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https://liujiacai.net/blog/2022/11/17/yes-in-zig/	[ "## 初始版\n\n `````` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 `````` ``````const std = @import(\"std\"); pub fn main() !void { const argv = std.os.argv; const output: []const u8 = if (argv.len > 1) argv.ptr[0..std.mem.len(argv.ptr)] else \"y\"; const out = std.io.getStdOut(); var f = out.writer(); // var f = std.io.bufferedWriter(out.writer()); while ((try f.write(output)) > 0) { _ = try f.write(\"\\n\"); } }``````\n\n ``````1 2 `````` ``````zig build-exe yes.zig -Drelease-safe ./yes \| pv -r > /dev/null``````\n\n## BufferedWriter 版本\n\n `````` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 `````` ``````const std = @import(\"std\"); pub fn main() !void { const argv = std.os.argv; const output: []const u8 = if (argv.len > 1) argv.ptr[0..std.mem.len(argv.ptr)] else \"y\"; const out = std.io.getStdOut(); var f = std.io.bufferedWriter(out.writer()); while ((try f.write(output)) > 0) { _ = try f.write(\"\\n\"); } }``````\n\n## 复用 Buffer 版本\n\n `````` 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 `````` ``````const std = @import(\"std\"); const BUFFER_CAP = 4 * 1024; fn fillBuffer(buf: []u8, output: []const u8) []const u8 { if (output.len + 1 > buf.len / 2) { // plus one newline return output; } std.mem.copy(u8, buf, output); std.mem.copy(u8, buf[output.len..], \"\\n\"); var buffer_size = output.len + 1; while (buffer_size < buf.len / 2) { std.mem.copy(u8, buf[buffer_size..], buf[0..buffer_size]); buffer_size *= 2; } return buf[0..buffer_size]; } pub fn main() !void { const argv = std.os.argv; const output: []const u8 = if (argv.len > 1) argv.ptr[0..std.mem.len(argv.ptr)] else \"y\"; var buffer: [BUFFER_CAP]u8 = undefined; const body = fillBuffer(&buffer, output); const stdout = std.io.getStdOut(); var writer = stdout.writer(); while ((try writer.write(body)) > 0) {} }``````" ]	[ null ]	{"ft_lang_label":"__label__zh","ft_lang_prob":0.97058606,"math_prob":0.912998,"size":604,"snap":"2022-40-2023-06","text_gpt3_token_len":485,"char_repetition_ratio":0.11666667,"word_repetition_ratio":0.0,"special_character_ratio":0.2781457,"punctuation_ratio":0.04901961,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9641593,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-02-08T20:39:33Z\",\"WARC-Record-ID\":\"<urn:uuid:cd25b07d-1832-4ed4-97a8-ae43d09602f7>\",\"Content-Length\":\"41154\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0b4cfe60-9f0d-41bb-a509-1da3063ea20f>\",\"WARC-Concurrent-To\":\"<urn:uuid:dcadcb93-6056-4812-a452-e6fbf74fc5ef>\",\"WARC-IP-Address\":\"185.199.111.153\",\"WARC-Target-URI\":\"https://liujiacai.net/blog/2022/11/17/yes-in-zig/\",\"WARC-Payload-Digest\":\"sha1:5SK3RY6FCXREROSML2UPIZQ7GVXC6IDP\",\"WARC-Block-Digest\":\"sha1:SVPRNPYJEQPGWJXTQFOP2KORJGZBJKGH\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-06/CC-MAIN-2023-06_segments_1674764500904.44_warc_CC-MAIN-20230208191211-20230208221211-00492.warc.gz\"}"}
https://jeeneetqna.in/1576/1-i2-h2o2-2oh-2i-2h2o-o2-2-h2o2-hocl-cl-h3o-o2	[ "# (1) I2 + H2O2 + 2OH− ⟶ 2I− + 2H2O + O2 (2) H2O2 + HOCl ⟶ Cl− + H3O+ + O2\n\nmore_vert\n\n(1) $\\require{mhchem}\\ce{I2 +H2O2 +2OH- -> 2I- +2H2O +O2}$\n\n(2) $\\ce{H2O2 +HOCl->Cl- +H3O+ +O2}$\n\n(1) H2O2 is acting as oxidising agent in both the reaction\n\n(2) H2O2 is acting as reducing agent in both the reaction\n\n(3) H2O2 is acting as oxidising agent in reaction (1) and as reducing agent in reaction (2)\n\n(4) H2O2 is acting as reducing agent in reaction (1) and as oxidising agent in reaction (2)" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9540445,"math_prob":0.99576175,"size":396,"snap":"2023-40-2023-50","text_gpt3_token_len":152,"char_repetition_ratio":0.20918368,"word_repetition_ratio":0.33846155,"special_character_ratio":0.36868685,"punctuation_ratio":0.0,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9629631,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-26T02:55:55Z\",\"WARC-Record-ID\":\"<urn:uuid:291f476e-e2e0-495d-bf7e-0a41c94d42d1>\",\"Content-Length\":\"38873\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:16e7dbd0-5667-4b15-b496-8332014602de>\",\"WARC-Concurrent-To\":\"<urn:uuid:e615dcfa-6d17-4c0b-a337-f7ecfe088182>\",\"WARC-IP-Address\":\"13.126.157.14\",\"WARC-Target-URI\":\"https://jeeneetqna.in/1576/1-i2-h2o2-2oh-2i-2h2o-o2-2-h2o2-hocl-cl-h3o-o2\",\"WARC-Payload-Digest\":\"sha1:YHMEPHS3XNRL3ZV552FQ64XWCSK3IANR\",\"WARC-Block-Digest\":\"sha1:VEDFNJMHEV7AEH6BZR4JJCJBOY3EN5LD\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510130.53_warc_CC-MAIN-20230926011608-20230926041608-00348.warc.gz\"}"}
https://www.k8mathsense.com/blog_f01	[ "", null, "", null, "Why are fractions on the number line often difficult? Can your students name locations with numbers? They must understand three essential concepts.\n\nThree Essential Concepts\n\n1\nPoints represent distance from zero, based on the scale of the number line. Equal distances must represent equal amounts. You may need to divide to find the scale, or interval between 0 and the first tick mark.\n2\nCount or skip count by tick marks on the line, not the spaces between them. This is important because the tick stand for specific numbers but there are many numbers between ticks, including fractions. Count or skip count starting with 0.\n3\nInsert more equally spaced tick marks to identify points between tick marks. Notice that inserting one new tick between ticks doubles the number of intervals. Inserting two new ticks between ticks triples the number of intervals.", null, "For practice with fractions on the number line, see the FREE online activity on the E-Games page. This page also shows links to printable games." ]	[ null, "https://ct.pinterest.com/v3/", null, "https://www.k8mathsense.com/assets/images/blog/number_line_pin_lt.jpg", null, "https://www.k8mathsense.com/assets/images/blog/num_line_examples.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.92397034,"math_prob":0.9842422,"size":1194,"snap":"2021-43-2021-49","text_gpt3_token_len":247,"char_repetition_ratio":0.1394958,"word_repetition_ratio":0.0,"special_character_ratio":0.19849247,"punctuation_ratio":0.09777778,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9555109,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,null,null,3,null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-21T04:55:32Z\",\"WARC-Record-ID\":\"<urn:uuid:8aa3819a-a4b4-4cdb-818d-1cd4376cd68d>\",\"Content-Length\":\"34327\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:fd8e79a8-2586-4147-99a5-db4fa75def23>\",\"WARC-Concurrent-To\":\"<urn:uuid:08f5b522-1ab9-41a9-931c-cbec184e4544>\",\"WARC-IP-Address\":\"104.19.178.121\",\"WARC-Target-URI\":\"https://www.k8mathsense.com/blog_f01\",\"WARC-Payload-Digest\":\"sha1:BRBNH3JWFALU7RXPP5INLIYQWEEB3SPB\",\"WARC-Block-Digest\":\"sha1:6TR5DPSRYO3QJDMOWNUO4IQS6LA5JB3V\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323585381.88_warc_CC-MAIN-20211021040342-20211021070342-00516.warc.gz\"}"}
https://www.apurvainstitute.in/study-materials/ncert-solutions/chapters/home.php?tab=ncert_book&class=10&subject=Mathematics&medium=english&chapter=4.%20Quadratic%20Equations&page=2	[ "Study Materials\n\n# NCERT Solutions for Class 10th Mathematics\n\nPage 2 of 4\n\n### Exercise 4.2\n\nExercise: 4.2\n\nQ1. Find the roots of the following quadratic equations by factorisation:\n\n(i) x2 - 3x - 10 = 0,\n\nSolution:\n\nx2 - 3x - 10 = 0\n\n⇒x2 - 5x + 2x - 10 = 0\n\n⇒ x( x - 5 ) + 2(x - 5) = 0\n\n⇒( x - 5 ) (x + 2) = 0\n\n⇒( x - 5 ) = 0, (x + 2) = 0\n\n x - 5 = 0 x = 5 x + 2 = 0 x = - 2\n\n(ii) 2x2 + x - 6 = 0;\n\nSolution:\n\n2x2 + x - 6 = 0\n\n⇒2x2 + 4x - 3x - 6 = 0\n\n⇒ 2x( x + 2 ) - 3(x + 2) = 0\n\n⇒( x + 2 ) (2x - 3) = 0\n\n⇒( x + 2 ) = 0, (2x - 3) = 0\n\nx + 2 = 0\n\nx = - 2\n\n2x - 3 = 0\n\n2x = 3\n\n x = 3 2\n\n(iii) √2x2 + 7x + 5√2 = 0;\n\nSolution:\n\n√2x + 2x + 5x + 5√2 = 0\n\n√2x(x + √2) + 5(x + √2) = 0\n\n(x + √2) (√2x + 5) = 0;\n\n(x + √2) = 0, (√2x + 5) = 0\n\nx = - √2, √2x = - 5\n\nx = - 5/√2\n\nx = -5√2/2\n\n(iv) 2x2 - x + 1/8 =0\n\nSolution:\n\n 2x2 - x + 1 = 0 8\n\nOr ⇒16x2 - 8x + 1 = 0;\n\n⇒16x2 - 4x - 4x + 1 = 0\n\n⇒ 4x( 4x - 1 ) - 1(4x - 1) = 0\n\n⇒( 4x - 1 ) (4x - 1) = 0\n\n⇒( 4x - 1 ) = 0, (4x - 1) = 0\n\n4x - 1 = 0\n\n4x = 1\n\n x = 1 4\n\n4x - 1 = 0\n\n4x = 1\n\n x = 1 4\n\n(v) 100x2 - 20x + 1 = 0;\n\nSolution:\n\n100x2 - 20x + 1 = 0\n\n⇒100x2 - 10x - 10x + 1 = 0\n\n⇒ 10x( 10x - 1 ) - 1(10x - 1) = 0\n\n⇒( 10x - 1 ) (10x - 1) = 0\n\n⇒( 10x - 1 ) = 0, (10x - 1) = 0\n\n10x - 1 = 0\n\n10x = 1\n\n x = 1 10\n\n10x - 1 = 0\n\n10x = 1\n\n x = 1 10\n\nQ2. Solve the problems given in Example 1.\n\nExample1:\n\n(i) John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. We would like to find out how many marbles they had to start with.\n\n(ii) A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs 750. We would like to find out the number of toys produced on that day.\n\nQ3. Find two numbers whose sum is 27 and product is 182.\n\nQ4. Find two consecutive positive integers, sum of whose squares is 365.\n\nQ5. The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.\n\nQ6. A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs 90, find the number of articles produced and the cost of each article.\n\nPage 2 of 4\n\nChapter Contents:" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.89995176,"math_prob":1.0000067,"size":2345,"snap":"2021-21-2021-25","text_gpt3_token_len":1100,"char_repetition_ratio":0.14651859,"word_repetition_ratio":0.1763754,"special_character_ratio":0.49850747,"punctuation_ratio":0.09369025,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9998629,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-05-13T02:50:48Z\",\"WARC-Record-ID\":\"<urn:uuid:8d43bace-49f7-43d1-a50b-ec0685a369e0>\",\"Content-Length\":\"40305\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:67278701-f17f-4d24-b311-a72d77812964>\",\"WARC-Concurrent-To\":\"<urn:uuid:d9a2415d-186b-4ea1-a07d-248f27488748>\",\"WARC-IP-Address\":\"148.66.137.24\",\"WARC-Target-URI\":\"https://www.apurvainstitute.in/study-materials/ncert-solutions/chapters/home.php?tab=ncert_book&class=10&subject=Mathematics&medium=english&chapter=4.%20Quadratic%20Equations&page=2\",\"WARC-Payload-Digest\":\"sha1:TBDBREI6DN4OMHEPIUUQJG6BDD576DOG\",\"WARC-Block-Digest\":\"sha1:PPZR4N3COUKEDQQJVSFN7WBWPDQKRRRB\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-21/CC-MAIN-2021-21_segments_1620243992721.31_warc_CC-MAIN-20210513014954-20210513044954-00027.warc.gz\"}"}
https://www.scribd.com/doc/289485924/Method-of-Slices-Slope-Analysis	[ "You are on page 1of 21\n\n# GLE/CEE 330: Soil Mechanics\n\n## Slope Stability Analysis:\n\nMethod of Slices\n\nGeological Engineering\n\nLearning Objectives\nDiscuss when rotational slope analysis may be\nappropriate\nLearn basic analysis approaches\nDescribe example problems for ordinary method\nof slices (OMS) and modified Bishops method\n\n## (La Conchita, CA, USGS)\n\n(Varnes)\n\nLandslide in Thailand\n\n## t Equilibrium: 1) Assume some circular (or other shape) failure surface\n\n2) Calculate driving forces (moment about O)\n3) Calculate resisting forces (moment about O)\n\nssues:\nWhere is the center of mass?\nHow does resistance vary along surface?\nHow does normal stress vary along surface?\nWater table and seepage forces?\nSoil layering?\nMore complex geometry?\n\n## ume some failure surface\n\ncretize failure surface into smaller elements (slices)\ntom of each slice passes through one type of material\nved bottom of each slice approximated as chord\ne slices = more refined solution\n40 slices typically sufficient (less for hand solutions)\nculate factor of safety for each slice (strength/stress) and overall factor of safety\nd lowest FS for different failure surfaces\n\nOMS\n\nModified Bishops\n\n## Side forces neglected (statically\n\ndeterminant)\nEffective Stress Analysis (ESA)\n\n## Total Stress Analysis (TSA)\n\nExample 1\nCompute the long term factor of safety for the failure surface using the OMS\n\n## Divide into slices (draw to scale)\n\n2) Compute weights\n\n## glecting side forces (OMS) produces FS too low (conservative)\n\nume side shear forces are zero but account for side normal forces\n\n## glecting side forces (OMS) produces FS too low (conservative)\n\nume side shear forces are zero but account for side normal forces\n\n## Total Stress Analysis (TSA)\n\nExample 2\n\nmpute the long term FS for the failure surface using the Modified Bishops Metho\n\n## S = 2,206/1,071 = 2.05 (too high)\n\n3) Trial FS = 2.10" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.87866044,"math_prob":0.8091555,"size":973,"snap":"2019-51-2020-05","text_gpt3_token_len":208,"char_repetition_ratio":0.095975235,"word_repetition_ratio":0.1594203,"special_character_ratio":0.17471737,"punctuation_ratio":0.089171976,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9665432,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-11T00:34:30Z\",\"WARC-Record-ID\":\"<urn:uuid:adf89547-07f3-4940-844d-dca5329ed542>\",\"Content-Length\":\"214380\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:69ce5d35-793e-40b8-a991-2c4c99e8051f>\",\"WARC-Concurrent-To\":\"<urn:uuid:151c4f8f-878f-4b09-a8b7-b96e8303af00>\",\"WARC-IP-Address\":\"151.101.250.152\",\"WARC-Target-URI\":\"https://www.scribd.com/doc/289485924/Method-of-Slices-Slope-Analysis\",\"WARC-Payload-Digest\":\"sha1:J4KKYK4RE3O6PD74PS4JUQGVEMQJ2KBP\",\"WARC-Block-Digest\":\"sha1:QYQYJ7PXDFOIGM2VCRULNS6RQ4CSDMOV\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575540529516.84_warc_CC-MAIN-20191210233444-20191211021444-00347.warc.gz\"}"}
https://www.studyvirus.com/set-8-alphanumeric-series-for-sbi-po-and-sbi-clerk-2019-must-go-through-these-questions/	[ "Set-8 Alphanumeric Series For SBI PO and SBI Clerk 2019 \| Must Go Through These Questions", null, "Dear Aspirants,\nWe are providing the most important Alphanumeric Series Questions for SBI PO 2019, SBI Clerk 2019 and all other competitive bank and insurance exams. These questions have very high chances to be asked in SBI PO 2019, SBI Clerk 2019.\nGet the Best Test Series for SBI PO 2019 at the most affordable price (Based on Real Exam Pattern) – Click Here\nDownload the Best GK Gaming App for Current Affairs and GK (Bank+SSC)– Click here (App No 1) (App No 2)\n\nDirections:(1-5) Study the following arrangement carefully and answer the questions given below—", null, "1. How many such prime numbers are there in the given arrangement each of which is immediately followed by a symbol and preceded by a consonant?\n\n2. If the places of the those symbols which are immediately followed by numbers are interchanged with those of the numbers in the given arrangement then which of the following will be the eleventh from the right end?", null, "3. Which of the following is the seventh letter to the left of ©?", null, "4.", null, "What should come in place of the question mark (?) in the following series based on the above arrangement?", null, "5. If the symbols and numbers are dropped from the given arrangement and then the letters are rearranged in alphabetical order which of the following will be the sixth from the left end?", null, "Directions:(6-10) Study the following elements (letters, digits and symbols sequence) to answer the questions given below:", null, "6. If each symbol of the above sequence is replaced with a letter and each digit is replaced with a new symbol, then how many letters will be there in the sequence?\n\n7. How many such digits are there in the sequence each of which is immediately preceded as well as followed by letters ?", null, "8. Which of the following letters is exactly midway between the letters falling between ‘C’ and ‘5’?", null, "9. If each symbol of the above sequence is replaced with the digits from ‘1’ to ‘9’ which are not there in the sequence, then what will be the sum of all digits ? [Each symbol should be replaced with a different digit.]", null, "10. How many letters to the left of the one who is 3rd right of S?", null, "• Directions:(1-5) Study the following arrangement carefully and answer the questions given below—", null, "1. Question\nHow many such prime numbers are there in the given arrangement each of which is immediately followed by a symbol and preceded by a consonant?\nAns:1\nThere is no such combination.\n\n• 2. Question\nStudy the following arrangement carefully and answer the questions given below—", null, "If the places of the those symbols which are immediately followed by numbers are interchanged with those of the numbers in the given arrangement then which of the following will be the eleventh from the right end?\nAns:3\nAccording to condition answer will be 4.\n\n• 3. Question\nStudy the following arrangement carefully and answer the questions given below—", null, "Which of the following is the seventh letter to the left of ©?\nAns:3\nThe seventh letter to the left of © is R.\n\n• 4. Question\nStudy the following arrangement carefully and answer the questions given below—", null, "What should come in place of the question mark (?) in the following series based on the above arrangement?", null, "Ans:4\nG#T\n\n• 5. Question\nStudy the following arrangement carefully and answer the questions given below—", null, "If the symbols and numbers are dropped from the given arrangement and then the letters are rearranged in alphabetical order which of the following will be the sixth from the left end?\nAns:5\nThe letter will be R.\n\n• Directions:(6-10) Study the following elements (letters, digits and symbols sequence) to answer the questions given below:", null, "6. Question\nIf each symbol of the above sequence is replaced with a letter and each digit is replaced with a new symbol, then how many letters will be there in the sequence?\nAns:1\nThere are 21 elements in the series. Among them, there are only 5 digits. Since symbols are replaced by letters and digits are replaced by symbols, ultimately there will be (21 – 5 =) 16 letters in the series.\n\n• 7. Question\nStudy the following elements (letters, digits and symbols sequence) to answer the questions given below:", null, "How many such digits are there in the sequence each of which is immediately preceded as well as followed by letters ?\nAns:4", null, "• 8. Question\nStudy the following elements (letters, digits and symbols sequence) to answer the questions given below:", null, "Which of the following letters is exactly midway between the letters falling between ‘C’ and ‘5’?\nAns:3\nThe letters falling between C and 5 are as follows:\nDZY PMKS. Hence, P is the required letter.\n\n• 9. Question\nStudy the following elements (letters, digits and symbols sequence) to answer the questions given below:", null, "If each symbol of the above sequence is replaced with the digits from ‘1’ to ‘9’ which are not there in the sequence, then what will be the sum of all digits ? [Each symbol should be replaced with a different digit.]\nAns:2\nIf the four symbols are replaced by the remaining digits from 1 to 9 (1, 4, 6, 8) then sum of the digits", null, "", null, "• 10. Question\nStudy the following elements (letters, digits and symbols sequence) to answer the questions given below:", null, "How many letters to the left of the one who is 3rd right of S?\nAns:2\nThere is only 10 letters to the left of 5 that is the 3rd right of S.", null, "" ]	[ null, "https://www.studyvirus.com/wp-content/uploads/2019/04/Alpha-numeric-1.jpg", null, "http://www.studyvirus.com/wp-content/uploads/2018/03/2-1-300x21.png", null, "http://www.studyvirus.com/wp-content/uploads/2018/03/2-1-300x21.png", null, "http://www.studyvirus.com/wp-content/uploads/2018/03/2-1-300x21.png", null, "http://www.studyvirus.com/wp-content/uploads/2018/03/2-1-300x21.png", null, "http://www.studyvirus.com/wp-content/uploads/2018/03/1-1780.png", null, "http://www.studyvirus.com/wp-content/uploads/2018/03/2-1-300x21.png", null, "http://www.studyvirus.com/wp-content/uploads/2018/03/1-1775-300x31.png", null, "http://www.studyvirus.com/wp-content/uploads/2018/03/1-1775-300x31.png", null, "http://www.studyvirus.com/wp-content/uploads/2018/03/1-1775-300x31.png", null, "http://www.studyvirus.com/wp-content/uploads/2018/03/1-1775-300x31.png", null, "http://www.studyvirus.com/wp-content/uploads/2018/03/1-1775-300x31.png", null, "http://www.studyvirus.com/wp-content/uploads/2018/03/2-1-300x21.png", null, "http://www.studyvirus.com/wp-content/uploads/2018/03/2-2-300x21.png", null, "http://www.studyvirus.com/wp-content/uploads/2018/03/2-3-300x21.png", null, "http://www.studyvirus.com/wp-content/uploads/2018/03/2-4-300x21.png", null, "http://www.studyvirus.com/wp-content/uploads/2018/03/1-1780.png", null, "http://www.studyvirus.com/wp-content/uploads/2018/03/2-5-300x21.png", null, "http://www.studyvirus.com/wp-content/uploads/2018/03/1-1775-300x31.png", null, "http://www.studyvirus.com/wp-content/uploads/2018/03/1-1776-300x31.png", null, "http://www.studyvirus.com/wp-content/uploads/2018/03/2-55-300x24.png", null, "http://www.studyvirus.com/wp-content/uploads/2018/03/1-1776-300x31.png", null, "http://www.studyvirus.com/wp-content/uploads/2018/03/1-1776-300x31.png", null, "http://www.studyvirus.com/wp-content/uploads/2018/03/1-1778.png", null, "http://www.studyvirus.com/wp-content/uploads/2018/03/3-39-300x55.png", null, "http://www.studyvirus.com/wp-content/uploads/2018/03/1-1777-300x31.png", null, "https://secure.gravatar.com/avatar/3b59581d03b40df50ecadef43339ade3", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.93304825,"math_prob":0.8657514,"size":4817,"snap":"2019-43-2019-47","text_gpt3_token_len":1084,"char_repetition_ratio":0.18533139,"word_repetition_ratio":0.531401,"special_character_ratio":0.22482873,"punctuation_ratio":0.09660297,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9883559,"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,null,null,null,null,null,null,null,null,null,null,4,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2,null,2,null,2,null,4,null,2,null,null,null,6,null,2,null,6,null,6,null,2,null,2,null,2,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-23T20:18:20Z\",\"WARC-Record-ID\":\"<urn:uuid:83b16d42-e7bb-4d93-9308-dd2bdabc7294>\",\"Content-Length\":\"85583\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1db62cfa-e877-4fad-b1cc-ac9d34242672>\",\"WARC-Concurrent-To\":\"<urn:uuid:1fc784e3-382a-4e47-86df-270556388421>\",\"WARC-IP-Address\":\"67.205.40.38\",\"WARC-Target-URI\":\"https://www.studyvirus.com/set-8-alphanumeric-series-for-sbi-po-and-sbi-clerk-2019-must-go-through-these-questions/\",\"WARC-Payload-Digest\":\"sha1:32W2NMG5JCUN4DGRJE3OBF3BX6RVXOH3\",\"WARC-Block-Digest\":\"sha1:3VLPEKYJM62CKV3PVYY2LCYBC7ZWQLUW\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570987836295.98_warc_CC-MAIN-20191023201520-20191023225020-00493.warc.gz\"}"}
https://encyclopedia2.thefreedictionary.com/Random+function	[ "Random Function\n\nAlso found in: Wikipedia.\n\nrandom function\n\n[′ran·dəm ′fəŋk·shən]\n(mathematics)\nA function whose domain is an interval of the extended real numbers and has range in the set of random variables on some probability space; more precisely, a mapping of the cartesian product of an interval in the extended reals with a probability space to the extended reals so that each section is a random variable.\n\nRandom Function\n\nIf a function of an arbitrary argument t is defined on the set T of the values of t and assumes numerical values or, more generally, values from some vector space, the function is said to be a random function if its values are determined by some trial and can differ depending on the outcome of the trial. It is also required that there exist a definite probability distribution function for the values. If the set T is finite, the random function is a finite set of random variables; this set can be regarded as a single random vector quantity.\n\nThe most thoroughly studied random function with an infinite T is the important special case where t assumes numerical values and is time. The random function X(t) in this case is called a stochastic process; when t assumes only integral values, the terms “random sequence” and “time series” are also sometimes applied to X(t). If the values of t are points in some region of a multidimensional space, the random function is called a random field. Typical examples of random functions that are not stochastic processes are the velocity, pressure, and temperature fields of a turbulent flow of a liquid or gas and the height z of the agitated surface of the sea or the surface of an artificial rough plate.\n\nThe mathematical theory of random functions coincides with the theory of probability distribution functions in the function space of the values of X(t). These distribution functions can be specified by the set of finite-dimensional probability distribution functions for the sets of random variables X(t1), X(t2), …, X(tn) corresponding to all possible finite subsets (t1, t2,…, tn) of points of T. Alternatively, the distribution functions can be specified by the characteristic functional of the random function X(t); this characteristic functional is the mathematical expectation of the random variable il[X(t)], where l[X(t)] is a linear functional of X(t) of general form. Much progress has been made in the theory of homogeneous random fields, which are a special class of random functions; this class is a generalization of the class of stationary stochastic processes.\n\nREFERENCES\n\nVybrosy sluchainykh polei: Sb. st. Moscow, 1972.\nYaglom (Iaglom), A. M. “Second-order Homogeneous Random Fields.” In Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, vol. 2. Berkeley-Los Angeles, 1961.\nWhittle, P. “Stochastic Processes in Several Dimensions.” Bulletin of the Institute of Statistics, 1963, vol. 40.\n\nA. M. IAGLOM\n\nReferences in periodicals archive ?\nMany researches on NIZK have been proposed to improve its efficiency, for example, from the earlier work, such as the Fiat-Shamir heuristic where the cryptographic hash function is introduced as a random function; recent works such as Lindell's transform of non-programmable random oracle (NPRO) model that needs no random oracles to achieve efficient NIZK arguments in the common reference string (CRS) model, and Ciampi's work which combines each own's advantage of both without a random oracle.\nDCF algorithm utilized the random function in the binary exponential backoff algorithm to produce the values of backoff.\nThe right-hand side of (1), F(t), is assumed to be a time-dependent random function that depends linearly on [[omega].sub.2] and expressed by\nIn this paper, the method of decomposing data by random function is proposed.\nFor a random function f : [[0, [infinity]).sub.T] x [OMEGA] [right arrow] R we define the extension [??] : [0, [infinity]) x [OMEGA] [right arrow] R by\nThe pattern generator selects at random pattern by using a random function with various rules given.\nLiu, \"Simulation of stochastic ocean states by random function methods,\" Journal of Vibration and Shock, vol.\nAn example for such random function f (i, j) to generate the Metadata M is\nIf any of the functional parameters are considered to be random, then analysed function itself is consequently also a random function. The general stochastic formulation of the reliability-based optimization problem can be expressed like this:\nAll the valid lottery tickets and the winning numbers must be verified via a verifiable random function.\nAs it is well known, a random field [PHI](x) is a 2-dimensional, real-valued random function. The function [PHI](x) is called macroscopically homogeneous (or stationary in the strict sense), if [PHI](x) is invariant with respect to translations, i.e., its finite-dimensional distributions are translation invariant.\n\nSite: Follow: Share:\nOpen / Close" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.81888545,"math_prob":0.98792225,"size":2602,"snap":"2019-43-2019-47","text_gpt3_token_len":560,"char_repetition_ratio":0.17090069,"word_repetition_ratio":0.014634146,"special_character_ratio":0.20599538,"punctuation_ratio":0.116564415,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.998038,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-21T15:12:00Z\",\"WARC-Record-ID\":\"<urn:uuid:fa7f41aa-426d-4474-9c4d-29a8e7ff122b>\",\"Content-Length\":\"50373\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4734ef24-4843-4dd7-9d66-7e218dd79172>\",\"WARC-Concurrent-To\":\"<urn:uuid:3a969ddc-001a-4e8f-b87e-3d2cbd276ab7>\",\"WARC-IP-Address\":\"209.160.67.6\",\"WARC-Target-URI\":\"https://encyclopedia2.thefreedictionary.com/Random+function\",\"WARC-Payload-Digest\":\"sha1:ZJQ2IOSWOUZVXX5VQZTRF54CD2ME3DB5\",\"WARC-Block-Digest\":\"sha1:HAG6ECCVXRCN5KN6QU6CKDNX72JEZ44S\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570987779528.82_warc_CC-MAIN-20191021143945-20191021171445-00267.warc.gz\"}"}
