Datasets:

Infi-MM
/

InfiMM-WebMath-40B

Dataset card Data Studio Files Files and versions Community

Split (1)

train · ~22.8M rows (showing the first 514k)

Subsets and Splits

No community queries yet

The top public SQL queries from the community will appear here once available.

URL stringlengths 15 1.68k	text_list sequencelengths 1 199	image_list sequencelengths 1 199	metadata stringlengths 1.19k 3.08k
https://brilliant.org/problems/thats-all/	[ "# That's all?\n\nGeometry Level 2\n\nThe two larger angles of an isosceles triangle have a combined measure of $135^\\circ$. If this triangle has a perpendicular height of $2\\text{ m}$, find the length of its base in meters.\n\nIf the latter can be expressed in the form $a\\sqrt { b } -c$, where $a,b$ and $c$ are positive integers with $b$ square-free, write your answer as $a\\times b\\times c$.\n\n×" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.87339836,"math_prob":0.99949384,"size":445,"snap":"2021-31-2021-39","text_gpt3_token_len":98,"char_repetition_ratio":0.11564626,"word_repetition_ratio":0.16,"special_character_ratio":0.2247191,"punctuation_ratio":0.21649484,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9999759,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-08-03T22:11:08Z\",\"WARC-Record-ID\":\"<urn:uuid:430df09a-491e-4fcf-8e3d-b580b4eed12d>\",\"Content-Length\":\"37310\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d93af2f7-2d87-4f58-8bb4-d3b9d3e7cebb>\",\"WARC-Concurrent-To\":\"<urn:uuid:d50de5ff-73ee-469e-b499-5724248694f3>\",\"WARC-IP-Address\":\"104.20.35.242\",\"WARC-Target-URI\":\"https://brilliant.org/problems/thats-all/\",\"WARC-Payload-Digest\":\"sha1:WATGHGCHQLQZRMVEY7QU3KXPU4PGSQK2\",\"WARC-Block-Digest\":\"sha1:P57ER75CEXAY3D66QAYYWWPSP4CGVZLF\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-31/CC-MAIN-2021-31_segments_1627046154471.78_warc_CC-MAIN-20210803191307-20210803221307-00472.warc.gz\"}"}
https://www.wired.com/2014/07/whats-the-difference-between-work-and-potential-energy/	[ "What's the Difference Between Work and Potential Energy?\n\nThe Work Energy Principle is one of the big ideas in introductory physics courses. It’s so big that the textbook presentation can get a little confusing – but it doesn’t have to be that way. How Do Textbooks Introduce the Work-Energy Principle? I haven’t looked in all the introductory textbooks, but it seems like they […]\n\nThe Work Energy Principle is one of the big ideas in introductory physics courses. It's so big that the textbook presentation can get a little confusing - but it doesn't have to be that way.\n\nHow Do Textbooks Introduce the Work-Energy Principle?\n\nI haven't looked in all the introductory textbooks, but it seems like they all follow a similar style. Oh, this is for the algebra-based physics course. That means no integration, no dot products.\n\nHere is how they do it (roughly).\n\nConservation of Energy. Many texts start off with some type of statement like \"energy is neither created nor destroyed\".\n\nTypes of Energy. There are many different types of energy: kinetic, potential, thermal energy, chemical energy.\n\nDefinition of Work. Work is defined as the ability to change energy. I know that sound silly, but sometimes textbooks make a circular definition like that. They then go on to define work in some way. Usually, it will look something like this:", null, "Just so you know, that's a fine definition of work.\n\nNon-Conservative Work. This is the part that most textbooks strive for. This is the version of the work-energy principle.", null, "Non-conservative work is a work that depends on the path. Conservative work is path independent. A great example of non-conservative work is the work done by friction. Suppose I push a block along a surface with friction from point A to point B along the two paths shown.", null, "The work done along path 2 will be greater than path 1. However, if this was work done by gravity (no friction) then the work done along the two paths would only depend on the starting and ending points. Gravity is conservative, friction is non-conservative. Why does this matter? Well, it turns out that for any conservative forces (like gravity, springs, electrostatic) you could make that work a potential instead of a \"work done by\". That's usually how a textbook explains it - perhaps it's not the best description.\n\nSpecial Cases. What about special cases where the work (non-conservative work) done is zero? In these cases, we can just say there is constant energy. Pick any two points in space and the following would be true:", null, "This isn't wrong, but it is just for the special case where the work is zero.\n\nA Different Approach\n\nWhy do we need a different approach? I think the above presentation is a little bit disjointed and confusing. Here is the way I present it in class. First, two notes. My views on work-energy are heavily influenced by the Matter and Interactions textbook (which I think is awesome). Second, it can cause a small problem when your approach isn't the same as the textbook.\n\nWhat is energy? Energy is just a way to view the world. The work-energy principle is a mathematical tool that works very well at predicting and explaining real world phenomena. That's it. The work-energy principle is just something that works (pun intended).\n\nThe simplest version of the work-energy principle is for a single point particle. The above definition of work is still fine, but in the case of a point particle the work-energy principle is:", null, "That's it. A point particle can only have kinetic energy. Note: in Matter and Interactions, this would be W = ΔE where is the energy of a particle. This version is different in that it includes an energy definition that works at relativistic speeds also.\n\nIt's all about the system. If you want a potential energy, you need to pick a system that includes more than just a mass. Let's consider a ball released from rest near the surface of the Earth that falls a distance h.\n\nIf I choose a system just consisting of the ball (which is sort of like a point mass) then I can look at the work done on this ball as it falls. What forces are acting on the ball? Just the gravitational force (mg). Since the gravitation force is in the same direction as the displacement, the angle between these two is zero. I can write:", null, "From here, you could solve for the velocity at the bottom position. Not too difficult.\n\nWhat if I change my system to include both the ball AND the Earth? In that case, I can subtract the work done by the gravitational force from both sides of the equation. I would get this:", null, "Algebraically, this is the same equation as before. However, this says that there is no work done on the system and instead we have a change in gravitational potential energy (U). The change in potential is then defined as the negative of the work done by that force. This is technically the gravitational potential energy of the ball-Earth system. In the end, you would get the same expression as before (with the system of just the point particle).\n\nBe careful. You can't have work done by gravity AND a change in gravitational potential energy. You have to do it one way or the other.\n\nThis means that the most important step in solving work-energy problems is choosing a system. For internal forces (like gravity) in a system, you will have a potential energy term.\n\nWhat about those special cases of conservation of energy? Yes, they can be useful at times - but you have to be careful to realize that they are just special cases.\n\nSummary\n\nAs I read over this post, it seems like I am that guy from Spinal Tap that tries to explain why his amplifier is better because the dial goes to 11. Yes, it might seem like I am basically saying the same thing as the textbooks. Let me emphasize the key points:\n\n• If you are talking about work but not a system, you are missing something.\n• You can do just about all of the basic problems in intro physics by picking a point particle as your system and having all the forces on that particle do work. You don't even need potential energy.\n• If you try to use energy = constant for some situation, be very careful. This is only true for some cases (not always true)." ]	[ null, "https://www.wired.com/wp-content/uploads/2014/06/la_te_xi_t_126.jpg", null, "https://www.wired.com/wp-content/uploads/2014/06/la_te_xi_t_127.jpg", null, "https://www.wired.com/wp-content/uploads/2014/06/summer_14_sketches_key5.jpg", null, "https://www.wired.com/wp-content/uploads/2014/06/la_te_xi_t_128.jpg", null, "https://www.wired.com/wp-content/uploads/2014/06/la_te_xi_t_129.jpg", null, "https://www.wired.com/wp-content/uploads/2014/06/la_te_xi_t_130.jpg", null, "https://www.wired.com/wp-content/uploads/2014/06/la_te_xi_t_1110.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9528406,"math_prob":0.83289087,"size":3051,"snap":"2022-05-2022-21","text_gpt3_token_len":640,"char_repetition_ratio":0.13324581,"word_repetition_ratio":0.0,"special_character_ratio":0.20681743,"punctuation_ratio":0.113144755,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9886342,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"im_url_duplicate_count":[null,4,null,4,null,4,null,4,null,4,null,4,null,4,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-19T02:43:24Z\",\"WARC-Record-ID\":\"<urn:uuid:daf0c0fc-20b5-4984-9d77-38985f02d59b>\",\"Content-Length\":\"613389\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:aaf983a4-7870-4b50-8576-d4c4b7606202>\",\"WARC-Concurrent-To\":\"<urn:uuid:175c6b16-5df0-4952-af8f-e74c1e3e4e5e>\",\"WARC-IP-Address\":\"146.75.34.194\",\"WARC-Target-URI\":\"https://www.wired.com/2014/07/whats-the-difference-between-work-and-potential-energy/\",\"WARC-Payload-Digest\":\"sha1:LKUH77V3P5BQK3LOGJTYO62TOEROOJOM\",\"WARC-Block-Digest\":\"sha1:WZ53LR3VHD4TCTPTGBVDUK75KGIXEIJV\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320301217.83_warc_CC-MAIN-20220119003144-20220119033144-00707.warc.gz\"}"}
https://masaka.luxiarweddingphoto.com/building-estimate-xls/	[ "", null, "building estimate xls - Masaka.luxiarweddingphoto.com\n\n# Building Estimate Xls\n\nfree estimating software building remodeling .\n\nfree construction estimating spreadsheet for building and .\n\n001 construction estimating spreadsheet free expenses excel .\n\nfree construction cost estimating spreadsheet expenses excel .\n\nbuilding cost estimator spreadsheet magdalene project org .\n\n016 free construction cost estimate excel template in india .\n\nhouse building cost estimator spreadsheet home building cost .\n\nfree construction estimate templates collections .\n\nconstruction estimate spreadsheet excel house costs building .\n\nhow to estimate a construction project fine homebuilding .\n\nfree residential construction cost estimator magdalene .\n\n015 construction cost tracking spreadsheet house expenses .\n\nhow to estimate a construction project fine homebuilding .\n\nfile estimating spreadsheet png wikimedia commons .\n\n003 building construction estimate spreadsheet excel .\n\nhome construction cost estimate spreadsheet template new .\n\nnew home construction cost spreadsheet magdalene project org .\n\nhouse construction costing spreadsheet sheet excel building .\n\nhome construction estimating spreadsheet excel template cost .\n\nhome building cost estimate spreadsheet x residential .\n\nbuilding schedule template excel construction expenses .\n\nestimated construction cost spreadsheet construction cost .\n\nbuilding cost estimator spreadsheet islamopedia se .\n\nexcel estimating spreadsheet magdalene project org .\n\nresidential construction cost estimator excel software .\n\n010 house construction budget worksheet fantastic new .\n\nhome buildingost estimate spreadsheetonstruction expenses .\n\nconstruction cost estimating spreadsheet construction cost .\n\ndetailed construction cost estimate spreadsheet house .\n\nhome construction cost estimate spreadsheet estimating india .\n\nconstruction estimating spreadsheet template beautiful free .\n\nhome building cost breakdown spreadsheet best of residential .\n\nhome building budget template house construction estimate .\n\nconstruction cost estimate te template excel residential tor .\n\nresidential construction cost estimator excel estimate .\n\nresidential construction cost estimator residential .\n\nconstruction estimating excel spreadsheet building estimate .\n\nexcavation estimating spreadsheet horoscopul org .\n\nconstruction estimating spreadsheete xls building estimate .\n\nconstruction cost estimate template spreadsheet free .\n\nresidential construction cost estimator excel philippines .\n\nconstruction cost estimate home sheet template xls india .\n\nhome building cost estimate spreadsheet home building cost .\n\nexcel template home construction estimating spreadsheet new .\n\nresidential construction cost estimator muramasa info .\n\ncost estimate template in format software estimation xls .\n\nexcel spreadsheet for construction estimating .\n\nfree rehab repair cost estimator house flipping spreadsheet .\n\ncost estimate sheet bicibague co .\n\ndetailed construction cost estimate spreadsheet construction .\n\ncost estimate spreadsheet template of construction bid .\n\nbuilding cost estimator spreadsheet magdalene project org .\n\n005 template ideas construction cost estimate spreadsheet .\n\nbuilding construction material estimate spreadsheet excel .\n\ncost estimate spreadsheet extension renovation .\n\nresidential construction cost estimator excel breakdown .\n\nresidential construction budget template excel free format .\n\nconstruction estimating spreadsheet excel report templates .\n\ncost estimate sheet linkefa co .\n\nother size s home construction estimating spreadsheet cost .\n\nfree construction cost estimate template project excel .\n\nconstruction estimating software _ free cost estimate .\n\nspreadsheet example of home building cost estimate .\n\nconstruction cost estimate spreadsheet tagua .\n\nresidential construction budget template excel free .\n\nhome building estimate spreadsheet beautiful house flipping .\n\nuda construction estimating templates light commercial .\n\nhow to estimate construction projects shawnvandyke com .\n\nhouse construction costing spreadsheet residential .\n\nit project estimation template project estimation document .\n\nconstruction cost estimate spreadsheet template umbrello co .\n\n19 free estimate templates pdf doc xls free premium .\n\nconstruction estimate templates work estimate free template .\n\nconstruction cost estimate template xls templates .\n\nconstruction cost spreadsheet template building costing estimate .\n\ndetailed construction cost estimate spreadsheet building ." ]	[ null, "https://mc.yandex.ru/watch/65499823", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.57100165,"math_prob":0.9036964,"size":5078,"snap":"2023-14-2023-23","text_gpt3_token_len":722,"char_repetition_ratio":0.38549468,"word_repetition_ratio":0.108597286,"special_character_ratio":0.15261914,"punctuation_ratio":0.13193403,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97293323,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-03-30T10:32:52Z\",\"WARC-Record-ID\":\"<urn:uuid:3d972bf9-fff8-4039-8a7a-63cbc47c5f00>\",\"Content-Length\":\"95097\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:cc973885-5c86-4234-a047-181db42f1cf6>\",\"WARC-Concurrent-To\":\"<urn:uuid:7614ed65-4a44-4e40-b79f-0a11f8fc65ad>\",\"WARC-IP-Address\":\"213.202.241.219\",\"WARC-Target-URI\":\"https://masaka.luxiarweddingphoto.com/building-estimate-xls/\",\"WARC-Payload-Digest\":\"sha1:V6N3FXCMELOYH6REJMGUSWTAXH5LJWAT\",\"WARC-Block-Digest\":\"sha1:QBE5TU6T2ETYJG45FEYDZUY5BHFAJCIY\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-14/CC-MAIN-2023-14_segments_1679296949181.44_warc_CC-MAIN-20230330101355-20230330131355-00105.warc.gz\"}"}
https://bodheeprep.com/base-system-advance	[ "Bodhee Prep-Online CAT Coaching \| Online CAT Preparation \| CAT Online Courses\n\n10% OFF on all CAT Courses. Discount code: BODHEE10. Valid till 31st May Enroll Now\n\| Best Online CAT PreparationFor Enquiry CALL @ +91-95189-40261", null, "### Addition, Subtraction and Multiplication in different bases\n\nThe process of addition, subtraction and multiplication in bases other than 10 might sound difficult because we haven’t done much practice of it during our school days. But the process is exactly same as we do in decimal system.\n\nLet us see the process of addition of two numbers in decimal system, and then we will extend the logic to add two numbers in bases other than 10.\n\nSay, we have to add 368 to 437 i.e", null, "We start from right and add the unit digits, i.e. 8 + 7 = 15. Then we write 5 at the unit digit of the final answer and carry over the number 1 to next column of ten’s digits. We repeat the same process till the end.\n\nThe entire logic lies on the answer of the question that why did we carry over 1 and kept 5 at the unit place? The logic is, 15 can be written as 10+5 or $1 \\times 10 + 5$ (read 1 time 10 plus 5). So we kept 5 at the unit place and carried over 1.\n\n(If the sum was say 47, it would have been written as $4 \\times 10 + 7$, so we would have kept 7 at unit place and carried over the number 4).\n\nHence the logic is, whenever the sum is greater than the base, we divide the sum by the base, keep the remainder and carry over the quotient.\n\nExample: Calculate (456)7 + (234)7\n\nSolution:", null, "The addition of unit digits (6 and 4) is 10, which is more than 7, and would be written as $1 \\times 7 + 3$. The quotient is 1 and the remainder of 3. The Remainder is kept at the units place of the answer and the quotient gets carried over to the ten’s place. The process is repeated till the end.\n\nSimilarly, the process of subtraction and multiplication is same as explained above. Let us take few worked out examples.\n\nExample: Calculate ${\\left( {54} \\right)_8} \\times {\\left( {36} \\right)_8}$\n\nSolution:\n\nFirst we multiple 6 with 4 = 24\n\n24 = 3$\\times$8 + 0, so the remainder 0 will be written at the unit place of the answer and 3 will be carried over to next column (ten’s digits column)", null, "Next, we multiply 6 with 5 and add 3 (carry) = 33. Again, 33 = 4$\\times$8 + 1 = (41)8. The Process till now looks like:", null, "Similarly, 3 multiplied by 4 = 12 = 1$\\times$8 + 4, so 4 is written in units place and 1 is carried over. Finally 3 multiplied by 5 + 1 (carry) = 16 = 2$\\times$8 +0 = (20)8. The process till now looks like:", null, "The last step is to add the two rows in base 8 to get the final answer which is equal to (2450)8\n\nExample: Calculate (753)9 – (476)9\n\nSolution:\n\nThe unit digits of the given numbers are 3 and 6, as 3 < 6 (we can’t subtract 6 from 3), we will take 1 carry from ten’s digit of the first number i.e 5 and the new ten’s place digit of the first number will become 4. As we are working in base 9, the weight-age of 1 carry is 9. So 3 + 1 (carry) = 3 + 9 = 12.\n\nNow, 12 – 6 = 6 is the unit digit of the answer.\n\nSimilarly moving to the next column, the new ten’s digit of first number is 4 and ten’s digit of second number is 7, again we will repeat the same concept of carry as above. The final answer is illustrated below.", null, "Therefore, (753)9 – (476)9 = (266)9\n\n### Converting number from base x to base y, none of x and y is equal to 10\n\nThe standard approach is to convert the number in base x to the number in base 10 and then again convert this number in base 10 to the number in base y. i.e.\n\n(number)x ————–> (number)10 —————> (number)y\n\nThe process is repetitive and tedious if the number is large. However if the base y is some power of x, then the conversion is easy.\n\nExample: Convert (10011110101)2 to base 4.\n\nSolution:\n\nNote that 22 = 4, also the digits used in base 4 are 0, 1, 2, and 3.\n\nThe conversions of these digits in base 4 to base 2 are as follow:\n\n(0)4 = (00)2\n\n(1)4 = (01)2\n\n(2)4 = (10)2\n\n(3)4 = (10)2\n\nTo convert (10011110101)2 into base 4, we write the digits in pairs starting from the right hand side. i.e.\n\n(10011110101)2 = (01 00 11 11 01 01)2\n\nNow substituting the above conversion from base 2 to base 4 we get\n\n(10011110101)2 = (1 0 3 3 1 1)4\n\nSimilarly, if we have to convert (2322310)4 into base 2, it can easily be done by substitution as we did in the above problem, i.e.\n\n(2322310)4 = (10 11 10 10 11 01 00)2\n\nThe logic can be extended to base 8 also by using the following substitution:\n\n Binary Octal 000 0 001 1 010 2 011 3 100 4 101 5 110 6 111 7\n\nExample: convert (100010101010100011110)2 into base 8.\n\nSolution:\n\nGrouping digits of the number in groups of three from the right hand side we get (100 010 101 010 100 011 110)2\n\nNow substituting each group of digits with the corresponding equivalence in base 8 we get:\n\n(100 010 101 010 100 011 110)2 = (4 2 5 2 4 3 6)8\n\n### Important results related to divisibility rules in different bases\n\n1. If the sum of all the digits of a number in base x is divisible by x-1, then the number itself is divisible by x-1.\n\nExample: Is (343626)9 divisible by 8?\n\nSolution:\n\nThe sum of digits = 3 + 4 + 3 + 6 + 2 + 6 = 24. As 24 is divisible by 8, the number (343626)9 is also divisible by 8.\n\n1. If a number in base x has even number of digits, and the number is a palindrome i.e. the digits equidistant from each end are the same, then the number is divisible by x+1.\n\nExample: (234432)7 is a six digit palindrome number and by the above result, it is divisible by 7+1 = 8.\n\nClick here to get one day FREE trial of full online CAT course\n\nFREE CAT Quant Practice Problems\n\nOnline CAT Quant Course\n\n### [PDF] CAT 2021 Question Paper (slot 1, 2 & 3) with Solutions\n\nCAT 2021 question paper PDF is available on this page. The page has the CAT 2021 question paper PDFs of all the three slots. There\n\n### All About CAT Mock Test Series\n\nTable of Content for CAT Mock Tests Ideal number of CAT Mock Test Series How many CAT mocks should one write What is the right\n\n### [PDF] CAT 2020 Question Paper (slot 1,2 &3) with Solution\n\nCAT 2020 question paper threw a number of surprises. Not only was there a change in exam pattern but also the difficulty level of almost\n\n### BIG change in CAT 2020 Paper Pattern\n\nAnnounced changes in CAT 2020 Pattern As we march towards the end of the year 2020, there is another unexpected turn in the sorry saga\n\n##### CAT Online Courses\n\nFREE CAT Prep Whatsapp Group" ]	[ null, "data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%20800%20456'%3E%3C/svg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%2089%20110'%3E%3C/svg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%2089%20126'%3E%3C/svg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%2078%2093'%3E%3C/svg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%2078%2093'%3E%3C/svg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%20132%20154'%3E%3C/svg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%2089%20102'%3E%3C/svg%3E", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.88518715,"math_prob":0.9945368,"size":5321,"snap":"2023-14-2023-23","text_gpt3_token_len":1622,"char_repetition_ratio":0.1346624,"word_repetition_ratio":0.018691588,"special_character_ratio":0.35275325,"punctuation_ratio":0.09288703,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99866545,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-05-31T01:09:38Z\",\"WARC-Record-ID\":\"<urn:uuid:943d51e2-8b19-48ea-a484-0947dfd0943e>\",\"Content-Length\":\"155675\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:84298500-5b04-4b37-b5aa-6da6ba2a2d86>\",\"WARC-Concurrent-To\":\"<urn:uuid:728523e4-a1cd-4bc4-a74a-926d2e4b6214>\",\"WARC-IP-Address\":\"104.21.68.107\",\"WARC-Target-URI\":\"https://bodheeprep.com/base-system-advance\",\"WARC-Payload-Digest\":\"sha1:VCWRZCH72UXW3AM6LLOGPJDFFHTQWO22\",\"WARC-Block-Digest\":\"sha1:JPXXTKLV5MWDNUV2HLSKXLSZSZLWK3MU\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224646181.29_warc_CC-MAIN-20230530230622-20230531020622-00114.warc.gz\"}"}
