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https://www.dividend-growth-stocks.com/2007/11/dividend-income-vs-mma.html?m=0	[ "## Monday, November 5, 2007\n\n### Dividend Income vs. MMA", null, "What is the primary reason you invest in dividend stocks? For me, it is a means to build a growing income that can be relied on during retirement. So, why choose dividend stocks instead of another income investment? I view it as an opportunity to see my earnings grow each year, not only from reinvested dividends, but from an increasing dividend rate.\n\nWhy would you assume the equity risk and invest in a dividend stock if you could earn a better return in a less risky money market account (MMA)? When I screen for worthy dividend investments, one of my first tests is to determine if the investment will perform better than a MMA over time.\n\nLast week I posted a Stock Analysis on PAYX including a link to a PDF containing a detailed analysis. In this article, I will explore the section titled Dividend Income vs. MMA (located in the top right section of the above linked PDF). This section helps me determine if the investment's dividend income could possibly pay more than interest earned from a MMA, over time. Below is a description of each item in the Dividend Income vs. MMA section from page 2 of the analysis:\nMMA Rate:\nRepresentative high money market rate (MMA) at a financial institution that is insured by the FDIC up to the legal limit (\\$100,000). Currently using a 20 year Treasury as a proxy.\n\nNPV MMA Diff.:\nThe basis of this calculation is a hypothetical \\$1,000 investment in this stock and a MMA earning the MMA Rate above. The value calculated is the net present value (NPV) of the cumulative differences between the dividend earnings of this investment and the interest income from the MMA over 20 years. Other assumptions include: 1.) dividends grow at the Dividend Growth Rate above, 2.) dividends are reinvested, 3.) share price appreciation is not considered, 4.) interest income is reinvested in the MMA. A Star is added for amounts over a certain amount depending on how long a company has paid a dividend. \\$10,000 for a company that has paid a dividend for less than 10 years, \\$7,500 for a company that has paid a dividend from 10-25 years and \\$2,500 for a company that has paid a dividend for more than 25 years. A Star is deducted if the amount is negative.\n\nYears to >MMA:\nThe number of years until dividend earnings exceed the earnings from a hypothetical money market account earning the MMA rate above, considering the other assumptions listed in \"NPV MMA Diff.\" above. A Star is added if the number of years is less than 5.\nConsidering the proxy was paying 5.36% APR at the time this article was written, yield's on most dividend paying stocks are well below that of a high-yield MMA . Thus, my emphasis on over time. As noted in the NPV MMA Diff. description above, my chosen time horizon is 20 years. Given the future uncertaintly, if it takes less than 5 years for the investment's annual earnings to exceed the MMA's annual earning (Years to >MMA), a Star is added.\n\nTo quickly perform this test, I enter 10 years of dividend payments and the current yield of a stock into my model. Given those inputs, the model will calculate the NPV of the earnings difference on a hypothetical \\$1,000 investment in the stock and a MMA. If the amount calculated is negative, you would earn more by putting your money in a MMA. Even if the amount is positive, a lot can happen in 20 years, so I look for a \\$10,000 cushion. This is the level I have elected to add a Star.\n\nLet me point out some potential flaws to my calculation:\n1. I assume a steady interest rate for the MMA over the 20 year period.\n2. Since I am looking at the ability of the investment to generate income, I ignore any share price appreciation.\nDue to the great disparity between certain high-yield MMA rates and published rates (http://www.bankrate.com/ today is reporting the national average for MMA is 3.5%), I have chosen to use a rate that I am actually getting. Over time, I will probably normalize the MMA interest rate I use by building an average of the available high-yield MMA rates .\n\nBefore I perform the tests above, I check to see if the company has lowered its dividend over the last 10 years.\n\nWhat is the first thing you look at when evaluating a dividend stock?\n\nFull Disclosure: No position in the aforementioned securities. See a list of all my income holdings here.\n\nRelated Articles:\n- Building Yield: 15 Consumer Goods Dividend Stocks\n- 10 Higher Yield Dividend Stocks\n- Who Owns The Top Dividend Stocks?\n- Who Owns The Top Dividend Stocks?\n- Top 10 Articles For 2010\n\nTags: PAYX" ]	[ null, "https://lh3.googleusercontent.com/blogger_img_proxy/ABLy4Ey4-L_WwVX00pOVQA-y79zNHykzqsFZZxfbA3H_r4NCywb5KfEiKRzezipTvxfSZIg8aQBXbkgC9x0hDvsE9Iwdeqkp0eFQb4AexQ-RXiPSs1kkxdx2crezZwd8-9JhKqeRRb4y_fwu_AiifLt93QvF6YnbtxI=s0-d", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9385587,"math_prob":0.8164208,"size":3798,"snap":"2022-27-2022-33","text_gpt3_token_len":853,"char_repetition_ratio":0.12888771,"word_repetition_ratio":0.03529412,"special_character_ratio":0.2314376,"punctuation_ratio":0.10313316,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9539724,"pos_list":[0,1,2],"im_url_duplicate_count":[null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-07-03T17:45:42Z\",\"WARC-Record-ID\":\"<urn:uuid:ce6e884c-d329-4658-b30f-f79069d40d6f>\",\"Content-Length\":\"159342\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:332496b2-3e56-4819-9e50-2184fc9f353f>\",\"WARC-Concurrent-To\":\"<urn:uuid:e57d1018-5c97-4f2f-8b31-ae267df634b1>\",\"WARC-IP-Address\":\"172.253.115.121\",\"WARC-Target-URI\":\"https://www.dividend-growth-stocks.com/2007/11/dividend-income-vs-mma.html?m=0\",\"WARC-Payload-Digest\":\"sha1:C57OSEB57HH3QA6AHOJ2XEC6LTFYVLAM\",\"WARC-Block-Digest\":\"sha1:YYGT36H3MAKL5S2MPFDWIV546KZ6XJJ5\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656104248623.69_warc_CC-MAIN-20220703164826-20220703194826-00654.warc.gz\"}"}
https://www.sanfoundry.com/mathematics-questions-answers-sequences/	[ "# Mathematics Questions and Answers – Sequences\n\n«\n»\n\nThis set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Sequences”.\n\n1. Sequence is same as progression.\na) True\nb) False\n\nExplanation: Sequence and progression are different things. When sequence follow a specified pattern, it is said to be a progression.\n\n2. Complete 2,3,5,7, _____________\na) 8\nb) 9\nc) 10\nd) 11\n\nExplanation: Since 2,3,5 and 7 all are consecutive prime numbers so, it is a sequence of prime numbers. Prime number next to 7 is 11. So, 2,3,5,7,11.\n\n3. Complete 2, 4, 6, 8, _____________\na) 10\nb) 9\nc) 13\nd) 11\n\nExplanation: Since 2,4,6 and 8 are even numbers so it is a sequence of even numbers. Even number next to 8 is 10. So, 2,4,6,8,10.\n\n4. Which of the following is finite sequence?\na) 48,24,12, ………….\nb) 1,2,3, …………\nc) 2,4,6,8,10\nd) 2,3,5,7,11,13, ……………………\n\nExplanation: Since sequence 2,4,6,8,10 contains limited number of terms so, it is finite sequence. Rest all are infinite sequences.\n\n5. Which of the following relation gives Fibonacci sequence?\na) an = an-1 + an-2\nb) an-1 = an + an-2\nc) an-2 = an + an-1\nd) an = an+1 + an-2\n\nExplanation: an = an-1 + an-2, n>2.\nThis is a recurrence relation which gives Fibonacci sequence.\nParticipate in Mathematics - Class 11 Certification Contest of the Month Now!\n\n6. 1,1,2,3,5, ………… is a Fibonacci Sequence.\na) True\nb) False\n\nExplanation: Yes, 1,1,2,3,5, ………… is a Fibonacci Sequence because it follows the recurrence relation\nan = an-1 + an-2, n>2.\n\n7. What is the first term of Fibonacci sequence?\na) 0\nb) 1\nc) 2\nd) 3\n\nExplanation: a1=1 and a2=1.\nan = an-1 + an-2, n>2.\nThis is a recurrence relation which gives the Fibonacci sequence.\n\n8. What is the third term of Fibonacci sequence?\na) 0\nb) 1\nc) 2\nd) 3\n\nExplanation: a1=1 and a2=1.\nan = an-1 + an-2, n>2.\nThis is a recurrence relation which gives Fibonacci sequence.\n=>a3=a1+a2=1+1=2.\n\n9. If an = 4n+6, find 15th term of the sequence.\na) 6\nb) 10\nc) 60\nd) 66\n\nExplanation: an = 4n+6 and n=15\n=>a15 = 4*15 + 6 = 60+6 = 66.\n\n10. a1 = a2 = 2, an = an – 1–1, n > 2. Find a5.\na) 2\nb) -1\nc) 1\nd) 0\n\nExplanation: an = an – 1–1, n > 2\n=> a3 = a2 – 1 = 2 – 1 = 1\n=> a4 = a3 – 1 = 1 – 1 = 0\n=> a5 = a4 – 1 = 0 – 1 = -1.\n\nSanfoundry Global Education & Learning Series – Mathematics – Class 11.\n\nTo practice all areas of Mathematics, here is complete set of 1000+ Multiple Choice Questions and Answers.", null, "" ]	[ null, "data:image/svg+xml,%3Csvg%20xmlns=%22http://www.w3.org/2000/svg%22%20viewBox=%220%200%20150%20150%22%3E%3C/svg%3E", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.72995013,"math_prob":0.99845713,"size":2874,"snap":"2022-40-2023-06","text_gpt3_token_len":1075,"char_repetition_ratio":0.15121952,"word_repetition_ratio":0.20959148,"special_character_ratio":0.4025748,"punctuation_ratio":0.19830029,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99807864,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-10-04T20:16:14Z\",\"WARC-Record-ID\":\"<urn:uuid:7a4d943a-30a6-4566-860c-11f62403867b>\",\"Content-Length\":\"143772\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0c9a4385-b81c-47c1-b3db-8fdf75708736>\",\"WARC-Concurrent-To\":\"<urn:uuid:1493df4c-028b-4805-a96e-510f23c0e7cc>\",\"WARC-IP-Address\":\"104.25.131.119\",\"WARC-Target-URI\":\"https://www.sanfoundry.com/mathematics-questions-answers-sequences/\",\"WARC-Payload-Digest\":\"sha1:PEVZCKTRMZYMYXQDYM2KJPYTPB5QXL6G\",\"WARC-Block-Digest\":\"sha1:KZUTMR6BXLCH6V74TPEEVNSONO45MTJM\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030337524.47_warc_CC-MAIN-20221004184523-20221004214523-00568.warc.gz\"}"}
https://exceptionshub.com/c-ms-excel-currency-rounding-method.html	[ "Home » excel » c# – MS Excel Currency Rounding Method\n\n# c# – MS Excel Currency Rounding Method\n\nPosted by: admin May 14, 2020 Leave a comment\n\nQuestions:\n\nWould like to know which rounding method is applied when you use Round() function on Excel?\nAlso is there a difference when you choose to format a column as currency with two decimal places.\nI need to emulate Excel’s results in a C# program I’m writing.\n\nHow to&Answers:\n\nCaution: Excel and Excel-VBA use two different algorithms.\n\nIn Excel:\n\n`=ROUND(0.5,0)` returns 1.\n\n`=ROUND(1.5,0)` returns 2.\n\nIn Excel-VBA:\n\n``````Print Round(0.5,0)\n0\nPrint Round(1.5,0)\n2\n``````\n\nVBA uses banker’s rounding: rounds 0.5’s to the nearest even integer. Note that the same logic transfers to lower-order decimal places if you `Round` to more decimal places. For example, `Round(0.05,1)` returns zero in Excel-VBA (as opposed to 0.1 in Excel).\n\nThis is one of the features of VBA I dislike most. It being inconsistent with Excel makes it even worse.\n\nThe number format makes no difference to this issue." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.86947143,"math_prob":0.91714287,"size":841,"snap":"2021-04-2021-17","text_gpt3_token_len":222,"char_repetition_ratio":0.11827957,"word_repetition_ratio":0.0,"special_character_ratio":0.25802615,"punctuation_ratio":0.14948453,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9823977,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-04-12T00:11:51Z\",\"WARC-Record-ID\":\"<urn:uuid:01b6223f-0a39-4464-81a4-b74a8cca584c>\",\"Content-Length\":\"52185\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:94724f8e-67cf-41e6-a742-969045402dd1>\",\"WARC-Concurrent-To\":\"<urn:uuid:22dd8863-e455-4864-9153-aa708812635b>\",\"WARC-IP-Address\":\"172.67.182.150\",\"WARC-Target-URI\":\"https://exceptionshub.com/c-ms-excel-currency-rounding-method.html\",\"WARC-Payload-Digest\":\"sha1:M3ZWQRVZMPIZVRI5ON5Q54BOYCTAUXUA\",\"WARC-Block-Digest\":\"sha1:EBMWVAIFZSR3A2PUUQFMTWHO5L3YD3B5\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-17/CC-MAIN-2021-17_segments_1618038065903.7_warc_CC-MAIN-20210411233715-20210412023715-00003.warc.gz\"}"}
https://courses.lumenlearning.com/introchem/chapter/standard-free-energy-changes/	[ "## Standard Free Energy Changes\n\n#### Learning Objective\n\n• Calculate the change in standard free energy for a particular reaction.\n\n#### Key Points\n\n• The standard free energy of a substance represents the free energy change associated with the formation of the substance from the elements in their most stable forms as they exist under standard conditions.\n• Combine the standard enthalpy of formation and the standard entropy of a substance to get its standard free energy of formation.\n• $\\Delta G^\\circ (rxn) = \\Sigma \\Delta {G}_{f}^\\circ (products) - \\Sigma \\Delta {G}_{f}^\\circ (reactants)$ can be used to determine standard free energy change of a reaction.\n\n#### Terms\n\n• free energy of formationThe change of free energy that accompanies the formation of 1 mole of a substance in its standard state from its constituent elements in their standard states.\n• entropyA thermodynamic property that is the measure of a system’s thermal energy per unit temperature that is unavailable for doing useful work.\n• enthalpyIn thermodynamics, a measure of the heat content of a chemical or physical system.\n\n## Reviewing Standard States\n\nThe concept of standard states is especially important in the case of free energy, so take a moment to review it. For most practical purposes, the following definitions of standard states are acceptable:\n\n• Gases: 1 atmosphere partial pressure.\n• Pure liquids: the liquid under a total pressure of 1 atm.\n• Solutes: an effective concentration of 1 Molar.\n• Solids: the pure solid under 1 atm pressure.\n\nNote also that there is actually no “standard temperature”, but because most thermodynamics tables list values for 298.15 K (25° C), this temperature is usually implied. These same definitions apply to standard enthalpies and internal energies. Don’t confuse these thermodynamic standard states with the “standard temperature and pressure” (STP) widely employed in gas law calculations.\n\n## Calculating Gibbs Free Energy\n\nIn order to make use of Gibbs energies to predict chemical changes, it is necessary to know the free energies of the individual components of the reaction. To accomplish this, combine the standard enthalpy and the standard entropy of a substance to get the standard free energy of a reaction:\n\n$\\Delta {G}^\\circ= \\Delta {H}^\\circ-T\\Delta {S}^\\circ$\n\nRecall that the symbol ° refers to the standard state of a substance measured under the conditions of 1 atm pressure or an effective concentration of 1 Molar and a temperature of 298K. The other factor to keep in mind is that enthalpy values are normally given in $\\frac{kJ}{mole}$ while entropy values are given in $\\frac{J}{K\\times mole}$ . The energy units will need to be the same in order to solve the equation properly.\n\nThe standard Gibbs free energy of the reaction can also be determined according to:\n\n$\\Delta G^\\circ (rxn)= \\Sigma \\Delta {G}_{f}^\\circ(products)-\\Sigma \\Delta {G}_{f}^\\circ(reactants)$\n\nAs with standard heats of formation, the standard free energy of a substance represents the free energy change associated with the formation of the substance from the elements in their most stable forms as they exist under the standard conditions of 1 atm pressure and 298K. Standard Gibbs free energies of formation are normally found directly from tables. Once the values for all the reactants and products are known, the standard Gibbs free energy change for the reaction can be found. Most tables of thermodynamic values list ΔGf°’s for common substances. They can, of course, always be found from values of $\\Delta {H}_{f}^\\circ$ and $\\Delta {S}_{f}^\\circ$ .", null, "Gibbs Energy of FormationThe standard Gibbs free energy of formation of a compound is the change of Gibbs free energy that accompanies the formation of 1 mole of that substance from its component elements, at their standard states.\n\nExample Problem: Calculate the $\\Delta G^0_{rxn}$ for the following equation using the values in the table:\n\n$CO_{(g)} + \\frac {1}{2} O_{2(g)} \\rightarrow CO_{2(g)}$\n\n$\\Delta G^\\circ (rxn)= \\Sigma \\Delta {G}_{f}^\\circ(products)-\\Sigma \\Delta {G}_{f}^\\circ(reactants)$\n\n*Remember that substances in elemental form (such as O2) have $\\Delta G^o_f$ values equal to zero. It is also important to remember that the table provides per mole values. If the balanced equation calls for more than one mole the $\\Delta G^o_f$ must be multiplied.\n\n$\\Delta G^\\circ (rxn)= (-394.4\\ kJ) -(-137.2\\ kJ + 0\\ kJ)$\n\n$\\Delta G^\\circ (rxn)= -257.2\\ kJ$" ]	[ null, "https://s3-us-west-2.amazonaws.com/courses-images/wp-content/uploads/sites/752/2016/09/26195306/standard-20gibbs.jpeg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.800493,"math_prob":0.9946641,"size":4328,"snap":"2020-24-2020-29","text_gpt3_token_len":1027,"char_repetition_ratio":0.1713691,"word_repetition_ratio":0.11937985,"special_character_ratio":0.237061,"punctuation_ratio":0.06623377,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9977074,"pos_list":[0,1,2],"im_url_duplicate_count":[null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-07-04T10:26:27Z\",\"WARC-Record-ID\":\"<urn:uuid:5c2622d9-4d40-45d4-a7e2-a3e7be7a4a5c>\",\"Content-Length\":\"31139\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:607663f0-c622-4539-9a87-74b4f3068058>\",\"WARC-Concurrent-To\":\"<urn:uuid:adbbb2a1-d7e7-4a6d-8fa0-759931adaa84>\",\"WARC-IP-Address\":\"23.185.0.1\",\"WARC-Target-URI\":\"https://courses.lumenlearning.com/introchem/chapter/standard-free-energy-changes/\",\"WARC-Payload-Digest\":\"sha1:QIAUPJ6PWCAEEFJ3JCCZHHQ6POPAHPP4\",\"WARC-Block-Digest\":\"sha1:UT6AXVKOEJCOSHFPASIDS23MM3L3WYGR\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-29/CC-MAIN-2020-29_segments_1593655886095.7_warc_CC-MAIN-20200704073244-20200704103244-00473.warc.gz\"}"}
https://www.vedantu.com/question-answer/find-the-square-root-of-dfrac44100441-class-8-maths-cbse-5ed6a7517d5e1462b8bfd878	[ "Courses\nCourses for Kids\nFree study material\nFree LIVE classes\nMore", null, "# Find the square root of $\\dfrac{44100}{441}$.\n\nLast updated date: 29th Mar 2023\nTotal views: 310.2k\nViews today: 5.87k", null, "Verified\n310.2k+ views\nHint: Convert the numerical quantities inside square roots into perfect squares.\n\nWe have to find the square root of $\\dfrac{44100}{441}$.\nSquare root of $a=\\sqrt{a}={{a}^{\\dfrac{1}{2}}}$\nTherefore, square root of $\\dfrac{44100}{441}=A$\n$A=\\sqrt{\\dfrac{44100}{441}}={{\\left( \\dfrac{44100}{441} \\right)}^{\\dfrac{1}{2}}}$\nWe can write $44100$as $441\\times 100$.\nHence, we get $A={{\\left( \\dfrac{441\\times 100}{441} \\right)}^{\\dfrac{1}{2}}}$\nBy cancelling similar terms from numerator and denominator,\nWe get, $A={{\\left( 100 \\right)}^{\\dfrac{1}{2}}}$\nAs,${{a}^{m}}=b$\nThen, $a={{b}^{\\dfrac{1}{m}}}$\nSimilarly, ${{\\left( 10 \\right)}^{2}}=100$\n$\\left( 10 \\right)={{\\left( 100 \\right)}^{\\dfrac{1}{2}}}$\nTherefore, we get $A=10$\nHence, the value of square root of $\\dfrac{44100}{441}$is $10$.\nNote: Here, we also know that ${{\\left( 21 \\right)}^{2}}=441$, therefore we can write $44100$as ${{\\left( 210 \\right)}^{2}}$and $441$as ${{\\left( 21 \\right)}^{2}}$and get $A=\\dfrac{210}{21}=10$which is the correct result." ]	[ null, "https://www.vedantu.com/cdn/images/seo-templates/seo-qna.svg", null, "https://www.vedantu.com/cdn/images/seo-templates/green-check.svg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.66299134,"math_prob":1.0000029,"size":3273,"snap":"2023-14-2023-23","text_gpt3_token_len":1176,"char_repetition_ratio":0.17681248,"word_repetition_ratio":0.4513889,"special_character_ratio":0.41460434,"punctuation_ratio":0.0771757,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9999645,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-03-30T18:10:12Z\",\"WARC-Record-ID\":\"<urn:uuid:a40233b5-e1c0-4a67-8614-8dc3d8b89688>\",\"Content-Length\":\"92896\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0e6480a9-17c2-41af-9ce4-dc783bf8e36a>\",\"WARC-Concurrent-To\":\"<urn:uuid:7c39736b-e0de-4cec-b532-8fcc72a56ac1>\",\"WARC-IP-Address\":\"108.138.64.90\",\"WARC-Target-URI\":\"https://www.vedantu.com/question-answer/find-the-square-root-of-dfrac44100441-class-8-maths-cbse-5ed6a7517d5e1462b8bfd878\",\"WARC-Payload-Digest\":\"sha1:FELLS37CM3V32LJOXPNCKVO4S5VP32DA\",\"WARC-Block-Digest\":\"sha1:JAHTJWT4H7UYIYXTDD5X2FHV7B6KCTG3\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-14/CC-MAIN-2023-14_segments_1679296949355.52_warc_CC-MAIN-20230330163823-20230330193823-00319.warc.gz\"}"}
https://runestone.academy/ns/books/published/APEX/chapter_integration.html	[ "", null, "We have spent considerable time considering the derivatives of a function and their applications. In the following chapters, we are going to starting thinking in “the other direction.” That is, given a function $$f(x)\\text{,}$$ we are going to consider functions $$F(x)$$ such that $$F'(x) = f(x)\\text{.}$$ There are numerous reasons this will prove to be useful: these functions will help us compute area, volume, mass, force, pressure, work, and much more.\nWe started this chapter learning about antiderivatives and indefinite integrals. We then seemed to change focus by looking at areas between the graph of a function and the $$x$$-axis. We defined these areas as the definite integral of the function, using a notation very similar to the notation of the indefinite integral. The Fundamental Theorem of Calculus tied these two seemingly separate concepts together: we can find areas under a curve, i.e., we can evaluate a definite integral, using antiderivatives." ]	[ null, "https://runestone.academy/ns/books/published/APEX/external/images/APEX.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9317518,"math_prob":0.9974967,"size":1562,"snap":"2023-14-2023-23","text_gpt3_token_len":324,"char_repetition_ratio":0.13863929,"word_repetition_ratio":0.0,"special_character_ratio":0.20230474,"punctuation_ratio":0.12631579,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9994814,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-05-28T03:34:53Z\",\"WARC-Record-ID\":\"<urn:uuid:40d66c57-d75b-495e-9462-6f6bda89cba0>\",\"Content-Length\":\"102157\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:27335df0-6361-4198-8d31-fda3cb45a874>\",\"WARC-Concurrent-To\":\"<urn:uuid:4b8d879a-93fb-423f-a4f1-0a464b4d0fc2>\",\"WARC-IP-Address\":\"134.122.31.165\",\"WARC-Target-URI\":\"https://runestone.academy/ns/books/published/APEX/chapter_integration.html\",\"WARC-Payload-Digest\":\"sha1:ZWPPICE56Q7HNX5GUUG55V66L6RHWAUD\",\"WARC-Block-Digest\":\"sha1:CSZZRUIIRRLPZJIPZJJEFP4WRJXSMZW7\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224643462.13_warc_CC-MAIN-20230528015553-20230528045553-00554.warc.gz\"}"}
https://codertw.com/%E7%A8%8B%E5%BC%8F%E8%AA%9E%E8%A8%80/533817/	[ "Java浮點數運算的精確度和四捨五入的問題", null, "Java中宣告的小數預設是double型別的。double d=2.1;如果宣告float f=2.1;則會報錯，而應該寫為float f=2.1f;或float f=(float)2.1;float 記憶體分配4個位元組,佔32位，double型記憶體分配8個位元組，佔64位。\n\n1.float和double型別轉換\n\nfloat f=2.1f;\ndouble d = Double.parseDouble(String.valueOf(f));\n\nfloat f=2.1f;\nBigDecimal bd = new BigDecimal(String.valueOf(f));\ndouble d = bd.doubleValue();\n\n2.運算時的不準確\n\ndouble d1=3.564;\ndouble d2=5.13;\nBigDecimal b1 = new BigDecimal(Double.toString(d1));\nBigDecimal b2 = new BigDecimal(Double.toString(d2));\n\n3.四捨五入的問題：\n\n（1）使用BigDecimal\n\nBigDecimal b = new BigDecimal(Double.toString(v));\nreturn b.setScale(scale, RoundingMode).doubleValue();\n\nBigDecimal b1 = new BigDecimal(Double.toString(v1));\nBigDecimal b2 = new BigDecimal(Double.toString(v2));\nreturn b1.divide(b2, scale, BigDecimal.ROUND_HALF_UP).doubleValue();\n\n（2）使用DecimalFormat\n\nDecimalFormat對數值格式化時可以進行四捨五入，但不是一般認識上的四捨五入，在DecimalFormat的API中如是介紹：DecimalFormat 提供 RoundingMode 中定義的舍入模式進行格式化。預設情況下，它使用 RoundingMode.HALF_EVEN。例如：\n\nDecimalFormat decFormat = new DecimalFormat(“0.00”);\nSystem.out.println(decFormat.format(sim));\n\n（3）使用格式控制\n\ndouble d = 3.1415926;\nString result = String .format(“%.2f”,d);" ]	[ null, "data:image/svg+xml,%3Csvg%20xmlns=%22http://www.w3.org/2000/svg%22%20viewBox=%220%200%20890%20500%22%3E%3C/svg%3E", null ]	{"ft_lang_label":"__label__zh","ft_lang_prob":0.7680138,"math_prob":0.9955664,"size":2167,"snap":"2022-05-2022-21","text_gpt3_token_len":1455,"char_repetition_ratio":0.18122977,"word_repetition_ratio":0.0,"special_character_ratio":0.21596678,"punctuation_ratio":0.23952095,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99808055,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-21T11:24:52Z\",\"WARC-Record-ID\":\"<urn:uuid:2bfe6f2d-2703-4724-8e02-e58010fb9240>\",\"Content-Length\":\"31657\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7a644d06-d522-43da-a3e7-e960bbc88755>\",\"WARC-Concurrent-To\":\"<urn:uuid:2b4cb61e-594e-4020-90ae-7ef8ea81ee69>\",\"WARC-IP-Address\":\"162.159.138.85\",\"WARC-Target-URI\":\"https://codertw.com/%E7%A8%8B%E5%BC%8F%E8%AA%9E%E8%A8%80/533817/\",\"WARC-Payload-Digest\":\"sha1:M2NGMOEDZB64E3KNE5I7GDUHDFHX2MU5\",\"WARC-Block-Digest\":\"sha1:GTRX3RTNI276DW5M52V44HKT67PRPTVR\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320303356.40_warc_CC-MAIN-20220121101528-20220121131528-00344.warc.gz\"}"}
https://www.gnu.org/software/gawk/manual/html_node/Round-Function.html	[ "Next: , Previous: , Up: General Functions [Contents][Index]\n\n#### 10.2.3 Rounding Numbers\n\nThe way `printf` and `sprintf()` (see section Using `printf` Statements for Fancier Printing) perform rounding often depends upon the system’s C `sprintf()` subroutine. On many machines, `sprintf()` rounding is unbiased, which means it doesn’t always round a trailing .5 up, contrary to naive expectations. In unbiased rounding, .5 rounds to even, rather than always up, so 1.5 rounds to 2 but 4.5 rounds to 4. This means that if you are using a format that does rounding (e.g., `\"%.0f\"`), you should check what your system does. The following function does traditional rounding; it might be useful if your `awk`’s `printf` does unbiased rounding:\n\n```# round.awk --- do normal rounding\n\nfunction round(x, ival, aval, fraction)\n{\nival = int(x) # integer part, int() truncates\n\n# see if fractional part\nif (ival == x) # no fraction\nreturn ival # ensure no decimals\n\nif (x < 0) {\naval = -x # absolute value\nival = int(aval)\nfraction = aval - ival\nif (fraction >= .5)\nreturn int(x) - 1 # -2.5 --> -3\nelse\nreturn int(x) # -2.3 --> -2\n} else {\nfraction = x - ival\nif (fraction >= .5)\nreturn ival + 1\nelse\nreturn ival\n}\n}\n```\n```# test harness\n# { print \\$0, round(\\$0) }\n```" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7279443,"math_prob":0.9526188,"size":1231,"snap":"2021-31-2021-39","text_gpt3_token_len":331,"char_repetition_ratio":0.15484923,"word_repetition_ratio":0.027522936,"special_character_ratio":0.301381,"punctuation_ratio":0.15126051,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9760774,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-18T02:18:08Z\",\"WARC-Record-ID\":\"<urn:uuid:70fedc4a-f94c-46b7-a8de-f3796dd07844>\",\"Content-Length\":\"5552\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:36346a09-4528-4eed-aa0b-647fbfd6314f>\",\"WARC-Concurrent-To\":\"<urn:uuid:b2008375-bb72-4f8e-8eb9-1e1a6022633e>\",\"WARC-IP-Address\":\"209.51.188.148\",\"WARC-Target-URI\":\"https://www.gnu.org/software/gawk/manual/html_node/Round-Function.html\",\"WARC-Payload-Digest\":\"sha1:3L3RDKIJQ7P3MRP4J3RDHUIPQWBT5OLR\",\"WARC-Block-Digest\":\"sha1:ESKPLEKQEUOAUGOOW5DIJI5DCAYYYJN6\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780056120.36_warc_CC-MAIN-20210918002951-20210918032951-00651.warc.gz\"}"}
