMgQMAmCFwAAAzBA4AYIbAAQDM/j8/NpilzxBOQgAAAABJRU5ErkJggg==",
null,
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null,
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null,
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VwWFkVGUJkk/7dI1f8upnZZ9uOX53Il1TDLFlWLS5R86u8vm9O6KGQg2sbpq1kqWEd9txm1gi6ZhGgKZ9GnNTfmVpTJip4aEC0ERAsB0UJAtBAQLQRECwHRQkC0EBAtBEQLAdFCQLQQEC0ERAsB0UL8HzWX5Pos2r9bAAAAAElFTkSuQmCC",
null,
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",
null,
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",
null,
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",
null,
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null,
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",
null,
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null,
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null,
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null,
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null,
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",
null,
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",
null,
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",
null,
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null,
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null,
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null,
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null,
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",
null,
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aPQQMwoNBAzCq2jv6SZUy94/aN3GZjFUi4is62ZO1zyJRr4t58kD1Do0UnyAIUenSQPIpld3gtuBPpoP9T8XvAM1OWYb/O94AWYb/O94EWYq30veA7qRTDrA3WiH+z3gfqUQi/mAW5caH3ouZWp5/pRKnybDfZuWej5fEEUGogZhYZiRh8dheMjm52KcXRmZppqTBeZQKEzM3OBd6tlCV1hM5yDSJ7ffzueK1Kv0DU2w1mcNmxxd0P2/JC5n/Mck0UfK7ShGdrmsKQBGHM/iz/neqquc1jmm6Ht3QS+uEWhXZuhfMd2Oz3R2h03KbQj9TKFrshHu1IvVGgw5nRx9CJ9NBzzVd6w1Mh8o0Jr7U73ywYf7ey2UWgDs9aT6JGGIepwD0Sghe676kCPjULPUveDj9AYBIWepV6G0Mv10WLVWrV6be1CwzOnEbp7XbxcJrhuH12AOb3QeGdoBAoNxJxE6AcjxJ4o5uRwZ6bj7T6DTABCq56P94b819I7Q5nH4aw0Ch3GXJvQKqgb+g++p0WhBSKFFpGcSWlex9FHCyQRuu1ewihcR+QTgBqETsyMQgMxJ/DRxshOf5FMGHMeLFVo7RalV4ud3uZqZc4EFHrInAlXIrTyF53QQR4EhR5Ra0FzzzGrUbw2pE9Eoe3UBlVRaIHrFNrhveDJkVXooQM2OOQSPvrq3qKcJv/LxBxX/OreC16r0FijnZkjy9f6XvBg6rjnKDbmXBgzA72xLuHAf0IACp3mNRsm5j7m57CM3/w7nMNSrdAu826qEZpNybJTVyu0C3M9QrO3pNqp0UcbmXu4zrTdCiehXqXQNU5CvUqhlzkXPJi6HPMi54KHUxdkdp8Lng45hc6HCKsqtTlGaGW88ePUZ89DMgHcZhQahc4KFHq4ORNQ6OHmTEChh5szAYUebs6ERQqNcAAKDQQUGggoNBBQaCCg0EBAoYGAQgMBhQYCCg2EOKFl2ua+mXip+PmJPfdvWcaT4R1hvGjTbK0sSVHI5jih9/xs7W47cQDZwXNn6eXtVxNHifTaSZakKGRzlNDHH96z85w/TOQydc/76afj+KE038dToSZZkqKUzTFCnz984s2QJUKavtrjm59EM6TvB5vKLRO1ZpIlJYrZHCP0fi383fH1s/m7PT5uxSvYaEubMFpunmRJiWI2RwhNrJEdC4XJW3V1wlI7ehMgMvvpcjZHCM37XpXTazrd6a/SVIu/2+lpwZmFLmdzkvCOfr/nH00W7WQzpDmH5h5ctbxplqQoZHO80PQ7JxXlzuzLNjTKpIdMxaSymdpYkqKQzXhnCAQUGggoNBBQaCCg0EBAoYGAQgMBhQYCCg0EFBoIKDQQUGggoNBAQKGBgEIDAYUGAgoNBBQaCCg0EFBoIIQKLR7Da0/jDzxnh+buTGX98aOnsqzEEbbdcShqc7IafXz96eOXd59PG2L43vzsuLTQ47MB2hxRo48/vH/1KznDgVWH45uvH1+ERfRpPH9of3r3M3scTxd03g6MFo/13/wka9V3f/mFbPr1+79lSsEranOM0I/MDJrPs1+Rk/6bGn1+EjVjt+Zb718Orz7Tq1BfvDSaH3F8XLM0FPLX4e6Z0a5Ny+QmQFGbY4T+nqWZqOy0Hc+1OrCUElZBeKsUaT3kr57R4gjJQi6dHNjRBtpVrc3xQsvV/Nrzxy8b3nyOr59ZPuvdM7simpu2o221bzQ/QrDQJCw4oQvYnEDolqWgHVbnjy+79YHlqu22Ip2bGk1soZVk2AzFEUVqdAGb44Wmvon8nN6SHvwtM4+ZumNe67RZ0V/s0NfPI38nd5Gfzt8BCF3A5gQ1eseDUN5Js9bF1gXdcLf3d/bXvmm+e7/lhfgrJVbiCMlC/vrDh+fzEwsKstdoeJsT3hmeP4673cmVek0AjKAl4GzOfAvubPT5CSRn1wV5bMaxDiCg0EBAoYGAQgMBhQYCCg0EFBoIKDQQUGggoNBAQKGBgEIDAYUGAgoNBBQaCCg0EP4PNauqZzkNP6cAAAAASUVORK5CYII=",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.70342374,"math_prob":0.95011586,"size":16114,"snap":"2020-10-2020-16","text_gpt3_token_len":5203,"char_repetition_ratio":0.14171322,"word_repetition_ratio":0.14548872,"special_character_ratio":0.33269206,"punctuation_ratio":0.18251173,"nsfw_num_words":2,"has_unicode_error":false,"math_prob_llama3":0.9897141,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-02-23T10:53:13Z\",\"WARC-Record-ID\":\"<urn:uuid:38de9799-7a48-4f19-bcdb-632bfd7aab3d>\",\"Content-Length\":\"991746\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0cc10b71-0eee-414a-9318-f61e6c594c73>\",\"WARC-Concurrent-To\":\"<urn:uuid:85603207-9e5d-474c-bafa-86bd0ac8e491>\",\"WARC-IP-Address\":\"52.216.160.67\",\"WARC-Target-URI\":\"https://rstudio-pubs-static.s3.amazonaws.com/7953_4e3efd5b9415444ca065b1167862c349.html\",\"WARC-Payload-Digest\":\"sha1:C5USMBPRCHP5BFTW3JR7LSHQF7YOGDRZ\",\"WARC-Block-Digest\":\"sha1:ECOY4HSJPUOHBUMTLW362X72QQ3ZGZ6V\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-10/CC-MAIN-2020-10_segments_1581875145767.72_warc_CC-MAIN-20200223093317-20200223123317-00061.warc.gz\"}"} |
https://www.allaboutcircuits.com/worksheets/bipolar-transistor-biasing-circuits/ | [
"Bipolar Transistor Biasing Circuits\n\nDiscrete Semiconductor Devices and Circuits\n\n• Question 1\n\n Don’t just sit there! Build something!!\n\nLearning to mathematically analyze circuits requires much study and practice. Typically, students practice by working through lots of sample problems and checking their answers against those provided by the textbook or the instructor. While this is good, there is a much better way.\n\nYou will learn much more by actually building and analyzing real circuits, letting your test equipment provide the “answers” instead of a book or another person. For successful circuit-building exercises, follow these steps:\n\n1. Carefully measure and record all component values prior to circuit construction, choosing resistor values high enough to make damage to any active components unlikely.\n2. Draw the schematic diagram for the circuit to be analyzed.\n3. Carefully build this circuit on a breadboard or other convenient medium.\n4. Check the accuracy of the circuit’s construction, following each wire to each connection point, and verifying these elements one-by-one on the diagram.\n5. Mathematically analyze the circuit, solving for all voltage and current values.\n6. Carefully measure all voltages and currents, to verify the accuracy of your analysis.\n7. If there are any substantial errors (greater than a few percent), carefully check your circuit’s construction against the diagram, then carefully re-calculate the values and re-measure.\n\nWhen students are first learning about semiconductor devices, and are most likely to damage them by making improper connections in their circuits, I recommend they experiment with large, high-wattage components (1N4001 rectifying diodes, TO-220 or TO-3 case power transistors, etc.), and using dry-cell battery power sources rather than a benchtop power supply. This decreases the likelihood of component damage.\n\nAs usual, avoid very high and very low resistor values, to avoid measurement errors caused by meter “loading” (on the high end) and to avoid transistor burnout (on the low end). I recommend resistors between 1 kΩ and 100 kΩ.\n\nOne way you can save time and reduce the possibility of error is to begin with a very simple circuit and incrementally add components to increase its complexity after each analysis, rather than building a whole new circuit for each practice problem. Another time-saving technique is to re-use the same components in a variety of different circuit configurations. This way, you won’t have to measure any component’s value more than once.\n\n• Question 2\n\nComplete the table of output voltages for several given values of input voltage in this common-collector amplifier circuit. Assume that the transistor is a standard silicon NPN unit, with a nominal base-emitter junction forward voltage of 0.7 volts:",
null,
"Vin Vout 0.0 V 0.5 V 1.0 V 1.5 V 5.0 V 7.8 V\n\nBased on the values you calculate, explain why the common-collector circuit configuration is often referred to as an emitter follower.\n\n• Question 3\n\nDescribe what the output voltage of this transistor circuit will do (measured with reference to ground), if the potentiometer wiper begins at the full-down position (common with ground), and is slowly moved in the upward direction (closer to V):",
null,
"• Question 4\n\nDescribe what the output voltage of this transistor circuit will do (measured with reference to ground), if the input voltage ramps from 0 volts to -10 volts (measured with respect to ground):",
null,
"• Question 5\n\nIf we were to apply a sinusoidal AC signal to the input of this transistor amplifier circuit, the output would definitely not be sinusoidal:",
null,
"It should be apparent that only portions of the input are being reproduced at the output of this circuit. The rest of the waveform seems to be “missing,” being replaced by a flat line. Explain why this transistor circuit is not able to amplify the entire waveform.\n\n• Question 6\n\nClass-A operation may be obtained from this simple transistor circuit if the input voltage (Vin) is “biased” with a series-connected DC voltage source:",
null,
"First, define what “Class A” amplifier operation is. Then, explain why biasing is required for this transistor to achieve it.\n\n• Question 7\n\nExplain how the following bias networks function:",
null,
"Each one has the same basic purpose, but works in a different way to accomplish it. Describe the purpose of any biasing network in an AC signal amplifier, and comment on the different means of accomplishing this purpose employed by each of the three circuits.\n\nHint: imagine if the AC signal source in each circuit were turned off (replaced with a short). Explain how each biasing network maintains the transistor in a partially “on” state at all times even with no AC signal input.\n\n• Question 8\n\nDescribe what the output voltage of this transistor circuit will do (measured with reference to ground), if the potentiometer wiper begins at the full-down position (common with ground), and is slowly moved in the upward direction (closer to V):",
null,
"• Question 9\n\nIf we were to apply a sinusoidal AC signal to the input of this transistor amplifier circuit, the output would definitely not be sinusoidal:",
null,
"It should be apparent that only portions of the input are being amplified in this circuit. The rest of the waveform seems to be “missing” in the output, being replaced by a flat line. Explain why this transistor circuit is not able to amplify the entire waveform.\n\n• Question 10\n\nClass-A operation may be obtained from this simple transistor circuit if the input voltage (Vin) is “biased” with a series-connected DC voltage source:",
null,
"First, define what “Class A” amplifier operation is. Then, explain why biasing is required for this transistor to achieve it.\n\n• Question 11\n\nExplain how the following bias networks function:",
null,
"Each one has the same basic purpose, but works in a different way to accomplish it. Describe the purpose of any biasing network in an AC signal amplifier, and comment on the different means of accomplishing this purpose employed by each of the three circuits.\n\n• Question 12\n\nA very common method of providing bias voltage for transistor amplifier circuits is with a voltage divider:",
null,
"However, if we were to directly connect a source of AC signal voltage to the junction between the two voltage divider resistors, the circuit would most likely function as if there were no voltage divider network in place at all:",
null,
"Instead, circuit designers usually place a coupling capacitor between the signal source and the voltage divider junction, like this:",
null,
"Explain why a coupling capacitor is necessary to allow the voltage divider to work in harmony with the AC signal source. Also, identify what factors would be relevant in deciding the size of this coupling capacitor.\n\n• Question 13\n\nExplain how it is possible for a fault in the biasing circuitry of a transistor amplifier to completely kill the (AC) output of that amplifier. How and why can a shift in DC bias voltage have an effect on the AC signal being amplified?\n\n• Question 14\n\nA student builds the following circuit and connects an oscilloscope to its output:",
null,
"The waveform shown on the oscilloscope display looks like this:",
null,
"Definitely not Class-A operation! Suspecting a problem with the input waveform, the student disconnects the oscilloscope probe from the amplifier output and moves it over to the amplifier input terminal. There, the following waveform is seen:",
null,
"How can this amplifier circuit be producing such a distorted output waveform with such a clean input waveform? Explain your answer.\n\n• Question 15\n\nSuppose you were building a Class-A transistor amplifier for audio frequency use, but did not have an oscilloscope available to check the output waveform for the presence of “clipping” caused by improper biasing. You do, however, have a pair of audio headphones you may use to listen to the signals.\n\nExplain how you would use a pair of headphones to check for the presence of severe distortion in a waveform.\n\n• Question 16\n\nCalculate the approximate quiescent (DC) base current for this transistor circuit, assuming an AC input voltage of 0 volts, and a silicon transistor:",
null,
"• Question 17\n\nCalculate the potentiometer wiper voltage (Vbias) required to maintain the transistor right at the threshold between cutoff and active mode. Then, calculate the input voltage required to drive the transistor right to the threshold between active mode and saturation. Assume ideal silicon transistor behavior, with a constant β of 100:",
null,
"• Question 18\n\nWhen inserting a signal coupling capacitor into the bias network for this transistor amplifier, which way should the (polarized) capacitor go? (Hint: the AC signal source outputs pure AC, with a time-averaged DC value of 0 volts).",
null,
"Explain why the orientation of this capacitor matters, and what might happen if it is connected the wrong way.\n\n• Question 19\n\nDescribe how proper biasing is accomplished in this headphone amplifier circuit (suitable for amplifying the audio output of a small radio):",
null,
"Also, describe the functions of the 10 kΩ potentiometer and the 22 μF capacitor.\n\n• Question 20\n\nThe following circuit is a three-channel audio mixer circuit, used to blend and amplify three different audio signals (coming from microphones or other signal sources):",
null,
"Suppose we measured a 9 kHz sinusoidal voltage of 0.5 volts (peak) at point Ä” in the diagram, using an oscilloscope. Determine the voltage at point “B” in the circuit, after this AC signal voltage “passes through” the voltage divider biasing network.\n\nThe voltage at point “B” will be a mix of AC and DC, so be sure to express both quantities! Ignore any “loading” effects of the transistor’s base current on the voltage divider.",
null,
""
] | [
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"https://sub.allaboutcircuits.com/images/quiz/02224x01.png",
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"https://sub.allaboutcircuits.com/images/quiz/02220x01.png",
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"https://sub.allaboutcircuits.com/images/quiz/00748x03.png",
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"https://sub.allaboutcircuits.com/images/quiz/00823x01.png",
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"https://sub.allaboutcircuits.com/images/quiz/00824x01.png",
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"https://sub.allaboutcircuits.com/images/quiz/01592x01.png",
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https://docs.astropy.org/en/stable/nddata/index.html | [
"# N-dimensional datasets (astropy.nddata)¶\n\n## Introduction¶\n\nThe nddata package provides classes to represent images and other gridded data, some essential functions for manipulating images, and the infrastructure for package developers who wish to include support for the image classes.\n\n## Getting started¶\n\n### NDData¶\n\nThe primary purpose of NDData is to act as a container for data, metadata, and other related information like a mask.\n\nAn NDData object can be instantiated by passing it an n-dimensional numpy array:\n\n>>> import numpy as np\n>>> from astropy.nddata import NDData\n>>> array = np.zeros((12, 12, 12)) # a 3-dimensional array with all zeros\n>>> ndd1 = NDData(array)\n\n\nor something that can be converted to an numpy.ndarray:\n\n>>> ndd2 = NDData([1, 2, 3, 4])\n>>> ndd2\nNDData([1, 2, 3, 4])\n\n\nand can be accessed again via the data attribute:\n\n>>> ndd2.data\narray([1, 2, 3, 4])\n\n\nIt also supports additional properties like a unit or mask for the data, a wcs (world coordinate system) and uncertainty of the data and additional meta attributes:\n\n>>> data = np.array([1,2,3,4])\n>>> mask = data > 2\n>>> unit = 'erg / s'\n>>> from astropy.nddata import StdDevUncertainty\n>>> uncertainty = StdDevUncertainty(np.sqrt(data)) # representing standard deviation\n>>> meta = {'object': 'fictional data.'}\n>>> from astropy.coordinates import SkyCoord\n>>> wcs = SkyCoord('00h42m44.3s', '+41d16m09s')\n... meta=meta, wcs=wcs)\n>>> ndd\nNDData([1, 2, 3, 4])\n\n\nThe representation only displays the data; the other attributes need to be accessed directly, for example ndd.mask to access the mask.\n\n### NDDataRef¶\n\nBuilding upon this pure container NDDataRef implements:\n\n• a read and write method to access astropy’s unified file io interface.\n\n• simple arithmetics like addition, subtraction, division and multiplication.\n\n• slicing.\n\nInstances are created in the same way:\n\n>>> from astropy.nddata import NDDataRef\n>>> ndd = NDDataRef(ndd)\n>>> ndd\nNDDataRef([1, 2, 3, 4])\n\n\nBut also support arithmetic (NDData Arithmetic) like addition:\n\n>>> import astropy.units as u\n>>> ndd2 = ndd.add([4, -3.5, 3, 2.5] * u.erg / u.s)\n>>> ndd2\nNDDataRef([ 5. , -1.5, 6. , 6.5])\n\n\nBecause these operations have a wide range of options these are not available using arithmetic operators like +.\n\nSlicing or indexing (Slicing and Indexing NDData) is possible (issuing warnings if some attribute cannot be sliced):\n\n>>> ndd2[2:] # discard the first two elements\nINFO: wcs cannot be sliced. [astropy.nddata.mixins.ndslicing]\nNDDataRef([6. , 6.5])\n>>> ndd2 # get the second element\nINFO: wcs cannot be sliced. [astropy.nddata.mixins.ndslicing]\nNDDataRef(-1.5)\n\n\n### Working with two-dimensional data like images¶\n\nThough the nddata package supports any kind of gridded data, this introduction will focus on the use of nddata for two-dimensional images. To get started, we’ll construct a two-dimensional image with a few sources, some Gaussian noise, and a “cosmic ray” which we will later mask out:\n\n>>> import numpy as np\n>>> from astropy.modeling.models import Gaussian2D\n>>> y, x = np.mgrid[0:500, 0:600]\n>>> data = (Gaussian2D(1, 150, 100, 20, 10, theta=0.5)(x, y) +\n... Gaussian2D(0.5, 400, 300, 8, 12, theta=1.2)(x,y) +\n... Gaussian2D(0.75, 250, 400, 5, 7, theta=0.23)(x,y) +\n... Gaussian2D(0.9, 525, 150, 3, 3)(x,y) +\n... Gaussian2D(0.6, 200, 225, 3, 3)(x,y))\n>>> data += 0.01 * np.random.randn(500, 600)\n>>> cosmic_ray_value = 0.997\n>>> data[100, 300:310] = cosmic_ray_value\n\n\nThis image has a large “galaxy” in the lower left and the “cosmic ray” is the horizontal line in the lower middle of the image:\n\n>>> import matplotlib.pyplot as plt\n>>> plt.imshow(data, origin='lower')\n\n\n()",
null,
"The “cosmic ray” can be masked out, in this simple test image, like this:\n\n>>> mask = (data == cosmic_ray_value)\n\n\n### CCDData class for images¶\n\nThe CCDData object, like the other objects in this package, can store the data, a mask, and metadata. The CCDData object requires that a unit be specified:\n\n>>> from astropy.nddata import CCDData\n... meta={'object': 'fake galaxy', 'filter': 'R'},\n\n\n### Slicing¶\n\nSlicing the works the way you would expect, with the mask and, if present, WCS, sliced appropriately also:\n\n>>> ccd2 = ccd[:200, :]\n>>> ccd2.data.shape\n(200, 600)\n(200, 600)\n>>> # Show the mask in a region around the cosmic ray:\narray([[False, False, False, False, False, False, False, False, False,\nFalse, False, False],\n[False, True, True, True, True, True, True, True, True,\nTrue, True, False],\n[False, False, False, False, False, False, False, False, False,\nFalse, False, False]]...)\n\n\nFor many applications it may be more convenient to use Cutout2D, described in image_utilities.\n\n### Image arithmetic, including uncertainty¶\n\nMethods are provided for basic arithmetic operations between images, including propagation of uncertainties. Three uncertainty types are supported: variance (VarianceUncertainty), standard deviation (StdDevUncertainty) and inverse variance (InverseVariance). The example below creates an uncertainty that is simply Poisson error, stored as a variance:\n\n>>> from astropy.nddata import VarianceUncertainty\n>>> poisson_noise = np.ma.sqrt(np.ma.abs(ccd.data))\n>>> ccd.uncertainty = VarianceUncertainty(poisson_noise ** 2)\n\n\nAs a convenience, the uncertainty can also be set with a numpy array. In that case, the uncertainty is assumed to be the standard deviation:\n\n>>> ccd.uncertainty = poisson_noise\nINFO: array provided for uncertainty; assuming it is a StdDevUncertainty. [astropy.nddata.ccddata]\n\n\nIf we make a copy of the image and add that to the original, the uncertainty changes as expected:\n\n>>> ccd2 = ccd.copy()\n>>> added_ccds.uncertainty.array[0, 0] / ccd.uncertainty.array[0, 0] / np.sqrt(2)\n0.99999999999999989\n\n\nA CCDData can be saved to a FITS file:\n\n>>> ccd.write('test_file.fits')\n\n\nand can also be read in from a FITS file:\n\n>>> ccd2 = CCDData.read('test_file.fits')\n\n\nNote the unit is stored in the BUNIT keyword in the header on saving, and is read from the header if it is present.\n\nDetailed help on the available keyword arguments for reading and writing can be obtained via the help() method as follows:\n\n>>> CCDData.read.help('fits') # Get help on the CCDData FITS reader\n>>> CCDData.writer.help('fits') # Get help on the CCDData FITS writer\n\n\n### Image utilities¶\n\n#### Cutouts¶\n\nThough slicing directly is one way to extract a subframe, Cutout2D provides more convenient access to cutouts from the data. The example below pulls out the large “galaxy” in the lower left of the image, with the center of the cutout at position:\n\n>>> from astropy.nddata import Cutout2D\n>>> position = (149.7, 100.1)\n>>> size = (81, 101) # pixels\n>>> cutout = Cutout2D(ccd, position, size)\n>>> plt.imshow(cutout.data, origin='lower')\n\n\n()",
null,
"This cutout can also plot itself on the original image:\n\n>>> plt.imshow(ccd, origin='lower')\n>>> cutout.plot_on_original(color='white')\n\n\n()",
null,
"The cutout also provides methods for find pixel coordinates in the original or in the cutout; recall that position is the center of the cutout in the original image:\n\n>>> position\n(149.7, 100.1)\n>>> cutout.to_cutout_position(position)\n(49.7, 40.099999999999994)\n>>> cutout.to_original_position((49.7, 40.099999999999994))\n(149.7, 100.1)\n\n\nFor more details, including constructing a cutout from world coordinates and the options for handling cutouts that go beyond the bounds of the original image, see 2D Cutout Images.\n\n#### Image resizing¶\n\nThe functions block_reduce and block_replicate resize images. The example below reduces the size of the image by a factor of 4. Note that the result is a numpy.ndarray; the mask, metadata, etc are discarded:\n\n>>> from astropy.nddata import block_reduce, block_replicate\n>>> smaller = block_reduce(ccd, 4)\n>>> smaller\narray(...)\n>>> plt.imshow(smaller, origin='lower')\n\n\n()",
null,
"By default, both block_reduce and block_replicate conserve flux.\n\n### Other image classes¶\n\nThere are two less restrictive classes, NDDataArray and NDDataRef, that can be used to hold image data. They are primarily of interest to those who may want to create their own image class by subclassing from one of the classes in the nddata package. The main differences between them are:\n\n• NDDataRef can be sliced and has methods for basic arithmetic operations, but the user needs to use one of the uncertainty classes to define an uncertainty. See NDDataRef for more detail. Most of its properties must be set when the object is created because they are not mutable.\n\n• NDDataArray extends NDDataRef by adding the methods necessary to all it to behave like a numpy array in expressions and adds setters for several properties. It lacks the ability to automatically recognize and read data from FITS files and does not attempt to automatically set the WCS property.\n\n• CCDData extends NDDataArray by setting up a default uncertainty class, sets up straightforward read/write to FITS files, automatically sets up a WCS property.\n\n### More general gridded data class¶\n\nThere are two additional classes in the nddata package that are of interest primarily to people that either need a custom image class that goes beyond the classes discussed so far or who are working with gridded data that is not an image.\n\n• NDData is a container class for holding general gridded data. It includes a handful of basic attributes, but no slicing or arithmetic. More information about this class is in NDData.\n\n• NDDataBase is an abstract base class that developers of new gridded data classes can subclass to declare that the new class follows the NDData interface. More details are in Subclassing.\n\nThe list of packages below that use the nddata framework is intended to be useful to either people writing their own image classes or for those looking for an image class that goes beyond what CCDData does.\n\n## Performance Tips¶\n\n• Using the uncertainty class VarianceUncertainty will be somewhat more efficient than the other two uncertainty classes, InverseVariance and StdDevUncertainty. The latter two are converted to variance for the purposes of error propagation and then converted from variance back to the original uncertainty type. The performance difference should be small.\n\n• When possible, mask values by setting them to np.nan and use the Numpy functions and methods that automatically exclude np.nan, like np.nanmedian and np.nanstd. That will typically be much faster than using numpy.ma.MaskedArray.\n\n## Reference/API¶\n\n### astropy.nddata Package¶\n\nThe astropy.nddata subpackage provides the NDData class and related tools to manage n-dimensional array-based data (e.g. CCD images, IFU Data, grid-based simulation data, …). This is more than just numpy.ndarray objects, because it provides metadata that cannot be easily provided by a single array.\n\n#### Functions¶\n\n add_array(array_large, array_small, position) Add a smaller array at a given position in a larger array. bitfield_to_boolean_mask(bitfield[, …]) Converts an array of bit fields to a boolean (or integer) mask array according to a bit mask constructed from the supplied bit flags (see ignore_flags parameter). block_reduce(data, block_size[, func]) Downsample a data array by applying a function to local blocks. block_replicate(data, block_size[, conserve_sum]) Upsample a data array by block replication. extract_array(array_large, shape, position) Extract a smaller array of the given shape and position from a larger array. fits_ccddata_reader(filename[, hdu, unit, …]) Generate a CCDData object from a FITS file. fits_ccddata_writer(ccd_data, filename[, …]) Write CCDData object to FITS file. interpret_bit_flags(bit_flags[, flip_bits]) Converts input bit flags to a single integer value (bit mask) or None. overlap_slices(large_array_shape, …[, mode]) Get slices for the overlapping part of a small and a large array. subpixel_indices(position, subsampling) Convert decimal points to indices, given a subsampling factor. support_nddata([_func, accepts, repack, …]) Decorator to wrap functions that could accept an NDData instance with its properties passed as function arguments.\n\n#### Classes¶\n\n CCDData(*args, **kwd) A class describing basic CCD data. Conf Configuration parameters for astropy.nddata. Cutout2D(data, position, size[, wcs, mode, …]) Create a cutout object from a 2D array. FlagCollection(*args, **kwargs) The purpose of this class is to provide a dictionary for containing arrays of flags for the NDData class. IncompatibleUncertaintiesException This exception should be used to indicate cases in which uncertainties with two different classes can not be propagated. InverseVariance([array, copy, unit]) Inverse variance uncertainty assuming first order Gaussian error propagation. MissingDataAssociationException This exception should be used to indicate that an uncertainty instance has not been associated with a parent NDData object. NDArithmeticMixin Mixin class to add arithmetic to an NDData object. NDData(data[, uncertainty, mask, wcs, meta, …]) A container for numpy.ndarray-based datasets, using the NDDataBase interface. NDDataArray(data, *args[, flags]) An NDData object with arithmetic. Base metaclass that defines the interface for N-dimensional datasets with associated meta information used in astropy. NDDataRef(data[, uncertainty, mask, wcs, …]) Implements NDData with all Mixins. NDIOMixin Mixin class to connect NDData to the astropy input/output registry. NDSlicingMixin Mixin to provide slicing on objects using the NDData interface. NDUncertainty([array, copy, unit]) This is the metaclass for uncertainty classes used with NDData. NoOverlapError Raised when determining the overlap of non-overlapping arrays. PartialOverlapError Raised when arrays only partially overlap. StdDevUncertainty([array, copy, unit]) Standard deviation uncertainty assuming first order gaussian error propagation. UnknownUncertainty([array, copy, unit]) This class implements any unknown uncertainty type. VarianceUncertainty([array, copy, unit]) Variance uncertainty assuming first order Gaussian error propagation.\n\nA module that provides functions for manipulating bit masks and data quality (DQ) arrays.\n\n#### Functions¶\n\n bitfield_to_boolean_mask(bitfield[, …]) Converts an array of bit fields to a boolean (or integer) mask array according to a bit mask constructed from the supplied bit flags (see ignore_flags parameter). interpret_bit_flags(bit_flags[, flip_bits]) Converts input bit flags to a single integer value (bit mask) or None.\n\n### astropy.nddata.utils Module¶\n\nThis module includes helper functions for array operations.\n\n#### Functions¶\n\n extract_array(array_large, shape, position) Extract a smaller array of the given shape and position from a larger array. add_array(array_large, array_small, position) Add a smaller array at a given position in a larger array. subpixel_indices(position, subsampling) Convert decimal points to indices, given a subsampling factor. overlap_slices(large_array_shape, …[, mode]) Get slices for the overlapping part of a small and a large array. block_reduce(data, block_size[, func]) Downsample a data array by applying a function to local blocks. block_replicate(data, block_size[, conserve_sum]) Upsample a data array by block replication.\n\n#### Classes¶\n\n NoOverlapError Raised when determining the overlap of non-overlapping arrays. PartialOverlapError Raised when arrays only partially overlap. Cutout2D(data, position, size[, wcs, mode, …]) Create a cutout object from a 2D array."
