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https://assignmentpoint.com/compound-interest/	[ "Finance\n\n# Compound Interest", null, "Compound interest (or compound interest) applies to interest payments made on the amount of the initial principal and the interest accrued in advance. It is the product of reinvesting interest, rather than paying it back, so that interest on the principal sum plus previously accrued interest is then paid in the next cycle. Thought to possess originated in 17th century Italy, interest is thought of as “interest on interest”, and can make a sum grow at a faster rate than interest, which is calculated only on the principal amount.\n\nIn finance and economics compound interest is the norm. It allows investors to gain potentially very high returns over a long period of time and is effectively a risk-free way to generate wealth. Multiplying the initial principal sum by one plus the average interest rate adjusted to the number of compound periods minus one determines compound interest. It is very different from equity investments, in which capital gains are generated only if the market value of the security rises over time (i.e., buy low, sell high).\n\nWhen measuring compound interest, a major difference is in the number of compounding times. Compound interest is not fully risk-free, as the interest payer may adjust the default or interest rates. Notwithstanding, the component of accumulating funds is the thing that makes it moderately riskless contrasted with different speculations. It is stood out from basic intrigue, where recently amassed intrigue isn’t added to the chief measure of the current time frame, so there is no intensifying.", null, "The following are the four main components of compound interest:\n\n• Principal – The principal is the amount that was initially deposited in a compounding system (for example, bank savings account with high-interest rates). It is the starting number from which the first payment of interest is measured.\n• Interest rate – The interest rate applies to the amount of the loan that is paid. The interest charge would be equal to the rate of interest plus the account balance (which is the amount of the initial principal and any interest earlier paid).\n• Compounding Frequency – The intensifying recurrence decides how frequently a year the intrigue is paid. It will impact the loan cost itself as high-recurrence exacerbating will regularly just be accessible with lower rates. Regularly, aggravating happens on a month to month, quarterly, or yearly premise.\n• Time horizon – Time horizon alludes to the measure of time over which the progressive accrual instrument can work. The more drawn out the time skyline, the more intrigue installments that can be made, and the bigger the consummation account worth will be. Time horizon is the absolute most significant part of progressive accrual, as it basically directs the future gainfulness of a venture. An aggravating domain with low rates and low intensifying recurrence can in any case be alluring if the accessible time horizon is exceptionally long.\n\nThe rate at which compound interest accumulates depends on the compounding frequency, so the higher the number of compounding periods, the greater the compound interest. The compounding frequency is the amount of times the accrued interest is paid out or capitalized (credited to the account) on a regular basis, every year (or occasionally, another unit time). Thus, the quantity of compound interest accrued on \\$100 compounded at 10% annually is less than that on \\$100 compounded at 5% semi-annually over the identical fundamental measure. Since the interest-on-interest effect can generate increasingly positive returns supported the initial principal amount, it’s sometimes been observed because of the “miracle of compound interest.”\n\nCompound interest was once considered the worst kind of usury and was heavily condemned in many other countries by Roman law and common laws. Multiplying the initial principal sum by one plus the average interest rate adjusted to the number of compound periods minus one determines compound interest. The original cumulative loan amount is then subtracted from the resulting value.\n\nThe formula for calculating compound interest is:\n\nCompound Interest = Total amount of Principal and Interest in future (or Future Value) less Principal amount at present (or Present Value)\n\n= (P (1 + i)n) – P\n\n= P ((1 + i)n – 1)\n\nWhere:\n\nP = Principal\n\ni = nominal annual interest rate in percentage terms\n\nn = number of compounding periods\n\nThe effect of compounding depends on:\n\n• The nominal interest rate is applied and\n• The frequency interest is compounded.\n\nWhen measuring compound interest, a major difference is in the number of compounding times. The basic rule is that the greater the amount of compound interest, the higher the number of compounding periods.\n\nInformation Sources:" ]	[ null, "https://assignmentpoint.com/wp-content/uploads/2020/09/Compound-Interest.jpg", null, "https://assignmentpoint.com/wp-content/uploads/2020/09/Compound-Interest-CI.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.94029546,"math_prob":0.96231127,"size":4757,"snap":"2022-40-2023-06","text_gpt3_token_len":915,"char_repetition_ratio":0.19377236,"word_repetition_ratio":0.091984235,"special_character_ratio":0.19045617,"punctuation_ratio":0.08131068,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99187595,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-10-07T20:08:20Z\",\"WARC-Record-ID\":\"<urn:uuid:45874bd3-0982-42c3-99fe-39d3ed399faf>\",\"Content-Length\":\"35996\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a5ab7085-1364-4153-a426-b625dddfa6aa>\",\"WARC-Concurrent-To\":\"<urn:uuid:7eb0b7a9-9d18-4b7a-a0e2-31a69fe0e95e>\",\"WARC-IP-Address\":\"178.63.81.55\",\"WARC-Target-URI\":\"https://assignmentpoint.com/compound-interest/\",\"WARC-Payload-Digest\":\"sha1:A6PPQ2USEHX2IMKVHMIYR7FSBP6TMXQS\",\"WARC-Block-Digest\":\"sha1:4JSBISO27EZN22J3QWFQE5NAIWGDIFEE\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030338244.64_warc_CC-MAIN-20221007175237-20221007205237-00428.warc.gz\"}"}
https://dba.stackexchange.com/questions/322124/why-changing-limit-triggers-different-query-plans-in-postgresql	[ "# Why changing limit triggers different query plans in postgresql?\n\nChanging only limit from 40 to 50 in following query triggers different execution plans. And unfortunatly one I needed is much slower. So the question is: why this happening and how can I force postgresql to use faster plan? I'm using postgresql 14.5\n\n``````SELECT \"Id\"\nFROM \"Podcasts\" AS P\nINNER JOIN \"PodcastCategories\" AS PC ON P.\"Id\"=PC.\"PodcastId\"\nWHERE \"LastPublishDate\" IS NOT NULL AND \"Dead\" = false AND \"Hidden\" = false AND PC.\"CategoryId\" = ANY (ARRAY)\nAND P.\"LastPublishDate\"<'2023-01-14 23:00:00+00'\nORDER BY \"LastPublishDate\" DESC\nLIMIT 50\n``````\n\nThis is plan for limit 40 and it is expected one and fast!\n\n``````Limit (cost=1000.87..53095.17 rows=40 width=12) (actual time=46.797..606.536 rows=40 loops=1)\n->Gather Merge (cost=1000.87..60909.31 rows=46 width=12) (actual time=46.796..606.518 rows=40 loops=1)\nWorkers Planned: 2\nWorkers Launched: 2\n->Nested Loop (cost=0.84..59903.98 rows=19 width=12) (actual time=23.367..448.066 rows=15 loops=3)\n-> Parallel Index Only Scan using \"\"IX_Podcasts_LastPublishDate\"\" on \"\"Podcasts\"\" p (cost=0.42..55488.81 rows=2442 width=12) (actual time=0.791..63.207 rows=259 loops=3)\nIndex Cond: (\"\"LastPublishDate\"\" < '2023-01-14 23:00:00+00'::timestamp with time zone)\nHeap Fetches: 776\n-> Index Only Scan using \"\"PK_PodcastCategories\"\" on \"\"PodcastCategories\"\" pc (cost=0.42..1.80 rows=1 width=4) (actual time=1.487..1.487 rows=0 loops=776)\nIndex Cond: ((\"\"PodcastId\"\" = p.\"\"Id\"\") AND (\"\"CategoryId\"\" = ANY ('{1}'::integer[])))\nHeap Fetches: 21\n\nPlanning Time: 2.468 ms\nExecution Time: 606.588 ms\n``````\n\nThis is plan, when limit is 50 and it runs much slower\n\n``````Limit (cost=59885.72..59888.83 rows=27 width=12) (actual time=34419.067..34436.304 rows=50 loops=1)\n->Gather Merge (cost=59885.72..59888.83 rows=27 width=12) (actual time=34419.065..34436.298 rows=50 loops=1)\nWorkers Planned: 1\nWorkers Launched: 1\n->Sort (cost=58885.71..58885.78 rows=27 width=12) (actual time=34415.504..34415.510 rows=40 loops=2)\nSort Method: top-N heapsort Memory: 28kB\nSort Key: p.\"\"LastPublishDate\"\" DESC\nWorker 0: Sort Method: top-N heapsort Memory: 29kB\n->Parallel Hash Join (cost=55858.19..58885.07 rows=27 width=12) (actual time=34386.500..34412.404 rows=10528 loops=2)\nHash Cond: (pc.\"\"PodcastId\"\" = p.\"\"Id\"\")\n->Parallel Bitmap Heap Scan on \"\"PodcastCategories\"\" pc (cost=336.90..3313.48 rows=19163 width=4) (actual time=94.378..2852.945 rows=16934 loops=2)\nRecheck Cond: (\"\"CategoryId\"\" = ANY ('{1}'::integer[]))\nHeap Blocks: exact=1292\"\n->Bitmap Index Scan on \"\"IX_PodcastCategories_CategoryId\"\" (cost=0.00..328.75 rows=32577 width=0) (actual time=91.542..91.543 rows=33879 loops=1)\nIndex Cond: (\"\"CategoryId\"\" = ANY ('{1}'::integer[]))\n->Parallel Hash (cost=55490.76..55490.76 rows=2442 width=12) (actual time=31518.266..31518.267 rows=130037 loops=2)\nBuckets: 131072 (originally 8192) Batches: 4 (originally 1) Memory Usage: 4128kB\n->Parallel Index Only Scan using \"\"IX_Podcasts_LastPublishDate\"\" on \"\"Podcasts\"\" p (cost=0.42..55490.76 rows=2442 width=12) (actual time=0.029..30960.929 rows=130037 loops=2)\nIndex Cond: (\"\"LastPublishDate\"\" < '2023-01-14 23:00:00+00'::timestamp with time zone)\nHeap Fetches: 260290\nPlanning Time: 0.348 ms\nExecution Time: 34436.367 ms\n``````\n\n• And, on top, I would check if `random_page_cost` is set correctly. Jan 16 at 7:03" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.5865011,"math_prob":0.73946095,"size":3181,"snap":"2023-14-2023-23","text_gpt3_token_len":1104,"char_repetition_ratio":0.15738118,"word_repetition_ratio":0.071625344,"special_character_ratio":0.44797233,"punctuation_ratio":0.2299169,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9843528,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-06-04T13:11:35Z\",\"WARC-Record-ID\":\"<urn:uuid:29f45236-d0f4-4d14-a03d-90a7b9684c2a>\",\"Content-Length\":\"157640\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:83d5686f-b53a-4fc7-bb30-d6a7f4772681>\",\"WARC-Concurrent-To\":\"<urn:uuid:81b098fe-ff2f-4391-8a06-4b640f0bc399>\",\"WARC-IP-Address\":\"151.101.1.69\",\"WARC-Target-URI\":\"https://dba.stackexchange.com/questions/322124/why-changing-limit-triggers-different-query-plans-in-postgresql\",\"WARC-Payload-Digest\":\"sha1:VVXRM32X7IXHR5JTC6JVFIKBXMPI4EXH\",\"WARC-Block-Digest\":\"sha1:HCXNWI4BLIIGBIBDZ4W4I6FC5OR63E7I\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224649986.95_warc_CC-MAIN-20230604125132-20230604155132-00314.warc.gz\"}"}
https://videoclass.com/video/solving-equations-containing-decimals1	[ "# Solving Equations Containing Decimals1", null, "To solve linear equations with decimals or fractions, the first step is to get rid of the decimals or fractions. There are simple techniques to get rid of both decimals and fractions and the techniques can... To solve linear equations with decimals or fractions, the first step is to get rid of the decimals or fractions. There are simple techniques to get rid of both decimals and fractions and the techniques can be used together in case both decimals and fractions appear in the same equation. Once the equations are simplified, graph all the linear equations together.\nMore... Collapse\n100 Views" ]	[ null, "https://s3.eu-central-1.amazonaws.com/videoclass-static/user-avatars/50x50.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8569703,"math_prob":0.9972284,"size":651,"snap":"2021-43-2021-49","text_gpt3_token_len":126,"char_repetition_ratio":0.19629057,"word_repetition_ratio":0.60194176,"special_character_ratio":0.19354838,"punctuation_ratio":0.108333334,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99970245,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-28T05:26:43Z\",\"WARC-Record-ID\":\"<urn:uuid:4531ebad-0708-47ff-bac4-09308902a30c>\",\"Content-Length\":\"52013\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b7815721-3b16-43f4-8a5b-dead5dfeda8c>\",\"WARC-Concurrent-To\":\"<urn:uuid:efeceef4-e3be-4e80-b6b9-a30c249140c3>\",\"WARC-IP-Address\":\"172.67.197.157\",\"WARC-Target-URI\":\"https://videoclass.com/video/solving-equations-containing-decimals1\",\"WARC-Payload-Digest\":\"sha1:P77E2C7ZDAKYWTDV7F54JQQZ7PQRK4FV\",\"WARC-Block-Digest\":\"sha1:R53I5E2XWZIJQUO5RV3JOBRBNNQ75ZZ7\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323588257.34_warc_CC-MAIN-20211028034828-20211028064828-00570.warc.gz\"}"}
https://www.drmaciver.com/2016/05/myhill-nerode-theorem/	[ "# The Myhill–Nerode theorem and the Minimal Deterministic Automaton\n\nI recently learned a whole bunch about a random corner of language theory that I hadn’t previously known much about. I thought it might be interesting to write up some of it. So this is the first post amongst several (I currently have two others planned but they may spawn more).\n\nThis is a post about the Myhill–Nerode theorem, behind which is a nice construction (in the abstract sense. You couldn’t perform it directly on an actual machine) for the minimal deterministic automaton matching any language.\n\nLets start with some terms: We’ve got some finite non-empty alphabet $$A$$. A string on $$A$$ is any finite sequence of elements from $$A$$. A language on $$A$$ is any set of strings.\n\nFor this post we’ll fix $$A$$ and then $$S$$ will be the set of strings on $$A$$.\n\nString notation:\n\n• $$\\epsilon$$ is the string of length $$0$$\n• If $$u, v$$ are strings then $$uv$$ is the string made by concatenating them in order.\n• Similarly if $$a \\in A$$ then $$au$$ is the string that consists of prepending $$a$$ to $$u$$ and $$ua$$ is the string that consists of appending $$a$$ to $$u$$.\n\nIn general we are interested in languages which have nice compact definitions rather than having to specify the whole set. One nice way of defining languages which often provides this is a deterministic automaton. These also have the advantage of being very simple to work with computationally once you have one.\n\nA deterministic automaton on $$A$$ consists of:\n\n• A set of states $$Q$$, (possibly infinite – if it’s a finite set we call it a deterministic finite automaton)\n• An initial state $$q_0 \\in Q$$\n• An update function $$\\delta : Q \\times A \\to Q$$\n• A set of accepting states $$F \\subseteq Q$$.\n\nWe can extend the update function to take any finite string: Let $$\\delta(q, \\epsilon) = q$$ and $$\\delta(q, au) = \\delta(\\delta(q, a), u)$$. i.e. we just follow the update function along the string.\n\nWe will additionally assume that every state $$Q$$ is reachable. That is it’s $$\\delta(q_0, s)$$ for some string $$s$$. This is a fairly harmless restriction because for any automaton we can just create the automaton that replaces $$Q$$ and $$F$$ with their reachable subsets.\n\nA deterministic automaton recognises a language $$L$$ if $$s \\in L$$ if and only if $$\\delta(q_0, s) \\in F$$. i.e. if you follow the automaton along the string then you end up in an accepting state if and only if the string is in the desired language.\n\nEvery language can be recognised by a deterministic automaton:\n\n• Let $$Q = S$$\n• Let $$q_0 = \\epsilon$$\n• Let $$\\delta(s, a) = sa$$\n• Let $$F = L$$\n\nThis works because every state in this automaton has a unique string that reaches it from the initial state (which is the string representing the state), and the state is accepting if and only if that string is in the language, so by construction recognises the language.\n\nThis simplifies matters not even slightly because we’ve just reframed the problem and determining if a state is accepting is equivalent to determining whether the string is in our language, and the automaton constructed this way is always infinite (though may have finitely many accepting states if $$L$$ is finite), even if a very small finite automaton might recognise our language. If anything we’ve made the problem worse because we’ve taken a potentially finite language and moved to an always infinite representation.\n\nSo, can we find a smaller automaton that recognises a given language?\n\nIn fact we can. For any language there is a unique minimal deterministic automaton for any language. We’ll see exactly what that means in a bit, but first we’ll construct the automaton we want.\n\nThe idea for constructing it is this: We take the above automaton, and we try to collapse it by conflating equivalent states. We look for equivalent states with the notion of a test.\n\nA test is just a string. The idea is that if we have some string $$t$$ and two strings $$u$$ and $$v$$ then if $$(ut \\in L) \\ne (vt \\in L)$$, $$u$$ and $$v$$ we must have $$\\delta(q_0, u) \\ne \\delta(q_0, v)$$ for any automaton recognising $$L$$ – if not then we would have $$\\delta(q_0, ut) = \\delta(q_0, vt)$$, which is impossible because one is an accepting state and the other is not.\n\nTwo strings are said to be word equivalent if there is no test that distinguishes them. The idea is that we can then shrink our above automaton by conflating all states that are word equivalent.\n\nSo if $$s$$ is a string let $$[s]$$ be the set of all strings that are word equivalent to $$s$$. We can then define the following automaton:\n\n• Let $$Q = \\{[s]: s \\in S\\}$$\n• Let $$q_0 = [\\epsilon]$$\n• Let $$\\delta([s], a) = [sa]$$\n• Let $$F = \\{[s]: s \\in L\\}$$\n\nWe’ll call this the Myhill-Nerode automaton and label it $$Z$$.\n\nWe first need to check that $$delta$$ is well defined. i.e. if $$u$$ is word equivalent to $$v$$ then $$ua$$ is word equivalent to $$va$$. This follows from the fact that if $$t$$ is a test distinguishing $$ua$$ and $$va$$ then $$at$$ is a test distinguishing $$u$$ and $$v$$.\n\nSo this is a well defined state machine, but does it recognise $$L$$?\n\nFirst note:\n\n• $$\\delta(q_0, s) = [s]$$ (more or less by definition)\n• If $$u, v$$ are word-equivalent then $$u \\in L = v \\in L$$ because otherwise $$\\epsilon$$ is a test distinguishing them\n\nSo the $$\\delta(q_0, s)$$ is an accepting state if and only if it is $$[t]$$ for some $$t \\in L$$, which is true if and only if $$s \\in L$$. i.e. this automaton recognises $$L$$.\n\nSo we’ve got another automaton recognising $$L$$, and it sure looks smaller than the first one, but is it minimal?\n\nAnd what do we even mean by minimal?\n\nFor that we’ll need the idea of an automaton reduction: Let $$P, Q$$ be automata (call the initial state of $$P$$ $$p_0$$ and we’ll use subscripts to distinguish $$\\delta$$ and $$F$$. $$Q$$ is a reduction of $$P$$ if there is a function $$r: P \\to Q$$ such that:\n\n1. $$r(p_0) = q_0$$\n2. If $$p \\in P$$ and $$a \\in A$$ then $$r(\\delta_P(p, a)) = \\delta_Q(r(p), a)$$.\n3. $$r(p) \\in F_Q$$ if and only if $$p \\in F_P$$\n4. Every $$q \\in Q$$ is $$r(p)$$ for some $$p$$\n\ni.e. we label every state in $$P$$ with a state in $$Q$$ such that everything lines up correctly for transitions.\n\nOur claim of minimality is this: If $$Q$$ is any automaton recognising $$L$$, then $$Z$$ is a reduction of $$Q$$.\n\nThe key property for proving this is that if $$u$$ and $$v$$ are two strings with $$\\delta_Q(q_0, u) = \\delta_Q(q_0, v) = q$$ then they must be word equivalent. Otherwise there would be some test $$t$$ such that $$\\delta(q, t) \\ne \\delta(q, t)$$. So we choose as our reduction function $$r$$ the function $$r(q) = [s]$$ where $$s$$ is any string such that $$\\delta_Q(q_0, s) = q$$ (recall we’re assuming all states are reachable).\n\nLets check that this has the desired properties:\n\n1. $$\\delta_Q(q_0, \\epsilon) = q_0$$, so $$r(q_0) = [\\epsilon] = z_0$$\n2. If $$\\delta_Q(q_0, s) = q$$ then $$delta_Q(q_0, sa) = \\delta(q, a)$$, so $$r(\\delta_Q(q_0, s), a)) = [sa] = \\delta_Z([s], a) = \\delta_Z(r(q), a)$$ as desired\n3. This follows automatically because both $$Q$$ and $$Z$$ recognise $$L$$\n4. $$[s] = r(\\delta(q_0, s))$$\n\nSo for any automaton we can reduce it to $$Z$$, as desired.\n\nAnd finally we need to prove uniqueness: The uniqueness claim is that if $$Q$$ is any other automaton that has this property then a reduction $$r: Z \\to Q$$ must also have the property that if $$s \\ne t$$ then $$r(s) \\ne r(t)$$. i.e. $$r$$ is an isomorphism, just relabelling the vertices.\n\nProof: Suppose $$[u] \\ne [v]$$ are two distinct states of $$Z$$. Then there is some $$t$$ such that $$\\delta_Z([u], t) \\in F_Z \\ne \\delta_Z(([v], t) \\in F_Z$$. But then by the properties of the reduction we must have $$\\delta_Q(r([u]), t) \\in F_Q \\ne \\delta_Q((r([v]), t) \\in F_Q$$ and thus $$r([u]) \\ne r([v])$$ as desired.\n\nWe’ll finally finish with the title of this post: The Myhill–Nerode theorem.\n\nIn the language we have so far, this states that $$L$$ is regular if and only if the $$Z$$ we constructed is finite. But this follows immediately from what we’ve done above: $$Z$$ is an automaton recognizing $$L$$, so by definition if $$Z$$ is finite then $$L$$ must be regular. Conversely, if there is any finite automaton that recognizes $$L$$ then it reduces to $$Z$$, so $$Z$$ must also be finite.\n\nWhy do we care about all of this?\n\nWell, as far as I know, the Myhill–Nerode theorem itself isn’t actually very important. It’s mostly an intellectual curiousity. I do like that it shows that every language regardless of structural properties has a minimal deterministic automaton, but I’m not sure I have any actual use for that fact.\n\nBut the machinery used to prove it is independently quite interesting. In particular, minimal (or at least small) deterministic finite automaton are very useful in practice and we can use a similar construction starting from an existing finite automaton to produce one (this is Hopcroft’s Algorithm).\n\nMoreover, the idea of a test that we started from proves quite interesting, and you can use it to construct alternative (often more compact) representations of a DFA, and it forms the basis for the inference of regular languages in certain circumstances. More on that in later posts.\n\nThis entry was posted in Automata Theory on by ." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8765713,"math_prob":0.9999553,"size":9393,"snap":"2019-43-2019-47","text_gpt3_token_len":2520,"char_repetition_ratio":0.14793907,"word_repetition_ratio":0.010989011,"special_character_ratio":0.2967103,"punctuation_ratio":0.096039064,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.0000058,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-11-17T10:18:12Z\",\"WARC-Record-ID\":\"<urn:uuid:1f4242d1-b5de-4378-91f2-b8e68c51fe69>\",\"Content-Length\":\"27746\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d768a0b9-5237-46c6-9154-65fdc57d64bb>\",\"WARC-Concurrent-To\":\"<urn:uuid:9105d2df-da25-473c-a15b-f26d4958edd3>\",\"WARC-IP-Address\":\"104.18.42.229\",\"WARC-Target-URI\":\"https://www.drmaciver.com/2016/05/myhill-nerode-theorem/\",\"WARC-Payload-Digest\":\"sha1:5DVUOVWXOVQ2FW2S2SRW7U2IQMZ4C4Z7\",\"WARC-Block-Digest\":\"sha1:MNLSRHODYKLNX3XQCXCTJ7VZTIHBR4EQ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-47/CC-MAIN-2019-47_segments_1573496668910.63_warc_CC-MAIN-20191117091944-20191117115944-00129.warc.gz\"}"}
http://rcompanion.org/handbook/J_01.html	[ "", null, "## Summary and Analysis of Extension Program Evaluation in R\n\nSalvatore S. Mangiafico\n\n# Regression for Count Data\n\n### Introduction\n\n#### Count data\n\nIn general, common parametric tests like t-test and anova shouldn’t be used for count data. One reason is technical in nature: that parametric analyses require continuous data. Count data is by its nature discrete and is left-censored at zero. (That is, usually counts can’t be less than zero.)\n\nA second reason is more practical in nature. Count data are often highly skewed, and often produce skewed residuals if a parametric approach is attempted. In this case, the hypothesis tests will not be accurate.\n\nFor further discussion, see the “Count data may not be appropriate for common parametric tests” section in the Introduction to Parametric Tests chapter.\n\n#### Regression approaches for count data\n\nThe most common regression approach for handling count data is probably Poisson regression. However, Poisson regression makes assumptions about the distribution of the data that may not be appropriate in all cases. Hermite regression is a more flexible approach, but at the time of writing doesn’t have a complete set of support functions in R. Quasi-Poisson regression is also flexible with data assumptions, but also but at the time of writing doesn’t have a complete set of support functions in R. Negative binomial regression allows for overdispersion in data; and zero-inflated regression is useful when there are a high proportion of zero counts in the data.\n\n#### Cautionary note\n\nNote that model assumptions and pitfalls of these regression techniques are not discussed in depth here. The reader is urged to understand the assumptions of this kind of modeling before proceeding.\n\n#### Generalized linear regression\n\nPoisson, Hermite, and related regression approaches are a type of generalized linear model. This should not be confused with general linear model, which is implemented with the lm function. Generalized linear models are implemented with the glm function or other functions.\n\nGeneralized linear models are used when the dependent variable is count, binary, multinomial, etc. More information on using the glm function can be found by using help(glm) and help(family). For examples of logistic regression, see the chapter Models for Nominal Data; the chapter Beta Regression for Percent and Proportion Data; or Mangiafico (2015) in the “References” section. For a table of common uses for family and link function in generalized linear models, see the Wikipedia article in the “References” section for this chapter.\n\n### Packages used in this chapter\n\nThe packages used in this chapter include:\n\n• pysch\n\n• hermite\n\n• lattice\n\n• plyr\n\n• boot\n\n• DescTools\n\n• ggplot2\n\n• car\n\n• multcompView\n\n• emmeans\n\n• MASS\n\n• pscl\n\n• rcompanion\n\n• robust\n\nThe following commands will install these packages if they are not already installed:\n\nif(!require(psych)){install.packages(\"psych\")}\nif(!require(hermite)){install.packages(\"hermite\")}\nif(!require(lattice)){install.packages(\"lattice\")}\nif(!require(plyr)){install.packages(\"plyr\")}\nif(!require(boot)){install.packages(\"boot\")}\nif(!require(DescTools)){install.packages(\"DescTools\")}\nif(!require(ggplot2)){install.packages(\"ggplot2\")}\nif(!require(car)){install.packages(\"car\")}\nif(!require(multcompView)){install.packages(\"multcompView\")}\nif(!require(emmeans)){install.packages(\"emmeans\")}\nif(!require(MASS)){install.packages(\"MASS\")}\nif(!require(pscl)){install.packages(\"pscl\")}\nif(!require(rcompanion)){install.packages(\"rcompanion\")}\nif(!require(robust)){install.packages(\"robust\")}\n\n### Count data example\n\nIn this example, extension researchers have set up garden plots with different suites of plants, with each suite identified as a level of the variable Garden below. In September, they counted the number of monarch butterflies in each garden plot.\n\nInput = (\"\nGarden Monarchs\nA 0\nA 4\nA 2\nA 2\nA 0\nA 6\nA 0\nA 0\nB 5\nB 9\nB 7\nB 5\nB 7\nB 5\nB 9\nB 5\nC 10\nC 14\nC 12\nC 12\nC 10\nC 16\nC 10\nC 10\n\")\n\n### Order factors by the order in data frame\n\n### Otherwise, R will alphabetize them\n\nData\\$Garden = factor(Data\\$Garden,\nlevels=unique(Data\\$Garden))\n\n### Check the data frame\n\nlibrary(psych)\n\nstr(Data)\n\nsummary(Data)\n\n### Remove unnecessary objects\n\nrm(Input)\n\n#### Histograms\n\nlibrary(lattice)\n\nhistogram(~ Monarchs \| Garden,\ndata=Data,\nlayout=c(1,3) # columns and rows of individual plots\n)", null, "### Poisson regression example\n\nPoisson regression makes certain assumptions about the relationship between the mean and the dispersion of the dependent variable. Because this assumption may not be met for all data sets, Poisson regression may not be recommended for routine use. Particularly, classic Poisson regression should be avoided if there is overdispersion in the data or if there are several zero counts in the dependent variable.\n\nAn alternate approach for data with overdispersion is negative binomial regression.\n\nAn alternative approach for data with many zeros is zero-inflated Poisson regression.\n\nFor further discussion, see the “Count data may not be appropriate for common parametric tests” section in the Introduction to Parametric Tests chapter.\n\nNote that model assumptions and pitfalls of this approach are not discussed here. The reader is urged to understand the assumptions of this kind of modeling before proceeding.