https://ca.answers.yahoo.com/question/index?qid=20090724133817AATfPlW	[ "# 8 Choices, 4 spots = number of options?\n\nThere is a commercial airing right now about a fast food chain having 8 menu items to choose from, pick four. You can pick the same item 1, 2, 3, even 4 times. The commercial claims that there are 320 possibilities. How so? My numbers are huge...\n\nRelevance\n\nLet C(n,k) be the binomial coefficient n!/k!(n-k)! (C(n,k) is the number of ways to select k things from n things, when order doesn't matter). Clearly, you want to use C(n,k), since your meal doesn't depend on the order in which you choose the menu items. (In case you're unfamiliar with the notation, n! = n(n-1)(n-2)...1).\n\nThe number of ways to pick 4 items is C(8,4) = 70\n\nThe number of ways to pick 3 items is 3C(8,3) = 168 (there are 3 ways in each choice to choose which item is doubled)\n\nThe number of ways to pick 2 items where one item is tripled is 2C(8,2) = 56.\n\nThe number of ways to pick 2 items where each item is doubled is C(8,2) = 28.\n\nThe number of ways to pick 1 item, quadrupled, is C(8,1) = 8.\n\nAdding these all together, the total is 330, so they were close. If the numbers you're getting are much bigger, it could be because you're counting the order in which the items are chosen.\n\nHope this helps (& please don't hold me responsible for any errors in arithmetic -- it's late).\n\nSource(s): just me.\n•", null, "Login to reply the answers" ]	[ null, "https://ct.yimg.com/cy/1768/39361574426_98028a_128sq.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.93480337,"math_prob":0.9816348,"size":1370,"snap":"2020-24-2020-29","text_gpt3_token_len":383,"char_repetition_ratio":0.15519765,"word_repetition_ratio":0.0627451,"special_character_ratio":0.29854015,"punctuation_ratio":0.14814815,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98771083,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-07-10T13:30:30Z\",\"WARC-Record-ID\":\"<urn:uuid:989663fa-f570-44f6-a7a1-d934dd575ac4>\",\"Content-Length\":\"79416\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6d03baed-2846-4326-8d06-fa4088fcde4b>\",\"WARC-Concurrent-To\":\"<urn:uuid:598126c5-4bec-4a50-8cdb-e8fde6c4b525>\",\"WARC-IP-Address\":\"76.13.32.153\",\"WARC-Target-URI\":\"https://ca.answers.yahoo.com/question/index?qid=20090724133817AATfPlW\",\"WARC-Payload-Digest\":\"sha1:RDQQJHCCH37YW6V7CSOCU27H7GFDKGXX\",\"WARC-Block-Digest\":\"sha1:75TEIVYPBGCGVBV73LV5EDXDSKQOMGDF\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-29/CC-MAIN-2020-29_segments_1593655908294.32_warc_CC-MAIN-20200710113143-20200710143143-00018.warc.gz\"}"}
https://needhamia.com/dog-weight-scale-part-7-choosing-matching-resistors/	[ "", null, "# Dog Weight Scale Part 7: Choosing Matching Resistors\n\nIn my previous post, I worked through the calculations of weight and center of gravity when using four Load Cell Amplifiers instead of one. In this post, I build the circuit for the first of the four Load Sensor / Load Cell Amplifier combinations I’ll be using.\n\nThe Sparkfun Load Cell Amplifier is designed to connect a Load Cell to an Arduino. A Load Cell contains a full (4 resistor) Wheatstone Bridge, but a Load Sensor contains only half of a Wheatstone bridge. To connect a Load Sensor to a Load Cell Amplifier, I need to add two resistors: R3 and R4 in the following diagram. The dotted box represents the Load Sensor. The triangle in the middle of the diagram represents the Load Cell Amplifier. As the weight on the Load Sensor increases, R1 decreases, which causes the voltage V1 to increase, causing the digitized amplifier output to increase.\n\nOnce I’d built the circuit, the next task was to find the right pair of resistors, R3 and R4. In the photo below, R3 and R4 are the two resistors at the left; the Load Cell Amplifier is the small red board in the center, and of course the Arduino is on the right.\n\nR3 and R4 need to have a ratio that is close to the ratio of the two (matched) resistors that are in the corresponding Load Sensor, so that the digitized voltage difference, V1 and V2 in the above schematic, is near zero.\n\nThe tricky part is that a normal multimeter shows that the two resistors of the Load Sensor are equal, and that R1, above, changes by only an ohm or so with pressure. That multimeter isn’t accurate enough to show the differences in resistance that you need to measure.\n\nSo either you can buy a high-precision multimeter (expensive), or you can use the Load Cell Amplifier to measure the resistances. I decided the use the Amplifier.\n\nI ordered a bunch of 1Kohm, 0.1% resistors. Then I picked 4 of them (I could have used more, but that’s more work), labeled them A, B, C, and D, then started measuring the Arduino ADC (Analog Digital Converter) values of various pairings of those resistors." ]	[ null, "https://needhamia.com/wp-content/uploads/2021/05/schem1-408x372.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9202472,"math_prob":0.8088726,"size":3429,"snap":"2021-31-2021-39","text_gpt3_token_len":827,"char_repetition_ratio":0.14978102,"word_repetition_ratio":0.015948962,"special_character_ratio":0.23651211,"punctuation_ratio":0.10378682,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9894291,"pos_list":[0,1,2],"im_url_duplicate_count":[null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-19T01:09:53Z\",\"WARC-Record-ID\":\"<urn:uuid:2b0b663e-6458-4e62-ae07-86a9bec4c608>\",\"Content-Length\":\"29295\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:ce4aa14d-962b-4ec6-8b24-fcb2fc116e9f>\",\"WARC-Concurrent-To\":\"<urn:uuid:294ec129-a1bc-4f9a-9c21-6bb9c9a9d54e>\",\"WARC-IP-Address\":\"192.124.249.115\",\"WARC-Target-URI\":\"https://needhamia.com/dog-weight-scale-part-7-choosing-matching-resistors/\",\"WARC-Payload-Digest\":\"sha1:LOKLUP2YQXOWBCUW5PFIKYYI2NHXLGEL\",\"WARC-Block-Digest\":\"sha1:4QBJER5PRIG5N6ZSJL6WUBJZOPGST7AP\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780056656.6_warc_CC-MAIN-20210919005057-20210919035057-00367.warc.gz\"}"}
http://www.mxcss.com/web-howto/i6I/how-to-change-css-where-idarrayindex/	[ "## How to change CSS where id=array(index)?\n\nTags: javascript,jquery,html,css,arrays\n\n### Problem :\n\ni just write an small code that should change CSS of X ids.\n\nI have 3 ids in HTML objects (every element has 1 Class)=\n\nelement 1 id = \"p1\" class=\"test1\"\nelement 2 id = \"p2\" class=\"test1\"\nelement 3 id = \"p3\" class=\"test1\"\n\ni create two Arrays :\n\n`````` var statArray = [\"p1\",\"p3\"];\nvar array = [\"p1\",\"p3\"];\n``````\n\nthan i check if Array 1 = Array 2\n\n``````for (var ix = 0; ix < array.length; ix++) {\nif (array[ix] === statArray[ix])\n``````\n\nNow i will change the css (background-color) of the ids.\n\nHow can i change the ids where id = array[ix]?\n\nmy attempt:\n\n``````\\$(\".test1\").attr(array[ix]).css(\"background-color\",\"#ff0000\");\n``````\n\n### Solution :\n\nJust use this\n\n``````for (var ix = 0; ix < array.length; ix++) {\nif (array[ix] === statArray[ix]){\n\\$(\".test1#\"+array[ix]).css(\"background-color\",\"#F00\");\n}\n}\n``````" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6579397,"math_prob":0.9705547,"size":6177,"snap":"2019-51-2020-05","text_gpt3_token_len":1600,"char_repetition_ratio":0.09104163,"word_repetition_ratio":0.019955654,"special_character_ratio":0.29399386,"punctuation_ratio":0.24094604,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9933479,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-11T01:26:05Z\",\"WARC-Record-ID\":\"<urn:uuid:1b94c619-9373-44d5-9392-ea95433aa2db>\",\"Content-Length\":\"116055\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:66172830-b16e-4689-a1e8-5d1e5e8f5ee4>\",\"WARC-Concurrent-To\":\"<urn:uuid:211b1f2c-03e5-4acd-a3ef-3cd373bc231a>\",\"WARC-IP-Address\":\"143.95.237.66\",\"WARC-Target-URI\":\"http://www.mxcss.com/web-howto/i6I/how-to-change-css-where-idarrayindex/\",\"WARC-Payload-Digest\":\"sha1:GYWUIEPGF47UADNGDYFENPW26JBOLV63\",\"WARC-Block-Digest\":\"sha1:OG3PSFPZ3UFONPOMMOI2JQ4NISZSQ3NB\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575540529516.84_warc_CC-MAIN-20191210233444-20191211021444-00519.warc.gz\"}"}
https://ericlippert.com/2023/01/	[ "# The names of birds, part 2\n\nReader “Joel” had an insightful comment on the first part of this series which I thought deserved a short episode of its own. Recall that we proved the theorem “if a compositional forest contains a mockingbird then every bird in the forest has a fixpoint“. An equivalent way to state that theorem is: “if a forest contains a bird without a fixpoint then either the forest is not compositional or it contains no mockingbird“. Joel’s question was whether there is a more “intuitive” way to understand why the mockingbird is so interesting that the presence of a bird without a fixpoint should prevent a mockingbird from existing in the same (compositional) forest.\n\nThe short version is: we’ll say that two birds agree on an input if their outputs are the same for that input. The mockingbird is a bird that agrees with every other bird on at least one input. A bird without a fixpoint is a bird that can always produce a different output than its input. Their composition is a bird which disagrees with every bird in the forest on one input and therefore is not in the forest at all.\n\nThe long version is:\n\nI find it easiest to get an intuition for a general rule by looking at some simple examples.\n\nThe first thing I’d note is that it is quite easy to construct a non-compositional forest containing a bird without a fixpoint. A simple example would be a non-compositional forest containing exactly two birds, A and M. Define them such that:\n\nAA = M\nAM = A\nMA = M\nMM = M\n\nPlainly these are two different birds, since their responses disagree on input M. Plainly M is a mockingbird, since Mx=xx for all x in the forest. And plainly A has no fixpoint. This forest is not compositional because there is no bird C in the forest such that Cx=A(Mx) for all x. With such a small number of birds in the forest it seems quite reasonable that one might have no fixpoint.\n\nLet’s look at a more interesting example, this one in a compositional forest. Let’s suppose there is a countable infinity of birds in the forest. By “countable infinity” I mean that we can number each bird with a natural number; we’ve got bird 0, bird 1, bird 2, and so on. In fact, let’s just use natural numbers as the names of the birds in this forest.\n\nSince each bird needs a response to hearing the name of every other bird in the forest, we can imagine an infinite lookup table that says what each bird responds when it hears the name of another bird in the forest. We’ll put the “called to” bird on the vertical axis and the “name called” on the horizontal axis:\n\n``` 0 1 2 3 ...\n------------\n0 \| 9 5 2 5 ...\n1 \| 8 3 6 7 ...\n2 \| 0 1 2 3 ...\n3 \| 3 1 4 1 ...\n... \|\nS \| 1 2 3 4 ...\n... \|\n```\n\nSo in our notation 0 1=5, 2 3=3, and so on.\n\nLet’s suppose this forest is compositional and contains a bird, call it S, which has no fixpoint. We could choose any such S, but without loss of generality we shall pick a specific S, the bird where S 0=1, S 1=2, S 2=3, S 3=4, … and so on; the “successor” bird. Of course S has some “number” name but we don’t really care what it is, so we’ll just “alias” that one as S.\n\nNow let’s suppose there’s a mockingbird in the forest and deduce a contradiction. The mockingbird tells us what is on the highlighted diagonal! That is, M 0=9, M 1=3, M 2=2, M 3=1, and so on. (As with S, M is an alias for some “number” name but we don’t know or care what it is.)\n\nNow comes the fun bit. The forest is compositional, so therefore there exists a bird C such that Cx=S(Mx) for all x. We do care what the number name of C is. So, which is it?\n\nC 0=10, and therefore C is not 0, because 0 0=9. But similarly, C 1=4, so C is not 1. And similarly C is not 2, 3, 4, 5, … because C definitely disagrees with each of those functions I mean birds at the diagonal. But if C has no number name, then it is not in the forest at all, contradicting the statement that the forest is compositional. We now have deduced a contradiction, and therefore our assumption that M is in the forest is shown to be false.\n\nBy looking at a specific example — a countable forest with a successor bird — perhaps you have a better intuition about why Mx=xx and any bird S that has no fixpoint cannot coexist in a compositional forest: if they did then the bird C such that Cx=S(Mx) definitely disagrees with every bird in the forest on at least one input, and therefore the forest would not be closed under composition; there would always be a missing bird.\n\nNext time on FAIC: We’ll look at some more fun examples and then get back to compilation.\n\n# The names of birds, part 1\n\nFor the next part in my Bean Machine retrospective to make sense I’ll need to make a short digression. In looking back on the almost 20 years I’ve been blogging, it is surprising to me that I’ve only briefly alluded to my appreciation of combinatory logic. In the next couple of episodes, I’ll do a quick introduction based on the delightful book that introduced it to me: To Mock A Mockingbird, by the late Raymond Smullyan.\n\nImagine a forest containing some birds, possibly finitely or infinitely many. These are unusual birds. When you call the species name of a bird in the forest to a bird in the forest, it calls one back to you. Maybe the same, maybe different, but when you tell a bird the name of a bird, it names a bird back to you. There might be a Red Capped Cardinal in the forest and when you call out Great Blue Heron to it, it calls back Belted Kingfisher.\n\n(Photos by me; click for higher resolution.)\n\nWe will notate “I called Q to P and got response R” as PQ = R. If I then called out S to R and R responded with T, we’ll notate that as PQS = RS = T. We’ll use parentheses in the obvious way: PQS = (PQ)S and this might be different from P(QS). The latter is “I called S to Q, and then called Q‘s response to P“. I’ll use capital letters to represent specific bird names, and small letters to represent variables.\n\nThe question we’re considering here is: under what circumstances will a bird call back the same name you called to it? That is, for a given bird y, under what circumstances does yx = x?\n\nSmullyan calls birds with this relationship “fondness” — that is, “y is fond of x” means that yx = x. If y is fond of x then x is said to be a “fixpoint” of y.\n\nA forest is said to be “compositional” if for every pair of birds (a, b) — a and b can be the same or different — there is a bird c in the forest such that cx = b(ax) for all x. That is, if we call any name x to a, and then call its response to b, we get the same result as simply calling x to c. c is the composition of “call x to a, and then call that response to b“.\n\nA mockingbird is the bird M with the property that Mx = xx. That is, for any bird name x, M tells you what x‘s response is to its own name. (The attentive reader will note that we have not said what MM is, but at least we know from the definition that MM = MM, so give me some credit for consistency at least.)\n\nTheorem: if a compositional forest contains a mockingbird then every bird in the forest is fond of at least one bird.\n\nProof: Try to prove it yourself; scroll down for the solution.\n\n.\n\n.\n\n.\n\n.\n\n.\n\n.\n\n.\n\nLet p be any bird. Let c be the bird that composes p with M. Therefore cx = p(Mx) for all x.\n\nIn particular, that’s true for c, so cc = p(Mc). But Mc = cc, thus cc = p(cc), and we’ve found a bird that p is fond of. Since p was any bird, every bird in the forest is fond of at least one bird. Or, put another way, every bird in a compositional forest with a mockingbird has at least one fixpoint.\n\nNext time on FAIC: we’ll take a look at a few more interesting birds, and then discuss why this whimsy is relevant to compilation before getting back to Bean Machine.\n\n# Bean Machine Retrospective, part 6\n\nHappy New Year all!\n\nLast time I briefly described the basic strategy of the Beanstalk compiler: transform the source code of each queried or observed function (and transitively their callees) into an equivalent program which partially evaluates the model, accumulating a graph as it goes. In this post I’ll go through the first step of the transformation.\n\nThe idea of the first source-to-source transformation is to take a relatively complicated language — Python — and replace it with what I think of as “simplified Python”. The Zen of Python famously says “there should be one — and preferably only one — obvious way to do it” but that is not the goal of this simplification step. The Zen of Python emphasizes obviousness. It is about making the code clear and the language discoverable. My goal with simplified Python is “there should be only one way to do it” — because it is easier to instrument a program to capture its meaning as it runs if there’s only one way to do everything.\n\nConsider for example how to call a function foo with three arguments:\n\n```foo(1, 2, 3)\nx = [1, 2, 3]\nfoo(x)\nfoo(1, 2, bar=3)\nx = {\"bar\":3}\nfoo(1, 2, x)\n```\n\n… and so on — there are a great many obvious ways to call a function in Python, but I’d like there to be exactly one in simplified Python.\n\nThe first thing we do when analyzing a queried or observed function is to obtain its source code, parse that into an abstract syntax tree (AST), and then do a series of AST transformations that reduce the function into an equivalent but simpler Python program. This is the most traditional-compiler-ish step in the pipeline.\n\n(How do we obtain the source code? Remember, we have an RVID for each observation and query; the RVID contains a reference to the original function object. Python’s runtime can provide the source code for a given function reference.)\n\nLet’s look at an only slightly more complicated version of our “hello world” model:\n\n```@random_variable\ndef fairness():\nreturn Beta(2,2)\n\n@random_variable\ndef flip(n):\nreturn Bernoulli(0.5 fairness())\n```\n\nIn our simplified Python:\n\n• Every value gets its own variable\n• Every computation gets its own statement\n• Every call has the same syntax: `a = b(c, d)`\n\nOur two methods in the simplified form would be:\n\n```def fairness():\n_t1 = 2\n_t2 = 2\n_t3 = [_t1, _t2]\n_t4 = {}\n_t5 = Beta(_t3, *_t4)\nreturn _t5\n\ndef flip(n):\n_t1 = 0.5\n_t2 = []\n_t3 = {}\n_t4 = fairness(_t2, *_t3)\n_t5 = _t1 t4\n_t6 = [_t5]\n_t7 = {}\n_t8 = Bernoulli(_t6, *_t7)\nreturn _t8\n```\n\nASIDE: Readers with some experience writing compilers might ask “is this static-single-assignment form?” SSA form is a transformation whereby every variable is assigned exactly once; it’s used for control flow analysis and other program analyses. I did not write a full-on SSA transformation but when I was doing initial prototyping I knew that I might need SSA form in the future. Think of it as SSA-light if that makes sense.\n\nWe can go further; in our simplified Python:\n\n• logical operators `and` and `or` are eliminated\n```x = y and z\n```\n\ncan be simplified to\n\n```x = y\nif x:\nx = z\n```\n\nand now the graph accumulator does not need to worry at all about logical operators, because there aren’t any in the simplified program.\n\n• Every `while` loop is `while True`.\n• No loop has an `else` clause. (Did you know that Python loops have `else` clauses? It’s true!)\n• There are no compound comparisons:\n```x = a < b < c\n```\n\ncan be simplified to\n\n```x = a < b\nif x:\nx = b < c\n```\n\nand now the graph accumulator does not need to worry about compound comparisons, because there aren’t any.\n\n• Similarly there are no lambdas, no function annotations, and so on. All the convenient syntactic sugars are desugared into their more fundamental form.\n\nThe simplified language is definitely not a language I’d like to write a long program in, but it is a language that is easy to analyze programmatically. Thus far, the transformations make the program longer and simpler, but do not change its meaning; if we compiled and ran the simplified version of the program it should do the same thing as the normal version.\n\nNext time on FAIC: let’s get into the details of how the AST-to-AST transformation code works. I had a lot of fun writing it." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.935467,"math_prob":0.94739294,"size":4487,"snap":"2023-14-2023-23","text_gpt3_token_len":1153,"char_repetition_ratio":0.15659156,"word_repetition_ratio":0.026436782,"special_character_ratio":0.25585023,"punctuation_ratio":0.11377245,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96303993,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-05-29T21:04:42Z\",\"WARC-Record-ID\":\"<urn:uuid:2b521d9f-a717-42a9-923b-57fb84367a7e>\",\"Content-Length\":\"98704\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:8b0ee76f-7e87-487e-b9bb-175e3ba85eee>\",\"WARC-Concurrent-To\":\"<urn:uuid:c6cf38c0-c4b7-4ff0-a200-841d1dbf8269>\",\"WARC-IP-Address\":\"192.0.78.25\",\"WARC-Target-URI\":\"https://ericlippert.com/2023/01/\",\"WARC-Payload-Digest\":\"sha1:6V27OUTTOX7UV7HYKF4VMXFV7WMRAY6W\",\"WARC-Block-Digest\":\"sha1:AHEYY2JJJFR6Q6WYKQIVCNV5K5VQKVPI\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224644913.39_warc_CC-MAIN-20230529205037-20230529235037-00647.warc.gz\"}"}
http://ianfinlayson.net/class/cpsc220/notes/16-simulation	[ "# Simulation\n\n### Introduction\n\nOne particular type of program that lends itself well to using objects is simulation programs. A simulation is a program that models some kind of process or system over time. Simulation programs are very important to many other disciplines.\n\nSome examples of areas that use computer simulation:\n\n• Astronomical events.\n• Particle physics.\n• Cell reproduction.\n• Chemical reactions.\n• Spread of disease.\n• Weather prediction.\n• Traffic patterns.\n• Crowd modelling.\n• Artificial intelligence.\n• Most video games.\n\nSimulations are done by keeping track of several objects, and how they change over time. The objects can possibly interact with each other or outside influences.\n\n### Example: Disease Simulation\n\nAs an example of how we could do a simulation on multiple objects, consider the problem of studying a disease outbreak. The general idea is we can keep track of a large number of virtual people, as they move about. Some people will start out sick, and can pass the disease to those they are near.\n\nBelow is a simple program which does just such a simulation. There are a number of parameters which control the simulation as it runs. They are grouped in a class so they can be changed in one place:\n\n\n// a class which just contains some numbers grouped together\nclass SimulationParameters {\n\nstatic final int POPULATION = 200;\nstatic final int MOVE_AMOUNT = 2;\nstatic final int HEAL_DAYS = 10;\nstatic final int INITIAL_SICK = 10;\nstatic final double INFECT_DISTANCE = 2.5;\n}\n\n\nTo keep track of whether someone is sick or not, we can use an enumeration:\n\n\n// represents whether a given person is healthy or sick\nenum State {\nHEALTHY,\nINFECTED\n};\n\n\nWe then can make a Person class for modeling one person in this simulation. They have variables which store their sate and position, and functions which modify them:\n\n\nclass Person {\n\n// variables used in simulating the person\n\nprivate State state;\nprivate int days_til_healed;\nprivate double x, y;\n\n// construct a healthy person, randomly positioned in space\nPerson() {\nstate = State.HEALTHY;\nRandom generator = new Random();\nx = generator.nextInt(100);\ny = generator.nextInt(100);\n}\n\n// move the person randomly\nvoid move() {\nRandom generator = new Random();\n\n// getr a random number between 0 and 1\ndouble val = generator.nextDouble();\n\n// multiply by twice the move amount - this gets us a value between\n// negative move amount, and positive move amount\nval = val * 2.0 * SimulationParameters.MOVE_AMOUNT;\nval = val - SimulationParameters.MOVE_AMOUNT;\n\n// move in the x direction by this much\nx += val;\n\n// do the same thing for y\ndouble val2 = generator.nextDouble();\nval2 = val2 * 2.0 * SimulationParameters.MOVE_AMOUNT;\nval2 = val2 - SimulationParameters.MOVE_AMOUNT;\ny += val2;\n\n// don't let them go off the edges\nif (x > 100) {\nx = 100;\n}\nif (y > 100) {\ny = 100;\n}\nif (x < 0) {\nx = 0;\n}\nif (y < 0) {\ny = 0;\n}\n}\n\n// called after each step in the simulation, if this person is sick,\n// is it time for them to get better yet?\nvoid checkHeal() {\nif (days_til_healed == 0) {\nstate = State.HEALTHY;\n} else {\ndays_til_healed--;\n}\n}\n\n// set this person as infected\nvoid setInfected() {\nstate = State.INFECTED;\ndays_til_healed = SimulationParameters.HEAL_DAYS;\n}\n\n// return the state of this person\nboolean isInfected() {\nreturn state == State.INFECTED;\n}\n\n// check if this person has been infected by another person\nvoid checkInfected(Person others[]) {\n// loop through each other person\nfor (int i = 0; i < SimulationParameters.POPULATION; i++) {\n// find the euclidean distance between them\ndouble distance = Math.sqrt((x - others[i].x) * (x - others[i].x)\n+ (y - others[i].y) * (y - others[i].y));\n\n// if they are too close\nif (distance < SimulationParameters.INFECT_DISTANCE) {\n// if they're sick and we are not, we are now sick too :(\nif (state == State.HEALTHY && others[i].state == State.INFECTED) {\nsetInfected();\n}\n}\n}\n}\n}\n\n\nOnce we have a class to keep track of an individual person, we can create an array of people, and loop through it, performing the simulation over time:\n\n\n// the main class which runs the simulation\nclass DiseaseSimulation {\n\npublic static void main(String args[]) {\n// make an array of people\nPerson people[] = new Person[SimulationParameters.POPULATION];\n\n// actually create the people\nfor (int i = 0; i < SimulationParameters.POPULATION; i++) {\npeople[i] = new Person();\n}\n\n// set the first so many to be sick\nfor (int i = 0; i < SimulationParameters.INITIAL_SICK; i++) {\npeople[i].setInfected();\n}\n\nScanner in = new Scanner(System.in);\n\n// keep going until the user says no\nboolean cont;\nint day = 1;\ndo {\n// go through each person\nfor (Person p : people) {\n// move them\np.move();\n\n// check if they are all better\np.checkHeal();\n\n// check if they are sick\np.checkInfected(people);\n}\n\n// count how many people are sick\nint sick = 0;\nfor (Person p : people) {\nif (p.isInfected()) {\nsick++;\n}\n}\n\n// print stats\nSystem.out.printf(\"After %d days, %d people are sick and %d people are well\\n\",\nday, sick, SimulationParameters.POPULATION - sick);\n\n// move to the next day\nday++;\n\n// check if we want to continue\nSystem.out.print(\"Continut (y/n): \");\ncont = in.next().charAt(0) == 'y';\n} while (cont);\n}\n}\n\n\nSome questions we could ask of this simulation:\n\n• Does the disease ever go away? After how many years?\n• Does the infection number level off? At what level?\n• What factors make the disease more deadly?\n• What if people who catch the disease become immune?\n• If the disease was fatal, how many would die?" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8184005,"math_prob":0.9832928,"size":5049,"snap":"2019-13-2019-22","text_gpt3_token_len":1265,"char_repetition_ratio":0.13201189,"word_repetition_ratio":0.026620371,"special_character_ratio":0.28005546,"punctuation_ratio":0.15376227,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96527743,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-03-21T09:38:00Z\",\"WARC-Record-ID\":\"<urn:uuid:aa5b0447-ca1f-49d7-a202-0ffdbc6a5a0d>\",\"Content-Length\":\"9192\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7bf68e80-7081-4105-9597-621ded73cdf4>\",\"WARC-Concurrent-To\":\"<urn:uuid:30a981a3-d5fd-419a-8b51-40cd2f89c17a>\",\"WARC-IP-Address\":\"35.207.63.9\",\"WARC-Target-URI\":\"http://ianfinlayson.net/class/cpsc220/notes/16-simulation\",\"WARC-Payload-Digest\":\"sha1:NPS32P6IENJ34G6MPK2VNME7RCAYPKGN\",\"WARC-Block-Digest\":\"sha1:S5ADGRD635AAT2JFXK73BKCQXCFMCRKO\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-13/CC-MAIN-2019-13_segments_1552912202510.47_warc_CC-MAIN-20190321092320-20190321114320-00226.warc.gz\"}"}