] | [
null,
"https://docs.astropy.org/en/stable/_images/index-11.png",
null,
"https://docs.astropy.org/en/stable/_images/index-22.png",
null,
"https://docs.astropy.org/en/stable/_images/index-32.png",
null,
"https://docs.astropy.org/en/stable/_images/index-42.png",
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.73337036,"math_prob":0.8172595,"size":14529,"snap":"2019-43-2019-47","text_gpt3_token_len":3675,"char_repetition_ratio":0.136179,"word_repetition_ratio":0.13339262,"special_character_ratio":0.2527359,"punctuation_ratio":0.16580118,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95353335,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,3,null,1,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-11-15T21:09:38Z\",\"WARC-Record-ID\":\"<urn:uuid:3cf3ebd9-3e98-4a9c-b0cb-8ab06a4bd5c4>\",\"Content-Length\":\"82582\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f4a2bdcb-5846-43f4-9d92-523ca3e8165d>\",\"WARC-Concurrent-To\":\"<urn:uuid:d1876a20-a53b-41ae-a3cb-68472733288b>\",\"WARC-IP-Address\":\"104.17.32.82\",\"WARC-Target-URI\":\"https://docs.astropy.org/en/stable/nddata/index.html\",\"WARC-Payload-Digest\":\"sha1:CSNZVHW6XSNCZ445P4V2I7IJJWU7IUXX\",\"WARC-Block-Digest\":\"sha1:RAEMXUHSJDKO5VTJ2AWSN4MZJSY2N2YI\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-47/CC-MAIN-2019-47_segments_1573496668712.57_warc_CC-MAIN-20191115195132-20191115223132-00468.warc.gz\"}"} |
https://mathematica.stackexchange.com/questions/265229/series-for-1xm-with-specific-notation | [
"# Series for $(1+x)^{m}$ with specific notation\n\nI'm trying to get mathematicas series function for $$(1+x)^{m}$$ to output a result that look like this:\n\n$$(1+x)^{m} = \\sum_{n=0}^{\\infty} \\frac{m !}{n !(m-n) !}x^{n}$$\n\nHowever,\n\nClear[\"Global*\"];\nseries[expr_, x_, x0_] :=\nDefer[expr = Sum[#, {n, 0, \\[Infinity]}]] &[\nFullSimplify@\nSeriesCoefficient[expr, {x, x0, n},\nAssumptions -> {n >= 0}] (x - x0)^n]\nseries[(1 + x)^m, x, 0]\n\n\n$$(1+x)^{m}=\\sum_{n=0}^{\\infty} x^{n}$$ Binomial $$[m, n]$$\n\nHow can I get the form without special function Binomial[m,n]?\n\n$$\\sum_{n=0}^{\\infty} x^{n}$$ Binomial $$[m, n] ---> \\sum_{n=0}^{\\infty} \\frac{m !}{n !(m-n) !}x^{n}$$\n\nI know that this result can be achieved by slightly modifying the code, but I have tried and can't do it yet.\n\n• \"but I have tried and can't do it yet\" Then what did you try? Mar 16 at 11:11\n• @xzczd Because FunctionExpand[Binomial[m, n]]==Gamma[1 + m]/(Gamma[1 + m - n] Gamma[1 + n]), so I modified some code in ComplexityFunction -> ((LeafCount@# + 10 Count[#, _Gamma | _Pochhammer, {0, \\[Infinity]}]) &). But I can't get the result. Mar 16 at 11:19\n• (Binomial[m, n] // FunctionExpand[#] &) /. Gamma[1 + a_] :> Factorial[a] // TraditionalForm\n– Syed\nMar 16 at 11:20\n• Simply define a rule: your expression /. Binomial[m_, n_] -> m!/(n! (m - n)!) Mar 16 at 11:54\n• @Syed I believe Gamma[a_] :> Factorial[a-1] is more robust (e.g. works on Gamma[2+n] and Gamma[n] etc.). Alternatively, one could simply write the rule to transform Binomial into factorials directly. Mar 16 at 16:48\n\nbitofac[test_] := test /. Binomial[n_, k_] -> n!/k!/(n - k)!\nseries[expr_, x_, x0_] :=\nDefer[expr = Sum[#, {n, 0, \\[Infinity]}]] &[\nFullSimplify@\nSeriesCoefficient[expr, {x, x0, n},\nAssumptions -> {n >= 0}] (x - x0)^n] // bitofac\nseries[(1 + x)^m, x, 0]",
null,
"Sadly, OP fails to understand the hint, so:\n\nseries[expr_, x_, x0_] :=\nDefer[expr = Sum[#, {n, 0, ∞}]] &[\nFullSimplify[#, Assumptions -> {m >= n >= 0 && {n, m} ∈ Integers}] &@\nFunctionExpand@SeriesCoefficient[expr, {x, x0, n}] (x - x0)^n]\nseries[(1 + x)^m, x, 0]\n`"
] | [
null,
"https://i.stack.imgur.com/DAfxE.png",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.55502915,"math_prob":0.9979631,"size":1304,"snap":"2022-40-2023-06","text_gpt3_token_len":475,"char_repetition_ratio":0.11230769,"word_repetition_ratio":0.011049724,"special_character_ratio":0.39187115,"punctuation_ratio":0.1835206,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99996746,"pos_list":[0,1,2],"im_url_duplicate_count":[null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-10-04T02:51:42Z\",\"WARC-Record-ID\":\"<urn:uuid:b9218355-81ab-421b-b9c6-382953a4bcf3>\",\"Content-Length\":\"239917\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:aa882719-d249-4166-9f01-b65f7dfa44b8>\",\"WARC-Concurrent-To\":\"<urn:uuid:6a66ea98-bb5b-405f-bda6-968d009a848e>\",\"WARC-IP-Address\":\"151.101.1.69\",\"WARC-Target-URI\":\"https://mathematica.stackexchange.com/questions/265229/series-for-1xm-with-specific-notation\",\"WARC-Payload-Digest\":\"sha1:5DEEEV3OBX3WDDQYOTFS2TL7DHV3B2HT\",\"WARC-Block-Digest\":\"sha1:PHF7MQZS4WGBNHVFCKQ7ZIF3I4UE2I6R\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030337473.26_warc_CC-MAIN-20221004023206-20221004053206-00733.warc.gz\"}"} |
http://www.kylesconverter.com/area-density/bushels-per-thousand-square-feet-to-grams-per-square-meter | [
"# Convert Bushels Per Thousand Square Feet to Grams Per Square Meter\n\n### Kyle's Converter > Area Density > Bushels Per Thousand Square Feet > Bushels Per Thousand Square Feet to Grams Per Square Meter\n\n Bushels Per Thousand Square Feet (bsh/MSF) Grams Per Square Meter (g/m2) Precision: 0 1 2 3 4 5 6 7 8 9 12 15 18\nReverse conversion?\nGrams Per Square Meter to Bushels Per Thousand Square Feet\n(or just enter a value in the \"to\" field)\n\nPlease share if you found this tool useful:\n\nUnit Descriptions\n1 Bushel per Thousand Square Feet:\nMass of bushels per area of a thousand square feet. Using a bushel of wheat having 60 pounds. 1 bsh/MSF ? 0.292 945 658 182 983 kg/m2.\n1 Gram per Square Meter:\nMass of grams per an area of a square meter. 1 g/m2 = 0.001 kg/m2.\n\nLink to Your Exact Conversion\n\nConversions Table\n1 Bushels Per Thousand Square Feet to Grams Per Square Meter = 292.945770 Bushels Per Thousand Square Feet to Grams Per Square Meter = 20506.1961\n2 Bushels Per Thousand Square Feet to Grams Per Square Meter = 585.891380 Bushels Per Thousand Square Feet to Grams Per Square Meter = 23435.6527\n3 Bushels Per Thousand Square Feet to Grams Per Square Meter = 878.83790 Bushels Per Thousand Square Feet to Grams Per Square Meter = 26365.1092\n4 Bushels Per Thousand Square Feet to Grams Per Square Meter = 1171.7826100 Bushels Per Thousand Square Feet to Grams Per Square Meter = 29294.5658\n5 Bushels Per Thousand Square Feet to Grams Per Square Meter = 1464.7283200 Bushels Per Thousand Square Feet to Grams Per Square Meter = 58589.1316\n6 Bushels Per Thousand Square Feet to Grams Per Square Meter = 1757.6739300 Bushels Per Thousand Square Feet to Grams Per Square Meter = 87883.6975\n7 Bushels Per Thousand Square Feet to Grams Per Square Meter = 2050.6196400 Bushels Per Thousand Square Feet to Grams Per Square Meter = 117178.2633\n8 Bushels Per Thousand Square Feet to Grams Per Square Meter = 2343.5653500 Bushels Per Thousand Square Feet to Grams Per Square Meter = 146472.8291\n9 Bushels Per Thousand Square Feet to Grams Per Square Meter = 2636.5109600 Bushels Per Thousand Square Feet to Grams Per Square Meter = 175767.3949\n10 Bushels Per Thousand Square Feet to Grams Per Square Meter = 2929.4566800 Bushels Per Thousand Square Feet to Grams Per Square Meter = 234356.5265\n20 Bushels Per Thousand Square Feet to Grams Per Square Meter = 5858.9132900 Bushels Per Thousand Square Feet to Grams Per Square Meter = 263651.0924\n30 Bushels Per Thousand Square Feet to Grams Per Square Meter = 8788.36971,000 Bushels Per Thousand Square Feet to Grams Per Square Meter = 292945.6582\n40 Bushels Per Thousand Square Feet to Grams Per Square Meter = 11717.826310,000 Bushels Per Thousand Square Feet to Grams Per Square Meter = 2929456.5818\n50 Bushels Per Thousand Square Feet to Grams Per Square Meter = 14647.2829100,000 Bushels Per Thousand Square Feet to Grams Per Square Meter = 29294565.8183\n60 Bushels Per Thousand Square Feet to Grams Per Square Meter = 17576.73951,000,000 Bushels Per Thousand Square Feet to Grams Per Square Meter = 292945658.183"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.5819517,"math_prob":0.99403,"size":2314,"snap":"2019-13-2019-22","text_gpt3_token_len":642,"char_repetition_ratio":0.35064936,"word_repetition_ratio":0.5412371,"special_character_ratio":0.35782194,"punctuation_ratio":0.081018515,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9738258,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-05-22T23:10:10Z\",\"WARC-Record-ID\":\"<urn:uuid:2789aac0-bad6-4680-852f-be18b0760de3>\",\"Content-Length\":\"20609\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6e5afdb2-e107-49eb-b659-c6bceb15cf64>\",\"WARC-Concurrent-To\":\"<urn:uuid:4a9e4f64-65c4-40d1-80a8-cd270f39265a>\",\"WARC-IP-Address\":\"99.84.222.157\",\"WARC-Target-URI\":\"http://www.kylesconverter.com/area-density/bushels-per-thousand-square-feet-to-grams-per-square-meter\",\"WARC-Payload-Digest\":\"sha1:6B3JBDMJWJTN3IK272E4JZT35CM4SIB4\",\"WARC-Block-Digest\":\"sha1:C7DRG3ASMDVQG3FUD3RWDBO2IBT53XIY\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-22/CC-MAIN-2019-22_segments_1558232256980.46_warc_CC-MAIN-20190522223411-20190523005411-00094.warc.gz\"}"} |
https://discuss.codechef.com/t/smallnum-editorial/100118 | [
"",
null,
"# SMALLNUM - Editorial\n\nMIN OPERATION\nAuthor: alpha_1205\nTester: anert\nEditorialist:anert\n\nCakewalk\n\n# PROBLEM:\n\nYou are given two arrays, namely a and b, of size n. Your task is to find the minimum possible steps to convert a such that the smallest integer in array a divides all elements of array b. In each step you can delete any single element of array a which was not previously removed. If it is not possible to convert array a into required array then print -1.\n\n# Prerequisites:\n\n• Knowledge of Euclidian algorithm for calculation of the greatest common divisor.\n• Basic array manipulation.\n• Sorting algorithms.\n• Pinch of common sense",
null,
"# Hint:\n\n1. You have to find a number which is a divisor of all elements of array b.\n2. Try finding GCD of all elements of array b.\n\n# QUICK EXPLAINATION:\n\nYou will have to find the gcd of array b using Euclidian algorithm. Then you will have to sort array a in ascending order. After that, you will have to check whether the smallest element of array a divides the gcd of array b. If it fails to do so, we will remove it. We will increment the counter by one for each removal. We will print the value of counter.\n\n# Explanation:\n\nWe can solve this problem by using greedy strategy. We will find the GCD of array B using Euclid’s GCD algorithm*. We will now sort array A in ascending order and then check whether any element in array A divides the GCD of array B. Suppose any a [i] where, 1 <= i <= n divides the GCD of B, proves that it will divide the whole array B. So, we have to delete the first (i-1) components of the sorted array A.\n*Euclid’s GCD algorithm:\nIt is a greedy algorithm in which we, generally, use recursive function to calculate gcd of two integers. We continuously find remainder of number, say x, when divided by y and if it is 0, we return x, otherwise we call the function again.\n\nPseudocode:\n\n``````def gcd(x,y):\nif(y==0):\nreturn x\nreturn gcd(x,x%y)\n``````\n\nThe time complexity of this algorithm O (log (min (x,y))) and for and array it is O (log (maximum element of array)). So the overall time complexity is:\n\nO (nlog (n) + nlog (maximum (b[i]))\nThis will satisfy our constraints.\n\nSetter’s solution\n``````import java.util.Scanner;\nimport java.util.*;\nimport java.util.Arrays;\n\npublic class Main{\npublic static int gcd(int a,int b){\nint max = Math.max(a,b);\nint min = Math.min(a,b);\na = max;\nb = min;\nif(b == 0){\nreturn a;\n}\nelse return gcd(b,a%b);\n}\npublic static int gcdarray(int[]arr){\nint g = arr;\nfor(int i = 0;i<arr.length;i++){\ng = gcd(arr[i],g);\n}\nreturn g;\n}\npublic static void main(String[]args){\nScanner at = new Scanner(System.in);\nRandom rand = new Random();\nint t = at.nextInt();\nwhile(t-->0){\nint n = at.nextInt();\nint[]a = new int[n];\nint[]b = new int[n];\nfor(int i = 0;i<n;i++){\na[i] = at.nextInt();\n\n}\nfor(int i = 0;i<n;i++){\nb[i] = at.nextInt();\n}\n\nArrays.sort(a);\nint gcd = gcdarray(b);\n\nboolean ok = false;\nfor(int i = 0;i<n;i++){\nif(gcd % a[i] == 0){\nSystem.out.println(i);\nok = true;\nbreak;\n}\n}\nif(!ok){\nSystem.out.println(-1);\n}\n\n}\n}\n}\n``````\nTester’s Solution\n``````/**\n* @file gcd.cpp\n* @author Aniruddh Modi\n* @brief\n* This is testers' solution.\n* @version 0.1\n* @date 2022-02-19\n*\n* @copyright Kaha se lagaenge 😂\n*\n*/\n#include<bits/stdc++.h>\nusing namespace std;\n\nint arr_gcd(int arr[],int n){\nint x=arr;\nfor(int i=1;i<n;i++){\nx = __gcd(x,arr[i]);\n}\nreturn x;\n}\n\nint main(){\nint t;\ncin>>t;\nwhile(t--){\nint n;\ncin>>n;\nint arr1[n],arr2[n];\nfor(int i=0;i<n;i++){\ncin>>arr1[i];\n}\nfor(int i=0;i<n;i++){\ncin>>arr2[i];\n}\nsort(arr1,arr1+n);\nbool f=1;\nint ct=0,gcd = arr_gcd(arr2,n);\nfor(int i=0;i<n;i++){\nif((gcd%arr1[i])==0){\ncout<<ct<<endl;\nf=0;\nbreak;\n}\nct++;\n}\nif(f) cout<<-1<<endl;\n}\nreturn 0;\n}\n``````\nSolution in python\n``````def gcd(x,y):\nif (y == 0):\nreturn x\nelse:\nreturn gcd (y, x % y)\n\ndef arr_gcd(l,n):\ng = 0\nfor i in range(n):\ng = gcd(g,l[i])\nreturn g\n\ndef main():\nt = int(input())\nwhile t>0:\nt-=1\nn=int(input())\nl1 = list(map(int,input().strip().split()))[:n]\nl2 = list(map(int,input().strip().split()))[:n]\ng = arr_gcd(l2,n)\nl1.sort()\nfor i in range(n):\nif(g%l1[i]==0):\nprint(i)\nprint(\"\\n\")\nbreak\nelse:\nprint(-1)\nprint(\"\\n\")\n\nreturn 0\nmain()\n``````"
] | [
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"https://s3.amazonaws.com/discourseproduction/original/3X/7/f/7ffd6e5e45912aba9f6a1a33447d6baae049de81.svg",
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https://www.geeksforgeeks.org/toggling-k-th-bit-number/?ref=rp | [
"# Toggling k-th bit of a number\n\nFor a given number n, if k-th bit is 0, then toggle it to 1 and if it is 1 then, toggle it to 0.\n\nExamples :\n\n```Input : n = 5, k = 1\nOutput : 4\n5 is represented as 101 in binary\nand has its first bit 1, so toggling\nit will result in 100 i.e. 4.\n\nInput : n = 2, k = 3\nOutput : 6\n\nInput : n = 75, k = 4\nOutput : 67\n```\n\n## Recommended: Please try your approach on {IDE} first, before moving on to the solution.\n\nBelow are simple steps to find value of k-th bit\n\n```1) Left shift given number 1 by k-1 to create\na number that has only set bit as k-th bit.\ntemp = 1 << (k-1)\n2) Return bitwise XOR of temp and n. Since temp\nhas only k-th bit set, doing XOR would toggle\nonly this bit.\n```\n\nExample :\n\n``` n = 75 and k = 4\ntemp = 1 << (k-1) = 1 << 3 = 8\nBinary Representation of temp = 0..00001000\nBinary Representation of n = 0..01001011\nBitwise XOR of two numbers = 0..01000011\n```\n\n## C++\n\n `// CPP program to toggle k-th bit of n ` `#include ` `using` `namespace` `std; ` ` ` `int` `toggleKthBit(``int` `n, ``int` `k) ` `{ ` ` ``return` `(n ^ (1 << (k-1))); ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ``int` `n = 5, k = 1; ` ` ``cout << toggleKthBit(n , k); ` ` ``return` `0; ` `} `\n\n## Java\n\n ` ` `// Java program to toogle ` `// k-th bit of a number ` ` ` `class` `Toggle ` `{ ` ` ``static` `int` `toggleKthBit(``int` `n, ``int` `k) ` ` ``{ ` ` ``return` `(n ^ (``1` `<< (k-``1``))); ` ` ``} ` ` ` ` ``// main function ` ` ``public` `static` `void` `main (String[] args) ` ` ``{ ` ` ``int` `n = ``5``, k = ``1``; ` ` ``System.out.println(toggleKthBit(n , k)); ` ` ``} ` `} `\n\n## Python3\n\n `# Python3 code to toggle k-th bit of n ` ` ` `def` `toggleKthBit(n, k): ` ` ``return` `(n ^ (``1` `<< (k``-``1``))) ` ` ` `# Driver code ` `n ``=` `5` `k ``=` `1` `print``( toggleKthBit(n , k)) ` ` ` `# This code is contributed by \"Sharad_Bhardwaj\". `\n\n## C#\n\n `// C# program to toogle ` `// k-th bit of a number ` `using` `System; ` ` ` `class` `GFG { ` ` ` ` ``static` `int` `toggleKthBit(``int` `n, ``int` `k) ` ` ``{ ` ` ``return` `(n ^ (1 << (k-1))); ` ` ``} ` ` ` ` ``// main function ` ` ``public` `static` `void` `Main() ` ` ``{ ` ` ``int` `n = 5, k = 1; ` ` ` ` ``Console.WriteLine(toggleKthBit(n , k)); ` ` ``} ` `} ` ` ` `//This code is contributed by Anant Agarwal. `\n\n## PHP\n\n ` `\n\nOutput :\n\n```4\n```\n\nThis article is contributed by SAKSHI TIWARI. If you like GeeksforGeeks(We know you do!) and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.\n\nAttention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.\n\nMy Personal Notes arrow_drop_up\n\nImproved By : jit_t\n\nArticle Tags :\nPractice Tags :\n\n2\n\nPlease write to us at contribute@geeksforgeeks.org to report any issue with the above content."