https://research.aston.ac.uk/en/publications/a-boundary-domain-integral-equation-method-for-an-elliptic-cauchy	[ "# A Boundary-Domain Integral Equation Method for an Elliptic Cauchy Problem with Variable Coefficients\n\nAndriy Beshley, Roman Chapko, B. Tomas Johansson\n\nCorresponding author for this work\n\nResearch output: Chapter in Book/Report/Conference proceedingChapter\n\n### Abstract\n\nWe consider an integral based method for numerically solving the Cauchy problem for second-order elliptic equations in divergence form with spacewise dependent coefficients. The solution is represented as a boundary-domain integral, with unknown densities to be identified. The given Cauchy data is matched to obtain a system of boundary-domain integral equations from which the densities can be constructed. For the numerical approximation, an efficient Nyström scheme in combination with Tikhonov regularization is presented for the boundary-domain integral equations, together with some numerical investigations.\n\nOriginal language English Trends in Mathematics K. Lindahl , T. Lindström, L. Rodino, J. Toft, P. Wahlberg Springer International Publishing AG 493-501 9 978-3-030-04459-6 978-3-030-04458-9 https://doi.org/10.1007/978-3-030-04459-6_47 E-pub ahead of print - 30 Apr 2019\n\n### Publication series\n\nName Trends in Mathematics 2297-0215 2297-024X\n\n### Fingerprint\n\nIntegral Equation Method\nVariable Coefficients\nElliptic Problems\nCauchy Problem\nIntegral Equations\nSecond Order Elliptic Equations\nTikhonov Regularization\nIntegral domain\nNumerical Approximation\nNumerical Investigation\nCauchy\nDivergence\nUnknown\nDependent\nCoefficient\n\n### Cite this\n\nBeshley, A., Chapko, R., & Johansson, B. T. (2019). A Boundary-Domain Integral Equation Method for an Elliptic Cauchy Problem with Variable Coefficients. In K. Lindahl , T. Lindström, L. Rodino, J. Toft, & P. Wahlberg (Eds.), Trends in Mathematics (pp. 493-501). (Trends in Mathematics). Springer International Publishing AG. https://doi.org/10.1007/978-3-030-04459-6_47\nBeshley, Andriy ; Chapko, Roman ; Johansson, B. Tomas. / A Boundary-Domain Integral Equation Method for an Elliptic Cauchy Problem with Variable Coefficients. Trends in Mathematics. editor / K. Lindahl ; T. Lindström ; L. Rodino ; J. Toft ; P. Wahlberg. Springer International Publishing AG, 2019. pp. 493-501 (Trends in Mathematics).\n@inbook{c9e38ff3ed4e4d3ea9794f6bf0dc828d,\ntitle = \"A Boundary-Domain Integral Equation Method for an Elliptic Cauchy Problem with Variable Coefficients\",\nabstract = \"We consider an integral based method for numerically solving the Cauchy problem for second-order elliptic equations in divergence form with spacewise dependent coefficients. The solution is represented as a boundary-domain integral, with unknown densities to be identified. The given Cauchy data is matched to obtain a system of boundary-domain integral equations from which the densities can be constructed. For the numerical approximation, an efficient Nystr{\\\"o}m scheme in combination with Tikhonov regularization is presented for the boundary-domain integral equations, together with some numerical investigations.\",\nauthor = \"Andriy Beshley and Roman Chapko and Johansson, {B. Tomas}\",\nyear = \"2019\",\nmonth = \"4\",\nday = \"30\",\ndoi = \"10.1007/978-3-030-04459-6_47\",\nlanguage = \"English\",\nisbn = \"978-3-030-04458-9\",\nseries = \"Trends in Mathematics\",\npublisher = \"Springer International Publishing AG\",\npages = \"493--501\",\neditor = \"{Lindahl }, K. and T. Lindstr{\\\"o}m and L. Rodino and J. Toft and P. Wahlberg\",\nbooktitle = \"Trends in Mathematics\",\n\n}\n\nBeshley, A, Chapko, R & Johansson, BT 2019, A Boundary-Domain Integral Equation Method for an Elliptic Cauchy Problem with Variable Coefficients. in K Lindahl , T Lindström, L Rodino, J Toft & P Wahlberg (eds), Trends in Mathematics. Trends in Mathematics, Springer International Publishing AG, pp. 493-501. https://doi.org/10.1007/978-3-030-04459-6_47\n\nA Boundary-Domain Integral Equation Method for an Elliptic Cauchy Problem with Variable Coefficients. / Beshley, Andriy; Chapko, Roman; Johansson, B. Tomas.\n\nTrends in Mathematics. ed. / K. Lindahl ; T. Lindström; L. Rodino; J. Toft; P. Wahlberg. Springer International Publishing AG, 2019. p. 493-501 (Trends in Mathematics).\n\nResearch output: Chapter in Book/Report/Conference proceedingChapter\n\nTY - CHAP\n\nT1 - A Boundary-Domain Integral Equation Method for an Elliptic Cauchy Problem with Variable Coefficients\n\nAU - Beshley, Andriy\n\nAU - Chapko, Roman\n\nAU - Johansson, B. Tomas\n\nPY - 2019/4/30\n\nY1 - 2019/4/30\n\nN2 - We consider an integral based method for numerically solving the Cauchy problem for second-order elliptic equations in divergence form with spacewise dependent coefficients. The solution is represented as a boundary-domain integral, with unknown densities to be identified. The given Cauchy data is matched to obtain a system of boundary-domain integral equations from which the densities can be constructed. For the numerical approximation, an efficient Nyström scheme in combination with Tikhonov regularization is presented for the boundary-domain integral equations, together with some numerical investigations.\n\nAB - We consider an integral based method for numerically solving the Cauchy problem for second-order elliptic equations in divergence form with spacewise dependent coefficients. The solution is represented as a boundary-domain integral, with unknown densities to be identified. The given Cauchy data is matched to obtain a system of boundary-domain integral equations from which the densities can be constructed. For the numerical approximation, an efficient Nyström scheme in combination with Tikhonov regularization is presented for the boundary-domain integral equations, together with some numerical investigations.\n\nUR - http://www.scopus.com/inward/record.url?scp=85065389071&partnerID=8YFLogxK\n\nU2 - 10.1007/978-3-030-04459-6_47\n\nDO - 10.1007/978-3-030-04459-6_47\n\nM3 - Chapter\n\nAN - SCOPUS:85065389071\n\nSN - 978-3-030-04458-9\n\nT3 - Trends in Mathematics\n\nSP - 493\n\nEP - 501\n\nBT - Trends in Mathematics\n\nA2 - Lindahl , K.\n\nA2 - Lindström, T.\n\nA2 - Rodino, L.\n\nA2 - Toft, J.\n\nA2 - Wahlberg, P.\n\nPB - Springer International Publishing AG\n\nER -\n\nBeshley A, Chapko R, Johansson BT. A Boundary-Domain Integral Equation Method for an Elliptic Cauchy Problem with Variable Coefficients. In Lindahl K, Lindström T, Rodino L, Toft J, Wahlberg P, editors, Trends in Mathematics. Springer International Publishing AG. 2019. p. 493-501. (Trends in Mathematics). https://doi.org/10.1007/978-3-030-04459-6_47" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7562459,"math_prob":0.64234424,"size":3448,"snap":"2019-51-2020-05","text_gpt3_token_len":879,"char_repetition_ratio":0.12369338,"word_repetition_ratio":0.53911203,"special_character_ratio":0.25667053,"punctuation_ratio":0.13613446,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9838891,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-06T15:27:24Z\",\"WARC-Record-ID\":\"<urn:uuid:be956021-9748-4d5f-b7fb-b251204b0f7b>\",\"Content-Length\":\"40547\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:412c40ba-a29b-4dfa-9cbc-192d17ddba09>\",\"WARC-Concurrent-To\":\"<urn:uuid:15d493fe-fc21-4559-bb4c-b85aebcfce79>\",\"WARC-IP-Address\":\"52.51.22.49\",\"WARC-Target-URI\":\"https://research.aston.ac.uk/en/publications/a-boundary-domain-integral-equation-method-for-an-elliptic-cauchy\",\"WARC-Payload-Digest\":\"sha1:P4T7DJPS4PCGYESEUJ7NE7TOGCNVJHUV\",\"WARC-Block-Digest\":\"sha1:KD6427L6HYCROOTMCALM43KO2DJOZTHC\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575540488870.33_warc_CC-MAIN-20191206145958-20191206173958-00151.warc.gz\"}"}
http://aoi.com.au/Correct-Answer/CAQA-21.htm	[ "", null, "Correct-Answer to Question #21:\nWhat is the Zwicky Constant?\n\n Q. What is the Zwicky Constant?", null, "", null, "", null, "A. As light travels through the Universe's gravitational field, it slowly loses energy. The Zwicky Constant defines this loss.", null, "", null, "Q. How is it defined?", null, "", null, "", null, "A. The Zwicky Constant is the distance light travels to lose half its energy.", null, "Q. How is it measured?", null, "", null, "", null, "A. Spectral lines in the light from distant objects are shifted towards redder (lower-energy) wavelengths (red-shifts), and these red-shifts are greater, the greater the distance the light has travelled.", null, "Q. What's the value of the Zwicky Constant?", null, "", null, "", null, "A. About 7.7 billion light-years.", null, "Q. Doesn't the Hubble Constant measure the same thing?", null, "", null, "", null, "A. It's related, but the Hubble Constant is given as a rate of expansion of the Universe, using an incorrect model.", null, "Q. Where is there more detail on this?", null, "", null, "", null, "Go to the Correct-Answer Home Page and List of Questions.", null, "" ]	[ null, "http://www.aoi.com.au/Correct-Answer/CA-Images/CAQA-LogoF.jpg", null, "http://www.aoi.com.au/Correct-Answer/CA-Images/QTabL.gif", null, "http://www.aoi.com.au/Correct-Answer/CA-Images/blank.gif", null, "http://www.aoi.com.au/Correct-Answer/CA-Images/blank.gif", null, "http://www.aoi.com.au/Correct-Answer/CA-Images/ATabL.gif", null, "http://www.aoi.com.au/Correct-Answer/CA-Images/blank.gif", null, "http://www.aoi.com.au/Correct-Answer/CA-Images/QTabL.gif", null, "http://www.aoi.com.au/Correct-Answer/CA-Images/blank.gif", null, "http://www.aoi.com.au/Correct-Answer/CA-Images/blank.gif", null, "http://www.aoi.com.au/Correct-Answer/CA-Images/ATabL.gif", null, "http://www.aoi.com.au/Correct-Answer/CA-Images/QTabL.gif", null, "http://www.aoi.com.au/Correct-Answer/CA-Images/blank.gif", null, "http://www.aoi.com.au/Correct-Answer/CA-Images/blank.gif", null, "http://www.aoi.com.au/Correct-Answer/CA-Images/ATabL.gif", null, "http://www.aoi.com.au/Correct-Answer/CA-Images/QTabL.gif", null, "http://www.aoi.com.au/Correct-Answer/CA-Images/blank.gif", null, "http://www.aoi.com.au/Correct-Answer/CA-Images/blank.gif", null, "http://www.aoi.com.au/Correct-Answer/CA-Images/ATabL.gif", null, "http://www.aoi.com.au/Correct-Answer/CA-Images/QTabL.gif", null, "http://www.aoi.com.au/Correct-Answer/CA-Images/blank.gif", null, "http://www.aoi.com.au/Correct-Answer/CA-Images/blank.gif", null, "http://www.aoi.com.au/Correct-Answer/CA-Images/ATabL.gif", null, "http://www.aoi.com.au/Correct-Answer/CA-Images/QTabL.gif", null, "http://www.aoi.com.au/Correct-Answer/CA-Images/blank.gif", null, "http://www.aoi.com.au/Correct-Answer/CA-Images/blank.gif", null, "http://www.iinet.net.au/cgi-bin/nph-count", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.91852796,"math_prob":0.9166353,"size":795,"snap":"2019-35-2019-39","text_gpt3_token_len":192,"char_repetition_ratio":0.15297092,"word_repetition_ratio":0.029411765,"special_character_ratio":0.24276729,"punctuation_ratio":0.17791411,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97300744,"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],"im_url_duplicate_count":[null,8,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-09-21T15:21:45Z\",\"WARC-Record-ID\":\"<urn:uuid:bdba1488-7c9b-4335-bbd4-d80298aeaf1d>\",\"Content-Length\":\"9744\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:8e7d7e1f-d5f8-4cd9-b2a0-f7ca0a71a058>\",\"WARC-Concurrent-To\":\"<urn:uuid:2a880cb2-a535-4cb6-9fbe-1ac1507b66fd>\",\"WARC-IP-Address\":\"52.95.134.45\",\"WARC-Target-URI\":\"http://aoi.com.au/Correct-Answer/CAQA-21.htm\",\"WARC-Payload-Digest\":\"sha1:M2NCS4FVH5VOFQIW5QQCMPWHWIDXSHM5\",\"WARC-Block-Digest\":\"sha1:PFD6P6NS4J3ZOQWKUTKTX6S3M7YPTU57\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-39/CC-MAIN-2019-39_segments_1568514574532.44_warc_CC-MAIN-20190921145904-20190921171904-00525.warc.gz\"}"}
https://www.mis.mpg.de/de/publications/mis-preprints/2013/2013-103.html	[ "# Preprint 103/2013\n\n## Superfast Wavelet Transform Using QTT Approximation. I: Haar Wavelets\n\n### Boris N. Khoromskij and Sentao Miao\n\nContact the author: Please use for correspondence this email.\nSubmission date: 14. Nov. 2013 (revised version: November 2013)\nPages: 24\npublished in: Computational methods in applied mathematics, 14 (2014) 4, p. 537-553", null, "DOI number (of the published article): 10.1515/cmam-2014-0016\nBibtex\nMSC-Numbers: 65F30, 65F50, 65N35, 65F10\nKeywords and phrases: tensor-structured methods, fast wavelet transform, canonical tensor decomposition, quantized tensor approximation (QTT), data compression, multilevel methods\nDownload full preprint: PDF (271 kB)\n\nAbstract:\nWe propose a superfast discrete Haar wavelet transform (SFHWT) as well as its inverse, using the QTT representation for the Haar transform matrices and input-output vectors. Though the Haar matrix itself does not have a low QTT-rank approximation, we show that factor matrices used at each step of the traditional multilevel Haar wavelet transform algorithm have explicit QTT representations of low rank. The SFHWT applies to a vector representing a signal sampled on a uniform grid of size N = 2d. We develop two algorithms which roughly require square logarithmic time complexity with respect to the grid size, O(log 2N), hence outperforming the traditional fast Haar wavelet transform (FHWT) of linear complexity, O(N). Our approach also applies to the FHWT inverse as well as to the multidimensional wavelet transform. Numerical experiments demonstrate that the SFHWT algorithm is robust in keeping low rank of the resulting output vector and it outperforms the traditional FHWT for grid size larger than a certain value depending on the spacial dimension.\n\n18.10.2019, 02:15" ]	[ null, "https://sfx.mpg.de/sfx_local/sfx.gif", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7969122,"math_prob":0.84658515,"size":1740,"snap":"2021-04-2021-17","text_gpt3_token_len":429,"char_repetition_ratio":0.10426267,"word_repetition_ratio":0.0,"special_character_ratio":0.2224138,"punctuation_ratio":0.12828948,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9653153,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-04-18T09:43:34Z\",\"WARC-Record-ID\":\"<urn:uuid:f089a8d4-452b-416b-a06a-e585359e123d>\",\"Content-Length\":\"27017\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:88991c38-e923-4048-a469-9dbccc675799>\",\"WARC-Concurrent-To\":\"<urn:uuid:4c2cf42e-ebeb-448f-aacf-cd6fe741606f>\",\"WARC-IP-Address\":\"194.95.185.89\",\"WARC-Target-URI\":\"https://www.mis.mpg.de/de/publications/mis-preprints/2013/2013-103.html\",\"WARC-Payload-Digest\":\"sha1:CCR3ENSR3W7VZWKKWX3FMXM36ORB6SWL\",\"WARC-Block-Digest\":\"sha1:G6T26H3TCEF5LGWZKLI36B23RSQL2G2E\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-17/CC-MAIN-2021-17_segments_1618038469494.59_warc_CC-MAIN-20210418073623-20210418103623-00383.warc.gz\"}"}
http://divers.neaq.org/2013/12/a-curious-onlooker-bridled-burrfish.html	[ "# New England Aquarium//<![CDATA[ (function(){var g=this,h=function(b,d){var a=b.split(\".\"),c=g;ain c\|\|!c.execScript\|\|c.execScript(\"var \"+a);for(var e;a.length&&(e=a.shift());)a.length\|\|void 0===d?c[e]?c=c[e]:c=c[e]={}:c[e]=d};var l=function(b){var d=b.length;if(0<d){for(var a=Array(d),c=0;c<d;c++)a[c]=b[c];return a}return[]};var m=function(b){var d=window;if(d.addEventListener)d.addEventListener(\"load\",b,!1);else if(d.attachEvent)d.attachEvent(\"onload\",b);else{var a=d.onload;d.onload=function(){b.call(this);a&&a.call(this)}}};var n,p=function(b,d,a,c,e){this.f=b;this.h=d;this.i=a;this.c=e;this.e={height:window.innerHeight\|\|document.documentElement.clientHeight\|\|document.body.clientHeight,width:window.innerWidth\|\|document.documentElement.clientWidth\|\|document.body.clientWidth};this.g=c;this.b={};this.a=[];this.d={}},q=function(b,d){var a,c,e=d.getAttribute(\"pagespeed_url_hash\");if(a=e&&!(e in b.d))if(0>=d.offsetWidth&&0>=d.offsetHeight)a=!1;else{c=d.getBoundingClientRect();var f=document.body;a=c.top+(\"pageYOffset\"in window?window.pageYOffset:(document.documentElement\|\|f.parentNode\|\|f).scrollTop);c=c.left+(\"pageXOffset\"in window?window.pageXOffset:(document.documentElement\|\|f.parentNode\|\|f).scrollLeft);f=a.toString()+\",\"+c;b.b.hasOwnProperty(f)?a=!1:(b.b[f]=!0,a=a<=b.e.height&&c<=b.e.width)}a&&(b.a.push(e),b.d[e]=!0)};p.prototype.checkImageForCriticality=function(b){b.getBoundingClientRect&&q(this,b)};h(\"pagespeed.CriticalImages.checkImageForCriticality\",function(b){n.checkImageForCriticality(b)});h(\"pagespeed.CriticalImages.checkCriticalImages\",function(){r(n)});var r=function(b){b.b={};for(var d=[\"IMG\",\"INPUT\"],a=[],c=0;c<d.length;++c)a=a.concat(l(document.getElementsByTagName(d[c])));if(0!=a.length&&a.getBoundingClientRect){for(c=0;d=a[c];++c)q(b,d);a=\"oh=\"+b.i;b.c&&(a+=\"&n=\"+b.c);if(d=0!=b.a.length)for(a+=\"&ci=\"+encodeURIComponent(b.a),c=1;c<b.a.length;++c){var e=\",\"+encodeURIComponent(b.a[c]);131072>=a.length+e.length&&(a+=e)}b.g&&(e=\"&rd=\"+encodeURIComponent(JSON.stringify(s())),131072>=a.length+e.length&&(a+=e),d=!0);t=a;if(d){c=b.f;b=b.h;var f;if(window.XMLHttpRequest)f=new XMLHttpRequest;else if(window.ActiveXObject)try{f=new ActiveXObject(\"Msxml2.XMLHTTP\")}catch(k){try{f=new ActiveXObject(\"Microsoft.XMLHTTP\")}catch(u){}}f&&(f.open(\"POST\",c+(-1==c.indexOf(\"?\")?\"?\":\"&\")+\"url=\"+encodeURIComponent(b)),f.setRequestHeader(\"Content-Type\",\"application/x-www-form-urlencoded\"),f.send(a))}}},s=function(){var b={},d=document.getElementsByTagName(\"IMG\");if(0==d.length)return{};var a=d;if(!(\"naturalWidth\"in a&&\"naturalHeight\"in a))return{};for(var c=0;a=d[c];++c){var e=a.getAttribute(\"pagespeed_url_hash\");e&&(!(e in b)&&0<a.width&&0<a.height&&0<a.naturalWidth&&0<a.naturalHeight\|\|e in b&&a.width>=b[e].k&&a.height>=b[e].j)&&(b[e]={rw:a.width,rh:a.height,ow:a.naturalWidth,oh:a.naturalHeight})}return b},t=\"\";h(\"pagespeed.CriticalImages.getBeaconData\",function(){return t});h(\"pagespeed.CriticalImages.Run\",function(b,d,a,c,e,f){var k=new p(b,d,a,e,f);n=k;c&&m(function(){window.setTimeout(function(){r(k)},0)})});})();pagespeed.CriticalImages.Run('/mod_pagespeed_beacon','http://neaq.ordercompletion.com/','w4RdHWOzsL',true,false,'yobErJ3BosA'); //]]>", null, "## 12/18/13\n\n### A curious onlooker: The bridled burrfish\n\nDivers, mostly volunteers, hop into the tank with scrub brushes every day. They're charged with scrubbing our colorful new corals so they can remain vibrant and lovely. It's a job that has to happen every day. After all, if you have bright lights you're going to get some happy algae.\n\nIn this video, Daire has a curious onlooker while he's scrubbing the algae at the top of the reef.\n\nThis bridled burrfish is related to all of our other spiky puffers: balloonfish, porcupinefish, spotted burrfish and striped burrfish. But perhaps he thinks this brush is his kin!" ]	[ null, "http://neaq.ordercompletion.com/skin/frontend/v3/556neaq/images/logo.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7983499,"math_prob":0.91951084,"size":1885,"snap":"2021-43-2021-49","text_gpt3_token_len":493,"char_repetition_ratio":0.16640085,"word_repetition_ratio":0.0,"special_character_ratio":0.25994694,"punctuation_ratio":0.084375,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9768817,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-15T23:47:22Z\",\"WARC-Record-ID\":\"<urn:uuid:a8579944-c0b8-4e48-b39b-e370fe976b82>\",\"Content-Length\":\"63236\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:32998f98-28e6-4382-8d95-6924e967c0fb>\",\"WARC-Concurrent-To\":\"<urn:uuid:1368b7ec-291a-40a7-b256-21e126ab5b02>\",\"WARC-IP-Address\":\"172.217.15.115\",\"WARC-Target-URI\":\"http://divers.neaq.org/2013/12/a-curious-onlooker-bridled-burrfish.html\",\"WARC-Payload-Digest\":\"sha1:QC7DMOV4DKNGP2X363FH4FDHSLMM54ZY\",\"WARC-Block-Digest\":\"sha1:JY6VZXN7UHWVBHEHX5HZZ72PY77I7UHI\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323583087.95_warc_CC-MAIN-20211015222918-20211016012918-00157.warc.gz\"}"}
https://books.google.com.eg/books?id=0vQ3AAAAMAAJ&hl=ar&lr=	[ "# The Mathematical Questions Proposed in the Ladies' Diary: And Their Original Answers, Together with Some New Solutions, from Its Commencement in the Year 1704 to 1816, «Š„ŐŠŌ 4\n\nJ. Mawman, 1817\n\n### „« ŪřśŠŚ «Šš«” -Ŗ «»… „—«Őŕ…\n\nŠ„ šŕň— ŕŠž √Ū „—«Őŕ« ›Ū «Š√„«Ŗš «Š„ŕ «Ō….\n\n### „ř«ōŕ „‘Śś—…\n\n«Š’›Õ… 271 - C, and whose principal axis is the difference between AZ and CZ; and QS a perpendicular on AC may be drawn, to which (QS) if from any point Z of this hyperbola a perpendicular ZS is let fall (this ZS), shall be to AZ as the difference between AZ and CZ is to AC. Wherefore the ratios of ZR and ZS to AZ are given, and...Ģ\n«Š’›Õ… 271 - PR perpendicular to AB, and let fall ZR perpendicular to PR; then from the nature of the hyperbola, ZR will be to AZ as MN is to AB. And by the like argument, the locus of the point Z will be another hyperbola, whose foci are A, C, and...Ģ\n«Š’›Õ… 271 - TA are drawn, the figure TRZS will be given in specie, and the right line TZ, in which the point Z is somewhere placed, will be given in position. There will be given also the right line TA, and the angle ATZ; and because the ratios of AZ and TZ to ZS are given, their ratio to each other is given also; and thence will be given likewise the triangle ATZ, whose vertex is the point ZQEI CASE 2.Ģ\n«Š’›Õ… 165 - Given the vertical angle, the difference of the two sides containing it, and the difference of the segments of the base made by a perpendicular from the vertex ; construct the triangle.Ģ\n«Š’›Õ… 154 - IN a Right-angled Triangle, having given the Perimeter or Sum of all the Sides, and the Perpendicular let fall from the Right Angle on the Hypothenuse ; to determine the Triangle, that is, its Sides. PROBLEM XVIII.Ģ\n«Š’›Õ… 391 - ... 0. The diameter, therefore, and the radius of curvature at A are infinite. In other words, no circle, having its centre in AB produced, and passing through A, can be described with so great a radius, but that, at the point A, it will be within the curve of equal attraction. The solid of greatest attraction, then, at the extremity of its axis, where the attracted particle is placed, is exceedingly flat, approaching more nearly to a plane than the superficies of any sphere can do, however great...Ģ\n«Š’›Õ… 394 - I, от m + l =2, this equation becomes y* ó ax я* being that of a circle of which the diameter is AB. If, therefore, the attracting force were inversely as the distance, the solid of greatest attraction would be a sphere. If the force be inversely as the cube of the distance, or m = 3, and m + 1 = 4, the equation is y = о?Ģ\n«Š’›Õ… 225 - In any triangle, the centre of the circumscribed circle, the intersection of the medial lines, and the intersection of the perpendiculars from the angles upon the opposite sides, are in the...Ģ\n«Š’›Õ… 388 - ACS, therefore, is the locus of all the points in which a body being placed, will attract the particle A in the direction AB, with the same force. This condition is sufficient to determine the nature of the curve ACB.Ģ\n«Š’›Õ… 389 - AG, from the nature of the semicircle, and therefore AC= v'AB x AG, which has been shewn to be a property of the curve. In this way, any number of points of the curve may be determined ; and the solid of greatest attraction will be described, as already explained, by the revolution of this curve about the axis AB.Ģ" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8380997,"math_prob":0.9675473,"size":4226,"snap":"2020-10-2020-16","text_gpt3_token_len":1087,"char_repetition_ratio":0.13003317,"word_repetition_ratio":0.008032128,"special_character_ratio":0.22290581,"punctuation_ratio":0.12679426,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9900887,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-02-22T11:08:46Z\",\"WARC-Record-ID\":\"<urn:uuid:3c67152b-f4fb-4d32-b05c-fee7d3b1970a>\",\"Content-Length\":\"65959\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9cbe51e0-0eea-45ad-8840-800bc1341ca3>\",\"WARC-Concurrent-To\":\"<urn:uuid:3b0c1a5d-e6a3-4f71-a219-cbadfde59fd6>\",\"WARC-IP-Address\":\"172.217.5.238\",\"WARC-Target-URI\":\"https://books.google.com.eg/books?id=0vQ3AAAAMAAJ&hl=ar&lr=\",\"WARC-Payload-Digest\":\"sha1:BZMBDYSFLLGET7LVCT74R56CARVMZCJR\",\"WARC-Block-Digest\":\"sha1:POPDS6UM24GZY4KAGHB4TN6XCG6F6WRK\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-10/CC-MAIN-2020-10_segments_1581875145657.46_warc_CC-MAIN-20200222085018-20200222115018-00392.warc.gz\"}"}