https://forum.polymake.org/viewtopic.php?f=8&t=1850&sid=baf0dd475d196c756fc5f5483b1b47d4	[ "", null, "## Stable intersection not contained in set-theoretic intersection\n\nQuestions and problems about using polymake go here.\nPaulH\nPosts: 4\nJoined: 22 Mar 2021, 17:07\n\n### Stable intersection not contained in set-theoretic intersection\n\nHi,\n\nI have a question about the \"intersect\" and \"set_theoretic_intersection\" commands in polymake. I made an example down below with two tropical hypersurfaces in R^{4}. Polymake then tells me that their stable intersection is two-dimensional, whereas their set-theoretic intersection is one-dimensional. Is polymake by any chance removing a lineality space in the set-theoretic intersection or?\n\nThe corresponding code is as follows:\n\nCode: Select all\n\napplication \"tropical\"; $f1 = toTropicalPolynomial(\"min(a+b+c-20,b+c+w+5,d+2b+1,c+2w)\", qw( a b c d w ));$f2 = toTropicalPolynomial(\"min(2a+b-5,a+b+w+3,2b+w-2,b+c+w+10)\", qw( a b c d w )); $V1 = new Hypersurface<Min>(POLYNOMIAL=>$f1); $V2 = new Hypersurface<Min>(POLYNOMIAL=>$f2); $W12 = set_theoretic_intersection($V1,$V2);$V12 = intersect($V1,$V2); print $W12->DIM; print$V12->DIM; \n\njoswig\nMain Author\nPosts: 245\nJoined: 24 Dec 2010, 11:10\n\n### Re: Stable intersection not contained in set-theoretic intersection\n\nThat's a difficult question in the sense that these functions reside in Simon Hampe's extension atint, which became bundled a while ago. Thing is: no-one is currently working on that code.\n\nNonetheless, we will check. Just be a bit patient, please.\n\nhampe\nDeveloper\nPosts: 48\nJoined: 29 Apr 2011, 10:42\n\n### Re: Stable intersection not contained in set-theoretic intersection\n\nOh dear, oh dear, this was all so long ago", null, "I haven't worked on polymake for four years and I can see from the source that a few changes were made. Also, I don't have a working local polymake at the moment, so my diagnosis is at least half guesswork.\n\nHere's what I can tell. The function set_theoretic_intersection eventually uses fan_intersection in convex_hull_tools.cc. The documentation in convex_hull_tools.h says that \"All coordinates should be given non-tropically-homogeneously\", i.e. dehomogenized. However as far as I can tell, the coordinates of the cycles are just given to the fan_intersection function as is:\n\nCode: Select all\n\n const Matrix<Rational> &arays = A.give(\"VERTICES\"); const IncidenceMatrix<> &acones = A.give(\"MAXIMAL_POLYTOPES\"); const Matrix<Rational> &alineality = A.give(\"LINEALITY_SPACE\"); const Matrix<Rational> &brays = B.give(\"VERTICES\"); const IncidenceMatrix<> &bcones = B.give(\"MAXIMAL_POLYTOPES\"); const Matrix<Rational> &blineality = B.give(\"LINEALITY_SPACE\"); fan_intersection_result result = fan_intersection(arays,alineality,acones, brays,blineality,bcones); \nInstead, dehomogenization takes place after the intersection.\n\nIf I perform this little cheat in the polymake-in-a-box:\n\nCode: Select all\n\n$cheat1 = new Cycle<Min>(VERTICES=>tdehomog($V1->VERTICES), MAXIMAL_POLYTOPES=>$V1->MAXIMAL_POLYTOPES,LINEALITY_SPACE=>tdehomog($V1->LINEALITY_SP ACE)); $cheat2 = new Cycle<Min>(VERTICES=>tdehomog($V2->VERTICES), MAXIMAL_POLYTOPES=>$V2->MAXIMAL_POLYTOPES, LINEALITY_SPACE=>tdehomog($V2->LINEALITY_S PACE)); $cheatintersect = set_theoretic_intersection($cheat1,$cheat2); the intersection now has the correct dimension 2! Of course the objects are nonsense since their vertices are not tropically homogenous, but the input to fan_intersection is now correct, hence so is the result. So, my diagnosis would be: This is a bug and someone should switch the dehomogenization to before the fan_intersection. It's probably faster if someone else than me does this, it'll take me ages to find the git repo url, see if my credentials still work, figure out ninja, etc. etc.... (Michael is so not buying me beer for this...) hampe Developer Posts: 48 Joined: 29 Apr 2011, 10:42 ### Re: Stable intersection not contained in set-theoretic intersection Just to blame the right guy: The bug seems to have been in the original already, see https://github.com/simonhampe/atint/blo ... l_tools.cc", null, "In earlier times a-tint used to not use tropically homogeneous coordinates, I suspect this got lost in the transition somehow? In that case this would have gone unnoticed for quite some time, so feel free to challenge my diagnosis... EDIT: I can currently only access https://github.com/polymake/polymake and I can't seem to find the testsuites in there - so I can't verify, whether we just chose sufficently naive tests to simply overlook this problem. hampe Developer Posts: 48 Joined: 29 Apr 2011, 10:42 ### Re: Stable intersection not contained in set-theoretic intersection Okay, I think I might have a minimal example worked out - and might have discovered a second bug (related to this one): When the set-theoretic-intersection is empty, I get a Code: Select all polymake: ERROR: Invalid chart coordinate The \"special\" thing about the example is that both hypersurfaces have lineality spaces, in particular the first one has one whose generator is not normalized w.r.t tropical homogeneity (which I think is fine?): Code: Select all tropical > print$V1->LINEALITY_SPACE; 0 1 1 -2 -2 1 \nNow, as long as all vertices and lin space generators are normalized, this bug won't occur: The additional tropical dimension just doesn't factor into the intersection since everything lives at x_0=0 anyway. Now if the lineality space is not normalized, things go awry.\n\nFor my minimal example, first of all note the following:\n\nCode: Select all\n\ntropical > $line1 = new Cycle<Max>(VERTICES=>[[1,0,0,0,0],[0,0,1,1,0],[0,0,0,-1,0],[0,0,-1,0,0]],MAXIMAL_POLYTOPES=>[[0,1],[0,2],[0,3]],WEIGHTS=>[1,1,1]); tropical >$line2 = new Cycle<Max>(VERTICES=>[[1,0,0,0,1],[0,0,1,1,0],[0,0,0,-1,0],[0,0,-1,0,0]],MAXIMAL_POLYTOPES=>[[0,1],[0,2],[0,3]],WEIGHTS=>[1,1,1]); tropical > print set_theoretic_intersection($line1,$line2); polymake: ERROR: Invalid chart coordinate \nThese are two tropical lines in threespace that don't intersect. I suspect that the error occurs when trying to dehomogenize the empty ray matrix at the end? I think this should be fixed automatically by putting the dehomogenization in the proper place. In any case it should definitely be a test case.\n\nIn any case, assuming that an empty intersection is indicated by an error message, let's look at the following:\n\nCode: Select all\n\ntropical > $line1 = new Cycle<Max>(VERTICES=>[[1,0,0,0,0],[0,0,1,1,0],[0,0,0,-1,0],[0,0,-1,0,0]],MAXIMAL_POLYTOPES=>[[0,1],[0,2],[0,3]],WEIGHTS=>[1,1,1]); tropical >$line2 = new Cycle<Max>(VERTICES=>[[1,0,0,0,1],[0,0,1,1,0],[0,0,0,-1,0],[0,0,-1,0,0]],MAXIMAL_POLYTOPES=>[[0,1],[0,2],[0,3]],WEIGHTS=>[1,1,1], LI NEALITY_SPACE=>[[0,0,0,0,1]]); tropical > print set_theoretic_intersection($line1,$line2)->DIM; 1 \nThis works fine, the lineality space is normalized. Let's try this with a non-normalized version:\n\nCode: Select all\n\ntropical > $line1 = new Cycle<Max>(VERTICES=>[[1,0,0,0,0],[0,0,1,1,0],[0,0,0,-1,0],[0,0,-1,0,0]],MAXIMAL_POLYTOPES=>[[0,1],[0,2],[0,3]],WEIGHTS=>[1,1,1]); tropical >$line2 = new Cycle<Max>(VERTICES=>[[1,0,0,0,1],[0,0,1,1,0],[0,0,0,-1,0],[0,0,-1,0,0]],MAXIMAL_POLYTOPES=>[[0,1],[0,2],[0,3]],WEIGHTS=>[1,1,1], LI NEALITY_SPACE=>[[0,1,1,1,2]]); tropical > print set_theoretic_intersection($line1,$line2)->DIM; polymake: ERROR: Invalid chart coordinate \nSo, all in all, I think my initial assumption was correct: The set-theoretic intersection needs non-homogenous coordinates to work and we didn't notice it until now because we were always being good little tropical geometers and using nicely homogenized coordinates", null, "blorenz\nDeveloper\nPosts: 119\nJoined: 10 Jan 2011, 17:21\n\n### Re: Stable intersection not contained in set-theoretic intersection\n\nThanks for looking into this Simon! We will try to take care of this next week.\n\npanizzut\nDeveloper\nPosts: 1\nJoined: 07 Jul 2021, 14:21\n\n### Re: Stable intersection not contained in set-theoretic intersection\n\nHi,\nI have fixed the problem with set_theoretic_intersection following Simon's comments.\nNow, we get the following dimensions in your example.\n\nCode: Select all\n\napplication \"tropical\"; $f1 = toTropicalPolynomial(\"min(a+b+c-20,b+c+w+5,d+2b+1,c+2w)\", qw( a b c d w ));$f2 = toTropicalPolynomial(\"min(2a+b-5,a+b+w+3,2b+w-2,b+c+w+10)\", qw( a b c d w )); $V1 = new Hypersurface<Min>(POLYNOMIAL=>$f1); $V2 = new Hypersurface<Min>(POLYNOMIAL=>$f2); $W12 = set_theoretic_intersection($V1,$V2);$V12 = intersect($V1,$V2); print $W12->DIM; 2 print$V12->DIM; 2 \nThe change will be available in the next polymake release. In the meanwhile, if you need to compute some more intersections, just let me know.", null, "" ]	[ null, "https://forum.polymake.org/theme_files/images/forumlogo.png", null, "https://forum.polymake.org/images/smilies/icon_e_wink.gif", null, "https://forum.polymake.org/images/smilies/icon_e_wink.gif", null, "https://forum.polymake.org/images/smilies/icon_e_wink.gif", null, "https://forum.polymake.org/cron/cron.task.primepostrevisions.prune", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8020818,"math_prob":0.9751058,"size":2946,"snap":"2021-31-2021-39","text_gpt3_token_len":1014,"char_repetition_ratio":0.1553365,"word_repetition_ratio":0.12650603,"special_character_ratio":0.35913104,"punctuation_ratio":0.29806453,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9773564,"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,6,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-07-30T16:49:52Z\",\"WARC-Record-ID\":\"<urn:uuid:f8cebedc-ddb9-4388-a3f9-90543a3b3784>\",\"Content-Length\":\"43824\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:8c3cb3f6-071f-4b96-9d04-c5e484e43e6a>\",\"WARC-Concurrent-To\":\"<urn:uuid:d36a6ca0-2bc8-40fa-9ed0-c48ee022c5c4>\",\"WARC-IP-Address\":\"130.149.13.185\",\"WARC-Target-URI\":\"https://forum.polymake.org/viewtopic.php?f=8&t=1850&sid=baf0dd475d196c756fc5f5483b1b47d4\",\"WARC-Payload-Digest\":\"sha1:7QSBYWIB5EOZDWCYPKGFKS2GY2WAATN4\",\"WARC-Block-Digest\":\"sha1:2WEQH3RZQHKYS36ZISSCLECBDTF2J5IT\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-31/CC-MAIN-2021-31_segments_1627046153971.20_warc_CC-MAIN-20210730154005-20210730184005-00526.warc.gz\"}"}
https://testbook.com/question-answer/what-will-come-at-the-place-of-in-6-6--5fe9ed94e6cec65018411dd4	[ "What will come at the place of ? in (6 × 6 × 6 × 6 )5 × (9 × 9)5 ÷ (18 × 18)3 = 214 × 3?\n\n1. 29\n2. 26\n3. 28\n4. 24\n\nOption 3 : 28\nFree\nMonthly Current Affair - April\n152561\n50 Questions 50 Marks 20 Mins\n\nDetailed Solution\n\nGiven:\n\n(6 × 6 × 6 × 6 )5 × (9 × 9)5 ÷ (18 × 18)3 = 214 × 3?\n\nConcept used:\n\nFollow the BODMAS rule according to the table given below:", null, "Calculation\n\n(6 × 6 × 6 × 6 )5 × (9 × 9)5 ÷ (18 × 18)3 = 214 × 3?\n\n⇒ 6 5 × 4 × 9 5 × 2 ÷ 18 3 × 2 = 214 × 3 ?\n\n⇒ 220 .× 320 × 310 × 310 ÷ (26 × 36 × 36) = 214 × 3?\n\n⇒ 214 × 328 = 214 × 3?\n\n∴ ? = 28" ]	[ null, "https://storage.googleapis.com/tb-img/production/20/12/Ashish_S_Quant_Assignment_Ravindra_40Q%27s_21Dec_solution_ashish%20singh_D1.PNG", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.83932126,"math_prob":0.9999697,"size":2743,"snap":"2022-05-2022-21","text_gpt3_token_len":911,"char_repetition_ratio":0.10003651,"word_repetition_ratio":0.09908257,"special_character_ratio":0.3773241,"punctuation_ratio":0.10517241,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9919448,"pos_list":[0,1,2],"im_url_duplicate_count":[null,5,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-25T20:18:30Z\",\"WARC-Record-ID\":\"<urn:uuid:d47109fa-c2e9-477c-b3dd-1b83085d4be5>\",\"Content-Length\":\"123918\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:193a4f2d-f9e6-4804-bae7-086b9ef3ad4c>\",\"WARC-Concurrent-To\":\"<urn:uuid:19bb8611-bc0c-4646-8c5f-0c43f3d8a8af>\",\"WARC-IP-Address\":\"104.22.45.238\",\"WARC-Target-URI\":\"https://testbook.com/question-answer/what-will-come-at-the-place-of-in-6-6--5fe9ed94e6cec65018411dd4\",\"WARC-Payload-Digest\":\"sha1:LW5NGG2QKAQ6K7GKNWAQDG3WPDOAL3IV\",\"WARC-Block-Digest\":\"sha1:L3RD3W3AJBE67ICC5YVZOPOHFHXPBQKC\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320304872.21_warc_CC-MAIN-20220125190255-20220125220255-00100.warc.gz\"}"}
https://www.geeksforgeeks.org/python-bokeh-visualizing-stock-data/?ref=rp	[ "Related Articles\n\n# Python Bokeh – Visualizing Stock Data\n\n• Last Updated : 03 Jul, 2020\n\nBokeh is a Python interactive data visualization. It renders its plots using HTML and JavaScript. It targets modern web browsers for presentation providing elegant, concise construction of novel graphics with high-performance interactivity.\nBokeh can be used to visualize stock market data. Visualization is be done using the `plotting` module. Here we will be using the sample stock datasets given to us by Bokeh.\n\nTo download the sample datasets run the following command on the command line :\n\n`bokeh sampledata`\n\nAlternatively, we can also execute the following Python code :\n\n```import bokeh\n```\n\n## Analyzing the dataset :\n\nIn the sample data provided by Bokeh, there are datasets of the stocks of the following companies :\n\n• AAPL which is Apple\n• IBM which is International Business Machines\n• MSFT which is Microsoft Corporation\n\nAll these datasets are available as CSV files. Below is a glimpse into the IBM.csv file :\n\n```Date Open High Low Close Volume Adj Close\n01-03-2000 102 105.5 100.06 100.25 10807800 84.48\n02-03-2000 100.5 105.44 99.5 103.12 11192900 86.9\n03-03-2000 107.25 110 106.06 108 10162800 91.01\n06-03-2000 109.94 111 101 103.06 10747400 86.85\n07-03-2000 106 107 101.69 103 10035100 86.8\n```\n\nThe file contains the stock data between the years 2000 and 2013 with over 3000 entries.\n\n## Visualizing the Stocks :\n\nWe will be plotting a line graph which will track the closing price of the stocks between the years 2000 and 2013 of all the 5 available companies.\n\n1. Import the required modules :\n• numpy\n• figure, output_file and show from bokeh.plotting\n• AAPL, FB, GOOG, IBM and MSFT from bokeh.sampledata.stocks\n2. Instantiate a figure object with the title and axis types.\n3. Give the names to x-axis and y-axis.\n4. Plot line graphs for all the 5 companies.\n5. Display the model.\n `# importing the modules``import` `numpy as np``from` `bokeh.plotting ``import` `figure, output_file, show``from` `bokeh.sampledata.stocks ``import` `AAPL, FB, GOOG, IBM, MSFT`` ` `# the file to save the model``output_file(``\"gfg.html\"``)`` ` `# instantiating the figure object``graph ``=` `figure(x_axis_type ``=` `\"datetime\"``, title ``=` `\"Stock Closing Prices\"``)`` ` `# name of the x-axis``graph.xaxis.axis_label ``=` `'Date'`` ` `# name of the y-axis``graph.yaxis.axis_label ``=` `'Price (in USD)'`` ` `# plotting the line graph for AAPL``x_axis_coordinates ``=` `np.array(AAPL[``'date'``], dtype ``=` `np.datetime64)``y_axis_coordinates ``=` `AAPL[``'adj_close'``]``color ``=` `\"lightblue\"``legend_label ``=` `'AAPL'``graph.line(x_axis_coordinates,`` ``y_axis_coordinates,`` ``color ``=` `color,`` ``legend_label ``=` `legend_label)`` ` `# plotting the line graph for FB``x_axis_coordinates ``=` `np.array(FB[``'date'``], dtype ``=` `np.datetime64)``y_axis_coordinates ``=` `FB[``'adj_close'``]``color ``=` `\"black\"``legend_label ``=` `'FB'``graph.line(x_axis_coordinates,`` ``y_axis_coordinates,`` ``color ``=` `color,`` ``legend_label ``=` `legend_label)`` ` `# plotting the line graph for GOOG``x_axis_coordinates ``=` `np.array(GOOG[``'date'``], dtype ``=` `np.datetime64)``y_axis_coordinates ``=` `GOOG[``'adj_close'``]``color ``=` `\"orange\"``legend_label ``=` `'GOOG'``graph.line(x_axis_coordinates,`` ``y_axis_coordinates,`` ``color ``=` `color,`` ``legend_label ``=` `legend_label)`` ` `# plotting the line graph for IBM``x_axis_coordinates ``=` `np.array(IBM[``'date'``], dtype ``=` `np.datetime64)``y_axis_coordinates ``=` `IBM[``'adj_close'``]``color ``=` `\"darkblue\"``legend_label ``=` `'IBM'``graph.line(x_axis_coordinates,`` ``y_axis_coordinates,`` ``color ``=` `color,`` ``legend_label ``=` `legend_label)`` ` `# plotting the line graph for MSFT``x_axis_coordinates ``=` `np.array(MSFT[``'date'``], dtype ``=` `np.datetime64)``y_axis_coordinates ``=` `MSFT[``'adj_close'``]``color ``=` `\"yellow\"``legend_label ``=` `'MSFT'``graph.line(x_axis_coordinates,`` ``y_axis_coordinates,`` ``color ``=` `color,`` ``legend_label ``=` `legend_label)`` ` `# relocating the legend table to ``# avoid abstruction of the graph``graph.legend.location ``=` `\"top_left\"`` ` `# displaying the model``show(graph)`\n\nOutput :", null, "Attention geek! Strengthen your foundations with the Python Programming Foundation Course and learn the basics.\n\nTo begin with, your interview preparations Enhance your Data Structures concepts with the Python DS Course. And to begin with your Machine Learning Journey, join the Machine Learning – Basic Level Course\n\nMy Personal Notes arrow_drop_up" ]	[ null, "https://media.geeksforgeeks.org/wp-content/uploads/20200625092716/bokeh-stock-visualization.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.60583496,"math_prob":0.7617411,"size":4189,"snap":"2021-43-2021-49","text_gpt3_token_len":1115,"char_repetition_ratio":0.1734767,"word_repetition_ratio":0.10696921,"special_character_ratio":0.2847935,"punctuation_ratio":0.15223464,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98596644,"pos_list":[0,1,2],"im_url_duplicate_count":[null,6,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-21T10:43:14Z\",\"WARC-Record-ID\":\"<urn:uuid:8badafad-f730-4a3f-bc16-ec6f4dcdc5b3>\",\"Content-Length\":\"115233\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:20ba1078-11bf-4397-9186-36bba2768a44>\",\"WARC-Concurrent-To\":\"<urn:uuid:3aecf92c-986d-412d-a6bb-d8fe1240e1f7>\",\"WARC-IP-Address\":\"23.40.207.67\",\"WARC-Target-URI\":\"https://www.geeksforgeeks.org/python-bokeh-visualizing-stock-data/?ref=rp\",\"WARC-Payload-Digest\":\"sha1:MNSCJ3FCZ3EMCKBKRPPIA4K52HA7TPX2\",\"WARC-Block-Digest\":\"sha1:XHFFKJZFSZRZNIT4YODWBA3O2KDWTKYE\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323585405.74_warc_CC-MAIN-20211021102435-20211021132435-00695.warc.gz\"}"}
https://www.jetbrains.com/help/webstorm/2016.1/extract-parameter-in-javascript.html	[ "# Extract Parameter in JavaScript\n\nThe Extract Parameter refactoring is used to add a new parameter to a method declaration and to update the method calls accordingly.\n\n## Examples\n\nThe following table shows two different ways of extracting a function parameter.\n\nIn the first of the examples a new parameter is extracted as an optional parameter. So the corresponding function call doesn't change.\n\nIn the second of the examples the parameter is extracted as a required parameter. So the corresponding function call changes accordingly.\n\nBeforeAfter\n```// A new parameter will be added to this // function to replace the 1's:functioncalculate_sum(i) { alert('Adding ' +1+ ' to ' + i);return1+ i; }functionshow_sum() { // Here is the function call: alert('Result: ' + calculate_sum(5)); } // When adding a new parameter we'll specify // that it should be an optional one.```\n```// The new parameter i2has been added // as an optional parameter:functioncalculate_sum(i,i2) {i2 = i2 \|\| 1;alert('Adding ' +i2+ ' to ' + i);returni2+ i; } function show_sum() { // The function call has not changed: alert('Result: ' + calculate_sum(5)); }```\n```// A new parameter will be added to this // function to replace the 1's:functioncalculate_sum(i) { alert('Adding ' +1+ ' to ' + i);return1+ i; }functionshow_sum() { // Here is the function call: alert('Result: ' + calculate_sum(5)); } // When adding a new parameter we'll specify // that it should be a required one.```\n```// The new parameter i2has been added // as a required parameter: function calculate_sum(i,i2) { alert('Adding ' +i2+ ' to ' + i); returni2+ i; } function show_sum() { // The function call changed accordingly: alert('Result: ' + calculate_sum(5,1)); }```\n\n## Extracting a Parameter in JavaScript\n\n1. In the editor, place the cursor within the expression to be replaced by a parameter.\n2. Do one of the following:\n• Press Ctrl+Alt+P.\n• Choose Refactor \| Extract \| Parameter in the main menu.\n• Choose Refactor \| Extract \| Parameter from the context menu.\n3. If more than one expression is detected for the current cursor position, the Expressions list appears. If this is the case, select the required expression. To do that, click the expression. Alternatively, use the Up and Down arrow keys to navigate to the expression of interest, and then press Enter to select it.\n\n4. In the Extract Parameter dialog:\n1. Specify the parameter name in the Name field.\n2. The Value field, initially, contains the expression that you have selected. Normally, you don't need to change this. (Depending on whether the option Optional parameter is selected or not, this will be the value assigned to the new parameter in the function body or passed to the function in the function calls.)\n3. If, when extracting a new parameter, you don't want to change the function calls, select the Optional parameter check box. If you do so, the value specified in the Value field will be assigned to the new parameter in the function body. The calls to the function (if any) won't change.\n\nIf you want to pass the value (specified in the Value field) to the new parameter through the existing function calls, clear the Optional parameter check box. If you do so, all the function calls will change according to the new function signature; no explicit assignment of the parameter value will be added to the function body.\n\n4. If more than one occurrence of the expression is found within the function body, you can choose to replace only the selected occurrence or all the found occurrences with the references to the new parameter. Use the Replace all occurrences check box to specify your intention.\n5. Click OK." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6807636,"math_prob":0.92080456,"size":2300,"snap":"2023-14-2023-23","text_gpt3_token_len":450,"char_repetition_ratio":0.19729964,"word_repetition_ratio":0.062176164,"special_character_ratio":0.19608696,"punctuation_ratio":0.1014151,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9756906,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-03-28T21:35:52Z\",\"WARC-Record-ID\":\"<urn:uuid:aea407d0-2672-4442-97a2-37606901d855>\",\"Content-Length\":\"19073\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b2921291-4d85-447c-979c-6877cb67c7e7>\",\"WARC-Concurrent-To\":\"<urn:uuid:029c3c32-0411-43e7-b56e-db10fc60c60a>\",\"WARC-IP-Address\":\"108.138.85.7\",\"WARC-Target-URI\":\"https://www.jetbrains.com/help/webstorm/2016.1/extract-parameter-in-javascript.html\",\"WARC-Payload-Digest\":\"sha1:32QA6SRPN45KTSX3DAC467TK22GMNCHI\",\"WARC-Block-Digest\":\"sha1:F6Q5HCGJ6UO6DW764XFZ6DGG2JV6XGIG\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-14/CC-MAIN-2023-14_segments_1679296948871.42_warc_CC-MAIN-20230328201715-20230328231715-00516.warc.gz\"}"}
https://metric-calculator.com/convert-miles-per-second-to-foot-per-hour.htm	[ "# Miles Per Second to Feet Per Hour Converter\n\nSelect conversion type:\n\nRounding options:\n\nConvert Feet Per Hour to Miles Per Second (ft/h to mi/s) ▶\n\n## Conversion Table\n\n miles per second to feet per hour mi/s ft/h 1 mi/s 19008000 ft/h 2 mi/s 38016000 ft/h 3 mi/s 57024000 ft/h 4 mi/s 76032000 ft/h 5 mi/s 95040000 ft/h 6 mi/s 114048000 ft/h 7 mi/s 133056000 ft/h 8 mi/s 152064000 ft/h 9 mi/s 171072000 ft/h 10 mi/s 190080000 ft/h 11 mi/s 209088000 ft/h 12 mi/s 228096000 ft/h 13 mi/s 247104000 ft/h 14 mi/s 266112000 ft/h 15 mi/s 285120000 ft/h 16 mi/s 304128000 ft/h 17 mi/s 323136000 ft/h 18 mi/s 342144000 ft/h 19 mi/s 361152000 ft/h 20 mi/s 380160000 ft/h\n\n## How to convert\n\n1 mile per second (mi/s) = 19008000 foot per hour (ft/h). Mile Per Second (mi/s) is a unit of Speed used in Standard system. Foot Per Hour (ft/h) is a unit of Speed used in Standard system.\n\n## Miles per second: A unit of speed\n\nMiles per second (mi/s) is a unit of speed or velocity in the US customary and imperial systems. It measures how fast an object is moving by calculating the distance traveled in miles divided by the time taken in seconds. For example, if a bullet travels 1 mile in 0.5 seconds, its speed is 2 mi/s.\n\n## How to convert miles per second\n\nMiles per second can be converted to other units of speed or velocity by using simple conversion factors. Here are some common units and their conversion factors:\n\n• Meters per second (m/s): To convert from mi/s to m/s, multiply by 1609.34. To convert from m/s to mi/s, divide by 1609.34. For example, 1 mi/s is equal to 1609.34 m/s, and 100 m/s is equal to 0.0621371 mi/s.\n• Kilometers per hour (km/h): To convert from mi/s to km/h, multiply by 5793.64. To convert from km/h to mi/s, divide by 5793.64. For example, 1 mi/s is equal to 5793.64 km/h, and 50 km/h is equal to 0.00863028 mi/s.\n• Miles per hour (mph): To convert from mi/s to mph, multiply by 3600. To convert from mph to mi/s, divide by 3600. For example, 1 mi/s is equal to 3600 mph, and 60 mph is equal to 0.0166667 mi/s.\n• Knots (kn): To convert from mi/s to kn, multiply by 3128.31. To convert from kn to mi/s, divide by 3128.31. For example, 1 mi/s is equal to 3128.31 kn, and 15 kn is equal to 0.00479717 mi/s.\n• Feet per second (ft/s): To convert from mi/s to ft/s, multiply by 5280. To convert from ft/s to mi/s, divide by 5280. For example, 1 mi/s is equal to 5280 ft/s, and 40 ft/s is equal to 0.00757576 mi/s.\n• Inches per second (in/s): To convert from mi/s to in/s, multiply by 63360. To convert from in/s to mi/s, divide by 63360. For example, 1 mi/s is equal to 63360 in/s, and 20 in/s is equal to 0.000315789 mi/s.\n\n## Where miles per second are used\n\nMiles per second are mainly used in physics and astronomy to measure the speed or velocity of very fast objects and phenomena.\n\nFor example, the escape velocity of the Earth is about 11 km/s or about 6.84 mi/s.\n\nThe orbital velocity of the Earth around the Sun is about 30 km/s or about 18.64 mi/s.\n\nThe speed of light in a vacuum is about 300000 km/s or about 186282 mi/s.\n\nThe speed of sound in air at sea level is about 343 m/s or about 0.213139 mi/s.\n\n## Definition of miles per second\n\nAccording to the US customary and imperial systems definition, one mile per second is the speed of a body that covers a distance of one mile in a time of one second.\n\nMathematically, it can be expressed as:\n\nwhere v is the speed or velocity in miles per second, s is the distance traveled in miles, and t is the time taken in seconds.\n\n## History of miles per second\n\nThe concept of speed or velocity has been studied since ancient times by philosophers and scientists such as Aristotle, Galileo, Newton, etc.\n\nThe mile was originally derived from the Roman mile which was defined as one thousand paces or about 5000 Roman feet.\n\nThe second was originally defined in terms of the Earth’s rotation as one eighty-six thousand four hundredth of a mean solar day.\n\nThe combination of these two units resulted in the mile per second as a unit of speed or velocity.\n\nThe mile per second was officially adopted as part of the US customary and imperial systems in the late 18th century.\n\n## Example conversions of miles per second to other units\n\nHere are some examples of converting miles per second to other units of speed or velocity:\n\n• 1 mi/s = 1609.34 m/s = 5793.64 km/h = 3600 mph = 3128.31 kn = 5280 ft/s = 63360 in/s\n• 2 mi/s = 3218.68 m/s = 11587.28 km/h = 7200 mph = 6256.62 kn = 10560 ft/s = 126720 in/s\n• 5 mi/s = 8046.7 m/s = 28968.2 km/h = 18000 mph = 15657.55 kn = 26400 ft/s = 316800 in/s\n• 10 mi/s = 16093.4 m/s = 57936.4 km/h = 36000 mph = 31283.1 kn = 52800 ft/s = 633600 in/s\n• 20 mi/s = 32186.8 m/s = 115872.8 km/h = 72000 mph = 62566.2 kn = 105600 ft/s = 1267200 in/s\n• 50 mi/s = 80467 m/s = 289682 km/h = 180000 mph = 156575.5 kn = 264000 ft/s = 3168000 in/s\n• 100 mi/s = 160934 m/s = 579364 km/h = 360000 mph = 312831 kn = 528000 ft/s = 6336000 in/s\nMiles per second also can be marked as mps.\n\n## Definition of Feet Per Hour\n\nFeet per hour (f/h) is a unit of speed that measures how fast something is moving in terms of feet per unit of time. It is a US Standard unit that is derived from the base unit of length, the foot, and the base unit of time, the hour. It is rarely used however, as the units of feet per second and miles per hour are considered sufficient for most situations.\n\nOne foot per hour is equal to 0.000084666666666667 meters per second, or 0.0003048 kilometers per hour. It can also be converted to other units of speed, such as miles per hour, knots, or meters per second, by using appropriate conversion factors.\n\n## How to Convert Feet Per Hour\n\nTo convert feet per hour to other units of speed, we need to multiply or divide by the corresponding conversion factors. For example, to convert feet per hour to miles per hour, we need to multiply by 0.0001893939394, since there are 0.0001893939394 miles in one foot. To convert feet per hour to meters per second, we need to multiply by 0.000084666666666667, since there are 0.000084666666666667 meters in one foot.