] | [
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.78248036,"math_prob":0.94107217,"size":3832,"snap":"2020-45-2020-50","text_gpt3_token_len":1156,"char_repetition_ratio":0.12748171,"word_repetition_ratio":0.11533587,"special_character_ratio":0.3152401,"punctuation_ratio":0.10913706,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99899644,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-10-24T17:26:33Z\",\"WARC-Record-ID\":\"<urn:uuid:06c3d387-02c9-496d-b463-2003822aff4c>\",\"Content-Length\":\"116595\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2b0736eb-1ec5-4f53-8d3a-f15309429bc4>\",\"WARC-Concurrent-To\":\"<urn:uuid:9679b1de-805d-4180-96b1-a07a5d71b147>\",\"WARC-IP-Address\":\"23.217.129.104\",\"WARC-Target-URI\":\"https://www.geeksforgeeks.org/toggling-k-th-bit-number/?ref=rp\",\"WARC-Payload-Digest\":\"sha1:DMTWUH3YBPVKPRKRSNMHISPY6BJRMXQT\",\"WARC-Block-Digest\":\"sha1:TPXCFHAIDZXH2HH7QMPTRQPXAZGH6PSX\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-45/CC-MAIN-2020-45_segments_1603107884322.44_warc_CC-MAIN-20201024164841-20201024194841-00151.warc.gz\"}"} |
https://betterlesson.com/community/unit/7268/3-oa-multiplication-division?from=consumer_breadcrumb_dropdown | [
"# Unit: 3.OA Multiplication & Division\n\n4763 Views\n23 Favorites\n\n### Unit Description\n\nThis unit focuses on multiplication and division.\n\n### Lessons\n\n Addition and Multiplication Resources: 2 Students will relate multiplication and addition. 2,839 The Basics of Multiplication Resources: 1 Students will be able to multiply whole numbers. 2,983 The Multiplication Table Resources: 3 Students will be able to practice basic multiplication facts unsing a multiplication table. 4,689 Fact Triangles Resources: 1 Students will solve multiplication facts using fact triangles 1,967 Multiplying Whole Numbers Resources: 2 Students will create arrays in order to determine the product of two factors. 2,296 Multiplying Multi-Digits Resources: 2 Students will be able to multiply 2- and 3-digit numbers by 1-digit numbers with regrouping. 2,625 Relating Multiplication and Division Resources: 1 Students will be about to relate multiplication and division by creating fact families. 7,467 Division without Remainders Resources: 1 Students will be able to divide whole numbers 4,186 Multiply with a Numberline Resources: 1 Students will find the product of a number using a numebrline. 3,385 Multiplication with Interlocking Cubes Resources: 1 Students will understand that multiplication is the a process of combining 1,383 The Turn-Around Rule Resources: 2 Students will illustrate multiplication problems using unifix cubes, and explain the turn-around rule (or commutative property of multiplication). 4,994\n\n### Unit Resources\n\n IP_Cookie Worksheet.docx 308\nSomething went wrong. See details for more info\n Nothing to upload details close"
] | [
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.73535454,"math_prob":0.6731348,"size":1504,"snap":"2019-35-2019-39","text_gpt3_token_len":357,"char_repetition_ratio":0.24133334,"word_repetition_ratio":0.04910714,"special_character_ratio":0.23736702,"punctuation_ratio":0.1328125,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9904083,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-08-21T01:44:43Z\",\"WARC-Record-ID\":\"<urn:uuid:9f3861fa-90cd-4e11-a850-171927d9545d>\",\"Content-Length\":\"44764\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:8a9c580c-c529-41af-adbf-225227e93bd8>\",\"WARC-Concurrent-To\":\"<urn:uuid:84edac2b-328f-4023-a0f4-cbb0c68b77b3>\",\"WARC-IP-Address\":\"54.161.30.234\",\"WARC-Target-URI\":\"https://betterlesson.com/community/unit/7268/3-oa-multiplication-division?from=consumer_breadcrumb_dropdown\",\"WARC-Payload-Digest\":\"sha1:M4IELCFOJ2ZRWP2NZ55WYO5O4ARC4C2G\",\"WARC-Block-Digest\":\"sha1:FNG45C5UL43KCIKAIZNB5W4GXMJ76H3L\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-35/CC-MAIN-2019-35_segments_1566027315695.36_warc_CC-MAIN-20190821001802-20190821023802-00348.warc.gz\"}"} |
http://csample.ml/wujip/help-with-pre-algebra-wyre.php | [
"Skip Nav\n\n# Algebra Homework Help -- People's Math!\n\n## Calculators\n\n❶Talk to Splotchy , an artificial intelligence robot with funny voice.\n\n## Popular Topics",
null,
"",
null,
"",
null,
"Estimating Sums and Differences 5. Addition and Subtraction Word Problems 6. Estimating Products and Quotients Multiplication and Division Word Problems Order of Operations Graphing and Writing Integers Opposites and Absolute Value Order of Operations with Integers Integer Word Problems Combining Like Terms Introduction to Equations One-Step Addition Equations One-Step Subtraction Equations One-Step Multiplication Equations One-Step Division Equations Writing and Solving One-Step Equations Equations with Variable on Both Sides Equations with the Distributive Property Writing and Solving Multi-Step Equations Distributive Property and Combining Like Terms Equations with Variable on Both Sides and Distributive Number Word Problems Factors and Primes Multiples and Least Common Multiple Greatest Common Factor Introduction to Fractions Equivalent Fractions Part I Reducing Fractions to Lowest Terms Equivalent Fractions Part II Improper Fractions and Mixed Numbers Comparing Proper Fractions Comparing Mixed Numbers and Improper Fractions Comparing Fractions Word Problems Adding and Subtracting Like Fractions Ask questions on our question board.\n\nCreated by the people. Each section has solvers calculators , lessons, and a place where you can submit your problem to our free math tutors. To ask a question , go to a section to the right and select \"Ask Free Tutors\". Most sections have archives with hundreds of problems solved by the tutors. Lessons and solvers have all been submitted by our contributors! Numeric Fractions Decimal numbers, power of 10, rounding Operations with Signed Numbers Exponents and operations on exponents Divisibility and Prime Numbers Roman numerals Inverse operations for addition and multiplication, reciprocals Evaluation of expressions, parentheses.\n\nSquare root, cubic root, N-th root Negative and Fractional exponents Expressions involving variables, substitution Polynomials, rational expressions and equations Radicals -- complicated equations involving roots Quadratic Equation Inequalities, trichotomy Systems of equations that are not linear.\n\nConic sections - ellipse, parabola, hyperbola Sequences of numbers, series and how to sum them Probability and statistics Trigonometry Combinatorics and Permutations Unit Conversion. Geometric formulas Angles, complementary, supplementary angles Triangles Pythagorean theorem Volume, Metric volume Circles and their properties Rectangles. Length, distance, coordinates, metric length Proofs in Geometry Bodies in space, right solid, cylinder, sphere Parallelograms Points, lines, angles, perimeter Polygons Area and Surface Area.\n\nEasy, very detailed Voice and Handwriting explanations designed to help middle school and high school math students. Lessons discuss questions that cause most difficulties. Over the years, these calculators have helped students solve over 15 million equations! Our calculators don't just solve equations though. See all the problems we can help with Need to practice a new type of problem? We have tons of problems in the Worksheets section. You can compare your answers against the answer key and even see step-by-step solutions for each problem.\n\nBrowse the list of worksheets to get started Still need help after using our algebra resources? Connect with algebra tutors and math tutors nearby. Prefer to meet online? Find online algebra tutors or online math tutors in a couple of clicks.\n\nSimplifying Use this calculator if you only want to simplify, not solve an equation. Expression Factoring Factors expressions using 3 methods. Factoring and Prime Factoring Calculator. Consecutive Integer Word Problems. Simplifying and Solving Equations with Multiple Signs.",
null,
"## Main Topics\n\nFree math lessons and math homework help from basic math to algebra, geometry and beyond. Students, teachers, parents, and everyone can find solutions to their math problems instantly.\n\n### Privacy FAQs\n\nWe can help. Coolmath Pre-Algebra has a ton of really easy to follow lessons and examples. Prealgebra at Cool csample.ml: Free Pre-Algebra Lessons and Practice Problems."
] | [
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null,
"http://opaquez.com/images/pre-algebra-help.jpg",
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"http://mathplane.com/yahoo_site_admin/assets/images/pre_algebra_quick_quiz_mathplane_factors_and_multiples_b_solutions.27102040_large.jpg",
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.8797903,"math_prob":0.94638807,"size":5174,"snap":"2019-13-2019-22","text_gpt3_token_len":1005,"char_repetition_ratio":0.1402321,"word_repetition_ratio":0.13261163,"special_character_ratio":0.17008117,"punctuation_ratio":0.12050985,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99558175,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,null,null,6,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-03-23T11:16:16Z\",\"WARC-Record-ID\":\"<urn:uuid:6fddaa62-c0b2-4f16-921f-6bb0628deb33>\",\"Content-Length\":\"17896\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:bcb03e08-0252-4620-aecd-fd126050f9fa>\",\"WARC-Concurrent-To\":\"<urn:uuid:2502b904-35c3-400a-8a9e-8ad052205896>\",\"WARC-IP-Address\":\"104.18.46.18\",\"WARC-Target-URI\":\"http://csample.ml/wujip/help-with-pre-algebra-wyre.php\",\"WARC-Payload-Digest\":\"sha1:WWA57LC5KSNR2EGZ6JWFG5CM455Y7FUC\",\"WARC-Block-Digest\":\"sha1:D66XWNOIVAB6FBSVRT3BQBX2FBLNEZ7U\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-13/CC-MAIN-2019-13_segments_1552912202781.83_warc_CC-MAIN-20190323101107-20190323123107-00179.warc.gz\"}"} |
https://it.mathworks.com/help/hydro/ref/heatexchangertltl.html;jsessionid=ff300a72a0cfd2f85eb79faef698 | [
"# Heat Exchanger (TL-TL)\n\nHeat exchanger for systems with two thermal liquid flows\n\n•",
null,
"Libraries:\nSimscape / Fluids / Fluid Network Interfaces / Heat Exchangers\n\n## Description\n\nThe Heat Exchanger (TL-TL) block models the complementary cooling and heating of fluids held briefly in thermal contact across a thin conductive wall. The wall can store heat in its bounds, adding to the heat transfer a slight transient delay that scales in proportion to its thermal mass. The fluids are single phase—each a thermal liquid. Neither fluid can switch phase and so, as latent heat is never released, the exchange is strictly one of sensible heat.",
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"### Block Variants\n\nThe heat transfer model depends on the choice of block variant. The block has two variants: `E-NTU Model` and ```Simple Model```. Use the Modeling option parameter to change the variant.\n\n### `E-NTU Model`\n\nThe default variant. Its heat transfer model derives from the Effectiveness-NTU method. Heat transfer in the steady state then proceeds at a fraction of the ideal rate which the flows, if kept each at its inlet temperature, and if cleared of every thermal resistance in between, could in theory support:\n\n`${Q}_{\\text{Act}}=ϵ{Q}_{\\text{Max}},$`\n\nwhere QAct the actual heat transfer rate, QMax is the ideal heat transfer rate, and ε is the fraction of the ideal rate actually observed in a real heat exchanger encumbered with losses. The fraction is the heat exchanger effectiveness, and it is a function of the number of transfer units, or NTU, a measure of the ease with which heat moves between flows, relative to the ease with which the flows absorb that heat:\n\n`$NTU=\\frac{1}{R{C}_{\\text{Min}}},$`\n\nwhere the fraction is the overall thermal conductance between the flows and CMin is the smallest of the heat capacity rates from among the flows—that belonging to the flow least capable of absorbing heat. The heat capacity rate of a flow depends on the specific heat of the fluid (cp) and on its mass flow rate through the exchanger ($\\stackrel{˙}{m}$):\n\n`$C={c}_{\\text{p}}\\stackrel{˙}{m}.$`\n\nThe effectiveness depends also on the relative disposition of the flows, the number of passes between them, and the mixing condition for each. This dependence reflects in the effectiveness expression used, with different flow arrangements corresponding to different expressions. For a list of the effectiveness expressions, see the E-NTU Heat Transfer block.\n\nFlow Arrangement\n\nUse the Flow arrangement parameter to set how the flows meet in the heat exchanger. The flows can run parallel to each other, counter to each other, or across each other. They can also run in a pressurized shell, one through tubes enclosed in the shell, the other around those same tubes. The figure shows an example. The tube flow can make one pass through the shell flow (shown right) or, for greater exchanger effectiveness, multiple passes (left).",
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"Other flow arrangements are possible through a generic parameterization based on tabulated effectiveness data and requiring little detail about the heat exchanger. Flow arrangement, mixing condition, and number of shell or tube passes, if relevant to the heat exchanger, are assumed to manifest in the tabulated data.\n\nMixing Condition\n\nUse the Cross flow type parameter to mix each of the flows, one of the flows, or none of the flows. Mixing in this context is the lateral movement of fluid in channels that have no internal barriers, normally guides, baffles, fins, or walls. Such movement serves to even out temperature variations in the transverse plane. Mixed flows have variable temperature in the longitudinal plane alone. Unmixed flows have variable temperature in both the transverse and longitudinal planes. The figure shows a mixed flow (i) and an unmixed flow (ii).",
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"The distinction between mixed and unmixed flows is considered only in cross flow arrangements. There, longitudinal temperature variation in one fluid produces transverse temperature variation in the second fluid that mixing can even out. In counter and parallel flow arrangements, longitudinal temperature variation in one fluid produces longitudinal temperature variation in the second fluid and mixing, as it is of little effect here, is ignored.\n\nEffectiveness Curves\n\nShell-and-tube exchangers with multiple passes (iv.b-e in the figure for 2, 3, and 4 passes) are most effective. Of exchangers with a single pass, those with counter flows (ii are most effective and those with parallel flows (i) are least.\n\nCross-flow exchangers are intermediate in effectiveness, with mixing condition playing a factor. They are most effective when both flows are unmixed (iii.a) and least effective when both flows are mixed (iii.b). Mixing just the flow with the smallest heat capacity rate (iii.c) lowers the effectiveness more than mixing just the flow with the largest heat capacity rate (iii.d).",
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"Thermal Resistance\n\nThe overall thermal resistance, R, is the sum of the local resistances lining the heat transfer path. The local resistances arise from convection at the surfaces of the wall, conduction through the wall, and, if the wall sides are fouled, conduction through the layers of fouling. Expressed in order from thermal liquid side 1 to thermal liquid side 2:\n\n`$R=\\frac{1}{{U}_{\\text{1}}{A}_{\\text{Th,1}}}+\\frac{{F}_{\\text{1}}}{{A}_{\\text{Th,1}}}+{R}_{\\text{W}}+\\frac{{F}_{\\text{2}}}{{A}_{\\text{Th,2}}}+\\frac{1}{{U}_{\\text{2}}{A}_{\\text{Th,2}}},$`\n\nwhere U is the convective heat transfer coefficient, F is the fouling factor, and ATh is the heat transfer surface area, each for the flow indicated in the subscript. RW is the thermal resistance of the wall.",
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"The wall thermal resistance and fouling factors are simple constants obtained from block parameters. The heat transfer coefficients are elaborate functions of fluid properties, flow geometry, and wall friction, and derive from standard empirical correlations between Reynolds, Nusselt, and Prandtl numbers. The correlations depend on flow arrangement and mixing condition, and are detailed for each in the E-NTU Heat Transfer block on which the ```E-NTU Model``` variant is based.\n\nThermal Mass\n\nThe wall is more than a thermal resistance for heat to pass through. It is also a thermal mass and, like the flows it divides, it can store heat in its bounds. The storage slows the transition between steady states so that a thermal perturbation on one side does not promptly manifest on the side across. The lag persists for the short time that it takes the heat flow rates from the two sides to balance each other. That time interval scales with the thermal mass of the wall:\n\n`${C}_{\\text{Q,W}}={c}_{\\text{p,W}}{M}_{\\text{W}},$`\n\nwhere is the cp,W is the specific heat capacity and MW the inertial mass of the wall. Their product gives the energy required to raise wall temperature by one degree. Use the Wall thermal mass parameter to specify that product. The parameter is active when the Wall thermal dynamics setting is `On`.\n\nThermal mass is often negligible in low-pressure systems. Low pressure affords a thin wall with a transient response so fast that, on the time scale of the heat transfer, it is virtually instantaneous. The same is not true of high-pressure systems, common in the production of ammonia by the Haber process, where pressure can break 200 atmospheres. To withstand the high pressure, the wall is often thicker, and, as its thermal mass is heftier, so its transient response is slower.\n\nSet the Wall thermal dynamics parameter to `Off` to ignore the transient lag, cut the differential variables that produce it, and, in reducing calculations, speed up the rate of simulation. Leave it `On` to capture the transient lag where it has a measurable effect. Experiment with the setting if necessary to determine whether to account for thermal mass. If simulation results differ to a considerable degree, and if simulation speed is not a factor, keep the setting `On`.\n\nThe wall, if modeled with thermal mass, is considered in halves. One half sits on thermal liquid side 1 and the other half sits on thermal liquid side 2. The thermal mass divides evenly between the pair:\n\n`${C}_{\\text{Q,1}}={C}_{\\text{Q,2}}=\\frac{{C}_{\\text{Q,W}}}{2}.$`\n\nEnergy is conserved in the wall. In the simple case of a wall half at steady state, heat gained from the fluid equals heat lost to the second half. The heat flows at the rate predicted by the E-NTU method for a wall without thermal mass. The rate is positive for heat flows directed from side 1 of the heat exchanger to side 2:\n\n`${Q}_{\\text{1}}=-{Q}_{\\text{2}}=ϵ{Q}_{\\text{Max}}.$`\n\nIn the transient state, the wall is in the course of storing or losing heat, and heat gained by one half no longer equals that lost to the second half. The difference in the heat flow rates varies over time in proportion to the rate at which the wall stores or loses heat. For side 1 of the heat exchanger:\n\n`${Q}_{\\text{1}}=ϵ{Q}_{\\text{Max}}+{C}_{\\text{Q,1}}{\\stackrel{˙}{T}}_{\\text{W,1}},$`\n\nwhere ${\\stackrel{˙}{T}}_{\\text{W,1}}$ is the rate of change in temperature in the wall half. Its product with the thermal mass of the wall half gives the rate at which heat accumulates there. That rate is positive when temperature rises and negative when it drops. The closer the rate is to zero the closer the wall is to steady state. For side 2 of the heat exchanger:${Q}_{\\text{2}}=-ϵ{Q}_{\\text{Max}}+{C}_{\\text{Q,2}}{\\stackrel{˙}{T}}_{\\text{W,2}},$\n\nComposite Structure\n\nThe `E-NTU Model` variant is a composite component built from simpler blocks. A Heat Exchanger Interface (TL) block models the thermal liquid flow on side 1 of the heat exchanger. Another models the thermal liquid flow on side 2. An E-NTU Heat Transfer block models the heat exchanged across the wall between the flows. The figure shows the block connections for the `E-NTU Model` block variant.",
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"### `Simple Model`\n\nThe alternative variant. Its heat transfer model depends on the concept of specific dissipation, a measure of the heat transfer rate observed when thermal liquid 1 and thermal liquid 2 inlet temperatures differ by one degree. Its product with the inlet temperature difference gives the expected heat transfer rate:\n\n`$Q=\\xi \\left({T}_{\\text{In,1}}-{T}_{\\text{In,2}}\\right),$`\n\nwhere ξ is specific dissipation and TIn is inlet temperature for thermal liquid 1 (subscript `1`) or thermal liquid 2 (subscript `2`). The specific dissipation is a tabulated function of the mass flow rates into the exchanger through the thermal liquid 1 and thermal liquid 2 inlets:\n\n`$\\xi =f\\left({\\stackrel{˙}{m}}_{\\text{1}},{\\stackrel{˙}{m}}_{\\text{2}}\\right)$`\n\nTo accommodate reverse flows, the tabulated data can extend over positive and negative flow rates, in which case the inlets can also be thought of as outlets. The data normally derives from measurement of heat transfer rate against temperature in a real prototype:\n\n`$\\xi =\\frac{Q}{{T}_{\\text{In,1}}-{T}_{\\text{In,2}}}$`\n\nThe heat transfer model, as it relies almost entirely on tabulated data, and as that data normally derives from experiment, requires little detail about the exchanger. Flow arrangement, mixing condition, and number of shell or tube passes, if relevant to the heat exchanger modeled, are assumed to manifest entirely in the tabulated data.\n\nSee the Specific Dissipation Heat Transfer block for more detail on the heat transfer calculations.\n\nComposite Structure\n\nThe `Simple Model` variant is a composite component. A Simple Heat Exchanger Interface (TL) block models the thermal liquid flow on side 1 of the heat exchanger. Another models the thermal liquid flow on side 2. A Specific Dissipation Heat Transfer block captures the heat exchanged across the wall between the flows.",
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"## Ports\n\n### Conserving\n\nexpand all\n\nOpening for thermal liquid 1 to enter and exit its side of the heat exchanger.\n\nOpening for thermal liquid 1 to enter and exit its side of the heat exchanger.\n\nOpening for thermal liquid 2 to enter and exit its side of the heat exchanger.\n\nOpening for thermal liquid 2 to enter and exit its side of the heat exchanger.\n\n## Parameters\n\nexpand all\n\nSet the heat transfer model for the block.\n\n### Block Variant: `Simple Model`\n\nHeat Transfer Tab\n\nMass flow rate of thermal liquid 1 at each breakpoint in the lookup table for the specific heat dissipation table. The block inter- and extrapolates the breakpoints to obtain the specific heat dissipation of the heat exchanger at any mass flow rate. Interpolation is the MATLAB `linear` type and extrapolation is `nearest`.\n\nThe mass flow rates can be positive, zero, or negative, but they must increase monotonically from left to right. Their number must equal the number of columns in the Specific heat dissipation table parameter. If the table has m rows and n columns, the mass flow rate vector must be n elements long.\n\nMass flow rate of thermal liquid 2 at each breakpoint in the lookup table for the specific heat dissipation table. The block inter- and extrapolates the breakpoints to obtain the specific heat dissipation of the heat exchanger at any mass flow rate. Interpolation is the MATLAB `linear` type and extrapolation is `nearest`.\n\nThe mass flow rates can be positive, zero, or negative, but they must increase monotonically from left to right. Their number must equal the number of columns in the Specific heat dissipation table parameter. If the table has m rows and n columns, the mass flow rate vector must be n elements long.\n\nSpecific heat dissipation at each breakpoint in its lookup table over the mass flow rates of thermal liquid 1 and thermal liquid 2. The block inter- and extrapolates the breakpoints to obtain the effectiveness at any pair of thermal liquid 1 and thermal liquid 2 mass flow rates. Interpolation is the MATLAB `linear` type and extrapolation is `nearest`.\n\nThe specific heat dissipation values must be not be negative. They must align from top to bottom in order of increasing mass flow rate in the thermal liquid 1 channel, and from left to right in order of increasing mass flow rate in the thermal liquid 2 channel. The number of rows must equal the size of the Thermal liquid 1 mass flow rate vector parameter, and the number of columns must equal the size of the Thermal liquid 2 mass flow rate vector parameter.\n\nWarning condition for specific heat dissipation in excess of minimum heat capacity rate. Heat capacity rate is the product of mass flow rate and specific heat, and its minimum value is the lowest between the flows. This minimum gives the specific dissipation for a heat exchanger with maximum effectiveness and cannot be exceeded. See the Specific Dissipation Heat Transfer block for more detail.\n\nThermal Liquid 1|2 Tab\n\nMass flow rate at each breakpoint in the lookup table for the pressure drop. The block inter- and extrapolates the breakpoints to obtain the pressure drop at any mass flow rate. Interpolation is the MATLAB `linear` type and extrapolation is `nearest`.\n\nThe mass flow rates can be positive, zero, or negative and they can span across laminar, transient, and turbulent zones. They must, however, increase monotonically from left to right. Their number must equal the size of the Pressure drop vector parameter, with which they are to combine to complete the tabulated breakpoints.\n\nPressure drop at each breakpoint in its lookup table over the mass flow rate. The block inter- and extrapolates the breakpoints to obtain the pressure drop at any mass flow rate. Interpolation is the MATLAB `linear` type and extrapolation is `nearest`.\n\nThe pressure drops can be positive, zero, or negative, and they can span across laminar, transient, and turbulent zones. They must, however, increase monotonically from left to right. Their number must equal the size of the Mass flow rate vector parameter, with which they are to combine to complete the tabulated breakpoints.\n\nAbsolute temperature established at the inlet in the gathering of the tabulated pressure drops. The reference inflow temperature and pressure determine the fluid density assumed in the tabulated data. During simulation, the ratio of reference to actual fluid densities multiplies the tabulated pressure drop to obtain the actual pressure drop.\n\nAbsolute pressure established at the inlet in the gathering of the tabulated pressure drops. The reference inflow temperature and pressure determine the fluid density assumed in the tabulated data. During simulation, the ratio of reference to actual fluid densities multiplies the tabulated pressure drop to obtain the actual pressure drop.\n\nMass flow rate below which its value is numerically smoothed to avoid discontinuities known to produce simulation errors at zero flow. See the Simple Heat Exchanger Interface (TL) block (on which the `Simple Model` variant is based) for detail on the calculations.\n\nVolume of fluid in the thermal liquid 1 or thermal liquid 2 flow channel.\n\nFlow area at the inlet and outlet of the thermal liquid 1 or thermal liquid 2 flow channel. Ports in the same flow channel are of the same size.