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https://math.stackexchange.com/questions/1707439/math-problem-forty-nine-points	[ "# Math Problem: Forty-nine points\n\n49 points are marked on a sheet of paper in a square. Adjacent points horizontally or vertically are separated by exactly 1 centimetre.\n\nHow many straight lines of length 5 centimetres can be drawn between points in the design?\n\nI have attempted to solve this problem taking...	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9676544,"math_prob":0.9750717,"size":556,"snap":"2019-51-2020-05","text_gpt3_token_len":121,"char_repetition_ratio":0.11050725,"word_repetition_ratio":0.0,"special_character_ratio":0.21223022,"punctuation_ratio":0.08256881,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9966879,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-10T02:36:09Z\",\"WARC-Record-ID\":\"<urn:uuid:07f0021e-5d3a-4bb2-9a8d-0c4ef720b0c8>\",\"Content-Length\":\"137880\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:ceb4c0b6-2420-4f54-a71b-5b31d81674a5>\",\"WARC-Concurrent-To\":\"<urn:uuid:679cd4df-c270-43ec-8dff-fa8225f1347a>\",\"WARC-IP-Address\":\"151.101.129.69\",\"WARC-Target-URI\":\"https://math.stackexchange.com/questions/1707439/math-problem-forty-nine-points\",\"WARC-Payload-Digest\":\"sha1:2LA7LGS7AFLDAAJTWPNK4S7MZP67YXL4\",\"WARC-Block-Digest\":\"sha1:MBLKPTIIBHOOV2TSZNZUSSSTLABM4UNP\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575540525781.64_warc_CC-MAIN-20191210013645-20191210041645-00199.warc.gz\"}"}
https://trace.tennessee.edu/utk_gradthes/4361/	[ "## Masters Theses\n\n### A Numerical Algorithm For Solving the Nonlinear Differential Equations that Describe a Multistage Flash Evaporator\n\n6-1970\n\nThesis\n\n#### Degree Name\n\nMaster of Science\n\n#### Major\n\nNuclear Engineering\n\nJ.C. Robinson\n\n#### Committee Members\n\nT.W. Kerlin, Hale C. Roland\n\n...	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8956062,"math_prob":0.9659814,"size":1764,"snap":"2023-40-2023-50","text_gpt3_token_len":346,"char_repetition_ratio":0.13522728,"word_repetition_ratio":0.072874494,"special_character_ratio":0.17120181,"punctuation_ratio":0.10069445,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96081436,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-11-28T12:52:37Z\",\"WARC-Record-ID\":\"<urn:uuid:af3a0d78-122d-44fd-99de-7c0f568e3a28>\",\"Content-Length\":\"36701\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4f4797f8-8c4b-4df1-a06f-d84b1b0ac56a>\",\"WARC-Concurrent-To\":\"<urn:uuid:712fe23b-9471-4423-99e8-1920dc50f952>\",\"WARC-IP-Address\":\"13.57.92.51\",\"WARC-Target-URI\":\"https://trace.tennessee.edu/utk_gradthes/4361/\",\"WARC-Payload-Digest\":\"sha1:GMQLGYQ22VDTWSJCEPO5LCNPS6IIJY2G\",\"WARC-Block-Digest\":\"sha1:5QGS57UPVXXI3L7MOSZBDX2MZBLJN72S\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679099514.72_warc_CC-MAIN-20231128115347-20231128145347-00249.warc.gz\"}"}
http://brauer.maths.qmul.ac.uk/Atlas/spor/M11/	[ "# ATLAS: Mathieu group M11\n\nOrder = 7920 = 24.32.5.11.\nMult = 1.\nOut = 1.\n\nThe following information is available for M11:\n\n### Standard generators\n\nStandard generators of M11 are a and b where a has order 2, b has order 4, ab has order 11 and ababababbababbabb has order 4. Two equivalent conditions to t...	[ null, "http://brauer.maths.qmul.ac.uk/Atlas/icons/atlas.gif", null, "http://brauer.maths.qmul.ac.uk/Atlas/icons/spor.gif", null, "http://brauer.maths.qmul.ac.uk/Atlas/icons/old.gif", null, "http://brauer.maths.qmul.ac.uk/Atlas/icons/ftp.gif", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6930524,"math_prob":0.96618026,"size":8692,"snap":"2021-43-2021-49","text_gpt3_token_len":2893,"char_repetition_ratio":0.3038674,"word_repetition_ratio":0.36897403,"special_character_ratio":0.32708237,"punctuation_ratio":0.16196448,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9799756,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-12-07T00:46:12Z\",\"WARC-Record-ID\":\"<urn:uuid:a3584e0c-f72c-4e83-a20b-996a80cacb19>\",\"Content-Length\":\"23268\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:ab98bcae-755c-4280-8cc0-d751f19f580a>\",\"WARC-Concurrent-To\":\"<urn:uuid:0c134218-f628-44dc-900f-433c046dda28>\",\"WARC-IP-Address\":\"161.23.64.143\",\"WARC-Target-URI\":\"http://brauer.maths.qmul.ac.uk/Atlas/spor/M11/\",\"WARC-Payload-Digest\":\"sha1:EL3EISGZWHGVWGKZPS2F5J6KDR5CLA6N\",\"WARC-Block-Digest\":\"sha1:MUW4C4PUJXTJMSUXEEL6HFZQHJJHB4EG\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964363327.64_warc_CC-MAIN-20211206224536-20211207014536-00372.warc.gz\"}"}
https://elo.mastermath.nl/course/info.php?id=129	[ "### M1: Differential Geometry - 8EC\n\nAim of the course\n\nProvide an introduction to vector bundles (with application to tubular neighborhoods), principal bundles, connections, the general theory of geometric structures (G-structures) and their integrabiliy, mentioning examples such as Riemannian, complex or sym...	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.91402286,"math_prob":0.97809345,"size":2400,"snap":"2022-27-2022-33","text_gpt3_token_len":496,"char_repetition_ratio":0.12813021,"word_repetition_ratio":0.0,"special_character_ratio":0.18833333,"punctuation_ratio":0.12135922,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.972301,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-07-04T14:57:30Z\",\"WARC-Record-ID\":\"<urn:uuid:2514f6d4-d9ba-4df2-b613-8351946890c6>\",\"Content-Length\":\"41112\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:8a62c343-81af-4a40-9a1c-42d22ef1b449>\",\"WARC-Concurrent-To\":\"<urn:uuid:b79f8c2e-0db3-498f-a9a9-3326c2f8d896>\",\"WARC-IP-Address\":\"87.233.196.71\",\"WARC-Target-URI\":\"https://elo.mastermath.nl/course/info.php?id=129\",\"WARC-Payload-Digest\":\"sha1:SGT7K4PQ32V2FK6IQRYQEFA3NSSTFJP5\",\"WARC-Block-Digest\":\"sha1:A7DAUE3TY7PPN3U6JRS3XNOQN3H5XXCN\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656104432674.76_warc_CC-MAIN-20220704141714-20220704171714-00012.warc.gz\"}"}
https://www.effortlessmath.com/tag/squeeze-theorem/	[ "# Squeeze Theorem\n\nSearch in Squeeze Theorem articles.", null, "## How to Determine Limits Using the Squeeze Theorem?\n\nIf two functions squeeze together at a certain point, then any function trapped between them will get squeezed to that same point. The following step-by-step guide helps you determine limi...	[ null, "data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACAAAAAPCAQAAAAviQWcAAAAGElEQVR42mP8X89AEWAcNWDUgFEDBokBAH4nFnKVxVNEAAAAAElFTkSuQmCC", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.85201126,"math_prob":0.8120233,"size":439,"snap":"2023-40-2023-50","text_gpt3_token_len":84,"char_repetition_ratio":0.101149425,"word_repetition_ratio":0.0,"special_character_ratio":0.17539863,"punctuation_ratio":0.102564104,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.972386,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-23T17:19:42Z\",\"WARC-Record-ID\":\"<urn:uuid:d4a920e5-194a-4f17-84d9-67a264c64f4d>\",\"Content-Length\":\"33425\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f03511d6-f9bb-48a7-9f11-5af4bf7db235>\",\"WARC-Concurrent-To\":\"<urn:uuid:394db9a9-3675-4e9f-8635-2b6f6e08b15b>\",\"WARC-IP-Address\":\"5.78.86.142\",\"WARC-Target-URI\":\"https://www.effortlessmath.com/tag/squeeze-theorem/\",\"WARC-Payload-Digest\":\"sha1:CRGSPLYEBTSKKTIICLZZECTFTRI4LN5I\",\"WARC-Block-Digest\":\"sha1:JWX63U3VAFGE4R3HNELZXZZONJMEI4V5\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233506528.19_warc_CC-MAIN-20230923162848-20230923192848-00003.warc.gz\"}"}