\n\nHere are some examples of how to convert feet per hour to other units of length in the US Standard system and the SI system:\n\n• To convert 10 f/h to miles per hour (mph), we multiply by 0.0001893939394: 10 f/h x 0.0001893939394 = 0.001893939394 mph\n• To convert 20 f/h to feet per second (fps), we divide by 3600, since there are 3600 seconds in one hour: 20 f/h / 3600 = 0.005555555556 fps\n• To convert 30 f/h to knots (kn), we multiply by 0.0001645788337, since there are 0.0001645788337 nautical miles in one foot: 30 f/h x 0.0001645788337 = 0.004937365011 kn\n• To convert 40 f/h to meters per second (m/s), we multiply by 0.000084666666666667: 40 f/h x 0.000084666666666667 = 0.003386666667 m/s\n• To convert 50 f/h to meters per minute (m/min), we multiply by 0.00508, since there are 0.00508 meters in one foot: 50 f/h x 0.00508 = 0.254 m/min\n• To convert 60 f/h to centimeters per second (cm/s), we multiply by 100, since there are 100 centimeters in one meter, and multiply by 0.000084666666666667: 60 f/h x 100 x 0.000084666666666667 = 0.508 cm/s\n\n## Where Feet Per Hour Are Used\n\nFeet per hour are mainly used for measuring very slow speeds or velocities of objects or phenomena that move in terms of feet per unit of time. They are often used in scientific fields such as geology, biology, astronomy, and physics, where the speed or velocity of an object or phenomenon is very small compared to the usual units of speed.\n\nFor example, a glacier may have a speed of a few feet per hour, which means that it moves a few feet in one hour. A snail may have a speed of up to 47 feet per hour, which means that it can travel up to 47 feet in one hour.1 A planet may have an orbital velocity of thousands of feet per hour, which means that it covers thousands of feet along its orbit in one hour.\n\nFeet per hour are also used in some other fields where the speed or velocity of an object or phenomenon is measured in terms of feet per unit of time.\n\n## History of Feet Per Hour\n\nThe origin of feet per hour as a unit of speed can be traced back to the development of the US Standard system and the foot as a unit of length in the late eighteenth century. The foot was defined as one third of a yard based on the English standard foot.\n\nThe term foot first appeared in English in the late fourteenth century, but it was not until later in the early nineteenth century that the use of feet per hour became more common; before that, other units such as inches per hour or yards per hour were preferred for expressing speed.\n\nFeet per hour have been used ever since as a standard unit of speed for measuring very slow speeds or velocities of objects or phenomena that move in terms of feet per unit of time. They have also been adopted by some international organizations and conventions, such as the International System of Units and the International Astronomical Union.\n\n## Example Conversions of Feet Per Hour to Other Units\n\nHere are some examples of how to convert feet per hour to other units of speed, using the conversion factors given above:\n\n• To convert 100 f/h to miles per hour, we multiply by 0.0001893939394: 100 f/h x 0.0001893939394 = 0.01893939394 mph\n• To convert 200 f/h to feet per second, we divide by 3600: 200 f/h / 3600 = 0.05555555556 fps\n• To convert 300 f/h to knots, we multiply by 0.0001645788337: 300 f/h x 0.0001645788337 = 0.04937365011 kn\n• To convert 400 f/h to meters per second, we multiply by 0.000084666666666667: 400 f/h x 0.000084666666666667 = 0.03386666667 m/s\n• To convert 500 f/h to meters per minute, we multiply by 0.00508: 500 f/h x 0.00508 = 2.54 m/min\n• To convert 600 f/h to centimeters per second, we multiply by 100 and multiply by 0.000084666666666667: 600 f/h x 100 x 0.000084666666666667 = 5.08 cm/s\n• To convert 700 f/h to millimeters per minute, we multiply by 1000, since there are 1000 millimeters in one meter, and multiply by 0.00508: 700 f/h x 1000 x 0.00508 = 3556 mm/min\nFoot per hour also can be marked as foot/hour.\n\nEspañol Russian Français" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9109782,"math_prob":0.9918323,"size":6914,"snap":"2023-40-2023-50","text_gpt3_token_len":1604,"char_repetition_ratio":0.20607814,"word_repetition_ratio":0.19496855,"special_character_ratio":0.22505063,"punctuation_ratio":0.06613947,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9989145,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-08T12:41:38Z\",\"WARC-Record-ID\":\"<urn:uuid:c1124530-a713-487e-9da9-f59e0ca076a4>\",\"Content-Length\":\"33126\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:27b1ac16-fdda-4033-98d0-fd1f03516c86>\",\"WARC-Concurrent-To\":\"<urn:uuid:664f802d-585b-4308-b4dd-fab20091b3ed>\",\"WARC-IP-Address\":\"67.222.24.105\",\"WARC-Target-URI\":\"https://metric-calculator.com/convert-miles-per-second-to-foot-per-hour.htm\",\"WARC-Payload-Digest\":\"sha1:GB6ZWPJKRIGMWOXQ6KXEIQN5NOXPZRUG\",\"WARC-Block-Digest\":\"sha1:LZEJFS6LYZQBMNEQNOD6KVNRZ4QYOSZO\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100745.32_warc_CC-MAIN-20231208112926-20231208142926-00023.warc.gz\"}"}
https://transwriters.com/solved/279042/	[ "## (Solved) I need help answering all of the following questions and diagrams\n\nI need help answering all of the following questions and diagrams for ET1310 Lab 2.1 Report (Parts 1, 2, and 3). Please and Thank you in advanced. Whom ever does this for me, you're a life savor!\n\nI am also willing to up the price\n\nET1310: Module 2 DC Power Supplies and BJTs\n\nLab/BJT Characteristics and Biasing\n\nLab 2.1 Report\n\nName:\n\nDate:\n\nInstructions:\n\nComplete the three parts?Part 1, Part 2, and Part 3 of Lab 1. When you have completed each part,\n\nanswer the questions and transcribe/transfer the test results recorded in the lab manual?s tables to the\n\ntables provided.\n\nPart 1?BJT Characteristics\n\nTheory:\n\n1. Name the three terminals of a BJT transistor.\n\n2. Why are BJT transistors considered current amplifiers?\n\n3. What is the relationship between IC and IE?\n\n4. Describe how to bias a BJT transistor correctly.\n\n5. What is the forward-biased voltage drop across the base-emitter junction?\n\nPreparation:\n\n6. Transcribe the component measurements from Table 6-1 to the table below.\n\nComponent\n\nR1\n\nR2\n\nRBB\n\nRCC\n\nListed Value\n\n22 k Ohm\n\n100 Ohm\n\n1 k Ohm\n\n5 k Ohm\n\nTable 6-1\n\nMeasured Value\n\n7. For a 2N3904 NPN General Purpose BJT transistor, how can you determine the location of pin 1?\n\nthe emitter?\n\nTest Procedure:\n\n8. Transcribe the collector current measurements and calculations from Table 6-2 to the table below.\n\nVCE\n\n1\n\nBase Current = 50 µA\n\nBase Current = 100 µA\n\nBase Current = 150 µA\n\nET1310: Module 2 DC Power Supplies and BJTs\n\nLab/BJT Characteristics and Biasing\n\nMeasured\n\nVR2\n\nIC\n\nVR2\n\nIC\n\nVR2\n\nMeasured\n\nComputed\n\nMeasured\n\nComputed\n\nMeasured\n\n2.0 V\n\n4.0 V\n\n6.0 V\n\n8.0 V\n\nTable 6-2\n\n9. Transcribe the three collector characteristic curves from Plot 6-1 to the plot below.\n\nPlot 6-1\n\n10. Transcribe the DC Beta calculations from Table 6-3 to the table below.\n\nVCE\n\nMeasured\n\nCurrent Gain ?DC\n\nIB = 50 µA\n\nIB = 100\n\nIB = 150\n\nµA\n\n3.0 V\n\n5.0 V\n\nTable 6-3\n\n2\n\nµA\n\nLab 2.1 Report\n\nIC\n\nComputed\n\nET1310: Module 2 DC Power Supplies and BJTs\n\nLab/BJT Characteristics and Biasing\n\nLab 2.1 Report\n\n11. Does the experimental data indicate that ?DC is a constant at all points? Does this have any effect on\n\nthe linearity of the transistor?\n\n12. What effect would a higher ?DC have on the characteristic curves you measured?\n\n13. What is the maximum power dissipated in the transistor for the data taken in the experiment?\n\n14. The DC alpha (?) of a bipolar transistor is the collector current, IC, divided by the emitter current, IE.\n\nUsing this definition and IE = IC + IB, prove that DC alpha can be written as:\n\n? DC =\n\n? DC\n\n? DC +1\n\n15. Compute DC alpha for your transistor at VCE = 4.0 V and IB = 100 ?A.\n\n16. What value of VCE would you expect if the base terminal of a transistor were open? Explain your\n\n3\n\nET1310: Module 2 DC Power Supplies and BJTs\n\nLab/BJT Characteristics and Biasing\n\nLab 2.1 Report\n\nPart 2?BJT Biasing\n\nTheory:\n\n17. How do we describe the nonchanging, no signal output of a biased transistor circuit?\n\n18. Why is the base biasing method unacceptable for linear circuits?\n\n19. For which application is base biasing most suitable?\n\n20. What is the advantage and disadvantage of the emitter bias circuit?\n\n21. What is the advantage of voltage-divider bias? What is stiff bias?\n\n22. What effect does negative feedback have in a collector-feedback bias circuit?\n\nPreparation:\n\n23. Transcribe the resister measurements from Table 7-1 to the table below.\n\nResisto\n\nListed Value\n\nMeasured Value\n\nr\n\nRB\n\nRC\n\n1 M Ohm\n\n2 k Ohm (Two 1 k\n\nresistors)\n\nTable 7-1\n\nTest Procedure:\n\n24. Transcribe the base biasing circuit calculations and measurements from Table 7-2 to the table below.\n\nDC\n\nParameter\n\nVRB\n\nIB\n\nIC\n\nVRC\n\nVC\n\nComputed\n\nValue\n\nQ1\n\nMeasured Value\n\nQ2\n\nQ3\n\nTable 2-5\n\n25. Describe the variation between the three VRC measurements. What does this variation represent?\n\n26. Transcribe the resister measurements from Table 7-3 to the table below.\n\nResisto\n\nr\n\n4\n\nListed Value\n\nMeasured Value\n\nET1310: Module 2 DC Power Supplies and BJTs\n\nLab/BJT Characteristics and Biasing\n\nLab 2.1 Report\n\nR1\n\nR2\n\nRE\n\nRC\n\n33 k Ohm\n\n6.8 k Ohm\n\n470 Ohm\n\n2 k Ohm (Two 1 k\n\nresistors)\n\nTable 7-3\n\n27. Transcribe the voltage divider biasing circuit calculations and measurements from Table 7-4 to the\n\ntable below.\n\nDC\n\nParameter\n\nVB\n\nVE\n\nIE?IC\n\nVRC\n\nVC\n\nComputed\n\nValue\n\nQ1\n\nMeasured Value\n\nQ2\n\nQ3\n\nTable 7-4\n\n28. Describe the variation between the three VRC measurements. Is this variation greater than, the\n\nsame, or less than the variation in the base bias circuit? Explain why.\n\n29. Transcribe the resister measurements from Table 7-5 to the table below.\n\nResisto\n\nListed Value\n\nMeasured Value\n\nr\n\nRB\n\nRC\n\n360 k Ohm\n\n2 k Ohm (Two 1 k\n\nresistors)\n\nTable 7-5\n\n30. Transcribe the collector feedback biasing circuit calculations and measurements from Table 7-6 to the\n\ntable below.\n\nDC\n\nParameter\n\nIC?IE\n\nVRC\n\nVC\n\nComputed\n\nValue\n\nQ1\n\nMeasured Value\n\nQ2\n\nQ3\n\nTable 7-6\n\n31. Describe the variation between the three VRC measurements. Is this variation greater than, the\n\nsame, or less than the variation in the base bias circuit? Explain why.\n\n32. Compare your observations of the three bias methods tested in the experiment. Which one showed\n\nthe least variation between the transistors?\n\n5\n\nET1310: Module 2 DC Power Supplies and BJTs\n\nLab/BJT Characteristics and Biasing\n\nLab 2.1 Report\n\n33. Draw each of the three bias circuits tested in the experiment for a PNP transistor. Assuming the same\n\nresistors as used in the experiment, compute the base, emitter, and collector voltages. Show these\n\nBase Bias\n\nVoltage-Divider Bias\n\nCollector-Feedback Bias\n\n6\n\nET1310: Module 2 DC Power Supplies and BJTs\n\nLab/BJT Characteristics and Biasing\n\nLab 2.1 Report\n\n34. Assume you need to bias the amplifier shown below. It is desired to have the Q-point set to\n\napproximately 20 mA of the collector current. Choose bias resistors for the voltage-divider bias that\n\nwill provide a reasonably stiff bias. Show your work.\n\n35. Assume you need to bias the amplifier shown below. It is desired to have the Q-point set to\n\napproximately 5.0 mA of the collector current. Choose a base resistor for the collector feedback bias\n\nthat will provide a reasonably stiff bias. Show your work.\n\n36. For the circuit shown below and using the values calculated in problem #34, predict the effect of each\n\nof the following problems on the collector voltage:\n\n7\n\nET1310: Module 2 DC Power Supplies and BJTs\n\nLab/BJT Characteristics and Biasing\n\nLab 2.1 Report\n\na. R1 opens.\n\nb. Base is shorted to ground through a solder bridge.\n\nc.\n\nRE is 470 Ohm instead of 47 Ohm.\n\nd. VCC drops to +15 V.\n\n8\n\nET1310: Module 2 DC Power Supplies and BJTs\n\nLab/BJT Characteristics and Biasing\n\nLab 2.1 Report\n\nPart 3?The Basic Power Supply\n\nTest Procedure:\n\n37. Transcribe the power supply fault observations from Table L2-1 to the table below.\n\nCircuit\n\nComponent\n\nFault\n\nPower Supply Fault 1a\n\nPower Supply Fault 1b\n\nPower Supply Fault 1c\n\nPower Supply Fault 2a\n\nPower Supply Fault 2b\n\nPower Supply Fault 2c\n\nTable L2-1\n\n9\n\nSymptoms of the Fault\n\nSolution details:\nSTATUS\nQUALITY\nApproved\n\nThis question was answered on: Oct 15, 2019\n\nSolution~000.zip (25.37 KB)\n\nSTATUS\n\nQUALITY\n\nApproved\n\nOct 15, 2019\n\nEXPERT\n\nTutor\n\n#### YES, THIS IS LEGAL\n\nWe have top-notch tutors who can do your essay/homework for you at a reasonable cost and then you can simply use that essay as a template to build your own arguments.\n\nYou can also use these solutions:\n\n• As a reference for in-depth understanding of the subject.\n• As a source of ideas / reasoning for your own research (if properly referenced)\n• For editing and paraphrasing (check your institution's definition of plagiarism and recommended paraphrase).\nThis we believe is a better way of understanding a problem and makes use of the efficiency of time of the student.\n\n### Order New Solution. 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Place a New Order using the button below.\n\nWE GUARANTEE, THAT YOUR PAPER WILL BE WRITTEN FROM SCRATCH AND WITHIN A DEADLINE.", null, "" ]	[ null, "https://transwriters.com/wp-content/themes/premier/images/order_now.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8274692,"math_prob":0.8583199,"size":8137,"snap":"2020-34-2020-40","text_gpt3_token_len":2219,"char_repetition_ratio":0.1300873,"word_repetition_ratio":0.20243205,"special_character_ratio":0.24714269,"punctuation_ratio":0.12099214,"nsfw_num_words":1,"has_unicode_error":false,"math_prob_llama3":0.9724858,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-23T11:58:58Z\",\"WARC-Record-ID\":\"<urn:uuid:57801e78-1bea-4261-94b6-394438b9e048>\",\"Content-Length\":\"49489\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:8bc23236-10f1-43fe-aed4-3a3c67ab47b3>\",\"WARC-Concurrent-To\":\"<urn:uuid:55cbae61-ed74-4051-8852-6c53cb7f77d7>\",\"WARC-IP-Address\":\"104.18.39.45\",\"WARC-Target-URI\":\"https://transwriters.com/solved/279042/\",\"WARC-Payload-Digest\":\"sha1:JICH7JMTBL6OPKTDTTOKJQN3GTDBH6HO\",\"WARC-Block-Digest\":\"sha1:ZLMYDGR6VB6TYU3OZWPALKHCCRPQXJYY\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600400210996.32_warc_CC-MAIN-20200923113029-20200923143029-00351.warc.gz\"}"}
https://www.colorhexa.com/036f9f	[ "# #036f9f Color Information\n\nIn a RGB color space, hex #036f9f is composed of 1.2% red, 43.5% green and 62.4% blue. Whereas in a CMYK color space, it is composed of 98.1% cyan, 30.2% magenta, 0% yellow and 37.6% black. It has a hue angle of 198.5 degrees, a saturation of 96.3% and a lightness of 31.8%. #036f9f color hex could be obtained by blending #06deff with #00003f. Closest websafe color is: #006699.\n\n• R 1\n• G 44\n• B 62\nRGB color chart\n• C 98\n• M 30\n• Y 0\n• K 38\nCMYK color chart\n\n#036f9f color description : Dark blue.\n\n# #036f9f Color Conversion\n\nThe hexadecimal color #036f9f has RGB values of R:3, G:111, B:159 and CMYK values of C:0.98, M:0.3, Y:0, K:0.38. Its decimal value is 225183.\n\nHex triplet RGB Decimal 036f9f `#036f9f` 3, 111, 159 `rgb(3,111,159)` 1.2, 43.5, 62.4 `rgb(1.2%,43.5%,62.4%)` 98, 30, 0, 38 198.5°, 96.3, 31.8 `hsl(198.5,96.3%,31.8%)` 198.5°, 98.1, 62.4 006699 `#006699`\nCIE-LAB 44.075, -8.262, -33.228 11.978, 13.89, 34.849 0.197, 0.229, 13.89 44.075, 34.24, 256.036 44.075, -28.854, -47.866 37.27, -7.852, -29.35 00000011, 01101111, 10011111\n\n# Color Schemes with #036f9f\n\n• #036f9f\n``#036f9f` `rgb(3,111,159)``\n• #9f3303\n``#9f3303` `rgb(159,51,3)``\nComplementary Color\n• #039f81\n``#039f81` `rgb(3,159,129)``\n• #036f9f\n``#036f9f` `rgb(3,111,159)``\n• #03219f\n``#03219f` `rgb(3,33,159)``\nAnalogous Color\n• #9f8103\n``#9f8103` `rgb(159,129,3)``\n• #036f9f\n``#036f9f` `rgb(3,111,159)``\n• #9f0321\n``#9f0321` `rgb(159,3,33)``\nSplit Complementary Color\n• #6f9f03\n``#6f9f03` `rgb(111,159,3)``\n• #036f9f\n``#036f9f` `rgb(3,111,159)``\n• #9f036f\n``#9f036f` `rgb(159,3,111)``\n• #039f33\n``#039f33` `rgb(3,159,51)``\n• #036f9f\n``#036f9f` `rgb(3,111,159)``\n• #9f036f\n``#9f036f` `rgb(159,3,111)``\n• #9f3303\n``#9f3303` `rgb(159,51,3)``\n• #023b54\n``#023b54` `rgb(2,59,84)``\n• #024c6d\n``#024c6d` `rgb(2,76,109)``\n• #035e86\n``#035e86` `rgb(3,94,134)``\n• #036f9f\n``#036f9f` `rgb(3,111,159)``\n• #0380b8\n``#0380b8` `rgb(3,128,184)``\n• #0492d1\n``#0492d1` `rgb(4,146,209)``\n• #04a3ea\n``#04a3ea` `rgb(4,163,234)``\nMonochromatic Color\n\n# Alternatives to #036f9f\n\nBelow, you can see some colors close to #036f9f. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #03969f\n``#03969f` `rgb(3,150,159)``\n• #03899f\n``#03899f` `rgb(3,137,159)``\n• #037c9f\n``#037c9f` `rgb(3,124,159)``\n• #036f9f\n``#036f9f` `rgb(3,111,159)``\n• #03629f\n``#03629f` `rgb(3,98,159)``\n• #03559f\n``#03559f` `rgb(3,85,159)``\n• #03489f\n``#03489f` `rgb(3,72,159)``\nSimilar Colors\n\n# #036f9f Preview\n\nThis text has a font color of #036f9f.\n\n``<span style=\"color:#036f9f;\">Text here</span>``\n#036f9f background color\n\nThis paragraph has a background color of #036f9f.\n\n``<p style=\"background-color:#036f9f;\">Content here</p>``\n#036f9f border color\n\nThis element has a border color of #036f9f.\n\n``<div style=\"border:1px solid #036f9f;\">Content here</div>``\nCSS codes\n``.text {color:#036f9f;}``\n``.background {background-color:#036f9f;}``\n``.border {border:1px solid #036f9f;}``\n\n# Shades and Tints of #036f9f\n\nA shade is achieved by adding black to any pure hue, while a tint is created by mixing white to any pure color. In this example, #000305 is the darkest color, while #f1faff is the lightest one.\n\n• #000305\n``#000305` `rgb(0,3,5)``\n• #001118\n``#001118` `rgb(0,17,24)``\n• #011e2b\n``#011e2b` `rgb(1,30,43)``\n• #012c3f\n``#012c3f` `rgb(1,44,63)``\n• #023952\n``#023952` `rgb(2,57,82)``\n• #024765\n``#024765` `rgb(2,71,101)``\n• #025478\n``#025478` `rgb(2,84,120)``\n• #03628c\n``#03628c` `rgb(3,98,140)``\n• #036f9f\n``#036f9f` `rgb(3,111,159)``\n• #037cb2\n``#037cb2` `rgb(3,124,178)``\n• #048ac6\n``#048ac6` `rgb(4,138,198)``\n• #0497d9\n``#0497d9` `rgb(4,151,217)``\n• #04a5ec\n``#04a5ec` `rgb(4,165,236)``\n• #0ab0fa\n``#0ab0fa` `rgb(10,176,250)``\n• #1db6fb\n``#1db6fb` `rgb(29,182,251)``\n• #30bdfb\n``#30bdfb` `rgb(48,189,251)``\n• #43c3fb\n``#43c3fb` `rgb(67,195,251)``\n• #57c9fc\n``#57c9fc` `rgb(87,201,252)``\n• #6acffc\n``#6acffc` `rgb(106,207,252)``\n• #7dd5fd\n``#7dd5fd` `rgb(125,213,253)``\n• #90dcfd\n``#90dcfd` `rgb(144,220,253)``\n• #a4e2fd\n``#a4e2fd` `rgb(164,226,253)``\n• #b7e8fe\n``#b7e8fe` `rgb(183,232,254)``\n• #caeefe\n``#caeefe` `rgb(202,238,254)``\n• #ddf4fe\n``#ddf4fe` `rgb(221,244,254)``\n• #f1faff\n``#f1faff` `rgb(241,250,255)``\nTint Color Variation\n\n# Tones of #036f9f\n\nA tone is produced by adding gray to any pure hue. In this case, #4e5254 is the less saturated color, while #036f9f is the most saturated one.\n\n• #4e5254\n``#4e5254` `rgb(78,82,84)``\n• #48555a\n``#48555a` `rgb(72,85,90)``\n• #415761\n``#415761` `rgb(65,87,97)``\n• #3b5967\n``#3b5967` `rgb(59,89,103)``\n• #355c6d\n``#355c6d` `rgb(53,92,109)``\n• #2f5e73\n``#2f5e73` `rgb(47,94,115)``\n• #28617a\n``#28617a` `rgb(40,97,122)``\n• #226380\n``#226380` `rgb(34,99,128)``\n• #1c6586\n``#1c6586` `rgb(28,101,134)``\n• #16688c\n``#16688c` `rgb(22,104,140)``\n• #0f6a93\n``#0f6a93` `rgb(15,106,147)``\n• #096d99\n``#096d99` `rgb(9,109,153)``\n• #036f9f\n``#036f9f` `rgb(3,111,159)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #036f9f is perceived by people affected by a color vision deficiency. This can be useful if you need to ensure your color combinations are accessible to color-blind users.\n\nMonochromacy\n• Achromatopsia 0.005% of the population\n• Atypical Achromatopsia 0.001% of the population\nDichromacy\n• Protanopia 1% of men\n• Deuteranopia 1% of men\n• Tritanopia 0.001% of the population\nTrichromacy\n• Protanomaly 1% of men, 0.01% of women\n• Deuteranomaly 6% of men, 0.4% of women\n• Tritanomaly 0.01% of the population" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.5327272,"math_prob":0.797855,"size":3675,"snap":"2019-43-2019-47","text_gpt3_token_len":1650,"char_repetition_ratio":0.12585127,"word_repetition_ratio":0.011111111,"special_character_ratio":0.5567347,"punctuation_ratio":0.23809524,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98923594,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-11-13T20:39:15Z\",\"WARC-Record-ID\":\"<urn:uuid:182cd737-a37a-41a8-b52d-e5458152cf84>\",\"Content-Length\":\"36239\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9331c204-f2c9-4140-808e-faa1ebc28161>\",\"WARC-Concurrent-To\":\"<urn:uuid:74eb7e50-f9bb-4ac5-94b4-badf7eb398c5>\",\"WARC-IP-Address\":\"178.32.117.56\",\"WARC-Target-URI\":\"https://www.colorhexa.com/036f9f\",\"WARC-Payload-Digest\":\"sha1:2ILSINMX7MVVDH7ZPEET36CSC5UEWZI6\",\"WARC-Block-Digest\":\"sha1:V6SXQEL36DBRAID5CJZ37L73KYDMJJM4\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-47/CC-MAIN-2019-47_segments_1573496667333.2_warc_CC-MAIN-20191113191653-20191113215653-00378.warc.gz\"}"}
https://bestftxjfjn.web.app/jame10461hut/what-is-annual-interest-rate-loan-get.html	[ "## What is annual interest rate loan\n\nAnnual Percentage Rate (APR) The cost to borrow money expressed as a yearly percentage. For mortgage loans, excluding home equity lines of credit, it includes the interest rate plus other charges or fees. For home equity lines, the APR is just the interest rate.\n\nThe effectual annual interest rate is a useful way of evaluating the actual return on investment and ascertaining the interest expense paid on a loan. Borrowers need to have a solid understanding of the impact cost of debt Cost of Debt The cost of debt is the return that a company provides to its debtholders and creditors. Like other types of debt, the interest rates for personal loans depend on the lender, your credit scores and your credit history. An estimated range of interest rates on personal loans for consumers with fair to good credit is currently between 6% and 36%. You can check on rates available in your state National Average Mortgage Rates. The mortgage rates vary depending upon the type of loan that will be acquired by the consumer. For instance, in February, 2010, the national average mortgage rate for a 30 year fixed rate loan was at 4.750 percent (5.016 APR). Interest rate refers to the annual cost of a loan to a borrower and is expressed as a percentage APR is the annual cost of a loan to a borrower — including fees. Like an interest rate, the APR is expressed as a percentage. Unlike an interest rate, however, it includes other charges or fees such as mortgage insurance,\n\n## Ideal choice for servicemembers, reservists and veterans who have already exhausted their VA loan benefit. Interest rate as low as. 4.750%. APR as low as. 5.038\n\nParts of total cost and effective APR for a 12-month, 5% monthly interest, \\$100 loan paid off in equally sized monthly 15 Jul 2019 An annual percentage rate (APR) is the annual rate charged for borrowing or earned through an investment. APR is expressed as a percentage The interest rate is the cost of borrowing the principal. APR includes other costs associated with borrowing the money. The Federal Truth in Lending Act requires The annual interest rate, sometimes called the standard annual interest rate or base It's the basic interest that you'll pay on your loan or earn on your savings\n\n### What is an interest rate? Interest is the cost of borrowing money typically expressed as an annual percentage of the loan. For savers it\n\nThe weekly Chartered Bank Interest Rates can now be found in a new table: Interest rates Effective October 1, 2019, the monthly rates will be discontinued. Higher rate will be paid on the entire balance if the balance exceeds \\$5,000, Regular Interest Rate, Momentum Savings Premium‡, Total Annual Interest Rate What is the interest rate (in percent) attached to this money? % per. Year (annual interest), 6 month period (semiannually), Month. After how much time The Annual Percentage Rate (APR) is a method to compute annualised credit cost which includes interest rate and processing fee. The APR calculator does not What is a 30-year fixed mortgage? A 30-year fixed mortgage is a loan whose interest rate stays the same for the duration of the loan. For example, on a 30 17 Feb 2020 Understanding annual percentage rates on personal loans. Learn how APR works and what interest rate you could expect on your personal loan. 2 Mar 2020 Compare personal loan interest rates and get the best offer from top banks. with lower annual incomes may have to pay a higher interest rate.\n\n### The Annual Percentage Rate (APR) is a method to compute annualised credit cost which includes interest rate and processing fee. The APR calculator does not\n\nAnnual percentage rate (APR) helps you understand the cost of a loan. Different APRs may have different implications. APRs help you get an apples-to-apples comparison of loans by accounting for every cost related to borrowing. Calculate Monthly Payment. The first step to 24 Sep 2019 The interest rate and the annual percentage rate (APR) on a personal loan are related, but they're not the same thing. An interest rate on a 18 Dec 2019 The APR is a broader measure of the cost of a mortgage because it includes the interest rate plus other costs such as broker fees, discount points 15 Nov 2019 An annual percentage rate (APR) reflects the mortgage interest rate plus other charges. There are many costs associated with taking out a ANZ home loan. View the current home loan interest rates for ANZ home loans. The current comparison interest rate is also included for each type of home loan.\n\n## As such, the annual interest rate on a loan or other form of debt is a percentage that describes the yearly cost of borrowing money. Yearly interest rate payments are calculated by multiplying the interest rate percentage by the total outstanding balance of the loan.\n\nThe following Annual Percentage Rate (“APR”) examples are for a typical transaction and are only examples. Please call 877.907.1043, email us, or find a loan (A)- HOME LOAN INTEREST CARD RATE STRUCTURE (FLOATING) :EBR 7.80 %. LOAN AMOUNT, SALARIED. TERM LOAN. MAXGAIN. Up to Rs While our average personal loan interest rate table above shows annual flat rates around 6%, this rate could jump to 9% to 13% for 3 = Annual Percentage Rates (APR) are calculated based on a loan amount of \\$100,000 for all products except the Jumbo Fixed and Ideal choice for servicemembers, reservists and veterans who have already exhausted their VA loan benefit. Interest rate as low as. 4.750%. APR as low as. 5.038 See if you're charged an establishment fee, monthly or annual fees for your personal loan. Comparing your options by the comparison rate rather than the interest What is APR. Annual Percentage Rate, or APR, is the annual rate charged by a financial institution to loan its funds to borrowers. And while it does include\n\nFor a daily interest rate, divide the annual rate by 360 (or 365, depending on your bank). For a quarterly rate, divide the annual rate by four. For a weekly rate, divide the annual rate by 52. Example: assume you pay interest monthly at 10 percent per year. Annual Percentage Rate (APR) The cost to borrow money expressed as a yearly percentage. For mortgage loans, excluding home equity lines of credit, it includes the interest rate plus other charges or fees. For home equity lines, the APR is just the interest rate. Interest rate is the amount charged by lenders to borrowers for the use of money, expressed as a percentage of the principal, or original amount borrowed; it can also be described alternatively as the cost to borrow money. For instance, an 8% interest rate for borrowing \\$100 a year will obligate a person to pay \\$108 The table below provides interest rates for Direct Subsidized Loans, Direct Unsubsidized Loans, and Direct PLUS Loans first disbursed on or after July 1, 2019, and before July 1, 2020. Perkins Loans (regardless of the first disbursement date) have a fixed interest rate of 5%." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.95920086,"math_prob":0.9234973,"size":6663,"snap":"2022-05-2022-21","text_gpt3_token_len":1447,"char_repetition_ratio":0.1842619,"word_repetition_ratio":0.10544816,"special_character_ratio":0.22107159,"punctuation_ratio":0.0977326,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9648291,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-24T08:32:48Z\",\"WARC-Record-ID\":\"<urn:uuid:c042ae10-bb4e-4b78-8944-6510ce114e24>\",\"Content-Length\":\"19572\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1f3a5840-abaa-49b9-acfa-c3b217500e86>\",\"WARC-Concurrent-To\":\"<urn:uuid:33db1543-38cd-4194-b888-001c1f105c5f>\",\"WARC-IP-Address\":\"199.36.158.100\",\"WARC-Target-URI\":\"https://bestftxjfjn.web.app/jame10461hut/what-is-annual-interest-rate-loan-get.html\",\"WARC-Payload-Digest\":\"sha1:6WW4LEZUWV7V5DU6N4HPNVPOKRXBUAUW\",\"WARC-Block-Digest\":\"sha1:ULSCLKZ4HZQSVSBP7OWCOVV6FFBAOBOA\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662570051.62_warc_CC-MAIN-20220524075341-20220524105341-00107.warc.gz\"}"}