\n\nmodel.p = glm(Monarchs ~ Garden,\ndata=Data,\nfamily=\"poisson\")\n\nlibrary(car)\n\nAnova(model.p,\ntype=\"II\",\ntest=\"LR\")\n\nAnalysis of Deviance Table (Type II tests)\n\nLR Chisq Df Pr(>Chisq)\nGarden 66.463 2 3.697e-15 *\n\nlibrary(rcompanion)\n\nnagelkerke(model.p)\n\n\\$Pseudo.R.squared.for.model.vs.null\nPseudo.R.squared\nCox and Snell (ML) 0.937293\nNagelkerke (Cragg and Uhler) 0.938037\n\n\\$Likelihood.ratio.test\nDf.diff LogLik.diff Chisq p.value\n-2 -33.231 66.463 3.6967e-15\n\nlibrary(multcompView)\n\nlibrary(emmeans)\n\nmarginal = emmeans(model.p,\n~ Garden)\n\npairs(marginal,\n\ncld(marginal,\nalpha=0.05,\nLetters=letters, ### Use lower-case letters for .group\n\nGarden emmean SE df asymp.LCL asymp.UCL .group\nA 0.5596158 0.2672450 NA -0.07849527 1.197727 a\nB 1.8718022 0.1386750 NA 1.54068251 2.202922 b\nC 2.4638532 0.1031421 NA 2.21757688 2.710130 c\n\nResults are given on the log (not the response) scale.\nConfidence level used: 0.95\nConf-level adjustment: sidak method for 3 estimates\nP value adjustment: tukey method for comparing a family of 3 estimates\nTests are performed on the log scale\nsignificance level used: alpha = 0.05\n\n### Note that estimates are on log scale\n\n### Negative binomial regression example\n\nNegative binomial regression is similar in application to Poisson regression, but allows for overdispersion in the dependent count variable.\n\nThis example will use the glm.nb function in the MASS package. The Anova function in the car package will be used for an analysis of deviance, and the nagelkerke function will be used to determine a p-value and pseudo R-squared value for the model. Post-hoc analysis can be conducted with the emmeans package.\n\nNote that model assumptions and pitfalls of this approach are not discussed here. The reader is urged to understand the assumptions of this kind of modeling before proceeding.\n\nlibrary(MASS)\n\nmodel.nb = glm.nb(Monarchs ~ Garden,\ndata=Data,\ncontrol = glm.control(maxit=10000))\n\nlibrary(car)\n\nAnova(model.nb,\ntype=\"II\",\ntest=\"LR\")\n\nAnalysis of Deviance Table (Type II tests)\n\nLR Chisq Df Pr(>Chisq)\nGarden 66.464 2 3.694e-15 \n\nlibrary(rcompanion)\n\nnagelkerke(model.nb)\n\n\\$Pseudo.R.squared.for.model.vs.null\nPseudo.R.squared\nCox and Snell (ML) 0.776007\nNagelkerke (Cragg and Uhler) 0.778217\n\n\\$Likelihood.ratio.test\nDf.diff LogLik.diff Chisq p.value\n-2 -17.954 35.907 1.5952e-08\n\nlibrary(multcompView)\n\nlibrary(emmeans)\n\nmarginal = emmeans(model.nb,\n~ Garden)\n\npairs(marginal,\n\ncld(marginal,\nalpha = 0.05,\nLetters = letters, ### Use lower-case letters for .group\ntype = \"response\", ### Report emmeans in orginal scale\n\nGarden response SE df asymp.LCL asymp.UCL .group\nA 1.75 0.4677072 NA 0.9244706 3.312707 a\nB 6.50 0.9013878 NA 4.6677750 9.051422 b\nC 11.75 1.2119200 NA 9.1850474 15.031223 c\n\nConfidence level used: 0.95\nConf-level adjustment: sidak method for 3 estimates\nIntervals are back-transformed from the log scale\nP value adjustment: tukey method for comparing a family of 3 estimates\nTests are performed on the log scale\nsignificance level used: alpha = 0.05\n\n### Zero-inflated regression example\n\nZero-inflated regression is similar in application to Poisson regression, but allows for an abundance of zeros in the dependent count variable.\n\nThis example will use the zeroinfl function in the pscl package. The Anova function in the car package will be used for an analysis of deviance, and the nagelkerke function will be used to determine a p-value and pseudo R-squared value for the model. Post-hoc analysis can be conducted with the emmeans package.\n\nlibrary(pscl)\n\nmodel.zi = zeroinfl(Monarchs ~ Garden,\ndata = Data,\ndist = \"poisson\")\n\n### dist = \"negbin\" may be used\n\nsummary(model.zi)\n\nCall:\nzeroinfl(formula = Monarchs ~ Garden \| Garden, data = Data, dist = \"poisson\")\n\nCount model coefficients (poisson with log link):\nEstimate Std. Error z value Pr(>\|z\|)\n(Intercept) 1.2182 0.2847 4.278 1.89e-05 *\nGardenB 0.6536 0.3167 2.064 0.039 \nGardenC 1.2457 0.3029 4.113 3.90e-05 *\n\nZero-inflation model coefficients (binomial with logit link):\nEstimate Std. Error z value Pr(>\|z\|)\n(Intercept) -7.046e-02 7.363e-01 -0.096 0.924\nGardenB -2.057e+01 1.071e+04 -0.002 0.998\nGardenC -2.057e+01 1.071e+04 -0.002 0.998\n\n### Note that there are separate coefficients for the\n### Poisson part of the analysis and for the zero-inflation part.\n\nlibrary(car)\n\nAnova(model.zi,\ntype=\"II\",\ntest=\"Chisq\")\n\nAnalysis of Deviance Table (Type II tests)\n\nDf Chisq Pr(>Chisq)\nGarden 2 23.914 6.414e-06 \n\nlibrary(rcompanion)\n\nnagelkerke(model.zi)\n\n\\$Pseudo.R.squared.for.model.vs.null\nPseudo.R.squared\nCox and Snell (ML) 0.797356\nNagelkerke (Cragg and Uhler) 0.800291\n\n\\$Likelihood.ratio.test\nDf.diff LogLik.diff Chisq p.value\n-4 -19.156 38.311 9.6649e-08\n\nlibrary(multcompView)\n\nlibrary(emmeans)\n\nmarginal = emmeans(model.zi,\n~ Garden)\n\npairs(marginal,\n\ncld(marginal,\nalpha=0.05,\nLetters=letters, ### Use lower-case letters for .group\n\nGarden emmean SE df asymp.LCL asymp.UCL .group\nA 1.75 0.7586301 NA -0.06140972 3.561410 a\nB 6.50 0.9013877 NA 4.34772229 8.652278 b\nC 11.75 1.2119199 NA 8.85625304 14.643747 c\n\nConfidence level used: 0.95\nConf-level adjustment: sidak method for 3 estimates\nP value adjustment: tukey method for comparing a family of 3 estimates\nsignificance level used: alpha = 0.05\n\n### Note, emmeans are on the original measurement scale\n\n### Robust Poisson regression example\n\nRobust Poisson regression is robust to outliers in the dependent variable.\n\nThis example uses the glmRob function in the robust package. The anova function can be used to conduct an analysis of deviance. The p-value for the model can be found by comparing the model to a null model. However, at the time of writing, I don’t know of any way to determine AIC or pseudo R-squared for the model.\n\nAt the time of writing, the glmRob function can only use the Poisson and binomial families of models.\n\nAn alternate method is the glmrob function in the robustbase package.\n\nlibrary(robust)\n\nmodel.rob = glmRob(Monarchs ~ Garden,\ndata = Data,\nfamily = \"poisson\")\n\nanova(model.rob, test=\"Chisq\")\n\nDf Deviance Resid. Df Resid.\nDev Pr(>Chi)\nNULL NA NA 23 430.19850 NA\nGarden 2 400.9221 21 29.27641 3.567693e-63\n\nmodel.rob.null = glmRob(Monarchs ~ 1,\ndata = Data,\nfamily = \"poisson\")\n\nanova(model.rob.null, model.rob, test=\"Chisq\")\n\nTerms Resid. Df Resid. Dev Test Df Deviance Pr(>Chi)\n1 1 23 95.12606 NA NA NA\n2 Garden 21 29.27641 2 65.84965 5.536815e-11\n\n### Quasi-Poisson regression\n\nQuasi-Poisson regression is useful since it has a variable dispersion parameter, so that it can model over-dispersed data. It may be better than negative binomial regression in some circumstances (Verhoef and Boveng. 2007).\n\nAt the time of writing, Quasi-Poisson regression doesn’t have complete set of support functions in R. Using the quasipoisson family option in the glm function, the results will have the same parameter coefficients as with the poisson option, but the inference statistics are adjusted in the summary function. The Anova function in the car package can be used for an analysis of deviance table, and the emmeans package can be used for post-hoc comparisons. Since the model doesn’t produce a log-likelihood value, I don’t know a way to produce a p-value for the mode, for a pseudo R-squared value for the model.\n\n.\n\nmodel.qp = glm(Monarchs ~ Garden,\ndata=Data,\nfamily=\"quasipoisson\")\n\nlibrary(car)\n\nAnova(model.qp,\ntype=\"II\",\ntest=\"LR\")\n\nAnalysis of Deviance Table (Type II tests)\n\nResponse: Monarchs\nLR Chisq Df Pr(>Chisq)\nGarden 52.286 2 4.429e-12 *\n\nlibrary(multcompView)\n\nlibrary(emmeans)\n\nmarginal = emmeans(model.qp,\n~ Garden)\n\npairs(marginal,\n\ncld(marginal,\nalpha=0.05,\nLetters=letters,\n\nGarden emmean SE df asymp.LCL asymp.UCL .group\nA 0.5596158 0.3013057 NA -0.1598233 1.279055 a\nB 1.8718022 0.1563493 NA 1.4984809 2.245123 b\nC 2.4638532 0.1162877 NA 2.1861887 2.741518 c\n\nResults are given on the log (not the response) scale.\nConfidence level used: 0.95\nConf-level adjustment: sidak method for 3 estimates\nP value adjustment: tukey method for comparing a family of 3 estimates\nsignificance level used: alpha = 0.05\n\n### Hermite regression\n\nThe generalized Hermite distribution is a more general distribution that can handle overdispersion or multimodality (Moriña and others, 2015). This makes generalized Hermite regression a powerful and flexible tool for modeling count data. It is implemented with the hermite package.\n\nFitting models with the hermite package can be somewhat difficult. One issue is that model fitting may fail without some parameters being specified. Often specifying an appropriate value for the m option will help.\n\nA further difficulty with this approach is that, at the time writing, the package isn’t supported by the anova function to compare models, the Anova function to test effects, or other useful functions like emmeans for factor effects.\n\nThe hermite package is used to conduct hermite regression. Here, the m=3 option is specified. Often the default m=NULL can be used. In this case, if the m value is not specified, the function cannot complete the model fitting, and errors are produced. Using m=2 often works. Here, m=3 was used because it produced a model with a lower AIC than did the m=2 option.\n\nlibrary(hermite)\n\nmodel = glm.hermite(Monarchs ~ Garden,\ndata = Data,\nm=3)\n\nsummary(model)\n\nCoefficients:\nEstimate Std. Error z value p-value\n(Intercept) 0.5081083 0.3251349 1.5627612 1.181088e-01\nGardenB 1.3700567 0.3641379 3.7624662 1.682461e-04\nGardenC 1.9596153 0.3476326 5.6370291 1.730089e-08\ndispersion.index 1.0820807 0.2877977 0.1281707 3.601681e-01\norder 3.0000000 NA NA NA\n(Likelihood ratio test against Poisson is reported by z value* for dispersion.index)\n\nAIC: 112.7762\n\n#### Post-hoc analysis: Medians and confidence intervals\n\nAt the time of writing, the emmeans package does not support post-hoc analysis of regressions produced with the hermite package.\n\nOne imperfect approach for post-hoc analysis would be to examine median counts for treatments and the confidence intervals of these medians. We can conclude that groups with non-overlapping 95% confidence intervals for their medians are significantly different.\n\nHowever, this approach does not represent any information learned from the Hermite regression.\n\nA second issue is that, because the dependent variable is not continuous, the distribution of the bootstrapped confidence intervals is not likely to be continuous, and so is may not be reliable.\n\nTo get confidence intervals for the medians for each group, we will use the groupwiseMedian function. Here I used the percentile method for confidence intervals.\n\nlibrary(rcompanion)\n\nSum = groupwiseMedian(Monarchs ~ Garden,\ndata=Data,\nconf=0.95,\nR=5000,\npercentile=TRUE,\nbca=FALSE,\ndigits=3)\n\nSum\n\nGarden n Median Conf.level Percentile.lower Percentile.upper\n1 A 8 1 0.95 0 4\n2 B 8 6 0.95 5 8\n3 C 8 11 0.95 10 14\n\n### In this case, none of the confidence intervals overlap.\n\n##### Plot of medians and confidence intervals\n\nThe data frame Sum created above will be passed to ggplot for plotting. At the end of the code, annotate is used to add text to the plot to indicate which medians are significantly different from one another.\n\nlibrary(ggplot2)\n\nggplot(Sum, ### The data frame to use.\naes(x = Garden,\ny = Median)) +\ngeom_errorbar(aes(ymin = Percentile.lower,\nymax = Percentile.upper),\nwidth = 0.05,\nsize = 1) +\ngeom_point(shape = 15,\nsize = 5) +\ntheme_bw() +\ntheme(axis.title = element_text(face = \"bold\")) +\nylab(\"Median count of monarch butterflies\") +\n\nannotate(\"text\",\nx = 1:3,\ny = c(5, 10, 15),\nlabel = c(\"Group 3\", \"Group 2\", \"Group 1\"))", null, "### Optional code for chi-square goodness-of-fit test\n\nAn alternative approach to handling count data is to sum up the counts for treatments, and use a chi-square test or related test. Here, a chi-square goodness-of-fit test is used to see if counts differ from “expected” equal proportions.\n\n#### Omnibus test\n\nTabla = xtabs(Monarchs ~ Garden,\ndata = Data)\n\nTabla\n\nGarden\nA B C\n14 52 94\n\nchisq.test(Tabla)\n\nChi-squared test for given probabilities\n\nX-squared = 60.05, df = 2, p-value = 9.127e-14\n\n#### Post-hoc chi-square tests\n\nGarden.A = sum(Data\\$Monarchs[Data\\$Garden==\"A\"])\nGarden.B = sum(Data\\$Monarchs[Data\\$Garden==\"B\"])\nGarden.C = sum(Data\\$Monarchs[Data\\$Garden==\"C\"])\n\nobserved = c(Garden.A, Garden.B) # observed frequencies\nexpected = c(1/2, 1/2) # expected proportions\n\nchisq.test(x = observed,\np = expected)\n\nChi-squared test for given probabilities\n\nX-squared = 21.879, df = 1, p-value = 2.904e-06\n\nobserved = c(Garden.B, Garden.C) # observed frequencies\nexpected = c(1/2, 1/2) # expected proportions\n\nchisq.test(x = observed,\np = expected)\n\nChi-squared test for given probabilities\n\nX-squared = 12.082, df = 1, p-value = 0.0005091\n\nobserved = c(Garden.A, Garden.C) # observed frequencies\nexpected = c(1/2, 1/2) # expected proportions\n\nchisq.test(x = observed,\np = expected)\n\nChi-squared test for given probabilities\n\nX-squared = 59.259, df = 1, p-value = 1.382e-14\n\n### Optional analysis: Vuong test to compare Poisson, negative binomial, and zero-inflated models\n\nThe Vuong test, implemented by the pscl package, can test two non-nested models. It works with negbin, zeroinfl, and some glm model objects which are fitted to the same data.\n\nThe null hypothesis is that there is no difference in models. The function produces three tests, a “Raw” test, an AIC-corrected, and a BIC-corrected, any of which could be used.\n\nIt has been suggested that the Vuong test not be used to test for zero-inflation (Wilson, 2015).\n\nDefine models\n\nmodel.p = glm(Monarchs ~ Garden,\ndata=Data,\nfamily=\"poisson\")\n\nlibrary(MASS)\n\nmodel.nb = glm.nb(Monarchs ~ Garden,\ndata=Data,\ncontrol = glm.control(maxit=10000))\n\nlibrary(pscl)\n\nmodel.zi = zeroinfl(Monarchs ~ Garden,\ndata = Data,\ndist = \"poisson\")\n\nVuong test\n\nlibrary(pscl)\n\nvuong(model.p,\nmodel.nb,\ndigits = 4)\n\nVuong Non-Nested Hypothesis Test-Statistic:\n(test-statistic is asymptotically distributed N(0,1) under the\nnull that the models are indistinguishible)\n-------------------------------------------------------------\nVuong z-statistic H_A p-value\nRaw 0.03324988 model1 > model2 0.48674\nAIC-corrected 0.03324988 model1 > model2 0.48674\nBIC-corrected 0.03324988 model1 > model2 0.48674\n\n### Positive Vuong z-statistic suggests that model 1 is superior,\n### but, in this case, the difference is not significant,\n### and the value of the statistic is probably too tiny to be meaningful.\n\nvuong(model.p,\nmodel.zi,\ndigits = 4)\n\nVuong Non-Nested Hypothesis Test-Statistic:\n(test-statistic is asymptotically distributed N(0,1) under the\nnull that the models are indistinguishible)\n-------------------------------------------------------------\nVuong z-statistic H_A p-value\nRaw -1.4424725 model2 > model1 0.074585\nAIC-corrected -0.4335210 model2 > model1 0.332318\nBIC-corrected 0.1607786 model1 > model2 0.436134\n\n### Negative Vuong z-statistic suggests that model 2 is superior.\n### If the Raw statistic is used, p = 0.07 gives some evidence\n### that zi model is superior.\n\nvuong(model.nb,\nmodel.zi,\ndigits = 4)\n\nVuong Non-Nested Hypothesis Test-Statistic:\n(test-statistic is asymptotically distributed N(0,1) under the\nnull that the models are indistinguishible)\n-------------------------------------------------------------\nVuong z-statistic H_A p-value\nRaw -1.4424725 model2 > model1 0.074585\nAIC-corrected -0.4335210 model2 > model1 0.332318\nBIC-corrected 0.1607786 model1 > model2 0.436134\n\n### Negative Vuong z-statistic suggests that model 2 is superior.\n### If the Raw statistic is used, p = 0.07 gives some evidence\n### that zi model is superior.\n\n### References\n\nMoriña, D., M. Higueras, P. Puig, and M. Oliveira. 2015. Generalized Hermite Distribution\n\nModelling with the R Package hermite. The R Journal 7(2):263–274. journal.r-project.org/archive/2015-2/morina-higueras-puig-etal.pdf.\n\nhelp(package=\"hermite\")\n\nlibrary(hermite); ?glm.hermite\n\nlibrary(MASS); ?glm.nb\n\nlibrary(pscl); ?zeroinfl\n\nlibrary(pscl); ?vuong\n\n“Simple Logistic Regression” in Mangiafico, S.S. 2015. An R Companion for the Handbook of Biological Statistics, version 1.09. rcompanion.org/rcompanion/e_06.html.\n\n\"Generalized linear model: Link function\". No date. Wikipedia. Retrieved 31 Jan. 2016. en.wikipedia.org/wiki/Generalized_linear_model#Link_function.\n\nVerhoef, J.M. and P.L. Boveng. 2007. Quasi-Poisson vs. negative binomial regression: How should we model overdispersed count data? Ecology 88(11) 2766–2772. http://fisher.utstat.toronto.edu/reid/sta2201s/QUASI-POISSON.pdf.\n\nWilson, P. 2015. The Misuse of the Vuong Test for Non-Nested Models to Test for Zero-Inflation. Economic Letters 127: 51–53. cybermetrics.wlv.ac.uk/paperdata/misusevuong.pdf\n\n### References for count data\n\nGrace-Martin, K. No date. \"Regression Models for Count Data\". The Analysis Factor. www.theanalysisfactor.com/regression-models-for-count-data/.\n\nGrace-Martin, K. No date. \" Zero-Inflated Poisson Models for Count Outcomes\". The Analysis Factor. www.theanalysisfactor.com/zero-inflated-poisson-models-for-count-outcomes/.\n\n[IDRE] Institute for Digital Research and Education. 2015. “R Data Analysis Examples: Poisson Regression”. UCLA. www.ats.ucla.edu/stat/r/dae/poissonreg.htm.\n\n[IDRE] Institute for Digital Research and Education. 2015. “R Data Analysis Examples: Negative Binomial Regression”.\n\n[IDRE] Institute for Digital Research and Education. 2015. “R Data Analysis Examples: Zero-Inflated Poisson Regression”.\n\n[IDRE] Institute for Digital Research and Education. 2015. “R Data Analysis Examples: Zero-Truncated Poisson Regression”." ]	[ null, "http://rcompanion.org/handbook/images/banner.jpg", null, "http://rcompanion.org/handbook/images/image178.png", null, "http://rcompanion.org/handbook/images/image179.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6846066,"math_prob":0.8776753,"size":22980,"snap":"2019-51-2020-05","text_gpt3_token_len":6503,"char_repetition_ratio":0.12552229,"word_repetition_ratio":0.2512547,"special_character_ratio":0.28646648,"punctuation_ratio":0.16736586,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9939243,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,null,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-16T08:32:42Z\",\"WARC-Record-ID\":\"<urn:uuid:5a01e7e4-d24e-45ae-90af-973e7080d568>\",\"Content-Length\":\"62920\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2cf82019-e6b0-49ae-a199-e8001632b514>\",\"WARC-Concurrent-To\":\"<urn:uuid:ba6dd475-7d6c-4383-9150-a6a9da5a00d7>\",\"WARC-IP-Address\":\"75.98.175.108\",\"WARC-Target-URI\":\"http://rcompanion.org/handbook/J_01.html\",\"WARC-Payload-Digest\":\"sha1:CGKUMZAEAVHZR5EO2EUGBOHSDQGHK5QY\",\"WARC-Block-Digest\":\"sha1:PWALFL3GGREIT7NC2JB3IUE4GWNQH3LX\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575541318556.99_warc_CC-MAIN-20191216065654-20191216093654-00442.warc.gz\"}"}
https://stackoverflow.com/questions/3354313/python-is-there-a-c-like-for-loop-available/3354369	[ "# Python: is there a C-like for loop available?\n\nCan I do something like this in Python?\n\n``````for (i = 0; i < 10; i++):\nif someCondition:\ni+=1\nprint i\n``````\n\nI need to be able to skip some values based on a condition\n\nEDIT: All the solutions so far suggest pruning the initial range in one way or another, based on an already known condition. This is not useful for me, so let me explain what I want to do.\n\nI want to manually (i.e. no getopt) parse some cmd line args, where each 'keyword' has a certain number of parameters, something like this:\n\n``````for i in range(0,len(argv)):\narg = argv[i]\nif arg == '--flag1':\nopt1 = argv[i+1]\ni+=1\ncontinue\nif arg == '--anotherFlag':\noptX = argv[i+1]\noptY = argv[i+2]\noptZ = argv[i+3]\ni+=3\ncontinue\n\n...\n``````\n• what is it you're actually trying to do? Jul 28, 2010 at 15:16\n• updated question with more info... Jul 28, 2010 at 15:39\n• There is always `while` for you. Jul 28, 2010 at 20:36\n\nYes, this is how I would do it\n\n``````>>> for i in xrange(0, 10):\n... if i == 4:\n... continue\n... print i,\n...\n0 1 2 3 5 6 7 8 9\n``````\n\nEDIT\nBased on the update to your original question... I would suggest you take a look at optparse\n\n• +1 for `optparse`. Parsing command-line arguments manually is completely unnecessary. Jul 28, 2010 at 16:12\n• Apparently optparse is obsoleted in 2.7, and the new flavor is called argparse. They both seem to be able to do what I need, but I'm wondering if it's worth the learning curve. Anyway, +1 for pointing out this module. Jul 28, 2010 at 23:18\n``````for (i = 0; i < 10; i++)\nif someCondition:\ni+=1\nprint i\n``````\n\nIn python would be written as\n\n``````i = 0\nwhile i < 10\nif someCondition\ni += 1\nprint i\ni += 1\n``````\n\nthere you go, that is how to write a c for loop in python.\n\n• @Cristi yes but that was in the original example code in the question, so I thought that was what he wanted. Feb 6, 2013 at 1:01\n\nThere are two things you could do to solve your problem:\n\n• require comma-separated arguments which are going to be grouped into the following option value, you could use `getopt`, or any other module then.\n• or do more fragile own processing:\n\n``````sys.argv.pop()\ncmd = {}\nwhile sys.argv:\narg = sys.argv.pop(0)\nif arg == '--arg1':\ncmd[arg] = sys.argv.pop(0), sys.argv.pop(0)\nelif:\npass\nprint(cmd)\n``````\n• The idea of using argv as a stack is great for my needs, and it removes the indexed based access to the list. Aug 6, 2010 at 14:37\n• I love it when people suggest everything but the answer for the question 👏 Feb 24, 2020 at 19:16\n\nStrange way:\n\n``````for x in (x for x in xrange(10) if someCondition):\nprint str(x)\n``````\n\nYou should use `continue` to skip a value, in both C and Python.\n\n``````for i in range(10):\nif someCondition:\ncontinue\nprint(i)\n``````\n\nYou probably don't actually need the indices, you probably need the actual items. A better solution would probably be like this:\n\n``````sequence = 'whatever'\nfor item in sequence:\nif some_condition:\ncontinue\ndo_stuff_with(item)\n``````\n• I would dearly use an iterator over a for loop any time of the day, however I can't think of a way to use iteration in my situation - see updated question Jul 28, 2010 at 15:41\n\nYou could first turn the argv list into a generator:\n\n``````def g(my_list):\nfor item in my_list:\nyield item\n``````\n\nYou could then step through the items, invoking the generator as required:\n\n``````my_gen = g(sys.argv[1:]):\nwhile True:\ntry:\narg = my_gen.next()\nif arg == \"--flag1\":\noptX = my_gen.next()\nopyY = my_gen.next()\n--do something\nelif arg == \"--flag2\":\noptX = my_gen.next()\noptY = my_gen.next()\noptZ = my_gen.next()\n--do something else\n...\nexcept StopIteration:\nbreak\n``````\n• how's that any different than iterating over a list? just more hassle. Jul 28, 2010 at 18:03\n• The idea is good, but why convert `sys.argv[1:]` to a generator instance rather than an iterator? E.g. `my_gen = iter(sys.argv[1:])` will get you the same results as your function `g`. Jul 28, 2010 at 19:01\n• Also, instead of using `while` with `try: except StopIteration:` a for loop will achieve the same thing. Simply: `for arg in my_gen`. You can still use `my_gen.next()` in the loop. Jul 28, 2010 at 19:08\n\nYou can ensure that an index is incremented within a `try...finally` block. This solve the common problem of wanting to `continue` to the next index without having to copy/past `i += 1` everywhere. Which is one of the main advantages the C-like `for` loop offers.\n\nThe main disadvantage to using a `try...finally` is having to indent your code once more. but if you have a `while` loop with many `continue` conditions its probably worth it.\n\n# Example\n\nThis example demonstrates that `i` still gets incremented in the `finally` block, even with `continue` being called. If `i` is not incremented its value will remain even forever, and the `while` loop will become infinite.\n\n``````i = 0\nwhile i < 10:\ntry:\nprint(i)\n\nif i % 2 == 0:\ncontinue\n\nfinally:\ni += 1\n``````\n\nwithout it you would have to increment `i` just before calling `continue`.\n\n``````i = 0\nwhile i < 10:\nprint(i)\n\nif i % 2 == 0:\ni += 1 # duplicate code\ncontinue\n\ni += 1\n``````\n`````` for i in xrange(0, 10):\nif i % 3 == 0\ncontinue\nprint i\n``````\n\nWill only values which aren't divisible by 3.\n\nIf you need to iterate over something, and need an index, use enumerate()\n\n``````for i, arg in enumerate(argv):\n...\n``````\n\nwhich does the same as the questioner's\n\n``````for i in range(0,len(argv)):\narg = argv[i]\n``````\n\nYour problem seems to be that you should loop not raw parameters but parsed parameters. I would suggest you to consider to change your decision not to use standard module (like the others).\n\n``````increament = 4 #say\nfor i in range(n):\n#write your code here\nn=n+increment\n``````\n\nthis might be the simple solution to the problem if you just want to iterate through the array by skipping 4 members" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.75578314,"math_prob":0.7471764,"size":689,"snap":"2022-40-2023-06","text_gpt3_token_len":201,"char_repetition_ratio":0.10656934,"word_repetition_ratio":0.0,"special_character_ratio":0.31204644,"punctuation_ratio":0.14375,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9731701,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-09-29T12:33:10Z\",\"WARC-Record-ID\":\"<urn:uuid:f38eba14-8746-46bf-a4db-7fd31ad8ff32>\",\"Content-Length\":\"249751\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:168d5d6a-d064-4f7b-b848-3ecec0475f2c>\",\"WARC-Concurrent-To\":\"<urn:uuid:f3eee143-00e3-4f8a-9c40-e31643b5a9b2>\",\"WARC-IP-Address\":\"151.101.1.69\",\"WARC-Target-URI\":\"https://stackoverflow.com/questions/3354313/python-is-there-a-c-like-for-loop-available/3354369\",\"WARC-Payload-Digest\":\"sha1:6Y6HBLHXIRPTMO6E5HXXJHJ4U6FJCP3F\",\"WARC-Block-Digest\":\"sha1:SK46654P6FLPFXKFKDH2G3MNNVQLJFZA\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030335350.36_warc_CC-MAIN-20220929100506-20220929130506-00052.warc.gz\"}"}
https://dsp.stackexchange.com/questions/69715/doopler-spread-and-delay-spread-in-an-equation-of-channel-freq-response	[ "# Doopler spread and delay spread in an equation of channel freq response\n\nAssumed the transmission system with channel impulse response is determined by the matrices $$H(\\tau_l) \\in C^{N_R \\times N_T}$$ ( $$N_R$$ and $$N_T$$ are numbers of received and transmit antennas)\n\nBy taking the Fourier Transform (FT) of the impulse response, we get the frequency response of the channel at subcarrier $$n$$.\n\n$$\\begin{equation} H(n)=\\sum_{l=1}^{L} H(\\tau_l) \\cdot e^{i \\cdot 2 \\pi (f_c+\\Delta f \\cdot n)\\tau_l}, \\end{equation}$$ where $$f_c$$ is the centre frequency, $$\\Delta f$$ is the subcarrier bandwidth, $$n$$ is a subcarrier index, $$n=1, \\ldots N$$.$$t$$ denote time, $$\\tau$$ is delay. $$\\tau_l$$ is the cluster delays.\n\nHow should I change the equation above if I need to check how the doppler delay is affected system?" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.79543847,"math_prob":0.99999166,"size":719,"snap":"2020-34-2020-40","text_gpt3_token_len":212,"char_repetition_ratio":0.11888112,"word_repetition_ratio":0.0,"special_character_ratio":0.28789985,"punctuation_ratio":0.08695652,"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\":\"2020-10-01T04:11:16Z\",\"WARC-Record-ID\":\"<urn:uuid:0537655d-7e4c-4713-b5b1-3941b4997d27>\",\"Content-Length\":\"141609\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:51970c8c-eb61-4c35-b84f-7cb2c4a12db2>\",\"WARC-Concurrent-To\":\"<urn:uuid:5d77e3e8-8314-4bf8-a1f8-4d57097100c6>\",\"WARC-IP-Address\":\"151.101.193.69\",\"WARC-Target-URI\":\"https://dsp.stackexchange.com/questions/69715/doopler-spread-and-delay-spread-in-an-equation-of-channel-freq-response\",\"WARC-Payload-Digest\":\"sha1:IA6Y6GQ36XJXPIFGTEFY7LW4TM43JGKQ\",\"WARC-Block-Digest\":\"sha1:242YEATKFIQJOG57SL7MPXQ4MBSFBCDR\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600402130615.94_warc_CC-MAIN-20201001030529-20201001060529-00248.warc.gz\"}"}