http://survo.fi/help/qu1_03.html	[ "#", null, "Help System (web edition)\n\n```TABTEST <table_of_frequencies>,L\nperforms various tests for independence etc. by simulation\nfor a two-dimensional table of frequencies. The table is\ngiven in edit field in the form used by the TAB operations.\nThe table can be also given in a simpler form without any labels:\nTABLE TEST / Example (An empty line indicates the end of the table.)\n7 2 0\n3 1 5\n\nDifferent assumptions about the stochastic structure of the table are\ndetermined by a FIX specification with following alternatives:\nFIX=Fisher Both row and column margins fixed (exact test)\nFIX=RC Both row and column margins fixed\nFIX=C Column margins (vertical sums) fixed\nFIX=R Row margins (horizontal sums) fixed\nFIX=N No fixed margins, only the grand total fixed\nFIX=F(i,j) Element of row i and column j fixed\nFIX=FIT Goodness of fit test for an n x 2 table\n\nThe test statistics used in simulation is selected by a TEST specification:\nTEST=X^2 is the common Pearson's chi-square statistics: sum of (O-E)^2/E .\nTEST=G^2 is the likelihood statistics: sum of -2Olog(O/E) .\nTEST=PROB is the probability of the simulated table. The unknown\nmargin probabilities are replaced by simulated relative\nfrequencies. We call this `Probability statistics'.\nIn case FIX=Fisher, TEST=PROB is always selected.\nIn other cases TEST=X^2 is default.\n\nMaximum number of replicates is given by SIMUMAX (default 10000000).\nThe seed number of the random number generator (either 'rand' or 'urand')\nis given by RAND (default RAND=rand(12345). See RAND? .\nThe process may be interrupted by pressing any key.\n\nThe results are displayed after each 100 replicates as a table of the form\nN P Confidence interval (level=0.95)\n# of replicates Estimate of P lower limit\ns.e. Standard error upper limit\n\nThe confidence level for P is set by CONF=p (0.8<p<1). Default is CONF=0.95\nThe two-way table is also saved as a matrix by using the specification\nMATRIX=<name_of_a_matrix_file> , say, MATRIX=T .\nThis matrix can be analyzed further, for example, by the sucro command\n/X2\nwhich computes various derived tables as matrices such as the expected\nfrequencies and decomposition of the X^2 statistics in cells and\nmargins.\n\n........................................................................\nExample:\nTABLE T / This 2x2 table is tested with default settings.\n7 2\n1 4\n\nTABTEST T,CUR+1\n\nG = Goodness of fit test for an n x 2 table" ]	[ null, "http://survo.fi/survologo1.gif", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.814963,"math_prob":0.9641067,"size":2432,"snap":"2020-34-2020-40","text_gpt3_token_len":553,"char_repetition_ratio":0.13797364,"word_repetition_ratio":0.04155844,"special_character_ratio":0.2598684,"punctuation_ratio":0.20973782,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9978242,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-08-14T10:09:59Z\",\"WARC-Record-ID\":\"<urn:uuid:6e28581a-9f47-4ad9-abfd-d184e4dd2965>\",\"Content-Length\":\"4275\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:49b35acf-10f6-4ff4-9f6f-e9ce6d323a6c>\",\"WARC-Concurrent-To\":\"<urn:uuid:b7cae138-ca40-48ce-adc7-509719408702>\",\"WARC-IP-Address\":\"164.215.39.201\",\"WARC-Target-URI\":\"http://survo.fi/help/qu1_03.html\",\"WARC-Payload-Digest\":\"sha1:QZWDWKBRVFNKHKO3LIQB25D236LKQLEZ\",\"WARC-Block-Digest\":\"sha1:OAMP6W34US45BQ2QDMLSZKYMZZ2JJEY5\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-34/CC-MAIN-2020-34_segments_1596439739211.34_warc_CC-MAIN-20200814100602-20200814130602-00500.warc.gz\"}"}
https://paramountestimating.com/7-steps-to-a-successful-roofing-job/	[ "# 7 Steps To A Successful Roofing Job\n\nUnderbidding is a common problem faced by the Roofing Industry nowadays. Most contractors not only underbid the job but undercut their profits as well. One of the major reasons behind this is that the roofer’s price by the number of squares instead of pricing by the time it takes them to get the job done which leads to them underestimating their overhead. Unprofessional bids are another mistake that the roofers make. There is a 90% chance of you underbidding a roofing job if you are unsure about roofing business pricing strategies.\nThe good news is you can always learn how to price and bid roofing jobs and attain a profit.\n\nFor effective pricing on the roofing job you need to follow this process:\n\n### 1. Properly understand the scope of your work\n\nInspecting the Roof\n\nDetermine the existing condition of the roof. If the flashings can’t be reused, then make sure to factor replacement flashings into your material costs. Identify all the unusual roof features, the condition, and the number of the valleys and all the damaged areas. Note down the number and condition of the vent stacks, eaves, and ridges. Also, determine whether the roof requires a complete tear-off and whether the existing materials can’t be used or not.\n\nChecking the Building Codes\n\nCheck the building codes to determine whether the existing layers can be shingled over and if the building codes allow another layer then make sure that the shingles are in good condition to support another layer. If another layer can’t be added that make sure to factor removal costs into the total estimate. Also determine which materials and colors are restricted by the Building Codes.\n\n### 2. Get the accurate measurements of the Roof\n\nCalculating the flat area of the Roof\n\nStand on the ground and measure the exterior of the house. Use these measurements to calculate the total area of the house. Then you need to divide the area of the home by 100 to find out the total number of squares. 1 square is usually covered by 3 shingles. Most of the residential roof are however pitched and we need to factor in the Roof Pitch into our calculations.\n\nDetermining the Pitch of the Roof\n\nThe roof pitch is the steepness or the slope of the roof that is created by the rafter. It is a measurement of how much the roof rises as compared to the horizontal measurement of the roof, also called the horizontal run of the roof.\n\nA ratio of 6:13 means that the roof rises 6 feet for every 13 feet of the horizontal length of the roof. The roof pitch can be either low, medium, or high. You need the measure the pitch of the house’s roof. Low pitch roofs have a ratio of 5:12 or less. Medium pitch roofs are in the ratio 6:12 or 9:12. High pitch roofs have a ratio of 10:12 to 12:12.\n\nDetermine the Roof Pitch Multiplier\n\nThe Roof Pitch multiplier is a number that is multiplied by the square foot area of the sloped roof to produce the actual surface area of the roof. A roof pitch multiplier chart is used to find out the pitch multiplier to which the ground level squares of the house’s roof, that is calculated, is multiplied to. Low pitch roofs are multiplied by a factor of 1.15 to 1.25. Medium pitch roofs are multiplied by a factor of 1.24 to 1.4. And a factor of 1.4 to 1.7 is used for high roof pitches.\n\n### 3. Estimating Material Costs\n\nDetermine the Materials Needed\n\nAfter you have the measurements of the roof, you will need to determine the type and the quantity of the required materials. List these materials down and calculate the total cost of materials. The material’s list usually includes Shingles, Nails, Flashing, Underlayment, Moisture Barriers, and Dumpsters for Shingle Removal.\n\nCalculating the Material Costs\n\nFor estimating the total number of shingles required, you will use the square footage of your house you just calculated above. The total number of squares will tell you how many shingles will be needed to cover the entire roof. Underlayment is another vital roofing material that is placed underneath the shingles and acts as a second line of defense against water damage to the roof. Once you have the total square footage of the roof you can use it to estimate the amount of underlayment. One roll of underlayment covers 4 squares. So by dividing the total number of squares by 4, we can find out the total number of underlayment required. Since Nails are sold by the pound, you will require 2 and a half pounds for each square. The most common roofing material is asphalt shingles but solar tiles, metal roofing, and rubber slate are also used. Contact your supplier to get the square footage cost of the roofing material you are using. Sum up the cost of all the materials you are using to get the total cost.\n\n### 4. Estimating the Labor Costs\n\nFor estimating the labor costs you need to first determine the labor hours, which are the hours the job will take, and then multiply it by the total number of employees on the job. Now you will need to work out the hourly labor cost. The hourly labor cost will include both the worker’s wage along with the taxes and worker’s compensation. Once you have the labor hours and the hourly wage, you will calculate the total labor cost by multiplying the labor hours with the hourly wage.\n\n### 5. Estimating the Overhead Costs\n\nOverhead costs include the costs for uniforms, accounting, rent, insurance and tools. For your business to be profitable, the price you charge must include the cost for all of these.\n\n### 6. Determining the Total Cost and Adding Markup\n\nAdd all the costs you just estimated in order to get the breakeven cost the roofing job requires. Add a markup into your total cost so that you can profit from the services you are providing. Markup is usually expressed as a percentage and it is calculated using the formula Profit/Cost * 100. The markup percentage you chose to add to the breakeven cost depends upon the Profit Margin. While pricing the roofing job, one must aim for the margin above the industry average which is 6%. You need to markup your total cost with a percentage greater than the margin to achieve your desired margin." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9320008,"math_prob":0.9530693,"size":7536,"snap":"2023-14-2023-23","text_gpt3_token_len":1660,"char_repetition_ratio":0.14471588,"word_repetition_ratio":0.012279355,"special_character_ratio":0.21536624,"punctuation_ratio":0.098,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9710835,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-06-09T04:59:28Z\",\"WARC-Record-ID\":\"<urn:uuid:e659d11f-dae9-45b7-a070-91d39328f058>\",\"Content-Length\":\"467565\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6c1305d5-41a8-4471-99ac-d287a889e731>\",\"WARC-Concurrent-To\":\"<urn:uuid:5a3fbe07-8846-4ab5-be8a-9379078b7f51>\",\"WARC-IP-Address\":\"162.0.215.250\",\"WARC-Target-URI\":\"https://paramountestimating.com/7-steps-to-a-successful-roofing-job/\",\"WARC-Payload-Digest\":\"sha1:QUWI2OQWMQQUDDVPIU5BZUBQK3ARBKPQ\",\"WARC-Block-Digest\":\"sha1:ERUKSQTEYDXDS4UQAGWSE7INSGWNYQSN\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224655247.75_warc_CC-MAIN-20230609032325-20230609062325-00208.warc.gz\"}"}
https://astarmathsandphysics.com/index.php?option=com_content&view=article&id=2047:cantor-s-theorem&catid=160&Itemid=1799	[ "## Cantor's Theorem\n\nWith the cardinality of a set defined as the number of elements of a set, it might seem obvious that thee is no largest cardinal number. To find a larger cardinal number, just find a set with more elemts. However, many sets have an infinite number of elements. What we really mean in saying that the is no largest cardinal number is that there is no limit to the order of infinity. No matter how infinitely large our set is, there is always an infinitely larger set.\n\nThis is called Cantor's Theorem. More concisely, it states: for any set", null, "", null, "(or", null, "where", null, "is the power set, the set of all subsets of", null, "If", null, "has", null, "elements, it has", null, "possible subsets.\n\nWe can prove the theorem by induction on successive power sets", null, "", null, "", null, "", null, "and so on", null, "Now set", null, "", null, "is infinite so", null, "and here is no largest cardinal number.", null, "" ]	[ null, "https://astarmathsandphysics.com/university-maths/set-theory/cantors-theorem_html_3a3f44a1.gif", null, "https://astarmathsandphysics.com/university-maths/set-theory/cantors-theorem_html_6202fcf.gif", null, "https://astarmathsandphysics.com/university-maths/set-theory/cantors-theorem_html_m4ff92a80.gif", null, "https://astarmathsandphysics.com/university-maths/set-theory/cantors-theorem_html_3a1bddbb.gif", null, "https://astarmathsandphysics.com/university-maths/set-theory/cantors-theorem_html_6c76a46c.gif", null, "https://astarmathsandphysics.com/university-maths/set-theory/cantors-theorem_html_m38ba65cf.gif", null, "https://astarmathsandphysics.com/university-maths/set-theory/cantors-theorem_html_5c8c621d.gif", null, "https://astarmathsandphysics.com/university-maths/set-theory/cantors-theorem_html_m6bab76fb.gif", null, "https://astarmathsandphysics.com/university-maths/set-theory/cantors-theorem_html_9a08917.gif", null, "https://astarmathsandphysics.com/university-maths/set-theory/cantors-theorem_html_m4ff92a80.gif", null, "https://astarmathsandphysics.com/university-maths/set-theory/cantors-theorem_html_48c02847.gif", null, "https://astarmathsandphysics.com/university-maths/set-theory/cantors-theorem_html_1ab5f47c.gif", null, "https://astarmathsandphysics.com/university-maths/set-theory/cantors-theorem_html_m76b8afdd.gif", null, "https://astarmathsandphysics.com/university-maths/set-theory/cantors-theorem_html_m3893a2ff.gif", null, "https://astarmathsandphysics.com/university-maths/set-theory/cantors-theorem_html_m52f29ed.gif", null, "https://astarmathsandphysics.com/university-maths/set-theory/cantors-theorem_html_7523650e.gif", null, "https://astarmathsandphysics.com/index.php", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.942915,"math_prob":0.96425384,"size":781,"snap":"2020-10-2020-16","text_gpt3_token_len":178,"char_repetition_ratio":0.15057915,"word_repetition_ratio":0.014705882,"special_character_ratio":0.20230474,"punctuation_ratio":0.102564104,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96804166,"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],"im_url_duplicate_count":[null,2,null,2,null,4,null,2,null,2,null,2,null,2,null,2,null,2,null,4,null,2,null,2,null,2,null,2,null,2,null,2,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-02-24T01:57:33Z\",\"WARC-Record-ID\":\"<urn:uuid:98c89b58-6214-48b3-b582-2afe04ee7608>\",\"Content-Length\":\"34266\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c4e5042c-3c98-41e1-a818-92259c8fa76a>\",\"WARC-Concurrent-To\":\"<urn:uuid:475616c2-2d95-42c4-a289-c7582fc8abec>\",\"WARC-IP-Address\":\"104.28.29.102\",\"WARC-Target-URI\":\"https://astarmathsandphysics.com/index.php?option=com_content&view=article&id=2047:cantor-s-theorem&catid=160&Itemid=1799\",\"WARC-Payload-Digest\":\"sha1:WXCKEIIQOO7VHM2H3KTCYB5IBISSTSEL\",\"WARC-Block-Digest\":\"sha1:5K6FJUJFOVQ2RDRTP5FLXMCUARYR6HKY\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-10/CC-MAIN-2020-10_segments_1581875145869.83_warc_CC-MAIN-20200224010150-20200224040150-00215.warc.gz\"}"}
https://www.khanacademy.org/math/calculus-1/cs1-analyzing-functions/cs1-connecting-f-f-and-f/v/justification-using-first-derivative	[ "If you're seeing this message, it means we're having trouble loading external resources on our website.\n\nIf you're behind a web filter, please make sure that the domains .kastatic.org and .kasandbox.org are unblocked.\n\n# Justification using first derivative\n\nAP.CALC:\nFUN‑4 (EU)\n,\nFUN‑4.A (LO)\n,\nFUN‑4.A.10 (EK)\n,\nFUN‑4.A.11 (EK)\n\n## Video transcript\n\n- [Instructor] \"The differentiable function f \"and its derivative f prime are graphed.\" So, let's see. We see the graph of y is equal to f of x here in the blue. And then f prime we see in this brownish-orangish color right over here. \"What is an appropriate calculus-based justification \"for the fact that f is decreasing \"when x is greater than three?\" So, we can see that that actually is indeed the case. When x is greater than three, we see that our function is indeed decreasing. As x increases, the y value, the value of our function, decreases. So, a calculus-based justification, without even looking at the choices, well, I could look at the derivative. And we're going to be decreasing if the slope of the tangent line is negative, which means that the derivative is negative. And we can see that for x is greater than three, the derivative is less than zero. So, my justification, I haven't even looked at these choices yet. I would say for x is greater than three, f prime of x is less than a zero. That would be my justification, not even looking at these choices. Now let's look at the choices. \"f prime is decreasing when x is greater than three.\" Now, this isn't right. What we care about is whether f prime is positive or negative. If f prime is negative, if it's less than zero, than the function itself is decreasing. The slope of the tangent line will be negative. f prime could be positive while decreasing. For example, f prime could be doing something like this. And even though f prime would be decreasing in this situation, the actual value of the derivative would be positive, which means the function would be increasing in that scenario, so I would rule this one out. \"For values of x larger than three, as x values increase, \"the values of f of x decrease.\" Now, that is actually true. This is actually the definition that f is decreasing. As x values increase, the values of f of x decrease. But this is not a calculus-based justification, so I am going to rule this one out as well. \"f prime is negative when x is greater than three.\" Well, that's exactly what I wrote up here. If f prime is negative, then that means that our slope of the tangent line of our original function f is going to be downward sloping, or that our function is decreasing, so this one is looking good. And this one right over here says, \"f prime of zero is equal to negative three,\" so they're just pointing out this point. This isn't relative to the interval that we care about, or this isn't even relevant when x is greater than three, so we definitely wanna rule that one out. Let's do one more of these. So, here we're told, \"The differentiable function g \"and its derivative g prime are graphed.\" So, once again, g is in this bluish color, and then g prime, its derivative, is in this orange color. \"What is an appropriate calculus-based justification \"for the fact that g has a relative minimum point \"at x is equal to negative three?\" And we could see here, when x is equal to negative three, it looks like g is equal to negative six, and it looks like a relative minimum point there. So, what's the best justification? So, once again, without even looking at the choices, I would say a good justification is before we get to x equals negative three, before we get to x equals negative three, our derivative, and this is a calculus-based justification, before we go to x equals negative three, our derivative is negative. And after x equals negative three, our derivative is positive. That would be my justification. Because if our derivative is negative before that value, that means that we are downward sloping before that value. And if it's positive after that value, that means we're upward sloping after that, which is a good justification that we are at relative minimum point right over there. So, let's see, \"The point where x equals negative three \"is the lowest point on the graph of g \"in its surrounding interval.\" That is true, but that's not a calculus-based justification. You wouldn't even have to look at the derivative to make that statement, so let's rule that one out. \"g prime has a relative maximum at zero comma three.\" At zero comma three, it actually does not. Oh, g prime, yes, g prime actually does have a relative maximum at zero comma three, but that doesn't tell us anything about whether we're at a relative minimum point at x equals negative three, so I would rule that out. \"g prime of negative three is equal to zero.\" So, g prime of negative three is equal to zero, so that tells us that the slope of the tangent line of our function is going to be zero right over there, but that by itself is not enough to say that we are at relative minimum point. For example, I could be at a point that does something like this where the slope of the tangent line is zero, and then it keeps increasing again, or it does something like this and it keeps decreasing. So, even though you're at a point where the slope of your tangent line is zero, it doesn't mean you're at a relative minimum point, so I would rule that out. \"g prime crosses the x-axis from below it to above it \"at x equals negative three.\" g prime crosses the x-axis from below it to above it. Yep, and that's the argument that I made, that we're going from below the x-axis, so g prime goes from being negative to positive, which means the slope of the tangent lines of our points as we approach x equals negative three go from being downward sloping to upward sloping, which is an indication that we are at a relative minimum point." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.966586,"math_prob":0.9869629,"size":5540,"snap":"2022-05-2022-21","text_gpt3_token_len":1301,"char_repetition_ratio":0.1486633,"word_repetition_ratio":0.09486166,"special_character_ratio":0.22166064,"punctuation_ratio":0.12017167,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9983535,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-24T20:01:55Z\",\"WARC-Record-ID\":\"<urn:uuid:c0da1487-7b84-40f5-ad53-d7df50c63a35>\",\"Content-Length\":\"245465\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7d90f9fe-b9f5-40d2-a2bb-623c8fd36b2b>\",\"WARC-Concurrent-To\":\"<urn:uuid:988b48f9-c0e5-427b-8083-43af4c0ff726>\",\"WARC-IP-Address\":\"146.75.33.42\",\"WARC-Target-URI\":\"https://www.khanacademy.org/math/calculus-1/cs1-analyzing-functions/cs1-connecting-f-f-and-f/v/justification-using-first-derivative\",\"WARC-Payload-Digest\":\"sha1:3RDTDEYWCAD5I34XY7XMGBMWGQ7EYNH4\",\"WARC-Block-Digest\":\"sha1:YCHYJTVSZMEINCHUE5EZ6464KJZNGQJS\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662573189.78_warc_CC-MAIN-20220524173011-20220524203011-00187.warc.gz\"}"}
http://xcelvations.com/blog/ActivityManager.ipynb	[ "# ActivityManager.ipynb\n\nIn :\nfrom xv.math.activity import ActivityManager\n\nIn :\nke = ActivityManager()\nke\n\nOut:\n2641992486576@ActivityManager\n\nMisc activities for students, with external links\n\nExample:\nke = ActivityManager()\nke.getRandomProblem()\nke.getRandomProblem(problem_type = 0)\n...\n\nke.printProblem()\nke.printSolution()\n\nke.printProblemTypes()\n\nIn :\nke.printProblemTypes()\n\n0. _problem_mobius_strip\n1. _problem_four_color_theorem\n2. _problem_right_angle_similar_triangles\n3. _problem_triangle_with_angles_more_than_2_pi\n\nIn :\nke.getRandomProblem(problem_type = 1)\n\nOut:\nTake picture of a map and color all different countries of a region with minimum number of colors. How many colors you need?\nIn :\nke.printAnswer()\n\nOut:\nYou need four colors.\nIn :\nke.printSolution()\n\nOut:\nIt is called Four Colour Theorem. Try to draw a network map of all countries you are coloring.\n\nDraw a network graph of countries with edges for direct contact. Color the nodes with different colors. You will find that all you need is four different colors.\n\n#### Resources:\n\nIn [ ]:" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.65058196,"math_prob":0.7791237,"size":1454,"snap":"2023-40-2023-50","text_gpt3_token_len":340,"char_repetition_ratio":0.15931034,"word_repetition_ratio":0.44444445,"special_character_ratio":0.24690509,"punctuation_ratio":0.21568628,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9574082,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-06T13:21:39Z\",\"WARC-Record-ID\":\"<urn:uuid:85dcc489-8438-434e-894c-1faaed607002>\",\"Content-Length\":\"47989\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:8ba871c5-9fb5-495e-a1f9-6126caee831d>\",\"WARC-Concurrent-To\":\"<urn:uuid:676a3ac9-e74b-42e5-bc1d-a4329dc59803>\",\"WARC-IP-Address\":\"207.246.127.30\",\"WARC-Target-URI\":\"http://xcelvations.com/blog/ActivityManager.ipynb\",\"WARC-Payload-Digest\":\"sha1:BVZMALJQFVNB2YTWJSJ7XFVDQGNMM2OO\",\"WARC-Block-Digest\":\"sha1:LSFTPT7VMTVAKZZIB3KYOQODIWKKLIJ6\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100599.20_warc_CC-MAIN-20231206130723-20231206160723-00832.warc.gz\"}"}