\n\n### Block Variant: `E-NTU Model`\n\nCommon Tab\n\nManner in which the flows align in the heat exchanger. The flows can run parallel to each other, counter to each other, or across each other. They can also run in a pressurized shell, one through tubes enclosed in the shell, the other around those tubes. Other flow arrangements are possible through a generic parameterization based on tabulated effectiveness data and requiring little detail about the heat exchanger.\n\nNumber of times the flow traverses the shell before exiting.\n\n#### Dependencies\n\nThis parameter applies solely to the Flow arrangement setting of ```Shell and tube```.\n\nMixing condition in each of the flow channels. Mixing in this context is the lateral movement of fluid as it proceeds along its flow channel toward the outlet. The flows remain separate from each other. Unmixed flows are common in channels with plates, baffles, or fins. This setting reflects in the effectiveness of the heat exchanger, with unmixed flows being most effective and mixed flows being least.\n\n#### Dependencies\n\nThis parameter applies solely to the Flow arrangement setting of ```Shell and tube```.\n\nNumber of transfer units at each breakpoint in the lookup table for the heat exchanger effectiveness number. The table is two-way, with both the number of transfer units and the thermal capacity ratio serving as independent coordinates. The block inter- and extrapolates the breakpoints to obtain the effectiveness at any number of transfer units. Interpolation is the MATLAB `linear` type and extrapolation is `nearest`.\n\nThe numbers specified must be greater than zero and increase monotonically from left to right. The size of the vector must equal the number of rows in the Effectiveness table parameter. If the table has m rows and n columns, the vector for the number of transfer units must be m elements long.\n\n#### Dependencies\n\nThis parameter applies solely to the Flow arrangement setting of ```Generic - effectiveness table```.\n\nThermal capacity ratio at each breakpoint in lookup table for heat exchanger effectiveness. The table is two-way, with both the number of transfer units and the heat capacity rate ratio serving as independent coordinates. The block inter- and extrapolates the breakpoints to obtain the effectiveness at any thermal capacity ratio. Interpolation is the MATLAB `linear` type and extrapolation is `nearest`.\n\nThe thermal capacity ratios must be greater than zero and increase monotonically from left to right. The size of the vector must equal the number of columns in the Nusselt number table parameter. If the table has m rows and n columns, the vector for the thermal capacity ratio must be n elements long. The thermal capacity ratio is the fraction of minimum over maximum heat capacity rates.\n\n#### Dependencies\n\nThis parameter applies solely to the Flow arrangement setting of ```Generic - effectiveness table```.\n\nHeat exchanger effectiveness at each breakpoint in its lookup table over the number of transfer units and thermal capacity ratio. The block inter- and extrapolates the breakpoints to obtain the effectiveness at any pair of number of transfer units and thermal capacity ratio. Interpolation is the MATLAB `linear` type and extrapolation is `nearest`.\n\nThe effectiveness values must be not be negative. They must align from top to bottom in order of increasing number of transfer units and from left to right in order of increasing thermal capacity ratio. The number of rows must equal the size of the Number of heat transfer units vector parameter, and the number of columns must equal the size of the Thermal capacity ratio vector parameter.\n\n#### Dependencies\n\nThis parameter applies solely to the Flow arrangement setting of ```Generic - effectiveness table```.\n\nModeling assumption for the transient response of the wall to thermal changes. Set to `On` to impart a thermal mass to the wall and to capture the delay in its transient response to changes in temperature or heat flux. Such delays are relevant in thick walls, such as those required to sustain high pressures. The default setting assumes a wall thin enough for its transient response to be virtually instantaneous on the time scale of the heat transfer.\n\nHeat required to raise wall temperature by one degree. Thermal mass is the product of mass with specific heat and a measure of the ability to absorb heat. A wall with thermal mass has a transient response to sudden changes in surface temperature or heat flux. The larger the thermal mass, the slower that response, and the longer the time to steady state. The default value corresponds to a wall of stainless steel with a mass of approximately 1 kg.\n\n#### Dependencies\n\nThis parameter applies solely to the Wall thermal dynamics setting of `On`.\n\nResistance of the wall to heat flow by thermal conduction, and the inverse of thermal conductance, or the product of thermal conductivity with the ratio of surface area to length. Wall resistance adds to convective and fouling resistances to determine the overall heat transfer coefficient between the flows.\n\nThermal Liquid 1|2 Tab\n\nCross-sectional area of the flow channel at its narrowest point. If the channel is a collection of ducts, tubes, slots, or grooves, the area is the sum of the areas in the collection—minus the occlusion due to walls, ridges, plates, or other barriers.\n\nTotal volume of fluid contained in the thermal liquid 1 or thermal liquid 2 flow channel.\n\nEffective inner diameter of the flow at its narrowest point. For channels not circular in cross section, that diameter is of an imaginary circle equal in area to the flow cross section. Its value is the ratio of the minimum free-flow area to a fourth of its gross perimeter.\n\nIf the channel is a collection of ducts, tubes, slots, or grooves, the gross perimeter is the sum of the perimeters in the collection. If the channel is a single pipe or tube and it is circular in cross section, the hydraulic diameter is the same as the true diameter.\n\nStart of transition between laminar and turbulent zones. Above this number, inertial forces take hold and the flow grows progressively turbulent. The default value is characteristic of circular pipes and tubes with smooth surfaces.\n\nEnd of transition between laminar and turbulent zones. Below this number, viscous forces take hold and the flow grows progressively laminar. The default value is characteristic of circular pipes and tubes with smooth surfaces.\n\nMathematical model for pressure loss by viscous friction. This setting determines which expressions to use for calculation and which block parameters to specify as input. See the Heat Exchanger Interface (TL) block for the calculations by parameterization.\n\nAggregate loss coefficient for all flow resistances in the flow channel—including the wall friction responsible for major loss and the local resistances, due to bends, elbows, and other geometry changes, responsible for minor loss.\n\nThe loss coefficient is an empirical dimensionless number commonly used to express the pressure loss due to viscous friction. It can be calculated from experimental data or, in some cases, obtained from product data sheets.\n\n#### Dependencies\n\nThis parameter applies solely to the Pressure loss parameterization setting of ```Constant loss coefficient```.\n\nTotal distance the flow must travel to reach across the ports. In multi-pass shell-and-tube exchangers, the total distance is the sum over all shell passes. In tube bundles, corrugated plates, and other channels in which the flow is split into parallel branches, it is the distance covered in a single branch. The longer the flow path, the steeper the major pressure loss due to viscous friction at the wall.\n\n#### Dependencies\n\nThis parameter applies solely to the Pressure loss parameterization setting of ```Correlations for tubes``` and ```Tabulated data - Darcy friction factor vs Reynolds number```.\n\nAggregate minor pressure loss expressed as a length. This length is that which all local resistances, such as elbows, tees, and unions, would add to the flow path if in their place was a simple wall extension. The larger the equivalent length, the steeper the minor pressure loss due to the local resistances.\n\n#### Dependencies\n\nThis parameter applies solely to the Pressure loss parameterization setting of ```Correlations for tubes```.\n\nMean height of the surface protrusions from which wall friction arises. Higher protrusions mean a rougher wall for more friction and so a steeper pressure loss. Surface roughness features in the Haaland correlation from which the Darcy friction factor derives and on which the pressure loss calculation depends.\n\n#### Dependencies\n\nThis parameter applies solely to the Pressure loss parameterization setting of ```Correlations for tubes```.\n\nPressure loss correction for flow cross section in laminar flow conditions. This parameter is commonly referred to as the shape factor. Its ratio to the Reynolds number gives the Darcy friction factor for the pressure loss calculation in the laminar zone. The default value belongs to cylindrical pipes and tubes.\n\nThe shape factor derives for certain shapes from the solution of the Navier-Stokes equations. A square duct has a shape factor of `56`, a rectangular duct with aspect ratio of 2:1 has a shape factor of `62`, and an annular tube has a shape factor of `96`, as does a slender conduit between parallel plates.\n\n#### Dependencies\n\nThis parameter applies solely to the Pressure loss parameterization setting of ```Correlations for tubes```.\n\nReynolds number at each breakpoint in the lookup table for the Darcy friction factor. The block inter- and extrapolates the breakpoints to obtain the Darcy friction factor at any Reynolds number. Interpolation is the MATLAB `linear` type and extrapolation is `nearest`.\n\nThe Reynolds numbers must be greater than zero and increase monotonically from left to right. They can span across laminar, transient, and turbulent zones. Their number must equal the size of the Darcy friction factor vector parameter, with which they are to combine to complete the tabulated breakpoints.\n\n#### Dependencies\n\nThis parameter applies solely to the Pressure loss parameterization setting of ```Tabulated data - Darcy friction factor vs. Reynolds number```.\n\nDarcy friction factor at each breakpoint in its lookup table over the Reynolds number. The block inter- and extrapolates the breakpoints to obtain the Darcy friction factor at any Reynolds number. Interpolation is the MATLAB `linear` type and extrapolation is `nearest`.\n\nThe Darcy friction factors must not be negative and they must align from left to right in order of increasing Reynolds number. Their number must equal the size of the Reynolds number vector for Darcy friction factor parameter, with which they are to combine to complete the tabulated breakpoints.\n\n#### Dependencies\n\nThis parameter applies solely to the Pressure loss parameterization setting of ```Tabulated data - Darcy friction factor vs. Reynolds number```.\n\nReynolds number at each breakpoint in the lookup table for the Euler number. The block inter- and extrapolates the breakpoints to obtain the Euler number at any Reynolds number. Interpolation is the MATLAB `linear` type and extrapolation is `nearest`.\n\nThe Reynolds numbers must be greater than zero and increase monotonically from left to right. They can span across laminar, transient, and turbulent zones. Their number must equal the size of the Euler number vector parameter, with which they are to combine to complete the tabulated breakpoints.\n\n#### Dependencies\n\nThis parameter applies solely to the Pressure loss parameterization setting of ```Tabulated data - Euler number vs. Reynolds number```.\n\nEuler number at each breakpoint in its lookup table over the Reynolds number. The block inter- and extrapolates the breakpoints to obtain the Euler number at any Reynolds number. Interpolation is the MATLAB `linear` type and extrapolation is `nearest`.\n\nThe Euler numbers must not be negative and they must align from left to right in order of increasing Reynolds number. Their number must equal the size of the Reynolds number vector for Euler number parameter, with which they are to combine to complete the tabulated breakpoints.\n\n#### Dependencies\n\nThis parameter applies solely to the Pressure loss parameterization setting of ```Tabulated data - Euler number vs. Reynolds number```.\n\nMathematical model for heat transfer between fluid and wall. The choice of model determines which expressions to apply and which parameters to specify for heat transfer calculation. See the E-NTU Heat Transfer block for the calculations by parameterization.\n\nEffective surface area used in heat transfer between fluid and wall. The effective surface area is the sum of primary and secondary surface areas, or those of the wall, where it is exposed to fluid, and of the fins, if any are used. Fin surface area is normally scaled by a fin efficiency factor.\n\nHeat transfer coefficient for convection between fluid and wall. Resistance due to fouling is captured separately in the Fouling factor parameter.\n\n#### Dependencies\n\nThis parameter applies solely to the Heat transfer parameterization setting of ```Constant heat transfer coefficient```.\n\nCharacteristic length traversed in heat transfer between fluid and wall. This length factors in the calculation of the hydraulic diameter from which the heat transfer coefficient and the Reynolds number, as defined in the tabulated heat transfer parameterizations, derives.\n\n#### Dependencies\n\nThis parameter applies solely to the Heat transfer parameterization setting of ```Tabulated data - Colburn factor vs. Reynolds number``` or ```Tabulated data - Nusselt number vs. Reynolds number & Prandtl number```.\n\nConstant assumed for Nusselt number in laminar flow. The Nusselt number factors in the calculation of the heat transfer coefficient between fluid and wall, on which the heat transfer rate depends. The default value belongs to cylindrical pipes and tubes.\n\n#### Dependencies\n\nThis parameter applies solely to the Heat transfer parameterization setting of ```Correlations for tubes```.\n\nReynolds number at each breakpoint in the lookup table for the Colburn factor. The block inter- and extrapolates the breakpoints to obtain the Colburn factor at any Reynolds number. Interpolation is the MATLAB `linear` type and extrapolation is `nearest`.\n\nThe Reynolds numbers must be greater than zero and increase monotonically from left to right. They can span across laminar, transient, and turbulent zones. Their number must equal the size of the Colburn factor vector parameter, with which they are to combine to complete the tabulated breakpoints.\n\n#### Dependencies\n\nThis parameter applies solely to the Heat transfer parameterization setting of ```Tabulated data - Colburn factor vs. Reynolds number```.\n\nColburn factor at each breakpoint in its lookup table over the Reynolds number. The block inter- and extrapolates the breakpoints to obtain the Euler number at any Reynolds number. Interpolation is the MATLAB `linear` type and extrapolation is `nearest`.\n\nThe Colburn factors must not be negative and they must align from left to right in order of increasing Reynolds number. Their number must equal the size of the Reynolds number vector for Colburn factor parameter, with which they are to combine to complete the tabulated breakpoints.\n\n#### Dependencies\n\nThis parameter applies solely to the Heat transfer parameterization setting of ```Tabulated data - Colburn factor vs. Reynolds number```.\n\nReynolds number at each breakpoint in the lookup table for the Nusselt number. The table is two-way, with both Reynolds and Prandtl numbers serving as independent coordinates. The block inter- and extrapolates the breakpoints to obtain the Nusselt number at any Reynolds number. Interpolation is the MATLAB `linear` type and extrapolation is `nearest`.\n\nThe Reynolds numbers must be greater than zero and increase monotonically from left to right. They can span across laminar, transient, and turbulent zones. The size of the vector must equal the number of rows in the Nusselt number table parameter. If the table has m rows and n columns, the Reynolds number vector must be m elements long.\n\n#### Dependencies\n\nThis parameter applies solely to the Heat transfer parameterization setting of ```Tabulated data - Nusselt number vs. Reynolds number & Prandtl number```.\n\nPrandtl number at each breakpoint in the lookup table for the Nusselt number. The table is two-way, with both Reynolds and Prandtl numbers serving as independent coordinates. The block inter- and extrapolates the breakpoints to obtain the Nusselt number at any Prandtl number. Interpolation is the MATLAB `linear` type and extrapolation is `nearest`.\n\nThe Prandlt numbers must be greater than zero and increase monotonically from left to right. They can span across laminar, transient, and turbulent zones. The size of the vector must equal the number of columns in the Nusselt number table parameter. If the table has m rows and n columns, the Prandtl number vector must be n elements long.\n\n#### Dependencies\n\nThis parameter applies solely to the Heat transfer parameterization setting of ```Tabulated data - Nusselt number vs. Reynolds number & Prandtl number```.\n\nNusselt number at each breakpoint in its lookup table over the Reynolds and Prandtl numbers. The block inter- and extrapolates the breakpoints to obtain the Nusselt number at any pair of Reynolds and Prandtl numbers. Interpolation is the MATLAB `linear` type and extrapolation is `nearest`. By determining the Nusselt number, the table feeds the calculation from which the heat transfer coefficient between fluid and wall derives.\n\nThe Nusselt numbers must be greater than zero. They must align from top to bottom in order of increasing Reynolds number and from left to right in order of increasing Prandlt numbers. The number of rows must equal the size of the Reynolds number vector for Nusselt number parameter, and the number of columns must equal the size of the Prandtl number vector for Nusselt number parameter.\n\n#### Dependencies\n\nThis parameter applies solely to the Heat transfer parameterization setting of ```Tabulated data - Nusselt number vs. Reynolds number & Prandtl number```.\n\nMeasure of thermal resistance due to fouling deposits which over time tend to build on the exposed surfaces of the wall. The deposits, as they impose between the fluid and wall a new solid layer through which heat must traverse, add to the heat transfer path an extra thermal resistance. Fouling deposits grow slowly and the resistance due to them is accordingly assumed constant during simulation.\n\nLower bound for the heat transfer coefficient between fluid and wall. If calculation returns a lower heat transfer coefficient, this bound replaces the calculated value.\n\n### Effects and Initial Conditions\n\nOption to model the pressure dynamics in the thermal liquid 1 or thermal liquid 2 channel. Setting this parameter to `Off` removes the pressure derivative terms from the component energy and mass conservation equations. The pressure inside the heat exchanger is then reduced to the weighted average of the two port pressures.\n\nTemperature in the thermal liquid 1 or thermal liquid 2 channel at the start of simulation.\n\nPressure in the thermal liquid 1 or thermal liquid 2 channel at the start of simulation.\n\n## Version History\n\nIntroduced in R2016a"
] | [
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"https://it.mathworks.com/help/hydro/ref/tltl_entu_heat_exchanger_ic.png",
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"https://it.mathworks.com/help/hydro/ref/shellandtubes1.png",
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"https://it.mathworks.com/help/hydro/ref/shellandtubes5.png",
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"https://it.mathworks.com/help/hydro/ref/entu_flow_arrangements_gray_red.png",
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"https://it.mathworks.com/help/hydro/ref/tl_heat_exch_thermal_transfer_schematic_b.png",
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"https://it.mathworks.com/help/hydro/ref/tl_tl_heat_exchanger_composite.png",
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https://socratic.org/questions/54ad71de581e2a06525ece03 | [
"# Question #ece03\n\nJan 7, 2015\n\nConsidering a GP of the type:\n$a , a r , a {r}^{2} , a {r}^{3} , \\ldots a {r}^{n}$\nwhere:\n$a$ is the first term;\n$r$ is the common ratio.\nWe have:\n$a {r}^{3} = 56$ and\n$a {r}^{5} = \\frac{7}{8}$\nFrom the first:\n$a = \\frac{56}{r} ^ 3$\nSubstituting in the second you get:\n$\\frac{56 {r}^{5}}{r} ^ 3 = \\frac{7}{8}$ and\n$r = \\frac{1}{8}$\n$a = 28672$\n\nand\n\n${\\sum}_{k = 0}^{\\infty} a {r}^{k} = \\frac{a}{1 - r} = \\frac{28672}{1 - \\frac{1}{8}} = 32768$"
] | [
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https://quantoisseur.com/2017/01/20/cointegrated-etf-pairs-part-ii/?like_comment=32&_wpnonce=1b46ac9eb4 | [
"# Cointegrated ETF Pairs Part II\n\nUpdate 5/17: As discussed in the comments, the reason the results are so exaggerated is because it is missing portfolio rebalancing to account for the changing hedge ratio. It would be interesting to try an adaptive hedge ratio that requires only weekly or monthly rebalancing to see how legitimately profitable this type of strategy could be.\n\nWelcome back! This week’s post will backtest a basic mean reverting strategy on a cointegrated ETF pair time series constructed using the methods described in part I. Since the EWA (Australia) – EWC (Canada) pair was found to be more naturally cointegrated, I decided to run the rolling linear regression model (EWA chosen as the dependent variable) with a lookback window of 21 days on this pair to create the spread below.\n\nWith the adaptive hedge ratio, the spread looks well suited to backtest a mean reverting strategy on. Before that, we should check what the minimum capital required to trade this spread is. Though everyone has a different margin requirement, I thought it would be useful to walkthrough how you would calculate the capital required. In this example we assume our broker allows a margin of 50%. We first will compute the daily ratio between the pair, EWC/EWA. This ratio represents the amount of EWA shares for each share of EWC that must be owned to have an equal dollar move for every 1% move. The ratio fluctuates daily but has a mean of 1.43. This makes sense because EWC, on average, trades at higher price. We then multiply these ratios by the rolling beta. Then for reference, we can fix the held EWC shares to 100 and multiply the previous values (ratios*rolling beta) by 100 to determine the amount of EWA shares that would be held. The amount of capital required to hold this spread can then be calculated with the equation: margin*abs((EWC price * 100) + (EWA price * calculated shares)). This is plotted for our example below.\n\nFrom this plot we can see that the series has a max value of \\$5,466 which is not a relatively large required capital. I hypothesize that the less cointegrated a pair is, the higher the minimum capital will be (try the EWZ-IGE pair).\n\nWe can now go ahead and backtest the figure 1 time series! A common mean reversal strategy uses Bollinger Bands, where we enter positions when the price deviates past a Z-score/standard deviation threshold from the mean. The exit signals can be determined from the half-life of its mean reversion or it can be based on the Z-score. To avoid look-ahead bias, I calculated the mean, standard deviation, and Z-score with a rolling 50-day window. Unfortunately, this window had to be chosen with data-snooping bias but was a reasonable choice. This backtest will also ignore transaction costs and other spread execution nuances but should still reasonably reflect the strategy’s potential performance. I decided on the following signals:\n\n• Enter Long/Close Short: Z-Score < -1\n• Close Long/Enter Short: Z-Score > 1\n\nThis is a standard Bollinger Bands strategy and results were encouraging.",
null,
"",
null,
"Though it made a relatively small amount of trades over 13 years, it boasts an impressive 2.7 Sharpe Ratio with 97% positive trades. Below on the left we can see the strategy’s performance vs. SPY (using very minimal leverage) and on the right the positions/trades are shown.",
null,
"Overall, this definitely supports the potential of trading cointegrated ETF pairs with Bollinger Bands. I think it would be interesting to explore a form of position sizing based on either market volatility or the correlation between the ETF pair and another symbol/ETF. This concludes my analysis of cointegrated ETF pairs for now.\n\nAcknowledgments: Thank you to Brian Peterson and Ernest Chan for explaining how to calculate the minimum capital required to trade a spread. Additionally, all of my blog posts have been edited prior to being published by Karin Muggli, so a huge thank you to her!\n\nNote: I’m currently looking for a full-time quantitative research/trading position beginning summer/fall 2017. I’m currently a senior at the University of Washington, majoring in Industrial and Systems Engineering and minoring in Applied Mathematics. I also have taken upper level computer science classes and am proficient in a variety of programming languages. Resume: https://www.pdf-archive.com/2017/01/31/coltonsmith-resume-g/. LinkedIn: https://www.linkedin.com/in/coltonfsmith. Please let me know of any open positions that would be a good fit for me. Thanks!\n\nFull Code:\n\n```detach(\"package:dplyr\", unload=TRUE)\nrequire(quantstrat)\nrequire(knitr)\nrequire(PerformanceAnalytics)\nrequire(quantstrat)\nrequire(tseries)\nrequire(roll)\nrequire(ggplot2)\n\n# Full test\ninitDate=\"1990-01-01\"\nfrom=\"2003-01-01\"\nto=\"2015-12-31\"\n\n## Create \"symbols\" for Quanstrat\n\n## Get data\ngetSymbols(\"EWA\", from=from, to=to)\ngetSymbols(\"EWC\", from=from, to=to)\ndates = index(EWA)\n\n## Ratio (EWC/EWA)\n\n## Rolling regression\nwindow = 21\n\n## Plot beta\nrollingbeta <- fortify.zoo(lm\\$coefficients[,2],melt=TRUE)\nggplot(rollingbeta, ylab=\"beta\", xlab=\"time\") + geom_line(aes(x=Index,y=Value)) + theme_bw()\n\nsprd <- vector(length=3273-21)\nfor (i in 21:3273) {\n}\nplot(sprd, type=\"l\", xlab=\"2003 to 2016\", ylab=\"EWA-hedge*EWC\")\n\n## Find minimum capital\nhedgeRatio = ratio*rollingbeta\\$Value*100\nplot(spreadPrice, type=\"l\", xlab=\"2003 to 2016\", ylab=\"0.5*(abs(EWA*100+EWC*calculatedShares))\")\n\n## Combine columns and turn into xts\nclose = sprd\ndate = as.data.frame(dates[22:3273])\ndata = cbind(date, close)\ndfdata = as.data.frame(data)\nxtsData = xts(dfdata, order.by=as.Date(dfdata\\$date))\nxtsData\\$close = as.numeric(xtsData\\$close)\nxtsData\\$dum = vector(length = 3252)\nxtsData\\$dum = NULL\nxtsData\\$dates.22.3273. = NULL\n\n## Add SMA, moving stdev, and z-score\nrollz<-function(x,n){\navg=rollapply(x, n, mean)\nstd=rollapply(x, n, sd)\nz=(x-avg)/std\nreturn(z)\n}\n\n## Varying the lookback has a large affect on the data\nxtsData\\$zScore = rollz(xtsData,50)\nsymbols = 'xtsData'\n\n## Backtest\ncurrency('USD')\nSys.setenv(TZ=\"UTC\")\nstock(symbols, currency=\"USD\", multiplier=1)\n\n#trade sizing and initial equity settings\n\nstrategy.st <- portfolio.st <- account.st <- \"EWA_EWC\"\nrm.strat(portfolio.st)\nrm.strat(strategy.st)\ninitPortf(portfolio.st, symbols=symbols, initDate=initDate, currency='USD')\ninitAcct(account.st, portfolios=portfolio.st, initDate=initDate, currency='USD',initEq=initEq)\ninitOrders(portfolio.st, initDate=initDate)\nstrategy(strategy.st, store=TRUE)\n\n#SIGNALS\nname=\"sigFormula\",\narguments = list(label = \"enterLong\",\nformula = \"zScore < -1\", cross = TRUE), label = \"enterLong\") add.signal(strategy = strategy.st, name=\"sigFormula\", arguments = list(label = \"exitLong\", formula = \"zScore > 1\",\ncross = TRUE),\nlabel = \"exitLong\")\n\nname=\"sigFormula\",\narguments = list(label = \"enterShort\",\nformula = \"zScore > 1\",\ncross = TRUE),\nlabel = \"enterShort\")\n\nname=\"sigFormula\",\narguments = list(label = \"exitShort\",\nformula = \"zScore < -1\",\ncross = TRUE),\nlabel = \"exitShort\")\n\n#RULES\nname = \"ruleSignal\",\narguments = list(sigcol = \"enterLong\",\nsigval = TRUE,\norderqty = 15,\nordertype = \"market\",\norderside = \"long\",\nreplace = FALSE,\nthreshold = NULL),\ntype = \"enter\")\n\nname = \"ruleSignal\",\narguments = list(sigcol = \"exitLong\",\nsigval = TRUE,\norderqty = \"all\",\nordertype = \"market\",\norderside = \"long\",\nreplace = FALSE,\nthreshold = NULL),\ntype = \"exit\")\n\nname = \"ruleSignal\",\narguments = list(sigcol = \"enterShort\",\nsigval = TRUE,\norderqty = -15,\nordertype = \"market\",\norderside = \"short\",\nreplace = FALSE,\nthreshold = NULL),\ntype = \"enter\")\n\nname = \"ruleSignal\",\narguments = list(sigcol = \"exitShort\",\nsigval = TRUE,\norderqty = \"all\",\nordertype = \"market\",\norderside = \"short\",\nreplace = FALSE,\nthreshold = NULL),\ntype = \"exit\")\n\n#apply strategy\nt1 <- Sys.time()\nout <- applyStrategy(strategy=strategy.st,portfolios=portfolio.st)\nt2 <- Sys.time()\nprint(t2-t1)\n\n#set up analytics\nupdatePortf(portfolio.st)\ndateRange <- time(getPortfolio(portfolio.st)\\$summary)[-1]\nupdateAcct(portfolio.st,dateRange)\nupdateEndEq(account.st)\n\n#Stats\ntStats[,4:ncol(tStats)] <- round(tStats[,4:ncol(tStats)], 2)\nprint(data.frame(t(tStats[,-c(1,2)])))\n\n#Averages\n(aggPF <- sum(tStats\\$Gross.Profits)/-sum(tStats\\$Gross.Losses))\n(aggCorrect <- mean(tStats\\$Percent.Positive))\n(meanAvgWLR <- mean(tStats\\$Avg.WinLoss.Ratio))\n\n#portfolio cash PL\n\n## Sharpe Ratio\n(SharpeRatio.annualized(portPL, geometric=FALSE))\n\n## Performance vs. SPY\ninstRets <- PortfReturns(account.st)\nportfRets <- xts(rowMeans(instRets)*ncol(instRets), order.by=index(instRets))\n\ncumPortfRets <- cumprod(1+portfRets)\nfirstNonZeroDay <- index(portfRets)[min(which(portfRets!=0))]\ngetSymbols(\"SPY\", from=firstNonZeroDay, to=\"2015-12-31\")\nSPYrets <- diff(log(Cl(SPY)))[-1]\ncumSPYrets <- cumprod(1+SPYrets)\ncomparison <- cbind(cumPortfRets, cumSPYrets)\ncolnames(comparison) <- c(\"strategy\", \"SPY\")\nchart.TimeSeries(comparison, legend.loc = \"topleft\", colorset = c(\"green\",\"red\"))\n\n## Chart Position\nrets <- PortfReturns(Account = account.st)\nrownames(rets) <- NULL\ncharts.PerformanceSummary(rets, colorset = bluefocus)\n```\n\n## 22 thoughts on “Cointegrated ETF Pairs Part II”\n\n1.",