https://php-legacy-docs.zend.com/manual/php5/en/pht-vector.updateAt	[ "Edit Report a Bug", null, "# pht\\Vector::updateAt\n\n(PECL pht >= 0.0.1)\n\npht\\Vector::updateAtUpdates a value in the vector\n\n### Description\n\npublic pht\\Vector::updateAt ( mixed `\\$value` , int `\\$offset` ) : void\n\nThis method updates a value at the specified offset in the vector (in linear time). The vector will automatically be resized if it is not large enough.\n\nSince the pht\\Vector class supports array access, updating values can also be performed using the array subset notation (`[]`).\n\n### Parameters\n\n`value`\n\nThe value to be inserted into the vector. This value will be serialised (since it may be passed around between threads).\n\n`offset`\n\nThe offset at which the value will be updated at. This offset must be within the 0..(N-1) range (inclusive), where N is the size of the vector. Attempting to update at offsets outside of this range will result in an Error exception.\n\nNo return value.\n\n### Examples\n\nExample #1 Updating a value in a vector\n\n``` <?phpuse pht\\Vector;\\$vector = new Vector();\\$vector[] = 1;\\$vector[] = 2;\\$vector->updateAt(3, 0);\\$vector = 4;var_dump(\\$vector); ```\n\nThe above example will output:\n\n```object(pht\\Vector)#1 (2) {\n=>\nint(3)\n=>\nint(4)\n}\n```" ]	[ null, "https://php-legacy-docs.zend.com/images/icon-github.svg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6596066,"math_prob":0.9125541,"size":1027,"snap":"2022-27-2022-33","text_gpt3_token_len":280,"char_repetition_ratio":0.16617791,"word_repetition_ratio":0.0,"special_character_ratio":0.28334957,"punctuation_ratio":0.14009662,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9838623,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-06-29T15:26:43Z\",\"WARC-Record-ID\":\"<urn:uuid:0f3af953-4248-4a16-8a39-3fab0351bdfa>\",\"Content-Length\":\"8597\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2e80a394-9a3e-45cd-9c54-3fa9d674f815>\",\"WARC-Concurrent-To\":\"<urn:uuid:4010550e-99c1-4b46-b59e-cc5a06acf1dd>\",\"WARC-IP-Address\":\"54.85.21.190\",\"WARC-Target-URI\":\"https://php-legacy-docs.zend.com/manual/php5/en/pht-vector.updateAt\",\"WARC-Payload-Digest\":\"sha1:KTIY3NP3HYTEZHKZILCA327JBR6ACXSZ\",\"WARC-Block-Digest\":\"sha1:YDLSAQIP6GTNCWDAQ436TJTHMZLHJFL7\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656103640328.37_warc_CC-MAIN-20220629150145-20220629180145-00352.warc.gz\"}"}
http://www.mathematics21.org/view/compact/index-4.html	[ "", null, "Then\n\ng\n\n=\n\nh\n\nf\n\n×\n\nf\n\ni\n\n.\n\nProof.\n\nFrom the above\n\nh\n\nf\n\n×\n\nf\n\ni\n\ng\n\ng\n\n1\n\ng\n\n.\n\n[FIXME: Funcoids and reloids are confused.]\n\nIt’s remainded to prove\n\ng\n\n⊑ h\n\nf\n\n×\n\nf\n\ni\n\n.\n\n[FIXME: Possible errors.]\n\nSuppose there is\n\nU\n\nxyGR\n\nh\n\nf\n\n×\n\nf\n\ni\n\nsuch that\n\nU\n\nGR\n\ng\n\n.\n\nThen\n\n{\n\nV\n\n\\\n\nU\n\n\|\n\nV\n\nGR\n\ng\n\n}\n\n=\n\ng\n\n\\\n\nU\n\nwould be a proper filter.\n\nThus by reflexivity\n\nh\n\nf\n\n×\n\nf\n\ni\n\n(\n\ng\n\n\\\n\nU\n\n)\n\n0\n\n.\n\nBy compactness of\n\nf\n\n×\n\nf\n\n, Cor\n\nh\n\nf\n\n×\n\nf\n\ni\n\n(\n\ng\n\n\\\n\nU\n\n)\n\n0\n\n.\n\nSuppose\n\n↑{\n\n(\n\nx\n\n;\n\nx\n\n)\n\n} ⊑ h\n\nf\n\n×\n\nf\n\ni\n\n(\n\ng\n\n\\\n\nU\n\n)\n\n; then\n\ng\n\n\\\n\nU\n\nh\n\nf\n\n1\n\n×\n\nf\n\n1\n\ni{\n\n(\n\nx\n\n;\n\nx\n\n)\n\n}\n\n;\n\nU\n\nh\n\nf\n\n1\n\n×\n\nf\n\n1\n\ni{\n\n(\n\nx\n\n;\n\nx\n\n)\n\n} ⊑ h\n\nf\n\n1\n\n×\n\nf\n\n1\n\ni\n\nwhat is impossible.\n\nThus there exist\n\nx\n\ny\n\nsuch that\n\n{\n\n(\n\nx\n\n;\n\ny\n\n)\n\n} ⊑\n\nCor\n\nh\n\nf\n\n×\n\nf\n\ni\n\n(\n\ng\n\n\\\n\nU\n\n)\n\n. Thus\n\n{\n\n(\n\nx\n\n;\n\ny\n\n)\n\n} ⊑ h\n\nf\n\n×\n\nf\n\ni\n\ng\n\n.\n\nThus by the lemma\n\n{\n\n(\n\nx\n\n;\n\ny\n\n)\n\n} ⊑\n\nwhat is impossible. So\n\nU\n\nGR\n\ng\n\n.\n\nWe have xyGR\n\nh\n\nf\n\n×\n\nf\n\ni\n\nGR\n\ng\n\n;\n\nh\n\nf\n\n×\n\nf\n\ni\n\ng\n\n.\n\nCorollary 18.\n\nLet\n\nf\n\nis a\n\nT\n\n1\n\n-separable (the same as\n\nT\n\n2\n\nfor symmetric transitive) compact funcoid\n\nand\n\ng\n\nis a uniform space (reflexive, symmetric, and transitive endoreloid) such that\n\n(\n\nFCD\n\n)\n\ng\n\n=\n\nf\n\n.\n\nThen\n\ng\n\n=\n\nh\n\nf\n\n×\n\nf\n\ni\n\n.\n\nAn (incomplete) attempt to prove one more theorem follows:\n\nTheorem 19.\n\nLet\n\nµ\n\nand\n\nν\n\nbe uniform spaces,\n\n(\n\nFCD\n\n)\n\nµ\n\nbe a compact funcoid. Then a map\n\nf\n\nis a\n\ncontinuous map from\n\n(\n\nFCD\n\n)\n\nµ\n\nto\n\n(\n\nFCD\n\n)\n\nν\n\niff\n\nf\n\nis a (uniformly) continuous map from\n\nµ\n\nto\n\nν\n\n.\n\nProof.\n\n[FIXME: errors in this proof.]\n\nWe have\n\nµ\n\n=\n\nh\n\n(\n\nFCD\n\n)\n\nµ\n\n×\n\n(\n\nFCD\n\n)\n\nµ\n\ni↑\n\nRLD\n\nf\n\nC\n\n?\n\n((\n\nFCD\n\n)\n\nµ\n\n; (\n\nFCD\n\n)\n\nν\n\n)\n\n. Then\n\nf\n\n×\n\nf\n\nC\n\n?\n\n((\n\nFCD\n\n)(\n\nµ\n\n×\n\nµ\n\n); (\n\nFCD\n\n)(\n\nν\n\n×\n\nν\n\n))\n\n(\n\nf\n\n×\n\nf\n\n)\n\n(\n\nFCD\n\n)(\n\nµ\n\n×\n\nµ\n\n)\n\n(\n\nFCD\n\n)(\n\nν\n\n×\n\nν\n\n)\n\n(\n\nf\n\n×\n\nf\n\n)\n\nFor every\n\nV\n\nGR\n\n(\n\nν\n\n×\n\nν\n\n)\n\nwe have\n\nh\n\ng\n\n1\n\ni\n\nV\n\n∈ h\n\n(\n\nFCD\n\n)(\n\nµ\n\n×\n\nµ\n\n)\n\ni{\n\ny\n\n}\n\nfor some\n\ny\n\n.\n\nh\n\ng\n\n1\n\ni\n\nV\n\n∈ h\n\n(\n\nFCD\n\n)\n\nµ\n\n×\n\n(\n\nFCD\n\n)\n\nµ\n\ni↑\n\nRLD\n\n∆ =\n\nGR\n\nµ\n\nh\n\ng\n\nih\n\ng\n\n1\n\ni\n\nV\n\nV\n\nWe need to prove\n\nf\n\nC\n\n(\n\nµ\n\n;\n\nν\n\n)\n\nthat is\n\np\n\nGR\n\nν\n\nq\n\nGR\n\nµ\n\n:\n\nh\n\nf\n\ni\n\nq\n\np\n\n. But this follows from the\n\nabove.\n\nBibliography\n\n\n\nVictor Porton. Categorical product of funcoids. At\n\nhttp://www.mathematics21.org/binaries/product.pdf\n\n.\n\n\n\nVictor Porton.\n\nAlgebraic General Topology. Volume 1\n\n. 2013.\n\n4" ]	[ null, "http://www.mathematics21.org/view/compact/index004.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.63594574,"math_prob":0.9547413,"size":1986,"snap":"2019-35-2019-39","text_gpt3_token_len":1146,"char_repetition_ratio":0.16094853,"word_repetition_ratio":0.27631578,"special_character_ratio":0.449144,"punctuation_ratio":0.13276231,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9997559,"pos_list":[0,1,2],"im_url_duplicate_count":[null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-08-26T06:29:39Z\",\"WARC-Record-ID\":\"<urn:uuid:0771cb4a-2b43-4b21-a582-f9367826b8fe>\",\"Content-Length\":\"50532\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:fe7b91ab-8252-4507-8a80-fc4afe6f2d38>\",\"WARC-Concurrent-To\":\"<urn:uuid:2cf7cc94-bdd9-4733-b40e-40d06222391f>\",\"WARC-IP-Address\":\"104.236.49.103\",\"WARC-Target-URI\":\"http://www.mathematics21.org/view/compact/index-4.html\",\"WARC-Payload-Digest\":\"sha1:ZLHUKSLJMCVU4MRYHWZQKRY4YF3DQF3I\",\"WARC-Block-Digest\":\"sha1:MM7QNKO4AHT5Q33DP4XGXA5ECNS4TW2D\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-35/CC-MAIN-2019-35_segments_1566027330968.54_warc_CC-MAIN-20190826042816-20190826064816-00522.warc.gz\"}"}
https://www.bartleby.com/questions-and-answers/a-particle-is-at-rest-and-at-x0-and-y0-at-time-0.-the-particle-then-moves-in-the-xy-plane-with-an-ac/05cc8e10-0ff4-424f-82b0-a0fc17474aea	[ "", null, "", null, "A particle is at rest and at x=0 and y=0 at time = 0. The particle then moves in the x-y plane with an acceleration in m/s^2 of a = 5t^2 i + 5t j , where t is in seconds. Determine the magnitude of the particle's velocity vector in m/s at instant the y-component of the position vector ry = 8 meters.\n\nQuestion\n\nA particle is at rest and at x=0 and y=0 at time = 0. The particle then moves in the x-y plane with an acceleration in m/s^2 of a = 5t^2 i + 5t j , where t is in seconds. Determine the magnitude of the particle's velocity vector in m/s at instant the y-component of the position vector ry = 8 meters.\n\nStep 1", null, "help_outlineImage TranscriptioncloseGiven Jntormation - At fime (tzo) x-0 cand yo At time tzo) Vx =o and Uyzo Acceleration vectpr a z 5ti+5tj fullscreen\nStep 2", null, "help_outlineImage TranscriptioncloseGiven a5t and ay 5t Velodty of the panticle a dv dt dv adt V -Ja,dt VxSstdt Jstdt Vyay dt 5 Vy At time Cto) Vyzo At time to), Vxo C20 . V St fullscreen\nStep 3", null, "help_outlineImage TranscriptioncloseDisplacement is calculated as ds dt ds Vd t S vdt SVndt Sx= S- 37 Sy 6 At fime (to) Sy 0 (2 At time (t-o) S0 5t S C20 (2 fullscreen\n\nWant to see the full answer?\n\nSee Solution\n\nWant to see this answer and more?\n\nOur solutions are written by experts, many with advanced degrees, and available 24/7\n\nSee Solution\nTagged in\n\nKinematics", null, "" ]	[ null, "https://www.bartleby.com/static/search-icon-white.svg", null, "https://www.bartleby.com/static/close-grey.svg", null, "https://prod-qna-question-images.s3.amazonaws.com/qna-images/answer/f9772908-ce96-424c-9aea-414c39919021/4a42967f-dc42-4a20-a1a4-cbc7a8043348/s6dnafo.png", null, "https://prod-qna-question-images.s3.amazonaws.com/qna-images/answer/f9772908-ce96-424c-9aea-414c39919021/4a42967f-dc42-4a20-a1a4-cbc7a8043348/15eezkg.png", null, "https://prod-qna-question-images.s3.amazonaws.com/qna-images/answer/f9772908-ce96-424c-9aea-414c39919021/4a42967f-dc42-4a20-a1a4-cbc7a8043348/kfp5q6.png", null, "https://www.bartleby.com/static/logo.svg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.87922275,"math_prob":0.94405425,"size":1865,"snap":"2019-43-2019-47","text_gpt3_token_len":494,"char_repetition_ratio":0.111767866,"word_repetition_ratio":0.037900876,"special_character_ratio":0.2756032,"punctuation_ratio":0.18077803,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98172104,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12],"im_url_duplicate_count":[null,null,null,null,null,1,null,1,null,1,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-21T22:46:55Z\",\"WARC-Record-ID\":\"<urn:uuid:994a6e99-3bd4-46d3-a72b-533b06277121>\",\"Content-Length\":\"102789\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1214bfa5-b45e-4a6e-adde-caaf18fc4a82>\",\"WARC-Concurrent-To\":\"<urn:uuid:9a53eae4-ca77-43f1-8d97-b9853c6b2260>\",\"WARC-IP-Address\":\"99.84.181.62\",\"WARC-Target-URI\":\"https://www.bartleby.com/questions-and-answers/a-particle-is-at-rest-and-at-x0-and-y0-at-time-0.-the-particle-then-moves-in-the-xy-plane-with-an-ac/05cc8e10-0ff4-424f-82b0-a0fc17474aea\",\"WARC-Payload-Digest\":\"sha1:IHJRKHNKGSLDT4HN6TIFJFG26IKNA32B\",\"WARC-Block-Digest\":\"sha1:JRSQ2TZ7I5ZXCZIZEJCOZXX444II3UE7\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570987795253.70_warc_CC-MAIN-20191021221245-20191022004745-00281.warc.gz\"}"}
https://xarray.pydata.org/en/latest/generated/xarray.Dataset.sortby.html	[ "# xarray.Dataset.sortby¶\n\nDataset.sortby(variables, ascending=True)\n\nSort object by labels or values (along an axis).\n\nSorts the dataset, either along specified dimensions, or according to values of 1-D dataarrays that share dimension with calling object.\n\nIf the input variables are dataarrays, then the dataarrays are aligned (via left-join) to the calling object prior to sorting by cell values. NaNs are sorted to the end, following Numpy convention.\n\nIf multiple sorts along the same dimension is given, numpy’s lexsort is performed along that dimension: https://docs.scipy.org/doc/numpy/reference/generated/numpy.lexsort.html and the FIRST key in the sequence is used as the primary sort key, followed by the 2nd key, etc.\n\nParameters\nReturns\n\nsorted – A new dataset where all the specified dims are sorted by dim labels.\n\nReturn type\n\nDataset" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7662463,"math_prob":0.8780469,"size":841,"snap":"2020-34-2020-40","text_gpt3_token_len":190,"char_repetition_ratio":0.119474314,"word_repetition_ratio":0.0,"special_character_ratio":0.20451844,"punctuation_ratio":0.14375,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98214656,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-22T02:05:07Z\",\"WARC-Record-ID\":\"<urn:uuid:13f1fb4f-b739-4618-b4d1-d7bb6a60c13f>\",\"Content-Length\":\"23770\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:eef91f92-278c-4084-a35f-09dbb62c868b>\",\"WARC-Concurrent-To\":\"<urn:uuid:d5b73523-0078-480b-971e-4f1f8350b04d>\",\"WARC-IP-Address\":\"104.26.1.204\",\"WARC-Target-URI\":\"https://xarray.pydata.org/en/latest/generated/xarray.Dataset.sortby.html\",\"WARC-Payload-Digest\":\"sha1:NIESAOTRJWDDJ2365UKIZJIGONWSXOTM\",\"WARC-Block-Digest\":\"sha1:75Z4OATXLIDI2TKOTJCVXRO25K72PVB5\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600400202686.56_warc_CC-MAIN-20200922000730-20200922030730-00684.warc.gz\"}"}
https://gitlab.eurecom.fr/dyyu/openairinterface5g/commit/2cb4d347d04242be04383433771626bd8ca26129	[ "### make the local tracer more robust\n\n```if a read from the remote tracer's socket fails, let's smash\nthe socket and wait for another remote tracer```\nparent 2219fe54\n ... ... @@ -131,35 +131,69 @@ process: static void forward_remote_messages(void _f) { #define PUT(x) do { \\ if (bufsize == bufmaxsize) { \\ bufmaxsize += 4096; \\ buf = realloc(buf, bufmaxsize); \\ if (buf == NULL) abort(); \\ } \\ buf[bufsize] = x; \\ bufsize++; \\ } while (0) #define PUT_BUF(x, l) do { \\ char zz = (char )(x); \\ int len = l; \\ while (len) { PUT(zz); zz++; len--; } \\ } while (0) forward_data f = _f; int from; int to; int l, len; char b; char buf; char buf = NULL; int bufsize = 0; int bufmaxsize = 0; char t; again: /* Note: if the remote socket dies while a transfer is running * then the state of the tracer will be totally messed up. * If that ever happens, things are messed up anyway, so no big * deal... (TODO: to be refined at some point, maybe) / while (1) { from = f->socket_remote; to = f->socket_local; len = read(from, buf, 1024); if (len <= 0) break; b = buf; while (len) { l = write(to, b, len); bufsize = 0; / let's read and process messages / len = read(from, &t, 1); if (len <= 0) goto dead; PUT(t); switch (t) { case 0: case 1: / message 0 and 1: get a length and then 'length' numbers / if (read(from, &len, sizeof(int)) != sizeof(int)) goto dead; PUT_BUF(&len, 4); while (len) { if (read(from, &l, sizeof(int)) != sizeof(int)) goto dead; PUT_BUF(&l, 4); len--; } break; case 2: break; } b = buf; while (bufsize) { l = write(to, b, bufsize); if (l <= 0) abort(); len -= l; bufsize -= l; b += l; } } dead: / socket died, let's stop all traces and wait for another tracer */ buf = 1; if (write(to, buf, 1) != 1) abort(); ... ...\nMarkdown is supported\n0% or\nYou are about to add 0 people to the discussion. Proceed with caution.\nFinish editing this message first!" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.55198574,"math_prob":0.9879138,"size":1968,"snap":"2020-10-2020-16","text_gpt3_token_len":675,"char_repetition_ratio":0.11608961,"word_repetition_ratio":0.094444446,"special_character_ratio":0.414126,"punctuation_ratio":0.24213076,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9762399,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-04-05T11:27:48Z\",\"WARC-Record-ID\":\"<urn:uuid:2ae49cbc-f705-4b04-8c75-00db31533f91>\",\"Content-Length\":\"155323\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:99a58201-fd3f-4631-9af9-41377c76071a>\",\"WARC-Concurrent-To\":\"<urn:uuid:97b460b4-6bf3-427f-bb4f-57c8b6356904>\",\"WARC-IP-Address\":\"193.55.113.249\",\"WARC-Target-URI\":\"https://gitlab.eurecom.fr/dyyu/openairinterface5g/commit/2cb4d347d04242be04383433771626bd8ca26129\",\"WARC-Payload-Digest\":\"sha1:ZGBGOGP6S5WCMVTEZWZH5DGZFDDBNG5K\",\"WARC-Block-Digest\":\"sha1:ISVUKT5BQKLPBT3PAWKPKWHANRIHGIDX\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-16/CC-MAIN-2020-16_segments_1585371576284.74_warc_CC-MAIN-20200405084121-20200405114121-00357.warc.gz\"}"}
https://pressbooks.online.ucf.edu/osuniversityphysics2/chapter/power-in-an-ac-circuit/	[ "Chapter 15. Alternating-Current Circuits\n\n# 15.4 Power in an AC Circuit\n\n### Learning Objectives\n\nBy the end of the section, you will be able to:\n\n• Describe how average power from an ac circuit can be written in terms of peak current and voltage and of rms current and voltage\n• Determine the relationship between the phase angle of the current and voltage and the average power, known as the power factor\n\nA circuit element dissipates or produces power according to $P=IV,$ where I is the current through the element and V is the voltage across it. Since the current and the voltage both depend on time in an ac circuit, the instantaneous power $p\\left(t\\right)=i\\left(t\\right)v\\left(t\\right)$ is also time dependent. A plot of p(t) for various circuit elements is shown in Figure 15.16. For a resistor, i(t) and v(t) are in phase and therefore always have the same sign (see Figure 15.5). For a capacitor or inductor, the relative signs of i(t) and v(t) vary over a cycle due to their phase differences (see Figure 15.7 and Figure 15.9). Consequently, p(t) is positive at some times and negative at others, indicating that capacitive and inductive elements produce power at some instants and absorb it at others.", null, "Figure 15.16 Graph of instantaneous power for various circuit elements. (a) For the resistor, ${P}_{\\text{ave}}={I}_{0}{V}_{0}\\text{/}2,$ whereas for (b) the capacitor and (c) the inductor, ${P}_{\\text{ave}}=0.$ (d) For the source, ${P}_{\\text{ave}}={I}_{0}{V}_{0}\\left(\\text{cos}\\phantom{\\rule{0.2em}{0ex}}\\varphi \\right)\\text{/}2,$ which may be positive, negative, or zero, depending on $\\varphi .$\n\nBecause instantaneous power varies in both magnitude and sign over a cycle, it seldom has any practical importance. What we’re almost always concerned with is the power averaged over time, which we refer to as the average power. It is defined by the time average of the instantaneous power over one cycle:\n\n${P}_{\\text{ave}}=\\frac{1}{T}{\\int }_{0}^{T}p\\left(t\\right)dt,$\n\nwhere $T=2\\pi \\text{/}\\omega$ is the period of the oscillations. With the substitutions $v\\left(t\\right)={V}_{0}\\phantom{\\rule{0.2em}{0ex}}\\text{sin}\\phantom{\\rule{0.2em}{0ex}}\\omega t$ and $i\\left(t\\right)={I}_{0}\\phantom{\\rule{0.2em}{0ex}}\\text{sin}\\phantom{\\rule{0.2em}{0ex}}\\left(\\omega t-\\varphi \\right),$ this integral becomes\n\n${P}_{\\text{ave}}=\\frac{{I}_{0}{V}_{0}}{T}{\\int }_{0}^{T}\\phantom{\\rule{0.2em}{0ex}}\\text{sin}\\phantom{\\rule{0.2em}{0ex}}\\left(\\omega t-\\varphi \\right)\\phantom{\\rule{0.2em}{0ex}}\\text{sin}\\phantom{\\rule{0.2em}{0ex}}\\omega t\\phantom{\\rule{0.2em}{0ex}}dt.$\n\nUsing the trigonometric relation $\\phantom{\\rule{0.2em}{0ex}}\\text{sin}\\phantom{\\rule{0.2em}{0ex}}\\left(A-B\\right)=\\phantom{\\rule{0.2em}{0ex}}\\text{sin}\\phantom{\\rule{0.2em}{0ex}}A\\text{cos}\\phantom{\\rule{0.2em}{0ex}}B-\\phantom{\\rule{0.2em}{0ex}}\\text{sin}\\phantom{\\rule{0.2em}{0ex}}B\\phantom{\\rule{0.2em}{0ex}}\\text{cos}\\phantom{\\rule{0.2em}{0ex}}A,$ we obtain\n\n${P}_{\\text{ave}}=\\frac{{I}_{0}{V}_{0}\\phantom{\\rule{0.2em}{0ex}}\\text{cos}\\phantom{\\rule{0.2em}{0ex}}\\varphi }{T}{\\int }_{0}^{T}\\phantom{\\rule{0.2em}{0ex}}\\text{sin}\\phantom{\\rule{0.2em}{0ex}}\\omega tdt-\\frac{{I}_{0}{V}_{0}\\phantom{\\rule{0.2em}{0ex}}\\text{sin}\\phantom{\\rule{0.2em}{0ex}}\\varphi }{T}{\\int }_{0}^{T}{\\phantom{\\rule{0.2em}{0ex}}\\text{sin}\\phantom{\\rule{0.2em}{0ex}}}^{2}\\omega t\\text{cos}\\phantom{\\rule{0.2em}{0ex}}\\omega tdt.$\n\nEvaluation of these two integrals yields\n\n$\\frac{1}{T}{\\int }_{0}^{T}{\\phantom{\\rule{0.2em}{0ex}}\\text{sin}\\phantom{\\rule{0.2em}{0ex}}}^{2}\\omega tdt=\\frac{1}{2}$\n\nand\n\n$\\frac{1}{T}{\\int }_{0}^{T}\\phantom{\\rule{0.2em}{0ex}}\\text{sin}\\phantom{\\rule{0.2em}{0ex}}\\omega t\\text{cos}\\phantom{\\rule{0.2em}{0ex}}\\omega tdt=0.$\n\nHence, the average power associated with a circuit element is given by\n\n${P}_{\\text{ave}}=\\frac{1}{2}{I}_{0}{V}_{0}\\phantom{\\rule{0.2em}{0ex}}\\text{cos}\\phantom{\\rule{0.2em}{0ex}}\\varphi .$\n\nIn engineering applications, $\\text{cos}\\phantom{\\rule{0.2em}{0ex}}\\varphi$ is known as the power factor, which is the amount by which the power delivered in the circuit is less than the theoretical maximum of the circuit due to voltage and current being out of phase. For a resistor, $\\varphi =0,$ so the average power dissipated is\n\n${P}_{\\text{ave}}=\\frac{1}{2}{I}_{0}{V}_{0}.$\n\nA comparison of p(t) and ${P}_{\\text{ave}}$ is shown in Figure 15.16(d). To make ${P}_{\\text{ave}}=\\left(1\\text{/}2\\right){I}_{0}{V}_{0}$ look like its dc counterpart, we use the rms values ${I}_{\\text{rms}}\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}{V}_{\\text{rms}}$ of the current and the voltage. By definition, these are\n\n${I}_{\\text{rms}}=\\sqrt{{i}_{\\text{ave}}^{2}}\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}{V}_{\\text{rms}}=\\sqrt{{v}_{\\text{ave}}^{2}},$\n\nwhere\n\n${i}_{\\text{ave}}^{2}=\\frac{1}{T}{\\int }_{0}^{T}{i}^{2}\\left(t\\right)dt\\phantom{\\rule{0.2em}{0ex}}\\text{and }\\phantom{\\rule{0.2em}{0ex}}{v}_{\\text{ave}}^{2}=\\frac{1}{T}{\\int }_{0}^{T}{v}^{2}\\left(t\\right)dt.$\n\nWith $i\\left(t\\right)={I}_{0}\\phantom{\\rule{0.2em}{0ex}}\\text{sin}\\phantom{\\rule{0.2em}{0ex}}\\left(\\omega t-\\varphi \\right)\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}v\\left(t\\right)={V}_{0}\\phantom{\\rule{0.2em}{0ex}}\\text{sin}\\phantom{\\rule{0.2em}{0ex}}\\omega t,$ we obtain\n\n${I}_{\\text{rms}}=\\frac{1}{\\sqrt{2}}{I}_{0}\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}{V}_{\\text{rms}}=\\frac{1}{\\sqrt{2}}{V}_{0}.$\n\nWe may then write for the average power dissipated by a resistor,\n\n${P}_{\\text{ave}}=\\frac{1}{2}{I}_{0}{V}_{0}={I}_{\\text{rms}}{V}_{\\text{rms}}={I}_{\\text{rms}}^{2}R.$\n\nThis equation further emphasizes why the rms value is chosen in discussion rather than peak values. Both equations for average power are correct for Equation 15.13, but the rms values in the formula give a cleaner representation, so the extra factor of 1/2 is not necessary.\n\nAlternating voltages and currents are usually described in terms of their rms values. For example, the 110 V from a household outlet is an rms value. The amplitude of this source is $110\\sqrt{2}\\phantom{\\rule{0.2em}{0ex}}\\text{V}=\\text{156 V}\\text{.}$ Because most ac meters are calibrated in terms of rms values, a typical ac voltmeter placed across a household outlet will read 110 V.\n\nFor a capacitor and an inductor, $\\varphi =\\pi \\text{/}2\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}-\\pi \\text{/}2\\phantom{\\rule{0.2em}{0ex}}\\text{rad,}$ respectively. Since $\\text{cos}\\pi \\text{/}2=\\text{cos}\\left(\\text{−}\\pi \\text{/}2\\right)=0,$ we find from Equation 15.12 that the average power dissipated by either of these elements is ${P}_{\\text{ave}}=0.$ Capacitors and inductors absorb energy from the circuit during one half-cycle and then discharge it back to the circuit during the other half-cycle. This behavior is illustrated in the plots of Figure 15.16, (b) and (c), which show p(t) oscillating sinusoidally about zero.\n\nThe phase angle for an ac generator may have any value. If $\\text{cos}\\phantom{\\rule{0.2em}{0ex}}\\varphi >0,$ the generator produces power; if $\\text{cos}\\phantom{\\rule{0.2em}{0ex}}\\varphi <0,$ it absorbs power. In terms of rms values, the average power of an ac generator is written as</p>\n\n${P}_{\\text{ave}}={I}_{\\text{rms}}{V}_{\\text{rms}}\\phantom{\\rule{0.2em}{0ex}}\\text{cos}\\phantom{\\rule{0.2em}{0ex}}\\varphi .$\n\nFor the generator in an RLC circuit,\n\n$\\text{tan}\\phantom{\\rule{0.2em}{0ex}}\\varphi =\\frac{{X}_{L}-{X}_{C}}{R}$\n\nand\n\n$\\text{cos}\\phantom{\\rule{0.2em}{0ex}}\\varphi =\\frac{R}{\\sqrt{{R}^{2}+{\\left({X}_{L}-{X}_{C}\\right)}^{2}}}=\\frac{R}{Z}.$\n\nHence the average power of the generator is\n\n${P}_{\\text{ave}}={I}_{\\text{rms}}{V}_{\\text{rms}}\\phantom{\\rule{0.2em}{0ex}}\\text{cos}\\phantom{\\rule{0.2em}{0ex}}\\varphi =\\frac{{V}_{\\text{rms}}}{Z}{V}_{\\text{rms}}\\frac{R}{Z}=\\frac{{V}_{\\text{rms}}^{2}R}{{Z}^{2}}.$\n\nThis can also be written as\n\n${P}_{\\text{ave}}={I}_{\\text{rms}}^{2}R,$\n\nwhich designates that the power produced by the generator is dissipated in the resistor. As we can see, Ohm’s law for the rms ac is found by dividing the rms voltage by the impedance.\n\n### Example\n\n#### Power Output of a Generator\n\nAn ac generator whose emf is given by\n\n$v\\left(t\\right)=\\left(4.00\\phantom{\\rule{0.2em}{0ex}}\\text{V}\\right)\\phantom{\\rule{0.2em}{0ex}}\\text{sin}\\phantom{\\rule{0.2em}{0ex}}\\left[\\left(1.00\\phantom{\\rule{0.2em}{0ex}}×\\phantom{\\rule{0.2em}{0ex}}{10}^{4}\\text{rad}\\text{/}\\text{s}\\right)t\\right]$\n\nis connected to an RLC circuit for which $L=2.00\\phantom{\\rule{0.2em}{0ex}}×\\phantom{\\rule{0.2em}{0ex}}{10}^{-3}\\phantom{\\rule{0.2em}{0ex}}\\text{H}$, $C=4.00\\phantom{\\rule{0.2em}{0ex}}×\\phantom{\\rule{0.2em}{0ex}}{10}^{-6}\\phantom{\\rule{0.2em}{0ex}}\\text{F}$, and $R=5.00\\phantom{\\rule{0.2em}{0ex}}\\text{Ω}$. (a) What is the rms voltage across the generator? (b) What is the impedance of the circuit? (c) What is the average power output of the generator?\n\n#### Strategy\n\nThe rms voltage is the amplitude of the voltage times $1\\text{/}\\sqrt{2}$. The impedance of the circuit involves the resistance and the reactances of the capacitor and the inductor. The average power is calculated by Equation 15.14, or more specifically, the last part of the equation, because we have the impedance of the circuit Z, the rms voltage ${V}_{\\text{rms}}$, and the resistance R.\n\n#### Solution\n\n1. Since ${V}_{0}=4.00\\phantom{\\rule{0.2em}{0ex}}\\text{V,}$ the rms voltage across the generator is\n\n${V}_{\\text{rms}}=\\frac{1}{\\sqrt{2}}\\left(4.00\\phantom{\\rule{0.2em}{0ex}}\\text{V}\\right)=2.83\\phantom{\\rule{0.2em}{0ex}}\\text{V}\\text{.}$\n2. The impedance of the circuit is\n\n$\\begin{array}{cc}\\hfill Z& =\\sqrt{{R}^{2}+{\\left({X}_{L}-{X}_{C}\\right)}^{2}}\\hfill \\\\ & ={\\left\\{{\\left(5.00\\phantom{\\rule{0.2em}{0ex}}\\text{Ω}\\right)}^{2}+{\\left[\\left(1.00\\phantom{\\rule{0.2em}{0ex}}×\\phantom{\\rule{0.2em}{0ex}}{10}^{4}\\phantom{\\rule{0.2em}{0ex}}\\text{rad/s}\\right)\\left(2.00\\phantom{\\rule{0.2em}{0ex}}×\\phantom{\\rule{0.2em}{0ex}}{10}^{-3}\\phantom{\\rule{0.2em}{0ex}}\\text{H}\\right)-\\frac{1}{\\left(1.00\\phantom{\\rule{0.2em}{0ex}}×\\phantom{\\rule{0.2em}{0ex}}{10}^{4}\\phantom{\\rule{0.2em}{0ex}}\\text{rad/s}\\right)\\left(4.00\\phantom{\\rule{0.2em}{0ex}}×\\phantom{\\rule{0.2em}{0ex}}{10}^{-6}\\phantom{\\rule{0.2em}{0ex}}\\text{F}\\right)}\\right]}^{2}\\right\\}}^{1\\text{/}2}\\hfill \\\\ & =7.07\\phantom{\\rule{0.2em}{0ex}}\\text{Ω}\\text{.}\\hfill \\end{array}$\n3. From Equation 15.14, the average power transferred to the circuit is\n\n${P}_{\\text{ave}}=\\frac{{V}_{\\text{rms}}^{2}R}{{Z}^{2}}=\\frac{{\\left(2.83\\phantom{\\rule{0.2em}{0ex}}\\text{V}\\right)}^{2}\\left(5.00\\phantom{\\rule{0.2em}{0ex}}\\text{Ω}\\right)}{{\\left(7.07\\phantom{\\rule{0.2em}{0ex}}\\text{Ω}\\right)}^{2}}=0.801\\phantom{\\rule{0.2em}{0ex}}\\text{W}\\text{.}$\n\n#### Significance\n\nIf the resistance is much larger than the reactance of the capacitor or inductor, the average power is a dc circuit equation of $P={V}^{2}\\text{/}R,$ where V replaces the rms voltage.\n\n### Check Your Understanding\n\nAn ac voltmeter attached across the terminals of a 45-Hz ac generator reads 7.07 V. Write an expression for the emf of the generator.\n\nShow Solution\n\n$v\\left(t\\right)=\\left(10.0\\phantom{\\rule{0.2em}{0ex}}\\text{V}\\right)\\phantom{\\rule{0.2em}{0ex}}\\text{sin}\\phantom{\\rule{0.2em}{0ex}}90\\pi t$\n\n### Check Your Understanding\n\nShow that the rms voltages across a resistor, a capacitor, and an inductor in an ac circuit where the rms current is ${I}_{\\text{rms}}$ are given by ${I}_{\\text{rms}}R,{I}_{\\text{rms}}{X}_{C},\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}{I}_{\\text{rms}}{X}_{L},$ respectively. Determine these values for the components of the RLC circuit of Equation 15.12.\n\nShow Solution\n\n2.00 V; 10.01 V; 8.01 V\n\n### Summary\n\n• The average ac power is found by multiplying the rms values of current and voltage.\n• Ohm’s law for the rms ac is found by dividing the rms voltage by the impedance.\n• In an ac circuit, there is a phase angle between the source voltage and the current, which can be found by dividing the resistance by the impedance.\n• The average power delivered to an RLC circuit is affected by the phase angle.\n• The power factor ranges from –1 to 1.\n\n### Conceptual Questions\n\nFor what value of the phase angle $\\varphi$ between the voltage output of an ac source and the current is the average power output of the source a maximum?\n\nDiscuss the differences between average power and instantaneous power.\n\nShow Solution\n\nThe instantaneous power is the power at a given instant. The average power is the power averaged over a cycle or number of cycles.\n\nThe average ac current delivered to a circuit is zero. Despite this, power is dissipated in the circuit. Explain.\n\nCan the instantaneous power output of an ac source ever be negative? Can the average power output be negative?\n\nShow Solution\n\nThe instantaneous power can be negative, but the power output can’t be negative.\n\nThe power rating of a resistor used in ac circuits refers to the maximum average power dissipated in the resistor. How does this compare with the maximum instantaneous power dissipated in the resistor?\n\n### Problems\n\nThe emf of an ac source is given by $v\\left(t\\right)={V}_{0}\\phantom{\\rule{0.2em}{0ex}}\\text{sin}\\phantom{\\rule{0.2em}{0ex}}\\omega t,$ where ${V}_{0}=100\\phantom{\\rule{0.2em}{0ex}}\\text{V}$ and $\\omega =200\\pi \\phantom{\\rule{0.2em}{0ex}}\\text{rad/s}\\text{.}$ Calculate the average power output of the source if it is connected across (a) a $20\\text{-}\\mu \\text{F}$ capacitor, (b) a 20-mH inductor, and (c) a $50\\text{-}\\text{Ω}$ resistor.\n\nCalculate the rms currents for an ac source is given by $v\\left(t\\right)={V}_{0}\\phantom{\\rule{0.2em}{0ex}}\\text{sin}\\phantom{\\rule{0.2em}{0ex}}\\omega t,$ where ${V}_{0}=100\\phantom{\\rule{0.2em}{0ex}}\\text{V}$ and $\\omega =200\\pi \\phantom{\\rule{0.2em}{0ex}}\\text{rad/s}$ when connected across (a) a $20\\text{-}\\mu \\text{F}$ capacitor, (b) a 20-mH inductor, and (c) a $50\\text{-}\\text{Ω}$ resistor.\n\nShow Solution\n\na. 0.89 A; b. 5.6A; c. 1.4 A\n\nA 40-mH inductor is connected to a 60-Hz AC source whose voltage amplitude is 50 V. If an AC voltmeter is placed across the inductor, what does it read?\n\nFor an RLC series circuit, the voltage amplitude and frequency of the source are 100 V and 500 Hz, respectively; $R=500\\phantom{\\rule{0.2em}{0ex}}\\text{Ω}$; and $L=0.20\\phantom{\\rule{0.2em}{0ex}}\\text{H}$. Find the average power dissipated in the resistor for the following values for the capacitance: (a) $C=2.0\\mu \\text{F}$ and (b) $C=0.20\\phantom{\\rule{0.2em}{0ex}}\\mu \\text{F}\\text{.}$\n\nShow Solution\n\na. 7.3 W; b. 6.3 W\n\nAn ac source of voltage amplitude 10 V delivers electric energy at a rate of 0.80 W when its current output is 2.5 A. What is the phase angle $\\varphi$ between the emf and the current?\n\nAn RLC series circuit has an impedance of $60\\phantom{\\rule{0.2em}{0ex}}\\text{Ω}$ and a power factor of 0.50, with the voltage lagging the current. (a) Should a capacitor or an inductor be placed in series with the elements to raise the power factor of the circuit? (b) What is the value of the reactance across the inductor that will raise the power factor to unity?\n\nShow Solution\n\na. inductor; b. ${X}_{L}=52\\phantom{\\rule{0.2em}{0ex}}\\text{Ω}$\n\n### Glossary\n\naverage power\ntime average of the instantaneous power over one cycle\npower factor\namount by which the power delivered in the circuit is less than the theoretical maximum of the circuit due to voltage and current being out of phase", null, "" ]	[ null, "https://pressbooks.online.ucf.edu/app/uploads/sites/372/2021/04/CNX_UPhysics_32_04_acpower.jpg", null, "https://pressbooks.online.ucf.edu/app/themes/pressbooks-book/packages/buckram/assets/images/cc-by.svg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.75210834,"math_prob":0.9993486,"size":13230,"snap":"2022-40-2023-06","text_gpt3_token_len":4246,"char_repetition_ratio":0.271057,"word_repetition_ratio":0.09492848,"special_character_ratio":0.30400604,"punctuation_ratio":0.103924416,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99980026,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,3,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-10-01T02:24:23Z\",\"WARC-Record-ID\":\"<urn:uuid:eec206e9-4d99-4d55-9ba7-993a7d2a60d2>\",\"Content-Length\":\"115523\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7ef65eca-351a-432f-99ca-f783e098361a>\",\"WARC-Concurrent-To\":\"<urn:uuid:47023927-f49d-4b58-bdc8-82d59976d935>\",\"WARC-IP-Address\":\"108.138.64.32\",\"WARC-Target-URI\":\"https://pressbooks.online.ucf.edu/osuniversityphysics2/chapter/power-in-an-ac-circuit/\",\"WARC-Payload-Digest\":\"sha1:Y5EWFXDI4VXLWIEQ447MRJAGJGCBQ5MF\",\"WARC-Block-Digest\":\"sha1:IPOP6KQJHXJ6TXLSKYMGB6NQV2XZSJBI\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030335514.65_warc_CC-MAIN-20221001003954-20221001033954-00432.warc.gz\"}"}