https://numberworld.info/53530	[ "# Number 53530\n\n### Properties of number 53530\n\nCross Sum:\nFactorization:\n2 * 5 * 53 * 101\nDivisors:\n1, 2, 5, 10, 53, 101, 106, 202, 265, 505, 530, 1010, 5353, 10706, 26765, 53530\nCount of divisors:\nSum of divisors:\nPrime number?\nNo\nFibonacci number?\nNo\nBell Number?\nNo\nCatalan Number?\nNo\nBase 2 ...	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7707437,"math_prob":0.99493504,"size":2004,"snap":"2019-51-2020-05","text_gpt3_token_len":707,"char_repetition_ratio":0.1795,"word_repetition_ratio":0.24074075,"special_character_ratio":0.48752496,"punctuation_ratio":0.16504854,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99706566,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-01-23T20:26:25Z\",\"WARC-Record-ID\":\"<urn:uuid:5755dc98-a297-438e-b0ff-204f9e834abc>\",\"Content-Length\":\"13829\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:52b01c36-e758-4485-b008-2ff4b406e9b8>\",\"WARC-Concurrent-To\":\"<urn:uuid:42a4ab94-3668-408e-bb05-e526340bcb55>\",\"WARC-IP-Address\":\"176.9.140.13\",\"WARC-Target-URI\":\"https://numberworld.info/53530\",\"WARC-Payload-Digest\":\"sha1:BDKIOUPNOHEK5MTAWZUB6URMAMNTSUGV\",\"WARC-Block-Digest\":\"sha1:BQB2TJBGG73VE6FR3ETUD6QS7FCP43AL\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-05/CC-MAIN-2020-05_segments_1579250613416.54_warc_CC-MAIN-20200123191130-20200123220130-00488.warc.gz\"}"}
http://xqpbx.com/cn/categorypage-836475-1.html	[ "微信：13662481022\n\n• 公司动态\n[2016-10-05]\n\n[2016-10-04]\n\n[2016-10-03]\n\n[2016-10-02]\n\n[2016-10-01]\n\n[2016-09-30]\n\n[2016-08-12]\n\n[2016-07-12]\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n```\n\n```\n`\t`\n\n`...	[ null ]	{"ft_lang_label":"__label__zh","ft_lang_prob":0.82451284,"math_prob":0.98954046,"size":1484,"snap":"2019-26-2019-30","text_gpt3_token_len":1501,"char_repetition_ratio":0.12972973,"word_repetition_ratio":0.0,"special_character_ratio":0.32345015,"punctuation_ratio":0.34074074,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9897171,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-06-16T18:47:44Z\",\"WARC-Record-ID\":\"<urn:uuid:454f030a-fd86-4e4f-bff9-facce51084c2>\",\"Content-Length\":\"184974\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:54395857-d0ff-4ac7-b25e-614f5c56f523>\",\"WARC-Concurrent-To\":\"<urn:uuid:fad9f7e9-9a79-4cb3-b33c-036d1b9d7389>\",\"WARC-IP-Address\":\"154.213.74.98\",\"WARC-Target-URI\":\"http://xqpbx.com/cn/categorypage-836475-1.html\",\"WARC-Payload-Digest\":\"sha1:L5C6W74MOHRXO64RZGITHPCMABNFDLEM\",\"WARC-Block-Digest\":\"sha1:CZ63DJGONYOD2EN2M726ZU556GMKHIOL\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-26/CC-MAIN-2019-26_segments_1560627998291.9_warc_CC-MAIN-20190616182800-20190616204800-00130.warc.gz\"}"}
https://brilliant.org/problems/floor-floor-floor-floor/	[ "Floor Floor Floor Floor\n\nAlgebra Level 5\n\nGiven the equation\n\n$x \\lfloor x \\lfloor x \\lfloor x \\rfloor \\rfloor \\rfloor = 41$\n\nIf $\\alpha$ denote the largest negative value of $x$ which satisfy the equation above, while $\\beta$ denote the smallest positive value of $x$ which satisfy the equation abo...	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.740464,"math_prob":1.0000056,"size":357,"snap":"2019-43-2019-47","text_gpt3_token_len":75,"char_repetition_ratio":0.13597734,"word_repetition_ratio":0.29090908,"special_character_ratio":0.21288516,"punctuation_ratio":0.23684211,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.0000092,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-23T03:45:44Z\",\"WARC-Record-ID\":\"<urn:uuid:8e3c928f-8b15-4049-b6cd-c1a1e4a454de>\",\"Content-Length\":\"40307\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:bd9064fc-5a1e-47d6-9f07-f9fe022a4201>\",\"WARC-Concurrent-To\":\"<urn:uuid:58cdfa56-e03d-47eb-a998-338f2c97a587>\",\"WARC-IP-Address\":\"104.20.34.242\",\"WARC-Target-URI\":\"https://brilliant.org/problems/floor-floor-floor-floor/\",\"WARC-Payload-Digest\":\"sha1:EETHGZU3SUZOZIG4YIC4H7GEVIOR4H7H\",\"WARC-Block-Digest\":\"sha1:U7YFP4HAQBTKDVDRDZNN76T4RNH5BBMC\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570987828425.99_warc_CC-MAIN-20191023015841-20191023043341-00431.warc.gz\"}"}
https://www.geeksforgeeks.org/square-root-of-a-number-without-using-sqrt-function/?ref=lbp	[ "# Square root of a number without using sqrt() function\n\nGiven a number N, the task is to find the square root of N without using sqrt() function.\n\nExamples:\n\nInput: N = 25\nOutput: 5\n\nInput: N = 3\nOutput: 1.73205\n\nInput: N = 2.5\nOutput: 1.58114\n\n## Recommended: Please try your approach on {IDE} firs...	[ null, "https://media.geeksforgeeks.org/auth/avatar.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6354042,"math_prob":0.97402257,"size":6826,"snap":"2020-45-2020-50","text_gpt3_token_len":2051,"char_repetition_ratio":0.15655233,"word_repetition_ratio":0.41386706,"special_character_ratio":0.32552007,"punctuation_ratio":0.13069016,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.999902,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-12-01T12:26:43Z\",\"WARC-Record-ID\":\"<urn:uuid:476b5c42-57bb-428b-b7cd-69da6e2ec4da>\",\"Content-Length\":\"145257\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:698d8032-7ac1-47d5-b31e-2a0139cb4ec9>\",\"WARC-Concurrent-To\":\"<urn:uuid:bb79a300-4d94-4160-89f3-372862d80273>\",\"WARC-IP-Address\":\"104.96.221.160\",\"WARC-Target-URI\":\"https://www.geeksforgeeks.org/square-root-of-a-number-without-using-sqrt-function/?ref=lbp\",\"WARC-Payload-Digest\":\"sha1:XF2WFB4IZBCLURA34PDA4NOWPLVLNNMN\",\"WARC-Block-Digest\":\"sha1:SFHJGNAK6OSL5JMZ323QD6LAENTKPUGL\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141674082.61_warc_CC-MAIN-20201201104718-20201201134718-00481.warc.gz\"}"}
https://patents.google.com/patent/KR20030029443A/en	[ "# KR20030029443A - Regulator circuit and control method thereof - Google Patents\n\n## Info\n\nPublication number\nKR20030029443A\nKR20030029443A KR1020020019889A KR20020019889A KR20030029443A KR 20030029443 A KR20030029443 A KR 20030029443A KR 1020020019889 A KR1020020019889 A KR 1020020019889A KR 20020019889 A K...	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8545831,"math_prob":0.9605766,"size":92428,"snap":"2020-45-2020-50","text_gpt3_token_len":21488,"char_repetition_ratio":0.29315978,"word_repetition_ratio":0.31352207,"special_character_ratio":0.23126109,"punctuation_ratio":0.07368488,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9674235,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-11-23T17:54:08Z\",\"WARC-Record-ID\":\"<urn:uuid:13485457-7805-4cf6-902c-aecc22b78193>\",\"Content-Length\":\"178233\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b76dca47-6ea8-440a-a181-704b93b5ca18>\",\"WARC-Concurrent-To\":\"<urn:uuid:e3b430b8-a211-4249-9ddc-a42edceba442>\",\"WARC-IP-Address\":\"172.217.13.78\",\"WARC-Target-URI\":\"https://patents.google.com/patent/KR20030029443A/en\",\"WARC-Payload-Digest\":\"sha1:OVF4FORNLC6P7BO4IPFMT53U5RLILKC3\",\"WARC-Block-Digest\":\"sha1:DKLHHFBYFFPMHVO2VB7REDSQW35AE7BP\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141163411.0_warc_CC-MAIN-20201123153826-20201123183826-00308.warc.gz\"}"}
http://mathnium.com/help/sum.html	[ "sum\nsum of the elements of an array along a specified dimension.\n`(y)=sum(x)`\n`(y)=sum(x, dim)`\n Inputs `x` Any numeric array. `dim` A positive integer not greater than the number of dimensions of `x` . Outputs `y` The array of sum of the elements of `x` along the dimension `dim` whose default value is `1` .\n...	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.60245717,"math_prob":0.99914545,"size":1072,"snap":"2019-13-2019-22","text_gpt3_token_len":375,"char_repetition_ratio":0.15355805,"word_repetition_ratio":0.03482587,"special_character_ratio":0.44589552,"punctuation_ratio":0.23648648,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9952299,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-03-20T22:09:56Z\",\"WARC-Record-ID\":\"<urn:uuid:a013780f-c795-4eb8-8bb2-8a9d2e564dde>\",\"Content-Length\":\"2511\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d035fca4-294c-4481-8430-31e2c965653a>\",\"WARC-Concurrent-To\":\"<urn:uuid:78f44779-8f5c-4665-ba2b-6948a3f70842>\",\"WARC-IP-Address\":\"74.208.236.241\",\"WARC-Target-URI\":\"http://mathnium.com/help/sum.html\",\"WARC-Payload-Digest\":\"sha1:IPMUTPSARTRYSCVQHCTYSYDSU4ZNB32Z\",\"WARC-Block-Digest\":\"sha1:LDO2HHBVVKBV46ME4MY536IQQOXAQRUR\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-13/CC-MAIN-2019-13_segments_1552912202471.4_warc_CC-MAIN-20190320210433-20190320232433-00556.warc.gz\"}"}