null,
"Ludo says:\n\nHello,\n\nWhy the code isn’t rigth formated ? t1 <- Sys.time()\nbut nice article !!\nRegards\nLudo.\n\nLike\n\n1.",
null,
"cfsmith says:\n\nFixed. For some reason it didn’t render the equality signs correctly. Thanks for catching that!\n\nLike\n\n2.",
null,
"Quant says:\n\nFirst of all, Thank you for a wonderful article. I have tested the code with CVX/XOM and GLD/SLV pairs. In both cases the returns are astronomical. This makes me a bit suspicious about the code that either there is some look ahead bias or the calculations are not correct somewhere. I will spend sometime over the weekend to see if I can find anything.\n\nBut the theory and the application are very helpful. Thanks.\n\nLike\n\n1.",
null,
"cfsmith says:\n\nHi, assuming you constructed those spreads correctly, I think the returns are largely inflated due to ignoring all the nuances in actually executing a pair trading strategy like this. I don’t believe there is any look-ahead bias or incorrect calculations. Looking at the spread’s time series, it makes sense that any reasonable mean reversion strategy should have astronomical returns with very few losing trades but if you were to actually implement this strategy then there would be other things that you would have to take into account. I’m not sure how much this would affect the backtest results but for this post I merely wanted to explore its potential.\n\nLike\n\n3.",
null,
"Quant says:\n\nUnderstood and thanks for your kind response. One other quick question. Where does the 98.86608 come from to make the mean 100? I am working on replicating this using my own framework to see what the results would look like. I should have an answer shortly. Thanks.\n\nLike\n\n1.",
null,
"cfsmith says:\n\nI just did 100-mean(EWA-hedge*EWC) to get that. It doesn’t matter what the mean of the time series is so I just made it 100 for easier numbers.\n\nLike\n\n4.",
null,
"eduardo gonzatti says:\n\nHi there, nice post , again!\n\nDid you by any chance , calculate the half life using the O-U Equation , or the in-sample-average-time(days)-in-trade-until-mean-reversion? If you did, what was it ?\n\nalso, i dont know if I read it right from the start, but, did you trade on the same period that you used to test for cointegration ? (in sample)\n\nor, did you use a rolling 21 days window for the moving hedge ratio between the pairs components while testing them for cointegrationinside this moving window and them filtering trades for both one of the triggers + cointegration at that time ?\n\ntanks again.\nbest regards!\n\nLike\n\n1.",
null,
"cfsmith says:\n\nHey,\n\nI did not calculate the half-life for this EWA-EWC series but in the last post my code to do so with the O-U equation is included if you want to!\n\nI constructed the series using the rolling 21 day window for the hedge ratio as explained in part I. I then added the the rolling Z-Score indicator using a 50 day window (this was chosen arbitrarily with data snooping bias).\n\nIf I understand your question correctly, this should be functionally the same as calculating the hedge ratio and the Z-Score indicator at the same time.\n\nLike\n\n1.",
null,
"Eduardo Gonzatti says:\n\nHi there,\n\nYeah, what I meant to ask was if you realized that you used the same in sample data, the same data where you tested the pair for cointegration, both for testing for cointegration + calculating the rolling 50 day statistics + calculating the rolling 21 day hedge ratio (beta) and trading.\n\nI didn’t have the time to run your script, yet, and debug it properly, so excuse me if that’s clear in the code and I’m making a redundant comment.\n\nThanks\n\nLike\n\n2.",
null,
"cfsmith says:\n\nYes, I create the series with the rolling 21 day hedge ratio and then calculated the rolling 50 day statistics from this series while trading it.\n\nI used these rolling windows to prevent any look-ahead bias. Is there a flaw in this? I don’t know what would be out of sample data for this example.\n\nThanks!\n\nLike\n\n3.",
null,
"Eduardo Gonzatti says:\n\nWell, as long as you are not trading the pair because it showed to be cointegrated on the same period that you are using for trading, it’s OK. (IF and only IF you are trading the pair BECAUSE of the cointegration, and wouldn’t do it otherwise).\n\nI’ll try to explain it better below :\nUsing a 21 days moving window for calculating the hedge ratio, a 50 days moving window for the BBs parameters, and assuming that you are using a one year (say 252 days) look back window for cointegration testing (I think I recall that Dr. Chan preferred at least 3yrs for this?).\n\nSo, in the first 21 days you calculate the first moving hedge ratio for the 22nd day, and update it daily. Your first data point will be at T+22.\nNow that you have the necessary information for creating the mean reverting spread (prices of each ETF and the hedge ratio) you can start populating this new vector and, after 50 data points you will have the first data points for the mean and stdv of the spread (y-hedge ratio *x). So, now we’re at the 22nd + 50 = 72nd day for the first data point of the spread + BBs.\n\nOK, so far so good.\nNow we can start trading the pair…\nUNLESS you still have to test it for cointegration.\n\nIf you do test it for cointegration and require it to be true for trading the pair, then your first data point for out of sample testing would be 22+252. From the first available point of the spread using the 21 days hedge ratio (22nd day) to one year after that (252 days), so your first out of sample data point would be @ day 274 onward, only taking trades if both the cointegration vector (imagine a binary vector where 1==cointegrated and 0==nope) shows 1 and one of the trigger points is hit by the spread (1 stdv as you said).\n\nThat’s it!\n\nPS: again, if that is already clear in the code, I’m sorry cause I haven’t been able to run it yet. I’ve been reading and posting from my cellphone.\n\nLike\n\n4.",
null,
"cfsmith says:\n\nAh okay, I understand what you are saying. I guess the strategy is based on the assumption that using an 21 day adaptive hedge ratio creates a sufficiently stationary series on a pair that is believed to be somewhat cointegrated. For example, in part I, the EWZ-IGE pair is much less cointegrated but with an adaptive hedge ratio produces a stationary series. This series is not as nice as the EWA-EWC pair so I would assume that in this case the strategy would not perform as well on the EWZ-IGE pair.\n\nLike\n\n5.",
null,
"Eduardo Gonzatti says:\n\nAre you sure there is no look ahead bias within the backtesting framework (I never used any if those packages) and the RollZ function for calculating the 50 days parameters in the spread series? It seems that the trading strategy core uses InitDate as the starting point for the test, and that would be before any of the calculations on the series and spread were made.\n\nI’m asking because of the stellar results. When the results are too good to be true, they normally are not true, even though you don’t account for slippage, liquidity, signal generation, costs, etc.\n\nI hope I’m wrong!\n\nBest\n\nLike\n\n1.",
null,
"cfsmith says:\n\nRun my code and then view the mktdata object. This shows when the indicators and signals are calculated. You’re correct, it isn’t able to start trading the strategy until awhile after the InitDate and mktdata shows this.\n\nSomeone else also questioned look-ahead bias but we were both unable to find any. Like I said, looking at the constructed time series, the returns should be incredible for any adequate mean reversion strategy. I personally don’t know the feasibility of actually trading this constructed series though. Let me know if you do have any ideas where look-ahead bias was introduced!\n\nThanks\n\nLike\n\n1.",
null,
"eduardo gonzatti says:\n\nI just ran all of your code , exported the dataframes and etcs to CSV and reviewed it in Excel, and indeed, it is right! there are some differences between the calculations, but that must be because of the regression methods in R and Excel, etc..\n\nI took a heavy beating from those R trading packages that i had never used. I tried to insert an 1 day delay for the trades, but couldn’t..\n\nthe series start @ “2003-01-01”, so the 1st one month is taken off by the calculation of the moving hedge ratio of 21 days. after that there is the 50 days calculation of the mean/stdv moving window, and only after that that the spread starts to exist.\nOne interesting point is that the strategy keeps scaling in when the spread is still outside the triggers, right ? so sometimes there are 3..4.. positions at the same time, pyramiding the trades.\n\nif you could share some links about the packages so one can understand their logic, id be very glad!\n\nbest regards\n\nLike\n\n6.",
null,
"Mat says:\n\nHi,\nI am trying to duplicate this algorithm with python and can’t get this stellar returns. I have some doubt about how I calculate rolling beta with this code :\nrolling_beta = statsmodels.api.OLS(price1, price2).fit().params\n\nDo you think I missed something with OLS function ?\nThanks\n\nLike\n\n7.",
null,
"Quant Trader says:\n\nColton, I think I may have figured out why the results are so good on paper but in reality this may not translate to real money trading this strategy…I may be completely off but I am still trying to make sense of the results.\n\nI have confirmed that there is no look ahead bias, So that’s not an issue.\n\nLet’s look at a sample transaction to show where the issue is.\n\nOn “3/6/2017” the strategy opens a short position of -15 shares @ \\$110.5143 for a total of (-\\$1657.7145).\nThis position is closed on “4/5/2017” @ \\$89.3274 for a total of \\$1339.911\n\nThis transaction on paper made a Profit of \\$317.8035.\n\nAll good so far. Now lest see what happens in the trading account to trade this position.\n\nOn “3/6/2017”\n\nEWA is @ \\$21.92 and EWC is @ \\$26.88. To initiate a short position you would have to\n\nsell 47 shares of EWA & Buy 100 shares of EWC\nThis transaction translates to 47 x \\$21.92 =1030.24 for EWA and 100 x 26.88 = \\$2688 for EWC.\n\nOn “4/5/2017” when the strategy closes the position, EWA is trading @ \\$22.45 and EWC is trading @ \\$26.77\n\nThis trade would have resulted in a Loss of \\$35.91 instead of a gain of \\$317.8035\n\nThe reason why the strategy makes money on paper is because the Synthetic Spread value shrunk because the Beta value changed not because the prices have changed in the right direction.\n\nHope I didn;t make any mistake here but happy to provide any additional details. I am happy to stand corrected and make money like the strategy does on paper 🙂\n\nThanks.\n\nLike\n\n8.",
null,
"V-Man says:\n\nThis strategy is missing any portfolio rebalancing. If the optimal hedge ratio according to the lookback n is recalculated every day then any open positions need to be rebalanced periodically to ensure that it is as close to the hedged spread as possible. In the code above I can see that the code is using the dynamically hedged spread as the price of the “portfolio” and buys and sells this according to the z-score signals. However, as the comment above by Quant Trader highlights, the profits will be greatly exaggerated due to the changes in the synthetic spread caused by the changing hedged ratio.\n\nPlease let me know what you think?\n\nLike\n\n9.",
null,
"cfsmith says:\n\nYes, Quant Trader and V-Man you are correct. This is missing portfolio rebalancing. It would be interesting to try a less frequent rebalancing/adaptive hedge ratio to see how legitimately profitable this type of strategy could be. Thanks for your exploration!\n\nLike\n\n10.",
null,
"krlitoos says:\n\nVery interesting article! Will you write another post testing different rebalancing periods?\n\nThanks\n\nLike\n\n11.",
null,
"Nathan Nobbe says:\n\nHi Colton,\n\nNeat article, thanks for sharing. I’m an old-school CS major looking at quant trading. What language are you using in the code example provided in this post?\n\nLike\n\n1.",
null,
"cfsmith says:\n\nHi Nathan,\n\nThe code is R. There are similar packages in Python as well.\n\nLike"
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https://nbodykit.readthedocs.io/en/latest/results/analyzing.html | [
"Several nbodykit algorithms compute binned clustering statistics and store the results as a BinnedStatistic object (see a list of these algorithms here. In this section, we provide an overview of some of the functionality of this class to help users better analyze their algorithm results.\n\nThe BinnedStatistic class is designed to hold data variables at fixed coordinates, i.e., a grid of $$(r, \\mu)$$ or $$(k, \\mu)$$ bins and is modeled after the syntax of the xarray.Dataset object.\n\nA BinnedStatistic object is serialized to disk using a JSON format. The to_json() and from_json() functions can be used to save and load BinnedStatistic objects. respectively.\n\nTo start, we read two BinnedStatistic results from JSON files, one holding 1D power measurement $$P(k)$$ and one holding a 2D power measurement $$P(k,\\mu)$$.\n\n:\n\nfrom nbodykit.binned_statistic import BinnedStatistic\n\ndata_dir = os.path.join(os.path.abspath('.'), 'data')\npower_1d = BinnedStatistic.from_json(os.path.join(data_dir, 'dataset_1d.json'))\npower_2d = BinnedStatistic.from_json(os.path.join(data_dir, 'dataset_2d.json'))\n\n\n## Coordinate Grid¶\n\nThe clustering statistics are measured for fixed bins, and the BinnedStatistic class has several attributes to access the coordinate grid defined by these bins:\n\n• shape: the shape of the coordinate grid\n\n• dims: the names of each dimension of the coordinate grid\n\n• coords: a dictionary that gives the center bin values for each dimension of the grid\n\n• edges: a dictionary giving the edges of the bins for each coordinate dimension\n\n:\n\nprint(\"1D shape = \", power_1d.shape)\nprint(\"2D shape = \", power_2d.shape)\n\n1D shape = (64,)\n2D shape = (64, 5)\n\n:\n\nprint(\"1D dims = \", power_1d.dims)\nprint(\"2D dims = \", power_2d.dims)\n\n1D dims = ['k']\n2D dims = ['k', 'mu']\n\n:\n\nprint(\"2D edges = \", power_2d.coords)\n\n2D edges = {'k': array([0.00613593, 0.01840777, 0.03067962, 0.04295147, 0.05522331,\n0.06749516, 0.079767 , 0.09203884, 0.10431069, 0.11658255,\n0.1288544 , 0.14112625, 0.1533981 , 0.1656699 , 0.17794175,\n0.1902136 , 0.20248545, 0.2147573 , 0.22702915, 0.239301 ,\n0.25157285, 0.2638447 , 0.27611655, 0.2883884 , 0.30066025,\n0.3129321 , 0.32520395, 0.3374758 , 0.3497476 , 0.36201945,\n0.3742913 , 0.38656315, 0.398835 , 0.41110685, 0.4233787 ,\n0.43565055, 0.4479224 , 0.46019425, 0.4724661 , 0.48473795,\n0.4970098 , 0.5092816 , 0.52155345, 0.5338253 , 0.54609715,\n0.558369 , 0.57064085, 0.5829127 , 0.59518455, 0.6074564 ,\n0.61972825, 0.6320001 , 0.64427195, 0.6565438 , 0.6688156 ,\n0.68108745, 0.6933593 , 0.70563115, 0.717903 , 0.73017485,\n0.7424467 , 0.75471855, 0.7669904 , 0.77926225]), 'mu': array([0.1, 0.3, 0.5, 0.7, 0.9])}\n\n:\n\nprint(\"2D edges = \", power_2d.edges)\n\n2D edges = {'k': array([0. , 0.01227185, 0.02454369, 0.03681554, 0.04908739,\n0.06135923, 0.07363108, 0.08590292, 0.09817477, 0.1104466 ,\n0.1227185 , 0.1349903 , 0.1472622 , 0.159534 , 0.1718058 ,\n0.1840777 , 0.1963495 , 0.2086214 , 0.2208932 , 0.2331651 ,\n0.2454369 , 0.2577088 , 0.2699806 , 0.2822525 , 0.2945243 ,\n0.3067962 , 0.319068 , 0.3313399 , 0.3436117 , 0.3558835 ,\n0.3681554 , 0.3804272 , 0.3926991 , 0.4049709 , 0.4172428 ,\n0.4295146 , 0.4417865 , 0.4540583 , 0.4663302 , 0.478602 ,\n0.4908739 , 0.5031457 , 0.5154175 , 0.5276894 , 0.5399612 ,\n0.5522331 , 0.5645049 , 0.5767768 , 0.5890486 , 0.6013205 ,\n0.6135923 , 0.6258642 , 0.638136 , 0.6504079 , 0.6626797 ,\n0.6749515 , 0.6872234 , 0.6994952 , 0.7117671 , 0.7240389 ,\n0.7363108 , 0.7485826 , 0.7608545 , 0.7731263 , 0.7853982 ]), 'mu': array([0. , 0.2, 0.4, 0.6, 0.8, 1. ])}\n\n\n## Accessing the Data¶\n\nThe names of data variables stored in a BinnedStatistic are stored in the variables attribute, and the data attribute stores the arrays for each of these names in a structured array. The data for a given variable can be accessed in a dict-like fashion:\n\n:\n\nprint(\"1D variables = \", power_1d.variables)\nprint(\"2D variables = \", power_2d.variables)\n\n1D variables = ['power', 'k', 'mu', 'modes']\n2D variables = ['power', 'k', 'mu', 'modes']\n\n:\n\n# the real component of the 1D power\nPk = power_1d['power'].real\nprint(type(Pk), Pk.shape, Pk.dtype)\n\n# complex power array\nPkmu = power_2d['power']\nprint(type(Pkmu), Pkmu.shape, Pkmu.dtype)\n\n<class 'numpy.ndarray'> (64,) float64\n<class 'numpy.ndarray'> (64, 5) complex128\n\n\nIn some cases, the variable value for a given bin will be missing or invalid, which is indicated by a numpy.nan value in the data array for the given bin. The BinnedStatistic class carries a mask attribute that defines which elements of the data array have numpy.nan values.\n\n## Meta-data¶\n\nAn OrderedDict of meta-data for a BinnedStatistic class is stored in the attrs attribute. Typically in nbodykit, the attrs dictionary stores information about box size, number of objects, etc:\n\n:\n\nprint(\"attrs = \", power_2d.attrs)\n\nattrs = {'N1': 4033, 'Lx': 512.0, 'Lz': 512.0, 'N2': 4033, 'Ly': 512.0, 'volume': 134217728.0}\n\n\nTo attach additional meta-data to a BinnedStatistic class, the user can add additional keywords to the attrs dictionary.\n\n## Slicing¶\n\nSlices of the coordinate grid of a BinnedStatistic can be achieved using array-like indexing of the main BinnedStatistic object, which will return a new BinnedStatistic holding the sliced data:\n\n:\n\n# select the first mu bin\nprint(power_2d[:,0])\n\n<BinnedStatistic: dims: (k: 64), variables: ('power', 'k', 'mu', 'modes')>\n\n:\n\n# select the first and last mu bins\nprint(power_2d[:, [0, -1]])\n\n<BinnedStatistic: dims: (k: 64, mu: 2), variables: ('power', 'k', 'mu', 'modes')>\n\n:\n\n# select the first 5 k bins\nprint(power_1d[:5])\n\n<BinnedStatistic: dims: (k: 5), variables: ('power', 'k', 'mu', 'modes')>\n\n\nA typical usage of array-like indexing is to loop over the mu dimension of a 2D BinnedStatistic, such as when plotting:\n\n:\n\nfrom matplotlib import pyplot as plt\n\n# the shot noise is volume / number of objects\nshot_noise = power_2d.attrs['volume'] / power_2d.attrs['N1']\n\n# plot each mu bin separately\nfor i in range(power_2d.shape):\npk = power_2d[:,i]\nlabel = r\"$\\mu = %.1f$\" % power_2d.coords['mu'][i]\nplt.loglog(pk['k'], pk['power'].real - shot_noise, label=label)\n\nplt.legend()\nplt.xlabel(r\"$k$ [$h$/Mpc]\", fontsize=14)\nplt.ylabel(r\"$P(k,\\mu)$ $[\\mathrm{Mpc}/h]^3$\", fontsize=14)\nplt.show()",
null,
"The coordinate grid can also be sliced using label-based indexing, similar to the syntax of xarray.Dataset.sel(). The method keyword of sel() determines if exact coordinate matching is required (method=None, the default) or if the nearest grid coordinate should be selected automatically (method='nearest').\n\nFor example, we can slice power spectrum results based on the k and mu coordinate values:\n\n:\n\n# get all mu bins for the k bin closest to k=0.1\nprint(power_2d.sel(k=0.1, method='nearest'))\n\n<BinnedStatistic: dims: (mu: 5), variables: ('power', 'k', 'mu', 'modes')>\n\n:\n\n# slice from k=0.01-0.1 for mu = 0.5\nprint(power_2d.sel(k=slice(0.01, 0.1), mu=0.5, method='nearest'))\n\n<BinnedStatistic: dims: (k: 8), variables: ('power', 'k', 'mu', 'modes')>\n\n\nWe also provide a squeeze() function which behaves similar to the numpy.squeeze() function:\n\n:\n\n# get all mu bins for the k bin closest to k=0.1, but keep k dimension\nsliced = power_2d.sel(k=[0.1], method='nearest')\nprint(sliced)\n\n<BinnedStatistic: dims: (k: 1, mu: 5), variables: ('power', 'k', 'mu', 'modes')>\n\n:\n\n# and then squeeze to remove the k dimension\nprint(sliced.squeeze())\n\n<BinnedStatistic: dims: (mu: 5), variables: ('power', 'k', 'mu', 'modes')>\n\n\nNote that, by default, array-based or label-based indexing will automatically “squeeze” sliced objects that have a dimension of length one, unless a list of indexers is used, as is done above.\n\n## Reindexing¶\n\nIt is possible to reindex a specific dimension of the coordinate grid using reindex(). The new bin spacing must be an integral multiple of the original spacing, and the variable values will be averaged together on the new coordinate grid.\n\n:\n\n# re-index into wider k bins\nprint(power_2d.reindex('k', 0.02))\n\n<BinnedStatistic: dims: (k: 32, mu: 5), variables: ('power', 'k', 'mu', 'modes')>\n\n/home/yfeng1/anaconda3/install/lib/python3.6/site-packages/nbodykit/binned_statistic.py:56: RuntimeWarning: Mean of empty slice\nndarray = operation(ndarray, axis=-1*(i+1))\n\n:\n\n# re-index into wider mu bins\nprint(power_2d.reindex('mu', 0.4))\n\n<BinnedStatistic: dims: (k: 64, mu: 2), variables: ('power', 'k', 'mu', 'modes')>\n\n/home/yfeng1/anaconda3/install/lib/python3.6/site-packages/nbodykit/binned_statistic.py:56: RuntimeWarning: Mean of empty slice\nndarray = operation(ndarray, axis=-1*(i+1))\n\n\nNote\n\nAny variable names passed to reindex() via the fields_to_sum keyword will have their values summed, instead of averaged, when reindexing.\n\n## Averaging¶\n\nThe average of a specific dimension can be taken using the average() function. A common use case is averaging over the mu dimension of a 2D BinnedStatistic, which is accomplished by:\n\n:\n\n# compute P(k) from P(k,mu)\nprint(power_2d.average('mu'))\n\n<BinnedStatistic: dims: (k: 64), variables: ('power', 'k', 'mu', 'modes')>\n\n/home/yfeng1/anaconda3/install/lib/python3.6/site-packages/nbodykit/binned_statistic.py:56: RuntimeWarning: Mean of empty slice\nndarray = operation(ndarray, axis=-1*(i+1))"
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https://gojiberries.io/2021/09/28/fooled-by-randomness/ | [
"# Fooled by Randomness\n\n28 Sep\n\nPermutation-based methods for calculating variable importance and interpretation are increasingly common. Here are a few common places where they are used:\n\n### Feature Importance (FI)\n\nThe algorithm for calculating permutation-based FI is as follows:\n\n1. Estimate a model\n2. Permute a feature\n3. Predict again\n4. Estimate decline in predictive accuracy and call the decline FI\n\nPermutation-based FI bakes in a particular notion of FI. It is best explained with an example: Say you are calculating FI for X (1 to k) in a regression model. Say you want to estimate FI of X_k. Say X_k has a large beta. Permutation-based FI will take the large beta into account when calculating the FI. So, the notion of importance is one that is conditional on the model.\n\nOften we want to get at a different counterfactual: If we drop X_k, what happens. You can get to that by dropping and re-estimating, letting other correlated variables get large betas. I can see a use case in checking if we can knock out say an ‘expensive’ variable. There may be other uses.\n\nAside: To my dismay, I kludged the two together here. In my defense, I thought it was a private email. But still, I was wrong.\n\nPermutation-based methods are used elsewhere. For instance:\n\n#### Creating Knockoffs\n\nWe construct our knockoff matrix X˜ by randomly swapping the n rows of the design matrix X. This way, the correlations between the knockoffs remain the same as the original variables but the knockoffs are not linked to the response Y. Note that this construction of the knockoffs matrix also makes the procedure random.\n\nFrom https://arxiv.org/pdf/1907.03153.pdf#page=4\n\n#### Local Interpretable Model-Agnostic Explanations\n\nThe recipe for training local surrogate models:\n\nSelect your instance of interest for which you want to have an explanation of its black box prediction.\n\nPerturb your dataset and get the black box predictions for these new points.\n\nWeight the new samples according to their proximity to the instance of interest.\n\nTrain a weighted, interpretable model on the dataset with the variations.\n\nExplain the prediction by interpreting the local model.\n\nFrom https://christophm.github.io/interpretable-ml-book/lime.html\n\n### Common Issue With Permutation Based Methods\n\n“Another really big problem is the instability of the explanations. In an article 47 the authors showed that the explanations of two very close points varied greatly in a simulated setting. Also, in my experience, if you repeat the sampling process, then the explantions that come out can be different. Instability means that it is difficult to trust the explanations, and you should be very critical.”\n\nFrom https://christophm.github.io/interpretable-ml-book/lime.html\n\n### Solution\n\nOne way to solve instability is to average over multiple rounds of permutations. It is expensive but the payoff is stability."