https://www.dadsworksheets.com/worksheets/subtraction-sequences.html	[ "# Subtraction Sequences Worksheets\n\nThese subtraction worksheets allow students to practice simple sequences of subtraction to arrive at a final answer to a problem. The worksheets start with very small differences and progress through multi-digit subtraction. There are also worksheets that mix addition and subtraction steps in the sequences for practicing both of these arithmetic skills together. They are a fun alternative to simple subtraction problems that keep the subtraction skills moving along!" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9014894,"math_prob":0.77418786,"size":711,"snap":"2021-31-2021-39","text_gpt3_token_len":114,"char_repetition_ratio":0.2446959,"word_repetition_ratio":0.0,"special_character_ratio":0.14627285,"punctuation_ratio":0.06666667,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99414515,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-08-05T16:41:40Z\",\"WARC-Record-ID\":\"<urn:uuid:e6c11893-3f44-40ae-8220-57cc58af8f08>\",\"Content-Length\":\"292961\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:820b3f5b-9ca6-4b82-8fa6-1c9b087f28b5>\",\"WARC-Concurrent-To\":\"<urn:uuid:f23af3e8-ffb8-41e4-89a7-9f0d10f71944>\",\"WARC-IP-Address\":\"172.67.75.70\",\"WARC-Target-URI\":\"https://www.dadsworksheets.com/worksheets/subtraction-sequences.html\",\"WARC-Payload-Digest\":\"sha1:O2N3Z2RLDI4QWA3I5EQIAHLFP2F5F7DK\",\"WARC-Block-Digest\":\"sha1:QLPCKG3AXPGNFKHSLGLAA2GKEVYOJ7KJ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-31/CC-MAIN-2021-31_segments_1627046156141.29_warc_CC-MAIN-20210805161906-20210805191906-00598.warc.gz\"}"}
https://www.lmfdb.org/EllipticCurve/Q/7260/l/	[ "# Properties\n\n Label 7260.l Number of curves $4$ Conductor $7260$ CM no Rank $0$ Graph", null, "# Related objects\n\nShow commands for: SageMath\nsage: E = EllipticCurve(\"l1\")\n\nsage: E.isogeny_class()\n\n## Elliptic curves in class 7260.l\n\nsage: E.isogeny_class().curves\n\nLMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality\n7260.l1 7260n4 $$[0, 1, 0, -30249556, 64026275300]$$ $$6749703004355978704/5671875$$ $$2572306572000000$$ $$$$ $$207360$$ $$2.6925$$\n7260.l2 7260n3 $$[0, 1, 0, -1890181, 1000400300]$$ $$-26348629355659264/24169921875$$ $$-685095855468750000$$ $$$$ $$103680$$ $$2.3459$$\n7260.l3 7260n2 $$[0, 1, 0, -381916, 83523284]$$ $$13584145739344/1195803675$$ $$542320423497388800$$ $$$$ $$69120$$ $$2.1432$$\n7260.l4 7260n1 $$[0, 1, 0, 26459, 6095384]$$ $$72268906496/606436875$$ $$-17189438667390000$$ $$$$ $$34560$$ $$1.7966$$ $$\\Gamma_0(N)$$-optimal\n\n## Rank\n\nsage: E.rank()\n\nThe elliptic curves in class 7260.l have rank $$0$$.\n\n## Complex multiplication\n\nThe elliptic curves in class 7260.l do not have complex multiplication.\n\n## Modular form7260.2.a.l\n\nsage: E.q_eigenform(10)\n\n$$q + q^{3} - q^{5} - 2q^{7} + q^{9} - 2q^{13} - q^{15} - 2q^{19} + O(q^{20})$$", null, "## Isogeny matrix\n\nsage: E.isogeny_class().matrix()\n\nThe $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the LMFDB numbering.\n\n$$\\left(\\begin{array}{rrrr} 1 & 2 & 3 & 6 \\\\ 2 & 1 & 6 & 3 \\\\ 3 & 6 & 1 & 2 \\\\ 6 & 3 & 2 & 1 \\end{array}\\right)$$\n\n## Isogeny graph\n\nsage: E.isogeny_graph().plot(edge_labels=True)\n\nThe vertices are labelled with LMFDB labels.", null, "" ]	[ null, 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AAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAAIDCCEAAgMIIQACAwghAaq6lpSWjRo1KS0tLo0cBKJp9zItpqqqqavQQAAD0H1cAAQAKIwABAAojAAEACiMAAQAKIwABAAojAKmZL3wh%2BZVfSY4/fv8/b3978vWvN3oqgLLYxRwMt4GhZr72teToo5NTTtn/%2B7//%2B%2BQzn0k2b07OPLOxswGUwi7mYAhA6mro0P2L5yMfafQkAOWyi/llxzR6AI5Me/cm//iPyZNP7n/5AYD%2BZxfzYgQgNfUv/7J/yTz1VHLccckttyRnnNHoqQDKYhdzIF4CpqZ6e5Mf/SjZuTP5yleSL34x%2Bda3LB6A/mQXcyACkLo677zkTW9Kli5t9CQA5bKL%2BWVuA0NdVVWye3ejpwAom13ML/MeQGpmzpzk3e9OXv/65PHHky9/OfnmN5M1axo9GUA57GIOhgCkZn7yk%2BSii5Lt25PBg/ffiHTNmuSd72z0ZADlsIs5GN4DCABQGO8BBAAojAAEACiMAAQAKIwABAAojAAEACiMAAQAKIwABAAojAAEACiMAAQAKIwApOYefPDBjB49Og8%2B%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%2B/Pi0trY2YGKAI5N9zMslAHlZqqrKunXrsnjx4tx8883p7e3Nia8ZkTGnnZLRbz4lZ570hgwa2JLmY49N79NP5/FdPbl/6w%2Bz6aGHs3HLw3nkJzvS3NycqVOnZsaMGTnnnHPS1NTU6P8sgFcc%2B5i%2BEIActFWrVmXe3Lm55957c9IJI3Pp5Pdk%2BoTxGdk67KDP2N7VnWVr1mbJytuy9dHtGfXWt2be/PmZOHFiHScHOLLYx/SVAOSAuru7M3PmzKxYsSLnjR2VKz/4vpx/TluOOurQ30K6b9%2B%2B3L6%2BI5/7h6/mjg2bc%2BGFF2bRokUZNuzglxdAaexjakUA8pJWrlyZSy%2B5JL1P9eS6Ky/NtPPH1/QlgqqqsmzNnZn1uaUZ0NKSJUuXZvLkyTU7H%2BBIYR9TSz4FzAuqqioLFy7MlClTcvapJ%2Be%2B5UsyfcI7av7%2BkKamplz07vNy/4olOfvUkzNlypS0t7f7pBrAL9jH1IMrgDxPVVWZM2dOrr322sy9eHo%2B%2BeFp/fLG4KqqMv%2BGZbnmhuWZPXt2FixY4A3JQNHsY%2BrlmEYPwOGnvb091157bT5z%2Be/nDy78zX77vk1NTZl38UUZNHBgrmpvz6BBgzJ79ux%2B%2B/4Ahxv7mHpxBZDnWLlyZaZMmZK5F0/P3I9Mb9gc8774pVxzw/KsXLkykyZNatgcAI1iH1NPApBndXd358wzzsjZp56clZ%2Be29DL/VVVZdJV87Lhe1tz/wMP%2BDQaUBT7mHrzIRCeNXPmzPQ%2B1ZMlV1/e8Pd6NDU1ZcnVM7O7pyezZs1q6CwA/c0%2Bpt4EIEn231R0xYoVue7KS1/WjUTr6XXDh%2BW6Ky/J8uXLc%2ButtzZ6HIB%2BYR/TH7wETKqqyuhRo9LafFRuv25hw59t/mdVVeX8WXPS/XSVjk2bDqvZAGrNPqa/uAJI1q1bl3vuvTdXfvB9h93/0E1NTbniA1Oy%2BZ57sn79%2BkaPA1BX9jH9RQCSxYsX56QTRub8c9oaPcoLOv%2Bctpx0wsgsXry40aMA1JV9TH8RgIXr6urKzTffnEsnv%2BeQf5bkuBlX5YrPLanxZP/h6KOPziWT35ObbropXV1ddfs%2BAI1kH9OfBGDh1q5dm97e3kyfML7mZ19y7XU56u0T8pdfvqXPZ100YXx6e3tz11131WAyeHHt7cnYscmgQcmIEcnkycmWLY2eihLUeh/P%2B%2BKXcvrUi3PcuEkZ%2Bq7fyjsv/0TW3/9Qn8%2B1j48MArBwHR0dOfE1I2r%2BSbOV3/o/%2BX8PbMnranTuyNZhOWHE8HR0dNTkPHgx3/pWctllybp1yTe%2BkezZk7zrXcmTTzZ6Mo50td7Hp77%2BxPzVH8zId5ctyT8v%2BfO8YeRrcv6sOen82c4%2BnWsfHxkEYOE2btiQMaedUtMzH93Rlcs/uzjL5v1Rjj3m6JqdO%2BbNp2Tjxg01Ow9eyJo1yYc%2BlJx5ZvKWtyQ33pj86EeJv%2Buot1rv4wvPH5fzzh6dk08YmTNPfmP%2BYtZH8/Mnd%2BW7D2/t89n28SufACxYVVXZtHlTRr%2B5dgtn3759%2BZ1rPpM/nPZbOfPkN9bs3CQZfdop2dSxKe5cRH967LH9vw4d2tg5OLLVYx//Z71PP53rV349g497Vd7y307u83n28SvfMY0egMbp7OzMzp2P5cyT3lCzMz/1pZtzzNFHZ%2Bb7a//zIs86%2BY352c6d6ezszIgRI2p%2BPvyyqko%2B/vHk134tOeusRk/Dkawe%2BzhJVt%2B9Ph/8ZHt2PbU7I4cNzT9dtzCtQwb3%2BVz7%2BJVPABZs165dSZJBA1tqcl7HQ9/LoptXpePvPl%2BX%2B1cd94s5N2zYkJEjR9b8fMrQ0tKS008//aAe%2B7GPJd/9bnL33Qd%2B7IMPPpienp4%2BTkeptm3blqR2%2B/gZ49reks1/vzhdjz2Wv1n19Uz9k4VZ98XrMmLokD6d%2B8w%2B9mf%2BlUsAFqy3tzdJ0nzssTU575/vuS87frYzb5hy0bNf27t3X/7wr/4m1910S7be8r/7dH7zMfv/uF5wwQV9OoeyjRo1Kps2bTrg4y6/PLn11uTb305OPPHA506bNi2bN2%2BuwYSUrFb7%2BBmvavkvOeX1r8spr39d3nbW6Tn1tz%2BcG762JrN/9wN9OveZfbx79%2B5ajEkDCMCCNTc3J9n/3pBauOjd78h5Y0c952sTrvjjTH/3O/J7v/HOPp/fu2dPkmT16tWuAHLIWlpe%2BgpLVe2Pv1tuSb75zeSkkw7u3OXLl7sawiHbtm1b3vve99ZsH7%2BYqqqyuwbf45l9PGDAgD6fRWMIwIINHDgwSfL4rtr8pTVs8PEZNvj453zt2GOOzmuHvjqnveH1fT7/iV/MOXbsWO85oW4uuyxZsSJZtWr/vQB//OP9Xx88OHmpdjzYl5XhhZz4i8vMtdrHT/Y8lQV/9w%2BZ%2BOtvy8hhQ9P9859n8VdW55HOrvz2%2BF/v8/nP7OMDPaHi8CUACzZ8%2BPAMGTI492/9Yaac%2B6uNHueA7vv%2BD/LqIUMyfPjwRo/CEewLX9j/67nnPvfrN964//YwUA%2B13sdHH3VUtvzw3/Nbt92Rrsd%2BnmGDB2Xs6afm21/485rcocE%2BfuVrqnyGu2jvGD8%2Bx%2B/dna9%2B6pONHuWAplw9P08c25I77riz0aMA1Jx9TH9yH8DCjRk7Nhu3PNzoMQ7KxocezpgxYxs9BkBd2Mf0JwFYuLa2tjzykx3Z3tXd6FFe0vau7jy6ozNtbW2NHgWgLuxj%2BpMALNz48ePT3NycZWvWNnqUl/SlNWvT3NyccePGNXoUgLqwj%2BlPArBwra2tef/7358lK2/Lvn37Gj3OC9q7d2%2BWrrwtU6dOTWtra6PHAagL%2B5j%2BJADJjBkzsvXR7bl9/eH50%2B5vX9%2BRrY9uz4wZMxo9CkBd2cf0F58CJlVVpW306Aw7tim3X7ewLj/G7VBVVZXzZ83JT/ckGzs6DqvZAGrNPqa/uAJImpqaMm/%2B/NyxYXOW3354vfdk2Zo7c8eGzZk7b55lAxzx7GP6iyuAPGvatGn5%2Buqv5b7lSzKydVijx8m2zu6cNe3S/MbEiVm2bFmjxwHoN/Yx9SYAeVZ3d3fOPOOMnH3qyVn56bkNfYZXVVUmXTUvG763Nfc/8ECGDWv8AgToL/Yx9eYlYJ41bNiwLFm6NF%2B7e12u%2BdvlDZ1l/g3Lsvo767P0%2BustG6A49jH1JgB5jsmTJ2fBggWZ/8Vl%2BeyKrzRkhs%2Bu%2BEquuWF5Fi5cmEmTJjVkBoBGs4%2Bpp2MaPQCHn9mzZ%2BeJJ57IVe3teXzXrsz9yPR%2BefmhqqrMv2FZrrlheWbPnp1PfOITdf%2BeAIcz%2B5h6EYA8T1NTUxYsWJBBgwZlzpw52bzl37Lk6svr%2BkbkbZ3dufRTi7L6O%2BvT3t5u2QDEPqZ%2BfAiEl7Rq1apc8tGPZndPT6678pJMn/COmj77rKoqy9bcmVmfW5oBLS1Zev31XmYAeAH2MbUkADmg7u7uzJw5MytWrMh5Y0flig9MyYS3jclRRx36W0j37t2b29d35C%2B/fEvu2LA506ZNy6JFizJ06NAaTg5wZLGPqRUByEFbtWpV5s%2Bbl8333JOTThiZSya/JxdNGP%2ByXorY3tWdL61Zm6Urb8vWR7dn1Fvfmnnz52fixIl1nBzgyGIf01cCkJelqqqsX78%2Bixcvzk033ZTe3t6c%2BJoRaTvtTRl92ik56%2BQ35riBLWk%2B5pj07tmTJ3b15L7v/yCbtjycjQ89nEd3dGbAgAGZOnVqZsyYkbPPPtsd5QEOgX1MXwhADllXV1fuuuuubNy4MR0dG9PR0ZGdOx973uOGDBmctra2jBkzNm1tbRk3blxaW1sbMDHAkck%2B5uUSgNRMVVXp7OxMT09Pdu/enQEDBqSlpSXDhw/3rBKgH9nHHIgABAAojJ8EAgBQGAEIAFAYAQgAUBgBCABQGAEIAFAYAQgAUBgBCABQGAEIAFAYAQgAUBgBCABQGAEIAFAYAQgAUBgBCABQGAEIAFAYAQgAUBgBCABQGAEIAFAYAQgAUBgBCABQGAEIAFAYAQgAUBgBCABQGAEIAFAYAQgAUBgBCABQGAEIAFAYAQgAUBgBCABQGAEIAFAYAQgAUBgBCABQGAEIAFAYAQgAUBgBCABQGAEIAFCY/w8pjNcGaiB0XgAAAABJRU5ErkJggg%3D%3D", 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http://www.yaldex.com/game-programming/0131020099_ch18lev1sec1.html	[ " Game Programming", null, "Free JavaScript Editor Ajax Editor \n\nMain Page\n\n### Types of Textures\n\nBefore we delve into specific texture mapping techniques, we must start by classifying textures and their uses. Textures is a very broad topic, and just using the term alone can result in misunderstandings.\n\nTextures can be classified as explicit or procedural. An explicit texture map consists of a regular bitmap, which we can create with a paint program, scan from a picture, and so on. It is very easy to apply and has almost no CPU cost. We just have to provide the texture coordinates, and the graphics subsystem will take care of the texturing process. On the other hand, a procedural texture is the output of a computer program that computes the texture map. Marble, fire, and many other materials can be decomposed in some primitive equations and functions, which can be implemented as a program. Procedural textures have several benefits over explicit textures. They are resolution independent because we can zoom into the texture and compute the details. Because they are defined by mathematical functions that include some randomness, they are usually not as repetitive as explicit maps. On the other hand, they have a significant performance hit. Whether they are executed on the CPU or on a dedicated shader platform, procedural maps will take up some system resources. This chapter will focus almost exclusively on explicit textures, whereas procedural maps are covered in Chapter 21, \"Procedural Techniques.\"\n\nAnother interesting classification can be established between static and dynamic texture maps. The difference between them is that dynamic maps are recomputed in real time, whereas static maps are just created at boot time. Both explicit and procedural textures can be static or dynamic. The most common type of texture map is both static and explicit. Games like Quake used a sequence of looping fire bitmaps to create torches, which is a good example of a dynamic and explicit technique. Marble and procedural fire would be adequate examples of static and dynamic procedural maps, respectively.\n\nDynamic, explicit textures are frequently encoded by storing all the frames in a single, large texture map, and somehow computing the texture coordinates automatically from the current timer value. So, if the texture holds NxN frames, and the speed (in frames per second) at which we want to animate the map is S, the following pseudocode computes texturing coordinates:\n\n```current_frame=(S/current_time) % (NN)\n\nrow=current_frame/N\ncolumn=current_frame % N\nu1=(1/N)row\nu2=(1/N)(row+1)\nv1=(1/N)column\nv2=(1/N)(column+1)\n```\n\nIn the preceding code, we are cycling through the texture map, using subimages as the actual texture map. Notice that I assume each image occupies a square zone.\n\n#### Texture Mapping\n\nWhichever the type, textures can be 1D, 2D, and 3D data sets. 2D maps are the most widely used because they can be represented with bitmaps. 3D textures are also called volume textures. They appear in fields like surgery to display 3D medical images and have slowly appeared on game-oriented hardware. They take up huge amounts of memory, and thus their use must be very limited. A 256x256x256 3D image with each texel representing a 256-color value (such as a grayscale image) can take up as much as 16MB. 1D maps have become increasingly popular over time as a way to implement a color translation table. The texture coordinate (in the range 0..1) is used as an index to a 1D table, where different colors are stored. A good example of this technique is cel shading, which produces quite convincing cartoonlike renderings. Cel shading is discussed in Chapter 17, \"Shading.\"\n\nNow, let's go back to our classic 2D texture maps. Because objects are inherently three dimensional, we need a way to precisely specify how the texture map should stretch and wrap the object, so we can place it. This process is called texture mapping.\n\nIn the 2D case, texture mapping is a function that goes from X,Y,Z to U,V, which are the mapping coordinates. This way it defines the correspondence between vertices on the geometry and texels in the map. For example, the following function is a proper texture mapping function:\n\n```U = X + Z\nV = Y\n```\n\nHowever, things are rarely this simple, and more involved functions must be used. Following is a survey of classic mapping functions.\n\n#### XYZ mapping\n\nThis function is used for 3D textures, especially procedural textures. It directly maps space to texture coordinates, possibly with translations, rotations, and scalings added on top. The general equation is as follows:\n\n```U = X\nV = Y\nW = Z\n```\n\nA scaled function would look something like this:\n\n```U = Xsx\nV = Ysy\nW = Zsz\n```\n\n#### Cylindrical Mapping\n\nAnother classic texture mapping function involves using a cylinder as the projector. Imagine a cylinder along the Y axis, wrapping the object with the material. That cylinder would be defined by the following parametric equations:\n\n```X = r cos(u* 2 pi)\nY = u * h\nZ = r sin(u* 2 pi)\n```\n\nwhere r and h would determine the cylinder's radii and height, respectively. Now, we can invert the preceding equation to solve for U and V, which are the mapping coordinates. In that case, the resulting equation would be:\n\n```V = arctan (X/Z)\nU = Y/h\n```\n\nNotice that this mapping is computed with the cylinder along the Y axis. Euclidean transforms could be applied to ensure that the cylinder lies in an arbitrary axis.\n\n#### Spherical Mapping\n\nMapping onto a sphere is somewhat similar to using a cylinder. All we have to do is use the parametric equations of the sphere to construct inverse equations that represent the texture mapping. Assume a sphere defined by the following:\n\n```x = r sin(v pi) cos(u 2 pi)\ny = r sin(v pi) sin(u 2 pi\nz = r cos(v pi)\n```\n\nNotice how we have used U and V (in the texture mapping sense) as the parameters for the sphere; both are in the range 0..1. Then, reversing the equation after half a page of algebra you get:\n\n```u = ( arccos(x/(r sin(v pi))) ) / (2 pi)\nv = arccos(z/r) / pi\n```\n\nThe preceding formula assumes that arccos returns a value from 0 to 2Pi. Most software implementations return values in the range 0..Pi, so some changes to the code are needed for correct rendering. Here is the source code for a spherical texture mapping function:\n\n```#define PI 3.141592654\n#define TWOPI 6.283185308\n\nvoid SphereMap(x,y,z,radius,u,v)\ndouble x,y,z,r,u,v;\n{\nv = acos(z/radius) / PI;\nif (y >= 0) u = acos(x/(radius * sin(PI(v)))) / TWOPI;\nelse u = (PI + acos(x/(radius sin(PI(v))))) / TWOPI;\n}\n```\n\nNotice how spherical mapping causes distortion to appear near the two poles of the sphere. To prevent this phenomenon called pinching, we need to preprocess the texture, either by using a commercial image processing software package or by implementing the process ourselves. Simply put, we need to convert the texture from polar to rectangular coordinates. Tools like Photoshop and Paint Shop Pro do this type of processing.\n\n#### Texture Mapping a Triangle\n\nThe methods discussed in the previous sections are used for full objects that more or less conform to the mapping shapes, such as a planet or a banana. Most objects, however, have complex shapes that cannot be easily assigned to a sphere or cylinder. In these cases, we will need a general method that offers triangle-level control over the texturing process. We will need to assign texture coordinates manually, so the maps wrap the object precisely and accurately.\n\nGiven a triangle p1, p2, p3 with texture coordinates (u1,v1), (u2,v2), and (u3, v3), deciding the texture coordinates for a point p (in world coordinates) inside the triangle is just a bilinear interpolation. We start by building two vectors from p1 to p2 and from p1 to p3, and construct the point p as the linear combination of these two vectors. Assuming the initial vectors were normalized, the components of the linear combination are the blending coefficients that, once applied to the per-vertex texture coordinates, will give us the U,V coordinates for the point p. See the example in Figure 18.1.\n\n##### Figure 18.1. Texture mapping triangles.", null, "On the other hand, rasterizers usually texture pixels in 2D after projection, but not full 3D points. Thus, a different mapping approach is followed. We start with the triangle defined not by 3D points, but by 2D, projected coordinates. Then, the triangle is painted one scanline at a time, drawing the horizontal line of pixels and texturing them along the way. Clearly, we need some kind of depth information to distinguish, from a texturing standpoint, two triangles that look the same onscreen but are not the same in 3D (see Figure 18.2). Thus, the 2D triangle coordinates are augmented with additional data that is then used to perform perspective-correct texture mapping, taking depth into consideration. Because these computations are performed on the hardware, they are beyond the duties of a game programmer these days.\n\n##### Figure 18.2. Two distinct triangles that share the same projection.", null, "", null, "\nBitcoin Gambling Site", null, "Ajax Editor JavaScript Editor" ]	[ null, "http://www.yaldex.com/FSimages/CoolJavaScriptEditor.gif", null, "http://www.yaldex.com/game-programming/FILES/18fig01.gif", null, "http://www.yaldex.com/game-programming/FILES/18fig02.gif", null, "http://www.yaldex.com/game-programming/FILES/pixel.gif", null, "http://www.yaldex.com/FSimages/CoolJavaScriptEditor.gif", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.90559906,"math_prob":0.96436495,"size":8891,"snap":"2021-04-2021-17","text_gpt3_token_len":1971,"char_repetition_ratio":0.13896704,"word_repetition_ratio":0.0013540961,"special_character_ratio":0.22101001,"punctuation_ratio":0.11672474,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9883674,"pos_list":[0,1,2,3,4,5,6,7,8,9,10],"im_url_duplicate_count":[null,null,null,1,null,1,null,9,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-04-21T20:41:55Z\",\"WARC-Record-ID\":\"<urn:uuid:1dcb7e1f-7729-4681-90cf-744dbfa16eb6>\",\"Content-Length\":\"15485\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:263bace5-3200-4ca6-a727-f088def3b7a6>\",\"WARC-Concurrent-To\":\"<urn:uuid:acb4ef18-6892-49b2-bf59-6e58ca28f87c>\",\"WARC-IP-Address\":\"173.249.8.108\",\"WARC-Target-URI\":\"http://www.yaldex.com/game-programming/0131020099_ch18lev1sec1.html\",\"WARC-Payload-Digest\":\"sha1:BWOTLEHBBBR67EGJAH5DNA5QXVSK77Y7\",\"WARC-Block-Digest\":\"sha1:URILELIU7UKG7N3KFQJXV66CBQAAEMKW\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-17/CC-MAIN-2021-17_segments_1618039550330.88_warc_CC-MAIN-20210421191857-20210421221857-00619.warc.gz\"}"}
https://www.idealady.com/category/sales/page/5/	[ "WordPress database error: [Table './idealady_idea/wp_wfblocks7' is marked as crashed and should be repaired]\n`SHOW FULL COLUMNS FROM `wp_wfblocks7``\n\nWordPress database error: [Table './idealady_idea/wp_wfblocks7' is marked as crashed and should be repaired]\n`SHOW FULL COLUMNS FROM `wp_wfblocks7``\n\nWordPress database error: [Table './idealady_idea/wp_wfhits' is marked as crashed and should be repaired]\n`SELECT MAX(attackLogTime) FROM wp_wfhits`\n\nWordPress database error: [Table './idealady_idea/wp_wfblocks7' is marked as crashed and should be repaired]\n```SELECT , CASE WHEN `type` = 3 THEN 0 WHEN `type` = 4 THEN 1 WHEN `type` = 7 THEN 2 WHEN `type` = 6 THEN 3 WHEN `type` = 5 THEN 4 WHEN `type` = 9 THEN 5 WHEN `type` = 8 THEN 6 WHEN `type` = 2 THEN 7 WHEN `type` = 1 THEN 8 ELSE 9999 END AS `typeSort`, CASE WHEN `type` = 3 THEN `parameters` WHEN `type` = 4 THEN `parameters` WHEN `type` = 1 THEN `IP` WHEN `type` = 9 THEN `IP` WHEN `type` = 5 THEN `IP` WHEN `type` = 6 THEN `IP` WHEN `type` = 7 THEN `IP` WHEN `type` = 2 THEN `IP` WHEN `type` = 8 THEN `IP` ELSE 9999 END AS `detailSort` FROM `wp_wfblocks7` WHERE `type` IN (4) AND (`expiration` = 0 OR `expiration` > UNIX_TIMESTAMP()) ORDER BY `typeSort` ASC, `id` DESC```\n\nWordPress database error: [Table './idealady_idea/wp_wfblocks7' is marked as crashed and should be repaired]\n```SELECT , CASE WHEN `type` = 3 THEN 0 WHEN `type` = 4 THEN 1 WHEN `type` = 7 THEN 2 WHEN `type` = 6 THEN 3 WHEN `type` = 5 THEN 4 WHEN `type` = 9 THEN 5 WHEN `type` = 8 THEN 6 WHEN `type` = 2 THEN 7 WHEN `type` = 1 THEN 8 ELSE 9999 END AS `typeSort`, CASE WHEN `type` = 3 THEN `parameters` WHEN `type` = 4 THEN `parameters` WHEN `type` = 1 THEN `IP` WHEN `type` = 9 THEN `IP` WHEN `type` = 5 THEN `IP` WHEN `type` = 6 THEN `IP` WHEN `type` = 7 THEN `IP` WHEN `type` = 2 THEN `IP` WHEN `type` = 8 THEN `IP` ELSE 9999 END AS `detailSort` FROM `wp_wfblocks7` WHERE `type` IN (3) AND (`expiration` = 0 OR `expiration` > UNIX_TIMESTAMP()) ORDER BY `typeSort` ASC, `id` DESC```\n\nWordPress database error: [Table './idealady_idea/wp_wfblocks7' is marked as crashed and should be repaired]\n`SHOW FULL COLUMNS FROM `wp_wfblocks7``\n\nWordPress database error: [Table './idealady_idea/wp_wfblocks7' is marked as crashed and should be repaired]\n`SHOW FULL COLUMNS FROM `wp_wfblocks7``\n\nSales Archives - Page 5 of 6 - Cathy Stucker - The Idea Lady\n\nWordPress database error: [Table './idealady_idea/wp_wfblocks7' is marked as crashed and should be repaired]\n```SELECT , CASE WHEN `type` = 3 THEN 0 WHEN `type` = 4 THEN 1 WHEN `type` = 7 THEN 2 WHEN `type` = 6 THEN 3 WHEN `type` = 5 THEN 4 WHEN `type` = 9 THEN 5 WHEN `type` = 8 THEN 6 WHEN `type` = 2 THEN 7 WHEN `type` = 1 THEN 8 ELSE 9999 END AS `typeSort`, CASE WHEN `type` = 3 THEN `parameters` WHEN `type` = 4 THEN `parameters` WHEN `type` = 1 THEN `IP` WHEN `type` = 9 THEN `IP` WHEN `type` = 5 THEN `IP` WHEN `type` = 6 THEN `IP` WHEN `type` = 7 THEN `IP` WHEN `type` = 2 THEN `IP` WHEN `type` = 8 THEN `IP` ELSE 9999 END AS `detailSort` FROM `wp_wfblocks7` WHERE `type` IN (4) AND (`expiration` = 0 OR `expiration` > UNIX_TIMESTAMP()) ORDER BY `typeSort` ASC, `id` DESC```\n\nWordPress database error: [Table './idealady_idea/wp_wfblocks7' is marked as crashed and should be repaired]\n```SELECT , CASE WHEN `type` = 3 THEN 0 WHEN `type` = 4 THEN 1 WHEN `type` = 7 THEN 2 WHEN `type` = 6 THEN 3 WHEN `type` = 5 THEN 4 WHEN `type` = 9 THEN 5 WHEN `type` = 8 THEN 6 WHEN `type` = 2 THEN 7 WHEN `type` = 1 THEN 8 ELSE 9999 END AS `typeSort`, CASE WHEN `type` = 3 THEN `parameters` WHEN `type` = 4 THEN `parameters` WHEN `type` = 1 THEN `IP` WHEN `type` = 9 THEN `IP` WHEN `type` = 5 THEN `IP` WHEN `type` = 6 THEN `IP` WHEN `type` = 7 THEN `IP` WHEN `type` = 2 THEN `IP` WHEN `type` = 8 THEN `IP` ELSE 9999 END AS `detailSort` FROM `wp_wfblocks7` WHERE `type` IN (3) AND (`expiration` = 0 OR `expiration` > UNIX_TIMESTAMP()) ORDER BY `typeSort` ASC, `id` DESC```\n\nWordPress database error: [Table './idealady_idea/wp_wfblocks7' is marked as crashed and should be repaired]\n```SELECT , CASE WHEN `type` = 3 THEN 0 WHEN `type` = 4 THEN 1 WHEN `type` = 7 THEN 2 WHEN `type` = 6 THEN 3 WHEN `type` = 5 THEN 4 WHEN `type` = 9 THEN 5 WHEN `type` = 8 THEN 6 WHEN `type` = 2 THEN 7 WHEN `type` = 1 THEN 8 ELSE 9999 END AS `typeSort`, CASE WHEN `type` = 3 THEN `parameters` WHEN `type` = 4 THEN `parameters` WHEN `type` = 1 THEN `IP` WHEN `type` = 9 THEN `IP` WHEN `type` = 5 THEN `IP` WHEN `type` = 6 THEN `IP` WHEN `type` = 7 THEN `IP` WHEN `type` = 2 THEN `IP` WHEN `type` = 8 THEN `IP` ELSE 9999 END AS `detailSort` FROM `wp_wfblocks7` WHERE `type` IN (1, 8, 9, 2, 5, 6) AND (`expiration` = 0 OR `expiration` > UNIX_TIMESTAMP()) ORDER BY `typeSort` ASC, `id` DESC```\n\nWordPress database error: [Table './idealady_idea/wp_wfblocks7' is marked as crashed and should be repaired]\n```SELECT , CASE WHEN `type` = 3 THEN 0 WHEN `type` = 4 THEN 1 WHEN `type` = 7 THEN 2 WHEN `type` = 6 THEN 3 WHEN `type` = 5 THEN 4 WHEN `type` = 9 THEN 5 WHEN `type` = 8 THEN 6 WHEN `type` = 2 THEN 7 WHEN `type` = 1 THEN 8 ELSE 9999 END AS `typeSort`, CASE WHEN `type` = 3 THEN `parameters` WHEN `type` = 4 THEN `parameters` WHEN `type` = 1 THEN `IP` WHEN `type` = 9 THEN `IP` WHEN `type` = 5 THEN `IP` WHEN `type` = 6 THEN `IP` WHEN `type` = 7 THEN `IP` WHEN `type` = 2 THEN `IP` WHEN `type` = 8 THEN `IP` ELSE 9999 END AS `detailSort` FROM `wp_wfblocks7` WHERE `type` IN (7) AND (`expiration` = 0 OR `expiration` > UNIX_TIMESTAMP()) ORDER BY `typeSort` ASC, `id` DESC```" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.96641743,"math_prob":0.971493,"size":3026,"snap":"2022-40-2023-06","text_gpt3_token_len":606,"char_repetition_ratio":0.11912641,"word_repetition_ratio":0.0,"special_character_ratio":0.1979511,"punctuation_ratio":0.1,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9922515,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-10-05T22:49:30Z\",\"WARC-Record-ID\":\"<urn:uuid:dea1e9cc-a56c-4988-848c-1e7011e080f1>\",\"Content-Length\":\"72520\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:18d11ec5-ae55-435f-add0-09e3ba6e3836>\",\"WARC-Concurrent-To\":\"<urn:uuid:0e949094-807a-4988-a13f-5cb9eb90003e>\",\"WARC-IP-Address\":\"72.52.171.245\",\"WARC-Target-URI\":\"https://www.idealady.com/category/sales/page/5/\",\"WARC-Payload-Digest\":\"sha1:XD7LETFDRRWW3NGN4PL6NJ26PS3DASEO\",\"WARC-Block-Digest\":\"sha1:P3TET2LTWPDZL4UTTBJHELUCKXUHMCW5\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030337668.62_warc_CC-MAIN-20221005203530-20221005233530-00218.warc.gz\"}"}