https://octopus-code.org/mediawiki/index.php?title=Manual:Linear_Response&oldid=4401	[ "# Manual:Linear Response\n\nOctopus can calculate dynamic polarizabilities and first order hyperpolarizabilites in a linear response scheme using the Sternheimer equation. It also possible to calculate optical spectra with this technique, but it is slower than time evolution.\n\n## Contents\n\n##### Ground state\n\nThe first thing we will need to do a linear response, it is a Ground State calculation. Unlike other techniques, when using the Sterheimer equation you needn't do a unoccupied states calculation. To improve the convergency of the linear response calculation, it is better to use tightly converged wave functions. For example you can add this parameteres to your gs calculation:\n\nEigenSolverFinalTolerance = 1e-10\nConvAbsDens = 1e-9\n\n\n##### Input\n\nThe CalculationMode for polarizability calculations is pol_lr. The main parameter you have to specify is the frequency of the perturbation, this is given by the PolFreqs block. You can also add an imaginary part to the frequency by setting the variable PolEta. Adding a small imaginary part is required if you want to get the imaginary part of the polarizability or to calculate polarizabilities near resonance, a reasonable value is 0.1 eV.\n\nTo get the hyperpolarizabilties, you also have to specify the PolHyper with the three coefficients with respect to the base frequency, the three values must sum zero.\n\n##### Output\n\nAfter running, fr each frequency in the input file, Octopus will generate a subdirectory under linear/. In each subdirectory there is a file called alpha that contains the real part of the polarizability tensor", null, "and the average polarizability", null, "there is also a file called cross_section_tensor that contains the photo-absorption cross section tensor for that frequency, that it is related to the imaginary part of the polarizability.\n\nThe hyperpolarizabilty will be in a file called beta, containing all the 27 components and some reduced quantities:", null, "#### Finite differences\n\nIn this mode only static polarizability can be obtained, the calculation is done by taking the numerical derivative of the energy with respect to an external static and uniform electric field. To use this run with CalculationMode =pol_fd. Octopus will run several ground state energy calculations (2 per dimension) and then calculate the polarizability using a finite differences formula for the derivative, the resulting tensor will be in the linear/polarizability_fd file.\n\nPrevious Manual:Casida - Next Manual:Spectrum_calculations\n\nBack to Manual" ]	[ null, "https://wikimedia.org/api/rest_v1/media/math/render/png/768573314617898450b38de70be02c6341de6235", null, "https://wikimedia.org/api/rest_v1/media/math/render/png/6e75680a24773e4af5527918381aae6993879156", null, "https://wikimedia.org/api/rest_v1/media/math/render/png/4223c9cce1c990041de4282fef6e6d5404793201", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6379229,"math_prob":0.97421205,"size":5793,"snap":"2021-31-2021-39","text_gpt3_token_len":1367,"char_repetition_ratio":0.24477457,"word_repetition_ratio":0.00486618,"special_character_ratio":0.15380631,"punctuation_ratio":0.040650405,"nsfw_num_words":3,"has_unicode_error":false,"math_prob_llama3":0.98812175,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,null,null,null,null,6,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-17T10:02:04Z\",\"WARC-Record-ID\":\"<urn:uuid:2cec8807-c3bd-497f-9523-ab0c3b2e2d0a>\",\"Content-Length\":\"49773\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6449ef5b-ef4a-4490-adaf-8260475294ff>\",\"WARC-Concurrent-To\":\"<urn:uuid:02c7da68-4078-491b-be9f-72a683670db1>\",\"WARC-IP-Address\":\"193.137.208.252\",\"WARC-Target-URI\":\"https://octopus-code.org/mediawiki/index.php?title=Manual:Linear_Response&oldid=4401\",\"WARC-Payload-Digest\":\"sha1:A4JMJLOZCGYD77Z4C75NHCUSGYUGWXQ5\",\"WARC-Block-Digest\":\"sha1:UZJHCZNHXLPCE7ECO2XDAOTITYXIB2JG\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780055632.65_warc_CC-MAIN-20210917090202-20210917120202-00506.warc.gz\"}"}
https://zonecalc.com/multiplication/what-is-7-times-26/	[ "# What is 7 times 26?\n\nHere we answer one simple question: What is 7 times 26? (or what is 7 multiplied by 26) Here is the answer:\n\n### 7 x 26 = 182\n\nLearning the multiplication of 7 times 26 is an essential skill for problems based upon fractions, decimals, and percentages. It helps in solving real-life problems quickly.\n\nIf you want to find what 7 times 26 means, think of it as 7 added together 26 times. To get the answer, you could just write down the number 7, 26 times and then add the 2 numbers together.\n\nIf you’re using a calculator, you can double-check that the answer is 182 by pressing 7 then x, then 26, and then to get the answer 182.\n\nX" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9344734,"math_prob":0.9663186,"size":651,"snap":"2023-40-2023-50","text_gpt3_token_len":167,"char_repetition_ratio":0.13446677,"word_repetition_ratio":0.0,"special_character_ratio":0.2764977,"punctuation_ratio":0.11347517,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9984018,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-27T08:41:16Z\",\"WARC-Record-ID\":\"<urn:uuid:effd96a3-52b8-4a18-b6dd-7e817366c8ee>\",\"Content-Length\":\"122184\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:76ece368-ceb7-4977-b649-7dcf44012e10>\",\"WARC-Concurrent-To\":\"<urn:uuid:d57fe99a-a516-4dfa-a607-a45c0923f54c>\",\"WARC-IP-Address\":\"172.67.138.214\",\"WARC-Target-URI\":\"https://zonecalc.com/multiplication/what-is-7-times-26/\",\"WARC-Payload-Digest\":\"sha1:MDXLD7IC2MEH2WEESI34UT37HQCTJYM2\",\"WARC-Block-Digest\":\"sha1:GYWIWJXCRMMOSC4SHVL5PTQUI7P4FQRZ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510284.49_warc_CC-MAIN-20230927071345-20230927101345-00178.warc.gz\"}"}
https://intellipaat.com/community/26655/how-to-add-new-elements-to-an-array	[ "# How to add new elements to an array?\n\n1 view\nin Java\n\nI have the following code:\n\nString[] where;\n\nwhere.append(ContactsContract.Contacts.HAS_PHONE_NUMBER + \"=1\");\n\nwhere.append(ContactsContract.Contacts.IN_VISIBLE_GROUP + \"=1\");\n\nThose two appends are not compiling. How would that work correctly?\n\nby (46.1k points)\n\nThe extent of an array can't be altered. If you require a bigger array you ought to instantiate a new one.\n\nA better resolution would be to apply an ArrayList which can develop as you need it. The program ArrayList.toArray( T[] a ) gives you back your array if you require it in this form.\n\nList<String> where = new ArrayList<String>();\n\nIf you require to alter it to a simple array...\n\nString[] simpleArray = new String[ where.size() ];\n\nwhere.toArray( simpleArray );\n\nBut most things you do with an array you can be donewith this ArrayList, too:\n\n// iterate over the array\n\nfor( String oneItem : where ) {\n\n...\n\n}\n\n// get specific items\n\nwhere.get( 1 );" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6577573,"math_prob":0.47612584,"size":767,"snap":"2019-51-2020-05","text_gpt3_token_len":178,"char_repetition_ratio":0.14547837,"word_repetition_ratio":0.0,"special_character_ratio":0.2607562,"punctuation_ratio":0.19333333,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9635302,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-01-22T05:34:19Z\",\"WARC-Record-ID\":\"<urn:uuid:ca5636cf-20d8-4035-8467-d157ea1e5156>\",\"Content-Length\":\"45581\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f8f86c64-3bb1-4ef0-b327-cb8222a25f63>\",\"WARC-Concurrent-To\":\"<urn:uuid:4187e1f9-5e56-41e1-ab87-97fca16034ae>\",\"WARC-IP-Address\":\"104.20.37.203\",\"WARC-Target-URI\":\"https://intellipaat.com/community/26655/how-to-add-new-elements-to-an-array\",\"WARC-Payload-Digest\":\"sha1:Z6QNMGGVYUGR2N5PPZGTBZV5HJBUIYUY\",\"WARC-Block-Digest\":\"sha1:2LC27RNSTPCBSEDHJVUL7NPZXAJXYLO5\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-05/CC-MAIN-2020-05_segments_1579250606696.26_warc_CC-MAIN-20200122042145-20200122071145-00395.warc.gz\"}"}
https://pdsa.gakhov.com/	[ "", null, "# Probabilistic Data Structures and Algorithms for Big Data Applications\n\n## Hashing\n\nWe give a brief overview of popular hash functions and hash tables that are widely used in probabilistic data structures.\n\n• Cryptographic hash functions\n• Non-Cryptographic hash functions\n• Hash tables\n\n## Membership\n\nWe study the most well-known known probabilistic data structures that are used to answer approximate membership queries.\n\n• Bloom filter\n• Counting Bloom filter\n• Quotient filter\n• Cuckoo filter\n\n## Cardinality\n\nWe learn data structures that allow to estimate the number of unique elements in a dataset.\n\n• Linear Counting\n• Probabilistic Counting\n• LogLog and HyperLogLog\n\n## Frequency\n\nWe discuss solutions for common problems in streaming applications, such as finding frequency of some element, filtering most frequent elements in the stream, detecting trending elements, etc.\n\n• Majority algorithm\n• Frequent algorithm\n• Count Sketch\n• Count–Min Sketch\n\n## Rank\n\nWe study data structures to estimate quantiles and percentiles in a data stream using only one pass through the data.\n\n• Random sampling\n• q-digest\n• t-digest\n\n## Similarity\n\nWe learn how to effciently solve the nearest neighbor problem for large datasets using sub-linear in time solutions.\n\n• Locality-Sensitive hashing\n• MinHash\n• SimHash\n\n# Andrii Gakhov, Ph.D.\n\n## Andrii Gakhov is a mathematician and software engineer holding a Ph.D.in mathematical modeling and numerical methods. He has been a teacher in the School of Computer Science at V. Karazin Kharkiv National University in Ukraine for a number of years and currently works as a software practitioner for ferret go GmbH, the leading community moderation, automation, and analytics company in Germany. His fields of interests include machine learning, stream mining, and data analysis.", null, "America\nUnited States Amazon.com Visit\nMexico Amazon.com.mx Visit\nBrazil Amazon.com.br Visit\nEurope\nUnited Kingdom Amazon.co.uk Visit\nGermany BoD (Verlag) Visit\nThalia Visit\nAmazon.de Visit\nAustria BoD (Verlag) Visit\nAmazon.de Visit\nFrance Amazon.fr Visit\nSpain Amazon.es Visit\nItaly Amazon.it Visit\nNetherlands BoD (Verlag) Visit\nAsia\nIndia Amazon.in Visit\nJapan Amazon.co.jp Visit\nOceania\nAustralia Amazon.com.au Visit\n\n## E-book editionExclusively at Amazon\n\nAmerica\nUnited States Amazon.com Visit\nMexico Amazon.com.mx Visit\nBrazil Amazon.com.br Visit\nEurope\nUnited Kingdom Amazon.co.uk Visit\nGermany Amazon.de Visit\nAustria Amazon.de Visit\nFrance Amazon.fr Visit\nSpain Amazon.es Visit\nItaly Amazon.it Visit\nNetherlands Amazon.nl Visit\nAsia\nIndia Amazon.in Visit\nJapan Amazon.co.jp Visit\nOceania\nAustralia Amazon.com.au Visit\n\n# Errata\n\n## If you have found any error that is not in the list below, please contact us by email pdsa@gakhov.com. As soon as the error is confirmed and fixed, its description will appear in this section (details are omitted in mobile view due to space restrictions).\n\nEdition Location Original text Corrected text\n1st, 2019 p. 31 \"... by bitwise XOR, however ...\" \"... by bitwise AND, however ...\"\n1st, 2019 p. 62, Example 3.1 \"... of unique elements is 23 GB.\" \"... of unique elements is 2.3 GB.\"\n1st, 2019 p. 65, Algorithm 3.2 $$\\mathbf{Add}(e, LINEARCOUNTER)$$ $$\\mathbf{Add}(x, LINEARCOUNTER)$$\n1st, 2019 p. 66, Example 3.3 $$V = \\frac{9}{16} = 0.5625$$ $$V = \\frac{7}{16} = 0.4375$$\n1st, 2019 p. 66, Example 3.3 $$n \\approx - 16 \\cdot \\ln{0.5625} \\approx 9.206$$ $$n \\approx - 16 \\cdot \\ln{0.4375} \\approx 13.22$$\n1st, 2019 p. 67 ... a fixed constant $$O(N)$$, where $$N$$ is the total number of elements, including duplicates. Thus, the algorithm has $$O(N)$$ time complexity. ... a fixed constant, and thus the algorithm has $$O(N)$$ time complexity, where $$N$$ is the total number of elements, including duplicates.\n1st, 2019 p. 81, Formula 3.12 $$\\hat n \\approx \\alpha_{m}\\cdot m^{2} \\cdot \\left(\\sum_{j=0}^{m-1}2^{-COUNTER[j]}\\right)$$ $$\\hat n \\approx \\alpha_{m}\\cdot m^{2} \\cdot \\left(\\sum_{j=0}^{m-1}2^{-COUNTER[j]}\\right)^{-1}$$\n1st, 2019 p. 96, Example 4.2 \"... 500 billion ...\" \"... 500 million ...\"\n1st, 2019 p. 135, Example 5.3 \"... remaining empty buffer $$B_{2}$$.\" \"... remaining empty buffer $$B_{4}$$.\"\n1st, 2019 p. 173, Example 6.8 $$c(d_1, d_4) = \\frac{255 \\cdot 0 + 0 \\cdot 191 + 0 \\cdot 255}{255 \\cdot 255} = 0$$ $$c(d_1, d_4) = \\frac{255 \\cdot 0 + 0 \\cdot 191 + 0 \\cdot 255}{\\sqrt{255^{2} + 0^2 + 0^2} \\cdot \\sqrt{0^{2} + 191^2 + 255^2}} = 0$$" ]	[ null, "https://pdsa.gakhov.com/images/pds-book-promo-amzn.jpg", null, "https://pdsa.gakhov.com/images/ebook-available-amazon.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.5604608,"math_prob":0.97758305,"size":3329,"snap":"2019-51-2020-05","text_gpt3_token_len":1072,"char_repetition_ratio":0.17593984,"word_repetition_ratio":0.23931624,"special_character_ratio":0.37578854,"punctuation_ratio":0.21794872,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96908987,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,5,null,5,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-01-23T15:30:22Z\",\"WARC-Record-ID\":\"<urn:uuid:6f4f91d3-d848-4cde-8da5-3ee55107d850>\",\"Content-Length\":\"38322\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7a3aee27-aa52-4fb7-be4c-a679016a56e3>\",\"WARC-Concurrent-To\":\"<urn:uuid:42b15cb0-e46c-47f2-ad64-c98ca765e05f>\",\"WARC-IP-Address\":\"138.201.152.189\",\"WARC-Target-URI\":\"https://pdsa.gakhov.com/\",\"WARC-Payload-Digest\":\"sha1:UOXWV7PT7V6GWFTBLK55G5PHASDECMFW\",\"WARC-Block-Digest\":\"sha1:BIQCMWOBLSZZIOFA6S4VOYG7ATXUVJ7R\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-05/CC-MAIN-2020-05_segments_1579250610919.33_warc_CC-MAIN-20200123131001-20200123160001-00050.warc.gz\"}"}
https://mathoverflow.net/questions/289683/existence-of-double-eigenvalue/289687#289687	[ "# Existence of double eigenvalue\n\nLet $A$ and $B$ be complex $4\\times 4$ matrices. Assume both are Hermitian, and that they are linearly independent.\n\nMust there exist a nonzero real linear combination $aA + bB$ which has a repeated eigenvalue?\n\nThe answer is 'no'. The generic pair $A$ and $B$ of $4$-by-$4$ Hermitian symmetric matrices will not have any nonzero real linear combination that has a double eigenvalue.\nFor a specific example, take $$A = \\begin{pmatrix}-1&0&0&0\\\\0&1&0&0\\\\0&0&-2&0\\\\0&0&0&2\\end{pmatrix} \\quad \\text{and}\\quad B = \\begin{pmatrix}0&i&0&0\\\\-i&0&0&0\\\\0&0&0&2i\\\\0&0&-2i&0\\end{pmatrix}.$$ Then $$\\det(aA+bB - tI_4) = (t^2-a^2-b^2)(t^2-4a^2-4b^2),$$ and the roots of this polynomial in $t$ are distinct unless $a=b=0$. (Recall that we are assuming that $a$ and $b$ are real, which, of course, implies that $t$ is real.)\nAdded Remark: To see the claim that this property holds for a generic linearly independent pair of Hermitian symmetric $4$-by-$4$ matrices $A$ and $B$, it is only necessary to observe the following: The question is whether, for a generic such pair $A$ and $B$ in the $16$-dimensional real vector space $\\mathcal{H}_4$ consisting of $4$-by-$4$ Hermitian symmetric matrices, the (real) span of $A$, $B$, and $I_4$ contains a nonzero element of rank at most $2$. Now, it is not difficult to show that the cone $C_2$ of elements in $\\mathcal{H}_4$ that have rank at most $2$ is a closed algebraic cone of dimension $12$ (one that is singular along the $7$-dimensional locus of elements of rank at most $1$). Hence the generic $3$-dimensional subspace of $\\mathcal{H}_4$ will meet this cone only at the zero matrix. It is also an open (though not dense) condition on a $3$-dimensional subspace that it contain a positive definite element. Since the standard $\\mathrm{GL}(4,\\mathbb{C})$-action on $\\mathcal{H}_4$ acts transitively on the space of positive definite elements, it follows that the generic pair $A$, $B$, together with $I_4$ will span a $3$-plane that meets $C_2$ only at the origin, which is what was to be shown." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8563484,"math_prob":0.999964,"size":2384,"snap":"2021-31-2021-39","text_gpt3_token_len":730,"char_repetition_ratio":0.10252101,"word_repetition_ratio":0.16260162,"special_character_ratio":0.3011745,"punctuation_ratio":0.07883818,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99990404,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-24T20:22:18Z\",\"WARC-Record-ID\":\"<urn:uuid:ba4cf7b6-14e8-473d-8ca6-107e3753bab4>\",\"Content-Length\":\"137951\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:46e6c0ea-704d-43ac-8d76-03042e9e5e20>\",\"WARC-Concurrent-To\":\"<urn:uuid:1aec9d2e-fa65-4ff4-a080-b606c4d1d87a>\",\"WARC-IP-Address\":\"151.101.1.69\",\"WARC-Target-URI\":\"https://mathoverflow.net/questions/289683/existence-of-double-eigenvalue/289687#289687\",\"WARC-Payload-Digest\":\"sha1:LP6Q76OMYWOFNFCKI5AFB3QSDKKVRPQ7\",\"WARC-Block-Digest\":\"sha1:3GHQTLYQC5CNNS7UHGFR7IEJ3V7H4LES\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780057580.39_warc_CC-MAIN-20210924201616-20210924231616-00291.warc.gz\"}"}
https://www.jpost.com/breaking-news/article-745804	[ "(function (a, d, o, r, i, c, u, p, w, m) { m = d.getElementsByTagName(o), a[c] = a[c] \|\| {}, a[c].trigger = a[c].trigger \|\| function () { (a[c].trigger.arg = a[c].trigger.arg \|\| []).push(arguments)}, a[c].on = a[c].on \|\| function () {(a[c].on.arg = a[c].on.arg \|\| []).push(arguments)}, a[c].off = a[c].off \|\| function () {(a[c].off.arg = a[c].off.arg \|\| []).push(arguments) }, w = d.createElement(o), w.id = i, w.src = r, w.async = 1, w.setAttribute(p, u), m.parentNode.insertBefore(w, m), w = null} )(window, document, \"script\", \"https://95662602.adoric-om.com/adoric.js\", \"Adoric_Script\", \"adoric\",\"9cc40a7455aa779b8031bd738f77ccf1\", \"data-key\");\nvar domain=window.location.hostname; var params_totm = \"\"; (new URLSearchParams(window.location.search)).forEach(function(value, key) {if (key.startsWith('totm')) { params_totm = params_totm +\"&\"+key.replace('totm','')+\"=\"+value}}); var rand=Math.floor(10*Math.random()); var script=document.createElement(\"script\"); script.src=`https://stag-core.tfla.xyz/pre_onetag?pub_id=34&domain=\\${domain}&rand=\\${rand}&min_ugl=0\\${params_totm}`; document.head.append(script);" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.98303604,"math_prob":0.96919554,"size":455,"snap":"2023-40-2023-50","text_gpt3_token_len":81,"char_repetition_ratio":0.08869179,"word_repetition_ratio":0.0,"special_character_ratio":0.17142858,"punctuation_ratio":0.10526316,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9789482,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-30T09:09:55Z\",\"WARC-Record-ID\":\"<urn:uuid:f9302079-190f-4fd4-8d62-e3bf3bfd84d3>\",\"Content-Length\":\"70545\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:8793b914-3689-4d66-95e5-9f3362657ab4>\",\"WARC-Concurrent-To\":\"<urn:uuid:a2bf68ba-8e5d-4ffa-9f27-d2a1c49ae58c>\",\"WARC-IP-Address\":\"159.60.130.79\",\"WARC-Target-URI\":\"https://www.jpost.com/breaking-news/article-745804\",\"WARC-Payload-Digest\":\"sha1:OQXR5ESKKMTFBLTHECG7CFPASIBBNS7R\",\"WARC-Block-Digest\":\"sha1:JNDQTUELKHSV6R3JPWP4OZHLYINTNYQY\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510671.0_warc_CC-MAIN-20230930082033-20230930112033-00578.warc.gz\"}"}
https://www.cheric.org/research/tech/periodicals/view.php?seq=694861	[ "Chemical Engineering Science, Vol.62, No.13, 3574-3579, 2007\nA dynamic coupling model for hybrid atomistic-continuum computations\nA dynamic coupling model is developed for a hybrid atomistic-continuum computation in micro- and nano-fluidics. In the hybrid atomistic-continuum computation, a molecular dynamics (MD) simulation is utilized in one region where the continuum assumption breaks down and the Navier-Stokes (NS) equations are used in another region where the continuum assumption holds. In the overlapping part of these two regions, a constrained particle dynamics is needed to couple the MD simulation and the NS equations. The currently existing coupling models for the constrained particle dynamics have a coupling parameter, which has to be empirically determined. In the present work, a novel dynamic coupling model is introduced where the coupling parameter can be calculated as the computation progresses rather than inputing a priori. The dynamic coupling model is based on the momentum constraint and exhibits a correct relaxation rate. The results from the hybrid simulation on the Couette flow and the Stokes flow are in good agreement with the data from the full MD simulation and the solutions of the NS equations, respectively. (c) 2007 Elsevier Ltd. All rights reserved." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.88833976,"math_prob":0.93091124,"size":1295,"snap":"2020-34-2020-40","text_gpt3_token_len":256,"char_repetition_ratio":0.14949651,"word_repetition_ratio":0.01058201,"special_character_ratio":0.1891892,"punctuation_ratio":0.09049774,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97504747,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-20T17:25:08Z\",\"WARC-Record-ID\":\"<urn:uuid:cbb4ff85-827d-489d-8fa9-c44d639c5dbd>\",\"Content-Length\":\"19306\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:678463d2-9ed3-407c-8d61-1332673072f6>\",\"WARC-Concurrent-To\":\"<urn:uuid:4270d276-b750-44a1-99e7-048950c01558>\",\"WARC-IP-Address\":\"14.52.99.14\",\"WARC-Target-URI\":\"https://www.cheric.org/research/tech/periodicals/view.php?seq=694861\",\"WARC-Payload-Digest\":\"sha1:XMTGLX33OOK6WDU7N7YJHVCWPIFDVDTW\",\"WARC-Block-Digest\":\"sha1:HDBETAKKGBUX4TS3RXQR6LYMR2ELF62C\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600400198287.23_warc_CC-MAIN-20200920161009-20200920191009-00483.warc.gz\"}"}
https://au.mathworks.com/matlabcentral/cody/problems/44394-how-to-calculate-the-length-of-a-triangle-s-side-given-two-angles-and-one-side/solutions/1698471	[ "Cody\n\n# Problem 44394. How to calculate the length of a triangle's side given two angles and one side\n\nSolution 1698471\n\nSubmitted on 22 Dec 2018\nThis solution is locked. To view this solution, you need to provide a solution of the same size or smaller.\n\n### Test Suite\n\nTest Status Code Input and Output\n1 Fail\nalpha = 30; beta=40; c=1; a_correct = 0.5300; assert(isequal(triangles(alpha,beta,c),a_correct))\n\nans = 0.5321\n\nAssertion failed.\n\n2 Fail\nalpha = 1; beta=70; c=0.5; a_correct = 0.0100; assert(isequal(triangles(alpha,beta,c),a_correct))\n\nans = 0.0092\n\nAssertion failed.\n\n3 Pass\nalpha = 40; beta=100; c=0.2; a_correct = 0.200; assert(isequal(triangles(alpha,beta,c),a_correct))\n\nans = 0.2000\n\n4 Fail\nalpha = 1; beta=1; c=11; a_correct = 5.5; assert(isequal(triangles(alpha,beta,c),a_correct))\n\nans = 5.5008\n\nAssertion failed.\n\n5 Fail\nalpha = 37; beta=62; c=3; a_correct = 1.8300; assert(isequal(triangles(alpha,beta,c),a_correct))\n\nans = 1.8280\n\nAssertion failed." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.5516296,"math_prob":0.99909437,"size":874,"snap":"2020-24-2020-29","text_gpt3_token_len":313,"char_repetition_ratio":0.15632184,"word_repetition_ratio":0.0,"special_character_ratio":0.40045768,"punctuation_ratio":0.24637681,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9996388,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-07-08T01:26:26Z\",\"WARC-Record-ID\":\"<urn:uuid:0276147f-fd2c-4c7f-b2e5-db4b5bba8fb7>\",\"Content-Length\":\"74105\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:64a2de3b-500b-41f4-abe0-eea6b4823a91>\",\"WARC-Concurrent-To\":\"<urn:uuid:0e1bc5c4-47e4-429d-b60f-112fd82ae33a>\",\"WARC-IP-Address\":\"23.66.56.59\",\"WARC-Target-URI\":\"https://au.mathworks.com/matlabcentral/cody/problems/44394-how-to-calculate-the-length-of-a-triangle-s-side-given-two-angles-and-one-side/solutions/1698471\",\"WARC-Payload-Digest\":\"sha1:W42ADXY2WOKY4T3FY4SPDM7XYFI2OG4A\",\"WARC-Block-Digest\":\"sha1:ZC62MYAOSCGRSHX3R36M44VIJALRJY4X\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-29/CC-MAIN-2020-29_segments_1593655896169.35_warc_CC-MAIN-20200708000016-20200708030016-00027.warc.gz\"}"}
https://astronomy.stackexchange.com/questions/26017/good-source-for-the-relationship-between-absolute-magnitude-diameter-and-albed	[ "# Good source for the relationship between absolute magnitude, diameter, and albedo?\n\nIn this answer I have rearranged an equation from somewhere, and now I can not relocate the source. My re-aranged form is:\n\n$$M_{Abs} = 5 \\left(\\log_{10}(1329) -\\frac{1}{2}\\log_{10}(\\text{albedo}) -\\log_{10}(D_{km})\\right)$$\n\nThis is the relationship between the absolute magnitude of an object and its diameter and albedo, assuming it is spherical.\n\nQuestion: What is a good source for any form of this equation to which I can link in my answer?\n\n• This shouldn't be hard to derive. Twice as large = 4 times as bright, double the albedo = double the brightness, convert both to changes in magnitude, and apply to original absolute magnitude. – barrycarter Apr 23 '18 at 21:53\n• Found while reading for another Q: Wikipedia: Absolute magnitude: Planets – Mike G Jun 25 at 4:57\n• @MikeG Yep, thanks! While I don't see the exact expression there verbatim but I see enough pieces of it in similar form that it is certainly there in spirit. Thanks! – uhoh Jun 25 at 5:03\n\nThe JPL CNEOS asteroid size estimator and various asteroid albedo papers cite Harris and Harris 1997. That paper is behind a paywall, but Stuart and Binzel 2004 attribute this formula to it: $$H = C - 5 \\log_{10} D - 2.5 \\log_{10} p_V$$ where $H$ is absolute magnitude, $p_V$ is albedo, and $C$ = 15.618.\n• That's numerically equivalent and so it will do, thank you! I'm still going to try to find the source that has the exact expression log${}_{10}$(1329) in my own quixocity because it bothers me that I've lost a reference (I suspect due to a variant of this). – uhoh Apr 23 '18 at 22:47" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9138457,"math_prob":0.9088305,"size":443,"snap":"2019-43-2019-47","text_gpt3_token_len":124,"char_repetition_ratio":0.107061505,"word_repetition_ratio":0.0,"special_character_ratio":0.29571107,"punctuation_ratio":0.07865169,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9924459,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-11-14T14:23:35Z\",\"WARC-Record-ID\":\"<urn:uuid:2f094298-42cf-4c32-a90b-beac8b236292>\",\"Content-Length\":\"139621\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4852c98b-f179-4744-8a19-a1a93fdc9a19>\",\"WARC-Concurrent-To\":\"<urn:uuid:1f0615bc-826a-4afb-b15c-42b1d3289165>\",\"WARC-IP-Address\":\"151.101.1.69\",\"WARC-Target-URI\":\"https://astronomy.stackexchange.com/questions/26017/good-source-for-the-relationship-between-absolute-magnitude-diameter-and-albed\",\"WARC-Payload-Digest\":\"sha1:3I2TTNS557RWWIFLLWKW3ZAUEC4KK6QA\",\"WARC-Block-Digest\":\"sha1:PB63VJXI45EY5C7DXLF7ML76Y4R2CWOA\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-47/CC-MAIN-2019-47_segments_1573496668525.62_warc_CC-MAIN-20191114131434-20191114155434-00205.warc.gz\"}"}