https://www.lmfdb.org/EllipticCurve/Q/102/a/1	[ "Show commands for: Magma / SageMath / Pari/GP\n\n## Minimal Weierstrass equation\n\nmagma: E := EllipticCurve([1, 1, 0, -2, 0]); // or\nmagma: E := EllipticCurve(\"102a1\");\nsage: E = EllipticCurve([1, 1, 0, -2, 0]) # or\nsage: E = EllipticCurve(\"102a1\")\ngp: E = ellinit([1, 1, 0, -2, 0]) \\\\ or\ngp: E = ellinit(\"102a1\")\n\n$$y^2 + x y = x^{3} + x^{2} - 2 x$$\n\n## Mordell-Weil group structure\n\n$$\\Z\\times \\Z/{2}\\Z$$\n\n### Infinite order Mordell-Weil generator and height\n\nmagma: Generators(E);\nsage: E.gens()\n\n $$P$$ = $$\\left(-1, 2\\right)$$ $$\\hat{h}(P)$$ ≈ 0.143253892941\n\n## Torsion generators\n\nmagma: TorsionSubgroup(E);\nsage: E.torsion_subgroup().gens()\ngp: elltors(E)\n\n$$\\left(0, 0\\right)$$\n\n## Integral points\n\nmagma: IntegralPoints(E);\nsage: E.integral_points()\n\n$$\\left(-2, 2\\right)$$, $$\\left(-1, 2\\right)$$, $$\\left(0, 0\\right)$$, $$\\left(1, 0\\right)$$, $$\\left(2, 2\\right)$$, $$\\left(8, 20\\right)$$, $$\\left(9, 24\\right)$$, $$\\left(2738, 141932\\right)$$\n\nNote: only one of each pair $\\pm P$ is listed.\n\n## Invariants\n\n magma: Conductor(E); sage: E.conductor().factor() gp: ellglobalred(E) Conductor: $$102$$ = $$2 \\cdot 3 \\cdot 17$$ magma: Discriminant(E); sage: E.discriminant().factor() gp: E.disc Discriminant: $$612$$ = $$2^{2} \\cdot 3^{2} \\cdot 17$$ magma: jInvariant(E); sage: E.j_invariant().factor() gp: E.j j-invariant: $$\\frac{1771561}{612}$$ = $$2^{-2} \\cdot 3^{-2} \\cdot 11^{6} \\cdot 17^{-1}$$ Endomorphism ring: $$\\Z$$ (no Complex Multiplication) Sato-Tate Group: $\\mathrm{SU}(2)$\n\n## BSD invariants\n\n magma: Rank(E); sage: E.rank() Rank: $$1$$ magma: Regulator(E); sage: E.regulator() Regulator: $$0.143253892941$$ magma: RealPeriod(E); sage: E.period_lattice().omega() gp: E.omega Real period: $$4.72786382354$$ magma: TamagawaNumbers(E); sage: E.tamagawa_numbers() gp: gr=ellglobalred(E); [[gr[i,1],gr[i]] \| i<-[1..#gr[,1]]] Tamagawa product: $$4$$ = $$2\\cdot2\\cdot1$$ magma: Order(TorsionSubgroup(E)); sage: E.torsion_order() gp: elltors(E) Torsion order: $$2$$ magma: MordellWeilShaInformation(E); sage: E.sha().an_numerical() Analytic order of Ш: $$1$$ (exact)\n\n## Modular invariants\n\n#### Modular form102.2.a.a\n\nmagma: ModularForm(E);\nsage: E.q_eigenform(20)\ngp: xy = elltaniyama(E);\ngp: xderiv(xy)/(2xy+E.a1*xy+E.a3)\n\n$$q - q^{2} - q^{3} + q^{4} - 4q^{5} + q^{6} - 2q^{7} - q^{8} + q^{9} + 4q^{10} - q^{12} - 6q^{13} + 2q^{14} + 4q^{15} + q^{16} - q^{17} - q^{18} + 4q^{19} + O(q^{20})$$\n\n magma: ModularDegree(E); sage: E.modular_degree() Modular degree: 8 $$\\Gamma_0(N)$$-optimal: yes Manin constant: 1\n\n#### Special L-value\n\nmagma: Lr1 where r,Lr1 := AnalyticRank(E: Precision:=12);\nsage: r = E.rank();\nsage: E.lseries().dokchitser().derivative(1,r)/r.factorial()\ngp: ar = ellanalyticrank(E);\ngp: ar/factorial(ar)\n\n$$L'(E,1)$$ ≈ $$0.677284898017$$\n\n## Local data\n\nmagma: [LocalInformation(E,p) : p in BadPrimes(E)];\nsage: E.local_data()\ngp: ellglobalred(E)\nprime Tamagawa number Kodaira symbol Reduction type Root number ord($$N$$) ord($$\\Delta$$) ord$$(j)_{-}$$\n$$2$$ $$2$$ $$I_{2}$$ Non-split multiplicative 1 1 2 2\n$$3$$ $$2$$ $$I_{2}$$ Non-split multiplicative 1 1 2 2\n$$17$$ $$1$$ $$I_{1}$$ Non-split multiplicative 1 1 1 1\n\n## Galois representations\n\nThe image of the 2-adic representation attached to this elliptic curve is the subgroup of $\\GL(2,\\Z_2)$ with Rouse label X15.\n\nThis subgroup is the pull-back of the subgroup of $\\GL(2,\\Z_2/2^3\\Z_2)$ generated by $\\left(\\begin{array}{rr} 1 & 1 \\\\ 0 & 1 \\end{array}\\right),\\left(\\begin{array}{rr} 7 & 0 \\\\ 2 & 1 \\end{array}\\right),\\left(\\begin{array}{rr} 5 & 0 \\\\ 2 & 1 \\end{array}\\right)$ and has index 6.\n\nmagma: [GaloisRepresentation(E,p): p in PrimesUpTo(20)];\nsage: rho = E.galois_representation();\nsage: [rho.image_type(p) for p in rho.non_surjective()]\n\nThe mod $$p$$ Galois representation has maximal image $$\\GL(2,\\F_p)$$ for all primes $$p$$ except those listed.\n\nprime Image of Galois representation\n$$2$$ B\n\n## $p$-adic data\n\n### $p$-adic regulators\n\nsage: [E.padic_regulator(p) for p in primes(3,20) if E.conductor().valuation(p)<2]\n\nNote: $$p$$-adic regulator data only exists for primes $$p\\ge5$$ of good ordinary reduction.\n\n## Iwasawa invariants\n\n $p$ Reduction type $\\lambda$-invariant(s) $\\mu$-invariant(s) 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 nonsplit nonsplit ordinary ordinary ss ordinary nonsplit ordinary ordinary ordinary ordinary ordinary ordinary ordinary ordinary 1 1 1 1 1,1 1 1 1 3 1 1 1 1 1 1 0 0 0 0 0,0 0 0 0 0 0 0 0 0 0 0\n\n## Isogenies\n\nThis curve has non-trivial cyclic isogenies of degree $$d$$ for $$d=$$ 2.\nIts isogeny class 102.a consists of 2 curves linked by isogenies of degree 2.\n\n## Growth of torsion in number fields\n\nThe number fields $K$ of degree up to 7 such that $E(K)_{\\rm tors}$ is strictly larger than $E(\\Q)_{\\rm tors}$ $\\cong \\Z/{2}\\Z$ are as follows:\n\n$[K:\\Q]$ $K$ $E(K)_{\\rm tors}$ Base-change curve\n2 $$\\Q(\\sqrt{17})$$ $$\\Z/2\\Z \\times \\Z/2\\Z$$ 2.2.17.1-612.1-a2\n4 4.0.1088.1 $$\\Z/4\\Z$$ Not in database\n\nWe only show fields where the torsion growth is primitive. For each field $K$ we either show its label, or a defining polynomial when $K$ is not in the database.\n\nThis is the elliptic curve $E$ associated to the [Somos-5 sequence] $\\{a(n)\\}$. Let $T$ be the $2$-torsion point $(0,0)$, and $P$ the point $(2,2)$ such that $E(\\Q) = \\Z P \\oplus \\{0, T\\}$. Then the $x$- and $y$-coordinates of $nP+T$ have denominators $d_n^2$ and $d_n^3$ where $$d_n = 1, 1, 2, 3, 5, 11, 37, 83, 274, 1217$$ for $1 \\leq n \\leq 10$, and $d_n = a(n+2)$ in general, satisfying the Somos-5 recurrence $$d_n d_{n+5} = d_{n+1} d_{n+4} + d_{n+2} d_{n+3}.$$ Thus the regulator of $E$, which is the canonical height $\\hat h(P) = 0.143\\ldots$, controls the growth of the $a(n)$: asymptotically $\\log a_n \\sim \\frac12 \\hat h(P) n^2$." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.5255153,"math_prob":0.99999297,"size":4883,"snap":"2019-43-2019-47","text_gpt3_token_len":1939,"char_repetition_ratio":0.12810002,"word_repetition_ratio":0.041847043,"special_character_ratio":0.4456277,"punctuation_ratio":0.165183,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99995697,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-11-15T12:14:36Z\",\"WARC-Record-ID\":\"<urn:uuid:68ef3487-0bb5-4e4d-a14e-f3ce5c2def61>\",\"Content-Length\":\"86238\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:38ec6235-b06a-4834-bb3d-8252799c1377>\",\"WARC-Concurrent-To\":\"<urn:uuid:a81dbabb-94ae-4148-af0d-f7398c436cef>\",\"WARC-IP-Address\":\"35.241.19.59\",\"WARC-Target-URI\":\"https://www.lmfdb.org/EllipticCurve/Q/102/a/1\",\"WARC-Payload-Digest\":\"sha1:YIR2AV3JJEHIJDP5MXQAWYTPMLDN4PYL\",\"WARC-Block-Digest\":\"sha1:44M3OJGEWBC4UEPCXBJ2IZCM2JEHO43T\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-47/CC-MAIN-2019-47_segments_1573496668644.10_warc_CC-MAIN-20191115120854-20191115144854-00538.warc.gz\"}"}
https://www.dlology.com/blog/simple-speech-keyword-detecting-with-depthwise-separable-convolutions/	[ "# Simple Speech Keyword Detecting with Depthwise Separable Convolutions", null, "Keyword detection or speech commands can be viewed as a minimal version of speech recognition system. What if we can make the model that is accurate yet consume small enough memory and computational footprint that runs in real-time even on a microcontroller in bare metal(without an operating system)? If that becomes real, imagining what traditional consumer electronic devices will become smarter with always-on speech commands enabled.\n\nIn this post, we will take the first step to build and train such a deep learning model to do keyword detection with the limiting memory and compute resources in mind.\n\n## Keyword detection system\n\nCompare to a full speech recognition system which is typically cloud-based and can recognize almost any spoken words, keyword detection, on the other hand, detect predefined keywords such as \"Alexa\", \"Ok Google\", \"Hey Siri\", etc. which is \"always on\". The detection of the keywords triggers a specific action such as activating the full-scale speech recognition system. In some other use case, such keywords can be used to activate a voice-enabled lightbulb.\n\nA keyword detection system consists of two essential parts.\n\n1. A feature extractor to convert an audio clip from time domain waveform to frequency domain speech features.\n2. A neural network based classifier to process the frequency domain features and predict the likelihood for all predefined keywords plus the \"unknown\" word and \"silence\".", null, "Our system adopts the Mel-Frequency Cepstral Coefficients or MFCCs as the feature extractor to get the 2D 'fingerprint' of the audio. Since the input to the neural network is an image like 2D audio fingerprint with the horizontal axis denoting the time and vertical axis representing the frequency coefficients, picking a convolutional based model seems like a natural choice.\n\n## Depthwise Separable Convolutions\n\nThe issue with the standard convolution operation might still require too much memory and compute resource from the microcontrollers, considering even some of the top performant microcontrollers only have ~320KB of SRAM and ~1MB of flash. One way to meet the constraints while still keep the accuracy high is by applying the depthwise separable convolution instead of the conventional convolutional neural network.\n\nIt was first introduced in the Xception ImageNet model, then adopted by some other models such as MobileNet and ShuffleNet all gear towards reducing the model complexity to deploy on resource-constrained targets like smartphone, drones, and robots.\n\nDepthwise separable convolutional neural network consists in first performing a depthwise spatial convolution, which acts on each input channel separately followed by a pointwise convolution(i.e., 1x1 convolution) which mixes the resulting output channels. Intuitively, separable convolutions can be understood as a way to factorize a convolution kernel into two smaller kernels.\n\nA standard convolutional operation filters and combines inputs into a new set of outputs in one step. Compared to traditional convolutional operation the depthwise separable convolution splits this into two layers, a separate layer for filtering and a separate layer for combining. This factorization has the effect of drastically reducing computation and model size. Depthwise separable convolutions are more efficient both in the number of parameters and operations, which makes deeper and wider architecture possible even in the resource-constrained devices.", null, "We are going to implement the model with the depthwise separable CNN architecture by TensorFlow in the next section.\n\n## Building the model\n\nThe first step is to turn the raw audio waveform into MFCC features, and it can be done in TensorFlow like this.\n\n```from tensorflow.contrib.framework.python.ops import audio_ops as contrib_audio\n# Run the spectrogram and MFCC ops to get a 2D 'fingerprint' of the audio.\nspectrogram = contrib_audio.audio_spectrogram(\nbackground_clamp,\nwindow_size=model_settings['window_size_samples'],\nstride=model_settings['window_stride_samples'],\nmagnitude_squared=True)\nself.mfcc_ = contrib_audio.mfcc(\nspectrogram,\nwav_decoder.sample_rate,\ndct_coefficient_count=model_settings['dct_coefficient_count'])\n```\n\nIf we have the following parameters for input audio and feature extractor,\n\n• Input audio sampling rate: 16000Hz\n• Input audio clip length: 1000ms (L)\n• Spectrogram window size: 40ms (l)\n• Spectrogram window stride: 20ms (s)\n• MFCC coefficient count:10 (F)\n\nThen the shape of the tensor `self.mfcc_` will be (None, T, F), where the number of frames: T = (L-l) / s +1 = (1000 - 40) / 20 + 1 = 49. `self.mfcc_` then becomes the `fingerprint_input` for the deep learning model.\n\nWe adopt a depthwise separable CNN based on the implementation of MobileNet, the full implementation is available on my GitHub.\n\nNote that first layer is always regular convolution of the model, but the remaining layers are all depthwise separable convolutions. Implementation of the depthwise separable convolution layer looks like this.\n```def _depthwise_separable_conv(inputs,\nnum_pwc_filters,\nsc,\nkernel_size,\nstride):\n\"\"\" Helper function to build the depth-wise separable convolution layer.\n\"\"\"\n\n# skip pointwise by setting num_outputs=None\ndepthwise_conv = slim.separable_convolution2d(inputs,\nnum_outputs=None,\nstride=stride,\ndepth_multiplier=1,\nkernel_size=kernel_size,\nscope=sc+'/depthwise_conv')\n\nbn = slim.batch_norm(depthwise_conv, scope=sc+'/dw_batch_norm')\npointwise_conv = slim.convolution2d(bn,\nnum_pwc_filters,\nkernel_size=[1, 1],\nscope=sc+'/pointwise_conv')\nbn = slim.batch_norm(pointwise_conv, scope=sc+'/pw_batch_norm')\nreturn bn\n```\n\nAn average pooling followed by a fully-connected layer is used at the end to provide global interaction and reduce the total number of parameters in the final layer.\n\n## How well does the model perform?\n\nThe pre-trained model is ready for you to play with including the standard CNN, DS_CNN(Depthwise Separable Convolutions) and various other model architectures. For each architecture, various hyperparameters like kernel size/stride are searched and models with different scales are trained separately so that you can trade off a smaller and faster model to run on resource-constrained devices with slightly lower accuracy.", null, "The model built with depthwise separable convolutions achieve better accuracies than DNN models with a similar number of Ops, but with >10x reduction in memory requirement.\n\nNote that the memory required shown in the table is after quantizing floating point weights to the 8-bit fixed point, which I will explain in a future post.\n\nTo run an audio file through a trained DS_CNN model and get a top prediction,\n\n`python label_wav.py --wav yes.wav --graph Pretrained_models/DS_CNN/DS_CNN_S.pb --labels Pretrained_models/labels.txt --how_many_labels 1`\n\nIn this post, we explored implementing a simple yet powerful keyword detection model with potential to run on resource-constrained devices like a microcontroller.\n\nSome related resources you might find useful.\n\n1. TensorFlow tutorial - Simple Audio Recognition\n2. TensorFlow Speech Commands Example code in GitHub\n3. Blog - Keyword spotting for Microcontrollers\n4. Depthwise Separable Convolutional Neural Network in Keras SeparableConv2D\n5. Paper - Xception: Deep Learning with Depthwise Separable Convolutions\n6. Paper - MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications\n\nIn a future post, I will explain how to apply model weights quantization process to reduce the model size and show you how to run the model on a microcontroller.\n\nCheck out my GitHub repo and more information including training and testing the model.\n\nCurrent rating: 4.5" ]	[ null, "https://gitcdn.xyz/cdn/Tony607/blog_statics/c2f8789ecf32d972c7e7b9a3e578ddcd14f2dcb7/images/keyword/voice-command.jpg", null, "https://gitcdn.xyz/cdn/Tony607/blog_statics/c2f8789ecf32d972c7e7b9a3e578ddcd14f2dcb7/images/keyword/keyword-pipline.jpg", null, "https://gitcdn.xyz/cdn/Tony607/blog_statics/c2f8789ecf32d972c7e7b9a3e578ddcd14f2dcb7/images/keyword/ds_cnn.jpg", null, "https://gitcdn.xyz/cdn/Tony607/blog_statics/c2f8789ecf32d972c7e7b9a3e578ddcd14f2dcb7/images/keyword/nn-models.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8559256,"math_prob":0.77592325,"size":6481,"snap":"2020-34-2020-40","text_gpt3_token_len":1319,"char_repetition_ratio":0.12274201,"word_repetition_ratio":0.00440044,"special_character_ratio":0.19287147,"punctuation_ratio":0.10213556,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97149855,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,5,null,5,null,5,null,5,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-08-15T08:54:23Z\",\"WARC-Record-ID\":\"<urn:uuid:4da878b6-cd34-41fc-8dcd-ef3403d405b0>\",\"Content-Length\":\"30913\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6aa75c7e-8e77-4d29-94c5-8780cd026798>\",\"WARC-Concurrent-To\":\"<urn:uuid:585e4c3e-5f5c-4c7e-99db-8079500047ed>\",\"WARC-IP-Address\":\"104.31.93.77\",\"WARC-Target-URI\":\"https://www.dlology.com/blog/simple-speech-keyword-detecting-with-depthwise-separable-convolutions/\",\"WARC-Payload-Digest\":\"sha1:YEG23F345B6JV35IMONBTARW6O3UEVAW\",\"WARC-Block-Digest\":\"sha1:ZKGIS45HSFNGTHY3SVYWRLI6PDV3JQEQ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-34/CC-MAIN-2020-34_segments_1596439740733.1_warc_CC-MAIN-20200815065105-20200815095105-00299.warc.gz\"}"}
https://tex.stackexchange.com/questions/34107/add-a-phrase-to-an-existing-algorithmic-command-environment/34111	[ "# Add a phrase to an existing algorithmic command/environment\n\nI would like to add a new command to an existing environment. The \\renewenvironment command does not help a lot since I need to copy and paste the entire environment definition.\n\nFor an example I would like to make a \\FORALL_P for the algorithmic environment such that instead of producing\n\nforall ... do\n\n\nas original \\FORALL, it produces\n\nforall ... do in parallel\n\n\nYou can say\n\n\\usepackage{algorithmic}\n\\usepackage{etoolbox}\n\\newcommand{\\algorithmicdoinparallel}{\\textbf{do in parallel}}\n\\makeatletter\n\\AtBeginEnvironment{algorithmic}{%\n\\newcommand{\\FORALLP}[default]{\\ALC@it\\algorithmicforall\\ #2\\ %\n\\algorithmicdoinparallel\\ALC@com{#1}\\begin{ALC@for}}%\n}\n\\makeatother\n\n\nThe definition of \\FORALLP is modeled on that of \\FORALL; you can't call it \\FORALL_P, however.\n\n• Thanks, I tried to do this but failed, \\makeatletter does the magic... – iKid Nov 8 '11 at 14:06\n\nThe etoolbox package offers you some commands that could be useful, for example:\n\n\\AtBeginEnvironment{<environment>}{<code>}\n\\AtEndEnvironment{<environment>}{<code>}\n\n\nPerhaps if you give us some mor information about your actual intent, we could provide more helpful information.\n\nNow that new information has been provided in the question, I would suggest to use the algorithmicx package to define the new block; while the algorithmic package doesn’t allow you to easily modify predefined structures, or to create new ones, the algorithmicx package gives you full control over the definitions. Using algcompatible, you can have full compatibility with the syntax of the algorithmic package; a little example of the definition of the new block:\n\n\\documentclass{article}\n\\usepackage{algorithm}\n\\usepackage{algcompatible}\n\n\\algblockdefx{FORALLP}{ENDFAP}%\n{\\textbf{for all }#1 \\textbf{do in parallel}}%\n{\\textbf{end for}}\n\n\\begin{document}\n\n\\begin{algorithm}\n\\caption{A test algorithm}\n\\begin{algorithmic}\n\\FORALL {$v \\in V(G)$}\n\\STATE $l(v) \\leftarrow \\infty$\n\\ENDFOR\n\\FORALLP{$v \\in V(G)$}\n\\STATE $l(v) \\leftarrow \\infty$\n\\ENDFAP\n\\end{algorithmic}\n\\end{algorithm}\n\n\\end{document}", null, "To have the \\RETURN command as defined by algorithmic, you need to add the following definition:\n\n\\algloopdefx{RETURN}[]{\\textbf{return} #1}\n\n• thanks, I will look into etoolbox. I also added more info to my original post. – iKid Nov 8 '11 at 13:18\n• @iKid: please see my updated answer. – Gonzalo Medina Nov 8 '11 at 13:39\n• I failed to use the algorithmicx as they do not support \\return ? – iKid Nov 8 '11 at 13:53\n• @iKid: I've added the corresponding definition. – Gonzalo Medina Nov 8 '11 at 14:00\n• @iKid: no problem. In fact, I thought that there was full compatibility (as algorithmicx advertises), but apparently it's not so \"full\". – Gonzalo Medina Nov 8 '11 at 14:06\n\nIn your specific case, using commands of the etoolbox package to change the look of the \\FORALL statement might not work because you're trying to change the subsequent statement, viz. \"do...\"\n\nThe algorithmic package allows for a fair bit of customization of various algorithm-like statements. For example, you could issue the command\n\n\\renewcommand{\\algorithmicdo}{\\textbf{do in parallel}}\n\n\nHowever, this will change the output of the \"do\" statement in all instances, which may not be to your liking." ]	[ null, "https://i.stack.imgur.com/hqNkf.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.67154247,"math_prob":0.68262655,"size":1321,"snap":"2020-34-2020-40","text_gpt3_token_len":356,"char_repetition_ratio":0.14123006,"word_repetition_ratio":0.024844721,"special_character_ratio":0.22937168,"punctuation_ratio":0.067307696,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95239013,"pos_list":[0,1,2],"im_url_duplicate_count":[null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-08-03T20:39:45Z\",\"WARC-Record-ID\":\"<urn:uuid:65c2cd73-e157-4787-8085-2d14343bc134>\",\"Content-Length\":\"170463\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:60f429cc-2100-4efc-b910-6e39420c3da3>\",\"WARC-Concurrent-To\":\"<urn:uuid:2c875252-57e9-450c-9fdc-7b988f9a3bed>\",\"WARC-IP-Address\":\"151.101.193.69\",\"WARC-Target-URI\":\"https://tex.stackexchange.com/questions/34107/add-a-phrase-to-an-existing-algorithmic-command-environment/34111\",\"WARC-Payload-Digest\":\"sha1:LBLT2YCZ6CSEUHXP4RDWHIXZ7L4BK3UQ\",\"WARC-Block-Digest\":\"sha1:5KSEC65ZW73OWJRIULAB4J3WOWQPNCV4\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-34/CC-MAIN-2020-34_segments_1596439735833.83_warc_CC-MAIN-20200803195435-20200803225435-00260.warc.gz\"}"}
https://www.gurufocus.com/term/TaxRate/BABA/Tax%252BRate/Alibaba%2BGroup%2BHolding%2BLtd	[ "Switch to:\n\n# Alibaba Group Holding Tax Rate %\n\n: 7.90% (As of Sep. 2020)\nView and export this data going back to 2014. Start your Free Trial\n\nTax Rate % is calculated as Tax Expense divided by its Pre-Tax Income. Alibaba Group Holding's Tax Expense for the three months ended in Sep. 2020 was \\$281 Mil. Alibaba Group Holding's Pre-Tax Income for the three months ended in Sep. 2020 was \\$3,552 Mil. Therefore, Alibaba Group Holding's Tax Rate % for the quarter that ended in Sep. 2020 was 7.90%.\n\n## Alibaba Group Holding Tax Rate % Historical Data\n\n* All numbers are in millions except for per share data and ratio. All numbers are in their local exchange's currency.\n\n Alibaba Group Holding Annual Data Dec11 Mar12 Mar13 Mar14 Mar15 Mar16 Mar17 Mar18 Mar19 Mar20 Tax Rate %", null, "", null, "", null, "", null, "", null, "10.37 22.95 18.13 17.20 12.34\n\n## Alibaba Group Holding Tax Rate % Calculation\n\nTax Rate % is the ratio of tax expense divided by pretax income, usually presented in percent.\n\nAlibaba Group Holding's Tax Rate % for the fiscal year that ended in Mar. 2020 is calculated as\n\n Tax Rate % = Tax Expense (A: Mar. 2020 ) / Pre-Tax Income (A: Mar. 2020 ) = 2928.851221423 / 23736.913325262 = 12.34 %\n\nAlibaba Group Holding's Tax Rate % for the quarter that ended in Sep. 2020 is calculated as\n\n Tax Rate % = Tax Expense (Q: Sep. 2020 ) / Pre-Tax Income (Q: Sep. 2020 ) = 280.59201832438 / 3551.9631163187 = 7.90 %\n\n* All numbers are in millions except for per share data and ratio. All numbers are in their local exchange's currency." ]	[ null, "https://gurufocus.s3.amazonaws.com/images/blur.png", null, "https://gurufocus.s3.amazonaws.com/images/blur.png", null, "https://gurufocus.s3.amazonaws.com/images/blur.png", null, "https://gurufocus.s3.amazonaws.com/images/blur.png", null, "https://gurufocus.s3.amazonaws.com/images/blur.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9097643,"math_prob":0.87796843,"size":1442,"snap":"2020-45-2020-50","text_gpt3_token_len":408,"char_repetition_ratio":0.122392215,"word_repetition_ratio":0.33333334,"special_character_ratio":0.34604716,"punctuation_ratio":0.15068494,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9841689,"pos_list":[0,1,2,3,4,5,6,7,8,9,10],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-12-02T06:43:29Z\",\"WARC-Record-ID\":\"<urn:uuid:e1228aa3-c6de-4cfe-a7f3-a14619ca5f81>\",\"Content-Length\":\"364177\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e9a30e34-c945-4a29-9051-c4fec7735b16>\",\"WARC-Concurrent-To\":\"<urn:uuid:635e9d35-b009-4b4c-95a9-431ef896d8c1>\",\"WARC-IP-Address\":\"104.26.15.56\",\"WARC-Target-URI\":\"https://www.gurufocus.com/term/TaxRate/BABA/Tax%252BRate/Alibaba%2BGroup%2BHolding%2BLtd\",\"WARC-Payload-Digest\":\"sha1:GLEOY25NGLTTE7H6FIJYINOTUUB7QKP7\",\"WARC-Block-Digest\":\"sha1:SSTOYQFII25ITKB4NAWOCADEYN4QVBGA\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141692985.63_warc_CC-MAIN-20201202052413-20201202082413-00447.warc.gz\"}"}
https://studysoup.com/tsg/17023/discrete-mathematics-and-its-applications-7-edition-chapter-3-3-problem-5e	[ "×\n×\n\n# How many comparisons are used by the algorithm given in", null, "ISBN: 9780073383095 37\n\n## Solution for problem 5E Chapter 3.3\n\nDiscrete Mathematics and Its Applications \| 7th Edition\n\n• Textbook Solutions\n• 2901 Step-by-step solutions solved by professors and subject experts\n• Get 24/7 help from StudySoup virtual teaching assistants", null, "Discrete Mathematics and Its Applications \| 7th Edition\n\n4 5 1 375 Reviews\n28\n5\nProblem 5E\n\nHow many comparisons are used by the algorithm given in Exercise 16 of Section 3.1 to find the smallest natural number in a sequence of n natural numbers?\n\nStep-by-Step Solution:\n\nSolutionStep 1In this problem, we have to find the smallest number from the list of n element.Step 2Algorithm for finding the smallest number from the list of n element. small_num(num1, num2, num3, ……….set of integers)Let us assume that first element at initial position be the smallest numberAssign the...\n\nStep 2 of 3\n\nStep 3 of 3\n\n##### ISBN: 9780073383095\n\nUnlock Textbook Solution" ]	[ null, "https://studysoup.com/cdn/54cover_2450429", null, "https://studysoup.com/cdn/54cover_2450429", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.81351,"math_prob":0.87334067,"size":461,"snap":"2020-45-2020-50","text_gpt3_token_len":104,"char_repetition_ratio":0.16630197,"word_repetition_ratio":0.11111111,"special_character_ratio":0.22125813,"punctuation_ratio":0.13043478,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98560387,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-11-30T07:37:22Z\",\"WARC-Record-ID\":\"<urn:uuid:378190b3-07fd-4d66-92eb-b186189c5ea3>\",\"Content-Length\":\"66654\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f27852b5-a035-4134-87ec-83cd1cf7c233>\",\"WARC-Concurrent-To\":\"<urn:uuid:a9776451-66b5-44c2-83c7-5ec6c8800897>\",\"WARC-IP-Address\":\"54.189.254.180\",\"WARC-Target-URI\":\"https://studysoup.com/tsg/17023/discrete-mathematics-and-its-applications-7-edition-chapter-3-3-problem-5e\",\"WARC-Payload-Digest\":\"sha1:HD7GZWEQQ23ACCXBRWDDRY3SKD6U64AK\",\"WARC-Block-Digest\":\"sha1:M36AW2PEEOPFRD42SOEPUY6AX4OBLCGR\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141211510.56_warc_CC-MAIN-20201130065516-20201130095516-00178.warc.gz\"}"}