https://cvgmt.sns.it/paper/5151/	[ "", null, "## On minimizers of the maximal distance functional for a planar convex closed smooth curve\n\ncreated by teplitskaya1 on 06 Jun 2021\n\n[BibTeX]\n\npreprint\n\nInserted: 6 jun 2021\nLast Updated: 6 jun 2021\n\nYear: 2020\n\nArXiv: 2011.10463 PDF\n\nAbstract:\n\nFix a compact $M \\subset \\mathbb{R}^2$ and $r>0$. A minimizer of the maximal distance functional is a connected set $\\Sigma$ of the minimal length, such that $max_{y \\in M} dist(y,\\Sigma) \\leq r.$ The problem of finding maximal distance minimizers is connected to the Steiner tree problem. In this paper we consider the case of a convex closed curve $M$, with the minimal radius of curvature greater than $r$ (it implies that $M$ is smooth). The first part is devoted to statements on structure of $\\Sigma$: we show that the closure of an arbitrary connected component of $B_r(M) \\cap \\Sigma$ is a local Steiner tree which connects no more than five vertices. In the second part we \"derive in the picture\". Assume that the left and right neighborhoods of $y \\in M$ are contained in $r$-neighborhoods of different points $x_1$, $x_2 \\in \\Sigma$. We write conditions on the behavior of $\\Sigma$ in the neighborhoods of $x_1$ and $x_2$ under the assumption by moving $y$ along $M$." ]	[ null, "https://cvgmt.sns.it/media/cvgmt_transparent.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8715225,"math_prob":0.99925745,"size":1058,"snap":"2022-40-2023-06","text_gpt3_token_len":285,"char_repetition_ratio":0.11100569,"word_repetition_ratio":0.0,"special_character_ratio":0.27221173,"punctuation_ratio":0.08374384,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9997027,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-10-06T03:16:06Z\",\"WARC-Record-ID\":\"<urn:uuid:29f6a978-fc86-4315-a42a-627ec5f07711>\",\"Content-Length\":\"8805\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b121a3db-39a6-426f-b8d4-fb13b247e3e2>\",\"WARC-Concurrent-To\":\"<urn:uuid:a500d17d-e208-434a-b21b-46da285b5e4b>\",\"WARC-IP-Address\":\"192.167.206.42\",\"WARC-Target-URI\":\"https://cvgmt.sns.it/paper/5151/\",\"WARC-Payload-Digest\":\"sha1:5F5AD7AQPG6KRNO27FG2BUHIGNCQIVUA\",\"WARC-Block-Digest\":\"sha1:ILU7A5R647XHWJOSM6CCTBA6CJG7HTLE\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030337723.23_warc_CC-MAIN-20221006025949-20221006055949-00297.warc.gz\"}"}
https://www.decisionmodels.com/optspeede.htm	[ "", 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, "# Optimising Lookups", null, "Importance of Speed Faster Calculations Microsoft's Advice Bottlenecks/size Lookups Dynamic Ranges Totalling Generating Workbooks Multi-Level Calculations Array Formulae SUMIF Example Worksheet Links", null, "", null, "Lookup Options Speeding Up Lookups Missing Values Multiple Cells Two-Dimensional Lookup Three-Dimensional Lookup\n\n## Lookup Options\n\nLookups are often the most significant factor in calculation times, and fortunately there are many ways of improving lookup calculation time.\n\nWith FastExcel Version 2 you can now use the AVLOOKUP function, which is faster than VLOOKUP and INDEX/MATCH in many circumstances.\n\n#### Make sure you have understood the options in MATCH, VLOOKUP and HLOOKUP.\n\nMATCH(lookup_value, lookup_array, match_type)\n\n• Match_type=1 returns the largest match less than or equal to lookup value if lookup array is sorted ascending. This is the default\n• Match_type=0 requests an exact match\n• Match_type=-1 returns the smallest match greater than or equal to lookup value if lookup array is sorted descending\n\nVLOOKUP(lookup_value, table_array, colnum, range_lookup)\n\n• Range_lookup=TRUE returns the largest match less than or equal to lookup value. This is the default option. Table array MUST be sorted ascending.\n• Range_lookup=FALSE requests an exact match. Table array does not need to be sorted.\n Avoid using exact match lookup if possible. If you are doing lookup’s using the exact match option the calculation time for the function is proportional to the number of cells scanned before a match is found. For lookups over large ranges this time can be very significant. Lookup time using the approximate match options of VLOOKUP, HLOOKUP, MATCH on sorted data is fast and not significantly increased by the length of the range you are looking up. (Characteristics are the same as binary search).\n\n#### VLOOKUP & MATCH with multiple matches.\n\nIf the table you are looking up contains more than one row with a value which matches your lookup value, which row gets found?\n\n• If the table is not sorted the first matching row found is returned.\n• If the table is sorted ascending then the last matching row is returned.\n\n#### VLOOKUP versus INDEX and MATCH or OFFSET.\n\n I recommend using INDEX and MATCH. VLOOKUP is slightly faster (approx. 5%), simpler and uses less memory than a combination of MATCH and INDEX or OFFSET. However the additional flexibility offered by MATCH and INDEX often allows you to make significant timesaving compared to VLOOKUP. INDEX is very fast and from Excel 97 onwards is a non-volatile function (speeds up recalculation). OFFSET is also very fast, but it’s a volatile function.\n\n#### Converting VLOOKUP to INDEX and MATCH.\n\nThese statements return the same answer:\n\nVLOOKUP(A1, Data!\\$A\\$2:\\$F\\$1000,3,False)\nINDEX(Data!\\$A\\$2:\\$F\\$1000,MATCH(A1,\\$A\\$1:\\$A\\$1000,0),3)\n\n### Speeding up Lookup’s\n\nBecause exact match lookups are so slow it’s worth looking for ways of speeding things up:\n\n#### Use FastExcel's AVLOOKUP function.\n\nAVLOOKUP is significantly faster than VLOOKUP in many circumstances.\n\n#### Use One Worksheet.\n\n If speed is critical keep Lookups and Data on the same sheet. Keep exact match lookups on the same worksheet as the data they are looking up: It’s significantly faster.\n\n#### Use Excel 2000 or later:\n\n Upgrade to Excel 2000. Excel 2000 is significantly faster than Excel 97 for exact matches. But make sure you have installed the SR1 Service Release which fixes a problem with Lookups into closed workbooks (see MSKB Q248173).\n\n#### SORT the Data Whenever Possible.\n\n SORT your data and use approximate Match. Whenever possible SORT the data first, (SORT is very fast) and use approximate match.\n\n#### Minimise the Range of Cells you are Looking Up.\n\n The smaller the Range the better. When doing exact match lookups restrict the range of cells to be scanned to a minimum. Use Dynamic Range Names rather than referring to a very large number of rows or columns. Sometimes you can pre-calculate a lower and upper range limit for the lookup.\n\n#### Sorted Data with Missing Values.\n\n Two approximate Lookups are usually faster than one exact Lookup. If you can sort your data but still cannot use approximate match because you can’t be sure that the value you are looking up exists in the lookup range, then try this: IF(lookup_val=Index(lookup_array,MATCH(lookup_val,lookup_list),1) ,Index(lookup_array,MATCH(lookup_val,lookup_array), colnum),“notexist”) This does an approximate lookup on the lookup list, and if the lookup value = the answer in the lookup column you have found an exact match, so redo the approximate lookup on the column you want, otherwise it’s a missing value. Note that this assumes you never lookup a value smaller than the smallest value in the list, so you may need to add a dummy very small entry into the list. Two approximate matches are significantly faster than one exact match for a lookup over a large number of rows (breakeven point is about 10-20 rows). FastExcel’s AVLOOKUP function allows you to handle the missing value problem very efficiently.\n\n#### Unsorted Data with Missing Values.\n\n Store the result of an exact MATCH and reuse it. If you have to use exact match lookup on unsorted data and you can’t be sure that the lookup value exists you often have to handle the #N/A that gets returned if no match is found. The simplest and slowest way is to use an IF function containing two lookups: IF(ISNA(VLOOKUP(lookupval,table,2,FALSE)),0, VLOOKUP(lookupval,table,2,FALSE)) You can avoid the double exact lookup if you use exact MATCH once, store the result in a cell, and then test the result before doing an INDEX: In A1 =MATCH(lookupvalue,lookuparray,0) In B1=IF(ISNA(A1),0,INDEX(table,A1,colnum)) If you cannot use two cells then use COUNTIF, on average it is faster than an exact match lookup: IF (COUNTIF(lookuparray,lookupvalue)=0, 0, VLOOKUP(lookupval, table, 2 FALSE)) FastExcel’s AVLOOKUP function allows you to handle the missing value problem very efficiently\n\n#### Exact Match Lookups returning values from Multiple Columns.\n\n You can often reuse a stored exact MATCH many times. If you are doing exact lookups on multiple columns you can save a lot of time using one MATCH and many INDEX statements rather than many VLOOKUPs. Add an extra column for the MATCH to store the result (stored_row). For each column use: INDEX(Lookup_Range,stored_row,column_number) Alternatively you can use VLOOKUP in an array formula: this example returns the value from the 2nd and 4th column in the lookup range. {VLOOKUP(lookupvalue,Lookup_Range,{4,2},FALSE)}\n\n#### Looking Up a Set of Contiguous Rows or Columns.\n\n Y ou can also return many cells from one Lookup operation. If you want to lookup a number of contiguous columns then you can use INDEX in an array formula to return multiple columns at once (use 0 as the column number). You can also use INDEX to return multiple rows at once. {INDEX(\\$A\\$1:\\$J\\$1000,stored_row,0)} This returns columns A to J in the stored row created by a previous MATCH\n\n#### Looking Up a Rectangular Block of Cells.\n\nYou can use MATCH and OFFSET to return a rectangular block of cells as a range.\n\n#### Two-Dimensional Lookup\n\n Multi-dimensional lookup can also be done efficiently. Two-dimensional table lookup using separate lookup's on the rows and columns of a table can be efficiently done using an INDEX with two embedded MATCH functions. This example assumes a table in A1:Z1000 with column A containing the row identifier and row 1 containing the column identifier. Both the row and column identifiers are sorted ascending. INDEX(\\$B\\$2:\\$Z\\$1000,MATCH(RowLookup_Value,\\$A\\$2:\\$A\\$1000),MATCH(colLookup_value,\\$B\\$1:\\$Z\\$1))\n\n#### Multiple-Index Lookup\n\nIn large spreadsheets you often need to lookup using multiple indexes, such as looking up product volumes in a country.\n\nThe simple way to do this is to concatenate the indexes and lookup using concatenated lookup values. This is inefficient when the data is sorted for two reasons:\n\n• Concatenating strings is a calculation-intensive operation.\n• The lookup will cover a large range.\n\nIt is often more efficient to calculate a subset range for the lookup: for example by using COUNTIF to count the number of rows for each country and then calculating the first and last row for each country from the counts, and then looking up the product within that range. See SUMIF Example or the FastExcel sample problem for an example of using this technique.\n\nThe FastExcel Version 2 AVLOOKUP function has built-in methods to easily and efficiently handle multiple-index lookup.\n\n#### Three-dimensional lookup.\n\nIf you need to lookup the table to use as well as the row and the column here are some techniques you can use, focussing on how to make Excel lookup/choose the table.\n\nIf each table you want to lookup (the third dimension) is stored as a set of range names, or as a table of text strings that represent ranges, then you may be able to use INDIRECT or CHOOSE.\nUsing CHOOSE and range names can be a very efficient method, and it is not volatile, but it is best suited to only a small number of tables:\n\nINDEX(CHOOSE(TableLookup_Value,TableName1,TableName2,TableName3,TableName4),MATCH(RowLookup_Value,\\$A\\$2:\\$A\\$1000),MATCH(colLookup_value,\\$B\\$1:\\$Z\\$1))\n\nThe example above dynamically uses TableLookup_Value to choose which range name (TableName1, TableName2, ...) to use for the lookup table.\n\nINDEX(INDIRECT(\"Sheet\" & TableLookup_Value & \"!\\$B\\$2:\\$Z\\$1000\"),MATCH(RowLookup_Value,\\$A\\$2:\\$A\\$1000),MATCH(colLookup_value,\\$B\\$1:\\$Z\\$1))\n\nThis example uses INDIRECT and TableLookup_Value to dynamically create the sheet name to use for the lookup table. This method has the advantage of being simple and can handle a large number of tables, but because INDIRECT is a volatile function the lookup will be calculated at every calculation even if none of the data has changed.\nYou could also use VLOOKUP to find the name of the sheet or the text string to use for the table, and then use INDIRECT to convert the resulting text into a range:\n\nINDEX(INDIRECT(VLOOKUP(TableLookup_Value,TableOfTAbles,1)),MATCH(RowLookup_Value,\\$A\\$2:\\$A\\$1000),MATCH(colLookup_value,\\$B\\$1:\\$Z\\$1))\n\nAnother technique is to aggregate all your tables into one giant table, but with an additional column which identifies the individual tables. You can then use the techniques for multiple-index lookup above.\n\n#### Wildcard Lookup\n\nAVLOOKUP, AMATCH, MATCH,VLOOKUP and HLOOKUP allow you to use the wildcard characters ? (Any single character) and * (no character or any number of characters) on alphabetic exact matches. Sometimes this can avoid multiple matches.", null, "© 2001-2020 Decision Models Legal Disclaimer Privacy Statement", null, "" ]	[ null, "https://www.decisionmodels.com/spacer.gif", null, "https://www.decisionmodels.com/spacer.gif", null, "https://www.decisionmodels.com/spacer.gif", null, "https://www.decisionmodels.com/spacer.gif", null, "https://www.decisionmodels.com/spacer.gif", null, "https://www.decisionmodels.com/spacer.gif", null, "https://www.decisionmodels.com/spacer.gif", null, "https://www.decisionmodels.com/spacer.gif", null, "https://www.decisionmodels.com/spacer.gif", null, "https://www.decisionmodels.com/NavBar-2_r1_c1.gif", null, "https://www.decisionmodels.com/spacer.gif", null, "https://www.decisionmodels.com/NavBar-2_r2_c1.gif", null, "https://www.decisionmodels.com/NavBar-2_r2_c2.gif", null, "https://www.decisionmodels.com/NavBar-2_r2_c7.gif", null, "https://www.decisionmodels.com/spacer.gif", null, "https://www.decisionmodels.com/NavBar-2_r3_c2.gif", null, "https://www.decisionmodels.com/spacer.gif", null, "https://www.decisionmodels.com/NavBar-2_r4_c2.gif", null, "https://www.decisionmodels.com/NavBar-2_r4_c6.gif", null, "https://www.decisionmodels.com/spacer.gif", null, "https://www.decisionmodels.com/NavBar-2_r5_c2.gif", null, "https://www.decisionmodels.com/spacer.gif", null, "https://www.decisionmodels.com/NavBar-2_r6_c2.gif", null, "https://www.decisionmodels.com/NavBar-2Y_r6_c3.gif", null, "https://www.decisionmodels.com/NavBar-2_r6_c5.gif", null, "https://www.decisionmodels.com/spacer.gif", null, "https://www.decisionmodels.com/NavBar-2_r7_c3.gif", null, "https://www.decisionmodels.com/spacer.gif", null, "https://www.decisionmodels.com/NavBar-2_r8_c3.gif", null, "https://www.decisionmodels.com/NavBar-2_r8_c4.gif", null, "https://www.decisionmodels.com/spacer.gif", null, "https://www.decisionmodels.com/NavBar-2_r9_c3.gif", null, "https://www.decisionmodels.com/spacer.gif", null, "https://www.decisionmodels.com/NavBar-2_r10_c3.gif", null, "https://www.decisionmodels.com/spacer.gif", null, "https://www.decisionmodels.com/NavBar-2_r11_c3.gif", null, "https://www.decisionmodels.com/spacer.gif", null, "https://www.decisionmodels.com/NavBar-2_r12_c1.gif", null, "https://www.decisionmodels.com/NavBar-2_r12_c8.gif", null, "https://www.decisionmodels.com/spacer.gif", null, "https://www.decisionmodels.com/NavBar-2_r13_c1.gif", null, "https://www.decisionmodels.com/spacer.gif", null, "https://www.decisionmodels.com/Titlebar-1.gif", null, "https://www.decisionmodels.com/shimmy.gif", null, "https://www.decisionmodels.com/shimmy.gif", null, "https://www.decisionmodels.com/shimmy.gif", null, "https://www.decisionmodels.com/shimmy.gif", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7763304,"math_prob":0.91883534,"size":10153,"snap":"2022-05-2022-21","text_gpt3_token_len":2414,"char_repetition_ratio":0.14149177,"word_repetition_ratio":0.03474416,"special_character_ratio":0.21757115,"punctuation_ratio":0.11375388,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9940254,"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],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3,null,null,null,3,null,3,null,3,null,null,null,3,null,null,null,3,null,3,null,null,null,3,null,null,null,3,null,3,null,3,null,null,null,3,null,null,null,3,null,3,null,null,null,3,null,null,null,3,null,null,null,3,null,null,null,3,null,3,null,null,null,3,null,null,null,3,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-19T09:17:24Z\",\"WARC-Record-ID\":\"<urn:uuid:4a6ce21e-015b-464e-8bbd-02ce2bd13546>\",\"Content-Length\":\"38265\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:085f3fb6-cc3c-4190-867a-adb63b761933>\",\"WARC-Concurrent-To\":\"<urn:uuid:90a38e69-09c2-42cf-9c15-23a3371ee673>\",\"WARC-IP-Address\":\"81.27.105.73\",\"WARC-Target-URI\":\"https://www.decisionmodels.com/optspeede.htm\",\"WARC-Payload-Digest\":\"sha1:D73FF2VZY2YYNBUASHLNLXVJAY3QKB33\",\"WARC-Block-Digest\":\"sha1:IAAHY335Y7NFP5W6SCUHW62QVNM4LMEH\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662526009.35_warc_CC-MAIN-20220519074217-20220519104217-00789.warc.gz\"}"}
https://engineering.calendar.utoronto.ca/course/rob313h1	[ "# ROB313H1: Introduction to Learning from Data\n\n0.50\n38.4L/25.6T\n\nThis course will introduce students to the topic of machine learning, which is key to the design of intelligent systems and gaining actionable insights from datasets that arise in computational science and engineering. The course will cover the theoretical foundations of this topic as well as computational aspects of algorithms for unsupervised and supervised learning. The topics to be covered include: The learning problem, clustering and k-means, principal component analysis, linear regression and classification, generalized linear models, bias-variance tradeoff, regularization methods, maximum likelihood estimation, kernel methods, the representer theorem, radial basis functions, support vector machines for regression and classification, an introduction to the theory of generalization, feedforward neural networks, stochastic gradient descent, ensemble learning, model selection and validation.\n\n47.2 (Fall), 51.2 (Winter), 98.4 (Full Year)" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8942669,"math_prob":0.8132627,"size":969,"snap":"2022-40-2023-06","text_gpt3_token_len":184,"char_repetition_ratio":0.10673575,"word_repetition_ratio":0.0,"special_character_ratio":0.18782249,"punctuation_ratio":0.17575757,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95777124,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-02-05T04:40:52Z\",\"WARC-Record-ID\":\"<urn:uuid:a6468a45-ed16-4013-b3ef-1c52465a2aa4>\",\"Content-Length\":\"30623\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:579120c9-f2a7-4243-8804-9bcc750ff7dc>\",\"WARC-Concurrent-To\":\"<urn:uuid:803d189d-67e5-4467-9642-5e81c808a49e>\",\"WARC-IP-Address\":\"23.185.0.2\",\"WARC-Target-URI\":\"https://engineering.calendar.utoronto.ca/course/rob313h1\",\"WARC-Payload-Digest\":\"sha1:HZFVJ5ZPQZYNASCHNO3NHKXIARLAXFR3\",\"WARC-Block-Digest\":\"sha1:QLXCNVKZKXLXWGDJ2D4UKQX3WWIN23Q6\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-06/CC-MAIN-2023-06_segments_1674764500215.91_warc_CC-MAIN-20230205032040-20230205062040-00105.warc.gz\"}"}
https://www.jobilize.com/online/course/3-2-independent-and-mutually-exclusive-events-by-openstax?qcr=www.quizover.com	[ "# 3.2 Independent and mutually exclusive events\n\n Page 1 / 4\nProbability: Independent and Mutually Exclusive Events is part of the collection col10555 written by Barbara Illowsky and Susan Dean and explains the concept of independent events, where the probability of event A does not have any effect on the probability of event B, and mutually exclusive events, where events A and B cannot occur at the same time. The module has contributions from Roberta Bloom.\n\nIndependent and mutually exclusive do not mean the same thing.\n\n## Independent events\n\nTwo events are independent if the following are true:\n\n• $\\mathrm{P\\left(A\|B\\right) = P\\left(A\\right)}$\n• $\\mathrm{P\\left(B\|A\\right) = P\\left(B\\right)}$\n\nTwo events $A$ and $B$ are independent if the knowledge that one occurred does not affect the chance the other occurs. For example, the outcomes of two roles of a fair die are independent events. The outcome of the first roll does not change the probability for the outcome of the secondroll. To show two events are independent, you must show only one of the above conditions. If two events are NOT independent, then we say that they are dependent .\n\nSampling may be done with replacement or without replacement .\n\n• With replacement : If each member of a population is replaced after it is picked, then that member has the possibility of being chosen more than once. When sampling is done with replacement, then events are considered to be independent, meaning the result of the first pick will not change the probabilities for the second pick.\n• Without replacement: : When sampling is done without replacement, then each member of a population may be chosen only once. In this case, the probabilities for the second pick are affected by the result of the first pick. The events are considered to be dependent or not independent.\n\nIf it is not known whether $A$ and $B$ are independent or dependent, assume they are dependent until you can show otherwise .\n\n## Mutually exclusive events\n\n$A$ and $B$ are mutually exclusive events if they cannot occur at the same time. This means that $A$ and $B$ do not share any outcomes and $\\text{P(A AND B)}=0$ .\n\nFor example, suppose the sample space $\\mathrm{S = \\left\\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\\right\\}}$ . Let $\\mathrm{A = \\left\\{1, 2, 3, 4, 5\\right\\}, B = \\left\\{4, 5, 6, 7, 8\\right\\}}$ , and $\\mathrm{C = \\left\\{7, 9\\right\\}}$ . $\\text{A AND B}=\\left\\{4,5\\right\\}$ . $\\text{P(A AND B) =}$ $\\frac{2}{10}$ and is not equal to zero. Therefore, $A$ and $B$ are not mutually exclusive. $A$ and $C$ do not have any numbers in common so $\\text{P(A AND C) = 0}$ . Therefore, $A$ and $C$ are mutually exclusive.\n\nIf it is not known whether A and B are mutually exclusive, assume they are not until you can show otherwise .\n\nThe following examples illustrate these definitions and terms.\n\nFlip two fair coins. (This is an experiment.)\n\nThe sample space is $\\mathrm{\\left\\{HH, HT, TH, TT\\right\\}}$ where $T$ = tails and $H$ = heads. The outcomes are $\\mathrm{HH}$ , $\\mathrm{HT}$ , $\\mathrm{TH}$ , and $\\mathrm{TT}$ . The outcomes $\\mathrm{HT}$ and $\\mathrm{TH}$ are different. The $\\mathrm{HT}$ means that the first coin showed heads and the second coin showed tails. The $\\mathrm{TH}$ means that the first coin showed tails and the second coin showed heads.\n\n• Let $A$ = the event of getting at most one tail . (At most one tail means 0 or 1 tail.) Then $A$ can be written as $\\mathrm{\\left\\{HH, HT, TH\\right\\}}$ . The outcome $\\mathrm{HH}$ shows 0 tails. $\\mathrm{HT}$ and $\\mathrm{TH}$ each show 1 tail.\n• Let $B$ = the event of getting all tails. $B$ can be written as $\\mathrm{\\left\\{TT\\right\\}}$ . $B$ is the complement of $A$ . So, $\\mathrm{B = A\\text{'}}$ . Also, $\\mathrm{P\\left(A\\right) + P\\left(B\\right) = P\\left(A\\right) + P\\left(A\\text{'}\\right) = 1}$ .\n• The probabilities for $A$ and for $B$ are $\\mathrm{P\\left(A\\right)}=\\frac{3}{4}$ and $\\mathrm{P\\left(B\\right)}=\\frac{1}{4}$ .\n• Let $C$ = the event of getting all heads. $\\mathrm{C = \\left\\{HH\\right\\}}$ . Since $\\mathrm{B = \\left\\{TT\\right\\}}$ , . $B$ and $C$ are mutually exclusive. ( $B$ and $C$ have no members in common because you cannot have all tails and all heads at the same time.)\n• Let $D$ = event of getting more than one tail. $D=\\mathrm{\\left\\{TT\\right\\}}$ . $\\mathrm{P\\left(D\\right)}=\\frac{1}{4}$ .\n• Let $E$ = event of getting a head on the first roll. (This implies you can get either a head or tail on the second roll.) $E=\\left\\{\\mathrm{HT},\\mathrm{HH}\\right\\}$ . $\\mathrm{P\\left(E\\right)}=\\frac{2}{4}$ .\n• Find the probability of getting at least one (1 or 2) tail in two flips. Let $F$ = event of getting at least one tail in two flips. $F=\\left\\{\\mathrm{HT},\\mathrm{TH},\\mathrm{TT}\\right\\}$ . $\\text{P(F)}=\\frac{3}{4}$\n\nwhere we get a research paper on Nano chemistry....?\nwhat are the products of Nano chemistry?\nThere are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..\nlearn\nEven nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level\nlearn\nda\nno nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts\nBhagvanji\nPreparation and Applications of Nanomaterial for Drug Delivery\nrevolt\nda\nApplication of nanotechnology in medicine\nwhat is variations in raman spectra for nanomaterials\nI only see partial conversation and what's the question here!\nwhat about nanotechnology for water purification\nplease someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.\nDamian\nyes that's correct\nProfessor\nI think\nProfessor\nNasa has use it in the 60's, copper as water purification in the moon travel.\nAlexandre\nnanocopper obvius\nAlexandre\nwhat is the stm\nis there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?\nRafiq\nindustrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong\nDamian\nHow we are making nano material?\nwhat is a peer\nWhat is meant by 'nano scale'?\nWhat is STMs full form?\nLITNING\nscanning tunneling microscope\nSahil\nhow nano science is used for hydrophobicity\nSantosh\nDo u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq\nRafiq\nwhat is differents between GO and RGO?\nMahi\nwhat is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq\nRafiq\nif virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION\nAnam\nanalytical skills graphene is prepared to kill any type viruses .\nAnam\nAny one who tell me about Preparation and application of Nanomaterial for drug Delivery\nHafiz\nwhat is Nano technology ?\nwrite examples of Nano molecule?\nBob\nThe nanotechnology is as new science, to scale nanometric\nbrayan\nnanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale\nDamian\nIs there any normative that regulates the use of silver nanoparticles?\nwhat king of growth are you checking .?\nRenato\nWhat fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?\nwhy we need to study biomolecules, molecular biology in nanotechnology?\n?\nKyle\nyes I'm doing my masters in nanotechnology, we are being studying all these domains as well..\nwhy?\nwhat school?\nKyle\nbiomolecules are e building blocks of every organics and inorganic materials.\nJoe\nhow did you get the value of 2000N.What calculations are needed to arrive at it\nPrivacy Information Security Software Version 1.1a\nGood\n1 It is estimated that 30% of all drivers have some kind of medical aid in South Africa. What is the probability that in a sample of 10 drivers: 3.1.1 Exactly 4 will have a medical aid. (8) 3.1.2 At least 2 will have a medical aid. (8) 3.1.3 More than 9 will have a medical aid.", null, "By Nicole Duquette", null, "By Jessica Collett", null, "By Caitlyn Gobble", null, "By OpenStax", null, "By Madison Christian", null, "By OpenStax", null, "By Sandhills MLT", null, "By OpenStax", null, "By OpenStax", null, "By Stephen Voron" ]	[ null, "https://farm1.staticflickr.com/288/18860755658_8f1c6343ec_t.jpg", null, "https://www.jobilize.com/quiz/thumb/understanding-societies-exam-1-by-dr-jessica-collett-notre-dame.png;jsessionid=gcXfzy0qNJ6ofVuL0mjvi1q8xYPFRwcBLPeEsL2M.web001", null, "https://farm9.staticflickr.com/8602/15982618451_48770f8a99_t.jpg", null, "https://www.jobilize.com/quiz/thumb/biology-ch-01-the-study-of-life-mcq-quiz-openstax-college.png;jsessionid=gcXfzy0qNJ6ofVuL0mjvi1q8xYPFRwcBLPeEsL2M.web001", null, "https://farm9.staticflickr.com/8640/16656923381_6bf805ffed_t.jpg", null, "https://www.jobilize.com/quiz/thumb/human-body-anatomy-physiology-essay-quiz.png;jsessionid=gcXfzy0qNJ6ofVuL0mjvi1q8xYPFRwcBLPeEsL2M.web001", null, "https://www.jobilize.com/quiz/thumb/microbiology-practice-test-by-sandhills-mlt.png;jsessionid=gcXfzy0qNJ6ofVuL0mjvi1q8xYPFRwcBLPeEsL2M.web001", null, "https://www.jobilize.com/quiz/thumb/microeconomics-01-what-is-economics-ch-01-flashcards-by-openstax.png;jsessionid=gcXfzy0qNJ6ofVuL0mjvi1q8xYPFRwcBLPeEsL2M.web001", null, "https://www.jobilize.com/quiz/thumb/human-body-anatomy-physiology-mcq-quiz.png;jsessionid=gcXfzy0qNJ6ofVuL0mjvi1q8xYPFRwcBLPeEsL2M.web001", null, "https://www.jobilize.com/quiz/thumb/ch-01-the-cranial-nerves-and-the-circle-of-willis-quiz-by-university.png;jsessionid=gcXfzy0qNJ6ofVuL0mjvi1q8xYPFRwcBLPeEsL2M.web001", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9455932,"math_prob":0.9929375,"size":1744,"snap":"2020-34-2020-40","text_gpt3_token_len":357,"char_repetition_ratio":0.14942528,"word_repetition_ratio":0.06984127,"special_character_ratio":0.22133027,"punctuation_ratio":0.12232416,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99644613,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],"im_url_duplicate_count":[null,null,null,1,null,null,null,1,null,null,null,1,null,1,null,1,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-18T21:20:12Z\",\"WARC-Record-ID\":\"<urn:uuid:0e0d7445-3dbc-4fb8-903a-e51b59b5f554>\",\"Content-Length\":\"122726\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c1e10fb8-f88e-49ee-aaea-d4a4be7377c0>\",\"WARC-Concurrent-To\":\"<urn:uuid:6d779b0a-2c6f-4ddc-b061-6bd825bd5bb7>\",\"WARC-IP-Address\":\"207.38.87.179\",\"WARC-Target-URI\":\"https://www.jobilize.com/online/course/3-2-independent-and-mutually-exclusive-events-by-openstax?qcr=www.quizover.com\",\"WARC-Payload-Digest\":\"sha1:5RKHZUNARLGSOMKAY6XXKSEKWN3I5CML\",\"WARC-Block-Digest\":\"sha1:4EFXJOW7I7JOOKDG5SEKQ77WQYSVKN3G\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600400188841.7_warc_CC-MAIN-20200918190514-20200918220514-00551.warc.gz\"}"}