https://www.rdocumentation.org/packages/earth/versions/5.3.0/topics/predict.varmod	[ "earth (version 5.3.0)\n\n# predict.varmod: Predict with a varmod model\n\n## Description\n\nYou probably won't need to call this function directly. It is called by `predict.earth` when that function's `interval` argument is used.\n\n## Usage\n\n```# S3 method for varmod\npredict(\nobject = stop(\"no 'object' argument\"),\nnewdata = NULL,\ntype = c(\"pint\", \"cint\", \"se\", \"abs.residual\"),\nlevel = .95,\ntrace = FALSE,\n…)```\n\n## Arguments\n\nobject\n\nA `varmod` object.\n\nnewdata\n\nMake predictions using `newdata`. Default is NULL, meaning return values predicted from the training set.\n\ntype\n\nType of prediction. This is the `interval` argument of `predict.earth`. One of\n\n`\"pint\"` Prediction intervals.\n\n`\"cint\"` Confidence intervals. Cannot be used with `newdata`.\n\n`\"se\"` Standard error of the parent model residuals.\n\n`\"abs.residual\"` The absolute residuals of the parent model on which the residual model regresses.\n\nlevel\n\nConfidence level for the `interval` argument. Default is `.95`, meaning construct 95% confidence bands (estimate the 2.5% and 97.5% levels).\n\ntrace\n\nCurrently unused.\n\nUnused, but provided for generic/method consistency.\n\n## See Also\n\n`predict.earth` `varmod`\n\n## Examples\n\n```# NOT RUN {\ndata(ozone1)\n\nset.seed(1) # optional, for cross validation reproducibility\n\n# note: should really use ncross=30 below but for a quick demo we don't\n\nearth.mod <- earth(O3~temp, data=ozone1, nfold=10, ncross=3, varmod.method=\"lm\")\n\n# call predict.earth, which calls predict.varmod\n\npredict(earth.mod, newdata=ozone1[200:203,], interval=\"pint\", level=.95)\n# }\n```" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6263187,"math_prob":0.7373188,"size":1303,"snap":"2021-04-2021-17","text_gpt3_token_len":343,"char_repetition_ratio":0.12625097,"word_repetition_ratio":0.0,"special_character_ratio":0.26170376,"punctuation_ratio":0.21343873,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9648122,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-04-19T20:04:33Z\",\"WARC-Record-ID\":\"<urn:uuid:34a738db-a45e-4824-a20b-e58831e1b943>\",\"Content-Length\":\"24987\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:88a8506c-d530-47fa-bd65-e45ba2c082bd>\",\"WARC-Concurrent-To\":\"<urn:uuid:5a400803-4463-425d-973e-cbe0d77b5616>\",\"WARC-IP-Address\":\"13.249.42.14\",\"WARC-Target-URI\":\"https://www.rdocumentation.org/packages/earth/versions/5.3.0/topics/predict.varmod\",\"WARC-Payload-Digest\":\"sha1:KK2UGJD7IVJXBDAAQMVBX4D4DOAG64XN\",\"WARC-Block-Digest\":\"sha1:66ZI4FUR6S3DTD3ISYDYOLHCX5YKOQ66\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-17/CC-MAIN-2021-17_segments_1618038916163.70_warc_CC-MAIN-20210419173508-20210419203508-00049.warc.gz\"}"}
https://www.neuron.yale.edu/phpBB/viewtopic.php?f=16&t=4105&sid=f106f0946aa9e571a64c68230591666f	[ "## How does a section recognize a mechanism's current?\n\nNMODL and the Channel Builder.\nduytanph\nPosts: 11\nJoined: Wed Jul 10, 2019 5:03 pm\n\n### How does a section recognize a mechanism's current?\n\nHello. I am quite new to NEURON. I am trying to implement a custom mechanism (mod file) that outputs a synaptic current. I noticed that when trying to record the current at the section that contains the custom mechanism, the current from the mechanism is not present. To illustrate, here is some Python code that successfully captures a section's current with an inserted Exp2Syn mechanism.\n\nCode: Select all\n\n``````from neuron import h\nimport matplotlib.pyplot as plt\n\ns0 = h.Section()\ns0.insert('pas')\n\nsyn = h.Exp2Syn(s0(0.5)) # define as exponential synapse\n\nh.tstop = 10000\nh.dt = .1\nh.steps_per_ms = 1.0/h.dt\n\nevec = h.Vector()\n\n# time of events\nevec.append(200)\nevec.append(1200)\nevec.append(7000)\n\ninput_vector = h.VecStim()\ninput_vector.play(evec)\n\nnc = h.NetCon(input_vector,syn)\nnc.weight = 1\n\ni = h.Vector()\ni.record(syn._ref_i) # record the current through the synapse\n\nsecI = h.Vector()\nsecI.record(s0(0.5)._ref_i_pas) # record the current at the section\n\nh.run()\n\n# plot currents\nplt.figure(1)\nplt.plot(i)\n\nplt.figure(2)\nplt.plot(secI)\nplt.show()\n``````\n\nWhen using Exp2Syn, you can directly see the effects of the synaptic current on the recording of the current of the section. When looking at the mod file for Exp2Syn, I thought the only significant part that would have the section \"recognize\" the current is to declare it as a NONSPECIFIC_CURRENT. So I tried making a very simple mod file to see if the current would be \"seen\" by the section:\n\nCode: Select all\n\n``````NEURON {\nPOINT_PROCESS netcontest\nRANGE i\nNONSPECIFIC_CURRENT i\n}\n\nUNITS {\n(nA) = (nanoamp)\n}\n\nASSIGNED {\ni (nA)\n}\n\nINITIAL {\ni = -70\n}\n\ni = i + 10\n}\n``````\nThe mod file simply initiates the current to -70nA and steps it up by 10nA every time an event is received. If you rerun the python code I copied but replace it to use my simple mod file ( syn = h.netcontest(s0(0.5) ) the plotted section current does not reflect the activity of the custom mechanism.\n\nMy main question is how do I get the section to \"see\" the current of my custom mechanism? Am I missing something crucial in the mod file? Thank you for any assistance!\nted\nPosts: 5892\nJoined: Wed May 18, 2005 4:50 pm\nLocation: Yale University School of Medicine\nContact:\n\n### Re: How does a section recognize a mechanism's current?\n\nI am quite new to NEURON. I am trying to implement a custom mechanism (mod file) that outputs a synaptic current.\nAre you quite sure that is necessary? There isn't something that already exists which, except for parameter values, would do exactly what you want? If there isn't, then have you tried looking for something that exists and is close to what you want to implement?\nWhen looking at the mod file for Exp2Syn, I thought the only significant part that would have the section \"recognize\" the current is to declare it as a NONSPECIFIC_CURRENT.\n\"Programming by example\" is a useful strategy, but as you found out, there are still many pitfalls. NMODL is very different from C, hoc, or Python. Have you taken a look at the enhanced preprint of\nHines, M.L. and Carnevale, N.T. Expanding NEURON's Repertoire of Mechanisms with NMODL. Neural Computation 12:995-1007, 2000\nwhich is available as\nhttps://neuron.yale.edu/neuron/static/p ... odl400.pdf\n(also note the errata https://neuron.yale.edu/neuron/static/p ... rrata.html)\n?\nhow do I get the section to \"see\" the current of my custom mechanism?\nUse a custom mechanism that actually generates a current. Your NMODL code needs a BREAKPOINT block that assigns a value to the current variable.\n\nWhat is to be done to your NMODL file to fix that and some other problems you haven't bumped into yet?\n\nIf you have a mechanism that is supposed to generate a current, the mechanism must have a BREAKPOINT block which contains a statement that assigns a value to that current. Absent such a statement, your mechanism won't affect the model's charge balance equations.\n\nCode: Select all\n\n``````BREAKPOINT {\ni = amp\n}``````\nwhere amp is the name of an intermediate variable whose value will be set to some initial value upon model initialization, and incremented by some amount every time the mechanism receives an event.\nOf course, amp must be declared in the ASSIGNED block\n\nCode: Select all\n\n``````ASSIGNED {\namp (nA)\ni (nA)\n}``````\nInstead of hard wiring magic numbers like -70 and 10 (which happen to be very poor choices, by the way) into your code, you'll want to parameterize your model. amp0 and delta are nice and mnemonic.\n\nCode: Select all\n\n``````PARAMETER {\namp0 = 0 (nA)\ndelta = -0.01 (nA) : < 0 depolarizes. after all, this is a synaptic mechanism, not an electrode\n}``````\nA synaptic mechanism is likely to be used more than once in a model, and you might want each instance to have its own parameters, so declare them to be RANGE in the NEURON block.\n\nCode: Select all\n\n``````NEURON {\nPOINT_PROCESS netcontest\nRANGE amp0, delta, i\nNONSPECIFIC_CURRENT i\n}\n``````\nTo ensure that amp is reset to its initial value when the model is initialized, the NMODL file's INITIAL block should be changed to\n\nCode: Select all\n\n``````INITIAL {\namp = amp0\n}``````\nand to use delta to increment amp when an event arrives, the NET_RECEIVE block should become\n\nCode: Select all\n\n``````NET_RECEIVE(weight (uS)) {\namp = amp + delta\n}``````\nWhat remains to be done? If you use modlunit to check the NMODL file for consistency of units, modlunit will complain that it doesn't know about uS, so the UNITS block should be\n\nCode: Select all\n\n``````UNITS {\n(nA) = (nanoamp)\n(uS) = (microsiemens)\n}``````\nduytanph\nPosts: 11\nJoined: Wed Jul 10, 2019 5:03 pm\n\n### Re: How does a section recognize a mechanism's current?\n\nThank you for the reply Ted, appreciate it! Will keep all the tips you suggested in mind moving forward and will have a look at the NEURON guide as well. The use of the BREAKPOINT block to affect charge balance is exactly what I needed." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9196998,"math_prob":0.7512233,"size":3008,"snap":"2021-21-2021-25","text_gpt3_token_len":737,"char_repetition_ratio":0.10619175,"word_repetition_ratio":0.0038986355,"special_character_ratio":0.22905585,"punctuation_ratio":0.125,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97025007,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-05-11T18:11:14Z\",\"WARC-Record-ID\":\"<urn:uuid:d068f87d-795c-42e1-96f3-0fd413ace5e1>\",\"Content-Length\":\"38455\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d9786dba-7c7a-4829-af87-f86cacf3d137>\",\"WARC-Concurrent-To\":\"<urn:uuid:6e68c74b-47e5-4914-a1e9-b68808c30084>\",\"WARC-IP-Address\":\"128.36.111.212\",\"WARC-Target-URI\":\"https://www.neuron.yale.edu/phpBB/viewtopic.php?f=16&t=4105&sid=f106f0946aa9e571a64c68230591666f\",\"WARC-Payload-Digest\":\"sha1:YXH4XKSYJCCD7HWSJLQC73HIJBOCDMCN\",\"WARC-Block-Digest\":\"sha1:VXOOX7OKWE7JCS2JKYVUMQULRNLBLRL7\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-21/CC-MAIN-2021-21_segments_1620243991648.10_warc_CC-MAIN-20210511153555-20210511183555-00619.warc.gz\"}"}
https://ihower.tw/rails/fullstack-testing-rspec.html	[ "# Rails 自動化測試課程簡介\n\n• 閏年程序\n• 停車計費應用\n• Web API 自動化測試\n\n# 一個簡單的閏年程序\n\n## 1-1 閏年程序(第一版)\n\n• 西元年分除以400可整除，為閏年。\n• 西元年分除以4可整除但除以100不可整除，為閏年。\n• 西元年分除以4不可整除，為平年。\n• 西元年分除以100可整除但除以400不可整除，為平年\n\n``````def is_leap_year?(year)\nif year % 4 == 0\nreturn true\nelse\nreturn false\nend\n\n# 同學們可能會發現這不是正確的版本，讓我們繼續做下去\nend\n``````\n\n``````require_relative './leap_year'\nis_leap_year?(2016) # => 應該得到 true\nis_leap_year?(2017) # => 應該得到 false\n\n``````\n\n``````is_leap_year?(2100) # => 得到 true，但是應該要 false 才對\n\n``````\n\n## 1-2 閏年程序(第二版)\n\n``````def is_leap_year?(year)\nif year % 4 == 0\nif year % 100 == 0\nreturn false\nelse\nreturn true\nend\nelse\nreturn false\nend\nend\n``````\n\n``````require_relative './leap_year'\nis_leap_year?(2016) # => 應該得到 true\nis_leap_year?(2017) # => 應該得到 false\nis_leap_year?(2100) # => 應該得到 false 了\n``````\n\n## 1-3 使用 RSpec 自動化測試\n\n`gem install rspec`\n\n``````--format documentation\n--color\n``````\n\n``````require_relative './leap_year'\n\ndescribe \"Leap Year\" do\nit \"2016 is leap year\" do\nresult = is_leap_year?(2016) # 把 2016 傳進去\nexpect(result).to eq(true) # 檢查結果應該要是 true\nend\n\nit \"2017 is common year\" do\nresult = is_leap_year?(2017) # 把 2017 傳進去\nexpect(result).to eq(false) # 檢查結果應該要是 false\nend\n\nit \"2100 is common year\" do\nresult = is_leap_year?(2100) # 把 2100 傳進去\nexpect(result).to eq(false) # 檢查結果應該要是 false\nend\n\nit \"2400 is leap year\" do\nresult = is_leap_year?(2400) # 把 2400 傳進去\nexpect(result).to eq(true) # 檢查結果應該要是 true\nend\n\nend\n\n``````", null, "### 1-4 閏年程序(完成版)\n\n``````def is_leap_year?(year)\nif year % 4 == 0\nif year % 100 == 0\nif year % 400 == 0\nreturn true\nelse\nreturn false\nend\nelse\nreturn true\nend\nelse\nreturn false\nend\nend\n\n``````", null, "## 1-5 重構閏年程序(最終版)\n\n``````def is_leap_year?(y)\ny % 400 == 0 \|\| ( y % 4 == 0 && y % 100 != 0)\nend\n\n``````", null, "" ]	[ null, "https://ihower.tw/rails/part2/04-testing/images/1-1.png", null, "https://ihower.tw/rails/part2/04-testing/images/1-2.png", null, "https://ihower.tw/rails/part2/04-testing/images/1-2.png", null ]	{"ft_lang_label":"__label__zh","ft_lang_prob":0.77263165,"math_prob":0.45930147,"size":2568,"snap":"2023-40-2023-50","text_gpt3_token_len":1997,"char_repetition_ratio":0.1649766,"word_repetition_ratio":0.253125,"special_character_ratio":0.30996886,"punctuation_ratio":0.083333336,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9716878,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,2,null,4,null,4,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-10-04T04:09:40Z\",\"WARC-Record-ID\":\"<urn:uuid:09fef0bf-9879-4fc2-9abc-46e48132919f>\",\"Content-Length\":\"41915\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:03ac4932-aaa0-422e-afb0-b44ef7bb7114>\",\"WARC-Concurrent-To\":\"<urn:uuid:8d048269-cead-4c25-a69e-ae3fb8229e9a>\",\"WARC-IP-Address\":\"172.104.102.228\",\"WARC-Target-URI\":\"https://ihower.tw/rails/fullstack-testing-rspec.html\",\"WARC-Payload-Digest\":\"sha1:WCBQCLPZLWJUXE2UPEE2FIMUHJLL4YZT\",\"WARC-Block-Digest\":\"sha1:M4YLRJ5L5WOZ7XB3DAQASLHU3BMU4XEH\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233511351.18_warc_CC-MAIN-20231004020329-20231004050329-00133.warc.gz\"}"}
https://dokumen.tips/documents/physics-of-dielectrics-and-dram.html	[ "", null, "", null, "", null, "", null, "", null, "# Physics of Dielectrics and DRAM\n\n• View\n40\n\n5\n\nTags:\n\nEmbed Size (px)\n\n### Text of Physics of Dielectrics and DRAM\n\nPhysics of Dielectrics and DRAMThomas Schroeder\n\nIHP Im Technologiepark 25 15236 Frankfurt (Oder) GermanyIHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com\n\nPhysics of Dielectrics and DRAM\n\nDielectrics\n\nIHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany\n\nwww.ihp-microelectronics.com\n\nDescription of a dielectric material Dielectric behavior in a nut shell: A dielectric material is a non-conducting substance whose bound charges are polarized under the influence of an externally applied electric field. The figure of merrit to describe the degree of polarization in a given material is the dielectric constant It is clear that the degree of polarization is related to the structure of the material. In consequence, dielectric behavior in electrostatic and alternating electric fields depends on static and dynamical properties of the structure. Dielectric behavior must be specified with respect to the time or frequency domainIHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com\n\nElectrostatics: Basic experiment to get the central idea\n\nPlate capacitor with oppositely charged plates and no material inserted. According to the surface charge density, a certain electric field E is created inside.\n\nIf dielectric material is inserted, polarized charges neutralizes some of the charges on the plates. In this way, one talks about free (unneutralized) and bound charges (neutralized) on the plates. As only free charges create electric field, a current must raise the free charge density and keep E constant.\n\nIf dielectric material is inserted and current source disconnectedm the polarized charges neutralize some of the free charges on the plates. In consequence, a constant D results in a decrease of the electric field between the plates.\n\nIHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany\n\nwww.ihp-microelectronics.com\n\nElectrostatics: Macroscopic description of dielectrics Poisson Equationelectric field E\n\ndivD = free\n\nPolarisation\n\nDielectric Displacement DElectric Susceptibility\n\nD = 0E + P\n\nPolarisation\n\nP = 0eE\n\nPutting things together:\n\nD = 0 (1 + e ) E = 0 r E\n\nResult: dielectric displacement D is linearly related to the electric field and the dielectric constant is the linear coefficient of the relationshipIHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com\n\nDielectric Constant\n\nElectrostatics: Microscopic Approach and the local field Polarisation: Local electric field:density of induced dipoles applied electric field polarisability\n\nP = N a p = N a ElocEloc = Ea + Edipole\n\nThe local electric field can be calculated according to the crystal structure by the method of Clausius and Mosotti. For example, for cubic structures the Clausius Mosotti equation reads:\n\nNa r 1 = 3 0 r + 2\n\nFor example, to design a material with high dielectric constant: - ions with high polarisability - material with high density of induced dipolesIHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com\n\nMicroscopic Mechanism of dielectric polarisation and frequency dependenceRelaxation Space charge polarisation materials with space charge inhomogeneities (ceramics with conducting grains and insulating boundaries)\n\nDifferent mechanism show different dynamic behavior in time domain. In consequence, adsorption occurs at different windows in frequency domain\n\nRelaxation\n\nOrientation polarization alignment of permanent dipoles in a material\n\nResonance Resonance\n\nIonic polarization mutual displacement of negative and positive sublattice in ionic crystals\n\nElectronic polarization displacement of electron shell against positive nucleusIHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com\n\nDielectric Behaviour in alternating electric fieldsIn alternating electric fields, a frequency dependent phase shift occurs between applied electric field and displacement of charges in the material To express this mathematically, a complex extension of dielectric function and susceptibilty is introduced:\n\nr = r + i r'\n\nur\n\n''\n\nuu r\n\ne = e + i e'\n\n''\n\nr' + ir'' r = r' + i r''urFigure of merrit for a dielectric material: the quality factor Q\n\nr = r + i r'\n\nur\n\nr tan := ' r''\n\n''\n\nr'' tan := ' r\n\nQ :=\n\n1 tan\n\nA low quality factor states that a material heavily dissipates energy from the alternating electric field by adsorbing mechanisms\n\ntan = (tan ) dipole + (tan )condIHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com\n\nDescription of ionic and electronic resonance phenomenafriction Equation of motion acting force acting force\n\n2 d u du * * 2 mi 2 + mi i u = qi Eloc + mi* 0, i dt dt\n\ndisplacement from equilibrium\n\nresonance frequency\n\nrestoring force\n\nCase 1: Acting force is a dc field and switched off at a given moment\n\nRestoring force pulls charges back in equilibrium position a) If friction force is negligible, we arrive at undamped oscillations b) If friction force is not negligible, we arrive at damped oscillation. (behavior similar to relaxation process with certain time constant)\n\nIHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany\n\nwww.ihp-microelectronics.com\n\nDescription of ionic and electronic resonance phenomenafriction Equation of motion acting force acting force\n\n2 d u du * * 2 mi 2 + mi i u = qi Eloc + mi* 0, i dt dt\n\ndisplacement from equilibrium\n\nresonance frequency\n\nrestoring force\n\nCase 2: Acting force is an ac field Electric ac field:\n\nAnsatz:\n\nResult: Frequency dependent amplitude u of oscillations and dipole field:\n\nuuu r i ( kr t ) Eloc = Eloc ,0 e r ur i ( kr t ) u = u0 e\n\nur (qi / mi* ) Eloc ,0 u0 = 2 0,i 2 + i iIHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany\n\nuu r uu r pi = qiu0 ei ( kr t ) = i Eoc ,0 ei ( kr t )www.ihp-microelectronics.com\n\nDescription of ionic and electronic resonance phenomenafriction Equation of motion acting force acting force\n\n2 d u du * * 2 mi 2 + mi i u = qi Eloc + mi* 0, i dt dt\n\ndisplacement from equilibrium\n\nresonance frequency\n\nrestoring force\n\nqi i i ( ) = 2 2 mi ( 0,i 2 ) 2 + i2 22 ''\n\nqi2 / mi* ' '' i ( ) = 2 = + ( ) i ( ) i i 2 0,i + i i 2 2 2 q i' ( ) = i 2 2 0,i 2 2 Reduces in the static case to: mi ( 0,i ) + i2 2 q i ,s := i (0) =' 2 2 mi2 0, i i\n\nuu r\n\nCase 2: Acting force is an ac field Frequency dependent complex polarisability for ionic and electronic mechanisms (f > 1011 Hz):\n\nand i'' (0) = 0\n\nIHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany\n\nwww.ihp-microelectronics.com\n\nDescription of ionic and electronic resonance phenomenafriction Equation of motion acting force acting force\n\nrestoring force resonance displacement from equilibrium frequency Case 2: Acting force is an ac field\n\n2 d u du * * 2 mi 2 + mi i u = qi Eloc + mi* 0, i dt dt\n\nWith the frequency dependent complex polarisability and the Clausius-Mosotti equation, we get the frequency dependent complex dielectric function in the frequency range > 1011Hz :' ' ( ) ( 0+ ) ' r r 0 r ( ) = r ( 0+ ) + 1 ( / 0 ) 2 + i / 02\n\nur\n\nIn the case of an ideal insulator with negligible magnetisation, the optical refractive index is given by Maxwell`s law\n\nr ur n( ) = r ( )\n\nOptical properties of matters: ectric properties under the influence of alternating electric fields with f > 1011 HzIHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com\n\nDescription of relaxation phenomena: orientation and space charge contributionsDebye Relaxation Debye relaxation denotes a system with a single relaxation time t. Example: Medium with one type of oriented dipole which can be oriented by external field Such a system can be directly described by the general expression when the term of the restoring force is omitted:' ' ( ) ( 0+ ) 0 r r r ( ) = r' ( 0+ ) + 1 ( / 0 ) 2 + i / 02\n\nur\n\nWe get:' ' ' ( ) ( ) ' 0+ r r r ( ) = r' ( 0+ ) + r 0 = ( ) + 0+ r 1 + i / 02 1 + i\n\nur\n\nThe relaxation step describes the part of the permittivity due to a relaxation process:\n\nr := r ( 0 ) r ( 0+ ) and := / 0' ' 'IHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com\n\n2\n\nDescription of relaxation phenomena: orientation and space charge contributionsDebye Relaxation The relaxation step describes the part of the permittivity due to a relaxation process:\n\nr := r ( 0 ) r ( 0+ ) and := / 0' ' '\n\n2\n\nFor microelectronics this means: There is no high-k material without energy dissipating process. Find a material which is well behavin in the frequency range of interest ! The real and imaginary part of the dielectric function for Debye relaxation than read:' r r' ( ) = r' ( 0+ ) + 2 2 1+ ' r '' r ( ) = 1 + 2 2IHP Im Technologiepark 25 15236 Frankfurt (Oder) Germany www.ihp-microelectronics.com\n\nDescription of relaxation phenomena: orientation and space charge contributionsHow to identify Debye relaxation ? 1) Thermal behaviour\n\n= 0 eW0 / kBTCertainly, this results in an exponential dependance of the relaxation frequency with temperature 2) Cole Cole diagram In case of true Debye behavior (only one relaxation time) plotting imaginary against real part forms a semi-circle This examp\n\nRecommended", null, "##### Brazilian Journal of Physics - Progress in High-Energy Electron and X-irradiation of Insulating Dielectrics\nDocuments", null, "##### REDUCING DRAM ACCESS LATENCY BY EXPLOITING DRAM DRAM tabanl¤± bellek, bilgisayar sisteminde darbogaz\nDocuments", null, "##### Frequency Dispersion: Dielectrics, Conductors, and Frequency Dispersion: Dielectrics, Conductors, and\nDocuments", null, "##### Dielectrics Unit – 1 Sub.- Physics. 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Department\nDocuments", null, "##### Spin-On Dielectrics Wafer Bonding Dielectrics Dry Film Dielectrics Electroplating Resists SINR-3570\nDocuments", null, "Documents" ]	[ null, "data:image/png;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=", null, "data:image/png;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=", null, "data:image/png;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=", null, "data:image/png;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=", null, "data:image/png;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=", null, "data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==", null, "data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==", null, "data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==", null, "data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==", null, "data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==", null, "data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==", null, "data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.72640705,"math_prob":0.93297905,"size":9086,"snap":"2021-43-2021-49","text_gpt3_token_len":2349,"char_repetition_ratio":0.14842546,"word_repetition_ratio":0.23699422,"special_character_ratio":0.24543254,"punctuation_ratio":0.07554417,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9591159,"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],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-16T07:11:07Z\",\"WARC-Record-ID\":\"<urn:uuid:fcd73732-a4a2-4fc6-889c-7dc6a20c7923>\",\"Content-Length\":\"98428\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:66fb09b1-1c49-462e-a56e-366ad0b4f4ad>\",\"WARC-Concurrent-To\":\"<urn:uuid:2652e58d-d29c-49bd-850e-df81b56316fe>\",\"WARC-IP-Address\":\"51.254.158.8\",\"WARC-Target-URI\":\"https://dokumen.tips/documents/physics-of-dielectrics-and-dram.html\",\"WARC-Payload-Digest\":\"sha1:U6YTZV7CFOD4KS2UBRGERFNVCSR5RVMJ\",\"WARC-Block-Digest\":\"sha1:ZXNADPT6PXCW5AJUWODCCXKNDDPLTP6B\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323583423.96_warc_CC-MAIN-20211016043926-20211016073926-00222.warc.gz\"}"}
http://math.ipm.ir/frontiers/printseminar.jsp?eventID=176	[ "Frontiers in Mathematical Sciences\n\n TITLE Logical Arithmetic and Real Algebraic Geometry SPEAKER Shahram Mohsenipour IPM ABSTRACT\n We will talk about the diophantine equations from a logical point of view and explain that for a subsystem $T$ of the Peano Arithmetic how diophantine equations can be studied within $T$. For a special $T$ called Open Induction, this study leads us, through Wilkie's theorem, to an algebro-geometric situation wherein we consider a kind of \"arithmetic\" solutions of diophantine equations in the space of all solutions. This latter space is the real spectrum of a commutative ring. In modern real algebraic geometry, the real spectrum has the importance of the Zariski spectrum in the usual algebraic geometry. We will also briefly discuss a recent result of the speaker on the distribution of the \"arithmetic\" points in the real spectrum." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.90595764,"math_prob":0.9926197,"size":742,"snap":"2019-35-2019-39","text_gpt3_token_len":163,"char_repetition_ratio":0.1300813,"word_repetition_ratio":0.0,"special_character_ratio":0.19407009,"punctuation_ratio":0.06923077,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9966766,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-08-23T23:45:52Z\",\"WARC-Record-ID\":\"<urn:uuid:e36b6c97-ec71-49ca-91fa-6820f3c00d72>\",\"Content-Length\":\"10218\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:272ecd60-e86e-4e8b-b42d-29a5e3916dc7>\",\"WARC-Concurrent-To\":\"<urn:uuid:e900d2b5-f25a-452b-b75c-63c35f3d10d1>\",\"WARC-IP-Address\":\"194.225.73.180\",\"WARC-Target-URI\":\"http://math.ipm.ir/frontiers/printseminar.jsp?eventID=176\",\"WARC-Payload-Digest\":\"sha1:OFWLU37KJHSFAQ6EZ2CDCPWM6Z5X542J\",\"WARC-Block-Digest\":\"sha1:KG3TXXGXUWQUGV4QLXFVMDV5AU4LHQCX\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-35/CC-MAIN-2019-35_segments_1566027319082.81_warc_CC-MAIN-20190823214536-20190824000536-00376.warc.gz\"}"}