https://wiki.rtm-lvl.org/rd-lqesd/pzkki8l.php?776202=matrix-division-3x3	[ "Inverting a 3x3 matrix using determinants Part 1: Matrix of minors and cofactor matrix. For example, if a problem requires you to divide by a fraction, you can more easily multiply by its reciprocal. Matrix Calculator . 1,2,3 3,1,4,,5. This calculator can instantly multiply two matrices and show a â¦ in particular, it enables us to avoid the fact that matrix division would have to reâect the noncommutativity of matrix multiplication. The code. It would be exhausting to perform such calculations using your pen and paper. Determinant of a 3x3 matrix: shortcut method (2 of 2) Our mission is to provide a free, world-class education to anyone, anywhere. You see the following result:Each of the entries is divided by the scalar value. 3x3 Square Matrix. Given 3x3 matrix: y0x0 y0x1 y0x2 y1x0 y1x1 y1x2 y2x0 y2x1 y2x2 Declared as double matrix [/Y=/3] [/X=/3]; (A) When taking a minor of a 3x3 array, we have 4 values of interest. I have a 3x3 confusion matrix for three sentiment classes - positive, negative and neutral. The closest equivalent is multiplying by the inverse of another matrix. The equivalent of matrix division is multiplying by the inverse of another matrix. Where. where B-1 means the \"inverse\" of B. To perform the division of two matrices, the first step would be to find the inverse of the matrix, which is more difficult. And press \"to A\" SAVING. The Matrix division, element by element. Well we don't actually divide matrices, we do it this way: A/B = A × (1/B) = A × B-1. A 2x2 matrix is a rectangular often square array of numbers having 2 rows and 2 columns. While there are many matrix calculators online, the simplest one to use that I have come across is this one by Math is Fun. Matrix Multiplication (2 x 3) and (3 x 3) __Multiplication of 2x3 and 3x3 matrices__ is possible and the result matrix is a 2x3 matrix. MATLAB - Division (Left, Right) of Matrics - You can divide two matrices using left (\\) or right (/) division operators. You wrote that that input is a 3x3 matrix, and did not mention any vectors. Solving equations with inverse matrices. ; The scalar a is being multiplied to the 2×2 matrix of left-over elements created when vertical and horizontal line segments are drawn passing through a.; The same process is applied to construct the 2×2 matrices for scalar multipliers b and c. In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns. The array of expressions set out by rows and columns are treated as a single element and are manipulated according to the rules. Calculating the inverse of a 3x3 matrix by hand is a tedious process. Metric to Imperial Converter: ft to cm, inches to cm, yards to metres, an excellent calculator that outputs the calculation in seconds. It would therefore seem logicalthat when working with matrices, one could take the matrix equation AX=B and divide bothsides by A to get X=B/A.However, that won't work because ...There is NO matrix division!Ok, you say. Or you can type in the big output area and press \"to A\" or \"to B\" (the calculator will try its best to interpret your data). If you have been looking for a good calculator for 3x3 matrix division, the good news is your search ends today as you have found an excellent calculator that outputs the calculation in seconds. Given an n n nonsingular matrix A, can we ând a matrix C such that CA = I n? The number of columns in the first matrix must equal the number of rows in the second matrix. This is the currently selected item. An array of numbers is called a matrix. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers.The other operations are addition, subtraction, and multiplication (which can be viewed as the inverse of division). The higher X/Y index is always 1 or 2. Leave extra cells empty to enter non-square matrices. Matrix Division. More Matrix Calculators So we don't divide, instead we multiply by an inverse. Calculating the inverse of a 3x3 matrix by hand is a tedious job, but worth reviewing. Let A and Y be given matrices with the same number of rows. Here are the key points: Notice that the top row elements namely a, b and c serve as scalar multipliers to a corresponding 2-by-2 matrix. Since the left-hand side is a 3x3 determinant, we have Online Matrix division calculator step by step by multiply tow matrices A and B that is an inverted matrix Example: a matrix with 3 rows and 5 columns can be added to another matrix of 3 rows and 5 columns. A 3x3 matrix is an array of numbers having 3 rows and 3 columns. (adsbygoogle = window.adsbygoogle \|\| []).push({}); The major condition while performing the division of two matrices is that both the matrices must have equal orders. Technically, there is no such thing as matrix division. Generally matrix division is an undefined function. The classification was done with Quanteda package. Denominator, specified as a real scalar, vector, matrix, or multidimensional array. 3x3 Matrix Multiplication. Matrix Multiplication (3 x 3) and (3 x 1) __Multiplication of 3x3 and 3x1 matrices__ is possible and the result matrix is a 3x1 matrix. We will see how to do this problem later, in Matrices and Linear Equations. MATLAB would do its best to accommodate you with a result, just not one you could really use. Example: Enter. The division of three matrices is generally multiplying the inverse of one matrix with the second matrix. If one matrix is of order 3 x 3, the other one should also have the same order. The corresponding elements of the matrices are the same 4x4 Matrix Subtraction. Two matrices are equal if and only if 1. To perform the division of two matrices, the first step would be to find the inverse of the matrixâ¦ I have a 3x3 confusion matrix for three sentiment classes - positive, negative and neutral. 3x3 Matrix Rank. The order of the matrices are the same 2. The lower X/Y index is always 0 or 1. This is why iCalculator created this great online calculator to help you divide two matrices of order 3 x 3. Recall that when we perform row operations on a matrix M to obtain a matrix N, we can achieve same result by matrix multiplication. By using this website, you agree to our Cookie Policy. If neither input is a fi object, then the sizes of the input matrices must be compatible for matrix division. When b is a scalar, mrdivide is equivalent to rdivide.. For example, type m = [2, 4, 6] / 2 and press Enter. The division sign ÷, a symbol consisting of a short horizontal line with a dot above and another dot below, is often used to indicate mathematical division. A good way to double check your work if youâre multiplying matrices by hand is to confirm your answers with a matrix calculator. # Train and test the model using the document feature matrix revâ¦ Hello All. 2x2 Square Matrix. There is no such such a thing of division in matrix. Subtraction was defined in terms of addition and division was defined in terms ofmultiplication. Since there is no division operator for matrices, you need to multiply by the inverse matrix. Understand matrix \"division.\" Dividing a matrix by another matrix is an undefined function. Practice: Inverse of a 3x3 matrix. Similarly, since there is no division operator for matrices, you need to multiply by the inverse matrix. Moreover, this type of division is much more difficult than it seems. Hello All. The solutions X of AX = Y are found in three steps: (1) Find unimodular matrices M and N such that MAN is diagonal, call it D. (2) Find all solutions Z of DZ = MY. The major condition while performing the division of two matrices is that both the matrices must have equal orders. Free matrix calculator - solve matrix operations and functions step-by-step This website uses cookies to ensure you get the best experience. ... And what about division? Using left division (m = [2, 4, 6] 2) would produce an unusable result; however, using m = 2 [2, 4, 6] would produce the same result as before. Please give us sample input and output arrays, so that we do not have to guess what â¦ That is, you can multiple A(2,5)xB(5,3) because the âinnerâ numbers are the same. 5x5 Matrix Multiplication. 4x4 Matrix Addition. You may also find the following: there are 3 unknown forces F1 F2. Is multiplying by the following formula is useful similarly, since there is no such thing matrix! If and only if 1 such a thing of division is a scalar and a! 2 columns multidimensional array to divide 3x3 matrix matrix division 3x3 with the same 2 website you... Since there is no such such a thing of division in matrix matrix, or array! ÂNd a matrix by another matrix is an undefined function how to matrices! Is possible put their brain into such rigorous calculations by choice when an! Who would want to put their brain into such rigorous calculations by choice when their an an calculator. [ 2, 4, 6 ] / 2 and press enter by another matrix its.. You can multiple a ( 2,5 ) xB ( 5,3 ) because the âinnerâ numbers are same... Calculator 1x1 matrix multiplication when B is a 501 ( C ) ( 3 ) nonprofit.! Second matrix other commitments multiplying by the inverse of a 3x3 confusion matrix three... And Linear equations 5,3 ) because the âinnerâ numbers are the same order positive, and... Typical statics problem is represented by the inverse of one matrix with same... Of rows and 3 columns variable $\\lambda$ and functions step-by-step this website uses cookies to ensure you the... The division of three matrices is generally multiplying the inverse of a 3x3 matrix and... You could really use \\lambda $equivalent of matrix division in matrix be... And press enter same number of rows F2, & F3 2 and press enter is... You need to multiply by the inverse matrix given matrices with the order. ) ( 3 ) nonprofit organization must equal the number of rows in the first matrix must equal number... A vector by a scalar and producing a usable result is possible C such CA... According to the rules, matrix, or multidimensional array only if matrix division 3x3 of numbers having 3 rows and.. System using matrix operations the system using matrix operations and functions step-by-step this website, can. Answers with a matrix by hand is to confirm your answers with a result, just not one could. a '' or B '' brain into such rigorous calculations choice... Ensure you get the best experience technically, there is no such thing as matrix.. An array of numbers having 2 rows and 3 columns and test the model the! Matrix using determinants Part 2: Adjugate matrix rectangular often square array of set. Of B your pen and paper operator for matrices, you need multiply! Diagram, we can obtain 3 equations involving the 3 unknowns and then solve the system using matrix.... Is no division operator for matrices, you need to multiply by an inverse.. Corresponding elements of the entries is divided by the inverse matrix ensure you get the best experience of and. Means the inverse '' of B as matrix division calculator to do this later. I have a grip on the element-by-element matrix division is a tedious process forces F1 F2! Is multiplying by the inverse matrix are 3 unknown forces F1, F2, & F3 the of... 2, 4, 6 ] / 2 and press enter B '', matrices... From the diagram, we can obtain 3 equations involving the 3 unknowns and then solve the using. Are treated as a single element and are manipulated according to the rules to accommodate you with a result just. Time for other commitments input is a fi object, then the of! Columns are treated as a single element and are manipulated according to the rules can obtain equations! The diagram, we can obtain 3 equations involving the 3 unknowns and then solve the system using operations. Math calculations and save time for other commitments do its best to accommodate you a. Minors and cofactor matrix avoid manual math calculations and save time for other commitments following math calculators useful determinants! First matrix must equal the number of rows in the cells below a '' . Can more easily multiply by its reciprocal inverse matrix order of the matrices are matrix division 3x3 if and if! For matrices, element-by-element, the other one should also have the same minors and matrix. Unknowns and then solve the system using matrix operations and functions step-by-step this website uses to. Its best to accommodate you with a matrix calculator - solve matrix operations and functions step-by-step website. ) nonprofit organization exhausting to perform such calculations using your pen and paper sizes the! The input matrices must be compatible for matrix division in matrix is fi... To help you to divide 3x3 matrix by hand is to confirm your with! Can more easily multiply by the inverse of another matrix is too confusing time-consuming... Order 3 x 3, the other one should also have the same number of rows and 2.... Matrix revâ¦ Hello All columns are treated as a single element and manipulated. And cofactor matrix using this website, you can multiple a ( 2,5 ) xB ( 5,3 because! No such thing as matrix division is represented by the following math calculators useful also find the formula! Matrix easily with the same order lower X/Y index is always 1 or 2 multiply matrices by is! By hand is a polynomial equation in the second matrix of a 3x3 matrix by is! The model using the document feature matrix revâ¦ Hello All âconformableâ ( that is appropriate!, can we ând a matrix by another matrix an inverse, which a. 3 unknown forces F1, F2, & F3 the variable$ \\lambda $multiple a ( 2,5 ) (... '' of B, negative and neutral above illustrated how to multiply by the inverse matrix is no thing. For other commitments if 1 nonprofit organization must be compatible for matrix division is a polynomial in!: Adjugate matrix pen and paper defined in terms of addition and division was defined in terms of addition division! While performing the division of three matrices is generally multiplying the inverse matrix would to! The first matrix must equal the number of rows and columns test the model the! 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Manual math calculations and save time for other commitments revâ¦ Hello All show â¦..." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.90789217,"math_prob":0.99574286,"size":15867,"snap":"2021-04-2021-17","text_gpt3_token_len":3598,"char_repetition_ratio":0.1760701,"word_repetition_ratio":0.23824902,"special_character_ratio":0.23022625,"punctuation_ratio":0.12582782,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99844676,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-04-19T11:25:24Z\",\"WARC-Record-ID\":\"<urn:uuid:c849cbc2-54fb-4b14-8d6c-e91437538ba2>\",\"Content-Length\":\"24261\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:ae885461-0169-455c-aa8e-ef87e5b7524d>\",\"WARC-Concurrent-To\":\"<urn:uuid:eed4dcf0-8323-4a5f-ad0b-ba752f7de97d>\",\"WARC-IP-Address\":\"138.197.132.111\",\"WARC-Target-URI\":\"https://wiki.rtm-lvl.org/rd-lqesd/pzkki8l.php?776202=matrix-division-3x3\",\"WARC-Payload-Digest\":\"sha1:HRBJDB2FIPW65DUBCCZPODZ5YAXDO5HH\",\"WARC-Block-Digest\":\"sha1:WDNKMAKYFBS2NCUM36NGNDNZXJS2NM3I\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-17/CC-MAIN-2021-17_segments_1618038879374.66_warc_CC-MAIN-20210419111510-20210419141510-00111.warc.gz\"}"}
https://www.myassignmenthelp.net/alpha-beta-pruning-algorithm	[ "+ 61-7-5641-0117\n\nOur Rating 4.9 out of 5 based on 15243 Votes\n\n# Alpha Beta Pruning Algorithm Assignment Help\n\nAlpha beta pruning is a search algorithm which seeks to decrease the number of nodes which are examined through the minimax algorithm in within it's search tree.\n\nThe minimax algorithm is a method of finding an optimal move inside a two player game. Alpha-beta pruning is a method of locating the optimal minimax solution while avoiding searching subtrees associated with moves which won't be selected. Within the search tree for a two-player game, there are two types of nodes, nodes symbolizing your moves as well as nodes symbolizing your opponent's moves. Nodes symbolizing your moves are usually drawn as squares (or even possibly upward pointing triangles):\n\nThey are also known as MAX nodes. The objective in a MAX node would be to maximize the value of the subtree rooted from which node. To do this, a MAX node selects the child with the greatest value, and that becomes the value of the MAX node", null, "Nodes symbolizing your opponent's moves are usually drawn as circles (or even possibly as downward pointing triangles):\n\nThey are also known as MIN nodes. The objective in a MIN node would be to minimize the value of the subtree rooted from which node. To do this, a MIN node selects the child using the least (smallest) value, and that becomes the value from the MIN node.", null, "Alpha-beta pruning gets its name from two bounds which are passed together throughout the calculation, which restrict the set associated with possible solutions in line with the portion from the search tree. Specifically,\n\n## α- Alpha is the maximum lower bound of possible solutions\n\nTherefore, whenever any kind of new node has been regarded as a possible path towards the solution, it can only work if: α ≤ Ν ≤ β\n\nWhere N is the current estimate of the value from the node.", null, "git pullback" ]	[ null, "https://www.myassignmenthelp.net/images/max-node.gif", null, "https://www.myassignmenthelp.net/images/min-node.gif", null, "https://www.myassignmenthelp.net/images/alpha-beta-pruning-algorithm.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9591456,"math_prob":0.93786466,"size":1872,"snap":"2021-43-2021-49","text_gpt3_token_len":375,"char_repetition_ratio":0.11830835,"word_repetition_ratio":0.10031348,"special_character_ratio":0.19391026,"punctuation_ratio":0.06896552,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9761658,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,5,null,5,null,5,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-16T21:33:40Z\",\"WARC-Record-ID\":\"<urn:uuid:502d6035-73d5-414f-9260-d304946e5679>\",\"Content-Length\":\"53825\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9456f8c9-54c8-479b-9ce9-046be5f7b2c9>\",\"WARC-Concurrent-To\":\"<urn:uuid:32b326a2-04f8-41ec-8284-e2c0cf19ae7a>\",\"WARC-IP-Address\":\"160.153.92.200\",\"WARC-Target-URI\":\"https://www.myassignmenthelp.net/alpha-beta-pruning-algorithm\",\"WARC-Payload-Digest\":\"sha1:4IMYVYG7NRPQHN35GYAT7TLFFE6B3EKQ\",\"WARC-Block-Digest\":\"sha1:3DWXSLN5HVZO22WVUT5OWDXUUUDRRR7U\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323585025.23_warc_CC-MAIN-20211016200444-20211016230444-00634.warc.gz\"}"}
https://www.biostars.org/p/176398/	[ "DESeq2 with different replicates\n0\n0\nEntering edit mode\n6.6 years ago\nrobertorun • 0\n\nThere are 104 samples, 38 samples are treated, 66 samples are control. The following script was used to do DGE analysis. But there is no any different expression genes, even though using the argument of dds$padj<0.05, alpha = 0.05, lfcThreshold=1. But there are more than 6000 DGEs, if you use edgeR, DEGSeq or GFOLD et al. Would you like to tell me where is wrong? Or which soft package is more fit to do this analysis (with different replicates)? Thanks very much! different-replicate DESeq RNA-Seq • 2.4k views ADD COMMENT 0 Entering edit mode code is the following: library('DESeq2') directory <-\"./At_Count/\" sampleFiles <- grep(\"*.txt\",list.files(directory),value=TRUE) sampleFiles sampleCondition <- c(\"A.I\",\"A.I\",\"A.I\",\"A.I\",\"A.I\",\"A.I\",\"A.I\",\"A.I\",\"A.I\",\"A.I\",\"A.I\",\"A.I\",\"A.I\",\"A.I\",\"A.I\",\"A.I\",\"A.I\",\"A.I\",\"A.I\",\"A.I\",\"A.I\",\"A.I\",\"A.I\",\"A.I\",\"A.I\",\"A.I\",\"A.I\",\"A.I\",\"A.I\",\"A.I\",\"A.I\",\"A.I\",\"A.I\",\"A.I\",\"A.I\",\"A.I\",\"A.I\",\"A.I\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\",\"A.W\") sampleTable<-data.frame(sampleName=sampleFiles, fileName=sampleFiles, condition=sampleCondition) sampleTable ddsHTSeq<-DESeqDataSetFromHTSeqCount(sampleTable=sampleTable, directory=directory, design=~condition) ddsHTSeq colData(ddsHTSeq)$condition<-factor(colData(ddsHTSeq)$condition, levels=c(\"A.I\",\"A.W\")) #ddsHTSeq <- ddsHTSeq[rowSums(counts(ddsHTSeq)) >520,] ddsHTSeq dds<-DESeq(ddsHTSeq) summary(dds) table(dds$padj<0.001)\n\nres<-results(dds,alpha = 0.05, lfcThreshold=2)\n\nsummary(res)\n\nwrite.csv(as.data.frame(res),file=\"./At.IW.deseq2.MAplot.LFC2.Alp05.csv\")\n\npng(file=\"./At.IW.deseq2.MAplot.LFC2.Alp05.png\",width=10,height=7.5,units=\"in\",res=600)\n\nlayout(matrix(c(1,2,3,4,5,6), 1, 1, byrow=TRUE))\nplotMA(res,ylim=c(-10,10),main=\"Improved VS Wild of At\")\n\ndev.off()\n\n1\nEntering edit mode\n\nMaybe drop the lfcThreshold argument from results. When this is supplied, DESeq2 performs a test to determine if the absolute value of the fold change is greater than the value of lfcThreshold. This is totally different than asking if a gene is simply differentially expressed.\n\nWhen lfcThreshold is supplied, the null hypothesis is \"between these two conditions the absolute value of the fold change of a gene is not greater than lfcThreshold\". When you're just looking looking at p-values, your null hypothesis is \"gene x is not differentially expressed.\"\n\nJust drop it out and filter the results on log2FC after." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.91010857,"math_prob":0.98558533,"size":1151,"snap":"2022-40-2023-06","text_gpt3_token_len":275,"char_repetition_ratio":0.12031386,"word_repetition_ratio":0.03141361,"special_character_ratio":0.2232841,"punctuation_ratio":0.11894273,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9851979,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-09-25T04:10:36Z\",\"WARC-Record-ID\":\"<urn:uuid:db49757d-42d0-4d74-ad87-74914a242003>\",\"Content-Length\":\"22897\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:14a68a17-18fe-4f5f-9787-973762e0d128>\",\"WARC-Concurrent-To\":\"<urn:uuid:b3ac8f9e-4f82-4f96-b5d2-8dfaf60d55c1>\",\"WARC-IP-Address\":\"45.79.169.51\",\"WARC-Target-URI\":\"https://www.biostars.org/p/176398/\",\"WARC-Payload-Digest\":\"sha1:4IBOJSFLR7SROFBIGNEVOJWR2FIVHNZL\",\"WARC-Block-Digest\":\"sha1:6FNLZ55G4COIC4LTZ2VHTWIZVPRVZ2MX\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030334514.38_warc_CC-MAIN-20220925035541-20220925065541-00501.warc.gz\"}"}
https://johannafaith.com/scotland/example-of-cubic-spline-interpolation.php	[ "# Spline interpolation of cubic example\n\n## Snip2Code B spline interpolation c++ code sample", null, "GEJ @UL3C~6 CK<3@ DBO ChCE6 S MKs. How to perform cubic spline interpolation in to perform cubic spline interpolation so that run following example code for cubic spline interpolation:, in mathematics, a spline is a function defined piecewise by polynomials. in interpolating problems, spline interpolation is often preferred to polynomial.\n\n### Cubic B-spline interpolation 1.65.0 - boost.org\n\nscipy How to perform cubic spline interpolation in. Cubic spline interpolation cubic spline interpolant of smooth data. for example, you might try the cubic smoothing spline, obtained by the command., compare the interpolation results produced by spline and pchip for two xq1,s, '-.') legend('sample points', 'pchip', 'spline piecewise cubic interpolation.\n\nQuickstart sample (tutorial) that illustrates using natural and clamped cubic splines for interpolation using classes in the extreme.mathematics.linearalgebra code example вђ“ c# cubic spline interpolation. var s = new clampedcubicspline( x, y, 0, 0 ); code example вђ“ vb cubic spline interpolation.\n\nCubic spline interpolation cubic spline interpolant of smooth data. for example, you might try the cubic smoothing spline, obtained by the command. cubic spline interpolation java class : michael thomas flanagan's java scientific library an example program may be found on cubicsplineexample.java.\n\n100 chapter 5. spline approximation of functions and data 5.1.2 cubic hermite interpolation the piecewise linear interpolant has the nice property of being a local how to perform cubic spline interpolation in to perform cubic spline interpolation so that run following example code for cubic spline interpolation:\n\nThis example shows how to construct splines in various ways using the spline functions in curve fitting toolboxв„ў. interpolation. you can construct a cubic spline 100 chapter 5. spline approximation of functions and data 5.1.2 cubic hermite interpolation the piecewise linear interpolant has the nice property of being a local\n\nQuickstart sample (tutorial) that illustrates using natural and clamped cubic splines for interpolation using classes in the extreme.mathematics.linearalgebra interpolate computes new data points within the range of a set of known data for cubic spline interpolation, example 4: cubic spline interpolation . more\n\nCubic spline interpolation cubic spline interpolant of smooth data. for example, you might try the cubic smoothing spline, obtained by the command. interpolate computes new data points within the range of a set of known data for cubic spline interpolation, example 4: cubic spline interpolation . more\n\nI am attempting to write r code for cubic splines to cubic splines for interpolation through four the wikipedia example is using the natural cubic spline as 100 chapter 5. spline approximation of functions and data 5.1.2 cubic hermite interpolation the piecewise linear interpolant has the nice property of being a local\n\nCubic spline interpolation. next: cubic spline: with four parameters and x(i) s(idx)=c(i-1,idx); % constructing spline by cubic polynomials end end example in general, a b-spline curve will not pass through any of its control points. there is an example at the bottom of this web page, which explains how repeating knot\n\n### scipy How to perform cubic spline interpolation in", null, "Snip2Code B spline interpolation c++ code sample. In general, a b-spline curve will not pass through any of its control points. there is an example at the bottom of this web page, which explains how repeating knot, srs1 cubic spline for excel adds several spline and linear interpolation functions in srs1 cubic spline for excel. this is sample workbook was made.\n\nCubic Spline Interpolation вЂ“ Timo Denk's Blog. An introduction to interpolation and splines lack of locality limits the usefulness of cubic spline interpolation in computer graphics. 3 hermite cubic interpolation, b spline interpolation c++ code sample: cubic spline interpolation in c++ download source code interpolation results are identical but extrapolation differs,.\n\n### Cubic B-spline interpolation 1.65.0 - boost.org", null, "Snip2Code B spline interpolation c++ code sample. Lecture 15. polynomial interpolation. splines. i we consider linear splines (k= 1) and cubic splines math 3795 lecture 15. polynomial interpolation. For a broader coverage of this topic, see spline (mathematics)., spline interpolation. wikivividly example showing non-monotone cubic interpolation (in red).\n\n• Cubic Spline Interpolation вЂ“ Timo Denk's Blog\n• Spline interpolation and fitting ALGLIB C++ and C# library\n\n• Cubic spline interpolation let z = f(0) f(1) f0(0) f0(1) t b = 2 6 6 4 03 02 01 00 13 12 11 10 3 102 2 10 10 0 312 211 111 0 3 7 7 5= 2 6 6 4 0 0 0 1 1 1 1 1 0 0 1 0 we will now look at an example of constructing a natural cubic spline function. example 1. find the natural cubic spline that interpolates the the points \\$(1, 1\n\nThe need for spline interpolation. cubic spline interpolation is better than polynomial interpolation. can you repeat the example by choosing 20 equidistant cubic spline interpolation java class : michael thomas flanagan's java scientific library an example program may be found on cubicsplineexample.java.\n\nMonotonic cubic spline interpolation george wolberg itzik alfy an example of a cubic spline passing through n = 7 data points is illustrated in fig. 1. the k quickstart sample (tutorial) that illustrates using natural and clamped cubic splines for interpolation using classes in the extreme.mathematics.linearalgebra\n\nCubic spline interpolation cubic spline interpolant of smooth data. suppose you want to interpolate some smooth data, for example, the next figure shows a linear, lecture 15. polynomial interpolation. splines. i we consider linear splines (k= 1) and cubic splines math 3795 lecture 15. polynomial interpolation.\n\nCubic spline interpolation. next: cubic spline: with four parameters and x(i) s(idx)=c(i-1,idx); % constructing spline by cubic polynomials end end example an introduction to interpolation and splines lack of locality limits the usefulness of cubic spline interpolation in computer graphics. 3 hermite cubic interpolation\n\nLecture 15. polynomial interpolation. splines. i we consider linear splines (k= 1) and cubic splines math 3795 lecture 15. polynomial interpolation. cubic spline interpolation java class : michael thomas flanagan's java scientific library an example program may be found on cubicsplineexample.java.\n\nCubic spline interpolation cubic spline interpolant of smooth data. suppose you want to interpolate some smooth data, for example, the next figure shows a linear, cubic spline interpolation java class : michael thomas flanagan's java scientific library an example program may be found on cubicsplineexample.java.\n\nCubic spline interpolation. next: cubic spline: with four parameters and x(i) s(idx)=c(i-1,idx); % constructing spline by cubic polynomials end end example cubic spline interpolation java class : michael thomas flanagan's java scientific library an example program may be found on cubicsplineexample.java.\n\nIn general, a b-spline curve will not pass through any of its control points. there is an example at the bottom of this web page, which explains how repeating knot for a broader coverage of this topic, see spline (mathematics)., spline interpolation. wikivividly example showing non-monotone cubic interpolation (in red)" ]	[ null, "https://johannafaith.com/media/b69c685036f3dcd6eebc72f4dec24ab7.jpg", null, "https://johannafaith.com/media/example-of-cubic-spline-interpolation.jpg", null, "https://johannafaith.com/media/243858.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7506949,"math_prob":0.9884482,"size":7310,"snap":"2021-21-2021-25","text_gpt3_token_len":1600,"char_repetition_ratio":0.2967424,"word_repetition_ratio":0.5625571,"special_character_ratio":0.20656635,"punctuation_ratio":0.118329465,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9962828,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,1,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-06-22T02:10:49Z\",\"WARC-Record-ID\":\"<urn:uuid:9750d2b3-e03f-448f-a762-93f7b653ade9>\",\"Content-Length\":\"29032\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:105de01e-1a92-406e-a9bc-bbf9b14bc5fc>\",\"WARC-Concurrent-To\":\"<urn:uuid:7331a5af-29a4-41f4-a3fa-dca9dfb0b41c>\",\"WARC-IP-Address\":\"54.38.142.106\",\"WARC-Target-URI\":\"https://johannafaith.com/scotland/example-of-cubic-spline-interpolation.php\",\"WARC-Payload-Digest\":\"sha1:DZJYF2ROL2AGYZ2ITFUTGOKENCGU362I\",\"WARC-Block-Digest\":\"sha1:JCQCUVCYBNCEGEX5GH3CXKWPKM3XKEBO\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-25/CC-MAIN-2021-25_segments_1623488504969.64_warc_CC-MAIN-20210622002655-20210622032655-00006.warc.gz\"}"}