https://www.flyingcoloursmaths.co.uk/blog/page/21/	[ "# The Flying Colours Maths Blog: Latest posts\n\n## The Dictionary of Mathematical Eponymy: Ackermann’s function\n\nFor 2019, I'm trying an experiment: every couple of weeks, writing a post about a mathematical object that a) I don't know much about and b) is named after somebody. These posts are a trial run - let me know how you find them! The chief use of the Ackermann\n\n## Ask Uncle Colin: A Strange Simultaneous Equation\n\nDear Uncle Colin, I have the simultaneous equations $3x^2 - 3y = 0$ and $3y^2 - 3x = 0$. I've worked out that $x^2 = y$ and $y^2 = x$, but then I'm stuck! - My Expertise Relatedto1 Simultaneous Equations? Not Nearly Enough! Hi, MERSENNE, and thanks for your message!\n\n## Sticks and Stones\n\nBecause I'm insufferably vain, I have a search running in my Twitter client for the words \"The Maths Behind\", in case someone mentions my book (which is, of course, available wherever good books are sold). On the minus side, it rarely is; on the plus side, the search occasionally throws\n\n## Ask Uncle Colin: A Factorial Sum\n\nDear Uncle Colin, I have been given the series $\\frac{1}{2} + \\frac{1}{3} + \\frac{1}{8} + \\frac{1}{30} + \\frac{1}{144} + ...$, which appears to have a general term of $\\frac{1}{k! + (k+1)!}$ - but I can't see how to sum that! Any ideas? - Series Underpin Maths! Hi, SUM, and thanks\n\n## A Christmas Decagon\n\nSince it's Christmas (more or less), let's treat ourselves to a colourful @solvemymaths puzzle: Have a go, if you'd like to! Below the line will be spoilers. Consistency The first and most obvious thing to ask is, is Ed's claim reasonable? At a glance, yes, it makes sense: there's a\n\n## Ask Uncle Colin: Some Ugly Trigonometry\n\nDear Uncle Colin, How do I verify the identity $\\frac{\\cos(\\theta)}{1 - \\sin(\\theta)} \\equiv \\tan(\\theta) + \\sec(\\theta)$ for $\\cos(\\theta) \\ne 0$? - Struggles Expressing Cosines As Nice Tangents Hi, SECANT, and thanks for your message! The key questions for just about any trigonometry proof are \"what's ugly?\" and \"how can I\n\n## Review: Festival of the Spoken Nerd, You Can’t Polish A Nerd\n\nMidway through the second half of You Can’t Polish A Nerd, Steve Mould neatly encapsulates the show in one line: “It creates images on your oscilloscope. It’s so cool!” Because of course you have an oscilloscope. And of course you would use it - or failing that, a balloon and\n\n## Ask Uncle Colin: A factorising trick\n\nDear Uncle Colin, How would you factorise $63x^2 + 32x - 63$? I tried the method where you multiply $a$ and $c$ (it gives you -3969) - but I'm not sure how to find factors of that that sum to 32! Factors Are Troublesomely Oversized, Urgh Hi, FATOU, and thanks\n\n## Wrong, But Useful: Episode 62\n\nIn this month’s episode of Wrong, But Useful, we’re joined by @ch_nira, who is Dr Nira Chamberlain in real life - and the World’s Most Interesting Mathematician. Nira is a professional mathematical modeller, president-designate of the IMA, and a visiting fellow at Loughborough university. We discuss Nira’s entry in the\n\n## Bone Marrow Odds\n\nI don't remember doing it - although I'd meant to for some time - but apparently I signed up for the British Bone Marrow Registry. (If you're between 17 and 40, you can sign up the next time you give blood; the more people on the register, the more likely" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.91723037,"math_prob":0.82537293,"size":2930,"snap":"2020-34-2020-40","text_gpt3_token_len":806,"char_repetition_ratio":0.101845525,"word_repetition_ratio":0.023210831,"special_character_ratio":0.27576792,"punctuation_ratio":0.122073576,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9563573,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-27T13:34:47Z\",\"WARC-Record-ID\":\"<urn:uuid:8789beba-4ffc-4f2a-b45c-14ee039728e5>\",\"Content-Length\":\"60161\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7113dc80-e714-4089-a57c-95afd4b0d4df>\",\"WARC-Concurrent-To\":\"<urn:uuid:93f1db6f-391e-4eb1-a66d-ae215f513080>\",\"WARC-IP-Address\":\"185.20.49.4\",\"WARC-Target-URI\":\"https://www.flyingcoloursmaths.co.uk/blog/page/21/\",\"WARC-Payload-Digest\":\"sha1:ITPFXLGSOQ62FYBR5NH34YLVXWY43WCG\",\"WARC-Block-Digest\":\"sha1:T5XOF4ZSNHD4636QT2YZCYMNZTRFN3UQ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600400279782.77_warc_CC-MAIN-20200927121105-20200927151105-00786.warc.gz\"}"}
https://answers.everydaycalculation.com/percent-is/20-120	[ "Solutions by everydaycalculation.com\n\n## 20 is what percent of 120?\n\n20 of 120 is 16.67%\n\n#### Steps to solve \"what percent is 20 of 120?\"\n\n1. 20 of 120 can be written as:\n20/120\n2. To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100\n\n20/120 × 100/100\n3. = (20 × 100/120) × 1/100 = 16.67/100\n4. Therefore, the answer is 16.67%\n\nIf you are using a calculator, simply enter 20÷120×100 which will give you 16.67 as the answer.\n\nMathStep (Works offline)", null, "Download our mobile app and learn how to work with percentages in your own time:" ]	[ null, "https://answers.everydaycalculation.com/mathstep-app-icon.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.86593837,"math_prob":0.9708145,"size":461,"snap":"2022-27-2022-33","text_gpt3_token_len":139,"char_repetition_ratio":0.18161926,"word_repetition_ratio":0.0,"special_character_ratio":0.37744033,"punctuation_ratio":0.08080808,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99291164,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-08-11T17:35:52Z\",\"WARC-Record-ID\":\"<urn:uuid:9ae2bc74-a903-49ae-b9aa-f21930e5a4e4>\",\"Content-Length\":\"6388\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1b73a1b4-da59-421a-99a5-149a2a7208de>\",\"WARC-Concurrent-To\":\"<urn:uuid:8e7e6065-1628-45f3-95f9-95ad2d55c29c>\",\"WARC-IP-Address\":\"96.126.107.130\",\"WARC-Target-URI\":\"https://answers.everydaycalculation.com/percent-is/20-120\",\"WARC-Payload-Digest\":\"sha1:I7L5O2MIPVYESWJCPIBB6OCNUDWHXFET\",\"WARC-Block-Digest\":\"sha1:AZL4DU5L444H4XUPFWS6ZAQOJPUT7U3P\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-33/CC-MAIN-2022-33_segments_1659882571483.70_warc_CC-MAIN-20220811164257-20220811194257-00032.warc.gz\"}"}
http://slideflix.net/doc/1895416/inverse-function-theorems	[ "", null, "# Inverse function theorems\n\nby user\n\non\n1\n\nviews\n\nReport\n\n#### Transcript\n\nInverse function theorems\n```(November 20, 2014)\nInverse function theorems\nPaul Garrett [email protected]\nhttp://www.math.umn.edu/egarrett/\n[This document is\nhttp://www.math.umn.edu/˜garrett/m/complex/notes 2014-15/05c inverse function.pdf]\n1.\n2.\n3.\n4.\nFixed-point lemma\nSmooth inverse function theorem\nHolomorphic inverse function theorem\nPerturbations f (z) + h · g(z)\n1. Fixed-point lemma\n[1.0.1] Lemma: Let X be a complete metric space with distance function d. Let f : X → X be a continuous\nmap uniformly contractive in the sense that there is 0 < c < 1 so that d(f x, f y) ≤ c · d(x, y) for all x, y ∈ X.\nThen f has a unique fixed point: there is a unique x ∈ X with f (x) = x. Further, limn→∞ f n y = x for any\ny ∈ X.\nProof: First, for any y ∈ X, by repeated application of the triangle inequality,\nd(y, f n (y)) ≤ d(y, f (y)) + d(f (y), f 2 (y)) + d(f 2 (y), f 3 (y)) . . . + d(f n−1 (y), f n (y))\n≤ (1 + c + c2 + . . . + cn−1 ) · d(y, f (y)) <\nd(y, f (y))\n1−c\nNext, claim that for any y ∈ X the sequence y, f (y), f 2 (y), . . . is Cauchy. Indeed, for no ≤ m ≤ n, using the\nprevious inequality,\nd(f m (y), f n (y)) ≤ cno · d(f m−no (y), f n−no (y)) ≤ cno · cm−no · d(y, f n−m (y)) ≤ cno ·\nd(y, f (y))\n1−c\nThis goes to 0 as no → +∞, so the sequence is Cauchy.\nSimilarly, for any y, z in X, with m ≤ n\nd(z, f (z)) d(f m (y), f n (z)) ≤ cm · d(y, f n−m (z)) ≤ cm · d(y, z) + d(z, f n−m (z)) ≤ cm · d(y, z) +\n1−c\nwhich goes to 0 as m → +∞. The limit is the same for y unchanged but z arbitrary. Thus, z, f (z), f 2 (z), . . .\nhas limit x for all z ∈ X. Further, taking z = x, f n (x) → x. Given ε > 0, take no large enough so that\nd(f n (x), x) < ε for n ≥ no . For n ≥ no ,\nd(f (x), x) ≤ d(f (x), f n+1 (x)) + d(f n+1 (x), x) < c · d(x, f n (x)) + ε < (c + 1) · ε\nThis holds for all ε > 0, so f (x) = x.\n///\n1\nPaul Garrett: Inverse function theorems (November 20, 2014)\n2. Smooth inverse function theorem\nThe derivative γ 0 of a smooth function γ : [a, b] → U ⊂ Rn is the usual\nγ 0 (t) = lim\nh→0\nγ(t + h) − γ(t)\nh\nFor this section, the derivative f 0 of an Rn -valued function on an open U ⊂ Rn is the n-by-n-matrix-valued\nfunction so that for every smooth path γ : [a, b] → U\n(f ◦ γ)0 (t) = f 0 (γ(t)) · γ 0 (t)\n(matrix multiplication)\nEquivalently, for small real h, xo ∈ U , and v ∈ Rn , as h → 0, using Landau’s little-oh notation, \nf (xo + h · v) = f (x) + h · f 0 (xo ) · v + o(h)\n(matrix multiplication)\n[2.0.1] Theorem: Let U be an open subset of Rn and f : U → Rn a continuously differentiable function.\nFor x0 ∈ U such that f 0 (x0 ) : Rn → Rn is a linear isomorphism, there is a neighborhood V ⊂ U of x0 so\nthat f \|V has a continuously differentiable inverse on f (V ).\nProof: Let x → \|x\| be the usual norm on Rn , and \|T \| the operator norm on n-by-n real matrices. Without\nloss of generality, xo = 0, f (xo ) = 0, and f 0 (xo ) = f 0 (0) = 1n . Let F (x) = x − f (x), so that F 0 (0) = 0. By\ncontinuity, there is δ > 0 so that \|F 0 (x)\| < 12 for \|x\| < δ.\nWith g(t) = F (tx) for t ∈ [0, 1], the Mean Value Theorem in one variable gives\nF (x) = g(1) = g(0) + g 0 (t)(1 − 0) = F (0) + F 0 (tx)(x) = F 0 (tx)(x)\n(for some 0 ≤ t ≤ 1)\nso\nδ\n2\nThus, F maps the closed ball Bδ of radius δ to the closed ball Bδ/2 .\n\|F (x)\| ≤ \|F 0 (tx)\| · \|x\| ≤\n1\n2\n· \|x\| ≤\n(for \|x\| < δ)\nWe claim that f (Bδ ) ⊃ Bδ/2 , and that f is injective on f −1 (Bδ/2 . To this end, take y ∈ Bδ/2 , and\nlet Φy (x) = y + F (x) = y + x − f (x). For \|y\| ≤ δ/2 and \|x\| ≤ δ, \|Φy (x)\| ≤ δ, so Φy is a continuous\nmap of the complete metric space Bδ to itself. A similar estimate shows that Φy is contractive: letting\ng(t) = F ((1 − t)x1 + tx2 ),\n\|Φy (x2 ) − Φy (x1 )\| = \|F (x2 ) − F (x1 )\| = \|g(1) − g(0)\| = \|g 0 (t)\| · \|1 − 0\|\n= \|F 0 ((1 − t)x1 + tx2 )\| · \|x2 − x1 \| ≤\n1\n2\n· \|x1 − x2 \|\n(for given x1 , x2 ∈ Bδ , for some 0 ≤ t ≤ 1)\nBy the fixed-point lemma, Φy has a unique fixed point xo , that is,\nxo = Φy (xo ) = y + xo − f (xo )\nso xo is the unique solution in Bδ to the equation f (xo ) = y. This proves f (Bδ ) ⊃ Bδ/2 as well as the\ninjectivity on f −1 (Bδ/2 ).\n When f (x)/g(x) → 0 as x → x , write f (x) = o(g(x)).\no\n The usual operator norm is \|T \| = sup\n\|x\|≤1 \|T x\|.\n2\nPaul Garrett: Inverse function theorems (November 20, 2014)\nTo prove differentiability of the inverse map ϕ = f −1 , take x1 , x2 ∈ Bδ . Continuity of ϕ follows from\n\|x1 − x2 \| ≤ \|f (x1 ) − f (x2 )\| + x1 − f (x1 ) − x2 − f (x2 ) ≤ \|f (x1 ) − f (x2 )\| + \|F (x1 ) − F (x2 )\| ≤ \|f (x1 ) − f (x2 )\| + 21 \|x1 − x2 \|\nby the inequality \|F (x1 ) − F (x2 )\| < 12 \|x1 − x2 \| from above. Subtracting 21 \|x1 − x2 \| from both sides,\n1\n2 \|x1\n− x2 \| ≤ \|f (x1 ) − f (x2 )\|\ngiving continuity of the inverse.\nFor differentiability, let y1 = f (x1 ) and y2 = f (x2 ) with y1 , y2 in the interior of Bδ/2 . Then\nϕ(y1 ) − ϕ(y2 ) − f 0 (x2 )−1 (y1 − y2 ) = x1 − x2 − f 0 (x2 )−1 (f (x1 ) − f (x2 ))\n= x1 − x2 − f 0 (x2 )−1 f 0 (x2 )(x1 − x2 ) + o(x1 − x2 )\n= x1 − x2 − (x1 − x2 ) + o(x1 − x2 ) = o(x1 − x2 )\n(as x1 → x2 )\n(as x1 → x2 )\nBy the already-established continuity, this is o(y1 − y2 ). Thus, the inverse ϕ is differentiable at y2 = f (x2 ),\nand its derivative is ϕ0 (y2 ) = f 0 (x2 )−1 , for \|y\| < δ/2.\n///\n[2.0.2] Remark: An elaboration of this discussion proves higher-order continuous differentiability in the\nreal-variables sense, but we do not need this for application to the holomorphic inverse function theorem\nbelow.\n3. Holomorphic inverse function theorem\n[3.0.1] Theorem: For f holomorphic on a neighborhood U of zo and f 0 (zo ) 6= 0, there is a holomorphic\ninverse function g on a neighborhood of f (zo ), that is, such that (g ◦ f )(z) = z and (f ◦ g)(z) = z.\nProof: The idea is to consider f as a real-differentiable map f : R2 → R2 , obtain a real-differentiable inverse\ng and then observe that complex differentiability of f implies that of g.\nThe complex differentiability of f can be expressed as\nf (zo + hw) = f (xo ) + hf 0 (zo ) · w + o(h)\n(small real h, complex w)\nwhere f 0 (zo ) · w denotes multiplication in C. Separate real and imaginary parts: let f 0 (zo ) = a + bi with\na, b ∈ R, and w = u + iv with u, v ∈ R, giving\nf (zo + hw) = f (xo ) + h(a + bi) · (u + iv) + o(h) = f (xo ) + h (au − bv) + i(av + bu) ) + o(h)\nThe multiplication in C is achieved by matrix multiplication of real and imaginary parts:\nau − bv\na −b\nu\n=\nav + bu\nb\na\nv\nso the real-variable derivative of f at zo is\nRe f 0 (zo ) −Im f 0 (zo )\nIm f 0 (zo )\nRef 0 (zo )\n3\nPaul Garrett: Inverse function theorems (November 20, 2014)\nThe real-variable derivative has determinant \|f 0 (zo )\|2 , so is invertible for f 0 (zo ) 6= 0. Let α = f 0 (zo ). Thus,\nthere exists a real-differentiable inverse g, with real-variable derivative at f (zo ) given by\nRe α\nIm α\n−Im α\nRe α\n−1\n1\n=\n\|α\|2\nReα\n−Im α\nIm α\nRe α\n=\nRe α−1 Im α−1\n−Im α−1 Re α−1\nThat is, with wo = f (zo ),\ng(wo + h(u + iv)) = g(wo ) + h(1 i)\nRe α−1 Im α−1\n−Im α−1 u\n+ o(h) = g(wo ) + hα−1 (u + iv) + o(h)\n−1\nv\nRe α\nThis holds for all real u, v, so g is complex-differentiable at f (zo ), with complex derivative 1/f 0 (zo ).\n///\n4. Perturbations f (z) + h · g(z)\n[4.0.1] Corollary: For f, g holomorphic near zo , with zo a simple zero of f (zo ), for all ε > 0 there is δ > 0\nsuch that f − h · g has a zero zh with \|zo − zh \| < ε, and zh is a holomorphic function of h.\nProof: In the anomalous case that g(zo ) = 0, then zh = zo suffices.\nFor g(zo ) 6= 0, solve f (z) + h · g(z) = 0 for h:\nh =\nand then\nh0 =\nand\nh0 (zo ) =\n−f (z)\ng(z)\n−f 0 (z) f (z) · g 0 (z)\n−\ng(z)\ng(z)2\n−f 0 (zo ) 0 · g 0 (z)\n−f 0 (zo )\n−\n=\n6= 0\n2\ng(zo )\ng(zo )\ng(zo )\nApply the holomorphic inverse function theorem to obtain the holomorphic inverse F (h) = z such that\nF (0) = zo .\n///\n4\n```\nFly UP" ]	[ null, "http://placehold.it/65x65", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7939279,"math_prob":0.9995975,"size":7736,"snap":"2019-13-2019-22","text_gpt3_token_len":3041,"char_repetition_ratio":0.12972064,"word_repetition_ratio":0.07647983,"special_character_ratio":0.43924507,"punctuation_ratio":0.118336886,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99994886,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-03-22T13:19:32Z\",\"WARC-Record-ID\":\"<urn:uuid:2e4bb441-963a-4af7-92b5-0f7792de2b08>\",\"Content-Length\":\"31549\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d30527d0-7f5c-4324-802f-3659676b4c28>\",\"WARC-Concurrent-To\":\"<urn:uuid:062ea984-6d62-4f14-a266-8331a78eb0d0>\",\"WARC-IP-Address\":\"104.18.59.110\",\"WARC-Target-URI\":\"http://slideflix.net/doc/1895416/inverse-function-theorems\",\"WARC-Payload-Digest\":\"sha1:PN4PE6GLRKXICO7HATSBCNRY3VYKZBYB\",\"WARC-Block-Digest\":\"sha1:BTKBV7GYNPOKYSCJLJFTFSD7OBQS4SYF\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-13/CC-MAIN-2019-13_segments_1552912202658.65_warc_CC-MAIN-20190322115048-20190322141048-00532.warc.gz\"}"}
https://cerfacs.fr/coop/coop-cse-test	[ "", null, "One important mission of COOP falls under the broad term Computer Science and Engineering, or CSE. To get a feel for what we do, we ask for candidates to play with a sample of Python code that represents many of the topics that are important to us. Specifically, the task is to edit the code so that:\n\n1. It can be called from an other module\n2. It is “clean”, i.e. follows coding standards\n3. It gains some flexibility and functionality\n\nIf you’ve been asked to perform this task and ended up here, please read the instructions below, and send your results to the person you’ve been in contact with. Note that if you are comfortable with Python, the full test should take less than an hour. If not, tentative ETAs are given for each task.\n\n##### The initial code\n\nWe start from a python script solving the equations of a SIR epidemiological model, found in this blog article.\n\n```import numpy as np\nfrom scipy.integrate import odeint\nimport matplotlib.pyplot as plt\n\n# Total population, N.\nN = 1000\n# Initial number of infected and recovered individuals, I0 and R0.\nI0, R0 = 1, 0\n# Everyone else, S0, is susceptible to infection initially.\nS0 = N - I0 - R0\n# Contact rate, beta, and mean recovery rate, gamma, (in 1/days).\nbeta, gamma = 0.2, 1./10\n# A grid of time points (in days)\nt = np.linspace(0, 160, 160)\n\n# The SIR model differential equations.\ndef deriv(y, t, N, beta, gamma):\nS, I, R = y\ndSdt = -beta * S * I / N\ndIdt = beta * S * I / N - gamma * I\ndRdt = gamma * I\nreturn dSdt, dIdt, dRdt\n\n# Initial conditions vector\ny0 = S0, I0, R0\n# Integrate the SIR equations over the time grid, t.\nret = odeint(deriv, y0, t, args=(N, beta, gamma))\nS, I, R = ret.T\n\n# Plot the data on three separate curves for S(t), I(t) and R(t)\nfig = plt.figure(facecolor='w')\nax.plot(t, S/1000, 'b', alpha=0.5, lw=2, label='Susceptible')\nax.plot(t, I/1000, 'r', alpha=0.5, lw=2, label='Infected')\nax.plot(t, R/1000, 'g', alpha=0.5, lw=2, label='Recovered with immunity')\nax.set_xlabel('Time /days')\nax.set_ylabel('Number (1000s)')\nax.set_ylim(0,1.2)\nax.yaxis.set_tick_params(length=0)\nax.xaxis.set_tick_params(length=0)\nax.grid(b=True, which='major', c='w', lw=2, ls='-')\nlegend = ax.legend()\nlegend.get_frame().set_alpha(0.5)\nfor spine in ('top', 'right', 'bottom', 'left'):\nax.spines[spine].set_visible(False)\nplt.show()\n```\n\nThis outputs the following graph:", null, "##### 1. Make it callable from another module\n\nETA: 10 - 20 min\n\nPaste the code in a file `sir_model.py` and create a caller code `test.py` in the same folder with the following lines:\n\n```from sir_model import sir, epidemic_plot\n\nresult = sir(days=160, population=1000, infected=1, contact_rate=0.2, infection_rate=0.1)\nepidemic_plot(result)\n```\n\nEdit `sir_model.py` to make `test.py` work. Just use the fact that these files are in the same folder, no `\\$PYTHON_PATH` or `setup.py` work needed here.\n\n##### 2. Clean the code\n\nETA: 30 min - 1h\n\nReadability counts for good code mainteance! Please tidy this code up so that it becomes easy for maintainers to read in the future, but keep the exact same functionalities.\n\nWe like to stick to Python standards for code quality, not for each dev to decide what “clean” should look like. The bible of Python style is PEP8, buy you can get some help from Pylint, if you wish. If you don’t know about Pylint, you can check it out online, or start with our blog post on the\n\nETA: 1 - 2 hours\n\nUpgrade the code to add an optional “lockdown mode”, with a choice of lockdown length in days. It should, for example, allow to set a lockdown period of 40 days each time the relative proportion of infected people reaches 5%. During the lockdown, the contact rate is decreased tenfold.\n\nThe API must keep the possibility to NOT include a quarantine mode in the simulation. The result should look like this:", null, "#### And that’s a wrap!\n\nAntoine Dauptain is a research scientist focused on computer science and engineering topics for HPC.\nCorentin Lapeyre is a research scientist focused on AI for physical modeling." ]	[ null, "https://uwaterloo.ca/student-success/sites/ca.student-success/files/styles/wide-body-750px-wide/public/uploads/images/tests-and-exams.jpg", null, "https://cerfacs.fr/coop/images/python_course_one/sir.png", null, "https://cerfacs.fr/coop/images/python_course_one/quarantine.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7881892,"math_prob":0.9093639,"size":3878,"snap":"2021-43-2021-49","text_gpt3_token_len":1088,"char_repetition_ratio":0.079504386,"word_repetition_ratio":0.0061919503,"special_character_ratio":0.2849407,"punctuation_ratio":0.18287037,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9868433,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,2,null,2,null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-21T21:26:18Z\",\"WARC-Record-ID\":\"<urn:uuid:f469d623-61be-47de-8d1b-e982bc2fe270>\",\"Content-Length\":\"27069\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:83d9e103-e89d-45a1-abb4-35361f457f24>\",\"WARC-Concurrent-To\":\"<urn:uuid:e4c4e18b-ac8f-4de0-a074-2a776518592f>\",\"WARC-IP-Address\":\"138.63.8.11\",\"WARC-Target-URI\":\"https://cerfacs.fr/coop/coop-cse-test\",\"WARC-Payload-Digest\":\"sha1:BOSW34I2KZXVKO6W5A7SOSXO4FWBS5GP\",\"WARC-Block-Digest\":\"sha1:A7JXHIAVYUXN7ZKA46X5G62ULXLMDOEQ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323585441.99_warc_CC-MAIN-20211021195527-20211021225527-00152.warc.gz\"}"}
http://ddsog.com/991.html	[ "# 1、模型架构\n\ntransformer的模型架构如下：", null, "## 1.1 seq2seq结构\n\nthis is a lovely dog.", null, "## 1.2 注意力机制", null, "e\n\ni\n\nj\n\n=\n\nf\n\n(\n\ns\n\ni\n\n1\n\n,\n\nh\n\nj\n\n)\n\ne_{ij}=f(s_{i-1}, hj)\n\neij=f(si1,hj)\n\nα\n\ni\n\nj\n\n=\n\ne\n\nx\n\np\n\n(\n\ne\n\ni\n\nj\n\n)\n\n/\n\nk\n\n=\n\n1\n\nT\n\nx\n\ne\n\nx\n\np\n\n(\n\ne\n\ni\n\nk\n\n)\n\n\\alpha_{ij}={exp(e_{ij})}/（{\\sum^{T_x}_{k=1}{exp(e_{ik})}}）\n\nαij=exp(eij)/k=1Txexp(eik)\n\nc\n\ni\n\n=\n\nj\n\n=\n\n1\n\nT\n\nx\n\nα\n\ni\n\nj\n\nh\n\nj\n\nc_i=\\sum^{T_x}_{j=1}{\\alpha_{ij}h_j}\n\nci=j=1Txαijhj\n\nf\n\nf\n\nf表示的是一个前向神经网络。", null, "• self-attention与word2vec\nword2vec是静态的表示一个token的特征，而self-attention则是动态的表示一个token的特征。比如这个苹果真好吃苹果手机真好用这两句中的苹果，在word2vec中都是只有一个相同的向量表示，而在self-attention中则会根据上下文的不同给出不同的向量表示。\n• self-attention与attention\nattention是获取一个句子与另一个句子之间token的权重关系，而self-attention则是获取句子自身token之间的权重关系。\n\n# 2、transformer各部分介绍\n\n• encoder\n• encoder部分的输入\n• layer normalize\n• feed forward\n• scaled dot-product attention\n• decoder\n• decoder部分的输入\n• encoder与decoder的连接\n\n## 2.1 encoder\n\n### 2.1.1 encoder的输入\n\nP\n\nE\n\n(\n\np\n\no\n\ns\n\n,\n\n2\n\ni\n\n)\n\n=\n\ns\n\ni\n\nn\n\n(\n\np\n\no\n\ns\n\n/\n\n1000\n\n0\n\n2\n\ni\n\n/\n\nd\n\nm\n\no\n\nd\n\ne\n\nl\n\n)\n\nPE_{(pos, 2i)}=sin(pos/10000^{2i/d_{model}})\n\nPE(pos,2i)=sin(pos/100002i/dmodel)\n\nP\n\nE\n\n(\n\np\n\no\n\ns\n\n,\n\n2\n\ni\n\n+\n\n1\n\n)\n\n=\n\nc\n\no\n\ns\n\n(\n\np\n\no\n\ns\n\n/\n\n1000\n\n0\n\n2\n\ni\n\n/\n\nd\n\nm\n\no\n\nd\n\ne\n\nl\n\n)\n\nPE_{(pos, 2i+1)}=cos(pos/10000^{2i/d_{model}})\n\nPE(pos,2i+1)=cos(pos/100002i/dmodel)\n\n2\n\ni\n\n2i\n\n2i或者\n\n2\n\ni\n\n+\n\n1\n\n2i+1\n\n2i+1表示在该向量中的位置。", null, "### 2.1.3 layer normalization\n\n• Batch normalization是对每个批次中的多个样本之间的相同位置的特征进行归一化；\n• layer normalization是对同一个样本中的不同特征进行归一化；\n• 对于一些结构化特征场景下，layer normalization看起来不太合理，但是对于nlp场景下layer normalization就比较合理。因为在nlp场景下，对每一个样本的多个token 向量进行layer normalization，实际上就是对token向量进行归一化。\n\n### 2.1.5 scaled dot-product attention\n\nAttention函数的本质可以被描述为一个查询（query）到一系列（键key-值value）对的映射。\n\n• 第一步是将query和每个key进行相似度计算得到权重，常用的相似度函数有点积，拼接，感知机等；\n• 第二步一般是使用一个softmax函数对这些权重进行归一化；\n• 最后将权重和相应的键值value进行加权求和得到最后的attention。\n\nsacled dot-product attention也是按照上述所说的流程进行计算的。首先我们来看一下multi-head attention和scaled dot-product attention的结构。", null, "W\n\nQ\n\n,\n\nW\n\nK\n\n,\n\nW\n\nV\n\nW^Q, W^K, W^V\n\nWQ,WK,WV相乘得到的。\n\nq\n\n1\n\n=\n\nX\n\n1\n\nW\n\nQ\n\nq1 = X_1W^Q\n\nq1=X1WQ\n\nk\n\n1\n\n=\n\nX\n\n1\n\nW\n\nK\n\nk1 = X_1W^K\n\nk1=X1WK\n\nv\n\n1\n\n=\n\nX\n\n1\n\nW\n\nV\n\nv1 = X_1W^V\n\nv1=X1WV\n\nq\n\n2\n\n=\n\nX\n\n2\n\nW\n\nQ\n\nq2 = X_2W^Q\n\nq2=X2WQ\n\nk\n\n2\n\n=\n\nX\n\n2\n\nW\n\nK\n\nk2 = X_2W^K\n\nk2=X2WK\n\nv\n\n2\n\n=\n\nX\n\n2\n\nW\n\nV\n\nv2 = X_2W^V\n\nv2=X2WV\n\nW\n\nQ\n\n,\n\nW\n\nK\n\n,\n\nW\n\nV\n\nW^Q, W^K, W^V\n\nWQ,WK,WV都是需要进行训练得到的。", null, "d\n\nk\n\n\\sqrt{d_k}\n\ndk\n\nd\n\nk\n\nd_k\n\ndk表示词向量的维度，之所以除以这个数的作用是避免将softmax函数push到梯度很小的区域，具体可以参考《transformer中的attention为什么scaled?》），然后进行softmax，得到softmax向量之后再与各value相乘求和，得到Thinking的进行scaled dot-product attention之后的向量。Machine的计算也是类似。", null, "", null, "", null, "A\n\nt\n\nt\n\ne\n\nn\n\nt\n\ni\n\no\n\nn\n\n(\n\nQ\n\n,\n\nK\n\n,\n\nV\n\n)\n\n=\n\ns\n\no\n\nf\n\nt\n\nm\n\na\n\nx\n\n(\n\nQ\n\nK\n\nT\n\nd\n\nk\n\n)\n\nV\n\nAttention(Q, K, V) = softmax(\\frac{QK^T}{\\sqrt{d_k}})V\n\nAttention(Q,K,V)=softmax(dk\nQKT\n)V\n\n## 2.2 decoder\n\n### 2.2.3 encoder与decoder的连接", null, "### 2.2.4 decoder的输出\n\nTHE END", null, "", null, "" ]	[ null, "https://img-blog.csdnimg.cn/20201111215549581.png#pic_center", null, "https://img-blog.csdnimg.cn/20201111215817888.png#pic_center", null, "https://img-blog.csdnimg.cn/20201111220244810.png#pic_center", null, "https://img-blog.csdnimg.cn/20201111222953201.png#pic_center", null, "https://img-blog.csdnimg.cn/2020111300391080.png#pic_center", null, 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https://artofproblemsolving.com/wiki/index.php?title=2006_UNCO_Math_Contest_II_Problems/Problem_5&diff=prev&oldid=81835	[ "# Difference between revisions of \"2006 UNCO Math Contest II Problems/Problem 5\"\n\n## Problem\n\nIn the figure", null, "$BD$ is parallel to", null, "$AE$ and also", null, "$BF$ is parallel to", null, "$DE$. The area of the larger triangle", null, "$ACE$ is", null, "$128$. The area of the trapezoid", null, "$BDEA$ is", null, "$78$. Determine the area of triangle", null, "$ABF$.", null, "$[asy] draw((0,0)--(1,2)--(4,0)--cycle,black); draw((1/2,1)--(2.5,1)--(2,0),black); MP(\"A\",(4,0),SE);MP(\"C\",(1,2),N);MP(\"E\",(0,0),SW); MP(\"D\",(.5,1),W);MP(\"B\",(2.5,1),NE);MP(\"F\",(2,0),S); [/asy]$\n\n## Solution\n\nThis problem needs a solution. If you have a solution for it, please help us out by adding it.\n\n## See Also\n\n 2006 UNCO Math Contest II (Problems • Answer Key • Resources) Preceded byProblem 4 Followed byProblem 6 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 All UNCO Math Contest Problems and Solutions\nInvalid username\nLogin to AoPS" ]	[ null, "https://latex.artofproblemsolving.com/8/9/f/89fff82bb65d0215e49c8c91cb7c553da52205e2.png ", null, "https://latex.artofproblemsolving.com/9/a/6/9a65c05bd85d2609bea5db2b109ed5f556463511.png ", null, "https://latex.artofproblemsolving.com/6/5/e/65e4f2d5cc59e5ffbed3734130e8c45b643adc91.png ", null, "https://latex.artofproblemsolving.com/6/d/5/6d5c9afa92ae3180f02754c177e530d9d0f8b4d4.png ", null, "https://latex.artofproblemsolving.com/f/3/4/f348b5890100fa57eaa4a3c548badc83b75af585.png ", null, "https://latex.artofproblemsolving.com/0/a/e/0aed56990dedba5a88a65e21245ccfd5d5e43ae2.png ", null, "https://latex.artofproblemsolving.com/7/c/9/7c9d11f822493c6fa024726ef0750b2917998e2c.png ", null, "https://latex.artofproblemsolving.com/7/6/d/76d15d808807bfa561e72dc8111649ed0a204ebe.png ", null, "https://latex.artofproblemsolving.com/c/e/e/cee88eb0e94e7831e4d242c8930836c02c7d5128.png ", null, "https://latex.artofproblemsolving.com/8/b/c/8bc13e1d9d8740bc4f6f48868cdc693e5c1b390c.png ", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8271617,"math_prob":0.99606985,"size":924,"snap":"2021-21-2021-25","text_gpt3_token_len":274,"char_repetition_ratio":0.14891304,"word_repetition_ratio":0.037037037,"special_character_ratio":0.32683983,"punctuation_ratio":0.0882353,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99558616,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],"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],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-06-16T23:15:22Z\",\"WARC-Record-ID\":\"<urn:uuid:17496adb-ad08-4ce6-b52a-69385e67496e>\",\"Content-Length\":\"42003\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:660b8270-639a-45ca-a7fd-0885e7beebf1>\",\"WARC-Concurrent-To\":\"<urn:uuid:26638762-4914-47ca-be8a-313c3fd41b0b>\",\"WARC-IP-Address\":\"172.67.69.208\",\"WARC-Target-URI\":\"https://artofproblemsolving.com/wiki/index.php?title=2006_UNCO_Math_Contest_II_Problems/Problem_5&diff=prev&oldid=81835\",\"WARC-Payload-Digest\":\"sha1:XHASMD6Q5A5JLRP4KOGMRJDOMOGSP2IN\",\"WARC-Block-Digest\":\"sha1:P7BVZL5AYOSZV3TLFY3MKPKV6K2IS645\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-25/CC-MAIN-2021-25_segments_1623487626122.27_warc_CC-MAIN-20210616220531-20210617010531-00557.warc.gz\"}"}