http://sdhacc.org/index.php?m=index&c=exhibitors_pro&a=company&id=184	[ "## 商会工作会员动态资讯中心供求信息培训交流 function searchnew(n,m) { var sUrl; var a; var sel=document.getElementsByName(\"cate_idser\"); var p= sel.options[sel.options.selectedIndex].value;//你要的值 if(p=='1'){a = \"/index.php?m=index&c=commerce&a=index&k={keyword}\";} if(p=='2'){a = \"/index.php?m=index&c=dynamic&a=index&k={keyword}\";} if(p=='3'){a = \"/index.php?m=index&c=news&a=index&k={keyword}\";} if(p=='4'){a = \"/index.php?m=index&c=supply&a=index&k={keyword}\";} if(p=='5'){a = \"/index.php?m=index&c=promote&a=index&k={keyword}\";} s = encodeURIComponent(document.getElementById(n).value); sUrl = a.replace(/\\{keyword}/, s) window.location.href = sUrl; return; }", null, "", null, "I am honored on behalf of the company, to express my most sincere thanks to thos。。。。[更多]", null, "", null, "", null, "", null, "" ]	[ null, "http://sdhacc.org/Public/Index/images/spcp01.jpg", null, "http://sdhacc.org/Uploads/Picture/2016-07-01/5775d25b26b0a.png", null, "http://sdhacc.org/Public/Index/images/spcp03.jpg", null, "http://sdhacc.org/Public/Index/images/spcp05.jpg", null, "http://sdhacc.org/Public/Index/images/kefu5.png", null, "http://sdhacc.org/Public/Index/images/kefu8.gif", null ]	{"ft_lang_label":"__label__zh","ft_lang_prob":0.6881037,"math_prob":0.8916826,"size":290,"snap":"2020-24-2020-29","text_gpt3_token_len":191,"char_repetition_ratio":0.0979021,"word_repetition_ratio":0.11111111,"special_character_ratio":0.35172415,"punctuation_ratio":0.10294118,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97073555,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12],"im_url_duplicate_count":[null,null,null,1,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-07-06T08:41:39Z\",\"WARC-Record-ID\":\"<urn:uuid:f8586579-0bab-4af6-a972-37353ed592ca>\",\"Content-Length\":\"16595\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4c175479-5376-4ff0-9a91-919511b4b7ee>\",\"WARC-Concurrent-To\":\"<urn:uuid:d7b1f841-3613-428b-a8a7-266cb2de565e>\",\"WARC-IP-Address\":\"139.129.158.195\",\"WARC-Target-URI\":\"http://sdhacc.org/index.php?m=index&c=exhibitors_pro&a=company&id=184\",\"WARC-Payload-Digest\":\"sha1:RCCKSFAFXWRFFTFSVVIFS4BZEY2XYGBC\",\"WARC-Block-Digest\":\"sha1:YKMWDYVHEU7ZF6KUP244RNHR72OUOW22\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-29/CC-MAIN-2020-29_segments_1593655890157.10_warc_CC-MAIN-20200706073443-20200706103443-00090.warc.gz\"}"}
http://www.jzus.zju.edu.cn/article.php?doi=10.1631/jzus.A1400199	[ "Full Text:", null, "<1759>\n\nSummary:", null, "<979>\n\nCLC number: U260.331\n\nOn-line Access: 2014-12-04\n\nRevision Accepted: 2014-11-03\n\nCrosschecked: 2014-11-07\n\nCited: 5\n\nClicked: 4506\n\nCitations: Bibtex RefMan EndNote GB/T7714", null, "ORCID:\n\nXue-song JIN\n\nhttp://orcid.org/0000-0003-3033-758X\n\nShuo-qiao ZHONG\n\nhttp://orcid.org/0000-0003-1990-5865\n\n Journal of Zhejiang University SCIENCE A 2014 Vol.15 No.12 P.984-1001 http://doi.org/10.1631/jzus.A1400199", null, "Effect of the first two wheelset bending modes on wheel-rail contact behavior\n\n Author(s): Shuo-qiao Zhong, Jia-yang Xiong, Xin-biao Xiao, Ze-feng Wen, Xue-song Jin Affiliation(s): . State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu 610031, China Corresponding email(s): zhongsq1234@163.com Key Words: High-speed railway vehicle, Wheel-rail contact behavior, Rigid wheelset, Flexible wheelset, Modal analysis, Random track irregularity Share this article to： More <<< Previous Article\|Next Article >>>\n\nShuo-qiao Zhong, Jia-yang Xiong, Xin-biao Xiao, Ze-feng Wen, Xue-song Jin. Effect of the first two wheelset bending modes on wheel-rail contact behavior[J]. Journal of Zhejiang University Science A, 2014, 15(12): 984-1001.\n\n@article{title=\"Effect of the first two wheelset bending modes on wheel-rail contact behavior\",\nauthor=\"Shuo-qiao Zhong, Jia-yang Xiong, Xin-biao Xiao, Ze-feng Wen, Xue-song Jin\",\njournal=\"Journal of Zhejiang University Science A\",\nvolume=\"15\",\nnumber=\"12\",\npages=\"984-1001\",\nyear=\"2014\",\npublisher=\"Zhejiang University Press & Springer\",\ndoi=\"10.1631/jzus.A1400199\"\n}\n\n%0 Journal Article\n%T Effect of the first two wheelset bending modes on wheel-rail contact behavior\n%A Shuo-qiao Zhong\n%A Jia-yang Xiong\n%A Xin-biao Xiao\n%A Ze-feng Wen\n%A Xue-song Jin\n%J Journal of Zhejiang University SCIENCE A\n%V 15\n%N 12\n%P 984-1001\n%@ 1673-565X\n%D 2014\n%I Zhejiang University Press & Springer\n%DOI 10.1631/jzus.A1400199\n\nTY - JOUR\nT1 - Effect of the first two wheelset bending modes on wheel-rail contact behavior\nA1 - Shuo-qiao Zhong\nA1 - Jia-yang Xiong\nA1 - Xin-biao Xiao\nA1 - Ze-feng Wen\nA1 - Xue-song Jin\nJ0 - Journal of Zhejiang University Science A\nVL - 15\nIS - 12\nSP - 984\nEP - 1001\n%@ 1673-565X\nY1 - 2014\nPB - Zhejiang University Press & Springer\nER -\nDOI - 10.1631/jzus.A1400199\n\nAbstract:\nThe objective of this paper is to develop a new wheel-rail contact model, which is suitable for considering the effect of wheelset bending deformation on wheel-rail contact behavior at high speeds. Dummies of the two half rigid wheelset are introduced to describe the spacial positions of the wheels of the deformed wheelset. In modeling the flexible wheelset, the first two wheelset bending modes are considered. Based on the modal synthesis method, these mode values of the wheelset axle are used to solve the motion equations of the flexible wheelset axle modeled as an Euler-Bernoulli beam. The wheel is assumed to be rigid and always perpendicular to the deformed axle at the wheel centre. In the vehicle model, two bogies and one car body are modeled as lumped masses. Spring-damper elements are adopted to model the primary and secondary suspension systems. The ballasted track is modeled as a triple layer discrete elastic supported model. Two high-speed vehicle-track models, one considering rigid wheelset models and the other considering flexible wheelset models, are used to analyze the differences of the numerical results of the two models in both frequency and time domains. In the simulation, a random high-speed railway track irregularity is used as wheel-rail excitations. Wheel-rail forces are calculated and analyzed in the time and frequency domains. The results clarify that this new contact model can characterize very well the influence of the first two bending modes of the wheelset on contact behavior.\n\n## 1. Introduction\n\nHigh-speed railways are currently popular globally. However, there are some problems including passenger riding comfort, noise pollution, and even operational safety (Jin et al., ). Rail corrugation, rail welding irregularity, wheel burning, and wheel out-of-roundness (OOR) generate high-frequency components of the dynamic wheel-rail contact forces that contribute significantly to the total wheel-rail contact forces (Nielsen et al., ), and reduce the life of the components of track and vehicle, such as wheels, rails, and fasteners. Rail grinding and wheel re-profiling are the most common measures that have been proved to be effective in controlling rail irregularities and wheel OOR. However, these measures lead to notably high maintenance costs. A lot of measurements at the sites and coupling vehicle-track dynamics modeling have been carried out to investigate the mechanism and development of these phenomena. In the vehicle-track dynamics modeling, a rigid multi-body system is often adopted to simulate railway vehicles, based on several commercial codes available for the low-frequency domain, such as GENSYS, NUCARS, SIMPACK, and VAMPIRE. These computer programs are generally used to analyze railway vehicle dynamics responses at frequencies below 20 Hz, where the influence of rigid motions of the vehicle on wheel-rail contact forces is dominant (Nielsen et al., ). To analyze the vehicle dynamic responses at mid- and high-frequencies, the vehicle structural flexibility should be taken into account in the modeling. It is obvious that wheelset structural flexibility has an influence on wheel-rail contact behaviors at mid- and high-frequencies. Different flexible wheelset models have been set up due to various motivations in the past (Chaar, ).\n\nThe methods applied to modeling flexible wheelset can be summarized as three major categories (Chaar, ). The first is a lumped model developed in a simple and convenient way, in which a wheelset is divided into several parts interconnected with springs and dampers. This model can describe the bending and torsional motions of the wheelset with only a few degrees of freedom, which could not be applied to studying wear phenomena on wheel treads or rails (Popp et al., ). The second is a continuous model developed by Szolc (; ), in which the wheelset axle was modeled as a beam, and two wheels and brake discs were modeled as rigid rings attached to the axle through a massless, elastically isotropic membrane. The model can characterize the wheelset dynamic behavior in the frequency range of 30–300 Hz. In the model proposed by Popp et al. (), the wheelset axle was considered as a 1D continuum, having the properties of a bar, a torsional rod, and a Rayleigh beam. The wheel was considered as a 2D continuum, having the properties of a disc and a Kirchhoff plate. The third was developed based on finite element method (FEM), which simulates wheelset flexibility more realistically than the first two categories of model. The wheelset modes and corresponding natural frequencies were obtained through the modal analysis of the finite element (FE) model by using the commercial software, and they were input into the simulation by means of the commercial codes (SIMPACK, NEWEUL) (Meinders and Meinker, ) or some non-commercial multi-body dynamic system codes. The non-commercial code developed by Fayos et al. () and Baeza et al. (; ) introduced the Eulerian coordinate system to replace the Lagrangian coordinate system in the flexible wheelset modeling. In this way it is convenient to obtain the motion of fixed physical nodes, and consider the inertial effect due to wheelset rotation. Relying on current computing power, it is feasible to use FEM to consider the effect of flexible wheelset in modeling a railway vehicle coupling with a track.\n\nRegarding the wheel-rail contact treatment in considering flexible wheelset influence, wheel-rail rolling contact condition is simplified based on different prior assumptions, especially in the detection of wheel-rail contact points. This is the prerequisite for the calculation of wheel-rail creepages and contact forces. Baeza et al. () neglected the effect of the high-frequency deformation and the deviation of a rotating flexible wheelset rolling over a flexible track model on the wheel-rail contact point in the investigation into the effect of the rotating flexible wheelset on rail corrugation. Through the detailed calculation Kaiser and Popp () found that the contact point was in the location where the wheel and the rail had positive penetration maxima, and the penetration direction was orthogonal to the common tangent plane of the wheel and the rail before their deformations. A linear wheel-rail contact model was proposed and used to carry out the detection of wheel-rail contact point and the contact zone’s normal direction (Andersson and Abrahamsson, ). In the detection, the functions were created using a first-order Taylor expansion around a reference state described by a group of parameters which represent a configuration, in which the train was in static equilibrium and the wheel and the track were free from geometric imperfections. The advantage of this approach is that the contact position and orientation in each time step can be calculated by interpolation replacing iterations, which results in a low computational cost. But the approach is only suitable for the case that the effect of all the parameters is very small on the contact point position and the contact patch orientation around the references is in static equilibrium. The wheel-rail contact point position and the contact patch orientation greatly depend on parameters, such as the curvatures of wheel and rail. In (Torstensson et al., ; Torstensson and Nielsen, ), the contact point detection was done before the simulation and used in the subsequent time integration analysis in the form of look-up table. The commercial software GENSYS allows for such calculations using the pre-processor KPF (from Swedish contact point function). In the KPF, the location and orientation of the contact patch were assumed to be dependent only on the relative displacement in the lateral direction between the wheelset and the rails, and hence the influence of the wheelset yaw angle was not taken into account. In some other papers detailed discussions on the wheel-rail contact model were omitted. In this study, the wheel-rail contact model considering the effect of wheelset flexibility (Zhong et al., ; ) is further improved and the new contact model is suitable for the analysis on the effect of the local higher-frequency deformation of the wheels on the wheel-rail contact behavior.\n\n## 2. Vehicle-track coupling dynamic system\n\nA flexible wheelset model (to be illustrated in Section 2.1) and a suitable wheel-rail contact model (to be discussed in Section 2.2) are integrated into the vehicle-track coupling dynamic system model. All parts of the vehicle system, except for its four wheelsets, are considered as rigid bodies. The primary and secondary suspension systems of the vehicle are modeled with spring-damper elements. A triple layer model of discrete elastic support is adopted to simulate the ballasted track. The rails are modeled as Timoshenko beams. The sleepers are modeled as rigid bodies and the ballast model consists of discrete equivalent masses. The equivalent spring-damper elements are used as the connections between the rails and the sleepers, the sleepers and the equivalent ballast bodies, and the ballast bodies and the roadbed. Fig. 1 shows the vehicle-track coupling dynamic system model. The equations of motion of each component of the vehicle excluding wheelsets and the track are illustrated in detail in (Xiao et al., ; ; ). The parameters and their values describing the dynamic models are given in Appendix A.\n\n### 2.1. Flexible wheelset model\n\nThe wheelset structural flexibility is considered by modeling the wheelset axle as an Euler-Bernoulli beam in two planes, one perpendicular to the track centerline and the other parallel to the track level. The crossing effect of the bending deformations in the two planes is ignored. In the first two bending modes obtained using the modal analysis of the FE model of a wheelset, two wheels have little deformation (Fig. 2), and their frequencies are in the available frequency range (0–500 Hz) of an Euler-Bernoulli beam model. Therefore, two wheels can be treated as rigid bodies in this study.", null, "Fig.2\nThe first two bending modes obtained using FE model\n\nThere are two force systems acting on the wheelset, one is the wheel-rail contact forces and the other is the forces of the primary suspension system (Fig. 3).", null, "Fig.3\nForce analysis diagram of the flexible wheelset\n\nIn Fig. 3, O fL and O fR are the left and right points on the axle, respectively, where the primary suspension force systems are applied. O CL and O CR are the left and right contact points of wheel-rail, respectively. O indicates the origin of the coordinate system O-XYZ that is a coordinate system with a translational motion along the tangent track centerline at operational speed. If the speed is constant, this coordinate system is an inertial coordinate system, and therefore regarded as an absolute coordinate system (geodetic coordinate system).\n\nTo analyze the axle’s deformation, the force systems from wheel-rail interaction acting on the left and right wheel treads are translated to the nominal circle centers O L and O R, respectively, and extra moments are produced in the procedure of translating contact forces. Thus, the force systems acting on the axle in the two planes are obtained in Fig. 4.", null, "Fig.4\nForce analysis diagram in the plane O-YZ (a) and in the O-XY plane (b)\n\nThe notations of the variables and symbols are defined in Table 1. The subscript p denotes the primary suspension, the subscripts x, y, and z denote X-, Y-, and Z-direction, respectively, and A denotes the axle.\n\n#### Table 1\n\nThe notations of the variables\n Variable Explanation u pLz , u pRz Z-direction components of the displacements of the nodes where the left and right primary suspension forces are applied on the axle, respectively u pLy , u pRy Y-direction components of the displacements of the nodes where the left and right primary suspension forces are applied on the axle, respectively u pLx , u pRx X-direction components of the displacements of the nodes where the left and right primary suspension forces are applied on the axle, respectively L Length of the wheelset axle F pLx , F pLy , F pLz X-, Y-, and Z-direction components of the primary suspension forces on the left sides of a wheelset F pRx , F pRy , F pRz X-, Y-, and Z-direction components of the primary suspension forces on the right sides of a wheelset F ALx , F ALy , F ALz X-, Y-, and Z-direction components of the forces between the left wheel and the axle of a wheelset F ARx , F ARy , F ARz X-, Y-, and Z-direction components of the forces between the right wheel and the axle of a wheelset M ALx , M ALz X- and Z-direction components of the moments between the left wheel and the axle of a wheelset M ARx , M ARz X- and Z-direction components of the moments between the right wheel and the axle of a wheelset E Young’s modulus Ix Cross-sectional area moment of inertia about the X axis Iz Cross-sectional area moment of inertia about the Z axis t Time uz (y,t), ux (y,t) X- and Z-direction components of the displacements of the nodes on the axle at time t, respectively Qz (y,t), Qx (y,t) X- and Z-direction components of the forces on the axle at time t, respectively Mz (y,t), Mx (y,t) X- and Z-direction components of the moments on the axle at time t, respectively m w Mass of a wheel g Gravity acceleration a Lz , a Rz Z-direction components of the accelerations of the left and right wheels, respectively a Lx , a Rx X-direction components of the accelerations of the left and right wheels, respectively J w Mass moment of inertia about the diameter of the wheel α Lx , α Rx X-direction components of the angular acceleration of the left and right wheels, respectively α Lz , α Rz Z-direction components of the angular acceleration of the left and right wheels, respectively u′ z (y,t), u′ x (y,t) The first derivative of uz (y, t), ux (y, t) with respect to y, respectively y wL, y wR y coordinates of the joints of the left and right wheels and the axle, respectively F wrLx , F wrLy , F wrLz X-, Y-, and Z-direction components of the left wheel-rail contact forces, respectively F wrRx , F wrRy , F wrRz X-, Y-, and Z-direction components of the right wheel-rail contact forces, respectively O cL, O cR Left and right wheel-rail contact point, respectively O wL, O wR Centers of the nominal circles of the left and right wheels, respectively O wL-X wL Y wL Z wL, O wR-X wR Y wR Z wR Body coordinate systems attached to the left and right wheels, respectively qzk , The kth generalized coordinate and the kth generalized acceleration coordinate in the plane O-YZ qxk , The kth generalized coordinate and the kth generalized acceleration coordinate in the plane O-XY ωk The kth circular frequency N Considered number of the modes Uzk (y), U′ zk (y) The kth mode function of the axle in the O-YZ plane and its first derivative with respect to y Uxk (y), U′ xk (y) The kth mode function of the axle in the O-XY plane and its first derivative with respect to y\n\nThe differential equation for the flexural vibration of an Euler-Bernoulli beam (the axle) in the plane O-YZ is written as , where , .\n\nThe force analysis diagram of the two wheels including the D’Alembert forces is shown in Fig. 5, based on which differential equations of motion of the two wheels are written as , .\n\nNote that the lateral accelerations of the wheels are assumed to be the same as the wheelset axle so there is no relative motion between wheels and axle.\n\nSubstituting the expressions of F A(L,R)z and M A(L,R)x obtained through Eqs. (4) and (5) into Eqs. (2) and (3), respectively, we can obtain: , , , where .\n\nConsider a solution of Eq. (8) in the form: . Using the calculus of variation (Qiu et al., ), the modal function satisfies: , , , where δij is the Kronecker delta. For i=j, Eq. (11) can be written as .\n\nTo obtain the mode shape functions with the wheelset axle modeled as a uniform Euler-Bernoulli beam carrying two particles (wheels), the segment of the beam from the left end to the first particle is referred to as the first portion, in between the two particles as the second portion and from the second particle to the right end as the third portion. The beam mode shape will be the superposition of the mode shapes of the three portions. The derivation of the mode shape functions is presented in Appendix B. The first three modes have the frequencies of f 1=111 Hz, f 2=245 Hz, and f 3=547 Hz, respectively. These mode shape functions are normalized so as to satisfy Eq. (14), as shown in Fig. 6. The third mode is not in the frequency range of 0–500 Hz where the Euler-Bernoulli beam is available to analyze the system. Hence, the effect of the first two modes on dynamic responses is conducted in this study.", null, "Fig.6\nThe first three bending mode shapes of the wheelset\n\nAccording to the modal analysis, we let the solution of Eq. (8) have the form: .\n\nSubstituting Eq. (15) into Eq. (8), the differential equation can be written as .\n\nMultiplying both sides of Eq. (16) by and integrating over the domain 0<y<L, we can obtain: .\n\nUsing the orthogonality of the modal shape function as expressed in Eqs. (11) and (13), Eq. (17) can be written as , where .\n\nEq. (18) can be expressed as . Eq. (20) can be written in the matrix form: , where\n\nThe explicit integral method illustrated in (Zhai, ) is used to obtain the vector of each acceleration coordinate.\n\nFor the vibration in the plane YOX, the differential equation expressed with respect to can be written as .\n\nThe derivation of Eq. (23) is similar to that of Eq. (20) and omitted here. Eq. (23) can be expressed in matrix form: , where\n\n### 2.2. Wheel-rail contact model\n\nAs mentioned in Section 2.1, the main concern in this work is the wheelset axle bending. The wheels are assumed to be rigid and their nominal rolling circles are always perpendicular to the deformed wheelset axle at their interference fit surfaces. Fig. 7 shows that the flexible wheelset moves from its initial reference state (O 1(t 1)) to its t 2 status (O 2(t 2)), which is described in the plane of O-YZ. O 1 is the center of the un-deformed wheelset at t 1, and O 2 is the center of the deformed wheelset at any time t. O 1 O 2 is the displacement vector of the wheelset center due to its rigid motion, and ϕ R1 is the roll angle due to the wheelset rigid motion. The auxiliary line, , is the central line of the un-deformed wheelset axle, is obtained by moving from O 1(t 1) to O 2(t 2), and is obtained through rotating by ϕ R1. is actually the central line of the rigid wheelset axle at t 2. Fig. 7 shows that the wheels are assumed to be rigid and always perpendicular to the deformed axle line at their connections at any time t 2.", null, "Fig.7\nA flexible wheelset moving from its initial reference state (O 1(t 1)) to its any status (O 2(t)) in the plane of O-YZ\n\nTo clearly describe the new wheel-rail contact model, the dummies of the two rigid half wheelsets, as shown in Fig. 8, are employed to describe wheel-rail rolling contact behavior affected by the wheelset bending. The two dummies are indicated by DWL and DWR, respectively, and the wheels of the DWL and the DWR are assumed to overlap the left and right wheels of the flexible wheelset, respectively, all the time, namely, the motion of the assumed rigid wheels of the flexible wheelset can be described by the DWL and the DWR (Fig. 8). ϕ R2 is the roll angle of the right wheel due to the bending deformation of the flexible wheelset. It is exactly the included angle between the line and the axle line of the right wheel or the wheel of the DWR.", null, "Fig.8\nThe relationship between the two rigid half-wheelset dummies and the flexible wheelset\n\nIt is not difficult to calculate the wheel-rail contact geometry considering the effect of the flexible deformation of the wheelset or the local high-frequency deformations of the wheels if the spatial positions of the DWL and the DWR are determined. Determining the spatial positions of the DWL and the DWR involves calculating their motion parameters, such as the lateral displacements of the centers of the wheels of the DWL and the DWR, indicated by y DWL and y DWR, respectively, the vertical displacements, z DWL and z DWR, the roll angles, ϕ DWL and ϕ DWR, and the yaw angles, ψ DWL and ψ DWR. These parameters are key to calculating the contact geometry of the flexible wheelset in rolling contact with a pair of rails by using this new wheel-rail contact model. This will now be demonstrated in detail.