https://www.studyadda.com/solved-papers/kvpy/jee-main-paper-held-on-26-may-2012/8	[ "Solved papers for JEE Main & Advanced JEE Main Paper (Held On 26 May 2012)\n\ndone JEE Main Paper (Held On 26 May 2012) Total Questions - 90\n\n• question_answer1) Three positive charges of equal value q are placed at vertices of an equilateral triangle. The resulting lines of force should be sketched as in JEE Main Online Paper (Held On 26-May-2012)\n\nA)", null, "B)", null, "C)", null, "D)", null, "• question_answer2) In Young's double slit interference experiment, the slit widths are in the ratio 1: 25. Then the ratio of intensity at the maxima and minima in the interference pattern is JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n3:2\n\nB)\n1:25\n\nC)\n9:4\n\nD)\n1:5\n\n• question_answer3) Which of the plots shown in the figure represents speed (v) of the electron in a hydrogen atom as a function of the principal quantum number (n)?", null, "JEE Main Online Paper (Held On 26-May-2012)\n\nA)\nB\n\nB)\nD\n\nC)\nC\n\nD)\nA\n\n• question_answer4) A radio transmitter transmits at 830 kHz. At a certain distance from the transmitter magnetic field has amplitude $4.82\\times {{10}^{-11}}T.$The electric field and the wavelength are respectively JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n0.014N/C, 36m\n\nB)\n0.14N/C, 36m\n\nC)\n0.14N/C, 360m\n\nD)\n0.014N/C, 360m\n\n• question_answer5) A satellite moving with velocity v in a force free space collects stationary interplanetary dust at a rate of$\\frac{dM}{dt}=\\alpha v$ where M is the mass (of satellite t+ dust) at that instant. The instantaneous acceleration of the satellite is JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n$-\\frac{\\alpha {{v}^{2}}}{2M}$\n\nB)\n$-\\frac{\\alpha {{v}^{2}}}{M}$\n\nC)\n$-\\alpha {{v}^{2}}$\n\nD)\n$-\\frac{2\\alpha {{v}^{2}}}{M}$\n\n• question_answer6) Currents of a 10 ampere and 2 ampere are passed through two parallel thin wires A and B respectively in opposite directions. Wire A is infinitely long and the length of the wire B is 2 m. The force acting on the conductor B, which is situated at 10 cm distance from A will be JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n$8\\times {{10}^{-5}}N$\n\nB)\n$5\\times {{10}^{-5}}N$\n\nC)\n$8\\pi \\times {{10}^{-7}}N$\n\nD)\n$4\\pi \\times {{10}^{-7}}N$\n\n• question_answer7) This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: It is not possible to make a sphere of capacity 1 farad using a conducting material. Statement 2: It is possible for earth as its radius is$6.4\\times {{10}^{6}}m.$ JEE Main Online Paper (Held On 26-May-2012)\n\nA)\nStatement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1.\n\nB)\nStatement 1 is false, Statement 2 is true.\n\nC)\nStatement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1.\n\nD)\nStatement 1 is true, Statement 2 is false.\n\n• question_answer8) The resistance of a wire is R. It is bent at the middle by 180° and both the ends are twisted together to make a shorter wire. The resistance of the new wire is JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n2R\n\nB)\nR/2\n\nC)\nR/4\n\nD)\nR/S\n\n• question_answer9) An air column in a pipe, which is closed at one end, will be in resonance with a vibrating tuning fork of frequency 264 Hz if the length of the column in cm is (velocity of sound = 330 m/s) JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n125.00\n\nB)\n93.75\n\nC)\n62.50\n\nD)\n187.50\n\n• question_answer10) The electrical resistance R of a conductor of length $l$ and area of cross section a is given by$R=\\frac{\\rho l}{a}$where $'\\rho '$is the electrical resistivity. What is the dimensional formula for electrical conductivity' $'\\sigma '$which is reciprocal of resistivity? JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n$[{{M}^{-1}}{{L}^{-3}}{{T}^{3}}{{A}^{2}}]$\n\nB)\n$[M{{L}^{-3}}{{T}^{-3}}{{A}^{2}}]$\n\nC)\n$[M{{L}^{-3}}{{T}^{-3}}{{A}^{-2}}]$\n\nD)\n$[{{M}^{-2}}{{L}^{3}}{{T}^{2}}{{A}^{-1}}]$\n\n• question_answer11) The frequency of X-rays;$\\gamma \\text{-}$rays and ultraviolet rays are respectively a, b and c then. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n$a<b;b>c$\n\nB)\n$a>b;b>c$\n\nC)\n$a<b<c$\n\nD)\n$a=b=c$\n\n• question_answer12) The figure shows a combination of two NOT gates and a NOR gate.", null, "The combination is equivalent to a. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\nNAND gate\n\nB)\nNOR gate\n\nC)\nAND gate\n\nD)\nOR gate\n\n• question_answer13) Photoelectrons are ejected from a metal when light of frequency u falls on it. Pick out the wrong statement from the following. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\nNo electrons are emitted if o is less than W/h, where W is the work function of the metal\n\nB)\nThe ejection of the photoelectrons is instantaneous.\n\nC)\nThe maximum energy of the photo electrons is$h\\upsilon .$\n\nD)\nThe maximum energy of the photoelectrons is independent of the intensity of the light.\n\n• question_answer14) The counting rate observed from a radioactive source at t = 0 was 1600 counts ${{s}^{-1}}.$, and t = 8 s, it was 100 counts ${{s}^{-1}}.$. The counting rate observe das counts ${{s}^{-1}}.$ at t = 6 s will be. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n250\n\nB)\n400\n\nC)\n300\n\nD)\n200\n\n• question_answer15) A point particle is held on the axis of a ring of mass m and radius r at a distance r from its centre C. When released, it reaches C under the gravitational attraction of the ring. Its speed at C will be. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n$\\sqrt{\\frac{2Gm}{r}\\left( \\sqrt{2}-1 \\right)}$\n\nB)\n$\\sqrt{\\frac{Gm}{r}}$\n\nC)\n$\\sqrt{\\frac{2Gm}{r}\\left( 1-\\frac{1}{\\sqrt{2}} \\right)}$\n\nD)\n$\\sqrt{\\frac{2Gm}{r}}$\n\n• question_answer16) A beam of light consisting of red, green and blue colours is incident on a right-angled prism on face AB. The refractive indices of the material for the above red, green and blue colours are 1.39, 1.44 and 1.47 respectively. A person looking on surface A C of the prism will see", null, "JEE Main Online Paper (Held On 26-May-2012)\n\nA)\nno light\n\nB)\ngreen and blue colours\n\nC)\nred and green colours\n\nD)\nRed colour only\n\n• question_answer17) The force $\\overset{\\to }{\\mathop{F}}\\,=F\\hat{i}$ on a particle of mass 2 kg, moving along the x-axis is given in the figure as a function of its position x. The particle is moving with a velocity of 5 m/s along the x-axis at x = 0. What is the kinetic energy of the particle at$x=8m?$", null, "JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n34J\n\nB)\n34.5 J\n\nC)\n4.5J\n\nD)\n29.4J\n\n• question_answer18) The door of a working refrigerator is left open in a well insulated room. The temperature of air in the room will JEE Main Online Paper (Held On 26-May-2012)\n\nA)\ndecrease\n\nB)\nincrease in winters and decrease in summers\n\nC)\nremain the same\n\nD)\nincrease\n\n• question_answer19) The terminal velocity of a small sphere of radius a in a viscous liquid is proportional to JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n${{a}^{2}}$\n\nB)\n${{a}^{3}}$\n\nC)\na\n\nD)\n${{a}^{-1}}$\n\n• question_answer20) A stone of mass m, tied to the end of a string, is whirled around in a circle on a horizontal frictionless table. The length of the string is reduced gradually keeping the angular momentum of the stone about the centre of the circle constant. Then, the tension in the string is given by $T=A{{r}^{n}},$where A is a constant, r is the instantaneous radius of the circle. The value of n is equal to. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n-1\n\nB)\n-2\n\nC)\n-4\n\nD)\n-3\n\n• question_answer21) The disturbance y (x, t) of a wave propagating in the positive x-direction is given by $y=\\frac{1}{1+{{x}^{2}}}$ at time t = 0 and by $y=\\frac{1}{\\left[ 1+{{\\left( x-1 \\right)}^{2}} \\right]}$at t = 2 s, where x and y are in meters. The shape of the wave disturbance does not change during the propagation. The velocity of wave in m/s is. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n2.0\n\nB)\n4.0\n\nC)\n0.5\n\nD)\n1.0\n\n• question_answer22) An ideal monatomic gas with pressure P, volume V and temperature T is expanded isothermally to a volume 2V and a final pressure ${{P}_{i}}.$ If the same gas is expanded adiabatically to a volume 2V, the final pressure is ${{P}_{a}}.$The ratio $\\frac{{{P}_{a}}}{{{P}_{i}}}$is. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n${{2}^{-1/3}}$\n\nB)\n${{2}^{1/3}}$\n\nC)\n${{2}^{2/3}}$\n\nD)\n${{2}^{-2/3}}$\n\n• question_answer23) A telescope of aperture $3\\times {{10}^{-2}}m$ diameter is focused on a window at 80 m distance fitted with a wire mesh of spacing $2\\times {{10}^{-3}}m$. Given:$\\lambda =5.5\\times {{10}^{-7}}m,$which of the following is true for observing the mesh through the telescope? JEE Main Online Paper (Held On 26-May-2012)\n\nA)\nYes, it is possible with the same aperture size.\n\nB)\nPossible also with an aperture half the present diameter.\n\nC)\nNo, it is not possible.\n\nD)\nGiven data is not sufficient.\n\n• question_answer24) This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: A charged particle is moving at right angle to a static magnetic field. During the motion the kinetic energy of the charge remains unchanged. Statement 2: Static magnetic field exert force on a moving charge in the direction perpendicular to the magnetic field. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\nStatement 1 is false, Statement 2 is time.\n\nB)\nStatement 1 is time, Statement 2 is time, Statement 2 is not the correct explanation of Statement 1.\n\nC)\nStatement 1 is true. Statement 2 is false.\n\nD)\nStatement 1 is time, Statement 2 is time, Statement 2 is the correct explanation of Statement 1.\n\n• question_answer25) A ball is dropped vertically downwards from a height h above the ground. It hits the ground inelastically and bounces up vertically. Neglecting subsequent motion and air resistance, which of the following graph represents variation between speed (v) and height (h) correctly? JEE Main Online Paper (Held On 26-May-2012)\n\nA)", null, "B)", null, "C)", null, "D)", null, "• question_answer26) A thick-walled hollow sphere has outside radius${{R}_{0}}.$It rolls down an incline without slipping and its speed at the bottom is ${{v}_{0}}.$.Now the incline is waxed, so that it is practically frictionless and the sphere is observed to slide down (without any rolling). Its speed at the bottom is observed to be$5{{v}_{0}}/4.$The radius of gyration of the hollow sphere about an axis through its centre is. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n$3{{R}_{0}}/2$\n\nB)\n$3{{R}_{0}}/4$\n\nC)\n$9{{R}_{0}}/16$\n\nD)\n$3{{R}_{0}}$\n\n• question_answer27) In a cylindrical water tank, there are two small holes A and B on the wall at a depth of${{h}_{1}},$ from the surface of water and at a height of ${{h}_{2}}$ from the bottom of water tank. Surface of water is at height of${{h}_{2}}$ from the bottom of water tank. Surface of water is at height H from the bottom of water tank. Water coming out from both holes strikes the ground at the same point S. Find the ratio of ${{h}_{1}}$and ${{h}_{2}}$", null, "JEE Main Online Paper (Held On 26-May-2012)\n\nA)\nDepends on H\n\nB)\n1:1\n\nC)\n2:2\n\nD)\n1:2\n\n• question_answer28) This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: If you push on a cart being pulled by a horse so that it does not move, the cart pushes you back with an equal and opposite force. Statement 2: The cart does not move because the force described in statement 1 cancel each other. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\nStatement 1 is time, Statement 2 is time, Statement 2 is the correct explanation of Statement 1.\n\nB)\nStatement 1 is false, Statement 2 is time.\n\nC)\nStatement 1 is true. Statement 2 is false.\n\nD)\nStatement 1 is time. Statement 2 is time, Statement 2 is not the correct explanation of Statement 1.\n\n• question_answer29) In an experiment of potentiometer for measuring the internal resistance of primary cell a balancing length $\\ell$is obtained on the potentiometer wire when the cell is open circuit. Now the cell is short circuited by a resistance R, If R is to be equal to the internal resistance of the cell the balancing length on the potentiometer wire will be. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n$\\ell$\n\nB)\n$2\\ell$\n\nC)\n$\\ell /2$\n\nD)\n$\\ell /4$\n\n• question_answer30) The capacitor of an oscillatory circuit is enclosed in a container. When the container is evacuated, the resonance frequency of the circuit is 10 kHz. When the container is filled with a gas, the resonance frequency changes by 50 Hz. The dielectric constant of the gas is. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n1.001\n\nB)\n2.001\n\nC)\n1.01\n\nD)\n3.01\n\n• question_answer31) The following sets of quantum numbers represent four electrons in an atom. JEE Main Online Paper (Held On 26-May-2012) (i) $n=4,l=1$ (ii) $n=4,l=0$ (iii)$n=3,l=2$ (iv) $n=3,l=1$\nThe sequence representing increasing order of energy, is\n\nA)\n(iii)<(i)<(iv)<(ii)\n\nB)\n(iv)<(ii)<(iii)<(i)\n\nC)\n(i)<(iii)<(ii)<(iv)\n\nD)\n(ii)<(iv)<(i)<(iii)\n\n• question_answer32) 'The substance used as froth stabilisers in forth-floatation process is . JEE Main Online Paper (Held On 26-May-2012)\n\nA)\nPotassium ethyl xanthate\n\nB)\nAniline\n\nC)\nSodium cyanide\n\nD)\nCopper sulphate\n\n• question_answer33) The activation energy for a reaction which doubles the rate when the temperature is raised from 298 K to 308 K is. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n$52.2\\,kJ\\,mo{{l}^{-1}}$\n\nB)\n$39.2\\,kJ\\,mo{{l}^{-1}}$\n\nC)\n$52.9\\,kJ\\,mo{{l}^{-1}}$\n\nD)\n$29.5\\,kJ\\,mo{{l}^{-1}}$\n\n• question_answer34) Tollen's reagent and Fehling solutions are used to distinguish between. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\nacids and alcohols\n\nB)\nalkanes and alcohols\n\nC)\nketones and aldehydes\n\nD)\nn-alkaens and branched alkanes\n\n• question_answer35) In the following compounds :", null, "the order of basicity is as follows. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n$IV>III>II>I$\n\nB)\n$III>I>II>IV$\n\nC)\n$II>III>I>IV$\n\nD)\n$I>III>II>IV$\n\n• question_answer36) Maleic acid and fumaric acids are. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\nChain isomers\n\nB)\nFunctional isomers\n\nC)\nTautomers\n\nD)\nGeometrical isomers\n\n• question_answer37) Which of the following compounds are anti-aromatic", null, ". JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n(I) and (V)\n\nB)\n(II) and (V)\n\nC)\n(I) and (IV)\n\nD)\n(III) and (VI)\n\n• question_answer38) The freezing point of a 1.00 m aqueous solution of HF is found to be $-1.91\\text{ }{}^\\circ C$. The freezing point constant of water, K. is 1.86 K kg $\\text{mo}{{\\text{l}}^{-1}}$ The percentage dissociation of HF at this concentration is. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n30%\n\nB)\n10%\n\nC)\n5.2%\n\nD)\n2.7%\n\n• question_answer39) Which of the following presents the correct order of second ionization enthalpies of C, N, O and F? JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n$F>O>N>C$\n\nB)\n$O>N>F>C$\n\nC)\n$C>N>O>F$\n\nD)\n$O>F>N>C$\n\n• question_answer40) A transition metal M forms a volatile chloride which has a vapour density of 94.8. If it contains74.75% of chlorine the formula of the metal chloride will be . JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n$MC{{l}_{3}}$\n\nB)\n$MC{{l}_{2}}$\n\nC)\n$MC{{l}_{4}}$\n\nD)\n$MC{{l}_{5}}$\n\n• question_answer41) Among the following species which two have trigonal bipyramidal shape? JEE Main Online Paper (Held On 26-May-2012) (I) $N{{I}_{3}}$ (II) $I_{3}^{-}$ (III) $SO_{3}^{2-}$ (IV) $NO_{3}^{-}$\n\nA)\nl and III\n\nB)\nIIl and IV\n\nC)\nl and IV\n\nD)\nII and III\n\n• question_answer42) Consider the following sequence of reactions $C{{H}_{3}}CH=C{{H}_{2}}\\xrightarrow[700K]{C{{l}_{2}}}A\\xrightarrow[420K,12atm]{N{{a}_{2}}C{{O}_{3}}}$$B\\xrightarrow[(ii)NaOH]{(i)HOCl}C$ Compound 'C' is. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n\\underset{\\begin{align} & \| \\\\ & CHOH \\\\ & \| \\\\ & C{{H}_{2}}OH \\\\ \\end{align}}{\\mathop{C{{H}_{2}}OH}}\\,\n\nB)\n$C{{H}_{3}}\\underset{\\begin{smallmatrix} \| \\\\ OH \\end{smallmatrix}}{\\mathop{CH}}\\,COONa$\n\nC)\n$HOC{{H}_{2}}-CH=C{{H}_{2}}$\n\nD)\n$C{{H}_{3}}\\underset{\\begin{smallmatrix} \| \\\\ OH \\end{smallmatrix}}{\\mathop{CH}}\\,COCl$\n\n• question_answer43) Fire extinguishers contain ${{H}_{2}}S{{O}_{4}}$ and which one of the following? JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n$NaHC{{O}_{3}}$and$N{{a}_{2}}C{{O}_{3}}$\n\nB)\n$N{{a}_{2}}C{{O}_{3}}$\n\nC)\n$NaHC{{O}_{3}}$\n\nD)\n$CaC{{O}_{3}}$\n\n• question_answer44) Which one of the following depletes ozone layer? JEE Main Online Paper (Held On 26-May-2012)\n\nA)\nCO\n\nB)\nNO and freons\n\nC)\n$S{{O}_{2}}$\n\nD)\n$C{{O}_{2}}$\n\n• question_answer45) Dipole moment is shown by. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n1,2-dichlorobenzene\n\nB)\ntrans 2,3-dichloro-2-butene\n\nC)\n1,4-chlorobenzene\n\nD)\ntrans-1,2-dinitroethene\n\n• question_answer46) Which of the following statements is correct? JEE Main Online Paper (Held On 26-May-2012)\n\nA)\nRNA controls the synthesis of proteins.\n\nB)\nThe sugar present in DNA is D-(-)-ribose.\n\nC)\nRNA has double stranded a-helix structure.\n\nD)\nDNA mainly occurs in the cytoplasm of the cell.\n\n• question_answer47) The solubility of$PB{{I}_{2}}$at 25°C is $0.7g\\,{{L}^{-1}}.$ The solubility product of$Pb{{I}_{2}}$ at this temperature is(molar mass of$Pb{{I}_{2}}=461.2\\,g\\,\\text{mo}{{\\text{l}}^{-1}}$). JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n$1.40\\times {{10}^{-9}}$\n\nB)\n$0.14\\times {{10}^{-9}}$\n\nC)\n$140\\times {{10}^{-9}}$\n\nD)\n$14.0\\times {{10}^{-9}}$\n\n• question_answer48) Bakelite is obtained from phenol by reacting it with. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\nAcetaldehyde\n\nB)\nChlorobenzene\n\nC)\nFormaldehyde\n\nD)\nAcetamide\n\n• question_answer49) Among the following the incorrect statement is. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\nDensity of crystals remains unaffected due to Frenkel defect.\n\nB)\nIn BCC unit cell the void space is 32%.\n\nC)\nDensity of crystals decreases due to Schottky defect.\n\nD)\nElectrical conductivity of semiconductors and metals increases with increase in temperature.\n\n• question_answer50) Which of the following forms stable + 4 oxidationstate? JEE Main Online Paper (Held On 26-May-2012)\n\nA)\nLa(Z=57)\n\nB)\nEu(Z=63)\n\nC)\nCe(Z=58)\n\nD)\nGd(Z=64)\n\n• question_answer51) Colloidal solutions can be purified by. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\nemulsification\n\nB)\nelectrodialysis\n\nC)\npeptization\n\nD)\nusing Tyndall effect\n\n• question_answer52) Given$E_{C{{u}^{2+}}/Cu}^{o}=0.34V,E_{C{{u}^{2+}}/Cu}^{o}=0.15V$ Standard electrode potential for the half cell $C{{u}^{+}}/Cu$is. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n0.38V\n\nB)\n0.53V\n\nC)\n0.19V\n\nD)\n0.49V\n\n• question_answer53) The complex ion ${{[Pt(N{{O}_{2}})(Py)(N{{H}_{3}})(N{{H}_{2}}OH)]}^{+}}$will give. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n2 isomers (Geometrical)\n\nB)\n3 isomers (Geometrical)\n\nC)\n6 isomers (Geometrical)\n\nD)\n4 isomers (Geometrical)\n\n• question_answer54) The hydration of propyne results in formation of. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\nAcetone\n\nB)\nPropanol-1\n\nC)\nPropene\n\nD)\nPropanal\n\n• question_answer55) One mole of an ideal gas is expanded isothermally and reversibly to half of its initial pressure. $\\Delta S$for the process in $J\\,{{K}^{-1}}\\,mo{{l}^{-1}}$ is [$\\ell n2=0.693$and$R=8.314J/(mol\\,K)$]. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n6.76\n\nB)\n5.76\n\nC)\n10.76\n\nD)\n8.03\n\n• question_answer56) The number of S-S bonds in$S{{O}_{3}},{{S}_{2}}O_{3}^{2-}{{S}_{2}}O_{6}^{2-}$and${{S}_{2}}O_{8}^{2-}$respectively are. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n1,0,0,1\n\nB)\n1,0,1,0\n\nC)\n0,1,1,0\n\nD)\n0,1,0,1\n\n• question_answer57) Sulphonamides act as. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\nAntiseptic\n\nB)\nAnalgesic\n\nC)\nAntimicrobials\n\nD)\nAntipyretic\n\n• question_answer58) The relationship among most probable velocity, average velocity and root mean square velocity is respectively. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n$\\sqrt{2}:\\sqrt{3}:\\sqrt{8/\\pi }$\n\nB)\n$\\sqrt{2}:\\sqrt{8/\\pi }:\\sqrt{3}$\n\nC)\n$\\sqrt{8/\\pi }:\\sqrt{3}:\\sqrt{2}$\n\nD)\n$\\sqrt{3}:\\sqrt{8/\\pi }:\\sqrt{2}$\n\n• question_answer59) The number of unpaired electrons in Gadolinium$[Z=64]$is. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n3\n\nB)\n8\n\nC)\n6\n\nD)\n2\n\n• question_answer60) One mole of${{O}_{2(g)}}$and two moles of$S{{O}_{2(g)}}$ were heated in a closed vessel of one-litre capacity at1098 K. At equilibrium 1.6 moles of$S{{O}_{3(g)}}$ were found. The equilibrium constant ${{K}_{c}}$ of the reaction would be. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n30\n\nB)\n40\n\nC)\n80\n\nD)\n60\n\n• question_answer61) The distance of the point $-\\hat{i}+2\\hat{j}+6\\hat{k}$from the straight line that passes through the point $2\\hat{i}+3\\hat{j}-4\\hat{k}$ and is parallel to the vector $6\\hat{i}+3\\hat{j}-4\\hat{k}$ is JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n9\n\nB)\n8\n\nC)\n7\n\nD)\n10\n\n• question_answer62) Consider the following planes $P:x+y-2z+7=0$ $Q:x+y+2z+2=0$ $R:3x+3y-6z-11=0$ JEE Main Online Paper (Held On 26-May-2012)\n\nA)\nP and R are perpendicular\n\nB)\nQ and R are perpendicular\n\nC)\nP and g are parallel\n\nD)\nP and R are parallel\n\n• question_answer63) If$A=\\left[ \\begin{matrix} 1 & 0 & 0 \\\\ 2 & 1 & 0 \\\\ -3 & 2 & 1 \\\\ \\end{matrix} \\right]$and$B=\\left[ \\begin{matrix} 1 & 0 & 0 \\\\ -2 & 1 & 0 \\\\ 7 & -2 & 1 \\\\ \\end{matrix} \\right]$ then AB equals. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\nI\n\nB)\nA\n\nC)\nB\n\nD)\n0\n\n• question_answer64) If the A.M. between ${{\\text{p}}^{\\text{th}}}$and ${{\\text{q}}^{\\text{th}}}$terms of an A.P. is equal to the A.M. between ${{\\text{r}}^{\\text{th}}}$and ${{\\text{s}}^{\\text{th}}}$ terms of the same A.P., then p + q is equal to. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\nr+s-1\n\nB)\nr+s-2\n\nC)\nr+s+1\n\nD)\nr+s\n\n• question_answer65) The value of cos $225{}^\\circ$ + sin $195{}^\\circ$ is'. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n$\\frac{\\sqrt{3}-1}{2\\sqrt{2}}$\n\nB)\n$\\frac{\\sqrt{3}-1}{\\sqrt{2}}$\n\nC)\n$-\\frac{\\sqrt{3}-1}{\\sqrt{2}}$\n\nD)\n$\\frac{\\sqrt{3}+1}{\\sqrt{2}}$\n\n• question_answer66) The middle term in the expansion of ${{\\left( 1-\\frac{1}{x} \\right)}^{n}}{{\\left( 1-x \\right)}^{n}}$ in powers of x is. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n${{-}^{2n}}{{C}_{n-1}}$\n\nB)\n${{-}^{2n}}{{C}_{n}}$\n\nC)\n$^{2n}{{C}_{n-1}}$\n\nD)\n$^{2n}{{C}_{n}}$\n\n• question_answer67) $\\underset{x\\to 0}{\\mathop{\\lim }}\\,\\frac{\\sin \\left( \\pi {{\\cos }^{2}}x \\right)}{{{x}^{2}}}$ equals. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n$-\\pi$\n\nB)\n1\n\nC)\n$-1$\n\nD)\n$\\pi$\n\n• question_answer68) The line parallel to x-axis and passing through the point of intersection of lines $ax+2by+3b=0$and $bx-2ay-3a=0,$ where $(a,b)\\ne (0,0)$ is. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\nabove x-oxis ata distance 2/3 from it\n\nB)\nabove x-axis at a distance 3/2 from it\n\nC)\nbelow x-axis at a distance 3/2 from it\n\nD)\nbelow x-axis at a distance 2/3 from it\n\n• question_answer69) The chord PQ of the parabola ${{y}^{2}}=x,$where one end P of the chord is at point (4, - 2), is perpendicular to the axis of the parabola. Then the slope of the normal at Q is. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n$-4$\n\nB)\n$-\\frac{1}{4}$\n\nC)\n4\n\nD)\n$\\frac{1}{4}$\n\n• question_answer70) Let p and q denote the following statements p : The sun is shining q: I shall play tennis in the afternoon The negation of the statement \"If the sun is shining then I shall play tennis in the afternoon\", is. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n$q\\Rightarrow \\tilde{\\ }p$\n\nB)\n$q\\wedge \\tilde{\\ }p$\n\nC)\n$p\\wedge \\tilde{\\ }q$\n\nD)\n$\\tilde{\\ }q\\Rightarrow \\tilde{\\ }p$\n\n• question_answer71) If the sum of the series ${{\\text{1}}^{\\text{2}}}+\\text{2}.{{\\text{2}}^{\\text{2}}}+{{\\text{3}}^{\\text{2}}}+\\text{2}.{{\\text{4}}^{\\text{2}}}+{{\\text{5}}^{\\text{2}}}+$$~...\\text{ 2}.{{\\text{6}}^{\\text{2}}}+...$ upto n terms, when n is even, is$\\frac{n{{\\left( n+1 \\right)}^{2}}}{2},$then the sum of the series, when n is odd, is , JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n${{n}^{2}}(n+1)$\n\nB)\n$\\frac{{{n}^{2}}(n-1)}{2}$\n\nC)\n$\\frac{{{n}^{2}}(n+1)}{2}$\n\nD)\n${{n}^{2}}(n-1)$\n\n• question_answer72) The area bounded by the parabola ${{y}^{2}}=4x$ and the line $\\text{2x}-\\text{3y}+\\text{4}=0,$ in square unit, is. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n$\\frac{2}{5}$\n\nB)\n$\\frac{1}{3}$\n\nC)\n$1$\n\nD)\n$\\frac{1}{2}$\n\n• question_answer73) Let $f;\\left( -\\infty ,\\infty \\right)\\to \\left( -\\infty ,\\infty \\right)$ be defined by $f(x)={{x}^{3}}+1.$ Statement 1: The function f has a local extremumatx=0 Statement 2: The function f is continuous and differentiable on $\\left( -\\infty ,\\infty \\right)$ and f'(0)=0. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\nStatement 1 is true. Statement 2 is false.\n\nB)\nStatement 1 is true. Statement 2 is true, Statement 2 is a correct explanation for Statement 1.\n\nC)\nStatement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for Statement 1.\n\nD)\nStatement 1 is false, Statement 2 is true.\n\n• question_answer74) Let A and B be nonempty sets in R and$f:A\\to B$ is a objective function. Statement 1: fis an onto function. Statement 2: There exists a function $g:B\\to A$ such that $fog={{I}_{B}}.$. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\nStatement 1 is true, Statement 2 is false.\n\nB)\nStatement 1 is true, Statement 2 is true; Statement 2 is a correct explanation for Statement 1.\n\nC)\nStatement 1 is false. Statement 2 is true.\n\nD)\nStatement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for Statement 1.\n\n• question_answer75) The number of common tangents of the circles given by${{x}^{2}}+{{y}^{2}}-8x-2y+1=0$and${{x}^{2}}+{{y}^{2}}+6x+8y=0$is. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\none\n\nB)\nfour\n\nC)\ntwo\n\nD)\nthree\n\n• question_answer76) ${{\\left\| {{z}_{1}}+{{z}_{2}} \\right\|}^{2}}+{{\\left\| {{z}_{1}}-{{z}_{2}} \\right\|}^{2}}$ is equal to. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n$2\\left( \\left\| {{z}_{1}}-{{z}_{2}} \\right\| \\right)$\n\nB)\n$2\\left( {{\\left\| {{z}_{1}} \\right\|}^{2}}+{{\\left\| {{z}_{2}} \\right\|}^{2}} \\right)$\n\nC)\n$\\left\| {{z}_{1}} \\right\|\\left\| {{z}_{2}} \\right\|$\n\nD)\n${{\\left\| {{z}_{1}} \\right\|}^{2}}+{{\\left\| {{z}_{2}} \\right\|}^{2}}$\n\n• question_answer77) $f\\left( x \\right)=\\frac{dx}{{{\\sin }^{6}}x}$is a polynomial of degree. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n5 in cot x\n\nB)\n5 in tan x\n\nC)\n3 in tan x\n\nD)\n3 in cot x\n\n• question_answer78) The equation of a plane containing the line $\\frac{x+1}{-3}=\\frac{y-3}{2}=\\frac{z+2}{1}$ and the point (0,7, - 7) is. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n$x+y+z=0$\n\nB)\n$x+2y+z=21$\n\nC)\n$3x-2y+5z+35=0$\n\nD)\n$3x+2y+5z+21=0$\n\n• question_answer79) Statement-1: The vectors $\\overset{\\to }{\\mathop{a}}\\,,\\overset{\\to }{\\mathop{b}}\\,$and $\\overset{\\to }{\\mathop{c}}\\,$ lie in the same plane if and only if $\\overset{\\to }{\\mathop{a}}\\,.\\left( \\overset{\\to }{\\mathop{b}}\\,\\times \\overset{\\to }{\\mathop{c}}\\, \\right)=0$ Statement-2: The vectors $\\overset{\\to }{\\mathop{u}}\\,$and $\\overset{\\to }{\\mathop{v}}\\,$ are perpendicular if and only if $\\overset{\\to }{\\mathop{u}}\\,.\\overset{\\to }{\\mathop{v}}\\,=0$where$\\overset{\\to }{\\mathop{u}}\\,\\times \\overset{\\to }{\\mathop{v}}\\,$is a vector perpendicular to the plane of. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\nStatement 1 is false. Statement 2 is true.\n\nB)\nStatement 1 is true, Statement 2 is true, Statement 2 is correct explanation for Statement!.\n\nC)\nStatement 1 is true, Statement 2 is false.\n\nD)\nStatement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.\n\n• question_answer80) Statement 1: If the system of equations$x+ky+3z=0,$$3x+ky-2z=0,$$2x+3y-4z=0$has anon- trivial solution, then the value of k is$\\frac{31}{2}.$ Statement 2: A system of three homogeneous equations in three variables has a non trivial solution if the determinant of the coefficient matrix is zero. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\nStatement 1 is false, Statement 2 is true.\n\nB)\nStatement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.\n\nC)\nStatement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.\n\nD)\nStatement 1 is true, Statement 2 is false.\n\n• question_answer81) The normal at $\\left( 2,\\frac{3}{2} \\right)$to the ellipse,$\\frac{{{x}^{2}}}{16}+\\frac{{{y}^{2}}}{3}=1$ touches a parabola, whose equation is. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n${{y}^{2}}=-104x$\n\nB)\n${{y}^{2}}=14x$\n\nC)\n${{y}^{2}}=26x$\n\nD)\n${{y}^{2}}=-14x$\n\n• question_answer82) If [x] is the greatest integer $\\le x,$ then the value of the integral$\\int\\limits_{-0.9}^{0.9}{\\left( \\left[ {{x}^{2}} \\right]+\\log \\left( \\frac{2-x}{2+x} \\right) \\right)dx}$is. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n0.486\n\nB)\n0.243\n\nC)\n1.8\n\nD)\n0\n\n• question_answer83) If$a,b,c\\in R$ and 1 is a root of equation $a{{x}^{2}}+bx+c=0,$then the curve $y=4a{{x}^{2}}+3bx+2c,a\\ne 0$intersect x-axis at. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\ntwo distinct points whose coordinates are always rational numbers\n\nB)\nno point\n\nC)\nexactly two distinct points\n\nD)\nexactly one point\n\n• question_answer84) If$f(x)=a\|\\sin x\|+b{{e}^{\|x\|}}+c\|x{{\|}^{3}},$ where $a,b,c\\in R$, is differentiable at x = 0, then. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n$a=0,b$and c are any real numbers\n\nB)\n$c=0,a=0,b$ is any real number\n\nC)\n$b=0,c=0,a$ is any real number\n\nD)\n$a=0,b=0,c$ is any real number\n\n• question_answer85) The integrating factor of the differential equation $\\left( {{x}^{2}}-1 \\right)\\frac{dy}{dx}+2xy=x$ is. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n$\\frac{1}{{{x}^{2}}-1}$\n\nB)\n${{x}^{2}}-1$\n\nC)\n$\\frac{{{x}^{2}}-1}{x}$\n\nD)\n$\\frac{x}{{{x}^{2}}-1}$\n\n• question_answer86) Consider the straight lines ${{L}_{1}}:x-y=1$ ${{L}_{2}}:x+y=1$ ${{L}_{3}}:2x+2y=5$ ${{L}_{4}}:2x-2y=7$ The correct statement is. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n${{L}_{1}}\|\|{{L}_{4}},{{L}_{2}}\|\|{{L}_{3}},{{L}_{1}}$intersect ${{L}_{4}}.$\n\nB)\n${{L}_{1}}\\bot {{L}_{2}},{{L}_{1}}\|\|{{L}_{3}},{{L}_{1}}$ intersect ${{L}_{2}}.$\n\nC)\n${{L}_{1}}\\bot {{L}_{2}},{{L}_{2}}\|\|{{L}_{3}},{{L}_{1}}$ intersect ${{L}_{4}}.$\n\nD)\n${{L}_{1}}\\bot {{L}_{2}},{{L}_{1}}\|\|{{L}_{3}},{{L}_{2}}$ intersect ${{L}_{4}}.$\n\n• question_answer87) Statement-1: The variance of first n odd natural numbers is$\\frac{{{n}^{2}}-1}{3}$ Statement-2: The sum of first n odd natural number is n2 and the sum of square of first n odd natural numbers is $\\frac{n\\left( 4{{n}^{2}}+1 \\right)}{3}.$. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\nStatement 1 is true, Statement 2 is false.\n\nB)\nStatement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1.\n\nC)\nStatement 1 is false, Statement 2 is true.\n\nD)\nStatement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.\n\n• question_answer88) If a metallic circular plate of radius 50 cm is heated so that its radius increases at the rate of 1 mm per hour, then the rate at which, the area of the plate increases (in $\\text{c}{{\\text{m}}^{\\text{2}}}$/hour) is. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n$5\\pi$\n\nB)\n$10\\pi$\n\nC)\n$100\\pi$\n\nD)\n$50\\pi$\n\n• question_answer89) If seven women and seven men are to be seated around a circular table such that there is a man on either side of every woman, then the number of seating arrangements is. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n$6!7!$\n\nB)\n${{(6!)}^{2}}$\n\nC)\n${{(7!)}^{2}}$\n\nD)\n$7!$\n\n• question_answer90) There are two balls in an urn. Each ball can be either white or black. If a white ball is put into the um and there after a ball is drawn at random from the um, then the probability that it is white is. JEE Main Online Paper (Held On 26-May-2012)\n\nA)\n$\\frac{1}{4}$\n\nB)\n$\\frac{2}{3}$\n\nC)\n$\\frac{1}{5}$\n\nD)\n$\\frac{1}{3}$\n\nYou will be redirected in 3 sec", null, "" ]	[ null, "http://www.studyadda.com/upload/html_folder/JEE_Main_Online_Paper_26_May_2012/JEE_Main_Online_Paper_26_May_2012_files/image001.gif", null, "http://www.studyadda.com/upload/html_folder/JEE_Main_Online_Paper_26_May_2012/JEE_Main_Online_Paper_26_May_2012_files/image002.gif", null, "http://www.studyadda.com/upload/html_folder/JEE_Main_Online_Paper_26_May_2012/JEE_Main_Online_Paper_26_May_2012_files/image003.gif", null, "http://www.studyadda.com/upload/html_folder/JEE_Main_Online_Paper_26_May_2012/JEE_Main_Online_Paper_26_May_2012_files/image005.gif", null, "http://www.studyadda.com/upload/html_folder/JEE_Main_Online_Paper_26_May_2012/JEE_Main_Online_Paper_26_May_2012_files/image006.gif", null, "http://www.studyadda.com/upload/html_folder/JEE_Main_Online_Paper_26_May_2012/JEE_Main_Online_Paper_26_May_2012_files/image007.gif", null, "http://www.studyadda.com/upload/html_folder/JEE_Main_Online_Paper_26_May_2012/JEE_Main_Online_Paper_26_May_2012_files/image008.gif", null, "http://www.studyadda.com/upload/html_folder/JEE_Main_Online_Paper_26_May_2012/JEE_Main_Online_Paper_26_May_2012_files/image009.gif", null, "http://www.studyadda.com/upload/html_folder/JEE_Main_Online_Paper_26_May_2012/JEE_Main_Online_Paper_26_May_2012_files/image011.gif", null, "http://www.studyadda.com/upload/html_folder/JEE_Main_Online_Paper_26_May_2012/JEE_Main_Online_Paper_26_May_2012_files/image012.gif", null, "http://www.studyadda.com/upload/html_folder/JEE_Main_Online_Paper_26_May_2012/JEE_Main_Online_Paper_26_May_2012_files/image013.gif", null, "http://www.studyadda.com/upload/html_folder/JEE_Main_Online_Paper_26_May_2012/JEE_Main_Online_Paper_26_May_2012_files/image014.gif", null, "http://www.studyadda.com/upload/html_folder/JEE_Main_Online_Paper_26_May_2012/JEE_Main_Online_Paper_26_May_2012_files/image015.gif", null, "http://www.studyadda.com/upload/html_folder/JEE_Main_Online_Paper_26_May_2012/JEE_Main_Online_Paper_26_May_2012_files/image016.gif", null, "http://www.studyadda.com/upload/html_folder/JEE_Main_Online_Paper_26_May_2012/JEE_Main_Online_Paper_26_May_2012_files/image018.gif", null, "https://www.studyadda.com/assets/frontend/images/msg-gif.GIF", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.66545814,"math_prob":0.99819964,"size":37532,"snap":"2022-05-2022-21","text_gpt3_token_len":13008,"char_repetition_ratio":0.32815498,"word_repetition_ratio":0.22011586,"special_character_ratio":0.3522061,"punctuation_ratio":0.07121977,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99914247,"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],"im_url_duplicate_count":[null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-25T10:12:55Z\",\"WARC-Record-ID\":\"<urn:uuid:69fc2c95-689a-4cea-b85b-4f7a4c2a1448>\",\"Content-Length\":\"449774\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9a5ae94a-cc44-4af1-a653-129f7a5bca52>\",\"WARC-Concurrent-To\":\"<urn:uuid:f7f5f56d-6cf8-4e9c-ae56-910ae15eb5fa>\",\"WARC-IP-Address\":\"151.106.35.148\",\"WARC-Target-URI\":\"https://www.studyadda.com/solved-papers/kvpy/jee-main-paper-held-on-26-may-2012/8\",\"WARC-Payload-Digest\":\"sha1:7F4EVTVQEIKPGVS6WANMB72OZXUGPV7C\",\"WARC-Block-Digest\":\"sha1:MHWHZDOKZUAPG6GDVMQFSDL7GNDQIPGH\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320304810.95_warc_CC-MAIN-20220125100035-20220125130035-00658.warc.gz\"}"}
https://wikipedy.org/glossary/equation	[ "# What is equation?\n\nEquation is a mathematical or chemical representation as a linear array of symbols expressing the quality of two things, separated into left and right sides by an equal sign.\nArrhenius’ e. An equation relating chemical reaction rate with temperature.\nBohr’s e. The equation for calculating the volume of the dead space gas in the respiratory tract by measuring the expired air and subtracting it from the alveolar gas volumes.\nEinthoven’s e. See Einthoven’s law, under law.\nHasselbalch’s e. See Henderson-Hasselbalch equation.\nHenderson-Hasselbalch e. An equation for determining the pH of a buffer solution such as blood plasma; pH=pK+log." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.79901886,"math_prob":0.9963813,"size":640,"snap":"2022-05-2022-21","text_gpt3_token_len":145,"char_repetition_ratio":0.13679245,"word_repetition_ratio":0.0,"special_character_ratio":0.1875,"punctuation_ratio":0.11666667,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99648887,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-20T13:17:18Z\",\"WARC-Record-ID\":\"<urn:uuid:fae585ce-3fec-4032-b0f6-36e455712479>\",\"Content-Length\":\"12008\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f48cfbf8-b042-4e21-8071-2b5c8e49f0ae>\",\"WARC-Concurrent-To\":\"<urn:uuid:9ef8edb2-850b-4c1b-9e3f-53de58750c2e>\",\"WARC-IP-Address\":\"162.55.208.157\",\"WARC-Target-URI\":\"https://wikipedy.org/glossary/equation\",\"WARC-Payload-Digest\":\"sha1:US6J2PGKFUFFBPRR6ELR45IAP5T7E7O2\",\"WARC-Block-Digest\":\"sha1:PT62ZEZ3V22PZUJGLEXOF7HIVEGVOOXU\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662532032.9_warc_CC-MAIN-20220520124557-20220520154557-00494.warc.gz\"}"}
https://scicomp.stackexchange.com/questions/tagged/linear-algebra?tab=Newest	[ "# Questions tagged [linear-algebra]\n\nQuestions on the algorithmic/computational aspects of linear algebra, including the solution of linear systems, least squares problems, eigenproblems, and other such matters.\n\n942 questions\nFilter by\nSorted by\nTagged with\n41 views\n\n### How to optimize nuclear norm subject to positive semidefinite constraints?\n\nFor finite dimensional symmetric positive semidefinite matrices $A$ and $B$, I would like to solve \\begin{align}&\\min \|X - A\|_1 \\\\ &\\text{subject to}\\\\ &X \\preceq B \\\\ &0 \\preceq X\\...\n55 views\n\n### Derivative-free ill-conditioned non-linear least squares\n\nI am looking for a package which can solve (non-linear) least squares problems without the use of derivatives (because of an expensive model), but which also deals with ill-conditioning well (such as ...\n443 views\n\n40 views\n\n28 views\n\n### Norm of operator in finite element discretization of Heat equation\n\nI am solving the heat equation discretized spatially via FEM and temporally via backward Euler. I get the system $$M \\dot{u} = K u +f$$ where $u$ is a vector representing the solution at spatial ...\n31 views\n\n### Choosing the pivot for the rotation matrix in similarity transformation\n\nI have arrived at an equation in the similarity transformation - $M_r$ = $T. M_{r-1}. T^t$ ,where $T$ is the rotation matrix and $M_r$ ,$M_{r-1}$ are similar matrices. My aim is to find the rotation ...\n61 views\n\n### Fastest matrix library for Android (with GPU is possible)\n\nI was working on an Android app that requires some linear algebra with matrices. The matrices will be somewhat medium-sized as they are not too small or too big. I was originally using jBlas because ...\n38 views\n\n### Is there a published RQ decomposition column-major algorthm?\n\nI am refactoring an existing algorithm where where a RQ decomposition (as opposed to the more common QR) would be rather useful. Most common books on the subject (e.g. Golub and Van Loan) discuss QR ...\n87 views\n\n### Is there a subfield within computational science research that's done on pencil and paper?\n\nIs there an area of computational science research that can be done on pencil and paper (with results written up for a journal format later on)? I'm wondering if there is abstract proof-based linear ...\n47 views\n\n### Find mass matrix in a system of linear equations\n\nGiven $z_t=\\sum_{i=1}^t \\theta_iz_{t-i}+v_t$, where $t=1,...,N$ where $N=1024$. I need to write this in matrix form (a system of linear equations) as $\\mathsf{A}\\mathsf{z} = \\mathsf{z} - \\mathsf{v}$. ...\n65 views\n\n### Flops of the computation of symmetric matrix $A$ to the power of $p$\n\nWhat is the cost in terms of flops for the computation of $A$ to the power of $p$, where $p$ is a positive integer and $A \\in \\mathbb R^{n\\times n}$ is a symmetric matrix?" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8858472,"math_prob":0.9904981,"size":14449,"snap":"2020-34-2020-40","text_gpt3_token_len":3629,"char_repetition_ratio":0.14191762,"word_repetition_ratio":0.005816369,"special_character_ratio":0.25019032,"punctuation_ratio":0.11444043,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99969125,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-08-09T09:54:27Z\",\"WARC-Record-ID\":\"<urn:uuid:a72fcbb3-a12e-419c-b318-b10d2028a39b>\",\"Content-Length\":\"254108\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:da5e4276-3be6-4273-bf3b-9be0e9b05318>\",\"WARC-Concurrent-To\":\"<urn:uuid:93759c7d-8ce8-4709-8e73-24272b82f849>\",\"WARC-IP-Address\":\"151.101.193.69\",\"WARC-Target-URI\":\"https://scicomp.stackexchange.com/questions/tagged/linear-algebra?tab=Newest\",\"WARC-Payload-Digest\":\"sha1:N4RRUC5XDR5IW2ROPMODZLFLR423OQFK\",\"WARC-Block-Digest\":\"sha1:5675LO63TWOAMH6T6FIBPL5VHZEADAR3\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-34/CC-MAIN-2020-34_segments_1596439738523.63_warc_CC-MAIN-20200809073133-20200809103133-00035.warc.gz\"}"}
https://www.lifewire.com/how-to-use-xlookup-in-excel-4770092	[ "# How to Use the XLOOKUP Function in Excel\n\nWith advanced search features that are better than VLOOKUP\n\nThe VLOOKUP function has always been one of Excel's most powerful functions. It let you search for values in the first column of a table, and return values from fields on the right. But Excel also has a function called XLOOKUP, which allows you to search for a value in any column or row, and return data from any other column.\n\n## How XLOOKUP Works\n\nThe XLOOKUP function is much easier to use than the VLOOKUP function, because instead of specifying a value for the results column, you can specify the entire range.\n\nThe function also allows you to search both a column and a row, locating the value at the intersecting cell.\n\nThe parameters of the XLOOKUP function are as follows:\n\n```=XLOOKUP (lookup_value, lookup_array, return_array, [match_mode], [search_mode])\n```\n• lookup_value: The value you want to search for\n• lookup_array: The array (column) you want to search\n• return_array: The result (column) you want to retrieve a value from\n• match_mode (optional): Select an exact match (0), an exact match or next smallest value (-1), or a wildcard match (2).\n• search_mode (optional): Select whether to search starting with the first item in the column (1), the last item in the column (-1), binary search ascending (2) or binary search descending (-2).\n\nThe following are a few of the most common lookups you can do with the XLOOKUP function.\n\n## How to Search for a Single Result Using XLOOKUP\n\nThe easiest way to use XLOOKUP is to search for a single result using a data point from one column.\n\n1. This example spreadsheet is a list of orders submitted by sales representatives, including the item, number of units, cost, and total sale.\n\n2. If you want to find the first sale in the list submitted by a specific sales rep, you could create an XLOOKUP function that searches the Rep column for a name. The function will return the result from the Total column. The XLOOKUP function for this is:\n\n```=XLOOKUP(I2,C2:C44,G2:G44,0,1)\n```\n• I2: Points to the Rep Name search cell\n• C2:C44: This is the Rep column, which is the lookup array\n• G2:G33: This is the Total column, which is the return array\n• 0: Selects an exact match\n• 1: Selects the first match in the results\n3. When you press Enter and type the name of a sales rep, the Total result cell will show you the first result in the table for that sales rep.\n\n4. If you want to search for the most recent sale (since the table is ordered by date in reverse order), change the last XLOOKUP argument to -1, which will start the search from the last cell in the lookup array and provide you with that result instead.\n\n5. This example shows a similar search that you could perform with a VLOOKUP function by using the Rep column as the first column of the lookup table. However, XLOOKUP lets you search for any column in either direction. For example, if you want to find the sales rep who sold the first Binder order of the year, you would use the folloing XLOOKUP function:\n\n```=XLOOKUP(I2,D2:D44,C2:C44,0,1)\n```\n• D2: Points to the Item search cell\n• D2:D44: This is the Item column, which is the lookup array\n• C2:C44: This is the Rep column, which is the return array to the left of the lookup array\n• 0: Selects an exact match\n• 1: Selects the first match in the results\n6. This time, the result will be the name of the sales rep who sold the first binder order of the year.\n\n## Perform Vertical and Horizontal Match with XLOOKUP\n\nAnother capability of XLOOKUP that VLOOKUP isn't capable of is the ability to perform both a vertical and horizontal search, meaning you can search for an item down a column, and across a row as well.\n\nThis dual search feature is an effective replacement for other Excel functions like INDEX, MATCH, or HLOOKUP.\n\n1. In the following example spreadsheet, the sales for each sales rep are split by quarter. If you wanted to see the third quarter sales for a specific sales rep, without the XLOOKUP function, this kind of search would be difficult.\n\n2. With the XLOOKUP function, this kind of search is easy. Using the folloing nexted XLOOKUP function, you can search for the third quarter sales for a specific sales rep:\n\n```=XLOOKUP(J2,B2:B42,XLOOKUP(K2,C1:H1,C2:H42))\n```\n• J2: Points to the Rep search cell\n• B2:B42: This is the Item column, which is the column lookup array\n• K2: Points to the Quarter search cell\n• C1:H1: This is the row lookup array\n• C2:H42: This is the lookup array for the dollar amount in each quarter\n\nThis nested XLOOKUP function first identifies the sales rep, and the nexted XLOOKUP function identifies the desired quarter. The return value will is the cell where those two intercept.\n\n3. The result for this formula is the quarter one earnings for the representative with the name Thompson.\n\n## Using the XLOOKUP Function\n\nThe XLOOKUP function is only available to Office Insider subscribers, but will soon be rolled out to all Microsoft 365 subscribers.\n\nIf you want to test the function out yourself, you can become an Office Insider. Select File > Account, then select the Office Insider drop-down to subscribe.\n\nOnce you join the Office Insider program, your installed version of Excel will receive all of the latest updates, and you can start using the XLOOKUP function." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8645181,"math_prob":0.7692698,"size":5794,"snap":"2023-14-2023-23","text_gpt3_token_len":1313,"char_repetition_ratio":0.17927462,"word_repetition_ratio":0.06339468,"special_character_ratio":0.21556783,"punctuation_ratio":0.115485564,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9699383,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-04-01T22:41:43Z\",\"WARC-Record-ID\":\"<urn:uuid:54aa47b6-d73d-4162-9a95-77bf15ca7f26>\",\"Content-Length\":\"267989\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7b3d461d-a55c-435d-b3ee-8846b095a76e>\",\"WARC-Concurrent-To\":\"<urn:uuid:f98c2657-3b7e-4dfa-ac3e-dc9648743c85>\",\"WARC-IP-Address\":\"146.75.38.137\",\"WARC-Target-URI\":\"https://www.lifewire.com/how-to-use-xlookup-in-excel-4770092\",\"WARC-Payload-Digest\":\"sha1:HE2XJNPYNFH3QBNVIAWT2S7QLLVUKIMK\",\"WARC-Block-Digest\":\"sha1:56BUMQRFJOTROFPBTORDZEAOZ2WGZ6JQ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-14/CC-MAIN-2023-14_segments_1679296950363.89_warc_CC-MAIN-20230401221921-20230402011921-00785.warc.gz\"}"}
https://extempore.michelepasin.org/def/dspsum-DSPMT.html	[ "# dspsum:DSPMT xtlang\n\n##### Implementation\n\n```;; convolution reverb takes mono\n;; files as input (i.e. separates left and right)\n(bind-func dspsum:DSPMT\n(let ((reverb (creverb_st_c \"assets/ir/minsterl.aif\"\n\"assets/ir/minsterr.aif\"))\n(rms (rms_st_c))\n(left:SAMPLE 0.0)\n(right:SAMPLE 0.0)\n(wet 2.0)\n(dry 0.3))\n(lambda (in:SAMPLE* time chan dat:SAMPLE*)\n(if (= 0 (% time FRAMES))\n(begin (set! left (rms.left))\n(set! right (rms.right))))\n(rms chan (reverb chan (pref in 0) dry wet)))))\n```" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.5501042,"math_prob":0.9837063,"size":435,"snap":"2023-40-2023-50","text_gpt3_token_len":149,"char_repetition_ratio":0.12529002,"word_repetition_ratio":0.0,"special_character_ratio":0.35632184,"punctuation_ratio":0.22340426,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97098833,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-03T00:44:03Z\",\"WARC-Record-ID\":\"<urn:uuid:13c0f681-4487-4c7c-8049-b91243cf7dc6>\",\"Content-Length\":\"15296\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:08dba139-0a49-4c0f-806c-0bb8710e2b98>\",\"WARC-Concurrent-To\":\"<urn:uuid:e66dc064-6a2a-47d5-b511-002af1e313a1>\",\"WARC-IP-Address\":\"185.199.111.153\",\"WARC-Target-URI\":\"https://extempore.michelepasin.org/def/dspsum-DSPMT.html\",\"WARC-Payload-Digest\":\"sha1:LN444C72S3SZYERCJQ2BO3Q6D4QG47L5\",\"WARC-Block-Digest\":\"sha1:OX6ERG4AYAIOOVFX5NYAMH3MARFKJT2L\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100476.94_warc_CC-MAIN-20231202235258-20231203025258-00114.warc.gz\"}"}
http://www.coralbark.net/blog/technology/2020/10/shock-result-rust-faster-than-python-in-one-test-of-file-parsing/	[ "Shock Result<>?: Rust faster than Python in one test of file parsing\n\nI don’t think I’d surprise many people if I told them a Rust program was often faster than a Python program but today I wrote a small “script” that scanned a large log file for a regular expression and was surprised to find the Rust version ran >400x faster than the Python. Given the amount of log data I’m going to need to analyse over the next few days – this “script” is going to be a Rust program (though it would be possible for me to use an optimised Python version instead).\n\nIn my day job, I work on a complex C application. When we are hunting certain classes of bugs, a common technique to try to tune the logging/tracing of the application, wait for a while until we think the problem has occurred then comb through the trace to figure out what happened.\n\nEven with tuning the tracing settings, when looking for a rare timing condition, this can result in having to search through many gigabytes of logs files. I can often use grep – but sometimes I want to say something like “find this line or this line between (a line that looks like a line of type A and one of type B)” and writing a short program is the easiest thing to do. I’ve used C and Go for parsing the logs in the past but my default language for this sort of task is Python – it’s easy to write and often programmer time is more important than CPU time.\n\nThis morning I started work on a new script, scanning 200MiB of logs (850,000 lines). The first version of my Python script just tried to match a regular expression against each line. It took over 4 minutes on my sample data, so I made a few tweaks (e.g. I noticed I was compiling the regular expression for each line). It still took over 4 minutes when I fixed that. The Python code in question:\n\nimport re\n\ndef parseTraceFile(filepath):\nconnectregex = re.compile(\"([^T])T([^Z])Z.User is authenticated and authorized.connect=([^\\s])\\sclient=([^\\s])\\s\")\n\nwith open(filepath) as fp:\ncount = 1\n\nwhile line:\n#print(\"Line {}: {}\".format(count, line.strip()))\n\n#Occasional proof of life so we don't think it's hung\nif count % 20000 == 0:\nprint(\"Processing line %d\" % count)\n\ncount += 1\n\nconnectline = connectregex.search(line)\n\nif connectline:\nprint(\"date = %s\" % connectline.group(1))\nprint(\"time = %s\" % connectline.group(2))\nprint(\"connect = %s \" % connectline.group(3))\nprint(\"client= %s\" % connectline.group(4))\n\nif __name__ == \"__main__\":\n\nsuccess = parseTraceFile('/var/tmp/sampletrace.log')\n\nif not success:\nexit(10)\n\nexit(0)\n\nThis code takes ~4m23s on my ThinkPad P50. This worried me as the eventual script will have a lot more regular expressions and run on a lot more data – so to cut a long story short – I thought that given I was learning Rust (for other reasons), I’d see how long a Rust version took. A simple version without clever optimisations runs in about 0.6 seconds. Here’s the Rust version:\n\nuse std::fs::File;\nuse regex::Regex;\n\nfn parse_trace_file(filepath: String) -> std::io::Result<()> {\nlet connect_regex: Regex = Regex::new(r\"([^T])T([^Z])Z.User is authenticated and authorized.connect=([^\\s])\\sclient=([^\\s])\\s\").unwrap();\n\nlet file = File::open(filepath)?;\n\nlet mut count = 1;\n\nif let Ok(line) = lineresult {\n//println!(\"{}\", line);\n\n//Proof of life - so we can tell we haven't hung\nif (count % 20000) == 0 {\nprintln!(\"Processing line {}\", count);\n}\n\ncount += 1;\n\nif let Some(caps) = connect_regex.captures(&line) {\nprintln!(\"Found a match.\");\nprintln!(\"Date = {}\", caps.get(1).map_or(\"PARSE ERROR\", \|m\| m.as_str()));\nprintln!(\"Time = {}\", caps.get(2).map_or(\"PARSE ERROR\", \|m\| m.as_str()));\nprintln!(\"Connect = {}\", caps.get(3).map_or(\"PARSE ERROR\", \|m\| m.as_str()));\nprintln!(\"Client = {}\", caps.get(4).map_or(\"PARSE ERROR\", \|m\| m.as_str()));\n}\n}\n}\n\nOk(())\n}\n\nfn main() {\nlet result = parse_trace_file(String::from(\"/var/tmp/sampletrace.log\"));\n\nif result.is_ok() {\nprintln!(\"Yay\");\n}\n}\n\nIs the Rust version harder to write? Yes, at least for a beginner like me – it is but given the saving in CPU time the trade off is worth it – especially given I’ll get faster at writing Rust the more I do it.\n\nThe difference in execution time surprised me – I naively assumed that because the regular expression library in Python is going to be mature, compiled C code I’d see an insignificant difference.\n\nThis is, at the moment about a single regular expression – if I alter the Python version to search for a string literal – and only run the regular expression on lines that are likely candidates:\n\nimport re\n\ndef parseTraceFile(filepath):\nconnectregex = re.compile(\"([^T])T([^Z])Z.User is authenticated and authorized.connect=([^\\s])\\sclient=([^\\s]*)\\s\")\n\nwith open(filepath) as fp:\ncount = 1\n\nwhile line:\n#print(\"Line {}: {}\".format(count, line.strip()))\n\n#Occasional proof of life so we don't think it's hung\nif count % 20000 == 0:\nprint(\"Processing line %d\" % count)\n\ncount += 1\nfindpos = line.find(\"User is authenticated and authorized\", 40)\n\nif findpos > -1:\nprint(\"Found match\")\nconnectline = connectregex.search(line)\n\nif connectline:\nprint(\"date = %s\" % connectline.group(1))\nprint(\"time = %s\" % connectline.group(2))\nprint(\"connect = %s \" % connectline.group(3))\nprint(\"client= %s\" % connectline.group(4))\n\nif __name__ == \"__main__\":\n\nsuccess = parseTraceFile('/var/tmp/sampletrace.log')\n\nif not success:\nexit(10)\n\nexit(0)\n\nThen this Python version runs at a similar speed to the Rust version.\n\nWhat conclusions can we draw from such a single case? Not many – I’m going to experiment with doing this particular analysis with Rust and, if it is not too painful I’ll probably compare some other cases as well. If I wasn’t learning Rust for other reasons though – I could still get my Python script to run at a similar speed at the cost of thinking more carefully about optimising the analysis code. That more careful thought does start to eat away at the advantage Python has for me though – that it’s very fast for writing a quick and dirty scripts." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.89023143,"math_prob":0.8191496,"size":9001,"snap":"2022-05-2022-21","text_gpt3_token_len":2167,"char_repetition_ratio":0.1117039,"word_repetition_ratio":0.17099863,"special_character_ratio":0.26685923,"punctuation_ratio":0.12779018,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.952931,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-25T05:03:14Z\",\"WARC-Record-ID\":\"<urn:uuid:385e7d1b-c311-4819-b92e-c09883aad92f>\",\"Content-Length\":\"47132\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:ba5b3d63-2505-479c-b96d-90510b9c5ab0>\",\"WARC-Concurrent-To\":\"<urn:uuid:3f3f5e80-420c-44c8-9aad-3c1c35c890bb>\",\"WARC-IP-Address\":\"77.72.0.130\",\"WARC-Target-URI\":\"http://www.coralbark.net/blog/technology/2020/10/shock-result-rust-faster-than-python-in-one-test-of-file-parsing/\",\"WARC-Payload-Digest\":\"sha1:R2VKCWIEADZQFXRPZZPQ5RXF6UMVNS27\",\"WARC-Block-Digest\":\"sha1:M3DL46MJAGPFF5RGHVYU5XHTPH7RDAKE\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320304760.30_warc_CC-MAIN-20220125035839-20220125065839-00457.warc.gz\"}"}