http://oeis.org/A083710	[ "This site is supported by donations to The OEIS Foundation.", null, "Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)\n A083710 Number of partitions of n each of which has a summand which divides every summand in the partition. 9\n 1, 1, 2, 3, 5, 6, 11, 12, 20, 25, 37, 43, 70, 78, 114, 143, 196, 232, 330, 386, 530, 641, 836, 1003, 1340, 1581, 2037, 2461, 3127, 3719, 4746, 5605, 7038, 8394, 10376, 12327, 15272, 17978, 22024, 26095, 31730, 37339, 45333, 53175, 64100, 75340, 90138 (list; graph; refs; listen; history; text; internal format)\n OFFSET 0,3 COMMENTS Since the summand (part) which divides all the other summands is necessarily the smallest, an equivalent definition is: \"Number of partitions of n such that smallest part divides every part.\" - Joerg Arndt, Jun 08 2009 The first few partitions that fail the criterion are 5=3+2, 7=5+2=4+3=3+2+2. So a(5) = A000041(5) - 1 = 6, a(7) = A000041(7) - 3 = 12. - Vladeta Jovovic, Jun 17 2003 Starting with offset 1 = inverse Mobius transform (A051731) of the partition numbers, A000041. - Gary W. Adamson, Jun 08 2009 REFERENCES L. M. Chawla, M. O. Levan and J. E. Maxfield, On a restricted partition function and its tables, J. Natur. Sci. and Math., 12 (1972), 95-101. LINKS FORMULA Equals left border of triangle A137587 starting (1, 2, 3, 5, 6, 11,...). - Gary W. Adamson, Jan 27 2008 Comment from Joerg Arndt, Jun 08 2009: Sequence has g.f. 1 + Sum_{n>=1} x^n/eta(x^n). The g.f. for partitions into parts that are a multiple of n is x^n/eta(x^n), now sum over n. Gary W. Adamson's comment is equivalent to the formula a(n) = Sum_{d\|n} p(d-1) where p(i) = number of partitions of i (A000041(i)). Hence A083710 has g.f. Sum_{d>=1} p(d-1)x^d/(1-x^d), - N. J. A. Sloane, Jun 08 2009 MAPLE with(combinat): with(numtheory): a := proc(n) c := 0: l := sort(convert(divisors(n), list)): for i from 1 to nops(l)-0 do c := c+numbpart(l[i]-1) od: RETURN(c): end: for j from 0 to 60 do printf(`%d, `, a(j)) od: # Zerinvary Lajos, Apr 14 2007 CROSSREFS Cf. A083711, A018783, A137587. Cf. A000041, A051731. - Gary W. Adamson, Jun 08 2009 Sequence in context: A033159 A199366 A318689 A127524 A117086 A081026 Adjacent sequences: A083707 A083708 A083709 * A083711 A083712 A083713 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Jun 16 2003 EXTENSIONS More terms from Vladeta Jovovic, Jun 17 2003 STATUS approved\n\nLookup \| Welcome \| Wiki \| Register \| Music \| Plot 2 \| Demos \| Index \| Browse \| More \| WebCam\nContribute new seq. or comment \| Format \| Style Sheet \| Transforms \| Superseeker \| Recent\nThe OEIS Community \| Maintained by The OEIS Foundation Inc.\n\nLast modified June 20 01:36 EDT 2019. Contains 324223 sequences. (Running on oeis4.)" ]	[ null, "http://oeis.org/banner2021.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.61623883,"math_prob":0.9516506,"size":2353,"snap":"2019-26-2019-30","text_gpt3_token_len":944,"char_repetition_ratio":0.10557684,"word_repetition_ratio":0.027842227,"special_character_ratio":0.5053124,"punctuation_ratio":0.25996533,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9916036,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-06-20T05:52:59Z\",\"WARC-Record-ID\":\"<urn:uuid:781738a4-eda3-4e11-b945-61223d12fe38>\",\"Content-Length\":\"18215\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d8771a3e-f58a-4c72-b1bc-b973d7db995b>\",\"WARC-Concurrent-To\":\"<urn:uuid:75f3a4f4-995d-462c-a83c-2f6ac4ef1a54>\",\"WARC-IP-Address\":\"104.239.138.29\",\"WARC-Target-URI\":\"http://oeis.org/A083710\",\"WARC-Payload-Digest\":\"sha1:SFVL3GEO7ASRMSXRHJKNLGMEL2ZYTRJC\",\"WARC-Block-Digest\":\"sha1:XDFWRRDYF4AU2DLOL2366VEZM3NOWJE6\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-26/CC-MAIN-2019-26_segments_1560627999141.54_warc_CC-MAIN-20190620044948-20190620070948-00004.warc.gz\"}"}
https://www.numberempire.com/516636	[ "Home \| Menu \| Get Involved \| Contact webmaster", null, "", null, "", null, "", null, "", null, "# Number 516636\n\nfive hundred sixteen thousand six hundred thirty six\n\n### Properties of the number 516636\n\n Factorization 2 * 2 * 3 * 3 * 113 * 127 Divisors 1, 2, 3, 4, 6, 9, 12, 18, 36, 113, 127, 226, 254, 339, 381, 452, 508, 678, 762, 1017, 1143, 1356, 1524, 2034, 2286, 4068, 4572, 14351, 28702, 43053, 57404, 86106, 129159, 172212, 258318, 516636 Count of divisors 36 Sum of divisors 1327872 Previous integer 516635 Next integer 516637 Is prime? NO Previous prime 516623 Next prime 516643 516636th prime 7632467 Is a Fibonacci number? NO Is a Bell number? NO Is a Catalan number? NO Is a factorial? NO Is a regular number? NO Is a perfect number? NO Polygonal number (s < 11)? triangular(1016) Binary 1111110001000011100 Octal 1761034 Duodecimal 20ab90 Hexadecimal 7e21c Square 266912756496 Square root 718.77395612251 Natural logarithm 13.155093843627 Decimal logarithm 5.7131846652067 Sine 0.88575455673642 Cosine 0.46415392406041 Tangent 1.9083207333202\nNumber 516636 is pronounced five hundred sixteen thousand six hundred thirty six. Number 516636 is a composite number. Factors of 516636 are 2 * 2 * 3 * 3 * 113 * 127. Number 516636 has 36 divisors: 1, 2, 3, 4, 6, 9, 12, 18, 36, 113, 127, 226, 254, 339, 381, 452, 508, 678, 762, 1017, 1143, 1356, 1524, 2034, 2286, 4068, 4572, 14351, 28702, 43053, 57404, 86106, 129159, 172212, 258318, 516636. Sum of the divisors is 1327872. Number 516636 is not a Fibonacci number. It is not a Bell number. Number 516636 is not a Catalan number. Number 516636 is not a regular number (Hamming number). It is a not factorial of any number. Number 516636 is an abundant number and therefore is not a perfect number. Number 516636 is a triangular number with n=1016. Binary numeral for number 516636 is 1111110001000011100. Octal numeral is 1761034. Duodecimal value is 20ab90. Hexadecimal representation is 7e21c. Square of the number 516636 is 266912756496. Square root of the number 516636 is 718.77395612251. Natural logarithm of 516636 is 13.155093843627 Decimal logarithm of the number 516636 is 5.7131846652067 Sine of 516636 is 0.88575455673642. Cosine of the number 516636 is 0.46415392406041. Tangent of the number 516636 is 1.9083207333202" ]	[ null, "https://www.numberempire.com/images/graystar.png", null, "https://www.numberempire.com/images/graystar.png", null, "https://www.numberempire.com/images/graystar.png", null, "https://www.numberempire.com/images/graystar.png", null, "https://www.numberempire.com/images/graystar.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.55378747,"math_prob":0.995714,"size":2644,"snap":"2020-34-2020-40","text_gpt3_token_len":965,"char_repetition_ratio":0.16704546,"word_repetition_ratio":0.21609196,"special_character_ratio":0.5139939,"punctuation_ratio":0.22095238,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9861366,"pos_list":[0,1,2,3,4,5,6,7,8,9,10],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-08-09T15:17:33Z\",\"WARC-Record-ID\":\"<urn:uuid:c806faf5-51cd-4f64-9f9e-2e5ba3e64182>\",\"Content-Length\":\"26735\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:5e6260c4-abac-4035-8b24-192a379f5548>\",\"WARC-Concurrent-To\":\"<urn:uuid:096d4a43-7e11-4178-a595-9294a245ef02>\",\"WARC-IP-Address\":\"172.67.208.6\",\"WARC-Target-URI\":\"https://www.numberempire.com/516636\",\"WARC-Payload-Digest\":\"sha1:HJZVFZX4IHHYTOIKV4EBNNZMABSLGLL6\",\"WARC-Block-Digest\":\"sha1:52W3FS54QDIDC3ULWOPBKARLC4W2VWRG\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-34/CC-MAIN-2020-34_segments_1596439738555.33_warc_CC-MAIN-20200809132747-20200809162747-00095.warc.gz\"}"}
https://scip.zib.de/doc-6.0.2/html/presol__symmetry_8c.php	[ "", null, "presol_symmetry.c File Reference\n\nDetailed Description\n\npresolver for storing symmetry information about current problem\n\nThis presolver computes symmetries of the problem and stores this information in adequate form. It does not perform additional actions. The symmetry information can be accessed through external functions. However, the user has to declare the type of symmetry that is needed before execution, see SYMsetSpecRequirement().\n\nNote\nWe treat implict integer variables as if they were continuous/real variables. The reason is that there is currently no distinction between implicit integer and implicit binary. Moreover, currently implicit integer variables hurt our code more than continuous/real variables (we basically do not handle integral variables at all).\nWe do not copy symmetry information, since it is not clear how this information transfers. Moreover, copying symmetry might inhibit heuristics. But note that solving the a sub-SCIP might then happen without symmetry information!\n\nDefinition in file presol_symmetry.c.\n\n#include <scip/cons_linear.h>\n#include <scip/cons_knapsack.h>\n#include <scip/cons_varbound.h>\n#include <scip/cons_setppc.h>\n#include <scip/cons_and.h>\n#include <scip/cons_logicor.h>\n#include <scip/cons_or.h>\n#include <scip/cons_xor.h>\n#include <scip/cons_bounddisjunction.h>\n#include <scip/presol_symmetry.h>\n#include <symmetry/compute_symmetry.h>\n#include <string.h>\n\nGo to the source code of this file.\n\nData Structures\n\nstruct SYM_Sortrhstype\n\nMacros\n\n#define PRESOL_NAME \"symmetry\"\n\n#define PRESOL_DESC \"presolver for computing and storing symmetry information about current problem\"\n\n#define PRESOL_PRIORITY 0\n\n#define PRESOL_MAXROUNDS -1\n\n#define PRESOL_TIMING SCIP_PRESOLTIMING_EXHAUSTIVE /* timing of the presolver (fast, medium, or exhaustive) /\n\n#define DEFAULT_MAXGENERATORS 1500\n\n#define DEFAULT_CHECKSYMMETRIES FALSE\n\n#define DEFAULT_DISPLAYNORBITVARS FALSE\n\n#define MAXGENNUMERATOR 64000000\n\n#define SCIP_SPECIALVAL 1.12345678912345e+19\n\nTypedefs\n\ntypedef struct SYM_Sortrhstype SYM_SORTRHSTYPE\n\nFunctions\n\nstatic SCIP_DECL_HASHGETKEY (SYMhashGetKeyVartype)\n\nstatic SCIP_DECL_HASHKEYEQ (SYMhashKeyEQVartype)\n\nstatic SCIP_DECL_HASHKEYVAL (SYMhashKeyValVartype)\n\nstatic SCIP_DECL_SORTINDCOMP (SYMsortRhsTypes)\n\nstatic SCIP_DECL_SORTINDCOMP (SYMsortMatCoef)\n\nstatic SCIP_Bool SymmetryFixVar (SYM_SPEC fixedtype, SCIP_VAR var)\n\nstatic SCIP_RETCODE getActiveVariables (SCIP scip, SCIP_VAR vars, SCIP_Real scalars, int nvars, SCIP_Real constant, SCIP_Bool transformed)\n\nstatic SCIP_RETCODE collectCoefficients (SCIP scip, SCIP_VAR linvars, SCIP_Real linvals, int nlinvars, SCIP_Real lhs, SCIP_Real rhs, SCIP_Bool istransformed, SYM_RHSSENSE rhssense, SYM_MATRIXDATA matrixdata)\n\nstatic SCIP_RETCODE checkSymmetriesAreSymmetries (SCIP scip, SYM_SPEC fixedtype, SYM_MATRIXDATA matrixdata, int nperms, int perms)\n\nstatic int getNSymhandableConss (SCIP scip)\n\nstatic SCIP_RETCODE computeSymmetryGroup (SCIP scip, int maxgenerators, SYM_SPEC fixedtype, SCIP_Bool local, SCIP_Bool checksymmetries, int npermvars, SCIP_VAR *permvars, SCIP_Real permvarsobj, int nperms, int nmaxperms, int **perms, SCIP_Real log10groupsize, SCIP_Bool success)\n\nstatic SCIP_RETCODE computeNOrbitVars (SCIP scip, SCIP_PRESOLDATA presoldata, SCIP_Bool completestatistic)\n\nstatic SCIP_RETCODE determineSymmetry (SCIP scip, SCIP_PRESOLDATA presoldata, SYM_SPEC symspecrequire, SYM_SPEC symspecrequirefixed)\n\nstatic SCIP_DECL_PRESOLINIT (presolInitSymmetry)\n\nstatic SCIP_DECL_PRESOLEXIT (presolExitSymmetry)\n\nstatic SCIP_DECL_PRESOLFREE (presolFreeSymmetry)\n\nstatic SCIP_DECL_PRESOLEXEC (presolExecSymmetry)\n\nSCIP_RETCODE SCIPincludePresolSymmetry (SCIP scip)\n\nSCIP_RETCODE SCIPgetGeneratorsSymmetry (SCIP scip, SYM_SPEC symspecrequire, SYM_SPEC symspecrequirefixed, SCIP_Bool recompute, int npermvars, SCIP_VAR **permvars, int nperms, int **perms, SCIP_Real log10groupsize, SCIP_Bool binvaraffected)\n\nSCIP_RETCODE SCIPgetPermvarsObjSymmetry (SCIP scip, SCIP_Real *permvarsobj)\n\n◆ PRESOL_NAME\n\n #define PRESOL_NAME \"symmetry\"\n\nDefinition at line 53 of file presol_symmetry.c.\n\n◆ PRESOL_DESC\n\n #define PRESOL_DESC \"presolver for computing and storing symmetry information about current problem\"\n\nDefinition at line 54 of file presol_symmetry.c.\n\nReferenced by SCIPincludePresolSymmetry().\n\n◆ PRESOL_PRIORITY\n\n #define PRESOL_PRIORITY 0\n\npriority of the presolver (>= 0: before, < 0: after constraint handlers)\n\nDefinition at line 55 of file presol_symmetry.c.\n\nReferenced by SCIPincludePresolSymmetry().\n\n◆ PRESOL_MAXROUNDS\n\n #define PRESOL_MAXROUNDS -1\n\nmaximal number of presolving rounds the presolver participates in (-1: no limit)\n\nDefinition at line 56 of file presol_symmetry.c.\n\nReferenced by SCIPincludePresolSymmetry().\n\n◆ PRESOL_TIMING\n\n #define PRESOL_TIMING SCIP_PRESOLTIMING_EXHAUSTIVE / timing of the presolver (fast, medium, or exhaustive) /\n\nDefinition at line 57 of file presol_symmetry.c.\n\nReferenced by SCIPincludePresolSymmetry().\n\n◆ DEFAULT_MAXGENERATORS\n\n #define DEFAULT_MAXGENERATORS 1500\n\nlimit on the number of generators that should be produced within symmetry detection (0 = no limit)\n\nDefinition at line 60 of file presol_symmetry.c.\n\nReferenced by SCIPincludePresolSymmetry().\n\n◆ DEFAULT_CHECKSYMMETRIES\n\n #define DEFAULT_CHECKSYMMETRIES FALSE\n\nShould all symmetries be checked after computation?\n\nDefinition at line 61 of file presol_symmetry.c.\n\nReferenced by SCIPincludePresolSymmetry().\n\n◆ DEFAULT_DISPLAYNORBITVARS\n\n #define DEFAULT_DISPLAYNORBITVARS FALSE\n\nShould the number of variables affected by some symmetry be displayed?\n\nDefinition at line 62 of file presol_symmetry.c.\n\nReferenced by SCIPincludePresolSymmetry().\n\n◆ MAXGENNUMERATOR\n\n #define MAXGENNUMERATOR 64000000\n\ndetermine maximal number of generators by dividing this number by the number of variables\n\nDefinition at line 65 of file presol_symmetry.c.\n\nReferenced by determineSymmetry().\n\n◆ SCIP_SPECIALVAL\n\n #define SCIP_SPECIALVAL 1.12345678912345e+19\n\nspecial floating point value for handling zeros in bound disjunctions\n\nDefinition at line 66 of file presol_symmetry.c.\n\nReferenced by computeSymmetryGroup().\n\n◆ SYM_SORTRHSTYPE\n\n typedef struct SYM_Sortrhstype SYM_SORTRHSTYPE\n\nDefinition at line 159 of file presol_symmetry.c.\n\n◆ SCIP_DECL_HASHGETKEY()\n\n static SCIP_DECL_HASHGETKEY ( SYMhashGetKeyVartype )\nstatic\n\ngets the key of the given element\n\nDefinition at line 99 of file presol_symmetry.c.\n\n◆ SCIP_DECL_HASHKEYEQ()\n\n static SCIP_DECL_HASHKEYEQ ( SYMhashKeyEQVartype )\nstatic\n\nreturns TRUE iff both keys are equal\n\nCompare the types of two variables according to objective, lower and upper bound, and variable type.\n\nDefinition at line 109 of file presol_symmetry.c.\n\nReferences FALSE, SYM_Vartype::lb, SYM_Vartype::obj, SCIPisEQ(), TRUE, SYM_Vartype::type, and SYM_Vartype::ub.\n\n◆ SCIP_DECL_HASHKEYVAL()\n\n static SCIP_DECL_HASHKEYVAL ( SYMhashKeyValVartype )\nstatic\n\nreturns the hash value of the key\n\nDefinition at line 140 of file presol_symmetry.c.\n\n◆ SCIP_DECL_SORTINDCOMP() [1/2]\n\n static SCIP_DECL_SORTINDCOMP ( SYMsortRhsTypes )\nstatic\n\nsort rhs types - first by sense, then by value\n\nDue to numerical issues, we first sort by sense, then by value.\n\nresult: < 0: ind1 comes before (is better than) ind2 = 0: both indices have the same value\n\n0: ind2 comes after (is worse than) ind2\n\nDefinition at line 171 of file presol_symmetry.c.\n\n◆ SCIP_DECL_SORTINDCOMP() [2/2]\n\n static SCIP_DECL_SORTINDCOMP ( SYMsortMatCoef )\nstatic\n\nsort matrix coefficients\n\nresult: < 0: ind1 comes before (is better than) ind2 = 0: both indices have the same value\n\n0: ind2 comes after (is worse than) ind2\n\nDefinition at line 205 of file presol_symmetry.c.\n\nReferences SCIP_Real, and SYM_Sortrhstype::vals.\n\n◆ SymmetryFixVar()\n\n static SCIP_Bool SymmetryFixVar ( SYM_SPEC fixedtype, SCIP_VAR var )\nstatic\n\ndetermines whether variable should be fixed by permutations\n\nParameters\n fixedtype bitset of variable types that should be fixed var variable to be considered\n\nDefinition at line 228 of file presol_symmetry.c.\n\nReferenced by checkSymmetriesAreSymmetries(), and computeSymmetryGroup().\n\n◆ getActiveVariables()\n\n static SCIP_RETCODE getActiveVariables ( SCIP * scip, SCIP_VAR * vars, SCIP_Real scalars, int * nvars, SCIP_Real * constant, SCIP_Bool transformed )\nstatic\n\nTransforms given variables, scalars, and constant to the corresponding active variables, scalars, and constant.\n\nNote\nconstant needs to be initialized!\nParameters\n scip SCIP data structure vars pointer to vars array to get active variables for scalars pointer to scalars a_1, ..., a_n in linear sum a_1x_1 + ... + a_nx_n + c nvars pointer to number of variables and values in vars and vals array constant pointer to constant c in linear sum a_1x_1 + ... + a_nx_n + c transformed transformed constraint?\n\nDefinition at line 249 of file presol_symmetry.c.\n\nReferenced by collectCoefficients().\n\n◆ collectCoefficients()\n\n static SCIP_RETCODE collectCoefficients ( SCIP * scip, SCIP_VAR ** linvars, SCIP_Real * linvals, int nlinvars, SCIP_Real lhs, SCIP_Real rhs, SCIP_Bool istransformed, SYM_RHSSENSE rhssense, SYM_MATRIXDATA * matrixdata )\nstatic\n\nfill in matrix elements into coefficient arrays\n\nParameters\n scip SCIP data structure linvars array of linear variables linvals array of linear coefficients values (or NULL if all linear coefficient values are 1) nlinvars number of linear variables lhs left hand side rhs right hand side istransformed whether the constraint is transformed rhssense identifier of constraint type matrixdata matrix data to be filled in\n\nDefinition at line 295 of file presol_symmetry.c.\n\nReferenced by computeSymmetryGroup().\n\n◆ checkSymmetriesAreSymmetries()\n\n static SCIP_RETCODE checkSymmetriesAreSymmetries ( SCIP * scip, SYM_SPEC fixedtype, SYM_MATRIXDATA * matrixdata, int nperms, int ** perms )\nstatic\n\nchecks whether given permutations form a symmetry of a MIP\n\nWe need the matrix and rhs in the original order in order to speed up the comparison process. The matrix is needed in the right order to easily check rows. The rhs is used because of cache effects.\n\nParameters\n scip SCIP data structure fixedtype variable types that must be fixed by symmetries matrixdata matrix data nperms number of permutations perms permutations\n\nDefinition at line 487 of file presol_symmetry.c.\n\nReferenced by computeSymmetryGroup().\n\n◆ getNSymhandableConss()\n\n static int getNSymhandableConss ( SCIP * scip )\nstatic\n\nreturns the number of active constraints that can be handled by symmetry\n\nParameters\n scip SCIP instance\n\nDefinition at line 633 of file presol_symmetry.c.\n\nReferences NULL, SCIPconshdlrGetNActiveConss(), and SCIPfindConshdlr().\n\nReferenced by computeSymmetryGroup(), and determineSymmetry().\n\n◆ computeSymmetryGroup()\n\n static SCIP_RETCODE computeSymmetryGroup ( SCIP * scip, int maxgenerators, SYM_SPEC fixedtype, SCIP_Bool local, SCIP_Bool checksymmetries, int * npermvars, SCIP_VAR * permvars, SCIP_Real permvarsobj, int * nperms, int * nmaxperms, int *** perms, SCIP_Real * log10groupsize, SCIP_Bool * success )\nstatic\n\ncompute symmetry group of MIP\n\nParameters\n scip SCIP pointer maxgenerators maximal number of generators constructed (= 0 if unlimited) fixedtype variable types that must be fixed by symmetries local Use local variable bounds? checksymmetries Should all symmetries be checked after computation? npermvars pointer to store number of variables for permutations permvars pointer to store variables on which permutations act permvarsobj objective values of permuted variables nperms pointer to store number of permutations nmaxperms pointer to store maximal number of permutations (needed for freeing storage) perms pointer to store permutation generators as (nperms x npermvars) matrix log10groupsize pointer to store log10 of size of group success pointer to store whether symmetry computation was successful\n\nDefinition at line 669 of file presol_symmetry.c.\n\nReferenced by determineSymmetry().\n\n◆ computeNOrbitVars()\n\n static SCIP_RETCODE computeNOrbitVars ( SCIP * scip, SCIP_PRESOLDATA * presoldata, SCIP_Bool completestatistic )\nstatic\nParameters\n scip SCIP instance presoldata presolver data completestatistic whether a complete statistic on affected vars should be computed\n\nDefinition at line 1308 of file presol_symmetry.c.\n\nReferenced by determineSymmetry().\n\n◆ determineSymmetry()\n\n static SCIP_RETCODE determineSymmetry ( SCIP * scip, SCIP_PRESOLDATA * presoldata, SYM_SPEC symspecrequire, SYM_SPEC symspecrequirefixed )\nstatic\n\ndetermine symmetry\n\nParameters\n scip SCIP instance presoldata presolver data symspecrequire symmetry specification for which we need to compute symmetries symspecrequirefixed symmetry specification of variables which must be fixed by symmetries\n\nDefinition at line 1369 of file presol_symmetry.c.\n\n◆ SCIP_DECL_PRESOLINIT()\n\n static SCIP_DECL_PRESOLINIT ( presolInitSymmetry )\nstatic\n\ninitialization method of presolver (called after problem was transformed)\n\nDefinition at line 1550 of file presol_symmetry.c.\n\n◆ SCIP_DECL_PRESOLEXIT()\n\n static SCIP_DECL_PRESOLEXIT ( presolExitSymmetry )\nstatic\n\ndeinitialization method of presolver (called before transformed problem is freed)\n\nDefinition at line 1569 of file presol_symmetry.c.\n\n◆ SCIP_DECL_PRESOLFREE()\n\n static SCIP_DECL_PRESOLFREE ( presolFreeSymmetry )\nstatic\n\ndestructor of presolver to free user data (called when SCIP is exiting)\n\nDefinition at line 1614 of file presol_symmetry.c.\n\n◆ SCIP_DECL_PRESOLEXEC()\n\n static SCIP_DECL_PRESOLEXEC ( presolExecSymmetry )\nstatic\n\nexecution method of presolver\n\nDefinition at line 1635 of file presol_symmetry.c.\n\nReferences NULL, PRESOL_NAME, SCIP_DIDNOTRUN, SCIP_OKAY, and SCIPpresolGetName().\n\n◆ SCIPincludePresolSymmetry()\n\n SCIP_RETCODE SCIPincludePresolSymmetry ( SCIP * scip )\n\ninclude symmetry constraint handler\n\nParameters\n scip SCIP data structure\n\nDefinition at line 1654 of file presol_symmetry.c.\n\nReferenced by SCIPincludeDefaultPlugins().\n\n SCIP_RETCODE SCIPgetGeneratorsSymmetry ( SCIP * scip, SYM_SPEC symspecrequire, SYM_SPEC symspecrequirefixed, SCIP_Bool recompute, int * npermvars, SCIP_VAR *** permvars, int * nperms, int *** perms, SCIP_Real * log10groupsize, SCIP_Bool * binvaraffected )\n\nreturn symmetry group generators\n\nParameters\n scip SCIP data structure symspecrequire symmetry specification for which we need to compute symmetries symspecrequirefixed symmetry specification of variables which must be fixed by symmetries recompute Have symmetries already been computed? npermvars pointer to store number of variables for permutations permvars pointer to store variables on which permutations act nperms pointer to store number of permutations perms pointer to store permutation generators as (nperms x npermvars) matrix log10groupsize pointer to store log10 of group size (or NULL) binvaraffected pointer to store whether binary variables are affected\n\nDefinition at line 1712 of file presol_symmetry.c.\n\nReferenced by getSymmetries(), and tryAddSymmetryHandlingConss().\n\n◆ SCIPgetPermvarsObjSymmetry()\n\n SCIP_RETCODE SCIPgetPermvarsObjSymmetry ( SCIP * scip, SCIP_Real ** permvarsobj )\n\nreturn objective coefficients of permuted variables at time of symmetry computation\n\nParameters\n scip SCIP data structure permvarsobj pointer to store objective coefficients of permuted variables (NULL if not available)\n\nDefinition at line 1799 of file presol_symmetry.c.\n\nReferenced by propagateOrbitalFixing()." ]	[ null, "https://scip.zib.de/doc-6.0.2/html/search/mag_sel.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.5458328,"math_prob":0.79404,"size":20824,"snap":"2019-43-2019-47","text_gpt3_token_len":5546,"char_repetition_ratio":0.195293,"word_repetition_ratio":0.13314176,"special_character_ratio":0.20231463,"punctuation_ratio":0.24795155,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9680594,"pos_list":[0,1,2],"im_url_duplicate_count":[null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-21T03:33:52Z\",\"WARC-Record-ID\":\"<urn:uuid:554929a1-05a9-40bd-9edb-2475a18af3ea>\",\"Content-Length\":\"110708\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:12d74b43-35c7-4b4f-9861-e6bb31f39614>\",\"WARC-Concurrent-To\":\"<urn:uuid:eb473e3a-5143-412d-b9de-2f34bfc0062d>\",\"WARC-IP-Address\":\"130.73.108.67\",\"WARC-Target-URI\":\"https://scip.zib.de/doc-6.0.2/html/presol__symmetry_8c.php\",\"WARC-Payload-Digest\":\"sha1:44ETHQCABICG4OMQBBCZQTXSBUS65BFA\",\"WARC-Block-Digest\":\"sha1:3XK64XCCRKV3QG2HWG2ZLQNKZELFLEMR\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570987751039.81_warc_CC-MAIN-20191021020335-20191021043835-00235.warc.gz\"}"}
https://www.encyclopediaofmath.org/index.php/Golubev%E2%80%93Privalov_theorem	[ "# Golubev-Privalov theorem\n\n(Redirected from Golubev–Privalov theorem)\n\nIf", null, "is a complex summable function on a closed rectifiable Jordan curve", null, "in the complex", null, "-plane, then a necessary and sufficient condition for the existence of a function", null, ", regular in the interior of the domain", null, "bounded by", null, "and whose angular boundary values coincide with", null, "almost-everywhere on", null, ", is", null, "(1)\n\nThese conditions are known as the Golubev–Privalov conditions. That they are sufficient has been shown by V.V. Golubev ; that they are necessary has been shown by I.I. Privalov . In other words, conditions (1) are necessary and sufficient for the integral of Cauchy–Lebesgue type (cf. Cauchy integral)", null, "constructed for the function", null, "and the curve", null, ":", null, "to be a Cauchy–Lebesgue integral.\n\nIn a more general formulation, let", null, "be a complex Borel measure on", null, ". Then the integral of Cauchy–Stieltjes type (cf. Cauchy integral),", null, "is a Cauchy–Stieltjes integral if and only if the generalized Golubev–Privalov conditions", null, "(2)\n\nare satisfied.\n\nIn other words, conditions (2) are necessary and sufficient for the existence of a regular function", null, "in", null, "such that its angular boundary values coincide almost-everywhere (with respect to Lebesgue measure) on", null, "with", null, "where", null, "is the angle between the positive direction of the abscissa axis and the tangent to", null, "at the point", null, "and", null, "is the derivative of", null, "with respect to Lebesgue measure (arc length) on", null, ".\n\nThe Golubev–Privalov theorem is of importance in the theory of boundary properties of analytic functions." ]	[ null, "https://www.encyclopediaofmath.org/legacyimages/g/g044/g044580/g0445801.png", null, "https://www.encyclopediaofmath.org/legacyimages/g/g044/g044580/g0445802.png", null, "https://www.encyclopediaofmath.org/legacyimages/g/g044/g044580/g0445803.png", null, "https://www.encyclopediaofmath.org/legacyimages/g/g044/g044580/g0445804.png", null, "https://www.encyclopediaofmath.org/legacyimages/g/g044/g044580/g0445805.png", null, "https://www.encyclopediaofmath.org/legacyimages/g/g044/g044580/g0445806.png", null, "https://www.encyclopediaofmath.org/legacyimages/g/g044/g044580/g0445807.png", null, "https://www.encyclopediaofmath.org/legacyimages/g/g044/g044580/g0445808.png", null, "https://www.encyclopediaofmath.org/legacyimages/g/g044/g044580/g0445809.png", null, "https://www.encyclopediaofmath.org/legacyimages/g/g044/g044580/g04458010.png", null, "https://www.encyclopediaofmath.org/legacyimages/g/g044/g044580/g04458011.png", null, "https://www.encyclopediaofmath.org/legacyimages/g/g044/g044580/g04458012.png", null, "https://www.encyclopediaofmath.org/legacyimages/g/g044/g044580/g04458013.png", null, "https://www.encyclopediaofmath.org/legacyimages/g/g044/g044580/g04458014.png", null, "https://www.encyclopediaofmath.org/legacyimages/g/g044/g044580/g04458015.png", null, "https://www.encyclopediaofmath.org/legacyimages/g/g044/g044580/g04458016.png", null, "https://www.encyclopediaofmath.org/legacyimages/g/g044/g044580/g04458017.png", null, "https://www.encyclopediaofmath.org/legacyimages/g/g044/g044580/g04458018.png", null, "https://www.encyclopediaofmath.org/legacyimages/g/g044/g044580/g04458019.png", null, "https://www.encyclopediaofmath.org/legacyimages/g/g044/g044580/g04458020.png", null, "https://www.encyclopediaofmath.org/legacyimages/g/g044/g044580/g04458021.png", null, "https://www.encyclopediaofmath.org/legacyimages/g/g044/g044580/g04458022.png", null, "https://www.encyclopediaofmath.org/legacyimages/g/g044/g044580/g04458023.png", null, "https://www.encyclopediaofmath.org/legacyimages/g/g044/g044580/g04458024.png", null, "https://www.encyclopediaofmath.org/legacyimages/g/g044/g044580/g04458025.png", null, "https://www.encyclopediaofmath.org/legacyimages/g/g044/g044580/g04458026.png", null, "https://www.encyclopediaofmath.org/legacyimages/g/g044/g044580/g04458027.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8440676,"math_prob":0.9692902,"size":2235,"snap":"2019-13-2019-22","text_gpt3_token_len":598,"char_repetition_ratio":0.12684895,"word_repetition_ratio":0.018867925,"special_character_ratio":0.23221476,"punctuation_ratio":0.15931372,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9659986,"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],"im_url_duplicate_count":[null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-03-25T18:41:17Z\",\"WARC-Record-ID\":\"<urn:uuid:18750544-233a-4510-bbe9-c301628f433e>\",\"Content-Length\":\"19827\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4d7dca10-2488-495d-b46a-b1e9aa0d3280>\",\"WARC-Concurrent-To\":\"<urn:uuid:0bf4a67d-bb6c-43a8-b350-2e31b702ef22>\",\"WARC-IP-Address\":\"80.242.138.72\",\"WARC-Target-URI\":\"https://www.encyclopediaofmath.org/index.php/Golubev%E2%80%93Privalov_theorem\",\"WARC-Payload-Digest\":\"sha1:BGJQ3CQRCPGZSITNGMLA5WEQO5I62UHJ\",\"WARC-Block-Digest\":\"sha1:URMQEVPGLHKE32NZD63AC6GURDHIZIR4\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-13/CC-MAIN-2019-13_segments_1552912204086.87_warc_CC-MAIN-20190325174034-20190325200034-00422.warc.gz\"}"}