https://tutorialspoint.dev/language/c/void-pointer-c	[ "# void pointer in C / C++\n\nA void pointer is a pointer that has no associated data type with it. A void pointer can hold address of any type and can be typcasted to any type.\n\n `int` `a = 10; ` `char` `b = ``'x'``; ` ` ` `void` `*p = &a; ``// void pointer holds address of int 'a' ` `p = &b; ``// void pointer...	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.74713266,"math_prob":0.96402293,"size":2087,"snap":"2021-31-2021-39","text_gpt3_token_len":555,"char_repetition_ratio":0.12193951,"word_repetition_ratio":0.1448468,"special_character_ratio":0.29516053,"punctuation_ratio":0.13801453,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9935041,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-08-02T15:12:19Z\",\"WARC-Record-ID\":\"<urn:uuid:249a4579-93e0-4478-b551-e66ca82b9d88>\",\"Content-Length\":\"26871\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2dc6581e-7f66-403d-9976-6120b2ffed69>\",\"WARC-Concurrent-To\":\"<urn:uuid:071d67cd-3c31-4834-ab81-e6fe224f417b>\",\"WARC-IP-Address\":\"104.21.79.77\",\"WARC-Target-URI\":\"https://tutorialspoint.dev/language/c/void-pointer-c\",\"WARC-Payload-Digest\":\"sha1:PA5R7WE7LHUNFS4GOEMALI26FLBZJEZ6\",\"WARC-Block-Digest\":\"sha1:4CDY5HK6YMC7U5ANAS64HHNSCMKYNJNT\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-31/CC-MAIN-2021-31_segments_1627046154321.31_warc_CC-MAIN-20210802141221-20210802171221-00080.warc.gz\"}"}
https://en.m.wikipedia.org/wiki/Rigid_body_dynamics	[ "# Rigid body dynamics\n\nRigid-body dynamics studies the movement of systems of interconnected bodies under the action of external forces. The assumption that the bodies are rigid, which means that they do not deform under the action of applied forces, simplifies the analysis by reducing the parameters that descri...	[ null, "https://upload.wikimedia.org/wikipedia/commons/thumb/f/f2/SteamEngine_Boulton%26Watt_1784.png/300px-SteamEngine_Boulton%26Watt_1784.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8834072,"math_prob":0.99915576,"size":21464,"snap":"2019-35-2019-39","text_gpt3_token_len":4525,"char_repetition_ratio":0.16188258,"word_repetition_ratio":0.070474565,"special_character_ratio":0.20443533,"punctuation_ratio":0.10875599,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9999999,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-09-18T10:31:31Z\",\"WARC-Record-ID\":\"<urn:uuid:5b29babe-7898-4c3d-8c3d-5638255b9595>\",\"Content-Length\":\"262194\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2128e437-347c-4538-8e8d-e666d846f3c6>\",\"WARC-Concurrent-To\":\"<urn:uuid:d33570de-0601-4de5-be13-3404d71d08f3>\",\"WARC-IP-Address\":\"208.80.154.224\",\"WARC-Target-URI\":\"https://en.m.wikipedia.org/wiki/Rigid_body_dynamics\",\"WARC-Payload-Digest\":\"sha1:ZOVKD4AG6IPDXDQTRGEMPHKP3KD4IDXB\",\"WARC-Block-Digest\":\"sha1:7A7UC5BIAIEEN2Q7ZHAARBRUWEZOU5QT\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-39/CC-MAIN-2019-39_segments_1568514573264.27_warc_CC-MAIN-20190918085827-20190918111827-00022.warc.gz\"}"}
https://www.gradesaver.com/textbooks/math/precalculus/precalculus-6th-edition-blitzer/chapter-9-section-9-5-parametric-equations-exercise-set-page-1020/52	[ "## Precalculus (6th Edition) Blitzer\n\nPublished by Pearson\n\n# Chapter 9 - Section 9.5 - Parametric Equations - Exercise Set - Page 1020: 52\n\n#### Answer\n\n$x=6t+3$ ; $y=13t-1$\n\n#### Work Step by Step\n\nFor a line, we have: $(3,-1); (9,12)$ $x_1=3, x_2=9,y_1=-1, y_2=12$ Now, in parametric from: $x=(x_2-x_...	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6846389,"math_prob":0.99281704,"size":474,"snap":"2021-04-2021-17","text_gpt3_token_len":184,"char_repetition_ratio":0.108510636,"word_repetition_ratio":0.02631579,"special_character_ratio":0.4092827,"punctuation_ratio":0.1491228,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99929905,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-04-11T00:56:14Z\",\"WARC-Record-ID\":\"<urn:uuid:13111b43-e2bd-4b21-b11a-67976c503257>\",\"Content-Length\":\"64246\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:33855b9c-d022-40ba-b413-d0a92c300fc9>\",\"WARC-Concurrent-To\":\"<urn:uuid:c077cd29-6f0f-4446-9dce-9bbc461526a3>\",\"WARC-IP-Address\":\"3.217.118.58\",\"WARC-Target-URI\":\"https://www.gradesaver.com/textbooks/math/precalculus/precalculus-6th-edition-blitzer/chapter-9-section-9-5-parametric-equations-exercise-set-page-1020/52\",\"WARC-Payload-Digest\":\"sha1:PZZNY6ACEPWJXZ7KOTZ4I7DCMBGCINSA\",\"WARC-Block-Digest\":\"sha1:FUREY7AIBIDJ5RX3ASC3ZSFRNVKTO2OY\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-17/CC-MAIN-2021-17_segments_1618038060603.10_warc_CC-MAIN-20210411000036-20210411030036-00549.warc.gz\"}"}
https://numbermatics.com/n/513/	[ "# 513\n\n## 513 is an odd composite number composed of two prime numbers multiplied together.\n\nWhat does the number 513 look like?\n\nThis visualization shows the relationship between its 2 prime factors (large circles) and 8 divisors.\n\n513 is an odd composite number. It is composed of two distinct prime numbe...	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.87221426,"math_prob":0.9885565,"size":2390,"snap":"2021-21-2021-25","text_gpt3_token_len":597,"char_repetition_ratio":0.10813076,"word_repetition_ratio":0.032828283,"special_character_ratio":0.2748954,"punctuation_ratio":0.16352202,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99596107,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-05-14T09:43:54Z\",\"WARC-Record-ID\":\"<urn:uuid:101a884a-945b-4fdb-9b56-9fd26bc51e51>\",\"Content-Length\":\"17102\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:aed50915-b1e7-4000-a6d3-44522273c8c7>\",\"WARC-Concurrent-To\":\"<urn:uuid:d8690f31-a998-49e4-ade2-bc24b4348dca>\",\"WARC-IP-Address\":\"72.44.94.106\",\"WARC-Target-URI\":\"https://numbermatics.com/n/513/\",\"WARC-Payload-Digest\":\"sha1:3LKDHIFR47JUUJ2NBHR2SIR2HG56UEQK\",\"WARC-Block-Digest\":\"sha1:RAKQCTJ5G6F5HOI2VRNLNTDDHI4FEBFJ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-21/CC-MAIN-2021-21_segments_1620243990449.41_warc_CC-MAIN-20210514091252-20210514121252-00547.warc.gz\"}"}
https://aaaknow.com/lessonFull.php?slug=geoAreaCircle&menu=Geometry	[ "## Area of a Circle\n\n### Area: Learn\n\nArea is the space within a shape. The units of area are the squares of the units of length (that is, if a shape's sides are measured in meters, then the shape's area is measured in square meters).\n\nFor a circle, we will need to incorporate the constant pi, which we will ...	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8374455,"math_prob":0.97747964,"size":1499,"snap":"2021-43-2021-49","text_gpt3_token_len":415,"char_repetition_ratio":0.11906355,"word_repetition_ratio":0.02166065,"special_character_ratio":0.2681788,"punctuation_ratio":0.11258278,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99888796,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-26T23:46:09Z\",\"WARC-Record-ID\":\"<urn:uuid:1fc156d7-c7c8-425a-8891-0217f2f2d86b>\",\"Content-Length\":\"20244\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:46b3f410-70a2-416f-a77b-b7c037b6eca4>\",\"WARC-Concurrent-To\":\"<urn:uuid:396da11d-6d70-4688-8ba4-2c5e205529cf>\",\"WARC-IP-Address\":\"216.37.42.100\",\"WARC-Target-URI\":\"https://aaaknow.com/lessonFull.php?slug=geoAreaCircle&menu=Geometry\",\"WARC-Payload-Digest\":\"sha1:4RGQOIYXWQFDSOQ5X7UM2V6BZFFEGU4Z\",\"WARC-Block-Digest\":\"sha1:SFXM6D3PEBGACE5KE2RU63RXKCJLISWY\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323587963.12_warc_CC-MAIN-20211026231833-20211027021833-00260.warc.gz\"}"}