] | [
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.90310156,"math_prob":0.8565459,"size":2808,"snap":"2023-40-2023-50","text_gpt3_token_len":597,"char_repetition_ratio":0.10663338,"word_repetition_ratio":0.0,"special_character_ratio":0.19586894,"punctuation_ratio":0.113851994,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9664333,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-08T03:18:25Z\",\"WARC-Record-ID\":\"<urn:uuid:76e3914b-128d-43bf-9e94-42c02be5462f>\",\"Content-Length\":\"65941\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:bc6b4c13-b636-419a-b229-99d5a7c2788e>\",\"WARC-Concurrent-To\":\"<urn:uuid:45520665-1c79-4aff-a163-0bfcbc561c7d>\",\"WARC-IP-Address\":\"162.210.96.122\",\"WARC-Target-URI\":\"https://gojiberries.io/2021/09/28/fooled-by-randomness/\",\"WARC-Payload-Digest\":\"sha1:EIBIG2KAILKOLLAD2PAZQPP2L3W5ROZZ\",\"WARC-Block-Digest\":\"sha1:QGS73AIC2GZANFA3PLFFHSBWERULQJDI\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100710.22_warc_CC-MAIN-20231208013411-20231208043411-00882.warc.gz\"}"} |
https://www.aqua-calc.com/what-is/speed/meter-per-hour | [
"# What is a meter per hour (unit)\n\n## The meter per hour is a unit of measurement of speed\n\nA meter per hour (m/h) is a derived metric SI (System International) measurement unit of speed or velocity with which to measure how many meters traveled per one hour.\n\n• What is speedInstant conversionsConversion tables\n• 1 m/h = 0.02777777778 cm/s\n• 1 m/h = 1.66666667 cm/min\n• 1 m/h = 100 cm/h\n• 1 m/h = 0.0002777777778 m/s\n• 1 m/h = 0.01666666667 m/min\n• 1 m/h = 2.777777778×10-7 km/s\n• 1 m/h = 1.666666667×10-5 km/min\n• 1 m/h = 0.001 km/h\n• 1 m/h = 0.0005399568028 kn\n• 1 m/h = 0.0009113444167 ft/s\n• 1 m/h = 0.054680665 ft/min\n• 1 m/h = 3.2808399 ft/h\n• 1 m/h = 1.726031088×10-7 mi/s\n• 1 m/h = 1.035618653×10-5 mi/min\n• 1 m/h = 0.0006213711917 mi/h\n• 1 m/h = 1.499880008×10-7 nmi/s\n• 1 m/h = 8.999280047×10-6 nmi/min\n• 1 m/h = 0.0005399568028 nmi/h\n• 1 m/h = 3 600 s/m\n• 1 m/h = 3 600 000 s/km\n• 1 m/h = 1 097.28 s/ft\n• 1 m/h = 5 793 638.4 s/mi\n• 1 m/h = 60 min/m\n• 1 m/h = 60 000 min/km\n• 1 m/h = 18.288 min/ft\n• 1 m/h = 96 560.64 min/mi\n• 1 m/h = 2.777777778×10-7 klick/s\n• 1 m/h = 1.666666667×10-5 klick/min\n• 1 m/h = 0.001 klick/h\n• 1 m/h = 3 600 000 s/klick\n• 1 m/h = 60 000 min/klick\n\n#### Foods, Nutrients and Calories\n\nTurkey, retail parts, thigh, meat only, cooked, roasted contain(s) 159 calories per 100 grams or ≈3.527 ounces [ price ]\n\n1403 foods that contain Vitamin D3 (cholecalciferol). List of these foods starting with the highest contents of Vitamin D3 (cholecalciferol) and the lowest contents of Vitamin D3 (cholecalciferol), and Recommended Dietary Allowances (RDAs) for Vitamin D\n\n#### Gravels, Substances and Oils\n\nCaribSea, Freshwater, African Cichlid Mix, White weighs 1 169.35 kg/m³ (73.00014 lb/ft³) with specific gravity of 1.16935 relative to pure water. Calculate how much of this gravel is required to attain a specific depth in a cylindricalquarter cylindrical or in a rectangular shaped aquarium or pond [ weight to volume | volume to weight | price ]\n\nCarbon suboxide, gas [C3O2] weighs 2.985 kg/m³ (0.00172544 oz/in³) [ weight to volume | volume to weight | price | mole to volume and weight | mass and molar concentration | density ]\n\nVolume to weightweight to volume and cost conversions for Refrigerant R-434A, liquid (R434A) with temperature in the range of -40°C (-40°F) to 60°C (140°F)\n\n#### Weights and Measurements\n\nA radian per minute (rad/min) is the SI multiple unit of angular frequency, and also a unit of angular velocity. [ radian per minute ]\n\nThe kinematic viscosity (ν) is the dynamic viscosity (μ) divided by the density of the fluid (ρ)\n\nym/min² to µin/s² conversion table, ym/min² to µin/s² unit converter or convert between all units of acceleration measurement.\n\n#### Calculators\n\nCalculate volume of a dodecahedron and its surface area"
] | [
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http://blog.shaynefletcher.org/2015/10/list-comprehensions-in-c-via-list-monad.html | [
"## Sunday, October 4, 2015\n\n### List comprehensions in C++ via the list monad\n\nAs explained in Monads for functional programming by Philip Wadler, a monad is a triple $(t, unit, *)$. $t$ is a parametric type, $unit$ and $*$ are operations:\n\n val unit : α -> α t\nval ( * ) : α t -> (α -> β t) -> β t\n\n\n$m * \\lambda\\;a.n$\n\nas, \"perform computation $m$, bind $a$ to the resulting value, and then perform computation $n$\". Referring to the signatures of $*$ and $unit$, in terms of types we see $m$ has the type α t, $\\lambda\\;a.n$ has type α -> β t and the whole expression has type β t.\n\nIn order for $(t, unit, *)$ to be a monad the operations $unit$ and $*$ need satisfy three laws :\n\n• Left unit. Compute the value $a$, bind $b$ to the result, and compute $n$. The result is the same as $n$ with value $a$ substituted for variable $b$.\n\n$unit\\;a * \\lambda\\;b.n = n[a/b]$.\n\n• Right unit. Compute $m$, bind the result to $a$, and return $a$. The result is the same as $m$.\n\n$m * \\lambda\\;a.unit\\;a = m$.\n\n• Associative. Compute $m$, bind the result to $a$, compute $n$, bind the result to $b$, compute $o$. The order of parentheses doesn't matter.\n\n$m * (\\lambda\\;a.n * \\lambda\\;b.o) = (m * \\lambda\\;a.n) * \\lambda\\;b.o$.\n\nLists can be viewed as monads.That is, there exist operations $unit$ and $*$ that we may define for lists such that the three monad laws from the preceding section hold.\n\n#include <list>\n#include <iterator>\n#include <type_traits>\n#include <algorithm>\n#include <iostream>\n\n/*\n*/\n\n//The unit list containing 'a'\n/*\nlet unit : 'a -> 'a t = fun a -> [a]\n*/\ntemplate <class A>\nstd::list<A> unit (A const& a) { return std::list<A> (1u, a); }\n\n//The 'bind' operator\n/*\nlet rec ( * ) : 'a t -> ('a -> 'b t) -> 'b t =\nfun l -> fun k ->\nmatch l with | [] -> [] | (h :: tl) -> k h @ tl * k\n*/\ntemplate <class A, class F>\ntypename std::result_of<F(A)>::type\noperator * (std::list<A> a, F k) {\ntypedef typename std::result_of<F(A)>::type result_t;\n\nif (a.empty ())\nreturn result_t ();\n\nresult_t res = k (a.front ());\na.pop_front ();\nres.splice (res.end (), a * k);\n\nreturn res;\n}\n\nThe invocation $unit\\;a$ forms the unit list containing $a$. The expression, $m * k$ applies $k$ to each element of the list $m$ and appends together the resulting lists.\n\nThere are well known derived forms. For example, $join\\;z$ is the expression $z * \\lambda\\;m. m$. In the list monad, it results in a function that concatenates a list of lists.\n\n//'join' concatenates a list of lists\n/*\nlet join : 'a t t z = z * fun m -> m\n*/\ntemplate <class A>\nstd::list <A> join (std::list<std::list<A>> const& z) {\nreturn z * [](auto m) { return m; };\n}\n\nThe function $map$ is defined by the expression $map\\;f\\;m = m * \\lambda\\;a.unit\\;(f\\;a)$.\n//'map' is the equivalent of 'std::transform'\n/*\nlet map : ('a -> b') -> 'a t -> 'b t =\nfun f -> fun m -> m * fun a -> unit (f a)\n*/\ntemplate <class A, class F>\nstd::list<A> map (F f, std::list<A> const& m) {\nreturn m * [=](auto a) { return unit (f (a)); };\n}\n\n\n## List comprehensions\n\nList comprehensions are neatly expressed as monad operations. Here are some examples.\nint main () {\n\n//l = [1, 2, 3]\nstd::list<int> l = {1, 2, 3};\n\n//m = [1, 4, 9]\nauto m = l * [](int x) { return unit (float (x * x)); };\n\n//n = l x m = [(1, 1), (1, 4), (1, 9), (2, 1), (2, 4), (2, 9), ...]\nauto n = l * ([&m](int x){ return m * ([=](float y){ return unit (std::make_pair (x, y)); });});\n\nreturn 0;\n}"
] | [
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https://virtualnerd.com/common-core/hsa-algebra/HSA-CED-/A/ | [
"# Create equations that describe numbers or relationships.\n\n### Popular Tutorials in Create equations that describe numbers or relationships.\n\n• #### How Do You Solve a Formula For a Variable?\n\nSo you're working on a math problem and you have the correct formula. Great! But the variable you need to solve for is not by itself in the formula. Not so great. Don't worry! In this tutorial, you'll learn how to solve a formula for the variable you want!\n\n• #### What is a Literal Equation?\n\nA literal equation is an equation where variables represent known values. Literal equations allow use to represent things like distance, time, interest, and slope as variables in an equation. Using variables instead of words is a real time-saver! Learn about literal equations with this tutorial.\n\n• #### How Do You Solve a Word Problem Using an AND Compound Inequality?\n\nWord problems allow you to see math in action! This tutorial deals with turning a word problem into a compound inequality and solving that compound inequality to get the answer. Learn how in this tutorial!\n\n• #### How Do You Solve a Word Problem with Exponential Growth?\n\nIf something increases at a constant rate, you may have exponential growth on your hands. In this tutorial, learn how to turn a word problem into an exponential growth function. Then, solve the function and get the answer!\n\n• #### How Do You Solve a Word Problem with Exponential Decay?\n\nIf something decreases in value at a constant rate, you may have exponential decay on your hands. In this tutorial, learn how to turn a word problem into an exponential decay function. Then, solve the function and get the answer!\n\n• #### How Do You Solve a Word Problem Using an Exponential Function?\n\nWord problems let you see math in the real world! This tutorial shows you how to create a table and identify a pattern from the word problem. Then you can see how to create an exponential function from the data and solve the function to get your answer!\n\n• #### What's a Function?\n\nFunction rules are like instructions on how to change input values into their respective output values. In this tutorial, see how to write a function rule for a given relation. Check it out!\n\n• #### How Do You Write an Equation of a Line in Standard Form if You Have the Slope and One Point?\n\nKnowing how to write linear equations is an important steping stone on the road to becoming a master mathematician! In this tutorial, you'll practice using a slope and one point to write the equation of the line in standard form.\n\n• #### How Do You Write an Equation of a Line in Slope-Intercept Form If You Have Two Points?\n\nTrying to write an equation in slope-intercept form? Have two points on your line? You'll need to find your slope and y-intercept. Watch this tutorial and see what needs to be done to write an equation in slope-intercept form!\n\n• #### How Do You Write an Equation of a Line in Slope-Intercept Form from a Word Problem?\n\nWord problems are a great way to see math in the real world! In this tutorial, you'll see how write an equation in slope-intercept form that represents the information given in the word problem. To see how it's done, check out this tutorial!\n\n• #### How Do You Write an Equation for Direct Variation Given a Point?\n\nLooking for some practice with direct variation? Watch this tutorial, and get that practice! This tutorial shows you how to take given information and turn it into a direct variation equation. Then, see how to use that equation to find the value of one of the variables.\n\n• #### How Do You Write an Equation for Direct Variation from a Table?\n\nLooking for some practice with direct variation? Watch this tutorial, and get that practice! This tutorial shows you how to take a table of values and describe the relation using a direct variation equation.\n\n• #### How Do You Graph a Line If You're Given the Slope and the Intercept?\n\nTrying to graph a line from a given slope and y-intercept? Think you need to find an equation first? Think again! In this tutorial, see how to use that given slope and y-intercept to graph the line.\n\n• #### How Do You Write an Equation of a Line in Point-Slope Form If You Have the Slope and One Point?\n\nTrying to write an equation in point-slope form? Got a point on the line and the slope? Plug those values correctly into the point-slope form of a line and you'll have your answer! Watch this tutorial to get all the details!\n\n• #### How Do You Write an Equation of a Line in Point-Slope Form If You Have Two Points?\n\nTrying to write an equation in point-slope form? Have two points but no slope? You'll need to use those points to find a slope first. Watch this tutorial and see what needs to be done to write an equation in point-slope form!\n\n• #### How Do You Write an Equation of a Line in Point-Slope Form and Standard Form If You Have Two Points?\n\nGet some practice with the point-slope form and standard form of an equation! This tutorial shows you how to use two given points to write an equation in both forms. Take a look!\n\n• #### How Do You Write an Equation of a Line in Slope-Intercept Form If You Have the Slope and the Y-Intercept?\n\nWant to write an equation in slope-intercept form? Already have the slope and y-intercept? Perfect! Just correctly plug those values into your equation and you're done! Learn how in this tutorial.\n\n• #### How Do You Solve a Word Problem Using a System of Inequalities?\n\nMath can sneak up in all sorts of places, so it's important to be prepared! Follow this tutorial to see a real world math problem involving a system of inequalities!\n\n• #### How Do You Use a System of Linear Equations to Find Coordinates on a Map?\n\nLike riddles? A word problem is just like a riddle! In this word problem, you'll need to find the solution to a system of linear equations solve the riddle and find a location on a map. Check it out!\n\n• #### What's an Example of a Word Problem That Has a System of Linear Equations with Infinite Solutions?\n\nLike riddles? A word problem is just like a riddle! In this word problem, you'll need to find the solution to a system of linear equations solve the riddle and find a location on a map. Check it out!\n\n• #### How Do You Find the Axis of Symmetry for a Quadratic Function?\n\nThe axis of symmetry is the vertical line that goes through the vertex of a quadratic equation. There's even a formula to help find it! In this tutorial, you'll see how to find the axis of symmetry for a given quadratic equation.\n\n• #### How Do You Find the Vertex of a Quadratic Function?\n\nThe vertex of a quadratic equation is the minimum or maximum point of the equation. Did you know that you can use the formula for the axis of symmetry to help find the vertex of a quadratic equation? Watch this tutorial and see how it's done!\n\n• #### How Do You Make a Table for a Quadratic Function?\n\nWhen you're trying to graph a quadratic equation, making a table of values can be really helpful. To figure out what x-values to use in the table, first find the vertex of the quadratic equation. That way, you can pick values on either side to see what the graph does on either side of the vertex. To see how to make a table of values for a quadratic equation, check out this tutorial!\n\n• #### How Do You Graph a Quadratic Function?\n\nWhen you're trying to graph a quadratic equation, making a table of values can be really helpful. Before you make a table, first find the vertex of the quadratic equation. That way, you can pick values on either side to see what the graph does on either side of the vertex. Watch this tutorial to see how you can graph a quadratic equation!\n\n• #### How Do You Graph the Parent Quadratic Function y=x2?\n\nDealing with graphs of quadratic equations? You should know about the parent function graph first! All graphs of quadratic equations start off looking like this before their transformed. Check it out!\n\n• #### How Do You Solve a Word Problem Using the Quadratic Formula?\n\nWhen you mail a package, you need the right sized box. But what if you don't have any boxes? Just make one out of cardboard! Follow along with this tutorial to see how math can help you figure out the dimensions of a box created from a piece of cardboard!\n\n• #### What is the Axis of Symmetry of a Quadratic Function?\n\nEver notice that the left side of the graph of a quadratic equation looks a lot like the right side of the graph? In fact, these sides are just mirror images of each other! If you were to cut a quadratic equation graph vertically in half at the vertex, you would get these symmetrical sides. That vertical line that you cut has a special name. It's called the axis of symmetry. To learn about the axis of symmetry, watch this tutorial!\n\n• #### What is a Parabola?\n\nIf you graph a linear function, you get a line. If you graph a quadratic function, you get something called a parabola. A parabola tends to look like a smile or a frown, depending on the function. Check out this tutorial and learn about parabolas!\n\n• #### How Do You Solve a Word Problem with an Equation Using Addition?\n\nWord problems are a great way to see math in action! See how to translate a word problem into an equation, solve to find the answer, and check your found answer all in this tutorial.\n\n• #### How Do You Solve a Word Problem with an Equation Using Subtraction?\n\nWord problems are a great way to see math in action! See how to translate a word problem into an equation, solve to find the answer, and check your found answer all in this tutorial.\n\n• #### How Do You Solve a Word Problem Using an Equation Where You're Multiplying Fractions?\n\nWorking with word problems AND fractions? This tutorial shows you how to take a word problem and translate it into a mathematical equation involving fractions. Then, you'll see how to solve and get the answer. Check it out!\n\n• #### How Do You Solve for a Variable in Terms of Another Variable?\n\nGot an equation with two variables? Want to solve for one variable in terms of the other? Want to go the other way around? See how in this tutorial!\n\n• #### How Do You Solve a Word Problem with an Equation Using Multiplication?\n\nWorking with word problems AND fractions? This tutorial shows you how to take a word problem and translate it into a mathematical equation involving fractions. Then, you'll see how to solve and get the answer. Check it out!\n\n• #### How Do You Solve a Word Problem Using a Multi-Step Equation?\n\nWorking with word problems AND fractions? This tutorial shows you how to take a word problem and translate it into a mathematical equation involving fractions. Then, you'll see how to solve and check your answer. Take a look!\n\n• #### How Do You Solve a Word Problem with an Equation Using Division?\n\nWord problems are a great way to see math in action! See how to translate a word problem into an equation, solve to find the answer, and check your found answer all in this tutorial.\n\n• #### How Do You Use an Equation with Consecutive Numbers to Solve a Word Problem?\n\nWord problems are a great way to see math in the real world. In this tutorial, you'll see how to translate a word problem into a mathematical equation involving consecutive numbers. Then you'll see how to solve that equation and check your answer!\n\n• #### How Do You Solve a Word Problem Using a Two-Step Equation with Decimals?\n\nWord problems are a great way to see math in the real world. In this tutorial, you'll see how to translate a word problem into a mathematical equation. Then you'll see how to solve that equation and check your answer!\n\n• #### How Do You Figure Out How Much Something is Marked Down?\n\nGoing shopping? Is something you want on sale? Trying to figure out the sale price of that item? Follow along with this word problem and you'll see how to calculate that price!\n\n• #### How Do You Figure Out Sales Tax?\n\nGoing shopping can be tons of fun, but things can go sour when you get to the register and realize that the sales tax puts you over your budget. Always stay under budget by figuring out your total cost BEFORE you hit the check out. Watch this tutorial and learn how to calculate sales tax!\n\n• #### How Do You Figure Out the Volume of a Solution Using Percents?\n\nWord problems are a great way to see math in action! See how to create a table from the information in a word problem. Then use that table to write an equation and solve to find the answer.\n\n• #### How Do You Solve an Opposite-Direction Travel Problem?\n\nTwo people leave a location at different times and travel in opposite directions. What time will they be a certain distance apart? This tutorial takes you step-by-step through this classic word problem!\n\n• #### How Do You Solve a Word Problem Using the Direct Variation Formula?\n\nWord problems allow you to see math in action! Take a look at this word problem involving an object's weight on Earth compared to its weight on the Moon. See how the formula for direct variation plays an important role in finding the solution. Then use that formula to see how much you would weigh on the Moon!\n\n• #### How Do You Use the Formula for Direct Variation?\n\nIf two things are directly proportional, you can bet that you'll need to use the formula for direct variation to solve! In this tutorial, you'll see how to use the formula for direct variation to find the constant of variation and then solve for your answer.\n\n• #### How Do You Solve a Word Problem Using an AND Absolute Value Inequality?\n\nWord problems allow you to see math in action! This tutorial shows you how to translate a word problem to an absolute value inequality. Then see how to solve for the answer, write it in set builder notation, and graph it on a number line. Learn all about it in this tutorial!\n\n• #### How Do You Use Subtraction to Solve an Inequality Word Problem?\n\nWord problems allow you to see the real world uses of math! In this tutorial, learn how to translate a word problem into an inequality. Then see how to solve the inequality and understand the meaning of the answer.\n\n• #### How Do You Use Addition to Solve an Inequality Word Problem?\n\nWord problems allow you to see math in action! This tutorial deals with inequalities and money in a bank account. See how to translate a word problem into an inequality, solve the problem, and understand the answer. Take a look!\n\n• #### How Do You Use Division with Positive Numbers to Solve an Inequality Word Problem?\n\nThis tutorial provides a great real world application of math. See how to turn a word problem into an inequality. Then solve the inequality by performing the order of operations in reverse. Don't forget that if you multiply or divide by a negative number, you MUST flip the sign of the inequality! That's one of the big differences between solving equalities and solving inequalities.\n\n• #### How Do You Use Division with Negative Numbers to Solve an Inequality Word Problem?\n\nThis tutorial provides a great real world application of math. See how to turn a word problem into an inequality. Then solve the inequality by performing the order of operations in reverse. Don't forget that if you multiply or divide by a negative number, you MUST flip the sign of the inequality! That's one of the big differences between solving equalities and solving inequalities.\n\n• #### How Do You Use Multiplication with Positive Numbers to Solve an Inequality Word Problem?\n\nThis tutorial provides a great real world application of math. See how to turn a word problem into an inequality. Then solve the inequality by performing the order of operations in reverse. Don't forget that if you multiply or divide by a negative number, you MUST flip the sign of the inequality! That's one of the big differences between solving equalities and solving inequalities.\n\n• #### How Do You Use Multiplication with Negative Numbers to Solve an Inequality Word Problem?\n\nThis tutorial provides a great real world application of math. See how to turn a word problem into an inequality. Then solve the inequality by performing the order of operations in reverse. Don't forget that if you multiply or divide by a negative number, you MUST flip the sign of the inequality! That's one of the big differences between solving equalities and solving inequalities.\n\n• #### How Do You Write an Absolute Value Inequality from a Word Problem?\n\nSometimes the hardest part of a word problem is figuring out how to turn the words into math. This tutorial let's you see the steps to take in order to do just that! You'll see how to take a word problem and dissect it to turn it into an absolute value inequality.\n\n• #### How Do You Solve a Word Problem Using a Multi-Step Inequality?\n\nThis tutorial provides a great real world application of math. See how to turn a word problem into an inequality. Then solve the inequality by performing the order of operations in reverse. Don't forget that if you multiply or divide by a negative number, you MUST flip the sign of the inequality! That's one of the big differences between solving equalities and solving inequalities.\n\n• #### How Do You Solve a Word Problem Using an Inequality With Variables on Both Sides?\n\nThis tutorial provides a great real world application of math. See how to turn a word problem into an inequality. Then solve the inequality by performing the order of operations in reverse. Don't forget that if you multiply or divide by a negative number, you MUST flip the sign of the inequality! That's one of the big differences between solving equalities and solving inequalities.\n\n• #### How Do You Write Inequalities in Set Builder Notation?\n\nNeed some extra practice converting solution phrases into set builder notation? This tutorial was made for you! Follow along as this tutorial shows you how to dissect each phrase and turn it into a solution in set builder notation.\n\n• #### What Are Some Words We Use To Write Inequalities?\n\nKnowing the definition for a compound inequality is one thing, but being able to identify one in a word problem or phrase can be an entirely different challenge. Arm yourself by learning some of the common phrases used to describe a compound inequality and an absolute value inequality.\n\n• #### How Do You Solve a Word Problem with a Rational Equation?\n\nThis tutorial provides a great real world application of math! This tutorial shows you how to take the information given in a word problem and turn it into a rational equation. Then, you'll see how to solve that equation and get your answer!\n\n• #### How Do You Solve and Graph Inequalities from a Word Problem?\n\nWord problems are a great way to see the real world applications of math! In this tutorial, you'll see how to graph multiple inequalities to find the solution. Take a look!\n\n• #### How Do You Solve an Optimization Word Problem?\n\nOptimization problems are used everyday to help businesses figure out how much of their products they need to sell in order to make a profit. Follow along with this tutorial to see a real world problem involving optimization!\n\n• #### What is Linear Programming?\n\nIf you want to solve an optimization problem, you can use linear programming to help! This tutorial introduces linear programming and the different pieces of this method.\n\n• #### How Do You Write an Equation For a Quadratic if You Have Three Points?\n\nThree points determine a parabola, so given three points you can write the parabola's equation. This tutorial will show you how!\n\n• #### How Do You Write a Quadratic Equation in Vertex Form if You Have the Vertex and Another Point?\n\nYou can write the vertex form for a quadratic equation if you have the vertex and one other point! This tutorial shows you how to take that information and write an equation for the quadratic in vertex form.\n\n• #### How Do You Figure Out the Price of a Marked Up Item?\n\nThe price of items is always changing. You've probably went to the store to buy an item and found that its price has been marked up. In this tutorial, learn how to figure out the new price of an item that was marked up. Take a look!\n\n• #### How Do You Write the Equation of a Line in Slope-Intercept Form If You Have a Graph?\n\nWorking with the graph of a line? Trying to find the equation for that graph? Just pick two points on the line and use them to find the equation. This tutorial shows you how to take two points on the graph of a line and use them to find the slope-intercept form of the line!\n\n• #### How Do You Write the Equation of a Line in Slope-Intercept Form If You Have a Table?\n\nLooking at a table of values that represents a linear equation? Want to find that equation? Then check out this tutorial! You'll see how to use values from a table to find the slope-intercept form of the line described in the table.\n\n• #### How Do You Use Point-Slope Form to Write an Equation from a Table?\n\nLooking at a table of values that represents a linear equation? Want to find that equation? Then check out this tutorial! You'll see how to use values from a table and the point-slope form of a line to find the slope-intercept form of the line described in the table.\n\n• #### How Do You Write and Use a Prediction Equation?\n\nScatter plots are a great way to see data visually. They can also help you predict values! Follow along as this tutorial shows you how to draw a line of fit on a scatter plot and find the equation of that line in order to make a prediction based on the data already given!"
] | [
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.93351084,"math_prob":0.94067526,"size":16281,"snap":"2022-40-2023-06","text_gpt3_token_len":3323,"char_repetition_ratio":0.19241875,"word_repetition_ratio":0.4033092,"special_character_ratio":0.20115472,"punctuation_ratio":0.09271318,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.999241,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-10-06T08:35:16Z\",\"WARC-Record-ID\":\"<urn:uuid:dd6d2f64-d349-4988-86d7-04c1b3fc59ad>\",\"Content-Length\":\"142766\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1cd800f8-f690-4fbb-a590-d613c8261f77>\",\"WARC-Concurrent-To\":\"<urn:uuid:aafc330c-50ef-428f-8e9f-7d8d3eba1834>\",\"WARC-IP-Address\":\"18.67.76.13\",\"WARC-Target-URI\":\"https://virtualnerd.com/common-core/hsa-algebra/HSA-CED-/A/\",\"WARC-Payload-Digest\":\"sha1:VTUMTVEZA4DDHGEP2KR3TKF3LH4SSXQN\",\"WARC-Block-Digest\":\"sha1:ANOQSFCTKINEAMMVYEAF352DIEW4LT4U\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030337731.82_warc_CC-MAIN-20221006061224-20221006091224-00727.warc.gz\"}"} |
https://www.keyence.co.uk/ss/products/measure/measurement_library/basic/si/ | [
"# Measurement FundamentalsInternational System of Units (SI)\n\nThe principle behind the International System of Units is to provide the same values for measurements such as length, weight, and time no matter where in the world measurement is performed. The units used in this system are referred to as “SI units.” The system was established at the 1960 General Conferences on Weights and Measures (CGPM). The abbreviation “SI” stands for “Le Système International d'Unités.”\n\nThe International System of Units comprises the following three categories.\n\n• Base units\n• Supplementary units\n• Derived units\n\n## Base Units\n\nAmount Unit name Unit symbol Definition\nLength Metre m The distance traveled by light in a vacuum in 1/299792458 second.\nWeight Kilogram kg This is the unit for weight. The mass of the international prototype kilogram.\nTime Second s The duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.\nCurrent Ampere A The constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 m apart in vacuum, would produce between these conductors a force equal to 2×10-7 newtons per metre of length.\nThermodynamic temperature Kelvin K 1/273.16 of the thermodynamic temperature of the triple point of water.\nSubstance amount Mole mol The amount of substance of a system that contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12. (Limited to objects with clarified composition.) Elementary entities are subatomic particles that compose matter and energy.\nLuminosity Candela cd The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540×1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.\n\n## Supplementary Units\n\nAmount Unit name Unit symbol Definition\nPlane angle Radian rad Radian describes the plane angle subtended by an arc of a circle with the same length as the radius of that circle corresponds to an angle of 1 radian.\nSolid angle Steradian sr A steradian is a solid angle at the centre of a sphere subtending a section on the surface equal in area to the square of the radius of the sphere.\n\n## Derived Units\n\nDerived units are a combination of base units and supplementary units and the mathematical symbols of multiplication and division.\n\nAmount Unit name Unit symbol\nArea Square metre m2\nVolume Cubic metre m3\nSpeed Metre per second m/s\nAcceleration Metre per second squared m/s2\nWavenumber Reciprocal metre m-1\nDensity Kilogram per cubic metre kg/m3\nCurrent density Ampere per square metre A/m2\nMagnetic field strength Ampere per metre A/m\nConcentration (of amount of substance) Mole per cubic metre mol/m3\nSpecific volume Cubic metre per kilogram m3/kg\nLuminance Candela per square metre cd/m2\n\nSome derived units are given unique names.\n\nAmount Unit name Unit symbol Composition\nFrequency Hertz Hz 1Hz=1s-1\nForce Newton N 1N=1kg･m/s2\nPressure, stress Pascal Pa 1Pa=1N/m2\nEnergy, work, amount of heat Joule J 1J=1N･m\nPower, radiant flux Watt W W=1J/s\nElectric charge, amount of electricity Coulomb C 1C=1A･s\nElectric potential/electric potential difference, voltage, electromotive force Volt V 1V=1J/C\nResistance (electrical) Ohm Ω 1Ω=1V/A\nConductance (electrical) Siemens S 1S=1Ω-1\nMagnetic Weber Wb 1Wb=1V･s\nMagnetic flux density, magnetic induction Tesla T 1T=1Wb/m2\nInductance Henry H 1H=1Wb/A\nCelsius temperature Degree Celsius 1t=T-To\nLuminous flux Lumen lm 1lm=1cd･sr\nIlluminance Lux lx 1lx=1lm/m2\n\n## Reference Information\n\nSI unit prefixes indicating integer powers of ten\n\nFactor Prefix Symbol Factor Prefix Symbol\n1018 exa E 10-1 deci d\n1015 peta P 10-2 centi c\n1012 tera T 10-3 milli m\n109 giga G 10-6 micro µ\n106 mega M 10-9 nano n\n103 kilo k 10-12 pico p\n102 hecto h 10-15 femto f\n10 deka da 10-18 atto a\n\nNon-SI units\n\nAmount Unit name Unit symbol Definition\nTime Minute min 1min=60s\nHour h 1h=60min\nDay d 1d=24h\nPlane angle Degree ° 1°= (π/180) rad\nMinute 1′= (1/60) °\nSecond 1″= (1/60) ′\nVolume Litre l, L 1l=7dm3\nWeight Metric ton t 1t=103kg"
] | [
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https://www.forwardjunction.com/2016/02/only-for-genius-find-answer.html | [
"ANSWER\n\n-13 is the Answer\nExplanation\nAccording to BODMAS Rule:\n3-(3x6)+2 (First we calculate multiplication or division)\n3-(18)+2\n(3-18)+2 (Since addition and subtraction has equal priority, we calculate in the order from beginning)\n-15 +2\n= -13\n\n#### 4 comments:\n\n1.",
null,
"Think of it as money coming in and out of your bank account...\n\nIf you have \\$3 and make a charge of \\$18, then you have -\\$15 in your account. Then adding \\$2 makes it overdrawn -\\$13.\n\nBEDMAS can confuse people. The acronym is to remember the order of the components, but you still have to remember the entire list of rules.\n\nBrackets\nExponents\nDivision and Multiplication\n*(in the order they occur)\nAddition and Subtraction\n*(in the order they occur).\n\nI was taught to do all the parenthesis then exponents, then insert brackets around the division & multiplication so it kept things in order.\n\nSo the equation is expressed as such\n\n3 - 3 x 6 + 2\n= 3 - (3 x 6) +2\n\nThen you remember to do the equations inside brackets first, left to right, in the order they occur.\n\n= 3 - (18) + 2\n\nThen, since addition and subtraction are EQUAL, you do them IN ORDER, left to right.\n\n= (3 - 18) + 2\n= (-15) + 2\n= (-13)\n\n2.",
null,
"3.",
null,
"You are almost correct except for one mistake. BODMAS must be taken literally. You went wrong on the last part...MAS = Multiply, Add, Subtract. (ADD first, then SUBTRACT). = 3-18+2 = 3-20 = -17\n\n1.",
null,
"hmm. no\nWhen it comes to multiply/divide or add/subtract you work from left to right."