\n\nFig. 8 describes the motion of the DWL and the DWR influenced by the wheelset bending and its rigid motion in the O-YZ plane only. After the rigid wheelset moves with the center displacement of O 1 O 2 and the rolling angle of ϕ R1 in the O-YZ plane of the global reference, O-XYZ, its center position O 1(t 1) reaches the position O 2(t 2) and reaches (or becomes) . Note that the vector O 1 O 2 and the roll angle ϕ R1 around axis X are described in the O-YZ plane. The dash-dot line is through point O 2(t 2) and parallel to . From Fig. 6, it is obvious that the rolling angle of the DWR caused by the wheelset rigid motion is just ϕ R1, and that caused by the wheelset bending deformation is ϕ R2, so the total rolling angle of the DWR is ϕ DWR=ϕ R1+ϕ R2, as shown in Fig. 6.\n\nIn addition, the displacement of the DWR is the vector O 1 O 3R, which could be written as .\n\nIn Fig. 8, the vector O 2 A 1 is parallel to O 3R A 2 with the same length l 0. l 0 is actually the distance between the center of the wheel nominal circle and the center of the un-deformed wheelset. The vector O 2 O 3R is parallel to A 1 A 2, with the same length. Thus, O 1 O 3R can be written as .\n\nMoreover, the vector O 2 A 1 is described by {x 1 y 1 z 1}[ i j k ]T in O-XYZ, and can be obtained by rotating the vector {0 l 0 0}[ i j k ]T (coinciding with the line ) about the X-axis by ϕ DWR. O 2 A 1 is written as .\n\nThe curve (Fig. 6) is the deformed axle center line of the wheelset, which does not consider the influence of the rotation caused by the wheelset rigid motion. The point B R is the center of the right nominal circle. The axle center line () of the deformed wheelset, can be obtained by rotating about the X-axis by ϕ R1. According to the definition of the curve , the vector O 2 B R is defined as , where {Δx 2 Δy 2 Δz 2}[ i j k ]T is the displacement vector of the center of the right nominal circle due to the axle bending. Then the vector O 2 A 2 is defined as {x 3 y 3 z 3}[ i j k ]T, and can be written as , which is obtained according to the relationship between and , or obtained by rotating by ϕ R1. The wheelset center displacement vector O 1 O 2 is defined as {x 0 y 0 z 0}[ i j k ]T.\n\nSubstituting Eqs. (28) and (30) and the expression of O 1 O 2 into Eq. (27), the vector O 1 O 3R can be written as\n\nSimilarly, when considering the wheelset bending deformation in the plane O-XY, the vector O 1 O 3R should be given as where ψ R1 and ψ R2 are the yaw angles caused by the rigid motion and the bending deformation in the plane O-XY, respectively.\n\nψ DWR=ψ R1+ψ R2 is the total yaw angle of the DWR. Similarly, the position of the DWL can be obtained. When the positions of the two dummies are known at t 2, the wheel-rail contact geometry can be calculated. Then the positions of the wheel-rail contact points are easily found and the wheel-rail contact forces can be calculated. The normal wheel-rail contact forces are calculated by the Hertzian nonlinear contact spring model, and the tangent contact forces and spin moments are calculated by means of the model by Shen et al. (). Compared with the conventional wheel-rail contact model (Wang, ; Zhai, ), this new wheel-rail contact model can characterize the independent high-frequency deformations of the two wheels of the flexible wheelset more conveniently.\n\n## 3. Results and discussion\n\nWhen a vehicle is running on an ideal track, it is only excited by sleepers. Note that the “flexible” wheelset model used in this section denotes the model considering the first two bending modes. The dynamic system with flexible wheelset models is used in the simulation on an ideal track at the speed of 300 km/h. Figs. 9a and 9b show the vertical forces in the frequency domain in steady and unsteady stages, respectively. In the unsteady stage, the peaks appear not only at a set of harmonic frequencies nf s (n=1, 2, 3, …) produced by passing sleeper but also at f b1, while the influence of the second bending mode is small since there is no peak at f b2. In the steady stage, the contribution of the component at f b1 is weakened and only the peaks at nf s (n=1, 2, 3, …) remain. These results are reasonable because when a system comes to a steady stage, its responses only contain the component at the excitation frequency.", null, "Fig.9\n\nBased on a large range of site measurements, the components of roughness on rails mostly appear in the range of 1–20 m. The natural frequencies of the first two bending modes are below 250 Hz, meaning the available frequency of this model is limited. Therefore, the components of the random irregularity on the rails are mainly in the frequency range of 0–150 Hz at the speed of 300 km/h. Fig. 10a presents the local section of 900–950 m in the time domain, and Fig. 10b shows the irregularity in the frequency domain. Note that the results below are from the steady stage.", null, "Fig.10\nRandom irregularity in the time domain (a) and frequency domain (b)\n\nFigs. 11 and 12 show the wheel-rail contact forces acting on the rigid and flexible wheelsets in the time and frequency domains, respectively. As shown in Fig. 11a, the average of the oscillation of the lateral contact force acting on the flexible model is a little smaller than that on the rigid wheelset model, and the shapes of the oscillation are different. As shown in Fig. 11b, the vertical contact forces acting on the two models oscillate around a similar average, while their shapes are different. These differences are caused by the wheelset flexibility.", null, "Fig.11\nLateral contact forces (a) and vertical contact forces (b) in the time domain\n\nIn the frequency domain, the distributions of the components contained in both the lateral and vertical contact forces are in the excitation frequency range of the random irregularity. A peak at frequency 2f s appears in Figs. 11a and 11b. The contribution of the component at frequency f s is overwhelmed by the effect of the irregularity. In addition, the uniform distribution in 0–150 Hz of the irregularity results in the non-uniform distribution of contact forces. As shown in Figs. 12a and 12b, the components in 80–150 Hz are higher than those in 0–80 Hz. This shows that under this present irregularity, this dynamic system is more sensitive to the excitation in 80–150 Hz than to those in 0–80 Hz.\n\nIn the frequency domain, the component at f b1 of the lateral contact force acting on the flexible model is a little larger than that on the rigid model, as marked using the arrow in Fig. 12a. This shows that the first bending mode is excited, and the availability of the model to characterize the wheelset bending is proved. However, there is no evident difference at f b1 for vertical contact forces acting on the two models. This shows that the wheelset bending deformation has a stronger effect on the lateral contact force than on the vertical contact force.", null, "Fig.12\nLateral contact forces (a) and vertical contact forces (b) in the frequency domain\n\nThe wheel-rail contact force is affected by the position of the lateral contact points. Figs. 13a and 13b show the oscillations of the contact points in lateral direction described in the body coordinate system attached to the rail cross-section in the time and frequency domains, respectively. The average of the magnitudes of oscillation of the contact points on the flexible model in the time domain is larger than that on the rigid model. This is caused by the wheelset bending. Moreover, it can weaken the relative movement between rail and wheel caused by the irregularity. Therefore, it is one cause of the smaller average of the lateral contact force acting on the flexible model (Fig. 11a). As shown in Fig. 13b, the difference of the components between the two models at f b1 is evident. This explains the difference in the time domain (Fig. 13a) and again shows the effectiveness of the proposed model.", null, "Fig.13\nOscillation of contact points in lateral direction in the time domain (a) and frequency domain (b)\n\n## 4. Conclusions\n\nIn this study a new wheel-rail contact model is integrated into the high-speed vehicle-track coupling dynamics system model, which takes into account the effect of wheelset structural flexibility. Based on the new vehicle-track model the effect of the first two bending modes of the wheelset on wheel-rail contact behavior is analyzed under the random irregularity in a frequency range of 0–150 Hz. The numerical results of the rigid wheelset model and the flexible wheelset model are compared in detail. The following conclusions can be drawn from the results:\n\n1. The present vehicle-track model considering flexible wheelsets can very well characterize the effect of the flexible wheelset on wheel-rail dynamic behavior.\n\n2. Under the excitation, the shapes of the oscillations of the wheel-rail contact forces and contact points for the new and conventional vehicle-track models are different. The difference is caused by the excited first bending mode of the wheelset.\n\nFor future work, the first improvement to be considered is to model a wheelset using the FEM or the Timoshenko beam theory to broaden the model’s available frequency range. This could allow it to help investigate the mechanisms behind the generation and development of wheel-rail wear and noise.\n\n Project supported by the National Natural Science Foundation of China (No. U1134202), the National Basic Research Program (973) of China (No. 2011CB711103), the Program for Changjiang Scholars and Innovative Research Team in University (Nos. IRT1178 and SWJTU12ZT01), the Fundamental Research Funds for the Central Universities, and the 2014 Doctoral Innovation Funds of Southwest Jiaotong University, China\n\n## APPENDIX A\n\nThe vehicle notations and track parameters are given in Table A1.\n\n## References", null, "Andersson, C., Abrahamsson, T., 2002. Simulation of interaction between a train in general motion and a track. Vehicle System Dynamics, 38(6):433-455.", null, "", null, "Baeza, L., Vila, P., Rodaa, A., 2008. Prediction of corrugation in rails using a non-stationary wheel-rail contact model. Wear, 265(9-10):1156-1162.", null, "", null, "Baeza, L., Vila, P., Xie, G., 2011. Prediction of rail corrugation using a rotating flexible wheelset coupled with a flexible track model and a non-Hertzian/non-steady contact model. Journal of Sound and Vibration, 330(18-19):4493-4507.", null, "", null, "Chaar, N., 2007. Wheelset Structural Flexibility and Track Flexibility in Vehicle/track Dynamic Interaction. PhD Thesis, Royal Institute of Technology,Stockholm, Sweden :", null, "Fayos, J., Baeza, L., Denia, F.D., 2007. An Eulerian coordinate-based method for analysing the structural vibrations of a solid of revolution rotating about its main axis. Journal of Sound and Vibration, 306(3-5):618-635.", null, "", null, "Jin, X.S., Xiao, X.B., Ling, L., 2013. Study on safety boundary for high-speed train running in severe environments. International Journal of Rail Transportation, 1(1-2):87-108.", null, "", null, "Kaiser, I., Popp, K., 2006. Interaction of elastic wheelsets and elastic rails: modeling and simulation. Vehicle System Dynamics, 44(S1):932-939.", null, "", null, "Meinders, T., Meinker, P., 2003. Rotor dynamics and irregular wear of elastic wheelsets, system dynamics and long-term behavior of railway vehicles, track and subgrade. System Dynamics and Long-term Behaviour of Railway Vehicles, Track and Subgrade, 6:133-152.", null, "", null, "Nielsen, J.C.O., Lundn, R., Johansson, A., 2003. Train-track interaction and mechanisms of irregular wear on wheel and rail surfaces. Vehicle System Dynamics, 40(1-3):3-54.", null, "", null, "Nielsen, J.C.O., Ekberg, A., Lundn, R., 2005. Influence of short-pitch wheel/rail corrugation on rolling contact fatigue of railway wheels. Journal of Rail and Rapid Transit, 219(3):177-188.", null, "", null, "Popp, K., Kruse, H., Kaiser, I., 1999. Vehicle/track dynamics in the mid-frequency range. Vehicle System Dynamics, 31(5-6):423-463.", null, "", null, "Popp, K., Kaiser, I., Kruse, H., 2003. System dynamics of railway vehicles and track. Archive of Applied Mechanics, 72(11-12):949-961.", null, "", null, "Qiu, J.B., Xiang, S.H., Zhang, Z.P., 2009. Computational Structural Dynamics. (in Chinese), Press of University of Science and Technology of China,Hefei, China :", null, "Shen, Z.Y., Hedrick, J.K., Elkins, J.A., 1983. A comparison of alternative creep force models for rail vehicle dynamic analysis. Vehicle System Dynamics, 12(1-3):79-83.", null, "", null, "Szolc, T., 1998. Medium frequency dynamic investigation of the railway wheelset-track system using a discrete-continuous model. Archive of Applied Mechanics, 68(1):30-45.", null, "", null, "Szolc, T., 1998. Simulation of bending-torsional-lateral vibrations of the railway wheelset-track system in the medium frequency range. Vehicle System Dynamics, 30(6):473-508.", null, "", null, "Torstensson, P.T., Nielsen, J.C.O., 2011. Simulation of dynamic vehicle-track interaction on small radius curves. Vehicle System Dynamics, 49(11):1711-1732.", null, "", null, "Torstensson, P.T., Pieringer, A., Nielsen, J.C.O., 2012. Simulation of rail roughness growth on small radius curves using a non-Hertzian and non-steady wheel-rail contact model. , 9th International Conference on Contact Mechanics and Wear of Rail/Wheel Systems, Chengdu, China, 223-230. :223-230.", null, "", null, "Wang, K.W., 1984. Wheel contact point trace line and wheel/rail contact geometry parameters computation. Journal of Southwest Jiaotong University, (in Chinese),1:89-99.", null, "Xiao, X.B., Jin, X.S., Wen, Z.F., 2007. Effect of disabled fastening systems and ballast on vehicle derailment. Journal of Vibration and Acoustics, 129(2):217-229.", null, "", null, "Xiao, X.B., Jin, X.S., Deng, Y.Q., 2008. Effect of curved track support failure on vehicle derailment. Vehicle System Dynamics, 46(11):1029-1059.", null, "", null, "Xiao, X.B., Jin, X.S., Wen, Z.F., 2010. Effect of tangent track buckle on vehicle derailment. Multibody System Dynamics, 25(1):1-41.", null, "", null, "Zhai, W.M., 2007. Vehicle/Track Coupling Dynamics (3rd Edition). (in Chinese), Chinese Science Press,Beijing, China :", null, "Zhong, S.Q., Xiao, X.B., Wen, Z.F., 2013. The effect of first-order bending resonance of wheelset at high speed on wheel-rail contact behavior. Advances in Mechanical Engineering, 2013:296106", null, "", null, "Zhong, S.Q., Xiao, X.B., Wen, Z.F., 2014. A new wheel-rail contact model integrated into a coupled vehicle-track system model considering wheelset bending. , 2nd International Conference on Railway Technology Research, Development and Maintenance, Ajacocia, France, 1-10. :1-10.", null, "<1>\n\nRamesh<rcdohare@gmail.com>\n\n2016-12-28 17:32:30\n\nNo where forces values are given ,Like if a 31Tonne axle load running at 300km/hr then at what force track will experiencing in longitudinal direction,vertical direction, thrust which over turn track?", null, "" ]	[ null, "http://www.jzus.zju.edu.cn/images/pdf_logo.png", null, "http://www.jzus.zju.edu.cn/images/ppt_logo.png", null, "http://www.jzus.zju.edu.cn/images/orcid.png", null, "http://www.jzus.zju.edu.cn/images/crossmark_button.png", null, "http://www.jzus.zju.edu.cn/2014/A1412/JZUSA15-0984-fig02.jpg", null, "http://www.jzus.zju.edu.cn/2014/A1412/JZUSA15-0984-fig03.jpg", null, "http://www.jzus.zju.edu.cn/2014/A1412/JZUSA15-0984-fig04.jpg", null, "http://www.jzus.zju.edu.cn/2014/A1412/JZUSA15-0984-fig06.jpg", null, "http://www.jzus.zju.edu.cn/2014/A1412/JZUSA15-0984-fig07.jpg", null, "http://www.jzus.zju.edu.cn/2014/A1412/JZUSA15-0984-fig08.jpg", null, "http://www.jzus.zju.edu.cn/2014/A1412/JZUSA15-0984-fig09.jpg", null, "http://www.jzus.zju.edu.cn/2014/A1412/JZUSA15-0984-fig10.jpg", null, "http://www.jzus.zju.edu.cn/2014/A1412/JZUSA15-0984-fig11.jpg", null, "http://www.jzus.zju.edu.cn/2014/A1412/JZUSA15-0984-fig12.jpg", null, "http://www.jzus.zju.edu.cn/2014/A1412/JZUSA15-0984-fig13.jpg", null, "http://www.jzus.zju.edu.cn/img/top.jpg", null, "http://www.jzus.zju.edu.cn/images/crossref.bmp", null, "http://www.jzus.zju.edu.cn/img/top.jpg", null, "http://www.jzus.zju.edu.cn/images/crossref.bmp", null, "http://www.jzus.zju.edu.cn/img/top.jpg", null, "http://www.jzus.zju.edu.cn/images/crossref.bmp", null, "http://www.jzus.zju.edu.cn/img/top.jpg", null, "http://www.jzus.zju.edu.cn/img/top.jpg", null, "http://www.jzus.zju.edu.cn/images/crossref.bmp", null, "http://www.jzus.zju.edu.cn/img/top.jpg", null, "http://www.jzus.zju.edu.cn/images/crossref.bmp", null, "http://www.jzus.zju.edu.cn/img/top.jpg", null, "http://www.jzus.zju.edu.cn/images/crossref.bmp", null, "http://www.jzus.zju.edu.cn/img/top.jpg", null, "http://www.jzus.zju.edu.cn/images/crossref.bmp", null, "http://www.jzus.zju.edu.cn/img/top.jpg", null, "http://www.jzus.zju.edu.cn/images/crossref.bmp", null, "http://www.jzus.zju.edu.cn/img/top.jpg", null, "http://www.jzus.zju.edu.cn/images/crossref.bmp", null, "http://www.jzus.zju.edu.cn/img/top.jpg", null, "http://www.jzus.zju.edu.cn/images/crossref.bmp", null, "http://www.jzus.zju.edu.cn/img/top.jpg", null, "http://www.jzus.zju.edu.cn/images/crossref.bmp", null, "http://www.jzus.zju.edu.cn/img/top.jpg", null, "http://www.jzus.zju.edu.cn/img/top.jpg", null, "http://www.jzus.zju.edu.cn/images/crossref.bmp", null, "http://www.jzus.zju.edu.cn/img/top.jpg", null, "http://www.jzus.zju.edu.cn/images/crossref.bmp", null, "http://www.jzus.zju.edu.cn/img/top.jpg", null, "http://www.jzus.zju.edu.cn/images/crossref.bmp", null, "http://www.jzus.zju.edu.cn/img/top.jpg", null, "http://www.jzus.zju.edu.cn/images/crossref.bmp", null, "http://www.jzus.zju.edu.cn/img/top.jpg", null, "http://www.jzus.zju.edu.cn/images/crossref.bmp", null, "http://www.jzus.zju.edu.cn/img/top.jpg", null, "http://www.jzus.zju.edu.cn/img/top.jpg", null, "http://www.jzus.zju.edu.cn/images/crossref.bmp", null, "http://www.jzus.zju.edu.cn/img/top.jpg", null, "http://www.jzus.zju.edu.cn/images/crossref.bmp", null, "http://www.jzus.zju.edu.cn/img/top.jpg", null, "http://www.jzus.zju.edu.cn/images/crossref.bmp", null, "http://www.jzus.zju.edu.cn/img/top.jpg", null, "http://www.jzus.zju.edu.cn/img/top.jpg", null, "http://www.jzus.zju.edu.cn/images/crossref.bmp", null, "http://www.jzus.zju.edu.cn/img/top.jpg", null, "http://www.jzus.zju.edu.cn/images/crossref.bmp", null, "http://www.jzus.zju.edu.cn/auimg.php", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.89457375,"math_prob":0.9354366,"size":36033,"snap":"2021-43-2021-49","text_gpt3_token_len":8673,"char_repetition_ratio":0.19145688,"word_repetition_ratio":0.089918725,"special_character_ratio":0.23189853,"punctuation_ratio":0.13564315,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96921074,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-16T09:56:01Z\",\"WARC-Record-ID\":\"<urn:uuid:06383dcb-05ee-426f-9bc6-17ebf84f34ba>\",\"Content-Length\":\"145709\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2eaf71de-7182-4dd3-bd54-7f17feb5606b>\",\"WARC-Concurrent-To\":\"<urn:uuid:599552d8-185e-4233-bf8f-8e184d6d0f74>\",\"WARC-IP-Address\":\"210.32.15.20\",\"WARC-Target-URI\":\"http://www.jzus.zju.edu.cn/article.php?doi=10.1631/jzus.A1400199\",\"WARC-Payload-Digest\":\"sha1:MJF5MN6JJPEFB7MKBJ2RNYN6MXPFC4HY\",\"WARC-Block-Digest\":\"sha1:A33CQ552H6HCC3ZQV73VUHMFKOBF42WN\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323584554.98_warc_CC-MAIN-20211016074500-20211016104500-00407.warc.gz\"}"}
https://www.rocknets.com/converter/temperature/64.4-c-to-f	[ "# Convert 64.4 Celsius to Fahrenheit (64.4 c to f)\n\n What is 64.4 Celsius in Fahrenheit? Celsius: ℃ Fahrenheit: ℉\n\nYou may also interested in: Fahrenheit to Celsius Converter\n\nThe online Celsius to Fahrenheit (c to f) Converter is used to convert temperature from Degrees Celsius (℃) to Fahrenheit (℉).\n\n#### The Celsius to Fahrenheit Formula to convert 64.4 C to F\n\nHow to convert 64.4 Celsius to Fahrenheit? You can use the following formula to convert Celsius to Fahrenheit :\n\nX(℉)\n= Y(℃) ×\n9 / 5\n+ 32\n\nTo convert 64.4 Celsius to Fahrenheit: ?\n\nX(℉)\n= 64.4(℃) ×\n9 / 5\n+ 32\n\n#### Frequently asked questions to convert C to F\n\nHow to convert 40 celsius to fahrenheit ?\n\nHow to convert 84 celsius to fahrenheit ?\n\nHow to convert 41 celsius to fahrenheit ?\n\nHow to convert 4 celsius to fahrenheit ?\n\nHow to convert 147 celsius to fahrenheit ?\n\nHow to convert 178 celsius to fahrenheit ?\n\nTo convert from degrees Celsius to Fahrenheit instantly, please use our Celsius to Fahrenheit Converter for free.\n\n#### Best conversion unit for 64.4 ℃\n\nThe best conversion unit defined in our website is to convert a number as the unit that is the lowest without going lower than 1. For 64.4 ℃, the best unit to convert to is 64.4 ℃." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6427743,"math_prob":0.7397708,"size":1925,"snap":"2023-40-2023-50","text_gpt3_token_len":618,"char_repetition_ratio":0.2727746,"word_repetition_ratio":0.067885116,"special_character_ratio":0.33454546,"punctuation_ratio":0.14285715,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99104244,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-09T01:36:47Z\",\"WARC-Record-ID\":\"<urn:uuid:db69e4cd-b749-42f0-ad27-ba57ed466765>\",\"Content-Length\":\"69524\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:8c44bb8c-9c7e-4f1a-b4bc-bc0f182ea830>\",\"WARC-Concurrent-To\":\"<urn:uuid:aeff5544-c696-442e-83a6-c9b7ffb238e3>\",\"WARC-IP-Address\":\"172.67.199.100\",\"WARC-Target-URI\":\"https://www.rocknets.com/converter/temperature/64.4-c-to-f\",\"WARC-Payload-Digest\":\"sha1:LFKYFZJKURQ3BSO6LURMFR6V2S7QH7NA\",\"WARC-Block-Digest\":\"sha1:FV3QLIZOMXLTEAMSSYC3R7TVNS3PIKDH\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100781.60_warc_CC-MAIN-20231209004202-20231209034202-00623.warc.gz\"}"}