http://clay6.com/qa/74825/two-amplifiers-are-connected-one-after-the-other-in-series-cascaded-the-fir	[ "", null, "# Two amplifiers are connected one after the other in series (cascaded). The first amplifier has a voltage gain of $10$ and the second has a voltage gain of 20. If the input signal is $0.01\\;V$ calculate the output a.c signal\n$\\begin{array}{1 1} 2\\;V \\\\ 4\\;V \\\\ 6\\;V \\\\ 1\\;V \\end{array}$" ]	[ null, "http://clay6.com/images/down_arrow_square.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.62305945,"math_prob":0.99916685,"size":819,"snap":"2020-34-2020-40","text_gpt3_token_len":244,"char_repetition_ratio":0.10306749,"word_repetition_ratio":0.044444446,"special_character_ratio":0.25274727,"punctuation_ratio":0.11464968,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9959471,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-27T00:28:46Z\",\"WARC-Record-ID\":\"<urn:uuid:79efab15-b20e-4113-9447-dbffc95408ab>\",\"Content-Length\":\"18320\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:19810b58-5bce-46c8-8308-312a8299506c>\",\"WARC-Concurrent-To\":\"<urn:uuid:09c82fa3-b797-4bf2-a9b4-0844832400cc>\",\"WARC-IP-Address\":\"139.162.17.55\",\"WARC-Target-URI\":\"http://clay6.com/qa/74825/two-amplifiers-are-connected-one-after-the-other-in-series-cascaded-the-fir\",\"WARC-Payload-Digest\":\"sha1:YTN2E27XBJPZ2AHEZSXILH6SHVAHVOIS\",\"WARC-Block-Digest\":\"sha1:K25WTMHNGT5TZOWYFP3JANX5QKNENSML\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600400249545.55_warc_CC-MAIN-20200926231818-20200927021818-00708.warc.gz\"}"}
https://lists.swift.org/pipermail/swift-evolution/Week-of-Mon-20160111/006565.html	[ "# [swift-evolution] Epic: Typesafe calculations\n\nMatt Whiteside mwhiteside.dev at gmail.com\nWed Jan 13 22:27:05 CST 2016\n\n```> On Jan 13, 2016, at 11:16, Stephen Canon <scanon at apple.com> wrote:\n>\n> … in exact arithmetic, not in floating-point, which is what people tend to actually use for matrices. For that matter, the entire notion of “invertible” as a binary attribute is problematic when dealing with approximate arithmetic; a matrix may be formally invertible but so ill-conditioned that the result is effectively meaningless.\n>\n> Not really trying to shoot you down, just observing that this is an extremely subtle example with lots of hidden sharp edges.\n>\n> – Steve\n\nThat’s a good point. So then I wonder if exact arithmetic wouldn’t be good enough for a lot of entry level math & science applications, especially the ones where this type of approach would come to mind in the first place.\n\nSomething like,\n\nstruct Rational:CustomDebugStringConvertible{\nlet numerator, denominator: Int\nvar debugDescription:String{\nget{\nreturn \"\\(Double(numerator)/Double(denominator))\"\n}\n}\n}\n\nfunc (lhs:Rational,rhs:Rational) -> Rational{\nreturn Rational(numerator: lhs.numeratorrhs.numerator,\ndenominator: lhs.denominator * rhs.denominator)\n}\n\nfunc (lhs:Int,rhs:Rational) -> Rational{\nreturn Rational(numerator: lhsrhs.numerator,\ndenominator: rhs.denominator)\n}\n\nlet π = Rational(numerator: 355, denominator: 113)\nlet two_π = 2 * π\n\nmight get you pretty far with 64 bits.\n\nMatt\n\n-------------- next part --------------\nAn HTML attachment was scrubbed...\nURL: <https://lists.swift.org/pipermail/swift-evolution/attachments/20160113/7700bdfe/attachment.html>\n```" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8146632,"math_prob":0.71792537,"size":1697,"snap":"2021-43-2021-49","text_gpt3_token_len":410,"char_repetition_ratio":0.13526285,"word_repetition_ratio":0.0,"special_character_ratio":0.25574544,"punctuation_ratio":0.18566775,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9687591,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-23T21:02:33Z\",\"WARC-Record-ID\":\"<urn:uuid:8577ad21-420b-48f4-bc82-97b3a18cfaae>\",\"Content-Length\":\"4896\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:054389fe-6709-4918-baa2-d272d4a59d3b>\",\"WARC-Concurrent-To\":\"<urn:uuid:17749a1f-709b-488c-87d6-8a5c8792f4fe>\",\"WARC-IP-Address\":\"17.188.22.4\",\"WARC-Target-URI\":\"https://lists.swift.org/pipermail/swift-evolution/Week-of-Mon-20160111/006565.html\",\"WARC-Payload-Digest\":\"sha1:G2EH74LCLUYSAMHKOL4UERJIU6ZXGGOR\",\"WARC-Block-Digest\":\"sha1:H3FI2FHHOL3XQ37UJ24UUTUEYBQDM2M2\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323585768.3_warc_CC-MAIN-20211023193319-20211023223319-00607.warc.gz\"}"}
https://calcforme.com/percentage-calculator/103-is-203-percent-of-what	[ "# 103 is 203 Percent of what?\n\n## 103 is 203 Percent of 50.74\n\n%\n\n103 is 203% of 50.74\n\nCalculation steps:\n\n103 ÷ ( 203 ÷ 100 ) = 50.74\n\n### Calculate 103 is 203 Percent of what?\n\n• F\n\nFormula\n\n103 ÷ ( 203 ÷ 100 )\n\n• 1\n\nPercent to decimal\n\n203 ÷ 100 = 2.03\n\n• 2\n\n103 ÷ 2.03 = 50.74 So 103 is 203% of 50.74\n\nExample" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7099776,"math_prob":0.98709553,"size":182,"snap":"2023-40-2023-50","text_gpt3_token_len":87,"char_repetition_ratio":0.21910113,"word_repetition_ratio":0.2,"special_character_ratio":0.6923077,"punctuation_ratio":0.1590909,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99883074,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-08T18:30:08Z\",\"WARC-Record-ID\":\"<urn:uuid:b9982eaa-90b7-4b36-965e-dc08b6013fd0>\",\"Content-Length\":\"15520\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:13931d09-c6e0-41b5-abfe-acb48ea9daef>\",\"WARC-Concurrent-To\":\"<urn:uuid:cd011694-6ec4-43c9-acb3-903ea58f2b9f>\",\"WARC-IP-Address\":\"76.76.21.164\",\"WARC-Target-URI\":\"https://calcforme.com/percentage-calculator/103-is-203-percent-of-what\",\"WARC-Payload-Digest\":\"sha1:XN252RQLHSNCXU4KBK4CL3V45NXS7YAC\",\"WARC-Block-Digest\":\"sha1:JLLC6CMKFWKPN4PFIMYHOJUJLKBQE6Y3\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100769.54_warc_CC-MAIN-20231208180539-20231208210539-00142.warc.gz\"}"}
https://superior-papers.com/indicate-the-effect-of-each-of-these-errors-on-working-capital-current-ratio-assume-that-the/	[ "# Indicate the effect of each of these errors on working capital, current ratio (assume that the…\n\n(Inventory Errors—Periodic) Thomason Company makes the following errors during the current year. (In all cases, assume ending inventory in the following year is correctly stated.)\n\n1. Both ending inventory and purchases and related accounts payable are understated. (Assume this purchase was recorded and paid for in the following year.)\n\n2. Ending inventory is overstated, but purchases and related accounts payable are recorded correctly.\n\n3. Ending inventory is correct, but a purchase on account was not recorded. (Assume this purchase was recorded and paid for in the following year.)\n\nInstructions\n\nIndicate the effect of each of these errors on working capital, current ratio (assume that the current ratio is greater than 1), retained earnings, and net income for the current year and the subsequent year.\n\n0 replies" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.96386,"math_prob":0.68482566,"size":971,"snap":"2020-45-2020-50","text_gpt3_token_len":193,"char_repetition_ratio":0.12512927,"word_repetition_ratio":0.2857143,"special_character_ratio":0.19258496,"punctuation_ratio":0.115606934,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96241933,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-11-23T17:04:12Z\",\"WARC-Record-ID\":\"<urn:uuid:ed2bfad6-9b7c-43ef-ae56-2b3a906ec12f>\",\"Content-Length\":\"66923\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:66586b21-d896-4318-a7da-8d2b9bad653f>\",\"WARC-Concurrent-To\":\"<urn:uuid:14d96cd7-b19e-446a-a8b5-66c2612e4fa2>\",\"WARC-IP-Address\":\"199.188.200.186\",\"WARC-Target-URI\":\"https://superior-papers.com/indicate-the-effect-of-each-of-these-errors-on-working-capital-current-ratio-assume-that-the/\",\"WARC-Payload-Digest\":\"sha1:F3KC7RJKUWOASXVTE3IYGUP4S6QMNWPO\",\"WARC-Block-Digest\":\"sha1:YXZ4KC675A75MF6DVL3O2UOAZ3GPWPNG\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141163411.0_warc_CC-MAIN-20201123153826-20201123183826-00523.warc.gz\"}"}
https://www.idealhometuition.com/2014/04/mechanical-properties-of-fluids-ncert_8136.html	[ "## Pages\n\n### Mechanical Properties of Fluids NCERT Solutions Class 11 Physics - Solved Exercise Question 10.26\n\nQuestion 10.26:\n(a) What is the largest average velocity of blood flow in an artery of radius 2 × 10–3 m if the flow must remain laminar? (b) What is the corresponding flow rate? (Take viscosity of blood to be 2.084 × 10–3 Pa s).\nSolution:\n(a)Radius of the artery, r = 2 × 10–3 m\nDiameter of the artery, d = 2 × 2 × 10–3 m = 4 × 10– 3 m\nViscosity of blood, η = 2.084 X 10-3 Pa s\nDensity of blood, ρ = 1.06 × 103 kg/m3\nReynolds’ number for laminar flow, NR = 2000\nThe largest average velocity of blood is given by the relation:\nVarg = NRη / ρd\n= 2000 X 2.084 X 10-3 / (1.06 X 103 X 4 X 10-3)\n= 0.983 m/s\nTherefore, the largest average velocity of blood is 0.983 m/s.\n\n(b) Flow rate is given by the relation:\nR = π r2Vavg\n= 3.14 X (2 X 10-3)2 X 0.983\n= 1.235 X 10-5 m3s-1\nTherefore, the corresponding flow rate is 1.235 X 10-5 m3s-1" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7938021,"math_prob":0.99651986,"size":1406,"snap":"2021-04-2021-17","text_gpt3_token_len":576,"char_repetition_ratio":0.13908702,"word_repetition_ratio":0.78807944,"special_character_ratio":0.45234707,"punctuation_ratio":0.12806539,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99453646,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-01-26T14:15:21Z\",\"WARC-Record-ID\":\"<urn:uuid:73496dc8-e2ee-4524-8329-7413adffc292>\",\"Content-Length\":\"47525\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:946b367d-9e77-42ba-9390-8ef10fd254a3>\",\"WARC-Concurrent-To\":\"<urn:uuid:9460e060-8b0e-4ba0-aaf2-5969e1cf1493>\",\"WARC-IP-Address\":\"172.217.2.115\",\"WARC-Target-URI\":\"https://www.idealhometuition.com/2014/04/mechanical-properties-of-fluids-ncert_8136.html\",\"WARC-Payload-Digest\":\"sha1:YPNGDIVPWFWJ6XZOX3PCJOIP4R3R56DZ\",\"WARC-Block-Digest\":\"sha1:JYIAPEVGBM7G4KGAE5VQIM6LRGGEME2J\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-04/CC-MAIN-2021-04_segments_1610704800238.80_warc_CC-MAIN-20210126135838-20210126165838-00124.warc.gz\"}"}
https://elearning.reb.rw/course/view.php?id=296&section=9	[ "•", null, "### General\n\n•", null, "### Unit :9 Mathematics\n\nUnit 9 Mathematics", null, "Exercise 1: Listen to numbers and write\nthem down\n1. Take turns to say the numbers from one\nto ten out loud.\n2. Write the numbers out as words.\n3. Complete the sentences.\na. Five comes after ___ and before ___.\nb. Three comes after ___.\nc. The number before eight is ___.\n\nExercise 2: Names of numbers\nSay the names of all the numbers in this\n\nnumber square.", null, "", null, "Learning box\nWhen we add ten hundreds together we\nget one thousand.\nTen hundreds equal one thousand.\n\nWe write a thousand as 1,000.", null, "When we do addition, we\ntogether to make a total.\nWe use the plus sign (+) to\n\n1. Write the calculations in words.\na. 4 + 7 = 11 b. 3 + 5 = 8\n2. Write the words below in the correct\norder to make a calculation.\nnine, four, equals, plus, five\n3. Complete the sentences.\nIn our class there are ____ boys and\n\n____ girls. ____ plus ____ equals ____.\n\nWhen we do subtraction, we take one amount\naway from another amount. It is the opposite\nof addition. We use the minus sign (–) to show\nthat we are taking something away.\n\nExercise 5: Practise subtraction\n1. There are eight bananas. The monkey\neats five. How many bananas are left?\nWrite it like this: Eight minus five\nequals ____.\n2. Write the calculations in words.\na. 7 – 4 = 3 b. 20 – 8 = 12\n3. Write the calculations in numbers.\na. Ten minus two equals eight.\n\nb. Eleven minus five equals six.", null, "", null, "When we multiply, we take\n\ntogether a number of times\n\nExample\n5 multiplied by 4 = 5 + 5 + 5 + 5 = 20\nWe took the number 5 and added it\ntogether 4 times. This is why\n\nmultiplication is sometimes called “times”.\n\nExercise 6: Practise multiplication", null, "1. A girl has three bags\nof apples, with six\napples in each bag.\na. How many apples\ndoes she have?\nb. Write the\ncalculation in\nnumbers.\n2. Write these calculations in words.\na. 3 × 3 = 9\n\nb. 2 × 7 = 14", null, "Division is breaking up or\ndividing a number into an\n\nequal number of parts.\n\nExample\n20 divided by 4 = ?\nIf you take 20 bananas and put them into\nfour equal-sized groups, there will be 5\n\nbananas in each group. The answer is 5.\n\nExercise 7: Practise division\n1. In this bag there are 24 sweets. There\nare 6 boys who want to\nshare them.", null, "24 divided by 6 = ____.\nEach boy will get ____\nsweets.\n2. What is ten divided by five? Write the\ncalculation in numbers.\n3. Write the calculations in words.\n\na. 10 ÷ 2 = 5 b. 12 ÷ 4 = 3\n\nExercise 8: Match the words and numbers\nMatch the sentences in column 1 with the\n\ncalculations in column 2.", null, "9.6 Review\n1. Write the numbers as words.", null, "a. 9 b. 3 c. 5\nd. 11 e. 20 f. 100\n2. Match the signs in the\ntable with the correct\nword.\n3. Count backwards from 20\nto 1. Write the numbers in\n4. Match the calculations\nwith the correct numbers\n\nin words.", null, "5. Do the following calculations in groups.\n\na. 19 – 4 =\nb. 30 ÷ 5 =\nc. 21 + 3 =\n\nd. 6 x 5 =\n\nUnit8: Animals, birds and insectsUnit 10 Talk about events in the past and future" ]	[ null, "https://elearning.reb.rw/theme/image.php/mb2mcl/core/1673317101/spacer", null, "https://elearning.reb.rw/theme/image.php/mb2mcl/core/1673317101/spacer", null, "https://elearning.reb.rw/pluginfile.php/2572/course/section/3284/41%20%282%29.PNG", null, "https://elearning.reb.rw/pluginfile.php/2572/course/section/3284/42%20%282%29.PNG", null, "https://elearning.reb.rw/pluginfile.php/2572/course/section/3284/43%20%281%29.PNG", null, "https://elearning.reb.rw/pluginfile.php/2572/course/section/3284/44%20%281%29.PNG", null, "https://elearning.reb.rw/pluginfile.php/2572/course/section/3284/46%20%281%29.PNG", null, "https://elearning.reb.rw/pluginfile.php/2572/course/section/3284/47%20%281%29.PNG", null, "https://elearning.reb.rw/pluginfile.php/2572/course/section/3284/48%20%281%29.PNG", null, "https://elearning.reb.rw/pluginfile.php/2572/course/section/3284/50%20%281%29.PNG", null, "https://elearning.reb.rw/pluginfile.php/2572/course/section/3284/51%20%283%29.PNG", null, "https://elearning.reb.rw/pluginfile.php/2572/course/section/3284/52%20%282%29.PNG", null, "https://elearning.reb.rw/pluginfile.php/2572/course/section/3284/53%20%281%29.PNG", null, "https://elearning.reb.rw/pluginfile.php/2572/course/section/3284/54%20%281%29.PNG", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8653651,"math_prob":0.99765986,"size":2987,"snap":"2022-40-2023-06","text_gpt3_token_len":877,"char_repetition_ratio":0.15119007,"word_repetition_ratio":0.023931624,"special_character_ratio":0.30532306,"punctuation_ratio":0.17316018,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9995476,"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],"im_url_duplicate_count":[null,4,null,4,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-01-27T15:37:31Z\",\"WARC-Record-ID\":\"<urn:uuid:13aa3b0e-e488-4e55-ae93-358935e5feab>\",\"Content-Length\":\"50249\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4099bc4e-d9e4-408b-91e1-c0a5cbe85678>\",\"WARC-Concurrent-To\":\"<urn:uuid:aae05b84-cb7d-4fca-b6a1-0a06a657be87>\",\"WARC-IP-Address\":\"197.243.23.249\",\"WARC-Target-URI\":\"https://elearning.reb.rw/course/view.php?id=296&section=9\",\"WARC-Payload-Digest\":\"sha1:CVYBTKW4E3Y6ZYYRWCLEQQZ5JXRBNIO7\",\"WARC-Block-Digest\":\"sha1:LJYYWMTE34HCVGQQMBK6CELULUWBMTWG\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-06/CC-MAIN-2023-06_segments_1674764494986.94_warc_CC-MAIN-20230127132641-20230127162641-00228.warc.gz\"}"}
https://ris-ai.com/stock-price-prediction-with-machine-learning	[ "• +91-9872993883\n• +91-8283824812\n• info@ris-ai.com\n\n# Stock Price Prediction with Machine Learning ¶\n\nThe Stock Market is known as a place where people can make a fortune if they can successfully predict stock prices as Stock Price Prediction is very important in finance and business for decision making. In this article , we will create a Linear Regression model and a Decision Tree Regression Model to Predict Apple’s Stock Price using Machine Learning and Python . Stock Dataset is also provided , you can down load it.\n\nA stock price may depend on several factors operating in the current world and stock market. We will try to take into account a combination of mainly two factors:\n\n• 1. How the increase and decrease of stock prices of the other companies affect the stock price of a given target company.\n• 2. The past performances of the target company.\n\nImport pandas to import a CSV file:\n\nIn :\nimport pandas as pd\n\n Date Open High Low Close Adj Close \\\n0 2014-09-29 100.589996 100.690002 98.040001 99.620003 93.514290\n1 2014-10-06 99.949997 102.379997 98.309998 100.730003 94.556244\n2 2014-10-13 101.330002 101.779999 95.180000 97.669998 91.683792\n3 2014-10-20 98.320000 105.489998 98.220001 105.220001 98.771042\n4 2014-10-27 104.849998 108.040001 104.699997 108.000000 101.380676\n\nVolume\n0 142718700\n1 280258200\n2 358539800\n3 358532900\n4 220230600\n\n\nTo get the number of training days:\n\nIn :\nprint(\"training days =\",apple.shape)\n\ntraining days = (184, 7)\n\n\nTo Visualize the close price Data:\n\nIn :\nimport matplotlib.pyplot as plt\nimport seaborn as sns\nsns.set()\nplt.figure(figsize=(10, 4))\nplt.title(\"Apple's Stock Price\")\nplt.xlabel(\"Days\")\nplt.ylabel(\"Close Price USD ($)\") plt.plot(apple[\"Close\"]) plt.show()", null, "To get the close price: In : apple = apple[[\"Close\"]] print(apple.head()) Close 0 99.620003 1 100.730003 2 97.669998 3 105.220001 4 108.000000 Creating a variable to predict ‘X’ days in the future: In : futureDays = 25 Create a new target column shifted ‘X’ units/days up: In : apple[\"Prediction\"] = apple[[\"Close\"]].shift(-futureDays) print(apple.head()) print(apple.tail()) Close Prediction 0 99.620003 123.250000 1 100.730003 125.320000 2 97.669998 127.099998 3 105.220001 124.750000 4 108.000000 130.279999 Close Prediction 179 179.979996 NaN 180 178.020004 NaN 181 164.940002 NaN 182 167.779999 NaN 183 167.779999 NaN To create a feature dataset (x) and convert into a numpy array and remove last ‘x’ rows/days: In : import numpy as np x = np.array(apple.drop([\"Prediction\"], 1))[:-futureDays] # print(x) To create a target dataset (y) and convert it to a numpy array and get all of the target values except the last ‘x’ rows days: In : y = np.array(apple[\"Prediction\"])[:-futureDays] print(y) [123.25 125.32 127.099998 124.75 130.279999 128.949997 127.620003 128.770004 132.539993 130.279999 128.649994 127.169998 126.599998 126.75 126.440002 123.279999 129.619995 124.5 121.300003 115.519997 115.959999 105.760002 113.290001 109.269997 114.209999 113.449997 114.709999 110.379997 112.120003 111.040001 119.080002 119.5 121.059998 112.339996 119.300003 117.809998 119.029999 113.18 106.029999 108.029999 105.260002 96.959999 97.129997 101.419998 97.339996 94.019997 93.989998 96.040001 96.910004 103.010002 102.260002 105.919998 105.669998 109.989998 108.660004 109.849998 105.68 93.739998 92.720001 90.519997 95.220001 100.349998 97.919998 98.830002 95.330002 93.400002 95.889999 96.68 98.779999 98.660004 104.209999 107.480003 108.18 109.360001 106.940002 107.730003 103.129997 114.919998 112.709999 113.050003 114.059998 117.629997 116.599998 113.720001 108.839996 108.43 110.059998 111.790001 109.900002 113.949997 115.970001 116.519997 115.82 117.910004 119.040001 120. 121.949997 129.080002 132.119995 135.720001 136.660004 139.779999 139.139999 139.990005 140.639999 143.660004 143.339996 141.050003 142.270004 143.649994 148.960007 156.100006 153.059998 153.610001 155.449997 148.979996 142.270004 146.279999 144.020004 144.179993 149.039993 150.270004 149.5 156.389999 157.479996 157.5 159.860001 164.050003 158.630005 159.880005 151.889999 154.119995 155.300003 156.990005 156.25 163.050003 172.5 174.669998 170.149994 174.970001 171.050003 169.369995 173.970001 175.009995 169.229996 175. 177.089996 178.460007 171.509995 160.5 156.410004 172.429993 175.5 176.210007 179.979996 178.020004 164.940002 167.779999 167.779999] ### Split the data into 75% training and 25% testing ¶ In : from sklearn.model_selection import train_test_split xtrain, xtest, ytrain, ytest = train_test_split(x, y, test_size=0.25) ### Creating Models¶ In : # Creating the decision tree regressor model from sklearn.tree import DecisionTreeRegressor tree = DecisionTreeRegressor().fit(xtrain, ytrain) # creating the Linear Regression model from sklearn.linear_model import LinearRegression linear = LinearRegression().fit(xtrain, ytrain) To get the last ‘x’ rows/days of the feature dataset: In : xfuture = apple.drop([\"Prediction\"], 1)[:-futureDays] xfuture = xfuture.tail(futureDays) xfuture = np.array(xfuture) print(xfuture) [[143.649994] [148.960007] [156.100006] [153.059998] [153.610001] [155.449997] [148.979996] [142.270004] [146.279999] [144.020004] [144.179993] [149.039993] [150.270004] [149.5 ] [156.389999] [157.479996] [157.5 ] [159.860001] [164.050003] [158.630005] [159.880005] [151.889999] [154.119995] [155.300003] [156.990005]] #### To see the model tree prediction¶ In : treePrediction = tree.predict(xfuture) print(\"Decision Tree prediction =\",treePrediction) Decision Tree prediction = [154.119995 163.050003 171.509995 174.669998 174.669998 174.970001 163.050003 163.18 173.970001 175.009995 169.229996 175. 177.089996 178.460007 171.509995 160.5 156.410004 176.210007 175.5 176.210007 176.210007 178.020004 174.669998 167.779999 167.779999] #### To see the model linear regression prediction ¶ In : linearPrediction = linear.predict(xfuture) print(\"Linear regression Prediction =\",linearPrediction) Linear regression Prediction = [152.36331808 157.55282578 164.53078983 161.55977169 162.09729294 163.89553212 157.57236115 151.01464554 154.93363781 152.72493108 152.8812893 157.63099658 158.83309374 158.08056419 164.81420173 165.87946237 165.8990124 168.2054556 172.3003698 167.0033731 168.22500563 160.41632462 162.59571315 163.74894208 165.40059121] ## Visualize decision tree predictions¶ In : predictions = treePrediction valid = apple[x.shape:] valid[\"Predictions\"] = predictions plt.figure(figsize=(10, 6)) plt.title(\"Apple's Stock Price Prediction Model(Decision Tree Regressor Model)\") plt.xlabel(\"Days\") plt.ylabel(\"Close Price USD ($)\")\nplt.plot(apple[\"Close\"])\nplt.plot(valid[[\"Close\", \"Predictions\"]])\nplt.legend([\"Original\", \"Valid\", \"Predictions\"])\nplt.show()\n\n/.local/lib/python3.5/site-packages/ipykernel_launcher.py:3: SettingWithCopyWarning:\nA value is trying to be set on a copy of a slice from a DataFrame.\nTry using .loc[row_indexer,col_indexer] = value instead\n\nSee the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\nThis is separate from the ipykernel package so we can avoid doing imports until", null, "## Visualize the linear model predictions¶\n\nIn :\npredictions = linearPrediction\nvalid = apple[x.shape:]\nvalid[\"Predictions\"] = predictions\nplt.figure(figsize=(10, 6))\nplt.title(\"Apple's Stock Price Prediction Model(Linear Regression Model)\")\nplt.xlabel(\"Days\")\nplt.ylabel(\"Close Price USD (\\$)\")\nplt.plot(apple[\"Close\"])\nplt.plot(valid[[\"Close\", \"Predictions\"]])\nplt.legend([\"Original\", \"Valid\", \"Predictions\"])\nplt.show()\n\n/.local/lib/python3.5/site-packages/ipykernel_launcher.py:3: SettingWithCopyWarning:\nA value is trying to be set on a copy of a slice from a DataFrame.\nTry using .loc[row_indexer,col_indexer] = value instead\n\nSee the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\nThis is separate from the ipykernel package so we can avoid doing imports until", null, "" ]	[ null, "https://ris-ai.com/static/images/models/apple-stock-price.jpg", null, "https://ris-ai.com/static/images/models/apple-stock-price-prediction-decision-tree.jpg", null, "https://ris-ai.com/static/images/models/apple-stock-price-prediction-linear-regression.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.5449079,"math_prob":0.7580628,"size":7442,"snap":"2023-40-2023-50","text_gpt3_token_len":2509,"char_repetition_ratio":0.12557139,"word_repetition_ratio":0.16484849,"special_character_ratio":0.5640957,"punctuation_ratio":0.24297924,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96232045,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,1,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-04T00:58:10Z\",\"WARC-Record-ID\":\"<urn:uuid:981accf4-b328-417c-a7c9-6b70f08d70f0>\",\"Content-Length\":\"109930\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f3647447-f159-45d7-ade1-455e6c7c32c8>\",\"WARC-Concurrent-To\":\"<urn:uuid:697eb6ca-a226-4461-8fe1-1fd311fb377e>\",\"WARC-IP-Address\":\"68.66.226.100\",\"WARC-Target-URI\":\"https://ris-ai.com/stock-price-prediction-with-machine-learning\",\"WARC-Payload-Digest\":\"sha1:XYZDI5SNQSBMVLEHDULNJKUJIED2QOQF\",\"WARC-Block-Digest\":\"sha1:OMHUPE6QGFQVKGNYWBV6Y62EIDGHHBPT\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100518.73_warc_CC-MAIN-20231203225036-20231204015036-00775.warc.gz\"}"}
https://www.cuemath.com/ncert-solutions/q-1-exercise-2-1-linear-equations-in-one-variable-class-8-maths/	[ "In the verge of coronavirus pandemic, we are providing FREE access to our entire Online Curriculum to ensure Learning Doesn't STOP!\n\n# EX.2.1 Q1 Linear Equations in One Variable Solutions - NCERT Maths Class 8\n\nGo back to 'Ex.2.1'\n\n## Question\n\nSolve the equation:\n\n$x- 2= 7$\n\nVideo Solution\nLinear Equations\nEx 2.1 \| Question 1\n\n## Text Solution\n\nWhat is known?\n\nEquations\n\nWhat is unknown?\n\nValue of the variable\n\nReasoning:\n\nIn an equation values of left-hand side (LHS) and right-hand side (RHS) are equal. The two sides of the equation are balanced. We perform mathematical operations so that the balance is not disturbed.\n\nSteps:\n\n$x- 2= 7$\n\nTransposing ($$-2$$) to RHS we get:\n\n\\begin{align}x &= {\\rm{7}} + {\\rm{ 2 }}\\\\\\text{ }\\!\\!~\\!\\!\\text{ }x&=9\\end{align}\n\nLearn from the best math teachers and top your exams\n\n• Live one on one classroom and doubt clearing\n• Practice worksheets in and after class for conceptual clarity\n• Personalized curriculum to keep up with school" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6960701,"math_prob":0.9881968,"size":613,"snap":"2020-10-2020-16","text_gpt3_token_len":197,"char_repetition_ratio":0.124794744,"word_repetition_ratio":0.0,"special_character_ratio":0.31973898,"punctuation_ratio":0.14285715,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9905456,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-04-06T21:50:27Z\",\"WARC-Record-ID\":\"<urn:uuid:410d9005-5c73-48b8-a958-6738c08dfe0d>\",\"Content-Length\":\"104947\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2ffe72d6-2af1-4c30-bd5f-c19cc2cc14cd>\",\"WARC-Concurrent-To\":\"<urn:uuid:6b4c62e6-42ed-4ddb-9eba-c25655b09a67>\",\"WARC-IP-Address\":\"13.251.150.116\",\"WARC-Target-URI\":\"https://www.cuemath.com/ncert-solutions/q-1-exercise-2-1-linear-equations-in-one-variable-class-8-maths/\",\"WARC-Payload-Digest\":\"sha1:CWDSPXD66ASQHTZC7YQYWTFSFEKCMCJ6\",\"WARC-Block-Digest\":\"sha1:ZZPHSMDZMFYKNO747UNUC2C5C5MUUQYE\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-16/CC-MAIN-2020-16_segments_1585371660550.75_warc_CC-MAIN-20200406200320-20200406230820-00066.warc.gz\"}"}
https://factorization.info/factors/factor-calculator.html	[ "Factor Calculator", null, "We have all the information you will ever need about the factors of any number. We will provide you with the definition of factors of your number, show you how to find the factors of your number, and give you all the factors of your number.\n\nNot only that, but we will also count the factors of your number and show you the factor pairs of your number to prove that our answer is solved correctly.\n\nTo get the factors for any number, please submit it below.\n\nHere are some examples what we can explain and calculate for you:" ]	[ null, "https://factorization.info/images/factors-of.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9165718,"math_prob":0.9776453,"size":589,"snap":"2023-40-2023-50","text_gpt3_token_len":119,"char_repetition_ratio":0.21025641,"word_repetition_ratio":0.0,"special_character_ratio":0.20373514,"punctuation_ratio":0.07826087,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9590441,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-25T17:01:42Z\",\"WARC-Record-ID\":\"<urn:uuid:27cc842e-b790-4c99-a753-049599701eda>\",\"Content-Length\":\"8074\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a781f45c-cbf8-4d23-8cfa-cb997e251e1c>\",\"WARC-Concurrent-To\":\"<urn:uuid:7f5bf6d1-3d9b-4a5b-a647-f8c9b4d7b7fc>\",\"WARC-IP-Address\":\"18.67.65.63\",\"WARC-Target-URI\":\"https://factorization.info/factors/factor-calculator.html\",\"WARC-Payload-Digest\":\"sha1:F7ZWR46WY5VWAJCSRNYX2BHCYIC4U4XZ\",\"WARC-Block-Digest\":\"sha1:TQOMQGL5I4MKLDGGDWRNDIJP3YJMI6H5\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233509023.57_warc_CC-MAIN-20230925151539-20230925181539-00320.warc.gz\"}"}