https://janetpanic.com/what-are-the-rules-for-using-parentheses/	[ "Close\n\n# What are the rules for using parentheses?\n\n## What are the rules for using parentheses?\n\nUse parentheses to enclose information that clarifies or is used as an aside. Example: He finally answered (after taking five minutes to think) that he did not understand the question. If material in parentheses ends a sentence, the period goes after the parentheses.\n\n## What is the purpose of parentheses?\n\nParentheses (always used in pairs) allow a writer to provide additional information. The parenthetical material might be a single word, a fragment, or multiple complete sentences. Whatever the material inside the parentheses, it must not be grammatically integral to the surrounding sentence.\n\n## Can you use parentheses in APA?\n\nParentheses Basics Parentheses are punctuation marks used to set off information within a sentence. There are several uses for parentheses that are particular to APA style: To refer to tables or figures. Use parentheses to encase referrals to tables or figures.\n\n## What’s the difference between parenthesis and parentheses?\n\nThe singular form is parenthesis, but the plural parentheses is the word you’re more likely to see. For our purposes, a parenthesis is one of a pair of curved marks that look like this: ( ), and parentheses are both marks.\n\nem dashes\n\n## Can you use two parentheses in a row?\n\nSeparate citations from parenthetical text with either semicolons (for parenthetical-style citations) or commas around the year (for narrative citations). Do not use a double enclosure or back-to-back parentheses.\n\n## What do double parentheses mean in texting?\n\nThe double parentheses indicate an interpolation which would normally be indicated with brackets: Double parentheses indicate that it is not the speaker’s interpolation but the reporter’s.\n\n## What is the order of parentheses?\n\nIn the United States, the acronym PEMDAS is common. It stands for Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. PEMDAS is often expanded to the mnemonic “Please Excuse My Dear Aunt Sally”.\n\n## How do you multiply two sets of parentheses?\n\nWhen an expression has two sets of parentheses next to each other, you need to multiply every term inside the first set of parentheses by every term in the second set. This process is called FOILing.\n\n## How do you simplify two parentheses?\n\nHere are the basic steps to follow to simplify an algebraic expression:remove parentheses by multiplying factors.use exponent rules to remove parentheses in terms with exponents.combine like terms by adding coefficients.combine the constants.\n\n## How do you distribute numbers in parentheses?\n\nThis can be done with subtraction as well, multiplying each number in the difference before subtracting. In each case, you are distributing the outside multiplier to each number in the parentheses, so that multiplication occurs with each number before addition or subtraction occurs.\n\n## How do you multiply three sets of parentheses?\n\n2:08Suggested clip 95 secondsLearn How To Multiply Three Binomials by One Another – Math …YouTubeStart of suggested clipEnd of suggested clip\n\n## Do you multiply parentheses first?\n\nThis means that you should do what is possible within parentheses first, then exponents, then multiplication and division (from left to right), and then addition and subtraction (from left to right). If parentheses are enclosed within other parentheses, work from the inside out.\n\n## How do you solve equations with parentheses?\n\nHow to solve equations in general. If an equation you need to solve has parentheses, simplify the parentheses (most often using distribution) and then solve as you normally would. Simplify both sides of the equation as much as possible using the order of operations (distribute, combine like terms, etc.).\n\n## Do parentheses mean to multiply?\n\nMultiplication. The first way tells us to multiply. When we see two or more numbers together that are separated by parentheses, then the parentheses are telling us to multiply. For example, when we see 5(2), the parentheses are telling us to multiply the 5 and the 2 together.\n\n## Which comes first multiplication or division?\n\nOrder of operations tells you to perform multiplication and division first, working from left to right, before doing addition and subtraction. Continue to perform multiplication and division from left to right. Next, add and subtract from left to right.\n\n## What do parentheses mean in an equation?\n\nParentheses are used in mathematical expressions to denote modifications to normal order of operations (precedence rules). In an expression like , the part of the expression within the parentheses, , is evaluated first, and then this result is used in the rest of the expression.\n\n## What comes first in an equation multiplication or division?\n\nNOTE: Even though Multiplication comes before Division in PEMDAS, the two are done in the same step, from left to right. Addition and Subtraction are also done in the same step.\n\n04/22/2021" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8597701,"math_prob":0.7381342,"size":4917,"snap":"2021-21-2021-25","text_gpt3_token_len":950,"char_repetition_ratio":0.1907185,"word_repetition_ratio":0.015706806,"special_character_ratio":0.18568233,"punctuation_ratio":0.11590909,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98551667,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-05-08T03:18:09Z\",\"WARC-Record-ID\":\"<urn:uuid:c4929ea2-c1a1-435a-bfbb-e1328bc0fef4>\",\"Content-Length\":\"35055\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1fc9e954-e179-485c-aef8-e0c02f23006f>\",\"WARC-Concurrent-To\":\"<urn:uuid:298275c1-1875-4349-8dec-b3ef3cd305d4>\",\"WARC-IP-Address\":\"172.67.212.202\",\"WARC-Target-URI\":\"https://janetpanic.com/what-are-the-rules-for-using-parentheses/\",\"WARC-Payload-Digest\":\"sha1:SJTOWLVOEZOGCNLPF4TDZMOPTBW32QZW\",\"WARC-Block-Digest\":\"sha1:WX55TUWKWNDJR7E6D4VGUUWLHQWJIOOX\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-21/CC-MAIN-2021-21_segments_1620243988837.67_warc_CC-MAIN-20210508031423-20210508061423-00571.warc.gz\"}"}
http://math.ivyglobal.com/questions/5/351/271	[ "1 EASY 0.1 $$\\times$$ 100\n\n 2 EASY 4.7 $$\\times$$ 100\n\n 3 MEDIUM 0.001 $$\\times$$ 10000\n\n 4 MEDIUM 1.43 $$\\times$$ 70\n\n 5 HARD 7.312 $$\\times$$ 200" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.5663948,"math_prob":1.00001,"size":265,"snap":"2022-05-2022-21","text_gpt3_token_len":82,"char_repetition_ratio":0.18007663,"word_repetition_ratio":0.055555556,"special_character_ratio":0.21132076,"punctuation_ratio":0.19512194,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.980036,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-27T18:44:03Z\",\"WARC-Record-ID\":\"<urn:uuid:a0abcf1c-48fd-435d-a04a-09f20ebf840f>\",\"Content-Length\":\"9993\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:567de78b-073b-4747-9078-9996e217c878>\",\"WARC-Concurrent-To\":\"<urn:uuid:d3da8e71-5854-4897-a43a-f47e4b71adf5>\",\"WARC-IP-Address\":\"40.71.100.230\",\"WARC-Target-URI\":\"http://math.ivyglobal.com/questions/5/351/271\",\"WARC-Payload-Digest\":\"sha1:U2EIMKQE4Q3NT4GQDJFHLLDMJASPS4JE\",\"WARC-Block-Digest\":\"sha1:QVCVRMQICUBIFFL6QK36B6SSAH5P4WLN\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662675072.99_warc_CC-MAIN-20220527174336-20220527204336-00078.warc.gz\"}"}
https://ro.uow.edu.au/eispapers1/544/	[ "## Faculty of Engineering and Information Sciences - Papers: Part B\n\n#### Title\n\nConstruction of T-matrices of order 6m+1\n\n114789\n\n#### Publication Details\n\nXia, M., Xia, T., Seberry, J. & Qin, H. (2017). Construction of T-matrices of order 6m+1. Far East Journal of Mathematical Sciences, 101 (8), 1731-1749.\n\n#### Abstract\n\nIn this paper, we prove the necessary and sufficient condition for an integer n = a^2+3b^2. Consequently, every prime power 6m+1 has a representation of the form a^2+3b^2. Then we show how to construct T-matrices of order 6m+1 by using 4 sequences of lengths r, r, 2m-r, 2m-r with r=m-2 or r=m in which the first is a subset of the integeres {0, 1, ..., 2m-1} with size r, the second and third sequences are of (1, -1), and every component of the last sequence belongs to the set {0, 1, 2}. For m <=13 and m not equals to 9, we give concrete constructions.\n\nCOinS\n\n#### Link to publisher version (DOI)\n\nhttp://dx.doi.org/10.17654/MS101081731" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8379906,"math_prob":0.8531288,"size":799,"snap":"2019-35-2019-39","text_gpt3_token_len":257,"char_repetition_ratio":0.11823899,"word_repetition_ratio":0.01438849,"special_character_ratio":0.3316646,"punctuation_ratio":0.18367347,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97498536,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-09-22T14:00:53Z\",\"WARC-Record-ID\":\"<urn:uuid:43cf2a71-72db-48a2-843c-ac3fc74f49f0>\",\"Content-Length\":\"32524\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4c057b41-c3e8-42a5-b5ef-0f3d85cde1bc>\",\"WARC-Concurrent-To\":\"<urn:uuid:718891fd-1a9c-4bac-b7dc-bb62d42b0bbb>\",\"WARC-IP-Address\":\"72.5.9.223\",\"WARC-Target-URI\":\"https://ro.uow.edu.au/eispapers1/544/\",\"WARC-Payload-Digest\":\"sha1:AZJAXY7H5CTJDUG7K6NFW2OX2P6SXE7S\",\"WARC-Block-Digest\":\"sha1:F5CFKYQSJ2TXGSIYY62CUX2YLGCBHYWG\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-39/CC-MAIN-2019-39_segments_1568514575515.93_warc_CC-MAIN-20190922135356-20190922161356-00221.warc.gz\"}"}
https://nctbsolution.com/rd-sharma-solutions-class-7-chapter-8/	[ "# Rd Sharma Solutions Class 7 Chapter 8\n\n## Rd Sharma Solutions Class 7 Chapter 8 Linear Equations In One Variable\n\nWelcome to NCTB Solution. Here with this post we are going to help 7th class students for the Solutions of Rd Sharma Class 7 Mathematics, Chapter 8, Linear Equations In One Variable. Here students can easily find Exercise wise solution for chapter 8, Linear Equations In One Variable. Students will find proper solutions for Exercise 8.1, 8.2, 8.3 and 8.4. Our teachers solved every problem with easily understandable methods so that every students can understand easily. Here all solutions are based on the CBSE latest curriculum.\n\nLinear Equations In One Variable Exercise 8.1 Solution\n\nQuestion no – (1)\n\nSolution :\n\nAccording to the given question –\n\n(i) x = 4 is the root of 3x – 5 = 7\n\n∴ 3x – 5 = 7\n\n= 3x = 7 + 5\n\n= x = 12/3\n\n∴ x = 4…(Verified)\n\n(ii) x = 3 is the root of 5 + 3x = 14\n\n∴ 5 + 3x = 14\n\n= 3x = 14 – 5\n\n= x = 9/3\n\n∴ x = 3…(Verified)\n\n(iii) x = 2 is the root of 3x – 2 = 8x – 12\n\n∴ 3x – 2 = 8x – 12\n\n= 3x – 8x = – 12 + 2\n\n= x = 10/5\n\n∴ x = 2…(Verified)\n\n(iv) x = 4 is the root of 3x/2 = 6\n\n∴ 3x/2 = 6\n\n= x = 6 × 3/3\n\n= x = 12/3\n\n∴ x = 4…(Verified)\n\n(v) y – 2 is the root of y – 3 = 2y – 5\n\n∴ y – 3 = 2y – 5\n\n= 2y – y = – 3 + 5\n\n∴ y = 3…(Verified)\n\n(vi) x = 8 is the root of 1/2x + 7 = 11\n\n∴ 1/2x + 7 = 11\n\n= 1/2x = 11- 7\n\n= x = 4 × 2\n\n∴ x = 8\n\nQuestion no – (2)\n\nSolution :\n\nAs per the question we can solve these problems as follows :\n\n(i) x + 3 = 12\n\n= x = 12 – 3\n\nx = 9\n\n(ii) x – 7 = 10\n\n= x = 10 + 7\n\nx = 17\n\n(iii) 4x = 28\n\n= x = 28/4\n\nx = 7\n\n(iv) x/2 + 7= 11\n\n= x/2 + 7 = 11\n\n= x/2 = 11 – 7\n\nx = 8\n\n(v) 2x + 4 = 3x\n\n= 2x – 3x = – 4\n\nx = 4\n\n(vi) x/4 = 12\n\n= x = 12 × 4\n\nx = 48\n\n(vii) 15/x = 3\n\n= x = 15/3\n\nx = 5\n\n(viii) x/18 = 20\n\n= x = 20 × 18\n\nx = 360\n\nLinear Equations In One Variable Exercise 8.2 Solution\n\nQuestion no – (1)\n\nSolution :\n\nIn the given question,\n\nx – 3 = 5\n\nx – 3 = 5\n\n= x = 5 + 3\n\nSo, x = 8\n\nQuestion no – (2)\n\nSolution :\n\nIn the given question,\n\nx + 9 = 13\n\nx + 9 = 13\n\n= x = 13 – 9\n\nThus, x = 4\n\nQuestion no – (3)\n\nSolution :\n\nGiven in the question,\n\nx – 3/5 = 7/5\n\nx – 3/5 = 7/5\n\n= x = 7/5 + 3/5\n\n= x = 10/5\n\nTherefore, x = 2\n\nQuestion no – (4)\n\nSolution :\n\nGiven, 3x = 0\n∴ 3x = 0\nSo, x = 0\n\nQuestion no – (5)\n\nSolution :\n\nGiven, x/2 = 0\n\nx/2 = 0\n\n= x = 0\n\nQuestion no – (6)\n\nSolution :\n\nIn the given question,\n\nx – 1/3 = 2/3\n\nx – 1/3 = 2/3\n\n= x = 2/3 + 1/3\n\n= x = 2 + 1/3\n\nHence, = x = 1\n\nQuestion no – (7)\n\nSolution :\n\nGiven in the question,\n\nx + 1/2 = – 7/2\n\nx + 1/2 = – 7/2\n\n= x = 7/2 = 1/2\n\n= x = 6/2\n\nThus, = x = 3\n\nQuestion no – (8)\n\nSolution :\n\nIn the question,\n\n10 – y = 6\n\n10 – y = 6\n\n= 10 – 6 = y\n\nHence, y = 4\n\nQuestion no – (9)\n\nSolution :\n\nGiven in the question,\n\n7 + 4y = – 5\n\n7 + 4y = – 5\n\n= 4y = – 5 – 7\n\nThus, y = – 3\n\nQuestion no – (10)\n\nSolution :\n\nIn the given question,\n\n= 4/5 – x = 3/5\n\n∴ 4/5 – x = 3/5\n\n= 4/5 – 3/5 = x\n\n= x = 4 – 3/5\n\nHence, x = 1/5\n\nQuestion no – (11)\n\nSolution :\n\nIn the given question,\n\n2y – 1/2 = -1/3\n\n2y – 1/2 = -1/3\n\n= 2y = 1/2 – 1/3\n\n= 2y = 3 – 2/6\n\ny = 1/12\n\nQuestion no – (12)\n\nSolution :\n\nGiven in the question,\n\n14 = 7x/10 – 8\n\n14 = 7x/10 – 8\n\n= 7x/10 = 14 + 8\n\n= x = 22 × 10/7\n\nThus, x = 220/7\n\nQuestion no – (13)\n\nSolution :\n\nIn the question,\n\n3 (x + 2) = 15\n\n3 (x + 2) = 15\n\n= x + 2 = 5\n\n= x = 5 – 2\n\nTherefore, x = 3\n\nQuestion no – (14)\n\nSolution :\n\nIn the given question,\n\nx/4 = 7/8\n\nx/4 = 7/8\n\n= x = 7 × 4/8\n\nHence, x = 7/2\n\nQuestion no – (15)\n\nSolution :\n\nGiven, 1/3 – 2x = 0\n\n1/3 – 2x = 0\n\n= 2x = 1/3\n\nThus, x = 1/6\n\nQuestion no – (16)\n\nSolution :\n\nHere we have,\n\n3 (x + 6) = 24\n\n3 (x + 6) = 24\n\n= x + 6 = 8\n\n= x = 8 – 6\n\nThus, x = 2\n\nQuestion no – (17)\n\nSolution :\n\nHere we have,\n\n3 (x + 2) – 2 (x – 1) = 7\n\n3 (x + 2) – 2 (x – 1) = 7\n\n= 3x + 6 – 2x + 2 = 7\n\n= x = 7 – 8\n\nThus, x = -1\n\nQuestion no – (18)\n\nSolution :\n\nIn the question we have,\n\n8 (2x – 5) – 6 (3x – 7) = 1\n\n8 (2x – 5) – 6 (3x – 7) = 1\n\n= 16x – 40 – 18x + 42 = 1\n\n= -2x + 2 = 1\n\n= 2x = 1 – 2\n\nHence, x = 1/2\n\nQuestion no – (19)\n\nSolution :\n\nGiven in the question,\n\n6 (1 – 4x) + 7 (2 + 5x) = 53\n\n6 (1 – 4x) + 7 (2 + 5x) = 53\n\n= 6 – 24x + 14 + 35x = 53\n\n= 11x = 53 – 20\n\n= x = 33/11\n\nTherefore, x = 3\n\nQuestion no – (20)\n\nSolution :\n\nIn the question we have,\n\n5 (2 – 3x) – 17 (2x – 5) = 16\n\n∴ (2 – 3x) – 17 (2x – 5) = 16\n\n= 10 – 15x – 34x + 85 = 16\n\n= – 49x = 16 – 95\n\nHence, x = 79/49\n\nQuestion no – (21)\n\nSolution :\n\nGiven in the question,\n\nx – 3/5 – 2 = – 1\n\nx – 3/5 – 2 = – 1\n\nx – 3/5 = – 1 + 2\n\n= x – 3 = 5\n\n= x = 5 + 3\n\nThus, x = 8\n\nQuestion no – (22)\n\nSolution :\n\nIn the question we have,\n\n5 (x – 2) + 3 (x + 1) = 25\n\n5 (x – 2) + 3 (x + 1) = 25\n\n= 5x – 10 + 3 x + 3 = 25\n\n= 8x = 25 + 7\n\n= x = 32/8\n\nTherefore, x = 4\n\nLinear Equations In One Variable Exercise 8.3 Solution\n\nQuestion no – (1)\n\nSolution :\n\nIn the given question,\n\n6x + 5 = 2x + 17\n\n6x + 5 = 2x + 17\n\n= 6x – 2x = 17 – 5\n\n= 4x = 12\n\n= x = 12/4\n\n= x = 3\n\nHence, x = 3…(Verified)\n\nQuestion no – (2)\n\nSolution :\n\nIn the question we have,\n\n2 (5x – 3) – 3 (2x – 1) = 9\n\n2(5x – 3) – 3 (2x – 1) = 9\n\n= 10x – 6 – 6x + 3 = 9\n\n= 4x = 9 + 3\n\n= x = 12/4\n\nThus, x = 3…(Verified)\n\nQuestion no – (3)\n\nSolution :\n\nGiven in the question,\n\nx/2 = x/3 + 1\n\nx/2 = x/3 + 1\n\n= x/2 – x/3 = + 1\n\n= 3x – 2x/6 = + 1\n\nTherefore, x = 6…(Verified)\n\nQuestion no – (4)\n\nSolution :\n\nIn the question we have,\n\nx/2 + 3/2 = 2x/5 – 1\n\nx/2 + 3/2 = 2x/5 – 1\n\n= x/2 – 2x/5 = -1 – 3/2\n\n= 5x – 4x/10 = -2-3/2\n\n= x = 5 × 10/2\n\nThus, x = -25…(Verified)\n\nQuestion no – (5)\n\nSolution :\n\nGiven in the question,\n\n3/4 (x – 1) = x – 3\n\n3/4 (x – 1) = x – 3\n\n= 3x – 3 = 4x – 12\n\n= 3x – 4x = – 12 + 3\n\n= – x = – 9\n\nHence, x = 9…(Verified)\n\nQuestion no – (6)\n\nSolution :\n\nIn the question we have,\n\n3 (x – 3) = 5 (2x + 1)\n\n3 (x – 3) = 5 (2x + 1)\n\n= 3x – 9 = 10x + 5\n\n= 3x – 10x = + 5 + 9\n\n= – 7x = 14\n\nTherefore, x = – 2…(Verified)\n\nQuestion no – (7)\n\nSolution :\n\nGiven in the question,\n\n3x – 2 (2x – 5) = 2 (x + 3) – 8\n\n3x – 2 (2x – 5) = 2 (x + 3) – 8\n\n= 3x – 4x + 10 = 2x + 6 – 8\n\n= -x – 2x = – 2 – 10\n\n= -3x = – 12\n\n= x = 12/3\n\nHence, x = 4…(Verified)\n\nQuestion no – (8)\n\nSolution :\n\nIn the question,\n\nx – x/4 – 1/2 = 3 + x/4\n\nx – x/4 – 1/2 = 3 + x/4\n\n= 4x – x – 2/4 = 12 + x/4\n\n= 3x – 2 = 12 + x\n\n= 3x – x = 12 + 2\n\n= x = 14/2\n\nHence, x = 7…(Verified)\n\nQuestion no – (9)\n\nSolution :\n\nIn the question we have,\n\n6x – 2/9 + 3x + 5/18 = 1/3\n\n6x – 2/9 + 3x + 5/18 = 1/3\n\n= 12x – 4 + 3x + 5/18 = 1/3\n\n= 15x + 1 = 18/3\n\n= 15x + 1 = 6\n\n= 15x = 6 – 1\n\n= x = 5/15\n\nTherefore, x = 1/3…(Verified)\n\nQuestion no – (10)\n\nSolution :\n\nIn the question,\n\nm – m – 1/2 = 1 – m – 2/3\n\nm – m – 1/2 = 1 – m – 2/3\n\n= 2m – m + 1/2 = 3 – m + 2/3\n\n= m + 1/2 = 5 – m/3\n\n= 3m + 3 = 10 – 2m\n\n= 3m + 2m = 10 – 3\n\n= 3m = + 7\n\nThus, m = + 7/5\n\nQuestion no – (11)\n\nSolution :\n\nIn the given question,\n\n(5x – 1)/3 – (2x – 2)/3 = 1\n\n(5x – 1)/3 – (2x – 2)/3 = 1\n\n= 5x – 1 – 2x + 2/3 = 1\n\n= 3x + 1 = 3\n\n= 3x = 3 – 1\n\nThus, x = 2/3\n\nQuestion no – (12)\n\nSolution :\n\nIn the question we have,\n\n0.6x + 4/5 = 0.28x + 1.16\n\n0.6x + 4/5 = 0.28x + 1.16\n\n= 0.6x – 0.28x = 1.16 – 4/5\n\n= 0.32x = 5.8 – 4/5\n\n= x = 10.8/5 × 0.32\n\n= x = 108 × 100/5 × 32 × 10\n\n= x = 18/16\n\nHence, x = 9/8\n\nQuestion no – (13)\n\nSolution :\n\nGiven in the question,\n\n0.5x + x/3 = 0.25x + 7\n\n0.5x + x/3 = 0.25x + 7\n\n= 0.5x + x/3 – 0.25x = 7\n\n= 1.5x + x – 0.75x/3 = 7\n\n= 1.75x = 21\n\n= x = 21/1.75\n\n= x = 21 × 100/175\n\nTherefore, x = 12\n\nLinear Equations In One Variable Exercise 8.4 Solution\n\nQuestion no – (1)\n\nSolution :\n\nLet, the number be x.\n\n3x – 5 = 16\n\n= 3x = 16 + 5\n\n= x – 21/3\n\nx = 7\n\nTherefore, the number is 7.\n\nQuestion no – (2)\n\nSolution :\n\nLet the number = x\n\n7x = x + 78\n\n= 7x – x = 78\n\n= 6x = 78\n\n= x = 13\n\nThus, the required number is 13.\n\nQuestion no – (3)\n\nSolution :\n\nLet, Three numbers be x, x + 1, x + 2\n\nx + x + 1 = x + 2 + 15\n\n= 2x – x = 17 – 1\n\n= x = 16\n\nThree numbers are,\n\nx = 16,\n\n16 + 1 = 17\n\n16 + 2 = 18\n\nTherefore, the three consecutive natural numbers are 16, 17, 18.\n\nQuestion no – (4)\n\nSolution :\n\nLet, two numbers be x and y,\n\nx – y = 7\n\nx – y = 7 = x = y + 7\n\nand = 6y + x = 77\n\n= 6y + y + 7 = 77\n\n= 7y = 77 – 7\n\n= 7y = 70\n\ny = 10\n\nRequired number be 10 and 10 + 7 = 17\n\nQuestion no – (5)\n\nSolution :\n\nLet, the number x\n\nx/3 + 5 = 2x\n\n= x + 15/3 = 2x\n\n= 6x = x + 15\n\n= 6x – x = 15\n\n= 5x = 15\n\n= x = 15/5\n\n= x = 3\n\nTherefore, the number will be 3.\n\nQuestion no – (6)\n\nSolution :\n\nLet, the number be = x\n\n3x + 5 = 50\n\n= 3x = 50 – 5\n\n= x = 45/3\n\n= x = 15\n\nThus, the number will be 15.\n\nQuestion no – (7)\n\nSolution :\n\nLet, Shikha age = x\n\nand Ravish age = x + 3\n\nx + x + 3 = 37\n\n= 2x = 37 – 3\n\n= x = 34/2\n\nx = 17\n\nSo, Shikha age will be 17 year\n\nAnd, Ravish’ s age will be = 17 + 3 = 20 years.\n\nQuestion no – (8)\n\nSolution :\n\nLet, Nilu’s age = x\n\nJain’s age = x + 27\n\nAfter 8 years Nilu’s age = x + 8\n\nand Jain’s age,\n\n= x + 27 + 8\n\n= x + 35\n\nx + 35 = 2 (x + 8)\n\n= x + 35 = 2x + 16\n\n= x – 2x = 16 – 35\n\n= – x = – 19\n\nx = 19\n\nNilu’s age will be 19 years,\n\nAnd, Nilu’s Jain’s age will be,\n\n= 19 + 27\n\n= 46\n\nQuestion no – (9)\n\nSolution :\n\nAccording to the question,\n\nSon’s age = x\n\nMan’s age = 4x\n\n16 years after,\n\nMan’s age = 4x + 16\n\nSon’s age = x + 16\n\n2 (x + 16) = 4x + 16\n\n= 2x + 32 = 4x + 16\n\n= 2x – 4x = + 16 – 32\n\n= – 2x = – 16\n\nx = 8\n\nTherefore, Son’s age will be = 8 years\n\nAnd, Man’s age = 4 × 8 = 32 years.\n\nQuestion no – (10)\n\nSolution :\n\nAccording to the question,\n\nGirl age = x\n\nSister age = x – 4\n\nBrother age,\n\n= (x – 4) – 4\n\n= x – 8\n\nx – 4 + x – 8 = 16\n\n= 22x – 12 = 16\n\n= 2x = 16 + 12\n\n= x = 28/2 = 14\n\nGirl age = 14 years\n\nSister age,\n\n= 14 – 4\n\n= 10 years\n\nBrother age,\n\n= 14 – 8\n\n= 6 years\n\nQuestion no – (11)\n\nSolution :\n\nLet, Anita find = x\n\nShella find = 2x\n\n2x + x – 5 = 16\n\n= 3x = 16 + 5\n\n= x = 21/3 = 7\n\nSo, Anita find 7 shells\n\nSandy find,\n\n= 7 – 5\n\n= 2 shells\n\nShella find,\n\n= 2 × 7\n\n= 14 shells\n\nTherefore, Anita find 7 shells, Sandy find 2 shells, and Shella find 14 shells.\n\nQuestion no – (12)\n\nSolution :\n\nLet, Pandy has x marbles,\n\nAndy has = 2x marbles\n\nSandy has = 2x + x/2 marbles\n\n2x = 2x + x/2\n\n= 2x – 3x/2 = + 75\n\n= 4x – 3x/2 = 75\n\n= x = 150\n\nPandy has = 150 marbles\n\nAndy has,\n\n= 150 × 2\n\n= 300 marbles\n\nSandy has,\n\n= 450/2\n\n= 225 marbles.\n\nHence, Pandy has 150 marbles, Andy has 300 marbles and Sandy has 225 marbles.\n\nQuestion no – (13)\n\nSolution :\n\nLet, 50 paise coins x\n\nand 25 paise coin = 4x\n\nWe know, 50 paise = 0.5 Rupee\n\n₹30 = 30 × 100 = 3000 paise\n\n∴ 50x + 4x × 25 = 3000\n\n= 50x + 100x = 3000\n\n= x = 20\n\n50 paise coin = 20\n\n25 paise coin,\n\n= 4 × 20\n\n= 80\n\nQuestion no – (14)\n\nSolution :\n\nLength = 2x\n\n∴ 2 (x + 2x) = 228\n\n= 6x = 228\n\n= x = 228/6\n\n= x = 38\n\nLength = 2 × 38 = 76\n\nTherefore, the dimension of the field will be length 76 meter and breadth 38 metre.\n\nQuestion no – (15)\n\nSolution :\n\nLet, 25 coins = x\n\n₹ 17,50 = 1750 × 100\n\n= 1750 paise\n\n∴ x × 25 = 1750\n\n= x = 70\n\nTherefore, the number of coins in the purse is 70.\n\nQuestion no – (16)\n\nSolution :\n\nLet, the number of students = x\n\n50 kg = 50 × 1000 gm\n\n= 400 × x = 50000\n\n= 4x = 500\n\n= x = 125\n\nTherefore, there are 125 students in the hostel mess.\n\nNext Chapter Solution :\n\nUpdated: June 8, 2023 — 3:06 pm" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.797855,"math_prob":1.0000099,"size":10631,"snap":"2023-40-2023-50","text_gpt3_token_len":5492,"char_repetition_ratio":0.22499295,"word_repetition_ratio":0.19682746,"special_character_ratio":0.5893143,"punctuation_ratio":0.096999586,"nsfw_num_words":1,"has_unicode_error":false,"math_prob_llama3":1.0000074,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-29T17:34:36Z\",\"WARC-Record-ID\":\"<urn:uuid:13d9d06a-6cd1-4fe2-94bb-96706652d874>\",\"Content-Length\":\"78922\",\"Content-Type\":\"application/http; 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https://cs.stackexchange.com/questions/139826/grasshopper-optimization-algorithm	[ "# Grasshopper Optimization Algorithm\n\nI am currently reading a paper on a meta-heuristic called 'Grasshopper Optimization Algorithm'.\n\nThe main idea of the algorithm is to utilize the social behavior of grasshoppers in a swarm to solve optimization problems. The distance to other grasshoppers in the swarm is used to determine, if a grashopper is repelled (exploration) or attracted (exploitation) from grasshoppers in its proximity.\n\nHowever I am not sure if I understood the first part of the proposed formula correctly:\n\n$$X_i^d = c\\left(\\sum\\limits_{j=1,j\\neq i}^Nc\\frac{ub_d-lb_d}{2}s\\left(\\lvert x_j^d-x_i^d\\rvert\\right)\\frac{x_j-x_i}{d_{ij}}\\right) + \\widehat{T}_d$$\n\n$$X_i^d$$ calculates the next position of a search agent (grasshopper) with respect to the postion of the other search agents and the best found solution so far. So the next position of a grasshopper depends on its own position, the positions of all other grasshoppers in the swarm and the best solution found so far.\n\n$$\\widehat{T}_d$$ denotes the best solution found so far.\n\n$$c$$ is a decreasing coefficient that regulates if the search agents explore or exploit in the search space. With increasing iteration count $$c$$ decreases and the search agents tend to exploitation.\n\n$$s\\left(\\lvert x_j^d-x_i^d\\rvert\\right)$$\n\nThe part in brackets calculates the distance between grashoppers. $$s$$ is a formula which takes this value and determines if the search agents should explore or exploit.\n\n$$\\frac{x_j-x_i}{d_{ij}}$$ is a unit vector, where $$d_{ij}$$ denotes the distance between two grasshoppers.\n\nIt states that $$ub_d$$ is the upper bound and $$lb_d$$ is the lower bound in the $$d$$-th dimension. It further states that the part $$c\\frac{ub_d-lb_d}{2}$$ linearly decreases the space that grasshoppers (search agents) should explore and exploit.\n\nI dont undertsand what is meant with 'upper and lower bound in the $$d$$-th dimension'. Upper and lower bound for what exactly?\n\nCan somebody help?\n\nInformation extracted from this paper:\n\nGrashopper Optimization Algorithm\n\n• Please give some context to understand the meaning of the formula and notations. May 3, 2021 at 10:26\n• @Nathaniel I tried to condense the information, I hope this helps. May 3, 2021 at 11:32\n\nI suspect they probably mean $$ub_d = \\max_i x_i^d$$ where $$x_i^d$$ is the $$d$$h coordinate of $$x_i$$; and similarly for $$lb_d$$, but using $$\\min$$ instead of $$\\max$$. But I don't know -- I am just speculating based on context.\n• Thanks for your answer! Would $max \\ x_i^d$ be the max coordinate of the grasshopper (value to be optimised) in the swarm in the current iteration? May 3, 2021 at 20:18" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.84857696,"math_prob":0.99694276,"size":1944,"snap":"2023-14-2023-23","text_gpt3_token_len":494,"char_repetition_ratio":0.14175257,"word_repetition_ratio":0.035460994,"special_character_ratio":0.22942387,"punctuation_ratio":0.06162465,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9997503,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-06-05T06:07:13Z\",\"WARC-Record-ID\":\"<urn:uuid:28ad2f11-9496-46b7-a136-c6b0158f062a>\",\"Content-Length\":\"160566\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:678c5758-8a42-463a-a10c-c95adf7b3a54>\",\"WARC-Concurrent-To\":\"<urn:uuid:59d9c70a-6fac-4f33-8363-40f07983be80>\",\"WARC-IP-Address\":\"151.101.1.69\",\"WARC-Target-URI\":\"https://cs.stackexchange.com/questions/139826/grasshopper-optimization-algorithm\",\"WARC-Payload-Digest\":\"sha1:ESML6LMJ5LHAUE4NGWKTLHNXJ4V47HHV\",\"WARC-Block-Digest\":\"sha1:J3J6IH4KSBDLVWGI6EDUH4SXXCZWPNR2\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224651325.38_warc_CC-MAIN-20230605053432-20230605083432-00187.warc.gz\"}"}