https://metanumbers.com/51513	[ "## 51513\n\n51,513 (fifty-one thousand five hundred thirteen) is an odd five-digits composite number following 51512 and preceding 51514. In scientific notation, it is written as 5.1513 × 104. The sum of its digits is 15. It has a total of 4 prime factors and 16 positive divisors. There are 26,640 positive integers (up to 51513) that are relatively prime to 51513.\n\n## Basic properties\n\n• Is Prime? No\n• Number parity Odd\n• Number length 5\n• Sum of Digits 15\n• Digital Root 6\n\n## Name\n\nShort name 51 thousand 513 fifty-one thousand five hundred thirteen\n\n## Notation\n\nScientific notation 5.1513 × 104 51.513 × 103\n\n## Prime Factorization of 51513\n\nPrime Factorization 3 × 7 × 11 × 223\n\nComposite number\nDistinct Factors Total Factors Radical ω(n) 4 Total number of distinct prime factors Ω(n) 4 Total number of prime factors rad(n) 51513 Product of the distinct prime numbers λ(n) 1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) 1 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0\n\nThe prime factorization of 51,513 is 3 × 7 × 11 × 223. Since it has a total of 4 prime factors, 51,513 is a composite number.\n\n## Divisors of 51513\n\n1, 3, 7, 11, 21, 33, 77, 223, 231, 669, 1561, 2453, 4683, 7359, 17171, 51513\n\n16 divisors\n\n Even divisors 0 16 8 8\nTotal Divisors Sum of Divisors Aliquot Sum τ(n) 16 Total number of the positive divisors of n σ(n) 86016 Sum of all the positive divisors of n s(n) 34503 Sum of the proper positive divisors of n A(n) 5376 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 226.965 Returns the nth root of the product of n divisors H(n) 9.58203 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors\n\nThe number 51,513 can be divided by 16 positive divisors (out of which 0 are even, and 16 are odd). The sum of these divisors (counting 51,513) is 86,016, the average is 5,376.\n\n## Other Arithmetic Functions (n = 51513)\n\n1 φ(n) n\nEuler Totient Carmichael Lambda Prime Pi φ(n) 26640 Total number of positive integers not greater than n that are coprime to n λ(n) 1110 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 5269 Total number of primes less than or equal to n r2(n) 0 The number of ways n can be represented as the sum of 2 squares\n\nThere are 26,640 positive integers (less than 51,513) that are coprime with 51,513. And there are approximately 5,269 prime numbers less than or equal to 51,513.\n\n## Divisibility of 51513\n\n m n mod m 2 3 4 5 6 7 8 9 1 0 1 3 3 0 1 6\n\nThe number 51,513 is divisible by 3 and 7.\n\n## Classification of 51513\n\n• Arithmetic\n• Deficient\n\n### Expressible via specific sums\n\n• Polite\n• Non-hypotenuse\n\n• Square Free\n\n### Other numbers\n\n• LucasCarmichael\n\n## Base conversion (51513)\n\nBase System Value\n2 Binary 1100100100111001\n3 Ternary 2121122220\n4 Quaternary 30210321\n5 Quinary 3122023\n6 Senary 1034253\n8 Octal 144471\n10 Decimal 51513\n12 Duodecimal 25989\n20 Vigesimal 68fd\n36 Base36 13qx\n\n## Basic calculations (n = 51513)\n\n### Multiplication\n\nn×i\n n×2 103026 154539 206052 257565\n\n### Division\n\nni\n n⁄2 25756.5 17171 12878.2 10302.6\n\n### Exponentiation\n\nni\n n2 2653589169 136694338862697 7041535477834110561 362730617069668537328793\n\n### Nth Root\n\ni√n\n 2√n 226.965 37.2082 15.0653 8.75756\n\n## 51513 as geometric shapes\n\n### Circle\n\n Diameter 103026 323666 8.3365e+09\n\n### Sphere\n\n Volume 5.72584e+14 3.3346e+10 323666\n\n### Square\n\nLength = n\n Perimeter 206052 2.65359e+09 72850.4\n\n### Cube\n\nLength = n\n Surface area 1.59215e+10 1.36694e+14 89223.1\n\n### Equilateral Triangle\n\nLength = n\n Perimeter 154539 1.14904e+09 44611.6\n\n### Triangular Pyramid\n\nLength = n\n Surface area 4.59615e+09 1.61096e+13 42060.2\n\n## Cryptographic Hash Functions\n\nmd5 9f36a921c26b879747bb6c172907d903 e0f7cff0aace8112eec2c9d5605fab043e49e138 8fb09d5d5ffc41ff1cd7a6feb86f021bd0bea84bc3b45c5e10bcb2d7e20e56d0 631e90e7892991c25489ee019b0e080cec3c50fdb573016d479fe59a026ce675822559991ec031e5e7cd30ec97bcf3069b69340b8b2c5fa698383b6d0476c7a2 d1d5ff341eb9336ec229506c08ddd2641d71a318" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.610897,"math_prob":0.9882308,"size":4557,"snap":"2020-34-2020-40","text_gpt3_token_len":1610,"char_repetition_ratio":0.11838348,"word_repetition_ratio":0.03372434,"special_character_ratio":0.4524907,"punctuation_ratio":0.07464608,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9948467,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-08-06T13:08:26Z\",\"WARC-Record-ID\":\"<urn:uuid:12a70c2c-43e1-4a41-973a-450a408507ef>\",\"Content-Length\":\"48591\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6a24e283-9508-468a-a253-5f8853f44fe4>\",\"WARC-Concurrent-To\":\"<urn:uuid:14cc62d1-9c34-4397-b1d6-c9eef75401b9>\",\"WARC-IP-Address\":\"46.105.53.190\",\"WARC-Target-URI\":\"https://metanumbers.com/51513\",\"WARC-Payload-Digest\":\"sha1:UCXZZR3SXT5YZVCYIOIBWK66TKCGQG7S\",\"WARC-Block-Digest\":\"sha1:QETDLEYER5EBJZXHI2Y6FJVT5L2BG2Z5\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-34/CC-MAIN-2020-34_segments_1596439736962.52_warc_CC-MAIN-20200806121241-20200806151241-00372.warc.gz\"}"}
https://polymerfem.com/community/constitutive-models/question-about-stress-update-in-umat/	[ "Clear all\n\n# Question about stress update in UMAT\n\n4 Posts\n2 Users\n0 Likes\n503 Views", null, "Posts: 7\nTopic starter\n(@donngall84)\nActive Member\nJoined: 15 years ago\n\nHi everyone,\n\nAny comments would be helpful for me, I really appreciate you guys.\n\nThank you.\n\nOkyle\n\nHi friends\n\nIt is inconvenient to download a zip file, so i uploaded the picture of my description to Flicker.\n\nLook forwards to your response, than you all.\n\nTopic Tags\n3 Replies", null, "Posts: 3993\n(@jorgen)\nMember\nJoined: 4 years ago\n\nThe stress you need to calculate is the stress at time t+dt.\nYou are given the stress at time t.\nHence: stress(t+dt) = stress(t) + dstress\n\nThere is no need to double the initial stress.\n\n-Jorgen\n\nTopic Tags\n3 Replies", null, "Posts: 7\nTopic starter\n(@donngall84)\nActive Member\nJoined: 15 years ago\n\nThank you very much, Jorgen.\n\nLet me make my question clearer: I want to calculate dstress, but I dont understand the expression (WSigma(t)-Sigma(t)W)delta t = RSigmaRT (just as the above picture describing).\n\nHow should I obtain RSigmaRT?\n\nOr should I just throw this item (RSigmaRT), and calculate the dtress via dstress= the co-rotational stress increment?", null, "Posts: 3993\n(@jorgen)\nMember\nJoined: 4 years ago\n\nI looked at your original equations again and the first equation in the image does not make sense. As you said, it would give twice the stress which does not make sense. Are you sure you wrote the equation right?\n\nI also agree with your statement regarding: (WSigma(t)-Sigma(t)W)delta t = RSigmaRT. That does not make sense to me.\n\nYou can obtain R from the deformation gradient so you can calculate RSigmaRT if you like.\n\nYou need to make sure you stress update is consistent, which will depend on your material model formulation.\n\n-Jorgen\n\nShare:" ]	[ null, "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7", null, "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7", null, "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7", null, "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.94885767,"math_prob":0.7694615,"size":367,"snap":"2023-40-2023-50","text_gpt3_token_len":82,"char_repetition_ratio":0.09917355,"word_repetition_ratio":0.0,"special_character_ratio":0.20708446,"punctuation_ratio":0.14285715,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9621269,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-01T20:20:12Z\",\"WARC-Record-ID\":\"<urn:uuid:3a89a7f9-28f2-49c9-a210-4c18fb21d77a>\",\"Content-Length\":\"227152\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:8fc9bb7a-d91c-42af-bea1-922718b51820>\",\"WARC-Concurrent-To\":\"<urn:uuid:bbab2b05-6d9f-4ddb-ac86-958b6474ef76>\",\"WARC-IP-Address\":\"35.212.48.245\",\"WARC-Target-URI\":\"https://polymerfem.com/community/constitutive-models/question-about-stress-update-in-umat/\",\"WARC-Payload-Digest\":\"sha1:GFWL252LVQPST2QJAD6DM7AJ33PKIDF3\",\"WARC-Block-Digest\":\"sha1:ANMIFVOQSLMTZUT43MWGFLDIHYTD27MK\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100304.52_warc_CC-MAIN-20231201183432-20231201213432-00509.warc.gz\"}"}
http://jfxpt.com/2020/draft-gbw-node-frontend-part-3/	[ "# Fixpoint\n\n## 2020-01-17\n\n### Draft gbw-node frontend, part 3\n\nFiled under: Bitcoin, Software — Jacob Welsh @ 18:02\n\nContinued from:\n\n### Base58\n\nBitcoin addresses are conventionally written in a special-purpose encoding and include a hash truncated to 32 bits for error detection. As the reference implementation explains:\n\nWhy base-58 instead of standard base-64 encoding?\n- Don't want 0OIl characters that look the same in some fonts and could be used to create visually identical looking account numbers.\n- A string with non-alphanumeric characters is not as easily accepted as an account number.\n- E-mail usually won't line-break if there's no punctuation to break at.\n- Doubleclicking selects the whole number as one word if it's all alphanumeric.\n\nOf course, all these points would have been answered just as well by hexadecimal, and without the various burdens: case-sensitivity for the user (the surest way I've found to read these out is the fully explicit: \"one five big-A three little-X ...\"); more code for the implementer; and more work for the machine (as the lack of bit alignment demands a general base conversion algorithm).\n\nWe start with lookup tables to convert the digits 0-57 to the specified alphabet and back. I was once surprised to learn the scope of iteration variables in a Python \"for\" loop is not restricted to the loop body: a potential source of referential confusion, reflecting the language's casual approach to mutation. Thus, when at the global scope I like to ensure throwaway names, like \"index\" and \"character\" here, are safely contained in a function.\n\n```base58_alphabet = (string.digits + string.uppercase + string.lowercase).translate(None, '0OIl')\nbase58_inverse = [None]256\ndef init_base58_inverse():\nfor index, character in enumerate(base58_alphabet):\nbase58_inverse[ord(character)] = index\ninit_base58_inverse()\n```\n\nTo do base conversion we'll need to treat byte sequences as integers with the same ordering conventions as the reference code. Otherwise put: to decode from base-256 to abstract integers. Python 2 doesn't have a builtin for this. The algorithm is not optimal, but the base-58 part will be worse anyway.\n\n```def bytes_to_int(b):\n\"Convert big-endian byte sequence to unsigned integer\"\ni = 0\nfor byte in b:\ni = (i << 8) + ord(byte)\nreturn i\n```\n\nTo complete the bytes-to-ASCII converter we extract digits from the integer, least significant first, by iterated division with remainder by 58. Since the conversion to integer loses track of field width, the convention is to pad with the same number of base-58 zeros as there were base-256 leading zeros in the input. In further fallout from using a non-bit-aligned encoding, these are not naturally constant time or constant control-flow operations.\n\nFor the same bit cost of the error detection code we could have had error correction. But that would have required, like, math, and stuff.\n\n```def b2a_base58check(data):\ndata += sha256d(data)[:4]\n\nfor b in data:\nif b != '\\x00':\nbreak\n\ndata_num = bytes_to_int(data)\n\ndigits = []\nwhile data_num:\ndata_num, digit = divmod(data_num, 58)\ndigits.append(digit)\n\nreturn ''.join(base58_alphabet[digit] for digit in reversed(digits))\n```\n\nConverting back to bytes uses the inverse operation at each step, but now there are cases of invalid input to reject: digits outside the specified alphabet and corruption detected by the checksum. (The precise function decomposition is a bit arbitrary and asymmetrical I'll admit.)\n\n```class Base58Error(ValueError):\npass\n\npass\n\npass\n\ndef a2b_base58(data):\ndigits = [base58_inverse[ord(b)] for b in data]\nif None in digits:\n\nfor digit in digits:\nif digit != 0:\nbreak\n\ndata_num = 0\nfor digit in digits:\ndata_num = 58data_num + digit\n\ndata_bytes = []\nwhile data_num:\ndata_bytes.append(data_num & 0xFF)\ndata_num = data_num >> 8\n\nreturn ''.join(chr(b) for b in reversed(data_bytes))\n\ndef a2b_base58check(data):\ndata = a2b_base58(data)\ncheck = data[-4:]\n```\n\nFinally we apply this encoding to Bitcoin addresses, which have a fixed 160-bit width plus an extra \"version\" byte that becomes the familiar leading \"1\".\n\n```class BadAddressLength(ValueError):\npass\n\npass\n\nb = a2b_base58check(a)\nif len(b) != 21:\nif b != '\\x00':\nreturn b[1:]\n\nreturn b2a_base58check('\\x00' + b)\n```\n\nAll this format conversion groundwork out of the way, we'll start talking to the database and putting it all together. To be continued!" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.76633894,"math_prob":0.92070514,"size":4919,"snap":"2023-40-2023-50","text_gpt3_token_len":1179,"char_repetition_ratio":0.10681587,"word_repetition_ratio":0.010943913,"special_character_ratio":0.26306158,"punctuation_ratio":0.140625,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9711575,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-01T16:07:36Z\",\"WARC-Record-ID\":\"<urn:uuid:e2fca984-f3ba-4ddf-8d02-2e560ca5f835>\",\"Content-Length\":\"25785\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:75a8662a-bc3a-4282-8e13-cd20378c9416>\",\"WARC-Concurrent-To\":\"<urn:uuid:6bfab770-45c4-4d56-a1ac-42af868dc7cc>\",\"WARC-IP-Address\":\"198.199.70.97\",\"WARC-Target-URI\":\"http://jfxpt.com/2020/draft-gbw-node-frontend-part-3/\",\"WARC-Payload-Digest\":\"sha1:SKADBC3C35L6DZGYLPNELIFLEUOYHQIX\",\"WARC-Block-Digest\":\"sha1:7SQ6BILRALF2UOW54X7FPDYJPNPCU7JX\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100290.24_warc_CC-MAIN-20231201151933-20231201181933-00083.warc.gz\"}"}
https://www.predictiveanalyticstoday.com/predictive-modeling/	[ "Predictive Analytics\nWhat is Predictive Modeling ?\n\n# What is Predictive Modeling ?\n\nWhat is Predictive Modeling ?\n4.7 (94.19%) 310 ratings\n\nPredictive modeling is the process of creating, testing and validating a model to best predict the probability of an outcome. A number of modeling methods from machine learning, artificial intelligence, and statistics are available in predictive analytics software solutions for this task.\n\nThe model is chosen on the basis of testing, validation and evaluation using the detection theory to guess the probability of an outcome in a given set amount of input data. Models can use one or more classifiers in trying to determine the probability of a set of data belonging to another set. The different models available on the Modeling portfolio of predictive analytics software enables to derive new information about the data and to develop the predictive models.\n\nEach model has its own strengths and weakness and is best suited for particular types of problems. A model is reusable and is created by training an algorithm using historical data and saving the model for reuse purpose to share the common business rules which can be applied to similar data, in order to analyze results without the historical data, by using the trained algorithm.", null, "Predictive Analytics Value Chain\n\nMost of the predictive modeling software solutions has the capability to export the model information into a local file in industry standard Predictive Modeling Markup Language, (PMML) format for sharing the model with other PMML compliant applications to perform analysis on similar data.\n\n## Business process on Predictive Modeling\n\n1. Creating the model : Software solutions allows you to create a model to run one or more algorithms on the data set.\n\n2. Testing the model: Test the model on the data set. In some scenarios, the testing is done on past data to see how best the model predicts.\n\n3. Validating the model : Validate the model run results using visualization tools and business data understanding.\n\n4. Evaluating the model : Evaluating the best fit model from the models used and choosing the model right fitted for the data.\n\n## Predictive modeling process\n\nThe process involve running one or more algorithms on the data set where prediction is going to be carried out. This is an iterative processing and often involves training the model, using multiple models on the same data set and finally arriving on the best fit model based on the business data understanding.", null, "Predictive Modeling\n\n## Models Category\n\n1.Predictive models :The models in Predictive models analyze the past performance for future predictions.\n\n2.Descriptive models: The models in descriptive model category quantify the relationships in data in a way that is often used to classify data sets into groups.\n\n3.Decision models: The decision models describe the relationship between all the elements of a decision in order to predict the results of decisions involving many variables.\n\n## Algorithms\n\nAlgorithms perform data mining and statistical analysis in order to determine trends and patterns in data. The predictive analytics software solutions has built in algorithms such as regressions, time series, outliers, decision trees, k-means and neural network for doing this. Most of the software also provide integration to open source R library.\n\n1. Time Series Algorithms which perform time based predictions. Example Algorithms are Single Exponential Smoothing, Double Exponential Smoothing and Triple Exponential Smoothing.\n\n2. Regression Algorithms which predicts continuous variables based on other variables in the dataset. Example algorithms are Linear Regression, Exponential Regression, Geometric Regression, Logarithmic Regression and Multiple Linear Regression.\n\n3. Association Algorithms which Finds the frequent patterns in large transactional dataset to generate association rules. Example algorithms are Apriori\n\n4. Clustering Algorithms which clustor observations into groups of similar Groups. Example algorithms are K-Means , Kohonen, and TwoStep.\n\n5. Decision Trees Algorithms classify and predict one or more discrete variables based on other variables in the dataset. Example algorithms are C 4.5 and CNR Tree\n\n6. Outlier Detection Algorithms detect the outlying values in the dataset. Example algorithms are Inter Quartile Range and Nearest Neighbour Outlier\n\n7. Neural Network Algorithms does the forecasting, classification, and statistical pattern recognition. Example algorithms are NNet Neural Network and MONMLP Neural Network\n\n8.Ensemble models are a form of Monte Carlo analysis where multiple numerical predictions are conducted using slightly different initial conditions.\n\n9.Factor Analysis deals with variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called factors. Example algorithms are Maximum likelihood algorithm.\n\n10.Naive Bayes are probabilistic classifier based on applying Bayes' theorem with strong (naive) independence assumptions.\n\n11.Support vector machines are supervised learning models with associated learning algorithms that analyze data and recognize patterns, used for classification and regression analysis.\n\n12.Uplift modeling, models the incremental impact of a treatment on an individual's behavior.\n\n13.Survival analysis are analysis of time to events.\n\n## Features in Predictive Modeling\n\n1) Data Analysis and manipulation : Tools for data analysis, create new data sets, modify, club, categorize, merge and filter data sets.\n\n2) Visualization : Visualization features includes interactive graphics, reports.\n\n3) Statistics : Statistics tools to create and confirm the relationships between variables in the data. Statistics from different statistical software can be integrated to some of the solutions.\n\n4) Hypothesis testing : Creation of models, evaluation and choosing of the right model.\n\n## Predictive Analytics Software\n\nYou may also like to review the predictive analytics free software list :\n\nYou may also like to review the predictive analytics software API :\n\nYou may also like to review the top predictive analytics proprietary software list:\n\nFor more information of predictive analytics process, please review the overview of each components in the predictive analytics process: data collection (data mining), data analysis, statistical analysis, predictive modeling and predictive model deployment.\n\nWhat is Predictive modeling?\n\nPredictive modeling is the process of creating, testing and validating a model to best predict the probability of an outcome. A number of modeling methods from machine learning, artificial intelligence, and statistics are available in predictive analytics software solutions for this task.\n\n2 Reviews\n•", null, "November 6, 2016 at 5:58 am\n\nGood summary on how to perform a predictive analysis! I just would like to share some more information about specific models and how to implement them…\n\nI’ve written a book on how to apply predictive models using Excel. In case it is of your interest, I’m publishing these models with ready-to-use templates in Excel.\n\n•", null, "January 10, 2017 at 4:10 am\n\nGood article. I´m mostly interested in predictive modeling classification. Any suggested readings?\n\nLove It\n4%\nVery Good\n8%\nINTERESTED\n46%\nCOOL\n39%" ]	[ null, "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7", null, "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7", null, "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7", null, "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.86466676,"math_prob":0.9160388,"size":7177,"snap":"2020-45-2020-50","text_gpt3_token_len":1295,"char_repetition_ratio":0.17858636,"word_repetition_ratio":0.10700758,"special_character_ratio":0.17249547,"punctuation_ratio":0.10794979,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98669684,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-12-02T03:09:32Z\",\"WARC-Record-ID\":\"<urn:uuid:f8214924-934c-4c82-bd32-6a053e0769f5>\",\"Content-Length\":\"262901\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:84b48adb-fd8e-4753-9669-468a4c3c7c83>\",\"WARC-Concurrent-To\":\"<urn:uuid:1f264c8b-a0ca-439c-9760-cb04bafd31c5>\",\"WARC-IP-Address\":\"104.26.2.98\",\"WARC-Target-URI\":\"https://www.predictiveanalyticstoday.com/predictive-modeling/\",\"WARC-Payload-Digest\":\"sha1:ALLXPKTOAPHLFUS4AXVTRZ32YJBHUPOU\",\"WARC-Block-Digest\":\"sha1:AE2TER6OZMGS3E5WDMV2F43Y7A65RPLA\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141686635.62_warc_CC-MAIN-20201202021743-20201202051743-00451.warc.gz\"}"}
https://www.webster-dictionary.org/definition/joule	[ "Word:\n\njoule\n\nPronunciation: jŌl\nn.1.(Physics.) A unit of work which is equal to 107 ergs (the unit of work in the C. G. S. system of units), and is equivalent to one watt-second, the energy expended in one second by an electric current of one ampere in a resistance of one ohm; also called the absolute joule. It is abbreviated J or j. The international joule is slightly larger, being 1.000167 times the absolute joule. The absolute joule is approximately equal to 0.737562 foot pounds, 0.239006 gram-calories (small calories), and 3.72506 x 10-7 horsepower-hours, and 0.000948451 B.t.u.\n Joule's equivalent See under Equivalent, n.\n Noun 1 joule - a unit of electrical energy equal to the work done when a current of one ampere passes through a resistance of one ohm for one secondSynonyms: J, watt second 2 Joule - English physicist who established the mechanical theory of heat and discovered the first law of thermodynamics (1818-1889)Synonyms: James Prescott Joule\nenergy unit, erg, heat unit, J, watt second, work unit\nDefinitions Index: # A B C D E F G H I J K L M N O P Q R S T U V W X Y Z" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.82903564,"math_prob":0.87002474,"size":401,"snap":"2019-43-2019-47","text_gpt3_token_len":108,"char_repetition_ratio":0.09823678,"word_repetition_ratio":0.0,"special_character_ratio":0.26433915,"punctuation_ratio":0.10526316,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9917948,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-22T04:59:42Z\",\"WARC-Record-ID\":\"<urn:uuid:4ae395d9-962b-4780-a29e-f8fd68abcef5>\",\"Content-Length\":\"16565\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:00e1b74a-31e8-4cec-ba2f-da557f5c8302>\",\"WARC-Concurrent-To\":\"<urn:uuid:81cf5e48-89ad-43fe-9f30-dab4ae9fd1d1>\",\"WARC-IP-Address\":\"45.34.10.164\",\"WARC-Target-URI\":\"https://www.webster-dictionary.org/definition/joule\",\"WARC-Payload-Digest\":\"sha1:OQEXLUOPTRFZ67PQI2623PPFAOCGDFTQ\",\"WARC-Block-Digest\":\"sha1:DRCQ5QAB53IIUYW6PQOAS4TMAOSFEEM5\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570987798619.84_warc_CC-MAIN-20191022030805-20191022054305-00254.warc.gz\"}"}