https://www.nagwa.com/en/videos/515136981469/	[ "# Lesson Video: Writing and Evaluating Formulas Mathematics\n\nIn this video, we will learn how to distinguish between formulas and expressions, write a formula from a given description, and substitute numbers into a simple formula.\n\n13:48\n\n### Video Transcript\n\nIn this video, we will learn how to distinguis...	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.932635,"math_prob":0.99915624,"size":8398,"snap":"2023-40-2023-50","text_gpt3_token_len":2260,"char_repetition_ratio":0.15665951,"word_repetition_ratio":0.05919003,"special_character_ratio":0.23779471,"punctuation_ratio":0.10870741,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9999639,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-21T13:20:15Z\",\"WARC-Record-ID\":\"<urn:uuid:b2617262-d51b-4a81-a62d-d197885b4445>\",\"Content-Length\":\"52812\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:eac4d847-d11b-491d-a37a-60821056cae3>\",\"WARC-Concurrent-To\":\"<urn:uuid:83978c05-5fe0-4601-bc41-2a67324b3e44>\",\"WARC-IP-Address\":\"172.67.69.52\",\"WARC-Target-URI\":\"https://www.nagwa.com/en/videos/515136981469/\",\"WARC-Payload-Digest\":\"sha1:7OSH3VSGBCVM52FJK4QUSJIBSFRTF7M2\",\"WARC-Block-Digest\":\"sha1:SYSUPWYN6PNFU567EBTOEQLNXYZC6DVV\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233506027.39_warc_CC-MAIN-20230921105806-20230921135806-00685.warc.gz\"}"}
https://blog.quantinsti.com/xgboost-python/	[ "# Introduction to XGBoost in Python\n\nBy Ishan Shah and compiled by Rekhit Pachanekar\n\nAh! XGBoost! The supposed miracle worker which is the weapon of choice for machine learning enthusiasts and competition winners alike. It is said that XGBoost was developed to increase computational speed and optimize model p...	[ null, "https://d1rwhvwstyk9gu.cloudfront.net/2020/02/Apple_returns.png", null, "https://d1rwhvwstyk9gu.cloudfront.net/2020/02/XG-Boost-FINAL-01.png", null, "https://d1rwhvwstyk9gu.cloudfront.net/2020/02/Feature-importance.png", null, "https://d1rwhvwstyk9gu.cloudfront.net/2020/02/xgboost_download.png"...	{"ft_lang_label":"__label__en","ft_lang_prob":0.87114096,"math_prob":0.88397586,"size":20954,"snap":"2021-43-2021-49","text_gpt3_token_len":4515,"char_repetition_ratio":0.13575178,"word_repetition_ratio":0.02602118,"special_character_ratio":0.21408801,"punctuation_ratio":0.10914761,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98816687,"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],"im_url_duplicate_count":[null,4,null,4,null,8,null,4,null,4,null,4,null,4,null,4,null,8,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-19T06:02:05Z\",\"WARC-Record-ID\":\"<urn:uuid:20ea0f22-9e2a-47b0-8265-9890a2ee4345>\",\"Content-Length\":\"172442\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:68db8d22-a5c1-42b3-ad6c-f07a4a90cb8d>\",\"WARC-Concurrent-To\":\"<urn:uuid:3460ec09-832c-40fe-9d9e-29ac26c9fbac>\",\"WARC-IP-Address\":\"174.129.255.252\",\"WARC-Target-URI\":\"https://blog.quantinsti.com/xgboost-python/\",\"WARC-Payload-Digest\":\"sha1:6IEZCUUPUZJHT7MI7UTRR33EZFD7UO5X\",\"WARC-Block-Digest\":\"sha1:NTFLA36RGEFHXBKDBU7JG2XY5YRWM4VN\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323585242.44_warc_CC-MAIN-20211019043325-20211019073325-00538.warc.gz\"}"}
https://howmanyis.com/temperature/211-degree-c-in-k/164327-1-degree-celsius-in-kelvin	[ "How many is\nConversion between units of measurement\nRating 4.00 (1 Vote)\n\nYou can easily convert 1 degree Celsius into Kelvin using each definition.\n\n¿How many K are there in 1 degree C?\n\nThe result of the absolute temperature conversion is that 1 °C are 274.15 K.\n\nOne degree Celsius equals to two hundre...	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7670791,"math_prob":0.9510312,"size":564,"snap":"2019-26-2019-30","text_gpt3_token_len":129,"char_repetition_ratio":0.18035714,"word_repetition_ratio":0.0,"special_character_ratio":0.22340426,"punctuation_ratio":0.094339624,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98836607,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-06-20T03:25:45Z\",\"WARC-Record-ID\":\"<urn:uuid:9092dc90-a9b9-4dc1-b7e0-2958a98a7667>\",\"Content-Length\":\"20540\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:532d2755-659f-456c-927c-d2f59c501d00>\",\"WARC-Concurrent-To\":\"<urn:uuid:bf2035d1-4b1f-47ed-bccf-d998b175d7e1>\",\"WARC-IP-Address\":\"104.31.72.117\",\"WARC-Target-URI\":\"https://howmanyis.com/temperature/211-degree-c-in-k/164327-1-degree-celsius-in-kelvin\",\"WARC-Payload-Digest\":\"sha1:PEENBPMZHREZ3TYZNB2TYXDEHRISCNJP\",\"WARC-Block-Digest\":\"sha1:CZGXA3KR7TKMRNBOZU2JINB75BSDGJCH\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-26/CC-MAIN-2019-26_segments_1560627999130.98_warc_CC-MAIN-20190620024754-20190620050754-00039.warc.gz\"}"}
https://programmer.group/chapter-ii-data-structure-monotonic-stack-and-monotonic-queue.html	[ "# Chapter II Data Structure Monotonic Stack and Monotonic Queue\n\nKeywords: C Algorithm data structure\n\n# 1. Algorithmic ideas\n\nThe core idea of these two algorithms is:\nOnly those elements that conform to a certain monotonicity are likely to be the answer. Screen out those elements that do not conform to a ...	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.81436867,"math_prob":0.99053425,"size":5906,"snap":"2021-43-2021-49","text_gpt3_token_len":1665,"char_repetition_ratio":0.11792613,"word_repetition_ratio":0.14069082,"special_character_ratio":0.30968505,"punctuation_ratio":0.1162614,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99399215,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-22T23:05:17Z\",\"WARC-Record-ID\":\"<urn:uuid:92fc9e2e-1064-4a53-a5ce-05c46abaed2b>\",\"Content-Length\":\"13870\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:3ff2c62d-069c-48ae-a589-777086b2e3f1>\",\"WARC-Concurrent-To\":\"<urn:uuid:028783fb-4929-48e0-8058-2d9942874a7c>\",\"WARC-IP-Address\":\"213.136.76.254\",\"WARC-Target-URI\":\"https://programmer.group/chapter-ii-data-structure-monotonic-stack-and-monotonic-queue.html\",\"WARC-Payload-Digest\":\"sha1:DXVJFGFOZ6GORCCXCED7JIEZOMQSLM4B\",\"WARC-Block-Digest\":\"sha1:LZVBEU5RY4DOVIQQHBZRUWFQHQZIBSGM\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323585522.78_warc_CC-MAIN-20211022212051-20211023002051-00513.warc.gz\"}"}
https://docs.neptune.ai/integrations/sklearn/	[ "# scikit-learn integration guide#", null, "", null, "Scikit-learn (also known as sklearn) is an open source machine learning framework commonly used for building predictive models. With the Neptune–scikit-learn integration, you can track your classifiers, regressors, and k-means clustering results, specifi...	[ null, "https://colab.research.google.com/assets/colab-badge.svg", null, "https://docs.neptune.ai/img/app/integrations/scikit-learn.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.59473556,"math_prob":0.44331002,"size":9586,"snap":"2023-40-2023-50","text_gpt3_token_len":2299,"char_repetition_ratio":0.13347945,"word_repetition_ratio":0.3188755,"special_character_ratio":0.23221365,"punctuation_ratio":0.17070143,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9554183,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,null,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-10-04T12:18:17Z\",\"WARC-Record-ID\":\"<urn:uuid:169d1c6e-d2fb-4ce8-b951-f32f9355ba92>\",\"Content-Length\":\"264627\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1477b209-7176-4754-b6b4-6415b9551705>\",\"WARC-Concurrent-To\":\"<urn:uuid:ba8e6923-3cd5-4163-9c76-30f0ca4c81a2>\",\"WARC-IP-Address\":\"35.186.223.74\",\"WARC-Target-URI\":\"https://docs.neptune.ai/integrations/sklearn/\",\"WARC-Payload-Digest\":\"sha1:U4TMCZ3YHR7EG24PG5SH7HTDTRZ4WC3V\",\"WARC-Block-Digest\":\"sha1:S5MQIAOTYJNISFODBEGPGQ3DIR5G5D3F\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233511369.62_warc_CC-MAIN-20231004120203-20231004150203-00060.warc.gz\"}"}