] | [
null,
"https://lh3.googleusercontent.com/zFdxGE77vvD2w5xHy6jkVuElKv-U9_9qLkRYK8OnbDeJPtjSZ82UPq5w6hJ-SA=s35",
null,
"https://lh5.googleusercontent.com/-uDMzWikEa6E/AAAAAAAAAAI/AAAAAAAAACY/959HWp2BVdw/s35-c/photo.jpg",
null,
"https://lh3.googleusercontent.com/zFdxGE77vvD2w5xHy6jkVuElKv-U9_9qLkRYK8OnbDeJPtjSZ82UPq5w6hJ-SA=s35",
null,
"https://lh3.googleusercontent.com/zFdxGE77vvD2w5xHy6jkVuElKv-U9_9qLkRYK8OnbDeJPtjSZ82UPq5w6hJ-SA=s35",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.92145044,"math_prob":0.9857736,"size":1460,"snap":"2019-35-2019-39","text_gpt3_token_len":399,"char_repetition_ratio":0.11332417,"word_repetition_ratio":0.0,"special_character_ratio":0.2931507,"punctuation_ratio":0.11418685,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9972634,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,null,null,1,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-08-20T21:10:31Z\",\"WARC-Record-ID\":\"<urn:uuid:40d34aeb-0e42-45a6-bb26-ad4a055e43ad>\",\"Content-Length\":\"289001\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a86ec492-3052-4971-8971-2983ccb62f40>\",\"WARC-Concurrent-To\":\"<urn:uuid:e2996221-8cac-422e-8bdc-62dad9d94796>\",\"WARC-IP-Address\":\"172.217.12.243\",\"WARC-Target-URI\":\"https://www.forwardjunction.com/2016/02/only-for-genius-find-answer.html\",\"WARC-Payload-Digest\":\"sha1:F46YPM3U2EL7L5NWIWJW3HYALVYALATJ\",\"WARC-Block-Digest\":\"sha1:HM35NJ3VM3JNNS5QHGSZYHANJJTXLLGQ\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-35/CC-MAIN-2019-35_segments_1566027315618.73_warc_CC-MAIN-20190820200701-20190820222701-00195.warc.gz\"}"} |
https://studylib.net/doc/10506854/ | [
"# Document 10506854",
null,
"```Page 1\nSection 5.7: Challenge Problems\n1. Find f (x)\n(a) f ′ (x) =\nx4 + 20x2 + 40\n5x3\n(b) f ′ (x) =\n7\n15\n3\n+ 2x + √ + e2\n2\n1+x\ne\nx\n2. Find r(t) given that r ′ (t) = 4 sec2 (4t), sin(5t)\n3. Find f (x) when f ′′ (x) = 12x2 − 6x + 2 when f (0) = 1 and f (2) = 0\n4. A car braked with a constant deceleration of 40ft/sec2 , producing skid\nmarks measuring 160ft before coming to a stop. How fast was the car\ntraveling when the brakes were first applied?\n```"
] | [
null,
"https://s2.studylib.net/store/data/010506854_1-00ffa584912b36f00719d7446a754a71.png",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.8326267,"math_prob":0.9992779,"size":482,"snap":"2020-10-2020-16","text_gpt3_token_len":208,"char_repetition_ratio":0.11087866,"word_repetition_ratio":0.0,"special_character_ratio":0.45435685,"punctuation_ratio":0.09821428,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9981477,"pos_list":[0,1,2],"im_url_duplicate_count":[null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-02-20T12:04:24Z\",\"WARC-Record-ID\":\"<urn:uuid:b7813825-5900-4aed-b72c-0a69407f0acd>\",\"Content-Length\":\"65389\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c31ca996-7ad1-4bf1-8951-2df38e28782b>\",\"WARC-Concurrent-To\":\"<urn:uuid:5fb94029-60c0-4e14-9bfc-ec34156118fd>\",\"WARC-IP-Address\":\"104.24.125.188\",\"WARC-Target-URI\":\"https://studylib.net/doc/10506854/\",\"WARC-Payload-Digest\":\"sha1:FGKAA4K25B7D6T6SLYIFIIMDEKOUZNUZ\",\"WARC-Block-Digest\":\"sha1:E3XOWDKDWY7BUJQVJQVM3N4BAPLJBPRT\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-10/CC-MAIN-2020-10_segments_1581875144722.77_warc_CC-MAIN-20200220100914-20200220130914-00201.warc.gz\"}"} |
https://physics.stackexchange.com/questions/467949/what-happens-to-p-f-%C3%97-v-for-a-car-moving-on-a-frictionless-surface-and-in-va | [
"# What happens to $P = F × v$ for a car moving on a frictionless surface and in vacuum?\n\nI'm considering a scenario in which a car with an engine capable of producing maximum power of 200 hp is moving on a frictionless surface and in vacuum. Since no work is lost due to friction or air drag, the car should accelerate indefinitely. For this scenario, let's assume that the 200 hp engine is working at full power and producing 2000 N at the wheels.\n\nNow since the car will be accelerating indefinitely, there will be a point at which the velocity of the car multiplied by the force will result in a power requirement more than what the engine of the car can produce.\n\nTo illustrate this, let's assume that the car has accelerated to a velocity of 500 m/s, the power then will be: P = F × v = 2000 N × 500 m/s which is equal to $$10^6$$ watts or about 1300 hp.\n\nMy question simply is: since the engine is incapable of producing any thing above 200 hp, then how will this situation alter the power equation to reflect this?\n\n• I think you're confusing the power provided by the engine with the actual power of the system. The part that accelerates the system, in this case the engine, can indeed have a smaller power than the total power that the system can achieve, as you're moving on a frictionless surface and there's nothing from stopping you from adding more power. Mar 21, 2019 at 23:55\n• To exemplify this, consider a rocket which moves in the vacuum (assume it has infinite, massless fuel). It will continue pushing the rocket even to relativistic speeds if there's nothing to stop it, and ultimately the net power of the rocket $P=F\\cdot v$ will be obviously way bigger than the power that the engine is able to provide, yet it will continue accelerating assymptotically towards the speed of light (it will never each it, though, as that would need an infinite amount of energy). So I think the same idea applies to your example. Mar 21, 2019 at 23:57\n• @Charlie: correct. Put it as an answer.\n– Gert\nMar 22, 2019 at 0:03\n• @Charlie. I understand what you mean. But now if we consider that F= ma, then it is obvious that the car should have a constant acceleration, but at the certain point, the engine will be unable to accelerate the car at the same rate since the system is increasingly requiring more power to accelerate at the same rate at higher velocities. So what will happen, will the force drop to compensate for this? Mar 22, 2019 at 0:03\n• @AbanobEbrahim not exactly. As you can see from $F=ma$, the acceleration will indeed be constant if the force is constant, so there's nothing stopping a small force from accelerating an object to great velocities. The power you provide doesn't have to be more or equal to the net power of the system, as there's no reason to compensate since you aren't losing energy (as you're on a frictionless surface). You will need to compensate only if there's a mechanism that causes the system to lose energy, like friction or radiation. Mar 22, 2019 at 0:06\n\nAs cars work due to friction, I'm going to assume that you mean a system without any drag rather than no friction. So that 100% of the power of the engine is developed into increasing the KE of the car.\n\nFor this scenario, let's assume that the 200 hp engine is working at full power and producing 2000 N at the wheels.\n\nUnfortunately, we can't do that with a real engine. For any real engine, the ability to develop force/torque decreases as the speed gets higher. In fact, you can use the speed and the power to find the max force at that speed.\n\nAt high speed the engine will still be able to accelerate the vehicle, but with ever decreasing amounts of force/torque.\n\nBut my question here is about the physical quantities rather than the true capability of an ICE. In other words and to make things simpler, let's use a 200 hp rocket producing 2000 N\n\nThis isn't a limitation of an internal combustion engine (or any engine). It's a limitation of how the force is produced. You only have two choices for producing the force:\n\n• You're pushing against some external mass (like the earth)\n• You're pushing against some mass you have with you (you're a rocket)\n\nMy answer above is limited to the first case. As your speed increases relative to the reaction mass, your ability to produce torque decreases. This doesn't matter if it's an ICE, an electric motor, a spring, or anything.\n\nIf you bring the reaction mass with you, then you are producing constant force, not constant power. But at the beginning, your system is horribly inefficient from an energy point of view. Whereas in the first case all of the energy of the engine can go into the KE of the car, in case of the rocket most of the energy is going into the KE of the exhaust.\n\nAt high speeds (when the rocket is going at speeds approaching the exhaust velocity), additional power comes from the fact that the KE of the now-accelerated fuel is reduced as it leaves the rocket.\n\nA rocket can produce constant thrust, but not constant power. The power will change as it accelerates.\n\nHere's one last way to think about it: The transmission from your power unit (engine) to your reaction mass (the ground) can be considered to be a moveable lever.\n\nYou have a choice with a lever, you can shorten the lever so that it produces high speed but reduces the force you apply, or you can lengthen the lever so that it produces lower speed, but increases the force you apply.\n\nAs your speed relative to the reaction mass increases, you have to bias your lever more to the \"speed\" side, which will reduce your applied force. In a car this happens through the gears in the transmission, but is true regardless of the method applied.\n\n• I agree with you from an ICE point of view. But my question here is about the physical quantities rather than the true capability of an ICE. In other words and to make things simpler, let's use a 200 hp rocket producing 2000 N. Mar 22, 2019 at 1:57\n• My answer is not specific to ICE. Amended. Mar 22, 2019 at 3:00\n• @AbanobEbrahim, added an analogy to a lever. That may be a bit more what you're looking for. Think of moving a lever's fulcrum closer to you. It allows you to keep up with a fast moving load, but it decreases the force you can apply. Mar 22, 2019 at 3:15\n\nFor this scenario, let's assume that the 200 hp engine is working at full power and producing 2000 N at the wheels.\n\n200 hp is approximately 150 kW so I am just going to use that for this answer.\n\nBecause $$P=F\\cdot v$$ if you specify both $$P$$ and $$F$$ then there is only one possible $$v$$. In this case $$P=150\\text{ kW}$$ and $$F=2\\text{ kN}$$ implies $$v=75\\text{ m/s}$$. No other velocity, either higher or lower, is possible to meet that combination of power and force.\n\nIf the car continues accelerating at peak power then the force will necessarily decrease as the velocity increases. Under the idealized conditions you listed you can continue accelerating indefinitely, but at progressively lower force and lower accelerations. This is directly implied by $$P=F\\cdot v$$\n\n• Thank you. I think your answer makes the most sense to me. If I understand you correctly, and in order to keep the force and acceleration constant, we would alternatively need to progressively increase the power of the engine to match the value calculated from P=Fv at constant force and increasing speed. Is that correct? Mar 22, 2019 at 2:04\n• Yes, that is exactly correct\n– Dale\nMar 22, 2019 at 2:30\n• Great. That makes perfect sense mathematically and from the equations. But practically in case we want to keep the power constant, how can I conceive the idea that the force will inevitably have to decrease while knowing that the engine should still produce 2000 N as this is independent on the system? Mar 22, 2019 at 2:35\n• “knowing that the engine should still produce 2000 N as this is independent on the system”. I don’t know where this idea came from, but it is not correct. The force produced by a drive train is not independent of the speed. Sometimes a force is listed as the force at v=0. Could you be misinterpreting the v=0 max force as a max force at all v?\n– Dale\nMar 22, 2019 at 2:56\n• No I understand this. But can't we for simplicity in this scenario just picture the engine as a rocket with massless fuel while neglecting the KE of the exhaust? By doing this we will skip the problems arising specifically from internal combustion engines since this scenario just requires a source of constant force of 2000 N. Mar 22, 2019 at 3:06\n\nI note your question says the car is\n\nmoving on a frictionless surface and in vacuum\n\nLet's go back to work for a moment: the work formulation is: $$W = F\\cdot{d}$$\n\nwhereby in your situation it means \"the additional distance covered by the car due to the engine power input during a certain time interval\"\n\nFollowing from that definition, power $$P$$ is \"The additional velocity given to the car by force $$F$$\", i.e.\n\n$$P = {F\\cdot d \\over{t}}$$\n\nTherefore, the expression $$P = F \\cdot v$$ means the power $$P$$ required to $$\\underline{increase}$$ the velocity of the car using force $$F$$, is that force $$F$$ multiplied by the $$\\underline{additional}$$ velocity given to the car during the applicable time interval.\n\nNow, if we simplify the situation and say that friction in the engine does not increase, even then, the engine will not be able to accelerate the car beyond a certain speed because of chemical limitations: there is a minimum time required to combust the fuel-air mixture in the engine cylinders.\n\nNote that in the real world, the force would be required to maintain a velocity because air resistance, friction and so on are trying to slow down the car with a 'power' output equal to the power input of the force being used to maintain that speed.\n\n• This answer is not correct. P=F.v is valid at every instant. There is no interval involved. At every instant the instantaneous power is equal to the force times the instantaneous velocity. There is no need to determine an interval nor what is additional velocity\n– Dale\nMar 22, 2019 at 1:53\n• @Dale It is useful and perhaps necessary to consider time since the question states no resistance, so no power would be required to maintain any velocity. In the real world, yes, the force would be required to maintain a velocity because air resistance, friction and so on are trying to slow down the car with a 'power' output equal to the power input of the force being used to maintain that speed. Consideration of time is valid. You may wish to simplify it for your own understanding, that's fine. Mar 22, 2019 at 2:25\n• It has nothing to do with simplification for my understanding. It is just about the meaning of the terms in the equation $P=F\\cdot v$. P is instantaneous power and v is instantaneous velocity and F is the force whose power we wish to calculate. There is no “additional velocity” nor any “applicable time interval” involved. Those concepts have no part in the equation. Bringing them in is simply wrong. Consideration of a time interval is not valid for a formula which uses only instantaneous quantities\n– Dale\nMar 22, 2019 at 3:28"
] | [
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.9553096,"math_prob":0.9652156,"size":2669,"snap":"2022-27-2022-33","text_gpt3_token_len":577,"char_repetition_ratio":0.13358349,"word_repetition_ratio":0.016632017,"special_character_ratio":0.21768452,"punctuation_ratio":0.08988764,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9941532,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-07-01T02:43:55Z\",\"WARC-Record-ID\":\"<urn:uuid:f5f3e4c1-0dca-4d12-98f4-f5a02c021cf4>\",\"Content-Length\":\"273930\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2635ce12-2089-4fed-8b50-1f4e07787735>\",\"WARC-Concurrent-To\":\"<urn:uuid:b289f13f-3700-45de-8f1d-81f901540b18>\",\"WARC-IP-Address\":\"151.101.129.69\",\"WARC-Target-URI\":\"https://physics.stackexchange.com/questions/467949/what-happens-to-p-f-%C3%97-v-for-a-car-moving-on-a-frictionless-surface-and-in-va\",\"WARC-Payload-Digest\":\"sha1:2OMOZDSZIVUA7RECJJDTD6QLJ4TONFI3\",\"WARC-Block-Digest\":\"sha1:T7CSGSXKD46OUOYZFG7XPU7XINA2DH47\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656103917192.48_warc_CC-MAIN-20220701004112-20220701034112-00656.warc.gz\"}"} |
https://tools.carboncollective.co/compound-interest/44877-at-22-percent-in-29-years/ | [
"# What is the compound interest on $44877 at 22% over 29 years? If you want to invest$44,877 over 29 years, and you expect it will earn 22.00% in annual interest, your investment will have grown to become $14,337,020.51. If you're on this page, you probably already know what compound interest is and how a sum of money can grow at a faster rate each year, as the interest is added to the original principal amount and recalculated for each period. The actual rate that$44,877 compounds at is dependent on the frequency of the compounding periods. In this article, to keep things simple, we are using an annual compounding period of 29 years, but it could be monthly, weekly, daily, or even continuously compounding.\n\nThe formula for calculating compound interest is:\n\n$$A = P(1 + \\dfrac{r}{n})^{nt}$$\n\n• A is the amount of money after the compounding periods\n• P is the principal amount\n• r is the annual interest rate\n• n is the number of compounding periods per year\n• t is the number of years\n\nWe can now input the variables for the formula to confirm that it does work as expected and calculates the correct amount of compound interest.\n\nFor this formula, we need to convert the rate, 22.00% into a decimal, which would be 0.22.\n\n$$A = 44877(1 + \\dfrac{ 0.22 }{1})^{ 29}$$\n\nAs you can see, we are ignoring the n when calculating this to the power of 29 because our example is for annual compounding, or one period per year, so 29 × 1 = 29.\n\n## How the compound interest on $44,877 grows over time The interest from previous periods is added to the principal amount, and this grows the sum a rate that always accelerating. The table below shows how the amount increases over the 29 years it is compounding: Start Balance Interest End Balance 1$44,877.00 $9,872.94$54,749.94\n2 $54,749.94$12,044.99 $66,794.93 3$66,794.93 $14,694.88$81,489.81\n4 $81,489.81$17,927.76 $99,417.57 5$99,417.57 $21,871.87$121,289.43\n6 $121,289.43$26,683.68 $147,973.11 7$147,973.11 $32,554.08$180,527.19\n8 $180,527.19$39,715.98 $220,243.18 9$220,243.18 $48,453.50$268,696.68\n10 $268,696.68$59,113.27 $327,809.94 11$327,809.94 $72,118.19$399,928.13\n12 $399,928.13$87,984.19 $487,912.32 13$487,912.32 $107,340.71$595,253.03\n14 $595,253.03$130,955.67 $726,208.70 15$726,208.70 $159,765.91$885,974.61\n16 $885,974.61$194,914.41 $1,080,889.03 17$1,080,889.03 $237,795.59$1,318,684.61\n18 $1,318,684.61$290,110.61 $1,608,795.23 19$1,608,795.23 $353,934.95$1,962,730.18\n20 $1,962,730.18$431,800.64 $2,394,530.82 21$2,394,530.82 $526,796.78$2,921,327.59\n22 $2,921,327.59$642,692.07 $3,564,019.67 23$3,564,019.67 $784,084.33$4,348,103.99\n24 $4,348,103.99$956,582.88 $5,304,686.87 25$5,304,686.87 $1,167,031.11$6,471,717.98\n26 $6,471,717.98$1,423,777.96 $7,895,495.94 27$7,895,495.94 $1,737,009.11$9,632,505.04\n28 $9,632,505.04$2,119,151.11 $11,751,656.15 29$11,751,656.15 $2,585,364.35$14,337,020.51\n\nWe can also display this data on a chart to show you how the compounding increases with each compounding period.\n\nAs you can see if you view the compounding chart for $44,877 at 22.00% over a long enough period of time, the rate at which it grows increases over time as the interest is added to the balance and new interest calculated from that figure. ## How long would it take to double$44,877 at 22% interest?\n\nAnother commonly asked question about compounding interest would be to calculate how long it would take to double your investment of $44,877 assuming an interest rate of 22.00%. We can calculate this very approximately using the Rule of 72. The formula for this is very simple: $$Years = \\dfrac{72}{Interest\\: Rate}$$ By dividing 72 by the interest rate given, we can calculate the rough number of years it would take to double the money. Let's add our rate to the formula and calculate this: $$Years = \\dfrac{72}{ 22 } = 3.27$$ Using this, we know that any amount we invest at 22.00% would double itself in approximately 3.27 years. So$44,877 would be worth $89,754 in ~3.27 years. We can also calculate the exact length of time it will take to double an amount at 22.00% using a slightly more complex formula: $$Years = \\dfrac{log(2)}{log(1 + 0.22)} = 3.49\\; years$$ Here, we use the decimal format of the interest rate, and use the logarithm math function to calculate the exact value. As you can see, the exact calculation is very close to the Rule of 72 calculation, which is much easier to remember. Hopefully, this article has helped you to understand the compound interest you might achieve from investing$44,877 at 22.00% over a 29 year investment period."
] | [
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.895373,"math_prob":0.99905056,"size":4636,"snap":"2023-14-2023-23","text_gpt3_token_len":1594,"char_repetition_ratio":0.13061313,"word_repetition_ratio":0.014144272,"special_character_ratio":0.47476274,"punctuation_ratio":0.23215751,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99987006,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-04-02T12:55:52Z\",\"WARC-Record-ID\":\"<urn:uuid:2dba6fd2-bba9-4b29-b8e8-522d2b629218>\",\"Content-Length\":\"30293\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2d712816-f9ab-4daf-b9a5-d812c425b7bc>\",\"WARC-Concurrent-To\":\"<urn:uuid:a98820e2-6920-4df7-83cf-591d99e13e6f>\",\"WARC-IP-Address\":\"138.197.3.89\",\"WARC-Target-URI\":\"https://tools.carboncollective.co/compound-interest/44877-at-22-percent-in-29-years/\",\"WARC-Payload-Digest\":\"sha1:TMHTNUCM47YPKBF53PGJ3VWOBZPWSWOL\",\"WARC-Block-Digest\":\"sha1:MFUV3M3FOSPCUQQWL53FSJDOVPOSX2N5\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-14/CC-MAIN-2023-14_segments_1679296950528.96_warc_CC-MAIN-20230402105054-20230402135054-00381.warc.gz\"}"} |
https://www.jiskha.com/questions/48942/a-2-kg-otter-starts-from-rest-at-the-top-of-a-muddy-incline-85-cm-long-ans-slides-down-to | [
"# Physics\n\nA 2 kg otter starts from rest at the top of a muddy incline 85 cm long ans slides down to the bottom in 0.5 s. What net external force acts on the otter along the incline?\n\nI know which equation I need to use. But how can I use the cm and s to get the acceleration?\n\n1. 👍\n2. 👎\n3. 👁\n\n## Similar Questions\n\n1. ### physics\n\nA small block is released from rest at the top of a frictionless incline. The distance from the top of the incline to the bottom, measured along the incline, is 3.60 m. The vertical distance from the top of the incline to the\n\n2. ### physics\n\nA small block with mass 0.200 kg is released from rest at the top of a frictionless incline. The block travels a distance 0.440 m down the incline in 2.00 s. The 0.200 kg block is replaced by a 0.400 kg block. If the 0.400 kg\n\n3. ### physics\n\nA frictionless incline is 5.00 m long (the distance from the top of the incline to the bottom, measured along the incline). The vertical distance from the top of the incline to the bottom is 4.03 m. A small block is released from\n\n4. ### Physics\n\nA 3.00-kg block starts from rest at the top of a 25.5° incline and slides 2.00 m down the incline in 1.75 s. (a) Find the acceleration of the block. m/s2 (b) Find the coefficient of kinetic friction between the block and the\n\n1. ### Physics\n\nA 2.0Kg otter starts from rest at the top of a muddy incline 85 cm long and slides down to the bottom in .50s. What net force acts on the otter along the incline?\n\n2. ### physics\n\nA 3.00 kg block starts from rest at the top of a 30° incline and accelerates uniformly down the incline, moving 1.94 m in 1.70 s. (a) Find the magnitude of the acceleration of the block. (b) Find the coefficient of kinetic\n\n3. ### Physics\n\nA block slides down a frictionless plane having an inclination of θ = 13.2°. The block starts from rest at the top, and the length of the incline is 1.70 m. -> Find the acceleration of the block. (m/s2 down the incline) -> Find\n\n4. ### physics\n\nA small block is released from rest at the top of a frictionless incline. The distance from the top of the incline to the bottom, measured along the incline, is 3.70 m. The vertical distance from the top of the incline to the\n\n1. ### physics\n\nA box slides down a frictionless 35 degree incline. Determine its acceleration. If the incline is 10.0 m long and the box starts from rest, how much time does it take to get to the bottom?\n\n2. ### Physics repost\n\nA 2 kg otter starts from rest at the top of a muddy incline 85 cm long ans slides down to the bottom in 0.5 s. What net external force acts on the otter along the incline? I know which equation I need to use. But how can I use the\n\n3. ### Physics\n\nA 2.92 kg block starts from rest at the top of a 30° incline and accelerates uniformly down the incline, moving 1.93 m in 1.60 s. (a) Find the magnitude of the acceleration of the block. __ m/s2 (b) Find the coefficient of\n\n4. ### physics\n\nA 2.6 kg block slides down a 25° inclined plane with constant acceleration. The block starts from rest at the top. At the bottom, its velocity is 0.75 m/s. The incline is 1.6 m long. (a) What is the acceleration of the block? (b)"
] | [
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https://www.exceltip.com/information-formulas/rri-function.html | [
"# RRI function\n\nRRI function\n\nRRI function has been introduced with Excel 2013. It returns the interest rate for the growth of an given investment based on it's present value and future value for a given period.\n\nFor example, to know what would be the interest rate for an intitial investment of Rs.1000 to become double i.e, Rs.2000 in 5 years, we can use RRI formula as\n\n= RR(5,1000,2000)\n\n= 14.87%\n\nSyntax:-\n\n=RRI(nper, pv, fv)\n\nwhere\n\nnper is the number of periods for the investment\n\nPv is the present value of the investment\n\nFv is the future value of the investment\n\nNote:- If you enter any non-numbers in above arguments, you'll get #VALUE! error.\n\nTerms and Conditions of use\n\nThe applications/code on this site are distributed as is and without warranties or liability. In no event shall the owner of the copyrights, or the authors of the applications/code be liable for any loss of profit, any problems or any damage resulting from the use or evaluation of the applications/code."