https://electronics.stackexchange.com/tags/feedback/new	[ "# Tag Info\n\n## New answers tagged feedback\n\n0\n\nThe best way to understand the differences between negative feedback and positive feedback is study the case when feed-forward block is dynamic system then extend the results to ideal linear block, let suppose that the transfer function of feedforward system is: The Feedforward block has a single pole at $s=-p_1$: $$A(s)=\\dfrac{a_0}{1+\\dfrac{s}{p_1}}$$...\n\n0\n\nIn an astable configuration, is there some way to measure output frequency, compare it with some desired value, and use this to change the resistance in the config? (Basically a feedback loop) Sure, thats relatively easy, but it requires that you have something to compare it to Ie. to check whether your output signal is actually let's say 100kHz, then you ...\n\n-1\n\nThe large swing slew Rate is always limited by drive current limit and load capacitance which near 0 ESR compare to load R. Thus dV/dt = Ic/C. Where Ic=V/R where for FETs, R = RdsOn or Ron and for BJT drivers , Ic is an active current limiter with the bulk Rce added to it. Where f(-3dB)=0.35/Tr , and Tr= 10~90% rise time, this is always less than the ...\n\n3\n\nI agree with you that the Professor's statement is unclear and confusing. When used as a voltage buffer, the DC voltage at inverting and non-inverting inputs and the output are determined by the DC voltage at the non-inverting input. As you mention, the feedback loop takes care of that. Designing the output to be biased at Vdd/2 by itself (without feedback)...\n\n1\n\nThe change in voltage with current is greater on the resistor side than on the transistor side when the current is in the normal operating range for this circuit. The derivative of voltage with respect to current is R on the resistor side and the dynamic resistance of the diode on the other side. At, say, 1uA the dynamic resistance will be around 26K ohms. ...\n\n0\n\nIn addition to Justin's answer here's a mathematical way of looking at it: Using Vout = A(Vp - Vn) The incorrect assumption that I was making was that Vout == Vp == Vn which is wrong as: Vp - Vn = 0, which is a contradiction as this would make Vout = 0 Looking as Justin's answer we can see that Vout (and therefore Vn) start at 0v and rises with time until ...\n\n1\n\nWhen you are considering a step response, you need to include the time delays at the different locations for the answer to be reasonable. One way to model this is to add an RC filter at the output of the op-amp. The other thing that you haven't accounted for is that the op-amp can't actually drive the output to greater than the positive supply voltage. ...\n\n0\n\nI'm trying to get an understanding of how negative feedback works. Think of it like a control system and an error amplifier. You set the \"demand\" on the non-inverting input and the negative feedback causes the op-amp output to rapidly change to a voltage that makes the input error minimal. In other words, the inverting input is made to be nearly the same ...\n\nTop 50 recent answers are included" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9014514,"math_prob":0.9448979,"size":4046,"snap":"2019-35-2019-39","text_gpt3_token_len":1081,"char_repetition_ratio":0.1192479,"word_repetition_ratio":0.0028530671,"special_character_ratio":0.2745922,"punctuation_ratio":0.09346991,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9825911,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-09-20T16:40:26Z\",\"WARC-Record-ID\":\"<urn:uuid:9159c0ad-905a-45d3-a950-4c98d71b6474>\",\"Content-Length\":\"102419\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:5e5740b9-8ee7-4938-88fc-bf59a76f619d>\",\"WARC-Concurrent-To\":\"<urn:uuid:03bb334a-2ed8-48d5-a6af-e31ff3a0a55c>\",\"WARC-IP-Address\":\"151.101.129.69\",\"WARC-Target-URI\":\"https://electronics.stackexchange.com/tags/feedback/new\",\"WARC-Payload-Digest\":\"sha1:JD6PE52CVZVVY3PROONZJSO73KXHPMET\",\"WARC-Block-Digest\":\"sha1:5SB7RIHNSL7IZBEZ7LX5ENVXANHIQ3CS\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-39/CC-MAIN-2019-39_segments_1568514574050.69_warc_CC-MAIN-20190920155311-20190920181311-00164.warc.gz\"}"}
http://www.kurpinskisclass.com/unit-d-mechanical-systems-i/	[ "# Mechanical Systems\n\n### Machines are tools that help humans do work\n\nMachines help people use energy more effectively.\n\n## Machine :\n\nA device that helps us to do work.\n\nAn example of technology developing is a combine harvester.\n\n# Simple Machines – Meet Human Needs\n\n### Early machines\n\n1) Were very simple devices\n\n2) Depended on people & animals for their source of energy.\n\n3) Example: Plow\n\n### How did earlier civilizations get water to their homes?\n\nRoman Aqueducts\n\nUsed for transporting water for many kilometres to supply cities.\n\nHad 3 parts: Pump – raise water into reservoirs.\n\nChannels – on a slope to carry the water.\n\nDistribution system – distributes water within a city.\n\nSakia (Persian wheel)\n\n• Series of buckets attached to a long rope, draped over a wheel.\n\n• Wheel is turned by animals which raises the buckets of water.\n\n• After water is raised it is stored in tanks.\n\n• Gravity moves water through pipes and into homes.\n\nArchimedes Screw\n\n• A screw picks up the water and carries it up to the top of the tube.\n\n• Originally powered by hand, then later by gas or electric motors.\n\n• Leonardo da Vinci later used 2 Archimedes screws to increase efficiency\n\nPresent Day Pumps\n\n• Pumps keep the water flowing and are powered by motors.\n\n# Simple Machines\n\n## Simple Machine:\n\nA tool or device made up of one basic machine.\n\n• There are 6 simple machines that help us do work.\n\n• Each machine has its own advantages and disadvantages.\n\n• A simple machine can increase or change the direction of the force that you apply. But, the cost is that the force the user applies must move farther than the load.\n\n## 1) Lever:\n\nA rigid bar or plank that can rotate around a fixed point called a pivot or fulcrum.\n\n• Enables the user to move a larger load than without.\n\n• But the user must move a greater distance than the load.\n\n### 3 types of Levers:\n\n1. First class lever – fulcrum between the load and the point of effort.\n\n2. Second class lever – load is between the effort and the fulcrum.\n\n3. Third class lever – has the effort between the load and the fulcrum.\n\n## 2) Inclined Plane:\n\nA flat surface that is at an angle to another flat surface, such as the ground.\n\n• Enables the user to move a larger load than without.\n\n• But the user must move a greater distance than the load.\n\n• The ramp cannot be too steep in order to work.\n\n## 3) Wedge:\n\nSimilar to an inclined plane, but is forced into an object.\n\n• By pressing on the wide end, the narrow end splits the object.\n\n• Can only be used in one direction, to push objects apart.\n\n• Enables the user to apply a greater force on an object.\n\n• But the user must move a greater distance than the split.\n\n## 4) Screw:\n\nConsists of a cylinder with a groove cut in a spiral on the outside.\n\n• Can penetrate materials using a relatively small force.\n\n• Convert rotational motion to linear motion.\n\n• Most screws move objects very slowly.\n\n## 5)Pulley:\n\nMade up of a wire, rope, or cable moving on a grooved wheel.\n\n• May be made up of one or many wheels.\n\n• Can be fixed in place or movable.\n\n## 6) Wheel and Axle:\n\nMade up of two wheels of different diameters the turn together.\n\n• A longer motion on the wheel produces a shorter more powerful motion on axle.\n\n• Enable the user to apply a greater force on an object.\n\n• But the user must move the wheel a greater distance to apply the force.\n\n• Can also be used to increase speed (ex. Bicycle).\n\n# Complex Machines – Simple machines working together\n\n### Why complex machines?\n\n1. As larger communities developed, newer more complicated machines developed.\n\n2. New larger energy sources like coal, oil, and electricity combined with new technologies, caused an industrial revolution.\n\n3. This led to an increase in people’s standard of living.\n\n4. But has also led to people now being dependent on technology.\n\n## Complex Machines:\n\nA system in which simple machines all work together.\n\n## System:\n\nA group of parts that work together to perform a function.\n\nEx. Bicycle (which simple machines does a bicycle employ)\n\n## Subsystem:\n\nA smaller group of parts in a complex machine with one function.\n\n(Ex) Car - braking and steering\n\n# Subsystems that Transfer Forces\n\nA belt or chain to transfer energy from a energy source to an object.\n\n• (Ex) bicycle chain\n\n## Transmission:\n\nA special type of linkage for transferring energy from the engine to the wheel in large vehicles such as cars or trucks.\n\n• more useful when larger loads must be moved.\n\n## Gears:\n\nA pair of wheels with teeth that interlink; when they rotate together, one gearwheel transfers turning motion and force to the other.\n\n• are important because control the transfer of energy in a system.\n\n• gear wheels work together in gear trains (2 or more gears).\n\n## DRIVING GEAR:\n\nGear that has original force applied to it.\n\n## DRIVEN GEAR:\n\nGear that receives the force after.\n\n### How do gears affect speed?\n\n(I) When driving gear is smaller than the driven gear = The turning speed in the system decreases.\n\n• For every turn the larger wheel makes the smaller gear will do many more.\n\n• Are called multiplying gears.\n\n(II) When the driving gear is larger than the driven gear = The turning speed in the system increases.\n\n• Are called reducing gears.\n\n• In some systems the gears are meshed together, but in some cases they are connected by a linkage.\n\n# Understanding of mechanical advantage and work helps determine the efficiency of machines\n\nUnderstanding simple & complex machines advanced world exploration,\n\n• (Ex) Sail boat\n\n### Machines Make Work Easier.\n\n- A winding road is actually a series of inclined planes with switchbacks, which allow cars to drive up a steep hill.\n\nSWITCHBACKS OF LOMBARD STREET SAN FRANCISCO\n\n## Mechanical Advantage :\n\nAmount by which a machine can multiply a force. Also called the force ratio\n\n## Input Force:\n\nForce applied to the machine.\n\n## Output Force:\n\nForce the machine applies to the object.\n\n### Force is measured in Newtons (N).\n\nMechanical Advantage (MA) = Force Output (N) / Force Input (N)\n\n### EX 1\n\nTo pull a weed out of a garden, you can apply a force of 50 N to the shovel. The shovel applies a force of 600 N to the weed. What is the mechanical advantage of the shovel?\n\n### EX 2\n\nTo pry open a soda can lid, you can apply a force of 50 N to a car key. The car key applies a force of 390 N to the lid. What is the mechanical advantage of the car key?\n\n### EX 3\n\nTo pry a wooden board off of a treehouse, you can apply a force of 50 N to a lever. The lever applies a force of 750 N to the board. What is the mechanical advantage of the lever?\n\nREVIEW QUESTIONS\n\n## Speed:\n\nMeasures the distance an object travels in a given amount of time.\n\nSpeed = Distance (m)/ Time (s)\n\n## Speed Ratio:\n\nMeasure of how the speed of the object is affected by a machine.\n\nSR describes how much faster the user is moving than the load is working.\n\nSpeed Ratio (SR) = Input Distance (m)/ Output Distance (m)\n\n### Ex 1\n\nA gear mechanism of two gear is in motion. The driving gear moves a total of 3m, while the driven gear moves a total of 12m. What is the speed ratio of this mechanism?\n\n### EX 2\n\nA pulley system is pulled a distance of 10 m, this moves a box that is attached to the pulley 1.5m. What is the speed ratio of the pulley system?\n\n** A machine can increase or change the direction of the force that you apply. But, the cost is that the force the user applies must move farther than the load.\n\nREVIEW QUESTIONS\n\n### A Mechanical Advantage Less Than 1\n\nUseful for tasks that do not require a large output force.\n\n• (Ex) Bicycle – the output force is used for speed.\n\n# The Effect of Friction\n\n• Mechanical Advantage does NOT always equal Speed Ratio.\n\n• Friction can affect MA, but not SR.\n\n• Speed ratio represents the ideal mechanical advantage (No friction).\n\nFRICTION WELDING OF TWO METAL PIECES\n\n## Friction:\n\nForce that opposes motion.\n\n• caused by the roughness of surfaces.\n\n• as roughness of a surface increases so does the effect of friction.\n\n• friction creates HEAT, and must be released to protect the system.\n\n# Efficiency\n\n## Efficiency:\n\nMeasurement of how well a machine or device uses energy.\n\n• affected by friction.\n\n• most energy lost is unusable (ex. Heat).\n\nEfficiency = Mechanical Advantage / Speed Ratio\n\nMost complex machines are very inefficient: waste energy.\n\nex) Car – 15% efficient.\n\n# The Science of Work\n\n## Work:\n\nDone when a force acts on an object to make the object move.\n\nMovement is needed before one can say that work has been done.\n\nAlso reffered to as 'Energy'\n\nMeasure in Joules (J) (N x m)\n\nAmount of work done depends on 2 things:\n\n1. amount of force exerted on the object\n\n2. distance the object moved in the direction of the applied force.\n\nWork (N x m) = Force (N) x Distance (m)\n\n- The joule is also used in calculating Energy.\n\n### EX 1\n\nYou apply 300 N of force in 15 m. How much work did you do?\n\n### EX 2\n\nA forklift lifts a box 2 m by applying 1000 N of force. How much work did the forklift do?\n\n### Ex 3\n\nYou have used 1000 J of energy to apply a force of 200 N to an object. How far did that object move?\n\nREVIEW QUESTIONS\n\n## Power:\n\nHow much work is achieved in a certain amount of time, measured in Watts\n\nPower (W) = Work (J) / Time (s)\n\n### EX 1\n\nYou apply 200 J to an object in 15 s. How much power did you use?\n\n### EX 2\n\nAn engine provides 5000 J of work to an axle over the period of 10 seconds. How much power does the engine have?\n\n### Ex 3\n\nA horse pulls a wagon by working 4500 J over a time of 6 s. How much power does the horse produce?\n\n# Energy and Work\n\nEnergy and work are closely related, can not have one without the other.\n\n(Ex) Car – needs energy (gasoline) in order to work (move)\n\n### Work and Machines\n\nUsing a machine does not decrease the amount of work, it decreases the force.\n\nWork Input = Work Output\n\nThis equation is affected by friction (just like mechanical advantage)\n\nHere is another way of calculating efficiency:\n\nEfficiency = Work Output/ Work Input\n\n### EX 1\n\nA construction worker puts 20 J of energy in to one strike of his hammer on the head of a nail. The energy transferred to driving the nail in to the wood is 8.0 J. What is the efficiency of the construction worker's hammering?\n\n### EX 2\n\nMr. K spent 25 J of energy to spike a volleyball over the net. A player received that volleyball and determined that the energy transferred to the ball was 20 J of energy. What is the efficiency of Mr. K's spike?\n\n### EX 3\n\nA particular chemical process has an energy efficiency of only 3.00%. To complete this large-scale chemical process, 140,000 J of energy is input. What is the energy output of this process?\n\nREVIEW QUESTIONS" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9155963,"math_prob":0.817656,"size":10116,"snap":"2019-13-2019-22","text_gpt3_token_len":2335,"char_repetition_ratio":0.124505535,"word_repetition_ratio":0.08791801,"special_character_ratio":0.22617635,"punctuation_ratio":0.10235064,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96018463,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-03-26T17:00:33Z\",\"WARC-Record-ID\":\"<urn:uuid:f6b1ebaa-45a6-4136-b87e-9b3c77305fd0>\",\"Content-Length\":\"114165\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0c18c239-2b65-46b9-8f3d-36a98c80a22e>\",\"WARC-Concurrent-To\":\"<urn:uuid:d69b04c6-9cbe-4c31-8a22-04ccee42c83f>\",\"WARC-IP-Address\":\"198.49.23.144\",\"WARC-Target-URI\":\"http://www.kurpinskisclass.com/unit-d-mechanical-systems-i/\",\"WARC-Payload-Digest\":\"sha1:RKWOJZR7IEMPBBKVDNH3LYPVNZ6QUCWV\",\"WARC-Block-Digest\":\"sha1:UXYRCE76JXFOXZ3E4CFFEBFVOEDDJ7IJ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-13/CC-MAIN-2019-13_segments_1552912205597.84_warc_CC-MAIN-20190326160044-20190326182044-00118.warc.gz\"}"}
https://www.learner.org/courses/mathilluminated/glossary/12.php	[ "", null, "Teacher resources and professional development across the curriculum\n\nTeacher professional development and classroom resources across the curriculum", null, "", null, "# Glossary\n\n## Deravative\n\nTo capture the notion of rates of change that can themselves change, we need the concept of a derivative.\n\n## Differential Calculus\n\nFirst described rigorously by Newton and Leibniz, differential calculus is the mathematics of changing quantities.\n\n## Differential Equation\n\nA differential equation is an expression that relates quantities and their rates of change. The solution to a differential equation is not simply a number; it is a function.\n\n## Non-Constant Slope\n\nA non-constant slope describes a rate of change that itself can change.\n\n## Oscillators\n\nAn oscillator is a function that varies between two values.\n\n## Slope-Intercept\n\nThe slope-intercept form of a linear equation is a common way to represent the mathematics of change. An example of this concern with relationships is the familiar slope-intercept form of the equation of a line: y = mx +b.", null, "## Spontaneous Synchronization\n\nSpontaneous synchronization is a special case of complicated dynamic phenomena. Understanding the mathematics of how, and under what circumstances, entities can come into synchronization with one another provides a starting point for exploring the vast world of nonlinear dynamics." ]	[ null, "https://www.learner.org/images/header/annenberg-learner.jpg", null, "https://www.learner.org/images/header/mail_list_icon.png", null, "https://www.learner.org/images/header/search_icon.jpg", null, "https://www.learner.org/courses/mathilluminated/images/units/12/1745.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.91833717,"math_prob":0.95824856,"size":1309,"snap":"2019-51-2020-05","text_gpt3_token_len":237,"char_repetition_ratio":0.1118774,"word_repetition_ratio":0.0,"special_character_ratio":0.17265087,"punctuation_ratio":0.08715596,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99324286,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,null,null,null,null,null,null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-12T07:38:11Z\",\"WARC-Record-ID\":\"<urn:uuid:bab4608c-c31a-4a5b-8b2a-fef9def8e410>\",\"Content-Length\":\"41246\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c5eb11ce-9f69-437a-a219-e828aa1027af>\",\"WARC-Concurrent-To\":\"<urn:uuid:391bd620-58e5-4274-b917-9391f216dbeb>\",\"WARC-IP-Address\":\"104.26.1.85\",\"WARC-Target-URI\":\"https://www.learner.org/courses/mathilluminated/glossary/12.php\",\"WARC-Payload-Digest\":\"sha1:QN5F3XSH6SPENXH56ZWJQO5KRJZ7RZK7\",\"WARC-Block-Digest\":\"sha1:XVJN7MSD4NTAVCIRHTDLYUQ6I5IGVUAT\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575540537212.96_warc_CC-MAIN-20191212051311-20191212075311-00535.warc.gz\"}"}
http://www.mdsk.net/read/0-d2-d1-d6-aa-b6-a8-d2-e5-d3-f2-ce-aaR-b5-c4-ba-af-ca-fdf-a3-a8x-a3-a9-ce-aa-c6-e6-ba-af-ca-fd-a3-ac-c7-d2-c2-fa-d7-e3f-a3-a8x-2b4-a3-a9-3df-a3-a8x-a3-a9-a3-ac-b5-b1x-a1-ca-5b0-a3-ac1-5d-ca-b1-a3-acf-a3-a8x-a3-a9-3d2....html	[ "# 已知定义域为R的函数F（x）为奇函数，且满足F（x+4）=F（x），当x∈[0，1]时，F（x）=2...\n\n（1）令x∈[-1，0），则-x∈（0，1]，∴f（-x）=2-x-1，又∵f（x）是奇函数，∴f（\n\n(x+1)=f(3−x)-------周期=4 x∈(0,2]时f(x)=&a\n\n(1)f(x)=-f(x-4),为奇函数 ∴f(x+2)=-f(x+2-4)=-f(x-2)=f(\n\n∵f（x-4）=-f（x） ∴f（x）=-f（x-4） ∴f（x+8）=-f（x+8-4）=\n\n∵f（x）是定义在R上的奇函数，故f（0）=0，即0是函数f（x）的零点，又由f（x）是定义在R上且" ]	[ null ]	{"ft_lang_label":"__label__zh","ft_lang_prob":0.9105936,"math_prob":0.9999546,"size":485,"snap":"2020-10-2020-16","text_gpt3_token_len":435,"char_repetition_ratio":0.12266112,"word_repetition_ratio":0.0,"special_character_ratio":0.5505155,"punctuation_ratio":0.051612902,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9771449,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-02-23T04:58:50Z\",\"WARC-Record-ID\":\"<urn:uuid:11af6eda-5c90-4635-96cb-1d0303ca8633>\",\"Content-Length\":\"11509\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:bca5b701-8bb3-493e-834b-f74b3a1697a1>\",\"WARC-Concurrent-To\":\"<urn:uuid:d680f52a-5ff3-4c57-b374-8afc30a55f88>\",\"WARC-IP-Address\":\"103.143.80.239\",\"WARC-Target-URI\":\"http://www.mdsk.net/read/0-d2-d1-d6-aa-b6-a8-d2-e5-d3-f2-ce-aaR-b5-c4-ba-af-ca-fdf-a3-a8x-a3-a9-ce-aa-c6-e6-ba-af-ca-fd-a3-ac-c7-d2-c2-fa-d7-e3f-a3-a8x-2b4-a3-a9-3df-a3-a8x-a3-a9-a3-ac-b5-b1x-a1-ca-5b0-a3-ac1-5d-ca-b1-a3-acf-a3-a8x-a3-a9-3d2....html\",\"WARC-Payload-Digest\":\"sha1:W2ACCV6QZLRIQ2LIPBNZPALTGZVDRTGM\",\"WARC-Block-Digest\":\"sha1:RL5EBAL5VKP5POUJJCCAHKPATVLUBDRR\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-10/CC-MAIN-2020-10_segments_1581875145746.24_warc_CC-MAIN-20200223032129-20200223062129-00230.warc.gz\"}"}
https://math.stackexchange.com/questions/132677/how-can-you-add-not-g-to-a-formal-system-without-introducing-omega-inconsisten	[ "# How can you add 'not G' to a formal system without introducing omega inconsistency?\n\nIn any formal system S that is susceptible to Godel's proof, we can make a formula G which is undecidable. That should mean that we can add either $G$ or $\\neg G$ as an axiom to S and still end up with a consistent system, but I'm not sure exactly how $S + \\neg G$ can be consistent.\n\nSo, $G$ says: \"There does not exist a number $n$, which is the Godel number for a proof of $G$.\" If G were provable, it would be false, and the system would be inconsistent (because $G$ implies $\\neg G$). If $\\neg G$ were provable, however, the system does not have to be blatantly inconsistent, but only omega-inconsistent. $\\neg G$ says \"There does exist a number $n$, which is the Godel number for a proof of $G$.\" But it doesn't specify what that number is. So S can still have theorems: \"1 does not prove $G$\", \"2 does not prove $G$\", \"3 does not prove $G$\" and so on, and it would only be omega-inconsistent (since there is no provable statement that is blatantly the negation of another). But we assume that $S$ is omega-consistent, so we are forced to conclude that $G$ is undecidable. Okay. (as a side-note, I thought that Godel's proof didn't need the assumption of omega-consistency, but it seems required here ... ?)\n\nNow, I understand what happens when you add $G$ to S. In this new $S+G$ system, $G$ says, \"There is no number which is the Godel number of a proof for $G$ in S\", which is, of course, true (and presumably consistent).\n\nBut in $S + \\neg G$, $\\neg G$ says \"There is a number which is the Godel number of a proof for $G$ in S\"; yet, since every provable statement of $G$ is also provable in $S + \\neg G$, this new system will also say \"1 does not prove $G$ in S\", \"2 does not prove $G$ in S\", ... and so on. So isn't $S + \\neg G$ omega-inconsistent? And doesn't that go against the idea that we should be able to add either $G$ or $\\neg G$ to S and still end up with a consistent system? Does that \"consistency promise\" not extend to omega-consistency? If not, isn't there a \"logically better\" way to extend S, even though both extensions are possible?\n\n• The notion of \"number\" in $S+\\neg G$ is not the same. In fact, you want to understand $G$ as saying \"there does not exist an '$S$-number' that is the number of a proof of $G$.