https://math.stackexchange.com/questions/1689723/integral-of-divergence-over-a-closed-surface	[ "# Integral of divergence over a closed surface\n\nI am reading a paper, where an integral of a divergence over a closed surface is used without proof.\n\n$$\\oint_S [\\nabla \\cdot \\vec{v}(\\vec{r})] d\\vec{s} = 0$$,\n\nwhere $$\\vec{v}$$ is tangential to the surface ($$\\vec{v}(r)\\cdot \\vec{n}(\\vec{r}) = 0$$)...	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8444028,"math_prob":0.999884,"size":1148,"snap":"2020-45-2020-50","text_gpt3_token_len":337,"char_repetition_ratio":0.1284965,"word_repetition_ratio":0.0,"special_character_ratio":0.27439025,"punctuation_ratio":0.09375,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99999416,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-11-26T15:26:26Z\",\"WARC-Record-ID\":\"<urn:uuid:70f2bf5d-5a2b-4ced-8d87-5e83776d3014>\",\"Content-Length\":\"154512\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:3858991d-b739-4398-bac4-21a12d0c9483>\",\"WARC-Concurrent-To\":\"<urn:uuid:aac47f59-4f11-410b-8614-aaf846c7a741>\",\"WARC-IP-Address\":\"151.101.129.69\",\"WARC-Target-URI\":\"https://math.stackexchange.com/questions/1689723/integral-of-divergence-over-a-closed-surface\",\"WARC-Payload-Digest\":\"sha1:BRTYVPQWGGP7RE6ZTRB5AD7JU446LSJU\",\"WARC-Block-Digest\":\"sha1:JHJSRNM2JMPN3PRX7S2VZO4FGMMWNAI5\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141188800.15_warc_CC-MAIN-20201126142720-20201126172720-00259.warc.gz\"}"}
https://ftp.aimsciences.org/article/doi/10.3934/dcds.2017256	[ "• PDF\n• Cite\n• Share\nArticle Contents", null, "", null, "Article Contents\n\n# Visco-Energetic solutions to one-dimensional rate-independent problems\n\n• Visco-Energetic solutions of rate-independent systems (recently introduced in ) are obtained by solving a modified time Incremental Minimization Sche...	[ null, "https://ftp.aimsciences.org/style/web/images/custom/icon_toright.png", null, "https://ftp.aimsciences.org/style/web/images/custom/icon_toleft.png", null, "https://ftp.aimsciences.org/style/web/images/article/shu.png", null, "https://ftp.aimsciences.org/style/web/images/article/1.gif", null, ...	{"ft_lang_label":"__label__en","ft_lang_prob":0.6627356,"math_prob":0.99759996,"size":5198,"snap":"2023-14-2023-23","text_gpt3_token_len":1575,"char_repetition_ratio":0.14150943,"word_repetition_ratio":0.027285129,"special_character_ratio":0.3339746,"punctuation_ratio":0.24609734,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9994167,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,1,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-05-30T12:22:09Z\",\"WARC-Record-ID\":\"<urn:uuid:3c8178ca-dc12-48a2-9cca-32079efe981e>\",\"Content-Length\":\"119602\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d6983800-77e4-4b3c-bf74-943f0723bedb>\",\"WARC-Concurrent-To\":\"<urn:uuid:a03fe06d-d32a-4690-a666-aee306c0f59a>\",\"WARC-IP-Address\":\"107.161.80.18\",\"WARC-Target-URI\":\"https://ftp.aimsciences.org/article/doi/10.3934/dcds.2017256\",\"WARC-Payload-Digest\":\"sha1:LKD7DUM3DUYGVTMXT7JYHVCV6WKWQVLP\",\"WARC-Block-Digest\":\"sha1:KJTYVP6R7CFP2CSKNI3UFZPCNIG7HZC7\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224645595.10_warc_CC-MAIN-20230530095645-20230530125645-00435.warc.gz\"}"}
https://www.futurestarr.com/blog/mathematics/what-is-14-as-a-percent-or	[ "FutureStarr\n\nWhat Is 14 As a Percent OR\n\n## What Is 14 As a Percent OR", null, "# What Is 14 As a Percent\n\nis a fun puzzle game designed to help you learn how to multiply. The goal: to find the missing number of a given sum.\n\n### Use\n\nDecimals Converted to PercentageDecimal to percentage is our categ...	[ null, "https://www.futurestarr.com/blog-media/e524343348a2fb2d11105b1f3aeb6237.jpg", null, "https://www.futurestarr.com/assets/images/default-ad-banner.png", null, "https://www.futurestarr.com/blog-media/1642436939Amir.png", null, "https://www.futurestarr.com/blog-media/3123e721d4aad90b6add978c60349e9...	{"ft_lang_label":"__label__en","ft_lang_prob":0.90502876,"math_prob":0.8528953,"size":2258,"snap":"2022-27-2022-33","text_gpt3_token_len":491,"char_repetition_ratio":0.13265306,"word_repetition_ratio":0.0,"special_character_ratio":0.21966343,"punctuation_ratio":0.11453745,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97181284,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62],"im_url_duplicate_count":[null,null,null,null,null,2,null,null,null,9,null,null,null,3,null,null,null,5,null,null,null,2,null,null,null,4,null,null,null,6,null,null,null,5,null,null,null,4,null,null,null,4,null,null,null,2,null,null,null,7,null,null,null,4,null,null,null,2,null,null,null,5,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-08-10T05:58:35Z\",\"WARC-Record-ID\":\"<urn:uuid:953089e3-f967-4a40-9ae3-c99abed637d9>\",\"Content-Length\":\"118021\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6aa14b58-2ba5-4fdd-a34d-c5087ad6fd5f>\",\"WARC-Concurrent-To\":\"<urn:uuid:2d0170d0-b557-4911-81a5-82c5ee4bfd36>\",\"WARC-IP-Address\":\"75.98.162.39\",\"WARC-Target-URI\":\"https://www.futurestarr.com/blog/mathematics/what-is-14-as-a-percent-or\",\"WARC-Payload-Digest\":\"sha1:XHKOW22DAIGJTDJEEH7OQL3AJ6C5RU6Z\",\"WARC-Block-Digest\":\"sha1:HOWW5KJTPG5BZDME5UWRIB3M4O3PCV6X\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-33/CC-MAIN-2022-33_segments_1659882571147.84_warc_CC-MAIN-20220810040253-20220810070253-00162.warc.gz\"}"}
http://www.greatestcommonfactor.net/gcf-of-811/	[ "X\nX\n\n# Calculate the Greatest Common Factor or GCF of 811\n\nThe instructions to find the GCF of 811 are the next:\n\n## 1. Decompose all numbers into prime factors\n\n 811 811 1\n\n## 2. Write all numbers as the product of its prime factors\n\n Prime factors of 811 = 811\n\n## 3. Choose the common prime factor...	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.86821914,"math_prob":0.92612326,"size":594,"snap":"2021-43-2021-49","text_gpt3_token_len":146,"char_repetition_ratio":0.19152543,"word_repetition_ratio":0.14851485,"special_character_ratio":0.26936027,"punctuation_ratio":0.08928572,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99950147,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-12-07T11:39:19Z\",\"WARC-Record-ID\":\"<urn:uuid:c1a8e54f-5950-4a56-9fc9-bf07202a36a8>\",\"Content-Length\":\"34793\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:074fb293-55bc-440f-99cd-acb8ace62543>\",\"WARC-Concurrent-To\":\"<urn:uuid:34a9cbaf-7006-4e5f-bd26-1a9c05554d34>\",\"WARC-IP-Address\":\"107.170.60.201\",\"WARC-Target-URI\":\"http://www.greatestcommonfactor.net/gcf-of-811/\",\"WARC-Payload-Digest\":\"sha1:ZQPHMBJFKJZWNYTS7RAEFK22DQWCWI5N\",\"WARC-Block-Digest\":\"sha1:EY2QWQDXZVQKX2HNCZ6MAJAFF4NLHMHH\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964363376.49_warc_CC-MAIN-20211207105847-20211207135847-00421.warc.gz\"}"}