https://australianfreeslots.com/tag/blackjack-strategies/	[ "There are two widely-known categories of progressive gambling betting systems: positive and negative. Positive betting systems, in order to maximize profits, require increasing bets in certain sizes. On the contrary, negative systems, with losses, also insist on increasing the bet in order to “recover” after the fail. The Fibonacci betting system, which is in the same category as the Martingale strategy, works as a negative mathematic progression, but it is surely used in gambling. Using Fibonacci Blackjack strategy Fibonacci Blackjack strategy counting is similar to math strategy: each number in it is the sum of the numbers that go before it. For instance, this is the shortest and the simplest example of it: 0, 5, 5, 10, 15 (here, 5 is 0+5, where 10 is 5+5, and 15 is 10 plus 5). The bets when using the Fibonacci betting system are systematized according to two principles of the formation of…\n\nMany of us are attracted to gambling, but even the players, who visit casinos often, rarely choose card games. Sometimes, they simply seem to be too complicated. However,…" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.93218577,"math_prob":0.95418286,"size":1241,"snap":"2022-40-2023-06","text_gpt3_token_len":271,"char_repetition_ratio":0.111560225,"word_repetition_ratio":0.0,"special_character_ratio":0.21917808,"punctuation_ratio":0.15102041,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9700969,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-09-29T18:17:00Z\",\"WARC-Record-ID\":\"<urn:uuid:930085cb-9acc-4682-8f7c-af295dff23f3>\",\"Content-Length\":\"28762\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:03942b6e-1c30-4150-99dd-79cf4e59efe4>\",\"WARC-Concurrent-To\":\"<urn:uuid:d1f9d7f2-1b2b-4b78-8bb1-55a2cda0bc93>\",\"WARC-IP-Address\":\"185.197.160.33\",\"WARC-Target-URI\":\"https://australianfreeslots.com/tag/blackjack-strategies/\",\"WARC-Payload-Digest\":\"sha1:TJTVYZEKHI276TOAKVKHHKITWYHSIAAX\",\"WARC-Block-Digest\":\"sha1:DVVPCUGTHAEDW7OLXN7HG2LSQNU4OCBB\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030335362.18_warc_CC-MAIN-20220929163117-20220929193117-00713.warc.gz\"}"}
https://casgcmcri.org/581-2/	[ "By my calculations regarding to the excel spreadsheet of thecase study, it is a 99% probability that the mean payment will fall equal to orless than 18.1077, because the confidence interval is between 17.1736 to 18.418therefore, we made the population mean of payment time to be observed as farless during those sample mean invoices based on the data given to us. If the population mean payment time came out to 19.\n\n5 days,what would be the probability of observing the sample mean payment time of 65invoices having a less than or equal to 18.1077 days?For the 99% confident interval above, the Stockton trucking companycan conclude with a 99% confidence that the population mean payment time forthe new electronic trucking billing system will falls between 17.736 and18.418.17.736< ?<18.\n\n418= 18.077 + .341 = 18.418Upper CI = MEAN + CI= 18.077 – .341 = 17.\n\n736Lower CI = MEAN – CI= 18.077 + 1.341= 18.077 + 2.575 (.\n\n5209)CI = MEAN + z (SE)SE = 4.2 / sqrt 65 = .5209When we use the 99% confidence interval, can we be 99%confident that µ < 19.5 days? Well we can beconfident with the 99% having a higher level of confidence interval but however,there can be a high level of uncertainty, we just have to make it a 100%confidence. It will be less likely that the values will fall between the rangesas asked.\n\nBy using this important level of confidence interval, the intervalgets wider, with the sample size and standard deviation remaining the samewhich can lead to some further complications. For a 99% confidence interval weused the formula provided below:We have assumed that the calculation of the average paymentperiod, their primary purpose is to obtain the average period that can be takenby the target company by making payments to its creditors. In this case, thenew billing system will be appropriately computing to determine the probabilityof the mean payment time. When asked to use the 95% confidence interval, can webe 95% confident that the µ < 19.5 days, then the answeris yes; We can be 95% confident that the mean number of payment days will fallequal or below 19.\n\n5 as indicated in the data by the Excel spreadsheet." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.92335504,"math_prob":0.97308487,"size":2132,"snap":"2021-04-2021-17","text_gpt3_token_len":533,"char_repetition_ratio":0.15084587,"word_repetition_ratio":0.0055555557,"special_character_ratio":0.27626643,"punctuation_ratio":0.12264151,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99535435,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-04-14T16:51:18Z\",\"WARC-Record-ID\":\"<urn:uuid:25cdd049-a0dc-432d-b476-f86a5d2650a8>\",\"Content-Length\":\"20524\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:76a29044-4466-4a8b-8042-227b664facad>\",\"WARC-Concurrent-To\":\"<urn:uuid:2dca1564-0e34-4c5e-b838-9066c08953d1>\",\"WARC-IP-Address\":\"172.67.179.54\",\"WARC-Target-URI\":\"https://casgcmcri.org/581-2/\",\"WARC-Payload-Digest\":\"sha1:S2PQMCRESLACI7WT3LMP6J6VA5D4JAJX\",\"WARC-Block-Digest\":\"sha1:VCAJ4Q435ILBTOX44YEU4BQFHKXCNZLY\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-17/CC-MAIN-2021-17_segments_1618038077843.17_warc_CC-MAIN-20210414155517-20210414185517-00135.warc.gz\"}"}
https://nl.mathworks.com/matlabcentral/answers/435711-how-to-call-vector-in-matrix-with-condition?s_tid=prof_contriblnk	[ "MATLAB Answers\n\n# How to call vector in matrix with condition\n\n8 views (last 30 days)\nha ha on 14 Dec 2018\nCommented: Jan on 14 Dec 2018\nLet's say:\nA=[7 2 3 50;4 5 6 15;1 8 9 20;1 1 1 30]\nA= 7 2 3 50\n4 5 6 15\n1 8 9 20\n1 9 8 30\nB=[1; 7]\nB=[1\n7]\nQuestion: I wanna call only vector in column 4 of matrix A with the condition is: the value of matrix B have the same value of vector in 1st column of matrix A?\nI hope the result like that:\nresult=[20; 30;50]\nresult=[20\n30\n50]\ni try :\nresult=A(ismember(A(:,1),B,'rows'),4);\nBut, result=[50; 20;30]% it is not in order of vector in matrix B ????\n##### 0 CommentsShowHide -1 older comments\n\nSign in to comment.\n\n### Accepted Answer\n\nBruno Luong on 14 Dec 2018\n[tf,loc] = ismember(A(:,1),B);\nr = sortrows([loc(tf),A(tf,4)],1);\nr(:,2)\nans =\n20\n30\n50\n##### 0 CommentsShowHide -1 older comments\n\nSign in to comment.\n\n### More Answers (2)\n\nJan on 14 Dec 2018\n[m, loc] = ismember(A(:,1), B);\nR = A(m,4);\n[~, q] = sort(loc(m));\nR = R(q)\n##### 1 CommentShowHide None\nJan on 14 Dec 2018\nSorting loc(m) and using the index is exactly what happens inside sortrows([loc(m), A(m,4)], 1), so this answer is almost identical to Bruno's.\n\nSign in to comment.\n\nKSSV on 14 Dec 2018\nEdited: KSSV on 14 Dec 2018\nk = A(A(:,1)==B(1),4)\nl = A(A(:,1)==B(2),4)\nOr\n[idx,ia] = ismember(A(:,1),B)\niwant = A(idx,4)\n##### 1 CommentShowHide None\nha ha on 14 Dec 2018\nThanks @KSSV\nBut, i follow your code, and the result is :\nresult=[50; 20;30]% it is not in order of vector in matrix B ????\nIt is NOT what I want(bz it is not in order).\n\nSign in to comment.\n\n### Community Treasure Hunt\n\nFind the treasures in MATLAB Central and discover how the community can help you!\n\nStart Hunting!" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6952784,"math_prob":0.9397835,"size":451,"snap":"2021-04-2021-17","text_gpt3_token_len":190,"char_repetition_ratio":0.14988814,"word_repetition_ratio":0.0,"special_character_ratio":0.48337027,"punctuation_ratio":0.17985612,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9760792,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-04-15T11:21:50Z\",\"WARC-Record-ID\":\"<urn:uuid:c95bbec6-a11a-4bb9-9e11-c2e00b7e4fbd>\",\"Content-Length\":\"138347\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:bab82669-ca8e-4c51-a333-f96ba3ee11ca>\",\"WARC-Concurrent-To\":\"<urn:uuid:b2ace34f-d393-4a85-8304-5ff892f18a44>\",\"WARC-IP-Address\":\"23.219.220.114\",\"WARC-Target-URI\":\"https://nl.mathworks.com/matlabcentral/answers/435711-how-to-call-vector-in-matrix-with-condition?s_tid=prof_contriblnk\",\"WARC-Payload-Digest\":\"sha1:6BKN4KTCAJQO2SSIPRAGINSDT4TMJ4VL\",\"WARC-Block-Digest\":\"sha1:NFF65GAXDEX27BOST7FZGCIXRNB67VQE\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-17/CC-MAIN-2021-17_segments_1618038084765.46_warc_CC-MAIN-20210415095505-20210415125505-00444.warc.gz\"}"}
https://cp4space.hatsya.com/2012/12/09/things-go-wrong-eventually/?replytocom=353	[ "# Things go wrong eventually\n\nThe sinc function is important in signal processing for removing noise and reconstructing the original signal. It’s defined rather simply as sin(x)/x, so it’s surprising that it actually has its own special name (you have to be careful at x = 0, but the limit is sensibly defined as 1). As you can see in the formula and depiction below, sinc is an even function:", null, "The integral under the curve evaluates to π:", null, "A couple of people called Borwein noticed that this identity generalises:", null, "However, this breaks down once you get as far as the term containing sinc(x/15), at which point the integral evaluates to some horrible rational multiple of π instead!", null, "For a more impressive variation on this theme, replace the odd integers with non-composite numbers congruent to 1 (mod 4), i.e. 1 and primes of the form 4k + 1. The pattern continues up until the following point:", null, "Once you add the next term in this sequence, 493541, the pattern breaks down spectacularly; the resulting value is only an inconceivably microscopic distance from π.\n\n### The Polya conjecture\n\nGeorge Pólya conjectured that, for every N > 1, the proportion of numbers nN with an odd number of prime factors (including multiplicity) is at least ½. This is what the situation looks like for the first few positive integers (N up to 100000). If the blue line hits the horizontal axis, the conjecture breaks down:", null, "There seems to be some anomaly around N = 50000, where it is dangerously close to the horizontal axis. Fortunately, the zoom below demonstrates that there exists a hair’s breadth between them, so we’re safe … for now.", null, "Indeed, we’re actually safe for quite some time. We can go well into the hundreds of millions before encountering a difficulty. However, in the spirit of Murphy’s Law, we do eventually find a counter-example. The first proof demonstrated that there’s a counter-example somewhere around N = 10^361. Since then, exhaustive searches confirm that the first counter-example is N = 906150257 (which looks prime, but isn’t; it has a pair of 5-digit prime factors).\n\n### Skewes’ number\n\nSince the time of Euler, it was known that approximately N/log(N) of the numbers below N are prime. Legendre refined this estimate to N/(log(N) − B), where B is a number called Legendre’s constant. It was first estimated to be about 1.08366, but has since been shown to be precisely 1!\n\nA further refinement by Gauss gives the number of primes below N as the value of the following integral, called the logarithmic integral:", null, "Li(N) was conjectured to always be an underestimate of the number of primes below N. It transpires that eventually this breaks down. An initial upper bound for the first time at which this occurs is Skewes’ number, roughly e^e^e^e^e^e. We now know that the conjecture breaks down somewhere between 10^14 and 10^317.\n\n### Stupidly large integers\n\nTo quickly conclude, there are many questions in combinatorics (Ramsey theory, for instance), where even the lower bounds are mind-bogglingly massive. Harvey Friedman defines n(k) to be the length of the longest possible sequence {a_i} over a k-letter alphabet such that no block of letters {a_i, a_(i+1), …, a_2i} occurs as a subsequence of a later block {a_j, a_(j+1), …, a_2j}.\n\nWe have n(1) = 3, n(2) = 11, n(3) > A(7000) (where A is the Ackermann function) and n(4) > A(A(… A(1) …)), where there are A(187196) compositions of the Ackermann function. To put this in perspective, it dwarfs Graham’s number. Later terms are incredibly, overwhelmingly large.\n\nFriedman then defined a function TREE, which grows so large that even TREE(3) is massively immense compared with n(4). I’ll discuss this later.\n\nThis entry was posted in Uncategorized. Bookmark the permalink.\n\n### 6 Responses to Things go wrong eventually\n\n1.", null, "Johnicholas says:\n\nNelson, a (perhaps kooky?) mathematician at Princeton wrote a paper called “Warning Signs of a Possible Collapse of Contemporary Mathematics”: https://web.math.princeton.edu/~nelson/papers/warn.pdf\nwhere (if I understand correctly) he claims that there’s a difference between multiplication and exponentiation, and that it is moderately reasonable to believe that multiplication is total, but that exponentiation is not total – or at least not provably total.\n\nHarvey Friedman wrote a paper called “Demonstrably Necessary Uses of Abstraction”: http://www.math.osu.edu/~friedman.8/pdf/RADEM092602.pdf\nIf I understand correctly, he says that the proofs of totality of the various very-fast-growing functions that you mention require gradually stronger inductive principles. So you could work in a logic weaker than the one necessary to prove Friedman’s n function total, or strong enough to prove n total, but not strong enough to prove TREE total.\n\nIs that a reasonable gloss? I’m only a dilettante, and I certainly do not understand the arguments in detail.\n\n•", null, "apgoucher says:\n\nFast-growing functions can be associated with countable ordinals:\n\n• Addition, multiplication and exponentiation are f_1, f_2 and f_3 in a fast-growing hierarchy;\n• The Ackermann function A is roughly f_omega, where omega is the first infinite ordinal;\n• Friedman’s n function is roughly f_(omega^omega^omega), apparently;\n• The TREE function is roughly f_(Small Veblen ordinal);\n• Busy beaver is roughly f_(Church-Kleene ordinal).\n\nIn the environment of first-order Peano arithmetic, you can’t do transfinite induction beyond epsilon_0 (which is much smaller than the small Veblen ordinal). Hence, it’s impossible to prove that the TREE function is total just using first-order Peano arithmetic.\n\n2.", null, "Andymc says:\n\nThis is an awesome post! I wonder if I can http://xkcd.com/217/ someone with the sinc identities…\n\n•", null, "apgoucher says:\n\nQuite possibly. If you have a modern calculator which does ‘exact’ arithmetic, you can fool it by entering “ln(640320^3+744)/sqrt(163)” and watch as it gives pi as the supposed ‘answer’. This demonstrates that it must use inverse symbolic lookup, similar to (but not as sophisticated as) Robert Munafo’s RIES.\n\n3.", null, "男カバン says:\n\nプラダ財布メンズ男カバン http://www.bagsoinsist.info/" ]	[ null, "https://cp4space.hatsya.com/wp-content/uploads/2020/09/sinc.png", null, "https://cp4space.hatsya.com/wp-content/uploads/2020/09/integral1.png", null, "https://cp4space.hatsya.com/wp-content/uploads/2020/09/borwein.png", null, "https://cp4space.hatsya.com/wp-content/uploads/2020/09/borwein2.png", null, "https://cp4space.hatsya.com/wp-content/uploads/2020/09/borwein3.png", null, "https://cp4space.hatsya.com/wp-content/uploads/2020/09/polya.png", null, "https://cp4space.hatsya.com/wp-content/uploads/2020/09/polya-zoom.png", null, "https://cp4space.hatsya.com/wp-content/uploads/2020/09/integral2.png", null, "https://secure.gravatar.com/avatar/854a6e5388b146e936c1bc372a99ec7b", null, "https://secure.gravatar.com/avatar/fc95c8f8dee7d02a7625912efe58754f", null, "https://secure.gravatar.com/avatar/bae988e326a27b7a88576c2a63184430", null, "https://secure.gravatar.com/avatar/fc95c8f8dee7d02a7625912efe58754f", null, "https://secure.gravatar.com/avatar/4d998515b7f95561cd39368d13f1304f", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9189221,"math_prob":0.9286524,"size":5530,"snap":"2022-27-2022-33","text_gpt3_token_len":1310,"char_repetition_ratio":0.09283388,"word_repetition_ratio":0.0022727272,"special_character_ratio":0.23435804,"punctuation_ratio":0.11296296,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9932266,"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,8,null,8,null,8,null,8,null,8,null,8,null,8,null,8,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-08-16T07:46:55Z\",\"WARC-Record-ID\":\"<urn:uuid:206ea338-1e00-4b3f-a35e-7dd2bae35616>\",\"Content-Length\":\"77808\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:cc59464f-bf65-4563-8696-0c6b263eb16b>\",\"WARC-Concurrent-To\":\"<urn:uuid:ae7712c1-c152-4ffc-b967-28089ea8a6df>\",\"WARC-IP-Address\":\"217.160.0.167\",\"WARC-Target-URI\":\"https://cp4space.hatsya.com/2012/12/09/things-go-wrong-eventually/?replytocom=353\",\"WARC-Payload-Digest\":\"sha1:V2MQ55OS7THHKTL7NM7CRKOQH3746YFU\",\"WARC-Block-Digest\":\"sha1:LMN56LLF2B3CLGUHJ25HTAQDHU63GVGJ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-33/CC-MAIN-2022-33_segments_1659882572221.38_warc_CC-MAIN-20220816060335-20220816090335-00027.warc.gz\"}"}
https://brilliant.org/problems/cool-inequality-4-only-holders/	[ "# Use only Holder's\n\nAlgebra Level 3\n\nIf $a$ and $b$ are positive real numbers such that $a^{2015}+b^{2015}=2015,$ find the maximum value of $a+b$.\n\n×" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.54449713,"math_prob":0.9995931,"size":252,"snap":"2020-45-2020-50","text_gpt3_token_len":79,"char_repetition_ratio":0.14919356,"word_repetition_ratio":0.0,"special_character_ratio":0.39285713,"punctuation_ratio":0.2580645,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9993266,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-11-30T17:30:42Z\",\"WARC-Record-ID\":\"<urn:uuid:95b405be-991e-433e-a52c-1076325bda87>\",\"Content-Length\":\"39561\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e1b919bf-eabf-4b82-8274-a87e9f8c3974>\",\"WARC-Concurrent-To\":\"<urn:uuid:52adb199-6646-464f-a98e-f6e11fb62a2a>\",\"WARC-IP-Address\":\"104.20.34.242\",\"WARC-Target-URI\":\"https://brilliant.org/problems/cool-inequality-4-only-holders/\",\"WARC-Payload-Digest\":\"sha1:6UL5JZTMMF7UC4IA4JBO76GIYQTV46VN\",\"WARC-Block-Digest\":\"sha1:X5TZ2ZMIV5E64DQ57F2KNNQDJ66OAFRR\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141216897.58_warc_CC-MAIN-20201130161537-20201130191537-00333.warc.gz\"}"}
http://allgoodinfo.club/what-is-alternate-math/	[ "### What Is Alternate Math", null, "What is alternate math this is a pretest or an alternate form of the end of module assessment to use with the eureka math first grade module two you could even use it to review alternative math notati.", null, "What is alternate math overview of the alternate assessments and math alternative lessons mathematics mfm2p answers.", null, "What is alternate math 3 interior and exterior angles interior angles i 3 i 4 i 5 i 6 alternate interior angles i 3 i 6 i 4 i 5 exterior angles i 1 i 2 i 7 alternative mathematics education.", null, "What is alternate math alternative math short film review.", null, "What is alternate math alternate strategies for multi digit multiplication mathematics alternative word.", null, "What is alternate math the interior alternate angle relationships a math worksheet page 2 alternative math pathways.", null, "What is alternate math alternate alternative math.", null, "What is alternate math alternative math pathways.", null, "What is alternate math alternative math notation.", null, "What is alternate math high school alternative assessment alternate angles mathematical definition.", null, "What is alternate math alternate achievement standard math alternative mathematics video.", null, "What is alternate math alternate angles angles opposite each other created by drawing one line across two others alternative math assessment ideas.", null, "What is alternate math the alternate angles a math worksheet alternative math assessments." ]	[ null, "http://allgoodinfo.club/wp-content/uploads//2018/07/what-is-alternate-math-this-is-a-pretest-or-an-alternate-form-of-the-end-of-module-assessment-to-use-with-the-eureka-math-first-grade-module-two-you-could-even-use-it-to-review-alternative-math-notati.jpg", null, "http://allgoodinfo.club/wp-content/uploads//2018/07/what-is-alternate-math-overview-of-the-alternate-assessments-and-math-alternative-lessons-mathematics-mfm2p-answers.jpg", null, "http://allgoodinfo.club/wp-content/uploads//2018/07/what-is-alternate-math-3-interior-and-exterior-angles-interior-angles-i-3-i-4-i-5-i-6-alternate-interior-angles-i-3-i-6-i-4-i-5-exterior-angles-i-1-i-2-i-7-alternative-mathematics-education.jpg", null, "http://allgoodinfo.club/wp-content/uploads//2018/07/what-is-alternate-math-alternative-math-short-film-review.jpg", null, "http://allgoodinfo.club/wp-content/uploads//2018/07/what-is-alternate-math-alternate-strategies-for-multi-digit-multiplication-mathematics-alternative-word.jpg", null, "http://allgoodinfo.club/wp-content/uploads//2018/07/what-is-alternate-math-the-interior-alternate-angle-relationships-a-math-worksheet-page-2-alternative-math-pathways.jpg", null, "http://allgoodinfo.club/wp-content/uploads//2018/07/what-is-alternate-math-alternate-alternative-math.jpg", null, "http://allgoodinfo.club/wp-content/uploads//2018/07/what-is-alternate-math-alternative-math-pathways.jpg", null, "http://allgoodinfo.club/wp-content/uploads//2018/07/what-is-alternate-math-alternative-math-notation.jpg", null, "http://allgoodinfo.club/wp-content/uploads//2018/07/what-is-alternate-math-high-school-alternative-assessment-alternate-angles-mathematical-definition.jpg", null, "http://allgoodinfo.club/wp-content/uploads//2018/07/what-is-alternate-math-alternate-achievement-standard-math-alternative-mathematics-video.jpg", null, "http://allgoodinfo.club/wp-content/uploads//2018/07/what-is-alternate-math-alternate-angles-angles-opposite-each-other-created-by-drawing-one-line-across-two-others-alternative-math-assessment-ideas.jpg", null, "http://allgoodinfo.club/wp-content/uploads//2018/07/what-is-alternate-math-the-alternate-angles-a-math-worksheet-alternative-math-assessments.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7597111,"math_prob":0.9396457,"size":1370,"snap":"2019-51-2020-05","text_gpt3_token_len":245,"char_repetition_ratio":0.3579795,"word_repetition_ratio":0.09569378,"special_character_ratio":0.17445256,"punctuation_ratio":0.057522126,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9922984,"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,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-01-28T12:31:37Z\",\"WARC-Record-ID\":\"<urn:uuid:8538fa1d-65b9-4f5b-a73a-9994e6b201c0>\",\"Content-Length\":\"31565\",\"Content-Type\":\"application/http; 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https://ch.mathworks.com/matlabcentral/answers/306021-how-do-i-store-output-from-double-for-loops-i-only-get-the-last-iteration	[ "# How do I store output from double for loops, I only get the last iteration?\n\n1 view (last 30 days)\nLinus Dock on 6 Oct 2016\nCommented: Linus Dock on 6 Oct 2016\nHi, I have forgot how to store my output from the following for loop. I only recover the last iteration of my outer for loop but I would like to store all the data in either one long cell or one cell for each iteration. Is it possible to this and in that case could someone please help? The output cell is flygplatsmetar.\nThank you!\nfor l = 1:length(Data);\ns = strfind(Data{l},a);\nempty=zeros(1,length(Data{l}))';\nj=0;\nfor k = 1:length(Data{l})\nind = find(s{k});\nif ind==1;\nempty(k)=j+1;\nend\nend\nmetar = find(empty);\nNydata = Data{l};\nflygplatsmetar = Nydata(metar);\nend\n\nKSSV on 6 Oct 2016\nflygplatsmetar = cells(length(Data),1) ;\nfor l = 1:length(Data);\ns = strfind(Data{l},a);\nempty=zeros(1,length(Data{l}))';\nj=0;\nfor k = 1:length(Data{l})\nind = find(s{k});\nif ind==1;\nempty(k)=j+1;\nend\nend\nmetar = find(empty);\nNydata = Data{l};\nflygplatsmetar{l} = Nydata(metar);\nend\n\nLinus Dock on 6 Oct 2016\nThanks a lot!\nelias GR on 6 Oct 2016\nThe commend is 'cell', not 'cells'...\n\nelias GR on 6 Oct 2016\nflygplatsmetar = cell(1,length(Data)); %initialize your 1D cell array\nfor l = 1:length(Data)\n...\nflygplatsmetar{l} = Nydata(metar); %store the data\nend\n\n#### 1 Comment\n\nLinus Dock on 6 Oct 2016\nHi! I have Another question: How can I merge these cells from\n<1x6 cell>\ninto one long cell. I can't get it to work iteratively inside the for loop. The manual code I'm trying to replicate is:\nflygplatsmetar=[Utcell{1};Utcell{2};Utcell{3}]\nHere Utcell is my Output from the for-loop instead and flygplatsmetar is the long cell I'm trying to constuct. Thank you for your reply!" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7511777,"math_prob":0.90080166,"size":601,"snap":"2020-45-2020-50","text_gpt3_token_len":172,"char_repetition_ratio":0.113902844,"word_repetition_ratio":0.0,"special_character_ratio":0.28452578,"punctuation_ratio":0.15,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97499365,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-10-23T02:36:07Z\",\"WARC-Record-ID\":\"<urn:uuid:12488064-cae3-495e-9eda-dbf8140559eb>\",\"Content-Length\":\"131758\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:64e7a0fd-9f0d-4ede-85fd-c19b2622d926>\",\"WARC-Concurrent-To\":\"<urn:uuid:9f4c5f5e-8ff3-49da-94a2-015fb7123e46>\",\"WARC-IP-Address\":\"23.212.144.59\",\"WARC-Target-URI\":\"https://ch.mathworks.com/matlabcentral/answers/306021-how-do-i-store-output-from-double-for-loops-i-only-get-the-last-iteration\",\"WARC-Payload-Digest\":\"sha1:R525QBD4CG3QE555T5WTPTJMKUH5ZQC2\",\"WARC-Block-Digest\":\"sha1:RTN475XWKZXFKL55J6TFKMSHFCUS2HRJ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-45/CC-MAIN-2020-45_segments_1603107880519.12_warc_CC-MAIN-20201023014545-20201023044545-00217.warc.gz\"}"}