\", however, there well can be an \"$S+\\neg G$\"-number that is a proof (and indeed there is), because you have new axioms, so your function \"is a proof in $S$ of\" is different from the function \"is a proof in $S+\\neg G$ of\". Also, note that there are versions of Goedel's proof that avoid the issue of $\\omega$-inconsistent. – Arturo Magidin Apr 16 '12 at 20:55\n• In addition to Arturo's previous comment, your first paragraph is slightly wrong. No one guarantees that $S+G$ and $S+\\lnot G$ are consistent. However if $S$ is consistent then so are $S+G$ and $S+\\lnot G$. We simply did not introduce contradictions to the system, but we might not be able to prove the consistency of $S$. – Asaf Karagila Apr 16 '12 at 21:02\n• @ArturoMagidin I understand that $\\neg G$ in $S + \\neg G$ talks about provability in $G$, but why would it talk about S numbers and not $S + \\neg G$ numbers? I understand that the function \"is provable in S\" is different from the function \"is provable in $S + \\neg G$\". But when I prove, in $S + \\neg G$, that \"there is a number that proves G in S\" and \"1 is not that number\", \"2 is not that number\", etc., am I not talking about the same type of numbers in each case? – Ord Apr 16 '12 at 21:03\n• @AsafKaragila But we assume the consistency of S, don't we? We assume it, and then go ahead and show that $S + \\neg G$ must be omega-inconsistent! How does that work? Surely, Godel's proof does not say that a consistent formal system cannot exist? – Ord Apr 16 '12 at 21:05\n• @Ord: There is no \"absolute\" consistency, you need to have some basic system which you believe is consistent. Even the rules of first-order logic require a certain degree of belief or the fact we can use induction. We have good reasons to believe these are consistent, but no proof of that. Suppose that we are all wrong, and all mathematics in its current form is inconsistent and we can only prove these things because our most basic intuition is inconsistent? This is why we say that if $S$ is consistent then $S+G$ and $S+\\lnot G$ are, but this is a big if sometimes. – Asaf Karagila Apr 16 '12 at 21:26\n\n## 2 Answers\n\nYour conclusion that $S+\\neg G$ is not $\\omega$-consistent is right. It is (assuming that $S$ is consistent) consistent, but fails to be $\\omega$-consistent. Being $\\omega$-consistent is a stronger condition than consistency, satisfied by fewer systems.\n\nWould it be \"logically better\" to extend $S$ in an $\\omega$-consistent way than in one that isn't? I don't think so. As a sometimes Platonist, I would certainly favor the extension $S+G$ over $S+\\neg G$, perhaps even claiming that the former is true whereas the latter isn't, but that preference is not based on logical properties (being true is not a logical property).\n\nPart of the confusion is that \"$\\omega$-consistency\" is something of a misnormer -- because the name contains \"consistency\" one is tempted to think that like ordinary consistency it is an intrinsic property of the theory. But really it isn't; saying that a theory is $\\omega$-consistent is a statement between the relation between what the theory proves and arithmetic at the meta-level. Being $\\omega$-consistent is a necessary criterion for the theorems of the theory to be truths about the intuitive naturals, but failure to express arithmetic truth is not a logical problem for the theory -- it is innocent of our ambitions about what we might like it to model or not.\n\nOne might consider modifications of the concept of $\\omega$-consistency such that it looks more intrinsic to the theory. For example we could define that a theory $T$ is $\\omega'$-consistent iff, whenever $T\\vdash \\exists x. \\phi(x)$ there is some closed term $t$ such that $T\\vdash \\phi(t)$. (The difference is that in ordinary $\\omega$-consistency we require $t$ to be a \"numeral\"; the generalized definition allows arbitrary closed terms). However, under this generalization it is still not clear why one would consider $\\omega'$-consistency to be a desirable property of theories in general, even if we don't intend the theory to model arithmetic.\n\n• Excuse my ignorance, but what exactly is a \"closed term\", and why would omega-prime-consistency be undesirable? – Ord Apr 16 '12 at 23:25\n• A closed term is one that contains no variables -- such as $S(S(S(0)))+S(0)$ in the language of arithmetic opposed to $S(S(S(x)))+y$. -- I'm not saying that $\\omega'$-consitency would be actively undesirable, just that I don't see why one would explicitly desire it. For example, ZFC is not $\\omega'$-consistent, but I don't think one should count that as a disadvantage. – Henning Makholm Apr 16 '12 at 23:31\n• Okay, thank you very much for your response! I think I have a much better handle on the situation now. – Ord Apr 16 '12 at 23:40\n• But your notion of $ω'$-consistency is not analogous, because it is not at all related to the original. To even say that ZFC is $ω$-consistent, we need a suitable translation of arithmetical terms and sentences into terms and sentences over ZFC, so of course the nature of natural numbers and their codes is inbuilt into the notion of $ω$-consistency. So it is justifiable to consider $ω$-consistency desirable but consider $ω'$-consistency a completely different notion, namely that the term model exists. No? – user21820 May 2 '16 at 13:24\n• @user21820: The relation is that a theory in the language of arithmetic that extends Q is $\\omega'$-consistent if and only if it is $\\omega$-consistent. The last paragraph was intended to explain that at least one way to escape the non-logicalness of $\\omega$-consistency by attempting to phrase it in a way that is not specific to the language of arithmetic, doesn't seem to work very well. – Henning Makholm May 2 '16 at 13:32\n\nOmega-consistency is certainly a syntactical property; in that sense, it is an intrinsic property of systems, not a property they have under a particular interpretation.\n\nHowever, if consistency is desirable on simple logical grounds, the desirability of omega-consistency is arithmetical, for only if we take our universe of discourse to be the natural numbers (or some other items with the same structure), we will consider desirable for a system denying a property P of each numeral (0, S0, SS0, ...) to not prove the existence of an object with P.\n\nIf we wish to admit objects other than the naturals in our universe, omega-consistency need not be desirable." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.96512204,"math_prob":0.9954726,"size":2060,"snap":"2019-35-2019-39","text_gpt3_token_len":561,"char_repetition_ratio":0.14883268,"word_repetition_ratio":0.14470284,"special_character_ratio":0.27815533,"punctuation_ratio":0.125,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99595046,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-08-18T07:06:16Z\",\"WARC-Record-ID\":\"<urn:uuid:dea58321-3f5a-43a8-a4a8-d476a353a045>\",\"Content-Length\":\"153867\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:539dfeba-26b4-4ec4-8f5a-60ca416b70a0>\",\"WARC-Concurrent-To\":\"<urn:uuid:6e72ac7b-b290-42ca-a5fd-16c202c62bca>\",\"WARC-IP-Address\":\"151.101.1.69\",\"WARC-Target-URI\":\"https://math.stackexchange.com/questions/132677/how-can-you-add-not-g-to-a-formal-system-without-introducing-omega-inconsisten\",\"WARC-Payload-Digest\":\"sha1:AE52LXBYRZXAYNTSIZYHZFFM5IWAQ6BD\",\"WARC-Block-Digest\":\"sha1:GUVZRBSWE2MBISHDBBB5BGB43MVB3M3O\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-35/CC-MAIN-2019-35_segments_1566027313715.51_warc_CC-MAIN-20190818062817-20190818084817-00305.warc.gz\"}"}
https://downloads.hindawi.com/journals/mpe/2009/696253.xml	[ "MPEMathematical Problems in Engineering1563-51471024-123XHindawi Publishing Corporation69625310.1155/2009/696253696253Research ArticleImproving Accuracy of Coarse Grid Numerical Solution of Solid-Solid Reactions by Taylor Series Expansion of the Reaction TermHassanzadehHassanPooladi-DarvishMehranAbediJalalJiangJ.Department of Chemical and Petroleum EngineeringSchulich School of EngineeringUniversity of Calgary2500 University Drive NWCalgary, ABCanadaT2N 1N4ucalgary.ca200928042009200928112008120220092009Copyright © 2009This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.\n\nExothermic solid-solid reactions lead to sharp reaction fronts that cannot be captured by coarse spatial mesh size numerical simulations that are often required for large-scale simulations. We present a coarse-scale formulation with high accuracy by using a Taylor series expansion of the reaction term. Results show that such expansion could adequately maintain the accuracy of fine-scale behavior of a constant pattern reaction front while using a smaller number of numerical grid cells. Results for a one-dimensional solid-solid reacting system reveal reasonable computational time saving. The presented formulation improves our capabilities for conducting fast and accurate numerical simulations of industrial-scale solid-solid reactions.\n\n1. Introduction\n\nModeling of reactive flow has diverse applications in engineering and science. Applications include heavy oil recovery processes, combustion in porous media, ground water flow, and transport and reaction processes in biofilms. An important class of reactions is that of solid-solid reactions. Modeling of solid-solid reactions is of significant interest in various industrial operations, including oxidation of metallic and nonmetallic mixed powders, cement industry , ferrites manufacturing, solid-state polymerization [2, 3], ceramic manufacturing , catalyst preparation , and drug storage (for more details, see a comprehensive review by Tamhankar and Doraiswamy ). Numerous investigations on modeling reactive flow have been reported over the years that greatly improved the understanding of such systems, where the emphasis has primarily been on approximate analytical solutions for special cases, fine grid direct numerical simulation, and upscaling of reaction-transport from pore scale to continuum scale .\n\nAccurate numerical simulation of solid-solid reactions is a challenging task due to the multiscale nature of the physical phenomena. Physical processes involved in solid-solid reactive systems include diffusive (heat and mass) and reactive processes. Reactions in porous media intrinsically often take place at the small scale, causing development of subdiffusive-scale concentration and temperature gradients, while heat and mass diffusive processes have scales orders of magnitude larger than the reactions. Large-scale simulation of such coupled processes is computationally expensive due to limitations in computational resources. Therefore, a formulation that captures the subdiffusive scale improves our capabilities for conducting industrial-scale simulation of the involved processes with high accuracy. In this paper, we provide a coarse-scale formulation to capture the subgrid-scale phenomena appropriate for large-scale numerical simulations. The paper is organized as follows. First, the fine-scale mathematical model used in this study is presented. Next, the coarse-scale model is described. Then, application of the coarse-scale model is given for a constant pattern reaction front, followed by summary and conclusions.\n\n2. Fine-Scale Conservation Equations\n\nThe exothermic solid-solid reaction is assumed to take place in a one-dimensional semi-infinite domain. The system, which consists of a mixture of two solid materials, is initially at temperature T0. The concentration of one of the solids is in excess such that the reaction can be considered of first order with respect to the second solid. The initial concentration of the second solid is C0. At time t=0, the initial temperature T0 at x=0 is suddenly raised to ignition temperature high enough to initiate the reaction by local heating. The temperature dependence of the reaction rate is assumed to follow Arrhenius type behavior, and all physical properties are assumed to be constant. Mass diffusion is considered to be negligible, and the reaction front is planar and nonoscillatory. It is further assumed that the solid reacting mixture acts as an isotropic homogeneous system and that radiation effects are negligible . The dimensionless energy and mass balances can be presented by parabolic coupled partial differential equations given by θtD=2θxD2+CDexp(θβθ+1),CDtD=γCDexp(θβθ+1), where the following dimensionless groups are used [11, 13]: θ=E(TT)RT2,CD=CC0,tD=tt,t=ρcpRT2Ek(ΔH)C0exp(ERT),xD=xx,x=λtρcp¯,γ=ρcp¯RT2E(ΔH)C0,β=RTE, where T is temperature, C is concentration of reactant, ρ is density, cp is heat capacity, λ is the average thermal conductivity, k is the pre-exponential factor, E is activation energy, ΔH is the heat of reaction, R is the universal gas constant, t is time, T is the scale temperature, and x is the spatial coordinate. We used a standard scaling available in the combustion literature to render the equations dimensionless [13, 1921]. The scaling variable x* corresponds to an approximate measure of the heating zone length, and x/t is a measure of the reaction front velocity .\n\nThe initial and boundary conditions are then given by θ=θ0,0xD,tD=0,CD=1,0xD,tD=0,θ=0,atxD=0,tD>0,θxD=0,x,tD>0,CDxD=0,x,tD>0. The behavior of such a reacting convection diffusion system is primarily determined by the inverse of dimensionless activation energy and inverse of dimensionless heat of reaction, namely, β and γ, respectively. Puszynski et al. presented a detailed analysis of the frontal behavior of such a system. Small β or γ values correspond to a reacting system with high activation energy or heat of reaction and vice versa. Large values of γ (small values of heat of reaction and/or small values of activation energy) lead to a degenerated combustion regime, whereas low values of γ (large values of heat of reaction and/or large values of activation energy) result in an oscillatory reaction front. Low β values (large activation energy) and intermediate γ values result in a constant pattern profile regime. Choosing large grid cells results in significant smearing of the reaction front, as we will see in the following sections. In the subsequent part of the paper, we present the model formulation that is able to maintain the accuracy of fine grid behavior while using coarse grid cell sizes.\n\n3. Coarse-Scale Conservation Equations\n\nNumerical simulation of reactive front propagation with a large number of grid cells is computationally expensive and therefore we are interested in using a coarse model that preserves the accuracy of fine grid behavior. The coarse-scale variable can be defined by ψ¯=1vvψdv, where v represents the coarse grid.\n\nWe intend to represent the differential equations (2.1) with their corresponding coarse grid equivalents (3.2). In these equations, ¯ represents the “equivalent” reaction rate that would allow close agreement between the (2.1) set and the (3.2) set, correspondingly. The coarse-scale numerical model can be expressed by θ¯tD=2θ¯xD2+¯,C¯DtD=γ¯, where =CDexp(θβθ+1),¯=1vvCDexp(θβθ+1)dv=CDexp(θβθ+1)¯ are the fine-scale reaction rate and coarse-scale average reaction rate, respectively. The reaction rate can be approximated by a Taylor series expansion around the coarse-scale temperature and concentration. The above expansion can be represented in terms of deviation from the coarse-scale variables as given by (C¯D,θ¯)+CD\|C¯D,θ¯CD+θ\|C¯D,θ¯θ+12!(2CD2\|C¯D,θ¯(CD)2+22CDθ\|C¯D,θ¯CDθ+2θ2\|C¯D,θ¯(θ)2)+, where CD=CDC¯D and θ=θθ¯ are the concentration and temperature deviations from the fine scale solution, respectively. The terms involving derivatives account for the information that is normally lost in a coarse grid numerical solution; those will be evaluated and accounted for herein. By using (3.1), the average coarse-scale reaction rate can be expressed by ¯(C¯D,θ¯)+12!(2CD2\|C¯D,θ¯(CD)2¯+22CDθ\|C¯D,θ¯CDθ¯+2θ2\|C¯D,θ¯(θ)2¯)+,2θ2\|C¯D,θ¯=12β(1+βθ¯)(βθ¯+1)4C¯Dexp(θ¯βθ¯+1),2CD2\|C¯D,θ¯=0,2CDθ\|C¯D,θ¯=exp(θ¯/(βθ¯+1))(βθ¯+1)2, where by definition the terms with first derivatives are dropped in the averaging process . Equation (3.5) is a coarse-scale representation of the reaction rate that includes both coarse-scale concentration and temperature and their deviations from fine scale, namely, CD and θ, respectively. We do not have an explicit definition of the deviation terms CD and θ as functions of the coarse-scale concentration and temperature. Instead, we intend to express the quantities (θ)2¯ and CDθ¯ in a form proportional to θ¯/xD and (θ¯/xD)(C¯D/xD) such that the final coarse-scale model can be presented as a function of coarse-scale temperature and concentration only. Similar approach has been used by Meile and Tuncay for linear convection-diffusion-reaction problem. The common practice in a volume averaging method [1417, 22] is to solve the closure problem, which is obtained by subtraction of the fine-scale and the coarse-scale equations. Here, due to the complexity arising from the nonlinearity of the problem, subtraction does not lead to (an) equation(s) in terms of the perturbed quantities. However, consistent with the volume averaging method , an appropriate approximation for the deviation terms is linear proportionality of temperature and concentration deviations with their corresponding gradient. Using this approximation, one may write (θ)2¯=α(θ¯xD)2,CDθ¯=α(θ¯xD)(C¯DxD). By substituting (3.9) in (3.5), the coarse-scale equations (3.2) can be written as θ¯tD=2θ¯xD2+(C¯D,θ¯)+α2!(22CDθ\|C¯D,θ¯(θ¯xD)(C¯DxD)+2θ2\|C¯D,θ¯(θ¯xD)2),C¯DtD=γ(C¯D,θ¯)γ{α2!(22CDθ\|C¯D,θ¯(θ¯xD)(C¯DxD)+2θ2\|C¯D,θ¯(θ¯xD)2)}, where α is the proportionality constant or coarse-scale parameter and is a function of coarse grid size. The coarse-scale formulation is not closed so far, and the proportionality constant α as a function of coarse grid size needs to be determined. Numerical experiments reveal that the term containing cross derivatives in the internal bracket in the right-hand side in (3.10) is small as compared to the second term. Given that the cross derivatives are small as compared to the second term, it may be ignored. Therefore, the coarse-scale formulation can be rendered as θ¯tD=2θ¯xD2+(C¯D,θ¯)+α2!2θ2\|C¯D,θ¯(θ¯xD)2,C¯DtD=γ(C¯D,θ¯)γ{+α2!2θ2\|C¯D,θ¯(θ¯xD)2}. The coarse grid model represented by (3.11) is of the same form as (2.1) with the same dimensionless groups, γ and β; however, the reaction term is replaced by (C¯D,θ¯)+α(2/θ2)C¯D,θ¯(θ¯/xD)2/2.\n\nIn order to find the proportionality constant α as a function of coarse spatial mesh size, a series of numerical experiments needs to be conducted for different spatial mesh sizes for each specific reacting system (i.e., using fixed γ and β). The functionality (α versus spatial mesh size) for a specific reacting system can be determined by matching the coarse spatial mesh size solution with the fine scale or reference solution. In matching process, to estimate the deviations of the coarse-scale model predictions from the fine-scale reference solution, we define a numerical error using the following expression as a measure of accuracy: ε={[(ψψ¯)2dxD][ψ2dxD]}1/2, where ψ can be either temperature or concentration.\n\nThe proportionality constant is obtained by the minimization of the numerical error given by (3.12). By repeating the matching process for different number of spatial mesh sizes, the proportionality constant for each spatial mesh size can be obtained. Once the functionality of the proportionality constant with respect to coarse spatial mesh size is obtained, the coarse-scale formulation (3.11) is complete and can be used for subsequent large-scale simulation of a solid-solid reactive system. In the following, we use the above procedure for determining the parameter α as a function of coarse spatial mesh size for some solid-solid reacting systems.\n\n4. Application of the Coarse-Scale Formulation\n\nBased on the scaling groups used in nondimensionalizing the governing equations, the frontal behavior of a solid-solid reaction depends on two parameters, namely, β (inverse of dimensionless activation energy) and γ (inverse of dimensionless heat of reaction). The coarse-scale formulation described previously is applied for two solid-solid reactions. The governing differential equations are discretized using an explicit-in-time finite difference approximation. A block-centered scheme is used, where the diffusive flux is calculated based on grid block center values. Numerical simulations are conducted to determine the parameter α appropriate for large-scale numerical simulation of such reacting systems. The dimensionless constants for these reacting systems are given in Table 1. The data are taken from examples of solid-solid reactions given by Puszynski et al. . For each reacting system, temperature at one end is rapidly increased to an ignition temperature. Since the temperature is scaled with the adiabatic temperature of the reaction (Ta=T), the minimum dimensionless temperature in the system is equal to the negative of the dimensionless heat of reaction (1/γ). Figure 1 shows α as a function of numerical spatial mesh size for different solid-solid reaction systems given in Table 1. In all cases, the conditions are selected such that a constant pattern profile exists. The condition for existence of a constant pattern reaction front can be predicted by the following expression : γc=12(θcθ0), where θc=θ0+212β. For γ<γc, a reacting system demonstrates constant pattern reaction front propagation. The parameter γc for reactions studied is given in Table 1.\n\nDimensionless parameters for solid-solid reacting systems used in this study.\n\nReaction βγθ0θiγc\n10.10.2500.2\n20.06450.147.14300.218\n\nCoarse-scale parameter α as a function of grid size for two reactions in Table 1.\n\nFigure 1 shows the coarse-scale parameter αobtained for the two reactions given in Table 1. Using this methodology, the coarse-scale parameter αas a function spatial mesh size can be obtained for a specific solid-solid reaction system. This parameter then can be used for large-scale numerical simulation of a reactive system. Figure 1 shows that for both reactions the coarse parameter α starts increasing about a dimensionless grid size of 5 suggesting that x=0.2Δx. Figure 2 shows the reaction rate as a function of dimensionless distance. The dimensionless size of the reaction zone ΔxDf=Δxf/x* is approximated by the region, where the reaction rate is larger than 0.01 times of the peak reaction rate. Results show that for both reactions the approximate dimensionless size of the reaction zone is about 13 suggesting that using fine-scale model one needs to use grid size of 5/13 of the size of the reaction zone to roughly capture the reaction front. The presented coarse-scale formulation allows us to use larger grid size while maintaining accuracy of the solution. Figures 3 and 4 show comparisons of concentration and temperature profiles with and without use of the presented coarse-scale formulation. Results show that the coarse-scale formulation could represent the location of the reaction front accurately with a small number of grid cells. Figures 3 and 4 also show that by using coarse-scale formulation one might choose a coarse spatial mesh size two times of the reaction zone while maintaining the numerical solution accuracy.\n\nReaction rate for the two reactions as a function of dimensionless distance.\n\nConcentration and temperature distributions at tD=400 for Reaction 1 given in Table 1 with and without coarse-scale formulation for three grid sizes of 25, 16.7, and 9.1. (—) reference solution, () without using coarse-scale parameter, and () with using coarse-scale parameter.\n\nConcentration and temperature distributions at tD=650 for Reaction 2 given in Table 1 with and without coarse-scale formulation for three grid sizes of 25, 16.7, and 9.1. (—) reference solution, () without using coarse-scale parameter, and () with using coarse-scale parameter.\n\nThe calculated numerical errors for the reactions given in Table 1 are presented in Figure 5 for concentration and temperature for different grid sizes. Results show that the presented coarse-scale formulation could significantly reduce the numerical error. In addition, the ratio of CPU time for coarse-scale formulation and fine grid reference solutions is presented in Figure 6. Results show that the CPU time ratio scales with the inverse of grid size, suggesting a ten-fold reduction in CPU time with a ten-fold increase in grid size. Currently, we are working toward finding scaling or proportionality constant for multidimensional problems. CPU time savings is expected to be much more significant for multidimensional problems.\n\nNumerical error in temperature (left) and concentration (right) distributions for reactions given in Table 1 with and without coarse-scale formulation for different grid sizes.\n\nRatio of coarse to fine grid (reference) CPU times versus dimensionless grid size for the two reactions given in Table 1.