https://www.statistics-lab.com/%E6%95%B0%E5%AD%A6%E4%BB%A3%E5%86%99%E4%BF%A1%E6%81%AF%E8%AE%BA%E4%BD%9C%E4%B8%9A%E4%BB%A3%E5%86%99information-theory%E4%BB%A3%E8%80%83run-length-encoding/	[ "### 数学代写\|信息论作业代写information theory代考\|Run Length Encoding", null, "statistics-lab™ 为您的留学生涯保驾护航在代写信息论information theory方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写信息论information theory代写方面经验极为丰富，各种代写信息论information theory相关的作业也就用不着说。\n\n• Statistical Inference 统计推断\n• Statistical Computing 统计计算\n• (Genera...	[ null, "data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%20245%20171'%3E%3C/svg%3E", null ]	{"ft_lang_label":"__label__zh","ft_lang_prob":0.5738912,"math_prob":0.9966951,"size":11036,"snap":"2023-40-2023-50","text_gpt3_token_len":5835,"char_repetition_ratio":0.0964467,"word_repetition_ratio":0.015887026,"special_character_ratio":0.20559986,"punctuation_ratio":0.07635747,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9978857,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-28T11:40:48Z\",\"WARC-Record-ID\":\"<urn:uuid:9831be65-9c08-4dd5-b90d-c7af28a72ae7>\",\"Content-Length\":\"183663\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a879aa87-be09-4b7f-a887-00b4015537de>\",\"WARC-Concurrent-To\":\"<urn:uuid:1b5174c8-a3df-4447-b534-2b0a0f3d3654>\",\"WARC-IP-Address\":\"172.67.148.182\",\"WARC-Target-URI\":\"https://www.statistics-lab.com/%E6%95%B0%E5%AD%A6%E4%BB%A3%E5%86%99%E4%BF%A1%E6%81%AF%E8%AE%BA%E4%BD%9C%E4%B8%9A%E4%BB%A3%E5%86%99information-theory%E4%BB%A3%E8%80%83run-length-encoding/\",\"WARC-Payload-Digest\":\"sha1:Z6YNJVKVYRZZS43LX4DZ2XPTPJ6TECEY\",\"WARC-Block-Digest\":\"sha1:QLTFC363EA7BFT7N5V6DNLZGJSV6OWY7\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510387.77_warc_CC-MAIN-20230928095004-20230928125004-00572.warc.gz\"}"}
https://nest-simulator.readthedocs.io/en/v2.20.0/auto_examples/intrinsic_currents_subthreshold.html	[ "# Intrinsic currents subthreshold¶\n\nThis example illustrates how to record from a model with multiple intrinsic currents and visualize the results. This is illustrated using the ht_neuron which has four intrinsic currents: I_NaP, I_KNa, I_T, and I_h. It is a slightly simplified implementation of neuron model pro...	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6845595,"math_prob":0.9623606,"size":6068,"snap":"2023-40-2023-50","text_gpt3_token_len":1630,"char_repetition_ratio":0.102242745,"word_repetition_ratio":0.002301496,"special_character_ratio":0.2643375,"punctuation_ratio":0.16550523,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9916412,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-28T05:25:40Z\",\"WARC-Record-ID\":\"<urn:uuid:772f0942-916c-41bf-8e38-abd036ab558f>\",\"Content-Length\":\"43605\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2723df24-4c19-476c-9036-578bee1c4da4>\",\"WARC-Concurrent-To\":\"<urn:uuid:f368cfc7-85a1-44d4-9e6d-9cf1d4bf34ab>\",\"WARC-IP-Address\":\"104.17.33.82\",\"WARC-Target-URI\":\"https://nest-simulator.readthedocs.io/en/v2.20.0/auto_examples/intrinsic_currents_subthreshold.html\",\"WARC-Payload-Digest\":\"sha1:GT6R6OJ4EQ7655D3A4Z22LVZ7NWAUQP5\",\"WARC-Block-Digest\":\"sha1:3W7AAGFJGTBDUJMDFOAGIYHXNT4J32NU\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510358.68_warc_CC-MAIN-20230928031105-20230928061105-00742.warc.gz\"}"}
https://eric-roca.github.io/courses/olg/olg_monotonicity_of_the_dynamics/	[ "# Multiple intertemporal equilibria\n\nIn the OLG model, a unique intertemporal equilibrium arises if, for a given $k_t$, the equation\n\n$$H(k_{t+1}) = k_{t+1} - \\frac{1}{1+n}s\\left(\\omega(k_t), f^\\prime(k_{t+1})\\right) = 0$$\n\nhas a unique solution. We know that $\\lim_{k\\rightarrow 0}H(k) < 0$ and $\\lim...	[ null, "https://eric-roca.github.io/img/olg/backwards.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.71613115,"math_prob":0.99997914,"size":2626,"snap":"2021-43-2021-49","text_gpt3_token_len":867,"char_repetition_ratio":0.13348588,"word_repetition_ratio":0.0,"special_character_ratio":0.35224676,"punctuation_ratio":0.13309352,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9999895,"pos_list":[0,1,2],"im_url_duplicate_count":[null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-12-01T15:05:25Z\",\"WARC-Record-ID\":\"<urn:uuid:35bc6e2a-b402-4d3c-ad8b-d019fe543b6a>\",\"Content-Length\":\"23546\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:48d2a529-ee06-4a9e-a364-2804861314ed>\",\"WARC-Concurrent-To\":\"<urn:uuid:4972f910-5429-4521-916d-25ddba4aa87d>\",\"WARC-IP-Address\":\"185.199.108.153\",\"WARC-Target-URI\":\"https://eric-roca.github.io/courses/olg/olg_monotonicity_of_the_dynamics/\",\"WARC-Payload-Digest\":\"sha1:ODSKMN5ZXUXSX5ZCHTKDOX66RBFR55FY\",\"WARC-Block-Digest\":\"sha1:43UFS4ALABFK2UTRDGVO7BS6OHOPUPET\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964360803.6_warc_CC-MAIN-20211201143545-20211201173545-00532.warc.gz\"}"}
https://math.stackexchange.com/questions/855828/what-is-abstract-algebra-essentially	[ "# What is Abstract Algebra essentially?\n\nIn the most basic sense, what is abstract algebra about?\n\nWolfram Mathworld has the following definition: \"Abstract algebra is the set of advanced topics of algebra that deal with abstract algebraic structures rather than the usual number systems. The most important of...	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9645238,"math_prob":0.9212374,"size":744,"snap":"2022-05-2022-21","text_gpt3_token_len":152,"char_repetition_ratio":0.12027027,"word_repetition_ratio":0.0,"special_character_ratio":0.19758065,"punctuation_ratio":0.16901408,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97911966,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-27T15:59:02Z\",\"WARC-Record-ID\":\"<urn:uuid:31b65493-e519-45ab-9a17-e7682ba4c395>\",\"Content-Length\":\"272879\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:35dea8e7-2b55-4954-9c44-7413c9029b39>\",\"WARC-Concurrent-To\":\"<urn:uuid:99e77aca-83de-4616-96da-6e56cb86e2e0>\",\"WARC-IP-Address\":\"151.101.193.69\",\"WARC-Target-URI\":\"https://math.stackexchange.com/questions/855828/what-is-abstract-algebra-essentially\",\"WARC-Payload-Digest\":\"sha1:KLRX3TBDFE5S53L5EXB5EAZD7CXN35KO\",\"WARC-Block-Digest\":\"sha1:AHJAMI2LRJD4JOYGXX7ZIRZI75EI7BEF\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662658761.95_warc_CC-MAIN-20220527142854-20220527172854-00677.warc.gz\"}"}
https://bqueennatural.com/article/mean-definition-meaning-how-to-find-the-mean-formula-examples	[ "# Mean (Definition & Meaning), How to Find the Mean, Formula, Examples. (2023)\n\nIn statistics, the mean is one of the measures of central tendency, apart from the mode and median. Mean is nothing but the average of the given set of values. It denotes the equal distribution of values for a given data set. The mea...	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8297379,"math_prob":0.99851596,"size":12929,"snap":"2022-40-2023-06","text_gpt3_token_len":3973,"char_repetition_ratio":0.172147,"word_repetition_ratio":0.09882965,"special_character_ratio":0.31974632,"punctuation_ratio":0.124692656,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99996877,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-01-31T07:35:42Z\",\"WARC-Record-ID\":\"<urn:uuid:3927e60c-fd4d-4839-a620-dee03c37d062>\",\"Content-Length\":\"102219\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:20094ddb-bffb-4d73-9a0d-8c836126e8b8>\",\"WARC-Concurrent-To\":\"<urn:uuid:78689e05-8e08-465d-b39a-a3372b02fb89>\",\"WARC-IP-Address\":\"104.21.73.40\",\"WARC-Target-URI\":\"https://bqueennatural.com/article/mean-definition-meaning-how-to-find-the-mean-formula-examples\",\"WARC-Payload-Digest\":\"sha1:4ZMDK425Z3ARCCKFKOUI44Y5SZ3FLKYX\",\"WARC-Block-Digest\":\"sha1:64EJ7U6RKDNRR7BPTC3JTR6Q5IM7FWE2\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-06/CC-MAIN-2023-06_segments_1674764499845.10_warc_CC-MAIN-20230131055533-20230131085533-00231.warc.gz\"}"}