https://www.onemathematicalcat.org/algebra_book/online_problems/par_perpen.htm	[ " Parallel and Perpendicular lines\nPARALLEL AND PERPENDICULAR LINES\nby Dr. Carol JVF Burns (website creator)\nFollow along with the highlighted text while you listen!\n• PRACTICE (online exercises and printable worksheets)\n• Want some other practice with lines?\n\nIf you know the slopes of two non-vertical lines,\ncan you easily determine if they're parallel? Perpendicular?\nYES!\n\nParallel lines have the same slope.\n\nPerpendicular lines have slopes that are opposite reciprocals.\n\nThis section explores these concepts.\n\nSlopes of Parallel Lines\n\nTwo lines in a plane are parallel if they never intersect; they have the same ‘slant’.\n(For a more rigorous study of parallel lines and related concepts, visit my Geometry course: Parallel Lines.)\nSlope (or lack of it!) can be used to decide if lines are parallel:\n\nCHARACTERIZATION OF PARALLEL LINES INVOLVING SLOPE\nSuppose two distinct lines lie in the same coordinate plane.\nThen,\nthe two lines are parallel\nif and only if\n(they are both vertical) or (they have the same slope)\n\nThis statement offers a good opportunity to review the mathematical words ‘if and only if’ and ‘or’.\nThe statement has been visually presented to help you see the mathematical sentence structure more clearly.\n\n• The basic set-up is two lines lying in the same coordinate plane.\nThis condition lurks in the background (is assumed to be true) for all that follows.\n• Two mathematical sentences are being compared with the words if and only if:\n• first sentence: the two lines are parallel\n• second sentence: (they are both vertical) OR (they have the same slope)\n• If and only if is a variation of ‘is equivalent to’.\nSentences that are equivalent always have the same truth values—they're true at the same time, and false at the same time.\nIf one is true, so is the other.\nIf one is false, so is the other.\n• An ‘or’ sentence is true when at least one of the subsentences is true.\nThe only time an ‘or’ is false is when both subsentences are false.\n• The nice, compact statement above is actually saying A LOT.\nTake a look, if you want, to increase your appreciation of the brevity of the mathematical language:\n\nSlopes of Perpendicular Lines\n\nNow, let's move on to perpendicular lines.\nTwo lines are perpendicular if they intersect at a $\\,90^{\\circ}$ angle.\nFor example, the $\\,x$-axis and $\\,y$-axis are perpendicular.\n\nCHARACTERIZATION OF PERPENDICULAR LINES\nINVOLVING SLOPE\nSuppose two non-vertical lines lie in the same coordinate plane.\nLet $\\,m_1\\,$ and $\\,m_2\\,$ denote the slopes of these lines.\n\nThe two lines are perpendicular if and only if their slopes are opposite reciprocals: $$\\,\\cssId{s54}{m_1 = -\\frac{1}{m_2}}\\,$$\nEquivalently, the two lines are perpendicular if and only if their slopes multiply to $\\,-1\\,$: $$\\,\\cssId{s59}{m_1m_2 = -1}\\,$$\n\nMake sure you understand the opposite reciprocal equation:\n\n$$\\cssId{s61}{m_1 = -\\frac{1}{m_2}}$$\n one of the slopes is the opposite of the reciprocal of the other slope $\\displaystyle \\cssId{s63}{m_1}$ $\\displaystyle \\cssId{s65}{=}$ $\\displaystyle \\cssId{s67}{-}$ $\\displaystyle \\cssId{s69}{\\frac{1}{m_2}}$\n\nFor example, what's the reciprocal of $\\,2\\,$? Answer: $\\frac12$\nWhat's the opposite [of the] reciprocal of $\\,2\\,$? Answer: $-\\frac12$\nSo, the numbers $\\,2\\,$ and $\\,-\\frac 12\\,$ are opposite reciprocals.\nAlso notice that $\\,(2)(-\\frac 12) = -1\\,$.\nSo, lines with slopes $\\,2\\,$ and $\\,-\\frac12\\,$ are perpendicular.\n\nIt's easy to see that this is the correct characterization for perpendicular lines, by studying the sketch below:", null, "The yellow triangle, with base of length $\\,1\\,$ and right side of length $\\,m\\,$,\nshows that the slope of the first line is $\\,\\cssId{s82}{\\frac{\\text{rise}}{\\text{run}}} \\cssId{s83}{= \\frac{m}1} \\cssId{s84}{= m}\\,$.\n\nNow, imagine that this yellow triangle is a block of wood that is glued to the line.\nRotate this block of wood counter-clockwise by $\\,90^{\\circ}\\,$ (so that the original base is now vertical).\nUsing the rotated triangle to compute the slope of the new, rotated, line gives: $\\,\\cssId{s89}{\\frac{\\text{rise}}{\\text{run}}} \\cssId{s90}{= \\frac{1}{-m}} \\cssId{s91}{= -\\frac1m}\\,$\nEasy! Voila!\n\nMaster the ideas from this section" ]	[ null, "https://www.onemathematicalcat.org/algebra_book/online_problems/graphics/perpen_lines.gif", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8278786,"math_prob":0.99590755,"size":2413,"snap":"2022-05-2022-21","text_gpt3_token_len":671,"char_repetition_ratio":0.12660855,"word_repetition_ratio":0.0,"special_character_ratio":0.29879817,"punctuation_ratio":0.16883117,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99919647,"pos_list":[0,1,2],"im_url_duplicate_count":[null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-17T18:59:14Z\",\"WARC-Record-ID\":\"<urn:uuid:b54c1c80-6743-4872-a235-752184543f98>\",\"Content-Length\":\"94282\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6b119aa9-0f30-4fae-8140-77b110b79bbf>\",\"WARC-Concurrent-To\":\"<urn:uuid:2008c758-6098-484d-9169-061f5fd9e46e>\",\"WARC-IP-Address\":\"8.21.33.48\",\"WARC-Target-URI\":\"https://www.onemathematicalcat.org/algebra_book/online_problems/par_perpen.htm\",\"WARC-Payload-Digest\":\"sha1:AUT6DNJ6MCMB26DV4WXII5XEXEBIUHY7\",\"WARC-Block-Digest\":\"sha1:YJ4WF5D6NUJ5UMCVPZWFUUQZECB7NELW\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320300616.11_warc_CC-MAIN-20220117182124-20220117212124-00593.warc.gz\"}"}
http://list.seqfan.eu/pipermail/seqfan/2009-June/001571.html	[ "# [seqfan] Re: A093893 Subsequence\n\nHagen von EItzen math at von-eitzen.de\nWed Jun 3 17:44:40 CEST 2009\n\n```> >> upper bounds:\n> >> a(14) <= 2311^6 * 50821 = 7741816606631194948471381\n> >> a(15) <= 120121^4 * 150151^2 = 4693882500443399337067739425681\n> >> a(16) <= 120121 * 150151 * 180181 * 270271 = 878325738218239130821\n> >> a(18) <= 4084081^2 * 5105101^2 * 8168161 =\n> >> 3550762793626881654061078595276521\n> >> a(19) <= 4084081^18\n> >>\n> >> For exact value of a(14), if it is not 7741816606631194948471381, then\n> >> a(14) = p6q where prime p<1400 and prime q>10^6.\n> >>\n> > In addition to this, I have: If a(14) is not ..., then p <= 1571 and\n> > a(14) > 592195652118678643207 (and counting)\n>\n> Nice. But please notice that 1571 is larger than 1400 in my bounds.\n> I've eliminated all larger primes p by brute-forcing q in the interval\n> up to\n> 7741816606631194948471381 / nextprime(1400)^6 < 10^6.\n\nUpdate: Meanwhile I can say that: If a(14) != 7741816606631194948471381\nthen a(14) > 2884960349615742355753 and a(14) = p^6q with p < 1000.\n\nHagen\n\n```" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.61065483,"math_prob":0.780536,"size":1095,"snap":"2020-10-2020-16","text_gpt3_token_len":435,"char_repetition_ratio":0.13473877,"word_repetition_ratio":0.0,"special_character_ratio":0.6502283,"punctuation_ratio":0.113513514,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99829906,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-04-09T03:11:03Z\",\"WARC-Record-ID\":\"<urn:uuid:8edb60e6-35b6-4231-850e-2ab0bb6f1fe2>\",\"Content-Length\":\"4312\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c157e2db-c048-468f-a64f-bfc140b391e9>\",\"WARC-Concurrent-To\":\"<urn:uuid:a41fe161-5a6d-4786-b438-d5d59e7d71d3>\",\"WARC-IP-Address\":\"92.243.17.179\",\"WARC-Target-URI\":\"http://list.seqfan.eu/pipermail/seqfan/2009-June/001571.html\",\"WARC-Payload-Digest\":\"sha1:YSMEYH5TO4Z6ARKDDAMJNHTIE64OSSSK\",\"WARC-Block-Digest\":\"sha1:M635YERJODXW5HA7UYYPUL3HGGML7ROZ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-16/CC-MAIN-2020-16_segments_1585371829677.89_warc_CC-MAIN-20200409024535-20200409055035-00209.warc.gz\"}"}
http://buildingonmosts.org/lvg-publications.html	[ "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "Learning to Become a Researcher in an Ongoing Research Project: A Communities of Practice Perspective\n\nArslan, O., Van Zoest, L. R., & Ruk, J. M. (2017). Learning to become a researcher in an ongoing research project: A communities of practice perspective. In E. Galindo, & J. Newton (Eds.), Proceedings of the 39th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1423–1426). Indianapolis, IN: Hoosier Association of Mathematics Teacher Educators.\n\nWe apply Wenger's (1998) communities of practice ideas to the process of incorporating new researchers into an ongoing mathematics education research project. We illustrate this application by describing how the Leveraging MOSTs research project coding team can be viewed as a community of practice. We describe how we have used this particular community of practice to bring new researchers into the project, and new researchers reflect on their experiences with the coding team. Mutual engagement in project work with experienced researchers and having a rich shared repertoire to draw on led to the new researchers developing a shared understanding of the project and being successfully incorporated into the MOST community. This work speaks to the importance of deliberately creating communities of practice for new mathematics researchers to participate within.\n\nTeachers' Responses To a Common Set of High Potential Instances of Student Mathematical Thinking\n\nStockero, S. L., Van Zoest, L. R., Peterson, B. E., Leatham, K. R., & Rougée, A. O. T. (2017). Teachers' responses to a common set of high potential instances of student mathematical thinking. In E. Galindo, & J. Newton (Eds.), Proceedings of the 39th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1178–1185). Indianapolis, IN: Hoosier Association of Mathematics Teacher Educators.\n\nThis study investigates teacher responses to a common set of high potential instances of student mathematical thinking to better understand the role of the teacher in shaping meaningful mathematical discourse in their classrooms. Teacher responses were coded using a scheme that disentangles the teacher move from other aspects of the teacher response, including who the response is directed to and the degree to which the student thinking is honored. Teachers tended to direct their response to the student who had shared their thinking and to explicitly incorporate ideas core to the student thinking in their response. We consider the nature of these responses in relation to principles of productive use of student mathematical thinking.\n\nBeyond the \"Move\": A Scheme for Coding Teachers' Responses To Student Mathematical Thinking\n\nPeterson, B. E., Van Zoest, L. R., Rougée, A. O. T., Freeburn, B., Stockero, S. L., & Leatham, K. R. (2017). Beyond the \"move\": A scheme for coding teachers' responses to student mathematical thinking. In B. Kaur, W. K. Ho, T. L. Toh, & B. H. Choy. (Eds.), Proceedings of the 41st annual meeting of the International Group for the Psychology of Mathematics Education, Vol. 4 (pp. 17–24). Singapore: International Group for the Psychology of Mathematics Education.\n\nTo contribute to the field's understanding of the teachers' role in using student thinking to shape classroom mathematical discourse, we developed the Teacher Response Coding Scheme (TRC). The TRC provides a means to analyze teachers' in-the-moment responses to student thinking during instruction. The TRC differs from existing schemes in that it disentangles the teacher move from the actor (the person publically asked to consider the student thinking), the recognition (the extent to which the student recognizes their idea in the teacher move), and the mathematics (the alignment of the mathematics in the teacher move to the mathematics in the student thinking). This disentanglement makes the TRC less value-laden and more useful across a broad range of settings.\n\nAttributes of Instances of Student Mathematical Thinking That Are Worth Building on in Whole-Class Discussion\n\nVan Zoest, L. R., Stockero, S. L., Leatham, K. R., Peterson, B. E., Atanga, N. A., & Ochieng, M. A. (2017). Attributes of instances of student mathematical thinking that are worth building on in whole-class discussion. Mathematical Thinking and Learning, 19, 33–54.\n\nThis study investigated attributes of 278 instances of student mathematical thinking during whole-class interactions that were identified as having high potential, if made the object of discussion, to foster learners' understanding of important mathematical ideas. Attributes included the form of the thinking (e.g., question vs. declarative statement), whether the thinking was based on earlier work or generated in the moment, the accuracy of the thinking, and the type of thinking (e.g., sense-making). Findings illuminate the complexity of identifying student thinking worth building on during whole-class discussion and provide insight into important attributes of these high potential instances that could be used to help teachers more easily recognize them. Implications for researching, learning, and enacting the teaching practice of building on student mathematical thinking are discussed.\n\nNoticing Distinctions Among and Within Instances of Student Mathematical Thinking\n\nStockero L. S., Leatham, K. R., Van Zoest, L. R., & Peterson, B. E. (2017) Noticing Distinctions Among and Within Instances of Student Mathematical Thinking. In E. Schack, J. Wilhelm, & M. H. Fisher (Eds.), Teacher noticing: A hidden skill of teaching (pp. 467). Cham, Switzerland: Springer International.\n\nIn this chapter, we argue that there are two critical aspects of noticing student mathematical thinking: noticing within an instance of student thinking and noticing among instances of student thinking. We use the noticing literature to illustrate these distinctions. We then discuss how the MOST Analytic Framework analysis provides structure and guidance for noticing both within and among instances, and illustrate the complex interaction of these two types of noticing through the analysis of an excerpt of classroom dialogue. We conclude by offering the perspective that studies of noticing must go beyond placing value on student mathematical thinking to discriminating among instances of student thinking based on their potential to be used to support students' understanding of important mathematics.\n\nImprecision in Classroom Mathematics Discourse\n\nLeatham, K. R., Peterson, B. E., Merrill, L., Van Zoest, L. R., & Stockero, S. L. (2016). Imprecision in classroom mathematics discourse. In M. B. Wood, E. E. Turner, M. Civil, & J. A. Eli (Eds.), Proceedings of the 38th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1236–1243). Tucson, AZ: University of Arizona.\n\nWe theorize about ambiguity in mathematical communication and define a certain subset of ambiguous language usage as imprecise. For us, imprecision in classroom mathematics discourse hinders in-the-moment communication because the instance of imprecision is likely to create inconsistent interpretations of the same statement among individuals. We argue for the importance of attending to such imprecision as a critical aspect of attending to precision. We illustrate various types of imprecision that occur in mathematics classrooms and the ramifications of not addressing this imprecision. Based on our conceptualization of these types and ramifications, we discuss implications for research on classroom mathematics discourse.\n\nConceptualizing the Teaching Practice of Building On Student Mathematical Thinking\n\nVan Zoest, L. R., Peterson, B. E., Leatham, K. R., & Stockero, S. L. (2016). Conceptualizing the teaching practice of building on student mathematical thinking. In M. B. Wood, E. E. Turner, M. Civil, & J. A. Eli (Eds.), Proceedings of the 38th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1281–1288). Tucson, AZ: University of Arizona.\n\nAn important aspect of effective teaching is taking advantage of in-the-moment expressions of student thinking that, by becoming the object of class discussion, can help students better understand important mathematical ideas. We call these high-potential instances of student thinking MOSTs and the productive use of them building. The purpose of this paper is to conceptualize the teaching practice of building on MOSTs as a first step toward developing a common language for and an understanding of productive use of high-potential instances of student thinking. We situate this work in the existing literature, introduce core principles that underlie our conception of building, and present a prototype of the teaching practice of building on MOSTs that includes four sub-practices.\n\nWe conclude by discussing the need for future research and our research agenda for studying the building prototype.\n\nTheorizing the Mathematical Point of Building on Student Mathematical Thinking\n\nVan Zoest, L. R., Stockero, S. L., Leatham, K. R., & Peterson, B. E. (2016). Theorizing the mathematical point of building on student mathematical thinking. In C. Csíkos, A. Rausch, & J. Szitányi (Eds.), Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 323–330). Szeged, Hungary: PME.\n\nDespite the fact that the mathematics education field recognizes the critical role that student thinking plays in high quality instruction, little is known about productive use of the in-the-moment student thinking that emerges in the context of whole-class discussion. We draw on and extend the work of others to theorize the mathematical understanding an instance of such student thinking can be used to build towards—the mathematical point (MP). An MP is a mathematical statement of what could be gained from considering a particular instance of student thinking. Examples and non-examples are used to illustrate nuances in the MP construct. Articulating the MP for an instance of student thinking is requisite for determining whether there is instructional value in pursuing that thinking.\n\nAttributes of Student Mathematical Thinking That is Worth Building on in Whole-Class Discussion\n\nVan Zoest, L. R., Stockero, S. L., Atanga, N. A., Leatham, K. R., Peterson, B. E. & Ochieng, M. A. (2015). Attributes of student mathematical thinking that is worth building on in whole-class discussion. Proceedings of the 37th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. East Lansing, MI: Michigan State University, MI.\n\nThis study investigated the attributes of 265 instances of student mathematical thinking during whole-class interactions that were identified as having the potential to foster learners' understanding of important mathematical ideas (MOSTs). Attributes included the form of the thinking (e.g., question vs. declarative statement), whether the thinking was based on earlier work or generated in the moment, the accuracy of the thinking, and the type of the thinking (e.g., sense making). Findings both illuminate the complexity of identifying student thinking worth building on during whole-class discussion and provide insight into important attributes of MOSTs that teachers can use to better recognize them. For example, 96% of MOSTs were of three types, making these three particularly salient types of student mathematical thinking for teachers to develop skills in recognizing.\n\nUncovering Teachers' Goals, Orientations, and Resources Related to the Practice of Using Student Thinking\n\nStockero, S. L., Van Zoest, L. R., Rougee, A., Fraser, E. H., Leatham, K. R. & Peterson, B. E. (2015). Uncovering teachers' goals, orientations, and resources related to the practice of using student thinking. Proceedings of the 37th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. East Lansing, MI: Michigan State University, MI.\n\nDespite years of efforts to promote using student thinking during instruction, the practice of productively using student thinking is still difficult for teachers to enact well. Improving teachers' use of this practice requires an understanding of why teachers currently respond to student thinking as they do; that is, an understanding of the goals, orientations and resources (Schoenfeld, 2011) that underlie their enactment of this practice. We describe a scenario-based interview tool developed to prompt teachers to discuss their decisions and rationales related to using student thinking. We examine cases of three individual teachers to illustrate how the tool allows us (1) to infer individual teachers' goals, orientations and resources and (2) to differentiate among teachers' uses of student thinking. Understanding reasons behind teachers' use of student thinking will help us to match professional development to teachers' needs.\n\nConceptualizing Mathematically Significant Pedagogical Opportunities to Build on Student Thinking\n\nLeatham, K. R., Peterson, B. E., Stockero, S. L., & Van Zoest, L. R. (2015). Conceptualizing Mathematically Significant Pedagogical Opportunities to Build on Student Thinking. Journal for Research in Mathematics Education, 46(1), 88-124.\n\nThe mathematics education community values using student thinking to develop mathematical concepts, but the nuances of this practice are not clearly understood. We conceptualize an important group of instances in classroom lessons that occur at the intersection of student thinking, significant mathematics, and pedagogical openings—what we call Mathematically Significant Pedagogical Opportunities to Build on Student Thinking (MOSTs). We analyze dialogue to illustrate the process for determining whether a classroom instance is a MOST. We conclude by discussing how the MOST construct contributes to facilitating and researching teachers' mathematically-productive use of student thinking through providing a lens and generating a common language for recognizing and agreeing upon high-leverage student mathematical thinking.\n\nThe \"MOST\" Productive Student Mathematical Thinking\n\nStockero, S. L., Peterson, B. E., Leatham, K. R., & Van Zoest, L. R. (2014). The \"MOST\" Productive Student Mathematical Thinking. Mathematics Teacher, 106(4), 308-312.\n\nMeaningfully incorporating student mathematical thinking into lessons requires identifying thinking that has potential to become the object of rich mathematical discussion. We conceptualize instances that (a) contain student thinking, (b) are about significant mathematics, and (c) create pedagogical opportunities as Mathematically Significant Pedagogical Opportunities to build on Student Thinking (MOSTs).\n\nTeachers' Perceptions of Productive Use of Student Mathematical Thinking\n\nLeatham, K. R., Van Zoest, L. R., Stockero, S. L., & Peterson, B. E. (2014). Teachers' perceptions of productive use of student mathematical thinking. In P. Liljedahl, S. Oesterle, C. Nicol, & D. Allan (Eds.), Proceedings of the Joint Meeting of PME 38 and PME-NA 36 (Vol. 4, pp. 73–80). Vancouver, Canada: PME.\n\nWe argue that the teaching practice of productively using student mathematical thinking [PUMT] needs to be better conceptualized for the construct to gain greater traction in the classroom and in research. We report the results of a study wherein we explored teachers' perceptions of PUMT. We interviewed mathematics teachers and analyzed these interviews using and refining initial conjectures about the process teachers might go through in learning PUMT. We found that teachers' perceptions of PUMT ranged from valuing student participation, to valuing student mathematical thinking, to using that thinking in a variety of ways related to eliciting, interpreting and building on that thinking.\n\nClassroom Mathematics Discourse: Broadening Perspectives by Integrating Tools for Analysis\n\nJohnson, K. R., Steele, M. D., Herbel-Eisenmann, B. A., Leatham, K. R., & Peterson, B. E., Stockero, S. L., … Merrill, L. (2013). Classroom mathematics discourse: Broadening perspectives by integrating tools for analysis. In M. V. Martinez & A. Castro Superfine (Eds.), Proceedings of the 35th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1340–1348). Chicago: University of Illinois at Chicago.\n\nThis working group explores tools for analyzing mathematics classroom discourse across two projects with different, but complementary perspectives. The goals of the working group include generating interaction about the theoretical lenses that we use to analyze and discuss classroom mathematics discourse and the relationships between these different theoretical frameworks. Participants will engage with the individual frameworks in the first two sessions and discuss interactions of the two frameworks in the third session.\n\nConceptualizing Mathematically Significant Pedagogical Openings to Build on Student Thinking\n\nVan Zoest, L. R., Leatham, K. R., Peterson, B. E., & Stockero, S. L. (2013). Conceptualizing mathematically significant pedagogical openings to build on student thinking. In A. M. Lindmeier & A. Heinze (Eds.), Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 345–352). Kiel, Germany: PME.\n\nThe mathematics education community values using student thinking to develop mathematical concepts, but the nuances of this practice are not clearly understood. We conceptualize an important group of instances in classroom lessons that occur at the intersection of student thinking, significant mathematics, and pedagogical openings—what we call Mathematically Significant Pedagogical Openings to Build on Student Thinking (MOSTs)—and introduce a framework for determining when they occur. We discuss how the MOST construct contributes to facilitating and researching teachers' mathematically-productive use of student thinking through providing a lens and generating a common language for recognizing and agreeing upon high-leverage student mathematical thinking.\n\nMathematically Important Pedagogical Opportunities\n\nLeatham, K. R., Peterson, B. E., Stockero, S. L., & Van Zoest, L. R. (2011). Mathematically important pedagogical opportunities. In L. R. Wiest & T. Lamberg (Eds.), Proceedings of the 33rd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 838–845). Reno, NV: University of Nevada, Reno.\n\nThe mathematics education community values using student thinking to develop mathematical concepts, but the nuances of this practice are not clearly understood. For example, not all student thinking provides the basis of productive discussions. In this paper we describe a conceptualization of instances in a classroom lesson that provide the teacher with opportunities to extend or change the nature of students' mathematical understanding—what we refer to as Mathematically Important Pedagogical Opportunities (MIPOs). We analyze classroom dialogue to illustrate how this lens can be used to make more tangible the often abstract but fundamental goal of pursuing students' mathematical thinking.\n\nInvestigating Mathematically Important Pedagogical Opportunities\n\nLeatham, K. R., Stockero, S. L., Van Zoest, L. R., & Peterson, B. E. (2010). Investigating mathematically important pedagogical opportunities. In P. Brosnan, D. B. Erchick, & L. Flevares (Eds.), Proceedings of the 32nd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. VI, pp. 1599–1605). Columbus, OH: The Ohio State University.\n\nMathematically Important Pedagogical Opportunities (MIPOs) are instances in a classroom lesson in which the teacher has an opportunity to move the class forward in their development of significant mathematics. Although this construct is widely recognized in the literature as important to mathematics teaching and learning, it is neither well defined nor clearly identified as a construct that can be studied. This working group will build on the efforts of two research groups, represented by the organizers, to define, identify, and characterize MIPOs. Specifically, Session 1 will focus on identifying MIPOs, including questioning and critiquing working definitions and preliminary dimensions of MIPOs. Session 2 will explore sub-constructs of MIPOs and the potential of sub-constructs to provide leverage in studying the broader construct. The first two sessions will include examining instances of classroom practice (written/video) that have been identified as containing MIPOs. 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https://gmatclub.com/forum/in-a-certain-district-the-ratio-of-the-number-of-registered-143983.html	[ "GMAT Question of the Day - Daily to your Mailbox; hard ones only\n\n It is currently 22 Nov 2019, 15:44", null, "### GMAT Club Daily Prep\n\n#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.\n\nCustomized\nfor You\n\nwe will pick new questions that match your level based on your Timer History\n\nTrack\n\nevery week, we’ll send you an estimated GMAT score based on your performance\n\nPractice\nPays\n\nwe will pick new questions that match your level based on your Timer History\n\n#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.", null, "", null, "# In a certain district, the ratio of the number of registered\n\nAuthor Message\nTAGS:\n\n### Hide Tags\n\nManager", null, "", null, "Joined: 02 Dec 2012\nPosts: 173\nIn a certain district, the ratio of the number of registered [#permalink]\n\n### Show Tags\n\n5\n36", null, "00:00\n\nDifficulty:", null, "", null, "", null, "55% (hard)\n\nQuestion Stats:", null, "71% (02:15) correct", null, "29% (02:30) wrong", null, "based on 1143 sessions\n\n### HideShow timer Statistics\n\nIn a certain district, the ratio of the number of registered Republicans to the number of registered Democrats was 3/5. After 600 additional Republicans and 500 additional Democrats registered, the ratio was 4/5. After these registrations, there were how many more voters in the district registered as Democrats than as Republicans?\n\n(A) 100\n(B) 300\n(C) 400\n(D) 1,000\n(E) 2,500\nMath Expert", null, "V\nJoined: 02 Sep 2009\nPosts: 59268\nRe: In a certain district, the ratio of the number of registered [#permalink]\n\n### Show Tags\n\n7\n12\nIn a certain district, the ratio of the number of registered Republicans to the number of registered Democrats was 3/5. After 600 additional Republicans and 500 additional Democrats registered, the ratio was 4/5. After these registrations, there were how many more voters in the district registered as Democrats than as Republicans?\n\n(A) 100\n(B) 300\n(C) 400\n(D) 1,000\n(E) 2,500\n\nOld ratio: $$\\frac{republicans}{democrats}=\\frac{3x}{5x}$$.\n\nNew ratio: $$\\frac{3x+600}{5x+500}=\\frac{4}{5}$$ --> $$x=200$$.\n\nCurrent difference is $$(5x+500)-(3x+600)=2x-100=300$$.\n\n_________________\n##### General Discussion\nIntern", null, "", null, "Joined: 12 Dec 2011\nPosts: 1\nIn a certain district, the ratio of the number of registered [#permalink]\n\n### Show Tags\n\n1\nIn a certain district, the ratio of the number of registered Republicans to the number of registered Democrats was 3/5. After 600 additional R and 500 additional D registered, the ratio was 4/5. After these registrations, the there were how many more voters in the district registered as D than as R?\n\nWhen you solve the two given equations, you arrive at D = 1000, which is perfectly logical. As R = 3/5 D, R must be 600.