] | [
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.9067867,"math_prob":0.90792906,"size":933,"snap":"2022-05-2022-21","text_gpt3_token_len":226,"char_repetition_ratio":0.13240042,"word_repetition_ratio":0.0,"special_character_ratio":0.24115756,"punctuation_ratio":0.11398964,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9659919,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-16T06:12:35Z\",\"WARC-Record-ID\":\"<urn:uuid:73497964-a78c-443b-8251-a546df9f98f3>\",\"Content-Length\":\"78462\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:3c86d055-2987-4505-a655-5b8cb8eb7a78>\",\"WARC-Concurrent-To\":\"<urn:uuid:4c6ed73a-fb0a-4d30-bd58-e4ef3e7bba94>\",\"WARC-IP-Address\":\"69.167.154.15\",\"WARC-Target-URI\":\"https://www.exceltip.com/information-formulas/rri-function.html\",\"WARC-Payload-Digest\":\"sha1:LLGZJWIBSUADHDSLG7AMQQODRYDXNDN4\",\"WARC-Block-Digest\":\"sha1:FSK2FIGO3JBJJBMLYWJTNJI2NNP3MONO\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662509990.19_warc_CC-MAIN-20220516041337-20220516071337-00333.warc.gz\"}"} |
https://www.jagranjosh.com/articles/important-reasoning-questions-for-rrb-je-exam-1558006236-1?ref=desktop_details_recommended | [
"",
null,
"Important Reasoning Questions for RRB JE CBT-1 2019 Exam\n\nWe have compiled for you the most important General Intelligence & Reasoning Questions that have maximum chances to come this year in the RRB JE CBT-1 2019 Exam. So start practicing these questions to ace the RRB JE CBT-1 2019 Exam this year.\n\nMay 16, 2019 18:56 IST",
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"Important Reasoning Questions for RRB JE CBT-1 2019 Exam\n\nRRB JE 1st Stage CBT 2019 Exam will be held from 22nd May 2019 onwards. The General Intelligence & Reasoning section of CBT 1 Exam is of 25 Marks. You can start practicing these questions and understand the problems in detail with the help of explanations given alongwith the answers in the below Quiz:\n\n Classification\n\nDirections (1- 5): Some groups of letters are given, all of which, except one, share a common similarity while one is different. Choose the odd one out.\n\n1.\n\na) Flower: Petal\n\nb) Triangle : Angle\n\nc) Cover : Page\n\nd) Table : Leg\n\nExplanation: In all other pairs, second is a part of the first.\n\n2.\n\na) Ostrich\n\nb) Penguin\n\nc) Emu\n\nd) Owl\n\nExplanation: Out of the four except owl, all is flightless birds.\n\n3.\n\na) Triangle\n\nb) Trifle\n\nc) Triathlon\n\nd) Trilingual\n\nExplanation: Except (b), tri indicates ‘three’.\n\n4.\n\na) Volcanoes\n\nb) Tsunamis\n\nd) Explosion\n\nExplanation: All except (d), are natural calamities.\n\n5.\n\na) E/7\n\nb) 1/13\n\nc) N/17\n\nd) X/26\n\nExplanation: In all other options, denominator is the numeric position of the alphabet plus 2.\n\nClick here to know the Best Books for RRB JE 2019 Exam\n\n Analogy\n\nDirections (6– 10): In each of the following questions, there is a certain relationship between two given words on one side of (: :) and one word is given on another side (: :) while another word is to be found from the given alternatives, having the same relation with this word as the words of the given pair bear. Choose the correct alternative.\n\n6. 12: 20 :: 30: __?\n\na) 40\n\nb) 42\n\nc) 50\n\nd) 44\n\nExplanation: 12 is 32 + 3\n\n20 is 42 + 4\n\n30 is 52 + 5\n\nAnd 62 + 6 = 42\n\n7. United states: Bald eagle :: India : ?\n\na) Cheetah\n\nb) Lion\n\nc) Sparrow\n\nd) Peacock\n\nExplanation: As Bald eagle is the national bird of US; similarly Peacock is the national animal of India.\n\n8. 10.1: 1.01 :: 0.1: __? __\n\na) 1\n\nb) 0.10\n\nc) 0.01\n\nd) 0.001\n\nExplanation: 10.1 is divided by 10 to get 1.01. Divide 0.1 by 10 to get 0.01\n\n9. Kidney: Nephrology :: Brain: __? __\n\na) Cardiology\n\nb) Physiology\n\nc) Anatomy\n\nd) Neurology\n\nExplanation: Study of Kidney is Nephrology and the study of brain is called Neurology.\n\n10. F: 37 :: I : __?\n\na) 52\n\nb) 27\n\nc) 75\n\nd) 82\n\nExplanation: F is the sixth letter in the series and square of 6 (6*6) + 1 is 37. I is the ninth letter and the square of 9 (9*9) +1 is 82.\n\n Coding Decoding\n\n11. In a certain code ‘415’ means ‘milk is hot’; ‘18’ means ‘hot soup’; and ‘895’ means ‘soup is brown’. What number will indicate the word ‘brown’?\n\na) 9\n\nb) 8\n\nc) 5\n\nd) 4\n\nExplanation: The code for ‘hot’ is 1. So, the code of ‘soup’ is 8. Now, the code for ‘is’ is 5. Hence, we can say that the code for ‘brown’ is 9.\n\n12. If CEJQ is coded as XVQJ, then BDIP will be coded as:\n\na) WURQ\n\nb) YWRK\n\nc) WUPI\n\nd) YWPI\n\nExplanation: The first 13 letters of the alphabet are coded by the 13 letters of the alphabet in reverse, i.e.\n\n= A B C D E F G H I J K L M (first 13 letters)\n\n= Z Y X W V U T S R Q P O N (13 letters in reverse)\n\nIt is obvious from the above coding scheme that:\n\nB = Y, D = W, I = R and K = P or P = K\n\nTherefore, B D I P will be coded as Y W R K.\n\n13. If LODES is coded as 46321, how will you code the word DOES?\n\na) 1234\n\nb) 4321\n\nc) 3621\n\nd) 3261\n\nExplanation: Here, you will observe that all the letters of DOES are included in the letters of LODES, for which you have the code D = 3, O = 6, E = 2, S = 1. Therefore DOES = 3621. So, the answer is (d).\n\nClick here to know the latest Exam Pattern and Syllabus of RRB JE 2019 Exam\n\n Syllogism\n\nDirections (14 – 16): In each question below are given three statements followed by three or four conclusions numbered I to IV. You have to take the two given statements to be true even if they seem to be at variance with commonly known facts. Read both the statements and then decide which of the given conclusions logically follows from the given statements, disregarding commonly known facts.\n\n14. Statements: All pencils are sharpeners. No sharpener is eraser. Some books are pencils.\n\nConclusions:\n\n1. Some erasers are pencils.\n2. Some erasers are books.\n3. Some sharpeners are books.\n4. No eraser is books.\n\na) Only either II or III, and IV follow\n\nb) Only either II or IV, and III follow\n\nc) Only either II or IV, and I follow\n\nd) Only either II or IV follows.\n\nExplanation:",
null,
"Either II or IV will follow and II will definitely be true.\n\n15. Statements: Some pigeons are eagles. All eagles are sparrows. Some sparrows are not pigeons.\n\nConclusions:\n\n1. Some sparrows are pigeons.\n2. All pigeons are sparrows.\n3. All eagles are pigeons.\n\na) Only I follows\n\nb) Only II follows\n\nc) Only III follows\n\nd) Both I and III follows\n\nExplanation:",
null,
"Only I is definitely true.\n\n16. Statements: Some computers are laptops. Some laptops are mobiles. Some mobiles are calculators. (Banking)\n\nConclusions:\n\n1. Some computers are calculators.\n2. Some calculators are laptops.\n3. Some mobiles are computers.\n\na) Only I follows\n\nb) Only II follows\n\nc) Only III follows\n\nd) None follows\n\nExplanation:",
null,
"None of the statement is necessarily true.\n\nClick here to know the RRB JE 2019 Exam Preparation Tips and Strategy\n\n Direction Sense\n\n17. Ram facing south. He turns right and walks 40 metre. Then he turns right again and walks 20 metre. Then he turns left and walks 20 metre and then turning right walk 40 metre. Then he turns right again and walks 120 metre. In which direction he is from the starting point?\n\na) North-East\n\nb) North-West\n\nc) North\n\nd) West\n\nExplanation:",
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"18. Rajat goes towards east kilometers, and then he takes a turn to South west and goes 12 kilometres. He again takes a turn towards North West and goes 12kilometres. With respect to the point from where he started, where is he now?\n\na) At the starting point.\n\nb) In the west\n\nc) In the east\n\nd) In the North West.\n\nExplanation:",
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"Blood Relations\n\n19. Ravi told Ram, “yesterday I defeated the only brother of the daughter of my grandmother”. Whom did Ravi defeat?\n\na) Father\n\nb) Brother\n\nc) Son\n\nd) Father –in –law\n\nExplanation: Daughter of grandmother –aunt, aunt’s only daughter—father.\n\nDirections (20 - 21): Read the following information carefully and answer the questions given below it:\n\nE x K, means E is brother of K.\n\nE – K, means E is mother of K.\n\nE % K, means E is father of k.\n\n20. Which of the following represents that’ N’ is the son of ’P ‘?\n\na) N x R %P\n\nb) N%R x P\n\nc) P % N x R\n\nd) N-R % T\n\nExplanation: P%N, means P is father of N and N x R, means N is brother of R, thus N is the son of P.\n\n21. How is ‘B’ related to ‘P’ in the relation P x Q % R- B?\n\na) Maternal uncle\n\nb) Nephew\n\nc) Grandson\n\nd) none of these\n\nExplanation: In P x Q % R-B, P x Q means, P is brother of Q and Q%R means, Q is father of R, R-B=R is mother of B. Thus, P is maternal –grandfather of B.\n\n Logical Venn Diagram\n\n22. Which of the options is true based on the Venn diagram below?",
null,
"a) Some honest people are also hardworking and are literate\n\nb) Illiterates are either honest or hard working\n\nc) All literates are rural\n\nd) No person is rural, literate, honest and hardworking\n\nClick here to know the RRB JE Salary after 7th Pay Commission, Job Profile and Promotion Policy\n\n Arrangements: Linear\n\nDirections (23 24): Read the following information carefully and answer the questions given below.\n\nSix boys A, B, C, D, E and F are marching in a line, their positions arranged according to their heights, the tallest at the back. F is between A and B. E is shorter than D but taller than C who is taller than A. E and F have two boys between them. A is the not the shortest.\n\n23. Where is E?\n\na) Between A and B\n\nb) Between A and C\n\nc) Between C and D\n\nd) In front of C\n\n24. How many boys are between E and F?\n\na) 1\n\nb) 2\n\nc) 3\n\nd) 4\n\nExplanation (23-24): Shortest…B F A C E D..Tallest\n\nDirections (25 - 26): Answer the questions on basis of the information given below:\n\nRohan, Ramesh, Geeta, Ankit and Govind are sitting on a straight table. Geeta is sitting next to Rohan, Ankit is sitting next to Ramesh is not sitting with Govind who is on the left end of the table. Ankit is second from the right. Geeta is right of Rohan and Govind. Geeta and Ankit are sitting together.\n\n25. Who is sitting extreme right?\n\na) Govind\n\nb) Ramesh\n\nc) Ankit\n\nd) Geeta\n\n26. In which position Geeta is sitting?\n\na) Between Rohan and Ramesh\n\nb) Between Rohan and Ankit\n\nc) Between Govind and Ramesh\n\nd) Between Ankit and Govind\n\nExplanation (25-26): By the information given we can have the following arrangement.\n\nGovind Rohan Geeta Ankit Ramesh\n\n Non Verbal Reasoning - Series\n\n27. Which number replaces the question mark?",
null,
"a) 4\n\nb) 3\n\nc) 5\n\nd) 7\n\nExplanation: Split the left and right hand circles in half, vertically.\n\nNow, the number appearing in middle circle follows the below series:\n\n(7 + 5) ÷ 2 = 6 (top left hand segment of the middle circle)\n\n(9 + 3) ÷ 4 = 3 (top right hand segment of the middle circle)\n\n(6 + 9) ÷ 5 = 3 (bottom left hand segment of the middle circle)\n\n(4 + 8) ÷ 6 = 2 (bottom right hand segment of the middle circle)\n\n28. Which letter replaces the question mark?",
null,
"a) B\n\nb) C\n\nc) H\n\nd) J\n\nExplanation: In each diagram, letters are written in sequence, starting in the top left circle and moving clockwise around the other 3 outer circles, in steps given by the numerical value of the central letter each time.\n\n Non Verbal Reasoning - Analogy\n\nDirections (29 - 30): Each of the following questions consists of two sets of figures. Figures A, B, C and D constitute the Problem Set while figures a), b), c) and d) constitute the Answer Set. There is a definite relationship between figures A and B. Establish a similar relationship between figures C and D by selecting a suitable figure from the Answer Set that would replace the question mark (?) in figure (D).\n\n29.",
null,
"Explanation: The second figure is divided into as many parts as the number of sides of the first figure. Similarly, Fourth figure will be divided by six lines as the third figure is a hexagon.\n\n30.",
null,
"Explanation: The inner element enlarges to become the outer element while the outer element reduces in size, turns black and becomes the inner element.\n\n Non Verbal Reasoning - Mirror Image\n\nDirections (31-32): In each of the following questions, choose the correct mirror image from the alternatives (a), (b), (c) and (d), when mirror is placed on the line AB.",
null,
"",
null,
"Non Verbal Reasoning - Paper Cutting and Folding\n\nDirections (33-34) - Choose a figure which would most closely resemble the unfolded form of the last question figure.\n\n33.",
null,
"34.",
null,
"Non Verbal Reasoning - Completion of Figure Pattern\n\nDirections (35-36): In each of the following questions, a part of question figure is missing. Find out from the given answer figures (a), (b), (c) and (d), that can replace the ‘?’ to complete the question figure.",
null,
"Explanation:",
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"",
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"Explanation:",
null,
"Alphanumeric Series\n\nDirections (37 - 40): Study the following arrangement carefully and answer the question given below.\n\nP S U 3 G D 6 Q F 5 = A 1 H B 7 I 9 T M 8 # E J 2 * R 4 W\n\n37. Which of the following is the fifth to the right of the fifteenth from the right end?\n\na) 8\n\nb) T\n\nc) #\n\nd) M\n\nExplanation: The fifteenth element from the right end of the arrangement is B, and the fifth element to the right of B is M.\n\n38. If order of the last eleven elements is reversed, which of the following will be seventh to the right of ninth from the left end?\n\na) B\n\nb) 7\n\nc) I\n\nd) H\n\nExplanation: P S U 3 G D 6 Q F 5 = A 1 H B 7 I 2 W 4 R * 2 J E # 7 M T\n\nThe ninth element from the left end of this arrangement is F, and the seventh element to the right of F is 7.\n\n39. Four of the following five are alike in a certain way on the basis of the above arrangement and hence form a group. Which one does not belong to that group?\n\na) P U G\n\nb) = 1 B\n\nc) Q = H\n\nd) I T 8\n\nExplanation: In all other groups, the first and second elements each move 2 steps forward to give the second and third elements respectively.\n\n40. If the position of 6 and 2 are interchanged and similarly the position of U and R are interchanged then how many symbols will be there each of which is either preceded or followed by a vowel?\n\na) 1\n\nb) 2\n\nc) 3\n\nd) 4\n\nExplanation: Such symbols in the new arrangement may be indicated as follow:",
null,
"Number Series\n\nDirections (41-45): Choose the next number in the series from the options below:\n\n41. 26, 24, 20, 18, 14, ?\n\na) 8\n\nb) 10\n\nc) 12\n\nd) 11\n\nExplanation: Sequence of -2, -4 is being followed in the question.\n\n42. 0, 1, 1, 2, 4, 8, ?\n\na) 12\n\nb) 15\n\nc) 14\n\nd) 16\n\nExplanation: Every term is the sum of all its previous numbers. So the last number should be 16.\n\n43. 37, 10, 79, 16, 48, ?\n\na) 22\n\nb) 20\n\nc) 12\n\nd) 18\n\nExplanation: Every second number is the sum of the digits of its previous number.\n\n44. -4, 3, -11, 10, ?\n\na) -27\n\nb) -18\n\nc) 18\n\nd) -35\n\nExplanation: The first term is added with 7 to get 3. The second term is subtracted with 14 to get -11. -11 is added with 21 to get 10. So 10 should be subtracted with the next factor of 7 that is 10-28= -18.\n\n45. 1, 0.05, 0.0025, ?\n\na) 0.000125\n\nb) 0.0000125\n\nc) 0.00125\n\nd) 0.00000125\n\nExplanation: Starting from 1 each number is being divided by 20.\n\n Letter Series\n\nDirections (46-47): In each of the following letter series, some of the letters are missing which are given in that order as one of the alternatives below it. Choose the correct alternative.\n\n46. _ baa _ aa _ aab _\n\na) baba\n\nb) bbab\n\nc) aabb\n\nd) abba\n\nExplanation: The series is aba/aba/aba/aba. Thus, the pattern ‘aba’ is repeated.\n\n47. _ cd _ ac _ b _ _ dbacd _\n\na) abdbca\n\nb) abdacb\n\nc) abdbac\n\nExplanation: The series acdb/ acdb/ acdb/ acdb. Thus, the pattern ‘ acdb ‘ is repeated.\n\n Word Formation\n\nDirections (48 – 50): Find the word which cannot be made from letters of the given word.\n\n48. IMPECCABLE\n\na) LIME\n\nb) BEAM\n\nc) PEBBLE\n\nd) CABLE\n\n49. PREDILECTION\n\na) DICTION\n\nb) DIRECTION\n\nc) ELECTION\n\nd) PREDICTIONS\n\n50. APPREHENSION\n\na) HOPE\n\nb) HAPPY\n\nc) PENSION\n\nd) NOISE\n\n•",
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https://whatisconvert.com/318-square-feet-in-square-kilometers | [
"# What is 318 Square Feet in Square Kilometers?\n\n## Convert 318 Square Feet to Square Kilometers\n\nTo calculate 318 Square Feet to the corresponding value in Square Kilometers, multiply the quantity in Square Feet by 9.290304E-8 (conversion factor). In this case we should multiply 318 Square Feet by 9.290304E-8 to get the equivalent result in Square Kilometers:\n\n318 Square Feet x 9.290304E-8 = 2.954316672E-5 Square Kilometers\n\n318 Square Feet is equivalent to 2.954316672E-5 Square Kilometers.\n\n## How to convert from Square Feet to Square Kilometers\n\nThe conversion factor from Square Feet to Square Kilometers is 9.290304E-8. To find out how many Square Feet in Square Kilometers, multiply by the conversion factor or use the Area converter above. Three hundred eighteen Square Feet is equivalent to zero point zero zero zero zero two nine five four Square Kilometers.\n\n## Definition of Square Foot\n\nThe square foot (plural square feet; abbreviated sq ft, sf, ft2) is an imperial unit and U.S. customary unit (non-SI, non-metric) of area, used mainly in the United States and partially in Bangladesh, Canada, Ghana, Hong Kong, India, Malaysia, Nepal, Pakistan, Singapore and the United Kingdom. It is defined as the area of a square with sides of 1 foot. 1 square foot is equivalent to 144 square inches (Sq In), 1/9 square yards (Sq Yd) or 0.09290304 square meters (symbol: m2). 1 acre is equivalent to 43,560 square feet.\n\n## Definition of Square Kilometer\n\nSquare kilometre (International spelling as used by the International Bureau of Weights and Measures) or square kilometer (American spelling), symbol km2, is a multiple of the square metre, the SI unit of area or surface area. 1 km2 is equal to 1,000,000 square metres (m2) or 100 hectares (ha). It is also approximately equal to 0.3861 square miles or 247.1 acres.\n\n## Using the Square Feet to Square Kilometers converter you can get answers to questions like the following:\n\n• How many Square Kilometers are in 318 Square Feet?\n• 318 Square Feet is equal to how many Square Kilometers?\n• How to convert 318 Square Feet to Square Kilometers?\n• How many is 318 Square Feet in Square Kilometers?\n• What is 318 Square Feet in Square Kilometers?\n• How much is 318 Square Feet in Square Kilometers?\n• How many km2 are in 318 ft2?\n• 318 ft2 is equal to how many km2?\n• How to convert 318 ft2 to km2?\n• How many is 318 ft2 in km2?\n• What is 318 ft2 in km2?\n• How much is 318 ft2 in km2?"
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https://answers.everydaycalculation.com/add-fractions/9-5-plus-5-27 | [
"Solutions by everydaycalculation.com\n\n## Add 9/5 and 5/27\n\n1st number: 1 4/5, 2nd number: 5/27\n\n9/5 + 5/27 is 268/135.\n\n#### Steps for adding fractions\n\n1. Find the least common denominator or LCM of the two denominators:\nLCM of 5 and 27 is 135\n2. For the 1st fraction, since 5 × 27 = 135,\n9/5 = 9 × 27/5 × 27 = 243/135\n3. Likewise, for the 2nd fraction, since 27 × 5 = 135,\n5/27 = 5 × 5/27 × 5 = 25/135\n4. Add the two fractions:\n243/135 + 25/135 = 243 + 25/135 = 268/135\n5. In mixed form: 1133/135\n\n#### Add Fractions Calculator\n\n+\n\nUse fraction calculator with our all-in-one calculator app: Download for Android, Download for iOS"
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http://physicshelpforum.com/energy-work/421-work-done-lift-body.html | [
"User Name Remember Me? Password\n\n Energy and Work Energy and Work Physics Help Forum",
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"Sep 19th 2008, 03:30 AM #1 Member Join Date: Apr 2008 Posts: 31 work done to lift a body",
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"",
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"$\\displaystyle W=\\frac{1}{2}F_R\\cdot{R}$ Am I approaching the problem correctly? Thanks.",
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"",
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"Sep 20th 2008, 04:16 PM #2\n\nJoin Date: Apr 2008\nLocation: On the dance floor, baby!\nPosts: 2,856\n Originally Posted by disclaimer",
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"",
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"$\\displaystyle W=\\frac{1}{2}F_R\\cdot{R}$ Am I approaching the problem correctly? Thanks.\nThe equation for the line forming the top of the boundary is\n$\\displaystyle F = \\frac{F_R}{R} \\cdot r$\nand the work done is\n$\\displaystyle W = \\int_0^RF~dr$\n(The applied force F and dr are in the same direction.)\n\nSo we have\n$\\displaystyle W = \\int_0^R \\frac{F_Rr}{R}~dr$\n\n$\\displaystyle W = \\frac{F_R}{2R} \\cdot R^2 + 0$\n\n$\\displaystyle W = \\frac{1}{2}F_R R$\n\n(Or you could simply find the area of the triangle, as I suspect you did.)\n\n-Dan\n__________________\nDo not meddle in the affairs of dragons for you are crunchy and taste good with ketchup.\n\nSee the forum rules here.",
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"",
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"Tags body, force, lift, work",
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"Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post THERMO Spoken Here Thermodynamics and Fluid Mechanics 0 Aug 24th 2016 02:40 PM THERMO Spoken Here Thermodynamics and Fluid Mechanics 0 Aug 24th 2016 02:36 PM Alluvius Thermodynamics and Fluid Mechanics 4 Nov 25th 2013 12:52 AM turtle1026 General Physics 6 Jun 11th 2012 12:17 PM baytom Kinematics and Dynamics 3 Feb 23rd 2009 04:23 AM"
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https://chemistry.stackexchange.com/questions/171508/activation-energy-of-the-reaction-between-magnesium-carbonate-and-hydrochloric-a | [
"# Activation energy of the reaction between magnesium carbonate and hydrochloric acid\n\nI've been working on a project that uses some abnormal methods to calculate the activation energy using only one trial of an exothermic reaction.\n\nHowever now that I've completed the lab, I want to find a literature value or at least another lab which calculated the activation energy before. Balanced equation below:\n\n$$\\ce{MgCO3(s) + 2HCl(aq) -> MgCl2(aq) + CO2(g) + H2O(l)}$$\n\nI've checked through all of the responses to Is there a database on chemical reactions, similar to NIST, but far more complete? However, all the replies focused on organic chemistry or purely gaseous reactions.\n\nWhere can I find a database or lab which measured the activation energy of similar/the same reaction?\n\n• Then better use something in your project that has actual chance of working, as far as Ea is concerned. Like a reaction between things in the same phase. Feb 18 at 19:44\n• Is there any \"activation energy\" (above a ground state) at all? This is an acid/base reaction. There does not seem to be any rate limiting step at all, rate would be based on concentration of reactants. However 2 H2 + O2 -> 2 H2O is reversible at high enough temperatures (and does have an Ea). This may be more what you are after. One interesting possibility: would HCl react with MgCO3 at near absolute zero temperatures? Feb 18 at 22:16\n• Robert DiGiovanni - I was under the impression that everything technically had an activation energy because at absolute zero (theoretically) there could be no reaction because nothing was moving. Therefore there has to be activation energy, even for an exothermic reaction, just to get started. Feb 19 at 2:11\n• Mithoron - if I assume that the MgCO3 had to dissolve in the water before reacting, then is there a way to find the Ea of MgCO3(aq) and HCl(aq)? Feb 19 at 2:11"
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