https://prowriters.firstclassessaywriters.com/2019/06/11/recommendedhow-do-we-make-informed-decisions-with-all-this-variation/	[ "# [Recommended]How do we make informed decisions with all this variation\n\nHow do we make informed decisions with all this variation BUS 308 Week 2 Lecture 1 Examining Differences – overview Expected Outcomes After reading this…\n\nHow do we make informed decisions with all this variation\nBUS 308 Week 2 Lecture ...	[ null, "http://ift.tt/2h3Rxhz", null, "http://ift.tt/2h4hMUS", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.95295423,"math_prob":0.96164185,"size":30977,"snap":"2020-24-2020-29","text_gpt3_token_len":6522,"char_repetition_ratio":0.15655571,"word_repetition_ratio":0.037614677,"special_character_ratio":0.21154405,"punctuation_ratio":0.09978699,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97459865,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-06-05T09:25:49Z\",\"WARC-Record-ID\":\"<urn:uuid:c4d38ff0-6fd9-4562-ab05-afca5542f52f>\",\"Content-Length\":\"66159\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d3f94b02-3819-4333-9610-f7f13a631a41>\",\"WARC-Concurrent-To\":\"<urn:uuid:c2893202-f363-4746-9378-a812fb567ab6>\",\"WARC-IP-Address\":\"212.1.208.83\",\"WARC-Target-URI\":\"https://prowriters.firstclassessaywriters.com/2019/06/11/recommendedhow-do-we-make-informed-decisions-with-all-this-variation/\",\"WARC-Payload-Digest\":\"sha1:OYJSIMQ7H7TFM4ANOVV2T5N5ZBLFFAY2\",\"WARC-Block-Digest\":\"sha1:7NII2YXYIAGAADDXJ5URMFDFKOUMKC7H\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-24/CC-MAIN-2020-24_segments_1590348496026.74_warc_CC-MAIN-20200605080742-20200605110742-00040.warc.gz\"}"}
https://mathoverflow.net/questions/51339/an-optimization-problem	[ "# An optimization problem\n\nThe following problem optimization problem arose in a project I am working on with a student. I would like to minimize the quantity:\n\n$$M=\\frac{1}{12} + \\int_0^\\frac{1}{2} \\left( \\tfrac{1}{2}-x \\right)^2 Q(x)^2 \\ dx - 4 \\left[ \\int_0^\\frac{1}{2} \\left( \\tfrac{1}{2}-x \\ri...	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.68923306,"math_prob":1.0000013,"size":2566,"snap":"2021-43-2021-49","text_gpt3_token_len":917,"char_repetition_ratio":0.25761124,"word_repetition_ratio":0.16052632,"special_character_ratio":0.39049104,"punctuation_ratio":0.08285164,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.0000007,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-12-02T00:53:40Z\",\"WARC-Record-ID\":\"<urn:uuid:8798ecdb-f052-46ac-a582-b3eaa29a858c>\",\"Content-Length\":\"125842\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:911782ef-deee-47ce-848a-0d8a1653a6ed>\",\"WARC-Concurrent-To\":\"<urn:uuid:bf5f78f4-2a75-4fe1-b891-b9116b09678c>\",\"WARC-IP-Address\":\"151.101.193.69\",\"WARC-Target-URI\":\"https://mathoverflow.net/questions/51339/an-optimization-problem\",\"WARC-Payload-Digest\":\"sha1:PRZFDP4JEEOKF336ETRVWDPNEKTRGAUT\",\"WARC-Block-Digest\":\"sha1:UTSIBOF3UFJDH4PUUGKVQOLEPAKBPTSS\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964361064.58_warc_CC-MAIN-20211201234046-20211202024046-00581.warc.gz\"}"}
https://www.geeksforgeeks.org/python-sympy-logcombine-method/	[ "# Python \| sympy.logcombine() method\n\nWith the help of `sympy.logcombine()`, we can combine the log terms in the mathematical expression by using the following properties that are listed below.\n\nProperties :\n1) log(xy)=log(x)+log(y)\n2) log(x*n)=nlog(x)\n\nSyntax : `sympy.logcombine()`\n\nReturn : Return th...	[ null, "https://media.geeksforgeeks.org/auth/profile/uv1fvtq244ld2v8nn1v7", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.5259543,"math_prob":0.5036004,"size":1944,"snap":"2020-24-2020-29","text_gpt3_token_len":534,"char_repetition_ratio":0.22783504,"word_repetition_ratio":0.18037975,"special_character_ratio":0.27211934,"punctuation_ratio":0.12195122,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99830955,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-07-15T12:47:58Z\",\"WARC-Record-ID\":\"<urn:uuid:fd4b2255-12f0-4ccc-ab74-b18773c72b46>\",\"Content-Length\":\"116339\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4fdd8d2a-9afd-4793-9e59-0cb5c34517a6>\",\"WARC-Concurrent-To\":\"<urn:uuid:524226b1-7e3b-45e8-82b0-1440eb8b9603>\",\"WARC-IP-Address\":\"168.143.243.236\",\"WARC-Target-URI\":\"https://www.geeksforgeeks.org/python-sympy-logcombine-method/\",\"WARC-Payload-Digest\":\"sha1:J477PPWKHRYUDFDDZAB6FVJYULOJVWUB\",\"WARC-Block-Digest\":\"sha1:WGPOXWGMI4EOTUV5Q7DUSR23S6LWK7OX\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-29/CC-MAIN-2020-29_segments_1593657167808.91_warc_CC-MAIN-20200715101742-20200715131742-00391.warc.gz\"}"}
http://en.statmania.info/2015/04/OR-basic.html	[ "# Operation Research: Basic Understanding\n\nDefinition: Operation Research is the representation of real world system by mathematical models with the use of quantitative methods for solving models with a view to optimizing.\nCharacteristics of OR:\n1. It is system oriented.\n2. The use of interdisciplinary teams....	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8899299,"math_prob":0.9875872,"size":9664,"snap":"2022-40-2023-06","text_gpt3_token_len":2010,"char_repetition_ratio":0.17774327,"word_repetition_ratio":0.97751325,"special_character_ratio":0.19950332,"punctuation_ratio":0.109908886,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9983634,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-09-30T00:50:15Z\",\"WARC-Record-ID\":\"<urn:uuid:043d1a63-1242-487b-bc5c-ad76eb1c6d94>\",\"Content-Length\":\"126486\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:5296bb9a-02e5-4862-bdc1-9f7eeda0f454>\",\"WARC-Concurrent-To\":\"<urn:uuid:ef801950-1eb8-4379-9273-d53dc8a0f2f7>\",\"WARC-IP-Address\":\"172.253.115.121\",\"WARC-Target-URI\":\"http://en.statmania.info/2015/04/OR-basic.html\",\"WARC-Payload-Digest\":\"sha1:IDB7ALI4LIIJBXBXF6GGZWHRPSYGN2XQ\",\"WARC-Block-Digest\":\"sha1:HWPBYL3JHCSANQ6SS7DRO7BGCVBF3NIA\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030335396.92_warc_CC-MAIN-20220929225326-20220930015326-00154.warc.gz\"}"}
https://tracewind.net/science/1025.html	[ "# 求导证明披萨定理", null, "", null, "$AP^2+BP^2+CP^2+DP^2=4r^2$", null, "$\\left(A’P^2+B’P^2+C’P^2+D’P^2\\right)\\frac{d\\alpha}{2}=2r^2d\\alpha$", null, "", null, "", null, "", null, "QED", null, "", null, "", null, "", null, "", null, "$A_1P^2+A_2P^2+\\ldots+A_{2n}P^2=2nr...	[ null, "https://tracewind.net/wp-content/uploads/2020/06/pizzathm1.png", null, "https://tracewind.net/wp-content/uploads/2020/06/pizzathm2.png", null, "https://tracewind.net/wp-content/uploads/2020/06/pizzathm3.png", null, "https://tracewind.net/wp-content/uploads/2020/06/pizzathm4.png", null, "htt...	{"ft_lang_label":"__label__zh","ft_lang_prob":0.9237983,"math_prob":0.99989116,"size":2874,"snap":"2021-43-2021-49","text_gpt3_token_len":2862,"char_repetition_ratio":0.080139376,"word_repetition_ratio":0.0,"special_character_ratio":0.22999305,"punctuation_ratio":0.013550135,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99973387,"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],"im_url_duplicate_count":[null,5,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-19T15:59:21Z\",\"WARC-Record-ID\":\"<urn:uuid:407e3bb1-eba0-4cb3-be6d-9934ac9b7000>\",\"Content-Length\":\"92783\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0c96afb8-b398-4996-9883-9f7ff0fb52e2>\",\"WARC-Concurrent-To\":\"<urn:uuid:32694916-4bc1-476e-8eaa-cb6f5b530236>\",\"WARC-IP-Address\":\"1.0.0.0\",\"WARC-Target-URI\":\"https://tracewind.net/science/1025.html\",\"WARC-Payload-Digest\":\"sha1:RGVPJFAZORI74LKNE2EAWKAC654LFNYL\",\"WARC-Block-Digest\":\"sha1:GZOIQOLOO72DVTIANQTUG3RAWNUG3V7A\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323585270.40_warc_CC-MAIN-20211019140046-20211019170046-00281.warc.gz\"}"}