\n\nNow comes the thing I don't understand. In the sample solution, the newly registered voters are now added to the above numbers, which results in D = 1000 + 600 = 1500, respectively R = 600 + 600 = 1200. The difference is 300 now, which corresponds to the OA. But isn't it true that the numbers which result from solving the given equations must already be post the additions?\nMath Expert", null, "V\nJoined: 02 Sep 2009\nPosts: 59268\nRe: In a certain district, the ratio of the number of registered [#permalink]\n\n### Show Tags\n\n1\n1\n\ntomtom1610 wrote:\nIn a certain district, the ratio of the number of registered Republicans to the number of registered Democrats was 3/5. After 600 additional R and 500 additional D registered, the ratio was 4/5. After these registrations, the there were how many more voters in the district registered as D than as R?\n\nWhen you solve the two given equations, you arrive at D = 1000, which is perfectly logical. As R = 3/5 D, R must be 600.\n\nNow comes the thing I don't understand. In the sample solution, the newly registered voters are now added to the above numbers, which results in D = 1000 + 600 = 1500, respectively R = 600 + 600 = 1200. The difference is 300 now, which corresponds to the OA. But isn't it true that the numbers which result from solving the given equations must already be post the additions?\n\nAs for your question: we are asked to find the difference between the numbers of Democrats and Republicans AFTER the registration of 600 additional Republicans and 500 additional Democrats, so it should be 1500-1200=300.\n\nHope it's clear.\n_________________\nIntern", null, "", null, "Joined: 28 Oct 2012\nPosts: 1\nRe: In a certain district, the ratio of the number of registered [#permalink]\n\n### Show Tags\n\n1\nwhy cant we write it down as R/D = 3/5 and go further with (R+600)/(D+500). If we combine them we get R = 600 and D = 1000. Difference = 400. Whats wrong with this logic. Thanks in advance\nMath Expert", null, "V\nJoined: 02 Sep 2009\nPosts: 59268\nRe: In a certain district, the ratio of the number of registered [#permalink]\n\n### Show Tags\n\nwhy cant we write it down as R/D = 3/5 and go further with (R+600)/(D+500). If we combine them we get R = 600 and D = 1000. Difference = 400. Whats wrong with this logic. Thanks in advance\n\nCheck my response here: in-a-certain-district-the-ratio-of-the-number-of-registered-143983.html#p1158046\n_________________\nIntern", null, "", null, "Joined: 03 Mar 2013\nPosts: 24\nRe: In a certain district, the ratio of the number of registered [#permalink]\n\n### Show Tags\n\nHi, just wondering what is wrong with my approach as follows:\n\n3/5 republican voters = 0.6x\nAnother 600 register as republican, with the total amount being 80% republican (4/5)\nTotal new voters is 1,100 (500+600)\n\nSo, 0.6x + 600 = 0.8(x+1,100)\n\n0.6x + 600 = 0.8x + 880\n\nHowever, this is where I go awry.\n\nCould someone pls explain why I can't use the approach noted above?\n\nMath Expert", null, "V\nJoined: 02 Sep 2009\nPosts: 59268\nRe: In a certain district, the ratio of the number of registered [#permalink]\n\n### Show Tags\n\n2\nHi, just wondering what is wrong with my approach as follows:\n\n3/5 republican voters = 0.6x\nAnother 600 register as republican, with the total amount being 80% republican (4/5)\nTotal new voters is 1,100 (500+600)\n\nSo, 0.6x + 600 = 0.8(x+1,100)\n\n0.6x + 600 = 0.8x + 880\n\nHowever, this is where I go awry.\n\nCould someone pls explain why I can't use the approach noted above?\n\nThe ratio of Republicans to Democrats was 3:5, which means that Republicans were 3/(3+5)=3/8 of the total number (not 3/5 of the total number)\n\nAfter 600 additional Republicans and 500 additional Democrats registered, the ratio was 4:5, which means that that Republicans were 4/(4+5)=4/9 of the total number (not 4/5 of the total number).\n\n3/8x+600=4/9(x+1100) --> x=1600 --> after registration = x+1100=2700 --> Republicans=4/91200 and Democrats=1500 --> the difference=300.\n\nHope it helps.\n_________________\nIntern", null, "", null, "Joined: 03 Mar 2013\nPosts: 24\nRe: In a certain district, the ratio of the number of registered [#permalink]\n\n### Show Tags\n\nBunuel wrote:\nHi, just wondering what is wrong with my approach as follows:\n\n3/5 republican voters = 0.6x\nAnother 600 register as republican, with the total amount being 80% republican (4/5)\nTotal new voters is 1,100 (500+600)\n\nSo, 0.6x + 600 = 0.8(x+1,100)\n\n0.6x + 600 = 0.8x + 880\n\nHowever, this is where I go awry.\n\nCould someone pls explain why I can't use the approach noted above?\n\nThe ratio of Republicans to Democrats was 3:5, which means that Republicans were 3/(3+5)=3/8 of the total number (not 3/5 of the total number)\n\nAfter 600 additional Republicans and 500 additional Democrats registered, the ratio was 4:5, which means that that Republicans were 4/(4+5)=4/9 of the total number (not 4/5 of the total number).\n\n3/8x+600=4/9(x+1100) --> x=1600 --> after registration = x+1100=2700 --> Republicans=4/91200 and Democrats=1500 --> the difference=300.\n\nHope it helps.\n\nThanks a lot, appreciate your help!\nVeritas Prep GMAT Instructor", null, "Joined: 11 Dec 2012\nPosts: 312\nRe: In a certain district, the ratio of the number of registered [#permalink]\n\n### Show Tags\n\n3\n1\nIf ever you're not seeing the math, you know one of the answers has to be correct, so you can just backsolve. Looking at the increase in numbers, it would make sense that the number of democrats MORE than republicans will probably be in the hundreds, so you'd likely start with B or C.\n\nIf you start with C: 400 is the difference between D's and R's in the new ratio: So there are 4x400 = 1600 Republicans and 5x400 = 2000 Democrats. If you subtract 600 from R and 500 from D, you get 1000 Republicans and 1500 Democrats, a 2/3 ratio. This isn't 3/5, but it's not far (66.7% vs 60%). The next attempt should be B since it's close but slightly too big:\n\nB: 300 is the difference between D's and R's in the new ratio: So there are 4x300 = 1200 Republicans and 5x300 = 1500 Democrats. If you subtract 600 from R and 500 from D, you get 600 Republicans and 1000 Democrats, a 3/5 ratio. Bingo.\n\nIf you started with B, you got to the right answer quickly. If you started with A, D or E, your answer will be way off. While this is not a better solution than the algebraic one, sometimes it is easier to see.\n\nHope this helps!\n-Ron\n_________________\nIntern", null, "", null, "Joined: 09 Sep 2013\nPosts: 2\nGPA: 3.53\nOfficial guide problem solving Q 113 [#permalink]\n\n### Show Tags\n\nIn a certain district, the ratio of the number of registered Republicans to the number of registered Democrats was 3/5. After 600 additional Republicans and 500 additional Democrats registered, the ratio was 4/5. After these registrations, there were how many more voters in the district registered as Democrats than as Republicans?\n\n(A) 100\n(B) 300\n(C) 400\n(D) 1,000\n(E) 2,500\n\n_________\n\nMy question is, why can't we take the multiplier which is 200, and multiply the new ratio 4/5 to get a difference of 200? Why is that wrong? that what was done In question 105 in the official guide. Thank you\nCurrent Student", null, "P\nStatus: Chasing my MBB Dream!\nJoined: 29 Aug 2012\nPosts: 1096\nLocation: United States (DC)\nWE: General Management (Aerospace and Defense)\nRe: Official guide problem solving Q 113 [#permalink]\n\n### Show Tags\n\nmjb2 wrote:\nIn a certain district, the ratio of the number of registered Republicans to the number of registered Democrats was 3/5. After 600 additional Republicans and 500 additional Democrats registered, the ratio was 4/5. After these registrations, there were how many more voters in the district registered as Democrats than as Republicans?\n\n(A) 100\n(B) 300\n(C) 400\n(D) 1,000\n(E) 2,500\n\n_________\n\nMy question is, why can't we take the multiplier which is 200, and multiply the new ration 4/5 to get a difference of 200? Why is that wrong? In question 105 in the official guide that what was done. Thank you\n\nBefore posting please check whether the same question is discussed or not. In this case it is already discussed.", null, "_________________\nMath Expert", null, "V\nJoined: 02 Sep 2009\nPosts: 59268\nRe: Official guide problem solving Q 113 [#permalink]\n\n### Show Tags\n\nmjb2 wrote:\nIn a certain district, the ratio of the number of registered Republicans to the number of registered Democrats was 3/5. After 600 additional Republicans and 500 additional Democrats registered, the ratio was 4/5. After these registrations, there were how many more voters in the district registered as Democrats than as Republicans?\n\n(A) 100\n(B) 300\n(C) 400\n(D) 1,000\n(E) 2,500\n\n_________\n\nMy question is, why can't we take the multiplier which is 200, and multiply the new ratio 4/5 to get a difference of 200? Why is that wrong? that what was done In question 105 in the official guide. Thank you\n\nMerging similar topics. Please refer to the solutions above and ask if anything is unclear.\n\nP.S. All OG13 questions with solutions are here: the-official-guide-quantitative-question-directory-143450.html\n_________________\nIntern", null, "", null, "Joined: 09 Sep 2013\nPosts: 2\nGPA: 3.53\nRe: In a certain district, the ratio of the number of registered [#permalink]\n\n### Show Tags\n\nsorry for violating the rules.. I didn't really know them as this was my first post. Anyway, I still don't understand why we can not take the multiplier and multiply it by the new ration 4/5 (2005)-(2004)= 200 difference.\nMath Expert", null, "V\nJoined: 02 Sep 2009\nPosts: 59268\nRe: In a certain district, the ratio of the number of registered [#permalink]\n\n### Show Tags\n\nmjb2 wrote:\nsorry for violating the rules.. I didn't really know them as this was my first post. Anyway, I still don't understand why we can not take the multiplier and multiply it by the new ration 4/5 (2005)-(2004)= 200 difference.\n\nSorry but I don't understand the logic behind your approach.\n_________________\nManager", null, "", null, "B\nJoined: 30 Mar 2013\nPosts: 101\nRe: In a certain district, the ratio of the number of registered [#permalink]\n\n### Show Tags\n\nR/D = 3x/5x\n\nR/D = 3x+600/(5x+500) = 4/5\nSolve for x to get x=200.\nNow put in original equation to get total Republicans as 1200, and the total number of democrats as 1500.\ndifference= 300\nManager", null, "", null, "Joined: 07 Feb 2015\nPosts: 60\nRe: In a certain district, the ratio of the number of registered [#permalink]\n\n### Show Tags\n\nBunuel wrote:\nmjb2 wrote:\nsorry for violating the rules.. I didn't really know them as this was my first post. Anyway, I still don't understand why we can not take the multiplier and multiply it by the new ration 4/5 (2005)-(2004)= 200 difference.\n\nSorry but I don't understand the logic behind your approach.\n\nIt's a shame this wasn't addressed, Bunuel. Let me follow up this question with the logic and you can let me know why it's wrong.\n\nAfter we find x = 200 as the multiplier, why can't we say that since AFTER these registrations the ratio is 4/5, then 4x/5x. Since x=200, 4x equals 800 registered Republicans, and 5x equals 1000 registered Democrats. Thats means that the difference after the registrations is 1000 Democrats - 800 Republicans is 200!\nMath Expert", null, "V\nJoined: 02 Sep 2009\nPosts: 59268\nRe: In a certain district, the ratio of the number of registered [#permalink]\n\n### Show Tags\n\n3\ngmatser1 wrote:\nBunuel wrote:\nmjb2 wrote:\nsorry for violating the rules.. I didn't really know them as this was my first post. Anyway, I still don't understand why we can not take the multiplier and multiply it by the new ration 4/5 (2005)-(200*4)= 200 difference.\n\nSorry but I don't understand the logic behind your approach.\n\nIt's a shame this wasn't addressed, Bunuel. Let me follow up this question with the logic and you can let me know why it's wrong.\n\nAfter we find x = 200 as the multiplier, why can't we say that since AFTER these registrations the ratio is 4/5, then 4x/5x. Since x=200, 4x equals 800 registered Republicans, and 5x equals 1000 registered Democrats. Thats means that the difference after the registrations is 1000 Democrats - 800 Republicans is 200!\n\nBecause x = 200 is for the old ratio and you cannot use it for the new one.\n_________________\nRetired Moderator", null, "Joined: 29 Apr 2015\nPosts: 817\nLocation: Switzerland\nConcentration: Economics, Finance\nSchools: LBS MIF '19\nWE: Asset Management (Investment Banking)\nRe: In a certain district, the ratio of the number of registered [#permalink]\n\n### Show Tags\n\nCan we solve this somehow with the \"change in ratio\" method?\n\nStarting ratio:\n5R=3D\nEnding ratio:\n5R=4D\n\nNow we have a change in ratio of 1 unit in democrats corresponding to 500 democrats. This means, 1 unit in 5:4 represents 500. However I believe this just holds true as long as only one number changes. Since we also have changing numbers of republicans, we can not calculate it like that. Can anyone agree/disagree?\n_________________\nSaving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!\n\nPS Please send me PM if I do not respond to your question within 24 hours.\nTarget Test Prep Representative", null, "V\nStatus: Founder & CEO\nAffiliations: Target Test Prep\nJoined: 14 Oct 2015\nPosts: 8484\nLocation: United States (CA)\nRe: In a certain district, the ratio of the number of registered [#permalink]\n\n### Show Tags\n\nIn a certain district, the ratio of the number of registered Republicans to the number of registered Democrats was 3/5. After 600 additional Republicans and 500 additional Democrats registered, the ratio was 4/5. After these registrations, there were how many more voters in the district registered as Democrats than as Republicans?\n\n(A) 100\n(B) 300\n(C) 400\n(D) 1,000\n(E) 2,500\n\nThe fractional ratio indicates that for every 3 Republicans, there are 5 Democrats, a ratio of 3 : 5. We first set up this ratio of registered Republicans to registered Democrats using a variable multiplier:\n\nRepublicans: Democrats = 3x : 5x\n\nWe are given that 600 additional Republicans and 500 additional Democrats registered and that the new ratio of Republicans to Democrats was 4 to 5. This means that the new number of Republicans can be expressed as (3x + 600), and the new number of Democrats can be expressed as (5x + 500). We can put all this into an equation:\n\nR/D  (3x+600)/(5x+500) = 4/5\n\nAfter cross multiplying we have:\n\n5(3x+600) = 4(5x+500)\n\n15x + 3,000 = 20x + 2,000\n\n1,000 = 5x\n\nx = 200\n\nThus after the registration we have the following:\n\nDemocrats = (5 × 200) + 500 = 1,500\n\nRepublicans = (3 × 200) + 600 = 1,200\n\nThere are 1,500 – 1,200 = 300 more Democrats than Republicans.\n\n_________________\n\n# Scott Woodbury-Stewart\n\nFounder and CEO\n\nScott@TargetTestPrep.com\n\nSee why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews\n\nIf you find one of my posts helpful, please take a moment to click on the \"Kudos\" button.", null, "Re: In a certain district, the ratio of the number of registered [#permalink] 10 Jun 2016, 11:48\n\nGo to page 1 2 Next [ 27 posts ]\n\nDisplay posts from previous: Sort by\n\n# In a certain district, the ratio of the number of registered", null, "", null, "" ]	[ null, "https://cdn.gmatclub.com/cdn/files/forum/styles/gmatclub_light/theme/images/profile/close.png", null, "https://cdn.gmatclub.com/cdn/files/forum/styles/gmatclub_light/theme/images/profile/close.png", null, "https://gmatclub.com/forum/styles/gmatclub_light/theme/images/search/close.png", null, "https://cdn.gmatclub.com/cdn/files/forum/images/ranks/rank_phpbb_3.svg", null, "https://cdn.gmatclub.com/cdn/files/forum/images/no_avatar.svg", null, "https://cdn.gmatclub.com/cdn/files/forum/styles/gmatclub_light/theme/images/viewtopic/timer_play.png", null, 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http://www.synergicpartners.com/en/deep-learning-from-the-basis/	[ "# Blogs\n\nDeep Learning from the basis\n• 1602 Views\n• 0 Comment\n• Artificial Intelligence . Deep Learning . Inteligencia Artificial . Machine Learning . Neural Networks . Perceptrones . Redes Neuronales .\n###### We want to start with a purely informative article, for those to whom Deep Learning sounds like a science fiction or a horror movie. We do not pretend you end up using neural network models on a daily basis, we are just interested that you have the base to be able to make the leap into the world of Deep Learning.\n\nStarting from the basics, it is convenient to ask ourselves the question: What is Deep Learning? The answer is simple; Deep Learning is a Machine Learning technique. In computer science, Machine Learning is the area of artificial intelligence whose objective is the development of techniques that allow computation-based systems (machines) to learn the hidden patterns of structured and unstructured data. Robotics, natural language processing, image recognition and artificial intelligence are some of the wonders derived from automatic learning.\n\nThen we need to continue asking, are neural networks and Deep Learning the same? No, on the one hand when we talk about neural networks we refer to the generic name we give to any scheme that connects multiple nodes (neurons). On the other hand, Deep Learning is a type of neural network that is characterized by having more than one layer of interconnected neurons. Neural networks are a powerful modeling tool that accounts for the interactions between our inputs.", null, "To know what neural networks are, it is best to start with simple perceptrons (perceptron). Perceptrons began to develop in the 1950s (yes, in the 50s!) by Frank Rosenblatt. Rosenblatt was based on the work developed by Warren McCulloch and Walter Pitts in the 1940s and on a learning rule based on error correction. This illustrates that it is a technology that began to take shape more than 70 years ago. Today the perceptron is not a widely used neural model due in part to the development of more advanced networks. However, to understand how the more complex networks work, it is best to start with the simplest perceptrons.", null, "A perceptron can be used in classification problems. It can get multiple entries {X1, X2 … Xn} of binary values {0.1}. In our example the perceptron will output two inputs (X1 y X2). Rosenblatt proposed a simple rule to get the output: He introduced the concept of weight {W1, W2 … Wn}. These weights are real numbers that indicate the importance of each of the inputs with respect to the output. The perceptron output, also zero or one, is determined if the weighted sum (the sum of each Wi·Xi) is less or greater than a certain threshold value ( a real number), being this value a parameter specific to the neuron.\n\nThe output will take a value of zero (deactivated) if the weighted sum is less than the threshold value and a value of one (activated) if the weighted sum is greater than or equal to that value. We can express it mathematically through the following expression:", null, "We will make a change in the expression, replacing the negative of the threshold with the bias (b=-θ). The bias resembles how easy it is to get an output from one. Therefore, our mathematical expression would look like:", null, "Let’s see an example to finish understanding how networks based on simple perceptrons work.\n\nLet’s imagine that we have to go back to university. The professor explains that for the final grade he takes into account two tests that we will do throughout the course. These tests will consist of an oral presentation (X1) and a written exam (X2). It would be a bit strange, but imagine that there are only two possible results for each test. We can fail (zero value) or pass (value of one). In addition, the teacher explains that each test has a weight with respect to the final grade. For him, the most important thing in the course will be the written exam, an essential condition to pass, so it will give him a high weight. Let’s say a weight of W2=5. The other test is important but we will consider it complementary to the written exam, so it will give a weight of W1=2.\n\nOnce the weights have been chosen, we decide on a bias of -4 (threshold of 4) for the perceptron. With this configuration the perceptron will apply a value of 1 if we pass the written test and 0 if we fail, regardless of the results of the other tests. Therefore, if we have failed the oral but passed the written the output result would be:", null, "We can vary the results of the model only by varying the weights and the threshold value. If we increase the threshold value, we will move to a situation in which not only will it be necessary to pass the written examination. So, by raising the threshold we are making it more difficult to pass. If we lower the threshold, it may happen that you can pass only with the oral test.\n\nIn order to “choose” the weights and the threshold value, we follow a process of error correction. It consists of starting with some random initial values and modifying them iteratively when the output obtained does not coincide with the observed output (remember, we are in supervised learning). Therefore, this learning is a method of error detection and correction. Weights are only modified when the results are not ideal.\n\nYears later, Minsky (1969) saw the existing limitations in networks based on simple perceptrons. He verified that they only serve for linearly separable classifications by a decision boundary. These problems were already solved by statistical methods, requiring a smaller amount of data. Partly because of this, it evolved into more complex neural networks.", null, "Junior Data Engineer @Synergic Partners" ]	[ null, "http://www.synergicpartners.com/wp-content/uploads/2018/10/Red-Neuronales_Deep-Learning-Blog_Pablo-Navarro.png", null, "http://www.synergicpartners.com/wp-content/uploads/2018/10/Red-Neuronal-simple_Deep-Learning-Blog_-Pablo-Navarro-150x83.png", null, "http://www.synergicpartners.com/wp-content/uploads/2018/10/Red-Neuronales_Formula1_Deep-Learning-Blog_Pablo-Navarro.png", null, "http://www.synergicpartners.com/wp-content/uploads/2018/10/Red-Neuronales_Formula2_Deep-Learning-Blog_Pablo-Navarro.png", null, "http://www.synergicpartners.com/wp-content/uploads/2018/10/Red-Neuronales_Formula3_Deep-Learning-Blog_Pablo-Navarro.png", null, "http://www.synergicpartners.com/wp-content/plugins/user-avatar/user-avatar-pic.php", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9324092,"math_prob":0.9292949,"size":5180,"snap":"2019-13-2019-22","text_gpt3_token_len":1091,"char_repetition_ratio":0.12152241,"word_repetition_ratio":0.009060022,"special_character_ratio":0.2057915,"punctuation_ratio":0.092479676,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9850888,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12],"im_url_duplicate_count":[null,1,null,1,null,1,null,1,null,1,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-03-22T07:27:53Z\",\"WARC-Record-ID\":\"<urn:uuid:f27ddef9-41d3-45db-9e35-147bdfd26dec>\",\"Content-Length\":\"50137\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a3a71d39-3ec0-4f7e-8d9e-9c29c8ced437>\",\"WARC-Concurrent-To\":\"<urn:uuid:35cb46e1-9103-4cf8-8735-11b5c30d6b4b>\",\"WARC-IP-Address\":\"185.195.97.109\",\"WARC-Target-URI\":\"http://www.synergicpartners.com/en/deep-learning-from-the-basis/\",\"WARC-Payload-Digest\":\"sha1:LS27YYVQHGCH2EHC2GLP3ZW46W3XS6JC\",\"WARC-Block-Digest\":\"sha1:C7M4FSF6CBZT3SVK4WKAXZTZ7AE5RZER\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-13/CC-MAIN-2019-13_segments_1552912202635.43_warc_CC-MAIN-20190322054710-20190322080710-00297.warc.gz\"}"}
https://math.stackexchange.com/questions/253440/vertex-cover-degree-problem	[ "# Vertex Cover degree problem\n\nSo Vertex cover (VC):\n\nInstance: a graph $G$ and an integer $k>0$. Question: Does $G$ have a vertex cover of size at most $k$?\n\nWe will now define a version of this problem in which we assume that the degree of each node in a given graph is $2$:\n\n2-vertex cover (2-VC). Instance: a graph $G$ in which each node has degree $2$ and an integer $k>0$. Question: Does $G$ have a vertex cover of size at most $k$?\n\nFor the following, decide whether the answer is “Yes”, “No” or “Unknown because it would resolve the $P =? NP$ question.” Prove your claim.\n\n(a) Is $2-VC ≤_P VC$?\n\n(b) Is $VC ≤_P 2-VC$?\n\nand\n\na second question here\n\nhttp://pastie.org/private/ljxo6aqg3a9troxpnpxriq\n\nThese questions ares really nagging me because i'm not sure what is meant by the phrase degree 2. Is this the cost of the vertex?\n\nAlso i'm aware of the general proof of vertex cover that shows how basically we use the compliment of the independent sets to show a vertex cover.\n\nI'm in the middle of revising for exams and these are eluding me, anyone have any suggestions?\n\nUPDATE: I think 1a) is basically just plugging in a 2 degree VC into a graph that can solve the problem in one step and then deriving the answer through that with a cast.\n\n• The degree of a vertex in a graph is the number of edges incident with that vertex. – Hagen von Eitzen Dec 7 '12 at 23:40\n\nFirst Question\n\nYou need two observations\n\n1. The problem 2-VC is in ${\\sf P}$. This can be shown as follows. In a graph, where every vertex has degree $2$, every connected component is a cycle. You can decide for every component (cycle) separately, how many vertices you need to cover it. In particular, if the cycle has $m$ edges the minimum vertex cover has size $\\lceil m/2 \\rceil$. Notice that every language in $X\\in {\\sf P}-\\{\\emptyset,\\Sigma^*\\}$ is also ${\\sf P}$-complete, since for any $L\\in {\\sf P}$, you can map easily $w\\in L \\iff f(w)\\in X$ with help of the decision algorithm for $L$.\n\n2. VC is a generalization of 2-VC. Hence any algortihm for VC, can answer 2-VC requests. Thus you can take the identity as reduction and you get 2-VC$\\le_p$VC. This is what you observed in Update 1.\n\nNow you can argue as follows. (a) holds independent of whether ${\\sf P}={\\sf NP}$ or not. If ${\\sf P}={\\sf NP}$, then VC is in ${\\sf P}$ and since 2-VC is ${\\sf P}$-complete (b) holds. On the other hand, (b) implies that 2-VC is ${\\sf NP}$-complete and in ${\\sf P}$, and hence ${\\sf P}={\\sf NP}$ has to hold (thus it is false when ${\\sf P}\\ne{\\sf NP}$).\n\nSecond Question\n\nYou can define a reduction from 3-SAT to ADV-3SAT as follows. Let $\\psi$ be the 3-SAT formula you want to transform into a ADV-3SAT formula $\\psi'$. Take every variable $x_i$, and replace it by a new variable $x_i^j$, for $j$ being the $j$th occurrence of $x_i$ in $\\psi$. As a next step you add clauses to assure that all the copies of a variable are either all true or all false. In other words, you want to ensure that $x_i^{j_1} \\iff x_i^{j_2}$. In CNF you get $(x_i^{j_1} \\lor \\overline{x_i^{j_2}}) \\land (x_i^{j_2} \\lor \\overline{x_i^{j_1}})$. Add this for every triplet $i,j_1,j_2$ to get $\\psi'$. Notice that $\|\\psi\|$ and $\|\\psi'\|$ are polynomially realated. By construction $\\psi$ is true, iff $\\psi'$ is true, and hence $\\psi$ is satisfiable, iff $\\psi'$ is satisfiable.\n\nFor the first question - If every vertex has 2 edges incident on it, then the graph is a union of disjoint cycles. Can you find a minimum vertex cover for a single cycle? How do vertex covers of disjoint cycles affect each other? What does that mean about how easy it is to solve 2-VC?\n\nFor the second question - Take an instance of 3-SAT. If each variable shows up in at most 3 clauses, we're done. If a variable shows up in more than 3 clauses, can you 'split' the variable into multiple new variables so that each of the new variables shows up in at most 3 clauses, the new variables are linked in the sense that they are all true or all false, and their truth/falsehood is a proxy for the original variable?" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.93838525,"math_prob":0.99738973,"size":1207,"snap":"2019-43-2019-47","text_gpt3_token_len":333,"char_repetition_ratio":0.12635079,"word_repetition_ratio":0.110091746,"special_character_ratio":0.26594862,"punctuation_ratio":0.10465116,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9998235,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-11-19T12:45:12Z\",\"WARC-Record-ID\":\"<urn:uuid:34c34486-27a1-4e60-b03c-2ffbb0228041>\",\"Content-Length\":\"140607\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:ef455545-c0f8-40f1-bdcd-bca9e9cfe8d4>\",\"WARC-Concurrent-To\":\"<urn:uuid:c6e186e8-e667-4819-8493-d658d06a8672>\",\"WARC-IP-Address\":\"151.101.65.69\",\"WARC-Target-URI\":\"https://math.stackexchange.com/questions/253440/vertex-cover-degree-problem\",\"WARC-Payload-Digest\":\"sha1:J4ZMV2RSAFDGEBQGMY7ACGXJOHCNWH5Z\",\"WARC-Block-Digest\":\"sha1:ZIYYAEH4VJBYS2TRYI4JBOG2DDXROEDP\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-47/CC-MAIN-2019-47_segments_1573496670151.97_warc_CC-MAIN-20191119121339-20191119145339-00519.warc.gz\"}"}