https://www.newhavendisplay.com/NHD_forum/index.php?action=profile;area=showposts;sa=topics;u=7791	[ "###", null, "Show Posts\n\nThis section allows you to view all posts made by this member. Note that you can only see posts made in areas you currently have access to.\n\n### Topics - DataL\n\nPages: \n1\n##### OLEDs / Bit-banged SPI conflicting with SPI.h and SD.h library (NHD-0420CW-Ax3 display\n« on: October...	[ null, "https://www.newhavendisplay.com/NHD_forum/Themes/default/images/icons/profile_sm.gif", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.5054712,"math_prob":0.91422457,"size":16261,"snap":"2019-26-2019-30","text_gpt3_token_len":4826,"char_repetition_ratio":0.14240019,"word_repetition_ratio":0.2631579,"special_character_ratio":0.33472726,"punctuation_ratio":0.18483257,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9585859,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-07-19T12:37:33Z\",\"WARC-Record-ID\":\"<urn:uuid:9e20e798-3e50-4138-b696-c53c2505ccf0>\",\"Content-Length\":\"44541\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:5616461c-67a6-4740-b1f0-80763969a806>\",\"WARC-Concurrent-To\":\"<urn:uuid:fff02a20-804f-4646-9380-b92c5064186c>\",\"WARC-IP-Address\":\"64.207.178.200\",\"WARC-Target-URI\":\"https://www.newhavendisplay.com/NHD_forum/index.php?action=profile;area=showposts;sa=topics;u=7791\",\"WARC-Payload-Digest\":\"sha1:TYCC664TITGSYGMR646RBXFOPMIGFLWD\",\"WARC-Block-Digest\":\"sha1:KNUZ6OR34WYSDG3QC2OVVBTGBQ6AN7YB\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-30/CC-MAIN-2019-30_segments_1563195526237.47_warc_CC-MAIN-20190719115720-20190719141720-00497.warc.gz\"}"}
https://usefulknot.com/calculators/dividing-polynomials-calculator/	[ "# Dividing Polynomials Calculator\n\n## Now, What Exactly Is A “Dividing Polynomials Calculator”?\n\nA dividing polynomials calculator is a tool that helps you divide one polynomial by another.\n\n## Dividing Polynomials Calculator with steps\n\nThis is a very simple tool for Dividing Polynomials Calculator. Follo...	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.85390717,"math_prob":0.9991549,"size":1581,"snap":"2023-40-2023-50","text_gpt3_token_len":474,"char_repetition_ratio":0.20101458,"word_repetition_ratio":0.13422818,"special_character_ratio":0.30487034,"punctuation_ratio":0.104761906,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9999889,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-07T18:12:15Z\",\"WARC-Record-ID\":\"<urn:uuid:2d319121-b569-4714-b0c0-9485f49b8aff>\",\"Content-Length\":\"53871\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:abdd9013-580b-451e-848e-81a30ca75ceb>\",\"WARC-Concurrent-To\":\"<urn:uuid:5a2209d4-e656-4ede-8e21-066e7f2e0e7c>\",\"WARC-IP-Address\":\"3.210.81.252\",\"WARC-Target-URI\":\"https://usefulknot.com/calculators/dividing-polynomials-calculator/\",\"WARC-Payload-Digest\":\"sha1:5OW4DRN44AQJ56XPSZEHNDMKZCJRIV36\",\"WARC-Block-Digest\":\"sha1:HKUXBFS44V6DQIFSCHPQQJLNUYSWZLQU\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100677.45_warc_CC-MAIN-20231207153748-20231207183748-00412.warc.gz\"}"}
https://www.matchfishtank.org/curriculum/mathematics/7th-grade-math/equations-and-inequalities/	[ "# Equations and Inequalities\n\nStudents solve equations and inequalities with rational numbers, and encounter real-world situations that can be modeled and solved using equations and inequalities.\n\n## Unit Summary\n\nIn Unit 4, seventh-grade students continue to build on the last two units by solving equations ...	[ null, "https://match-fishtank.s3.amazonaws.com/static/images/vocab_math.png", null, "https://cdn.matchfishtank.org/uploads/2019/01/24/g7u4_ipa.PNG", null, "https://cdn.matchfishtank.org/uploads/2019/01/24/g7u4_ipb.PNG", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.899962,"math_prob":0.9756981,"size":3648,"snap":"2020-24-2020-29","text_gpt3_token_len":940,"char_repetition_ratio":0.17837541,"word_repetition_ratio":0.10982659,"special_character_ratio":0.25877193,"punctuation_ratio":0.15514994,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99378055,"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\":\"2020-07-04T18:35:00Z\",\"WARC-Record-ID\":\"<urn:uuid:f5d4227c-0af9-4a61-95bd-b7ac8a93c383>\",\"Content-Length\":\"97707\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a3228e36-1c6a-49bd-a69c-c205cd2e96ee>\",\"WARC-Concurrent-To\":\"<urn:uuid:680aed4c-53d5-48c7-9089-87709e8cdda6>\",\"WARC-IP-Address\":\"104.27.155.58\",\"WARC-Target-URI\":\"https://www.matchfishtank.org/curriculum/mathematics/7th-grade-math/equations-and-inequalities/\",\"WARC-Payload-Digest\":\"sha1:AWBWWSEPEAQJAXTM5BP6QZGDJQLQNG7X\",\"WARC-Block-Digest\":\"sha1:MG2PUMEQDVZMTRLDIAHMJ7GJC4UOQT4A\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-29/CC-MAIN-2020-29_segments_1593655886516.43_warc_CC-MAIN-20200704170556-20200704200556-00275.warc.gz\"}"}
https://www.basic-mathematics.com/finding-the-average.html	[ "# Finding the average\n\nFinding the average or the mean is a very straightforward concept. If you have a set of numbers, the average is found by adding all numbers in the set and dividing their sum by the total number of numbers added in the set.\n\nWe can generalize the concept of average with the formula below:...	[ null, "data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 178 127'%3E%3C/svg%3E", null, "data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 179 132'%3E%3C/svg%3E", null, "https://www.basic-mathematics.com/objects/xrss.png.pagespeed.ic.nVmUyyfqP7.png", null, ...	{"ft_lang_label":"__label__en","ft_lang_prob":0.9046632,"math_prob":0.9991432,"size":1259,"snap":"2022-27-2022-33","text_gpt3_token_len":446,"char_repetition_ratio":0.18645418,"word_repetition_ratio":0.13405797,"special_character_ratio":0.42891183,"punctuation_ratio":0.18987341,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9998958,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-07-02T14:00:42Z\",\"WARC-Record-ID\":\"<urn:uuid:cf90a360-c068-4e61-b437-c549dc9cf87c>\",\"Content-Length\":\"39901\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6da4e8ec-c366-4851-b4ad-1b50a4fea7ad>\",\"WARC-Concurrent-To\":\"<urn:uuid:86b7ea63-287b-4a10-8edb-b4b3d8df736f>\",\"WARC-IP-Address\":\"173.247.219.163\",\"WARC-Target-URI\":\"https://www.basic-mathematics.com/finding-the-average.html\",\"WARC-Payload-Digest\":\"sha1:KCSWLOA64EOKHZ47DPZD42FM4EONCSTY\",\"WARC-Block-Digest\":\"sha1:YGLH2NJ67J6YY33NF4WTJXZVUASOGKTE\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656104141372.60_warc_CC-MAIN-20220702131941-20220702161941-00488.warc.gz\"}"}
https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Statistical_Mechanics/Advanced_Statistical_Mechanics/Classical_microstates%2C_Newtonian%2C_Lagrangian_and_Hamiltonian_mechanics/The_Hamiltonian_formulation_of_classical_mechanics	[ "# The Hamiltonian formulation of classical mechanics\n\nThe Lagrangian formulation of mechanics will be useful later when we study the Feynman path integral. For our purposes now, the Lagrangian formulation is an important springboard from which to develop another useful formulation of classical mechanics known as...	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8057094,"math_prob":0.99989116,"size":3290,"snap":"2020-24-2020-29","text_gpt3_token_len":995,"char_repetition_ratio":0.16189897,"word_repetition_ratio":0.067857146,"special_character_ratio":0.31641337,"punctuation_ratio":0.089108914,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.0000087,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-05-29T01:34:56Z\",\"WARC-Record-ID\":\"<urn:uuid:9876f687-8ec4-48e7-8165-7fd15d8e5a36>\",\"Content-Length\":\"105574\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:ec6e65a5-819b-4b51-840a-48d02d3d0238>\",\"WARC-Concurrent-To\":\"<urn:uuid:fad4e5fa-242e-4241-a55c-aeeca8af9aef>\",\"WARC-IP-Address\":\"99.84.191.114\",\"WARC-Target-URI\":\"https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Statistical_Mechanics/Advanced_Statistical_Mechanics/Classical_microstates%2C_Newtonian%2C_Lagrangian_and_Hamiltonian_mechanics/The_Hamiltonian_formulation_of_classical_mechanics\",\"WARC-Payload-Digest\":\"sha1:K4VLMHGKJ5H5B6L6ZR5YV4S7AGQBVRMA\",\"WARC-Block-Digest\":\"sha1:7CKHWFT7J2BUP4DDHV7ZKKYBPWRJQOSH\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-24/CC-MAIN-2020-24_segments_1590347401004.26_warc_CC-MAIN-20200528232803-20200529022803-00416.warc.gz\"}"}