\n\n5. Concluding Remarks\n\nPropagation of solid-solid reaction fronts often results in a thin reaction zone that is difficult to resolve numerically unless a large number of numerical grid cells are used. Such numerical simulations are computationally expensive to perform. In this study, a coarse-scale formulation for numerical modeling of a one-dimensional solid-solid reacting system is presented. The presented formulation is based on a Taylor series expansion of the reaction term and presents the modification of the reaction term in the coarse model that would allow an accurate solution. A key parameter in this formulation is α or so-called coarse-scale parameter, which is a function of the coarse-scale spatial mesh size. Using the presented formulation, this parameter as a function of spatial mesh size can be obtained. This parameter then can be used for numerically solving a large scale and computationally intensive reacting system. It is shown that this formulation could reasonably obtain the accuracy of a fine grid numerical solution. It is shown that the coarse-scale formulation considerably reduces the numerical error. In addition, it is revealed that the ratio of CPU times of a coarse-scale model to that of a fine grid solution scales with the inverse of grid size. Such inverse proportionality implies a significant reduction in CPU time of a coarse-scale model compared to that of a fine grid-scale model for large-scale simulations. Results obtained in this study for a one-dimensional reacting system are promising in terms of reducing computational time. However, the presented methodology has a number of limitations that are the subject of our current research. First, the coarse-scale parameter needs to be characterized as a function of the governing dimensionless numbers. In addition, the applicability of this method needs to be tested for multidimensional problems, where we expect a major reduction in CPU time. Presently, we are working toward implementation of the presented methodology for multidimensional problems and determination of the coarse-scale parameter as a function of dimensionless numbers for solid-solid reactions. We anticipate that the computational time saving for multidimensional problems is more promising. The presented formulation improves our capabilities for conducting more accurate and faster numerical simulation of industrial-scale solid-solid reactions.\n\nNomenclaturecp:\n\nHeat capacity, Jkg1K1\n\nC:\n\nConcentration, kg/m3\n\nD:\n\nMolecular diffusion coefficient, m2/s\n\nE:\n\nActivation energy, Jkmol1\n\nΔH:\n\nHeat of reaction, J/kg\n\nk:\n\nPre-exponential rate constant, s1\n\nR:\n\nGas constant, Jkmol1K1\n\nt:\n\nTime, s\n\nT:\n\nTemperature, K\n\nx:\n\nCoordinate, m.\n\nGreek Lettersα:\n\nCoarse-scale parameter\n\nβ:\n\nInverse of dimensionless activation energy\n\nγ:\n\nInverse of dimensionless heat of reaction\n\nε:\n\nNumerical error\n\nv:\n\nCoarse-scale volume, m3\n\nψ:\n\nFine-scale variable can be temperature, concentration, or reaction rate\n\n:\n\nReaction rate, kgm3s1\n\nλ:\n\nEffective thermal conductivity, Jm1s1K1\n\nρ:\n\nDensity, kgm3\n\nθ:\n\nDimensionless temperature.\n\nSubscriptsa:\n\nc:\n\nCritical\n\nD:\n\nDimensionless\n\ni:\n\nIgnition\n\n0:\n\nInitial value\n\n*:\n\nScale value.\n\nSuperscripts':\n\nDeviation from coarse scale\n\n:\n\nAverage or coarse scale.\n\nAcknowledgments\n\nThe authors would like to acknowledge constructive comments from Dr. Brian Wood and Dr. Christof Meile. Helpful discussion with Dr. Mohsen Sadeghi is also acknowledged. The financial support of the Alberta Ingenuity Centre for In Situ Energy (AICISE) is acknowledged. The authors would like to thank the reviewers for useful comments.\n\nLeaF. M.The Chemistry of Cement and Concrete19703rdLondon, UKEdward ArnoldsChechiloN. M.KhvilivitskiiR. J.EnikolopyanN. S.On the phenomenon of polymerization reaction spreadingDoklady Akademii Nauk SSSR197220411801181IlyashenkoV. M.SolovyovS. E.PojmanJ. A.Theoretical aspects of self-propagating reaction fronts in condensed mediumAIChE Journal199541122631263610.1002/aic.690411212KingeryW. D.Introduction to Ceramics1967New York, NY, USAJohn Wiley & SonsBleijenbergA. C. A. M.LippensB. C.SchuitG. C. A.Catalytic oxidation of 1-butene over bismuth molybdate catalysts. I. The system Bi2O3-MoO3Journal of Catalysis19654558158510.1016/0021-9517(65)90163-6TamhankarS. S.DoraiswamyL. K.Analysis of solid-solid reactions: a reviewAIChE Journal197925456158210.1002/aic.690250402ZeldovichYa. B.Frank-KamenetzkiiD. A.A theory of thermal propagation of flameACTA Physico-Chimica URSS193892341350MargolisS. B.An asymptotic theory of condensed two-phase flame propagationSIAM Journal on Applied Mathematics198343235136910.1137/0143024MR700343ZBL0511.76098MargolisS. B.An asymptotic theory of heterogeneous condensed combustionCombustion Science and Technology1985433-419721510.1080/00102208508947004MargolisS. B.ArmstrongR. C.Two asymptotic models for solid propellant combustionCombustion Science and Technology1986471-213810.1080/00102208608923862PuszynskiJ.DegreveJ.HlavacekV.Modeling of exothermic solid-solid noncatalytic reactionsIndustrial and Engineering Chemistry Research19872671424143410.1021/ie00067a026RajaiahJ.DandekarH.PuszynskiJ.DegreveJ.HlavacekV.Study of gas-solid, heterogeneous, exothermic, noncatalytic reactions in a flow regimeIndustrial and Engineering Chemistry Research198827351351810.1021/ie00075a023DandekarH.PuszynskiJ. A.DegreveJ.HlavacekV.Reaction front propagation characteristics in non-catalytic exothermic gas-solid systemsChemical Engineering Communications19909219922410.1080/00986449008911431WoodB. D.WhitakerS.Diffusion and reaction in biofilmsChemical Engineering Science199853339742510.1016/S0009-2509(97)00319-9WoodB. D.WhitakerS.Erratum to “Diffusion and reaction in biofilms”Chemical Engineering Science20005512234910.1016/S0009-2509(99)00504-7WoodB. D.brian.wood@pnl.govWhitakerS.Multi-species diffusion and reaction in biofilms and cellular mediaChemical Engineering Science200055173397341810.1016/S0009-2509(99)00572-2WoodB. D.brian.wood@oregonstate.eduRadakovichK.GolfierF.Effective reaction at a fluid-solid interface: applications to biotransformation in porous mediaAdvances in Water Resources2007306-71630164710.1016/j.advwatres.2006.05.032MeileC.cmeile@uga.eduTuncayK.Scale dependence of reaction rates in porous mediaAdvances in Water Resources2006291627110.1016/j.advwatres.2005.05.007MerzhanovA. G.FilonenkoA. K.BorovinskayaI. P.New phenomena in combustion of condensed systemsDoklady Akademii Nauk SSSR1973208892894MerzhanovA. G.BorovinskayaI. P.A new class of combustion processesCombustion Science and Technology1975105-619520110.1080/00102207508946671MerzhanovA. G.KhaikinB. I.Theory of combustion waves in homogeneous mediaProgress in Energy and Combustion Science198814119810.1016/0360-1285(88)90006-8WoodB. D.brian.wood@orst.eduCherblancF.QuintardM.quintard@imft.frWhitakerS.swhitaker@ucdavis.eduVolume averaging for determining the effective dispersion tensor: closure using periodic unit cells and comparison with ensemble averagingWater Resources Research2003398121010.1029/2002WR001723" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.82244134,"math_prob":0.9188107,"size":23419,"snap":"2022-40-2023-06","text_gpt3_token_len":6152,"char_repetition_ratio":0.17194106,"word_repetition_ratio":0.05232929,"special_character_ratio":0.22507367,"punctuation_ratio":0.12404536,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97265184,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-09-28T22:52:39Z\",\"WARC-Record-ID\":\"<urn:uuid:9d0daac8-447c-4b61-801e-37f257ea741a>\",\"Content-Length\":\"118432\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:ea6ef3f9-40de-4540-b272-fe30372e52b0>\",\"WARC-Concurrent-To\":\"<urn:uuid:66cb340a-d179-4d0a-bf69-89a41fd3da91>\",\"WARC-IP-Address\":\"13.249.39.21\",\"WARC-Target-URI\":\"https://downloads.hindawi.com/journals/mpe/2009/696253.xml\",\"WARC-Payload-Digest\":\"sha1:NKU6SNJNBN3M6O6Z2MCSFM2QMNK3H7GH\",\"WARC-Block-Digest\":\"sha1:CO3DBUVT7IABU6NOOGYYXUCYELTBMG6B\",\"WARC-Identified-Payload-Type\":\"application/xml\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030335286.15_warc_CC-MAIN-20220928212030-20220929002030-00225.warc.gz\"}"}
https://www.friedsamengineering.com/polymerase-chain-reaction	[ "# Polymerase Chain Reaction Machine\n\nPolymerase chain reaction is the process of DNA replication. It consists of three phases: denaturation, annealing and extension. Those phases are cycled through between 30 and 40 times to exponentially generate copies of a a DNA segment. For more information on the reaction you can read this Wikipedia article or watch the video to the right. The science department at my high school wanted an additional PCR machine and rather than spending thousands of dollars buying one, they tasked me with building one. I created a Github Repository with all of the code, schematics and other necessary files for anyone interested in recreating the machine.\n\n# Final Product:", null, "# Components and Schematic:", null, "# PCB:\n\nIn efforts to consolidate the circuitry and build a more robust machine I designed and ordered a printed circuit board. The printed circuit board will also ensure better connections soldered down rather than connected with a breadboard. An image of the circuit board schematic is to the right. If you are interested in recreating this project I highly recommend using a PCB. To order a copy of the one that I made you can download the gerber file (along with all other important files) from my Github Repository and then order the board from a PCB fabricator. I recommend JLCPCB.com.", null, "# Testing:", null, "This is a photograph of all of the components put together without an enclosure/case which I am currently designing and plan to make using a laser cutter.\n\n# Cycle Data:", null, "This graph shows the temperature in celsius of the aluminum block throughout one cycle. The three plateaus at 95C, 50C and 72C show the machine holding a steady temperature at each of the 3 PCR stages.\n\n# Code:\n\n/* Pin Layout:\n\n* JOYSTICK:\n\n* X to A0\n\n* SW to D2\n\n* LCD\n\n* SDA to A4\n\n* SCL to A5\n\n* Thermocouple\n\n* DO to D3\n\n* CS to D4\n\n* CLK to D5\n\n* Relay\n\n* Pos to D13\n\n/\n\n//Include libraries required for components\n\n#define MAXDO 3\n\n#define MAXCS 4\n\n#define MAXCLK 5\n\n#include <Wire.h>\n\n#include <LiquidCrystal_I2C.h>\n\nLiquidCrystal_I2C lcd(0x27, 2,1,0,4,5,6,7);\n\n// Define variables\n\nlong duration;\n\nint cycles = 1;\n\nint currentCycle = 1;\n\nlong startTime;\n\nlong timeEllapsed;\n\nlong firstDenaturationDuration;\n\nlong fDDSeconds = 0;\n\nlong fDDMins = 02;\n\nlong lastExtensionDuration;\n\nlong fEDSeconds = 0;\n\nlong fEDMins = 05;\n\nlong endTime;\n\nlong remainder;\n\ndouble annealingTemp = 50.00;\n\n// Create non-return functions to turn on the heater and fan\n\nvoid heaterOn() {digitalWrite(13, HIGH);}\n\nvoid fanOn() {digitalWrite(13, LOW);}\n\n// Non return function to set up how many cycles to run\n\nvoid getCycles() {\n\nlcd.setCursor(5,0);\n\nlcd.print(\"CYCLES:\");\n\nlcd.setCursor(7,1);\n\nlcd.print(cycles);\n\n// Read Joystick and determine if user is going up or down\n\nif (analogRead(0) < 100 && cycles >= 2) {\n\ncycles -= 1;\n\ndelay(200);\n\n}\n\ncycles += 1;\n\ndelay(200);\n\n}\n\n// Keep prompting for input\n\ngetCycles();\n\n}\n\n}\n\n// Non return func to determine first denaturation duration (different duration from rest)\n\nvoid getFirstDenaturationDuration() {\n\n// Set up screen and times\n\nlcd.setCursor(0,0);\n\nlcd.print(\"1st Denaturation\");\n\nlcd.setCursor(0,1);\n\nlcd.print(\"Time: \");\n\nlcd.setCursor(6,1);\n\nlcd.print(fDDMins);\n\nlcd.setCursor(7,1);\n\nlcd.print(\":\");\n\n// Handle seconds over 59\n\nif (fDDSeconds > 59) {\n\nfDDMins += 1;\n\nfDDSeconds = 0;\n\ndelay(250);\n\n}\n\n// Handle seconds less than 0\n\nif (fDDSeconds == 0 && analogRead(0) < 100) {\n\nfDDMins -= 1;\n\nfDDSeconds = 59;\n\ndelay(250);\n\n}\n\nif (fDDSeconds >= 9) {\n\nlcd.setCursor(8,1);\n\nlcd.print(fDDSeconds);\n\n}\n\nif (fDDSeconds < 10 && fDDSeconds > 0) {\n\nlcd.setCursor(8,1);\n\nlcd.print(\"0\");\n\nlcd.setCursor(9,1);\n\nlcd.print(fDDSeconds);\n\n}\n\n// Print seconds when seconds = 0\n\nif (fDDSeconds == 0) {\n\nlcd.setCursor(8,1);\n\nlcd.print(\"00\");\n\n}\n\n// Define duration\n\nfirstDenaturationDuration = ((fDDMins 60000) + (fDDSeconds * 1000));\n\nif (analogRead(0) < 100 && firstDenaturationDuration>30000) {\n\nfDDSeconds -= 1;\n\ndelay(200);\n\n}\n\n// Plus 1 second\n\nif (analogRead(0) > 900 && fDDMins < 8) {\n\nfDDSeconds += 1;\n\ndelay(200);\n\n}\n\n// Set duration\n\nfirstDenaturationDuration = (fDDMins * 60000) + (fDDSeconds * 1000);\n\n// Keep prompting for input\n\ngetFirstDenaturationDuration();\n\n}\n\n}\n\n// Get annealing temp\n\nvoid getAnnealTemp() {\n\n// Set up LCD\n\nlcd.setCursor(1,0);\n\nlcd.print(\"ANNEALING TEMP:\");\n\nlcd.setCursor(5,1);\n\nlcd.print(annealingTemp);\n\n// Read joystick and inc/dec in decrements of 0.25 degrees C\n\nif (analogRead(0) < 100 && annealingTemp >= 49) {\n\nannealingTemp -= 0.25;\n\ndelay(200);\n\n}\n\nannealingTemp += 0.25;\n\ndelay(200);\n\n}\n\n// Keep prompting for input\n\ngetAnnealTemp();\n\n}\n\n}\n\n// Get last extension duration function (diff from other extension durrations)\n\nvoid getLastExtensionDuration() {\n\n// Set up LCD\n\nlcd.setCursor(1,0);\n\nlcd.print(\"Last Extension\");\n\nlcd.setCursor(0,1);\n\nlcd.print(\"Time: \");\n\nlcd.setCursor(6,1);\n\nlcd.print(fEDMins);\n\nlcd.setCursor(7,1);\n\nlcd.print(\":\");\n\n// Same as above: Handle joystick input, change times based on input, keep prompting until joystick is clicked\n\nif (fEDSeconds > 59) {\n\nfEDMins += 1;\n\nfEDSeconds = 0;\n\ndelay(250);\n\n}\n\nif (fEDSeconds == 0 && analogRead(0) < 100) {\n\nfEDMins -= 1;\n\nfEDSeconds = 59;\n\ndelay(250);\n\n}\n\nif (fEDSeconds >= 9) {\n\nlcd.setCursor(8,1);\n\nlcd.print(fEDSeconds);\n\n}\n\nif (fEDSeconds < 10 && fEDSeconds > 0) {\n\nlcd.setCursor(8,1);\n\nlcd.print(\"0\");\n\nlcd.setCursor(9,1);\n\nlcd.print(fEDSeconds);\n\n}\n\nif (fEDSeconds == 0) {\n\nlcd.setCursor(8,1);\n\nlcd.print(\"00\");\n\n}\n\nlastExtensionDuration = ((fEDMins * 60000) + (fEDSeconds * 1000));\n\nif (analogRead(0) < 100 && lastExtensionDuration>60000) {\n\nfEDSeconds -= 1;\n\ndelay(200);\n\n}\n\nif (analogRead(0) > 900 && fEDMins < 8) {\n\nfEDSeconds += 1;\n\ndelay(200);\n\n}\n\nlastExtensionDuration = (fEDMins * 60000) + (fEDSeconds * 1000);\n\ngetLastExtensionDuration();\n\n}\n\n}\n\n// Configure LCD to prompt for begin command\n\nvoid enter() {\n\nlcd.setCursor(2,0);\n\nlcd.print(\"FRIEDSAM PCR\");\n\nlcd.setCursor(1,1);\n\nlcd.print(\"CLICK TO BEGIN\");\n\nenter();\n\n}\n\n}\n\n// Function to run above functions to set up machine\n\nvoid getInput() {\n\ngetCycles();\n\nlcd.clear();\n\ndelay(500);\n\ngetFirstDenaturationDuration();\n\nlcd.clear();\n\ndelay(500);\n\ngetAnnealTemp();\n\nlcd.clear();\n\ndelay(500);\n\ngetLastExtensionDuration();\n\nlcd.clear();\n\ndelay(500);\n\nenter();\n\nlcd.clear();\n\ndelay(500);\n\n}\n\n//Function to be called recursively until temp for denaturation is reached\n\nvoid prepDenaturation() {\n\nheaterOn();\n\ndelay(500);\n\nlcd.clear();\n\nlcd.setCursor(5,0);\n\nlcd.print(\"HEATING\");\n\nlcd.setCursor(2,1);\n\nlcd.print(\"Temp: \");\n\nif (isnan(temp) == false) {\n\nlcd.setCursor(8,1);\n\nlcd.print(temp);\n\n}\n\nif (temp<95 \|\| isnan(temp)) {\n\nprepDenaturation(); //if it is less than 95 degrees keep heating\n\n}\n\n}\n\n// Function to be called recursivley until denature duration has passed\n\nvoid denature() {\n\n// Switch between fan and heater to keep tempt between 94.75 and 95.25\n\nif (temp <= 94.75) {\n\nheaterOn();\n\n}\n\nif (temp >= 95.25) {\n\nfanOn();\n\n}\n\ntimeEllapsed = millis();\n\nendTime = startTime + duration;\n\nremainder = endTime - timeEllapsed;\n\ndelay(500);\n\nlcd.clear();\n\nlcd.setCursor(0,0);\n\nlcd.print(\"PHASE: DENATURE\");\n\nlcd.setCursor(0,1);\n\nlcd.print(\"CYCLE:\");\n\nlcd.setCursor(7,1);\n\nlcd.print(currentCycle);\n\nlcd.setCursor(10,1);\n\nlcd.print(temp);\n\nlcd.setCursor(15,1);\n\nlcd.print(\"C\");\n\nif (timeEllapsed < endTime) {\n\ndenature();\n\n}\n\n}\n\n// Function to cool down until temp is met for annealing\n\nvoid prepAnnealing() {\n\nfanOn();\n\ndelay(500);\n\nlcd.clear();\n\nlcd.setCursor(5,0);\n\nlcd.print(\"COOLING\");\n\nlcd.setCursor(2,1);\n\nlcd.print(\"Temp: \");\n\nif (isnan(temp) == false) {\n\nlcd.setCursor(8,1);\n\nlcd.print(temp);\n\n}\n\nif (temp >= annealingTemp + 0.25 \|\| isnan(temp)) {\n\nprepAnnealing();\n\n}\n\n}\n\n// Anneal until annealing duration has passed (recursion)\n\nvoid anneal() {\n\nif (temp <= annealingTemp - 0.25) {\n\nheaterOn();\n\n}\n\nif (temp >= annealingTemp + 0.25) {\n\nfanOn();\n\n}\n\ntimeEllapsed = millis();\n\nendTime = startTime + duration;\n\nremainder = endTime - timeEllapsed;\n\ndelay(500);\n\nlcd.clear();\n\nlcd.setCursor(0,0);\n\nlcd.print(\"PHASE: ANNEAL\");\n\nlcd.setCursor(0,1);\n\nlcd.print(\"CYCLE:\");\n\nlcd.setCursor(7,1);\n\nlcd.print(currentCycle);\n\nlcd.setCursor(10,1);\n\nlcd.print(temp);\n\nlcd.setCursor(15,1);\n\nlcd.print(\"C\");\n\nif (timeEllapsed < endTime) {\n\nanneal();\n\n}\n\n}\n\n// Heat back up to prep for extension\n\nvoid prepExtension() { //heat back up\n\nheaterOn();\n\ndelay(500);\n\nlcd.clear();\n\nlcd.setCursor(5,0);\n\nlcd.print(\"HEATING\");\n\nlcd.setCursor(2,1);\n\nlcd.print(\"Temp: \");\n\nif (isnan(temp) == false) {\n\nlcd.setCursor(8,1);\n\nlcd.print(temp);\n\n}\n\nif (temp < 72 \|\| isnan(temp)) {\n\nprepExtension();\n\n}\n\n}\n\n// Maintain extension tempt until extension time duration has passed (recursion)\n\nvoid extend() {\n\nif (temp <= 71.75) {\n\nheaterOn();\n\n}\n\nif (temp >= 72.25) {\n\nfanOn();\n\n}\n\ntimeEllapsed = millis();\n\nendTime = startTime + duration;\n\nremainder = endTime - timeEllapsed;\n\ndelay(500);\n\nlcd.clear();\n\nlcd.setCursor(0,0);\n\nlcd.print(\"PHASE: EXTEND\");\n\nlcd.setCursor(0,1);\n\nlcd.print(\"CYCLE:\");\n\nlcd.setCursor(7,1);\n\nlcd.print(currentCycle);\n\nlcd.setCursor(10,1);\n\nlcd.print(temp);\n\nlcd.setCursor(15,1);\n\nlcd.print(\"C\");\n\nif (timeEllapsed < endTime) {\n\nextend();\n\n}\n\n}\n\n// Run everything multiple times based on number of cycles defined above\n\nvoid PCR() {\n\nfor (int i = 0; i <= cycles-1; i++) {\n\nprepDenaturation();\n\nlcd.clear();\n\nif (currentCycle == 1) {duration = firstDenaturationDuration;}\n\nelse {duration = 30000;}\n\nstartTime = millis();\n\ndenature();\n\nlcd.clear();\n\nprepAnnealing();\n\nlcd.clear();\n\nduration = 30000;\n\nstartTime = millis();\n\nanneal();\n\nlcd.clear();\n\nprepExtension();\n\nlcd.clear();\n\nif (cycles - currentCycle == 0) {duration = lastExtensionDuration;}\n\nelse {duration = 60000;}\n\nstartTime = millis();\n\nextend();\n\nlcd.clear();\n\ncurrentCycle += 1;\n\n}\n\nfanOn();\n\nlcd.clear();\n\nlcd.setCursor(2,0);\n\nlcd.print(\"FRIEDSAM PCR\");\n\nlcd.setCursor(0,1);\n\nlcd.print(\"PHASE: COMPLETE\");\n\n}\n\nvoid setup() {\n\n// Configure I/O\n\npinMode(13, OUTPUT);\n\nlcd.begin (16,2);\n\nlcd.setBacklightPin(3,POSITIVE);\n\nlcd.setBacklight(HIGH);\n\nSerial.begin(9600);\n\npinMode(2, INPUT);\n\ndigitalWrite(2, HIGH);\n\n// Get input and run machine\n\ngetInput();\n\nPCR();\n\n}\n\nvoid loop() {\n\n}" ]	[ null, "https://lh4.googleusercontent.com/-hdsF0WyTpqcPYm0Oretz5VpypGi28j1bIxkGEdzv5PDY4clA4lVGdHX11T50FsC2FiTcoRomhbwB_ETQRfVndF18HuqEXUcvH6hQqvMEYYvbGVL=w1280", null, "https://lh4.googleusercontent.com/J6fAvZpuDuGAm_1KKd3C2od43kUK9lpMehEZoL_g8QwpiWDSoc73hO0QYfW6FL3DBSi5XosY0TQOMKUrl4ghrFsQdWCas_Q_7KD8ouR3l2WkCsNz=w1280", null, "https://lh3.googleusercontent.com/4rmFL27DctRm3tOUJM2dvG90tqGiQhHB1ZKynUolEvLm6zTimN1ubNlV9DCvDowQxp5_L5gBnLbPqgC4EV6J3vs7kM7F-2stK_lmXUfb3HjwI5UR=w1280", null, "https://lh6.googleusercontent.com/rPxtB2nmamI1aAdK5GlZ0uiO51yq4jiSLHDa87kF0L9jTNnqwUPj5cOx2lUCxQykhmUeAt1C-v2RDKN7hZFI8qta1VbsmP5eqHdy-O-w6t0Sk4AI=w1280", null, "https://lh3.googleusercontent.com/GAacmXFkTH8IRYkmnxrbuU0Y5K5_fOgg1PvJAxLW7xc9QBgPU5WnIqy5siStt4c3dijwoLv7NvbmYXVc3SOIJ4vhUNfdBuFVU_6ThURjOmuEEH8q=w1280", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.5315989,"math_prob":0.94170177,"size":10349,"snap":"2022-40-2023-06","text_gpt3_token_len":3002,"char_repetition_ratio":0.21237312,"word_repetition_ratio":0.15666902,"special_character_ratio":0.332206,"punctuation_ratio":0.2506342,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9579924,"pos_list":[0,1,2,3,4,5,6,7,8,9,10],"im_url_duplicate_count":[null,1,null,1,null,1,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-02-05T03:26:39Z\",\"WARC-Record-ID\":\"<urn:uuid:c0f65e65-80fa-4a26-a50c-2b9fdb234224>\",\"Content-Length\":\"297185\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c91b5b62-dae9-4760-bd89-cb764793cba7>\",\"WARC-Concurrent-To\":\"<urn:uuid:2cf7a981-20da-4e59-980a-613b8bcba846>\",\"WARC-IP-Address\":\"142.251.111.121\",\"WARC-Target-URI\":\"https://www.friedsamengineering.com/polymerase-chain-reaction\",\"WARC-Payload-Digest\":\"sha1:OP4KBUXXULXKNKSBBIOZLKKZOTCBT6IJ\",\"WARC-Block-Digest\":\"sha1:C7RNWZU3472G3OFU6FOSG2KKHEOIHO3Q\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-06/CC-MAIN-2023-06_segments_1674764500215.91_warc_CC-MAIN-20230205032040-20230205062040-00666.warc.gz\"}"}
https://pure.au.dk/portal/en/publications/a-linear-time-algorithm-for-the-k-maximal-sums-problem(43737830-9d8e-11dc-bee9-02004c4f4f50).html	[ "", null, "## A Linear Time Algorithm for the k Maximal Sums Problem\n\nResearch output: Contribution to book/anthology/report/proceedingArticle in proceedingsResearchpeer-review\n\n• Department of Computer Science\nFinding the sub-vector with the largest sum in a sequence of n numbers is known as the maximum sum problem. Finding the k sub-vectors with the largest sums is a natural extension of this, and is known as the k maximal sums problem. In this paper we design an optimal O(n + k) time algorithm for the k maximal sums problem. We use this algorithm to obtain algorithms solving the two-dimensional k maximal sums problem in O(m 2·n + k) time, where the input is an m ×n matrix with m ≤ n. We generalize this algorithm to solve the d-dimensional problem in O(n 2d − 1 + k) time. The space usage of all the algorithms can be reduced to O(n d − 1 + k). This leads to the first algorithm for the k maximal sums problem in one dimension using O(n + k) time and O(k) space.\nOriginal language English Mathematical Foundations of Computer Science 2007 : 32nd International Symposium, MFCS 2007 Ceský Krumlov, Czech Republic, August 26-31, 2007 Proceedings Ludek Kucera, Antonin Kucera 12 Springer 2007 442-453 978-3-540-74455-9 https://doi.org/10.1007/978-3-540-74456-6_40 Published - 2007 32nd International Symposium on Mathematical Foundations of Computer Science - Cesky Krumlov, Czech RepublicDuration: 26 Aug 2007 → 31 Aug 2007Conference number: 32\n\n### Conference\n\nConference 32nd International Symposium on Mathematical Foundations of Computer Science 32 Czech Republic Cesky Krumlov 26/08/2007 → 31/08/2007\nSeries Lecture Notes in Computer Science 4708 0302-9743\n\n### Research areas\n\n• maximum sum problem\n\nCitationformats" ]	[ null, "https://cdn.au.dk/2016/assets/img/au_segl.svg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8506931,"math_prob":0.7000387,"size":966,"snap":"2023-40-2023-50","text_gpt3_token_len":232,"char_repetition_ratio":0.14449064,"word_repetition_ratio":0.047058824,"special_character_ratio":0.24430642,"punctuation_ratio":0.07329843,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9898222,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-27T04:43:13Z\",\"WARC-Record-ID\":\"<urn:uuid:14bf131e-ae2d-4d7a-8f2c-810bc40b6718>\",\"Content-Length\":\"54856\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:96857793-f4cf-4e28-a6e5-cad1541ae127>\",\"WARC-Concurrent-To\":\"<urn:uuid:25b5678e-c7f4-49ba-8b43-54de32e11d93>\",\"WARC-IP-Address\":\"34.253.178.11\",\"WARC-Target-URI\":\"https://pure.au.dk/portal/en/publications/a-linear-time-algorithm-for-the-k-maximal-sums-problem(43737830-9d8e-11dc-bee9-02004c4f4f50).html\",\"WARC-Payload-Digest\":\"sha1:RGVRDGEADXTG33JTAE4ZY7D3T4K7Y6WS\",\"WARC-Block-Digest\":\"sha1:TZ247W62726TKRRQZ6MGSTQGXXK2IKYM\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510259.52_warc_CC-MAIN-20230927035329-20230927065329-00648.warc.gz\"}"}
http://npvw.xhrh.pw/anova-lmer.html	[ "In a repeated-measures design, each participant provides data at multiple time points. Random and mixed e ects ANOVA STAT 526 Professor Olga Vitek January 27, 2011 Reading: KNNL Ch. stats = anova(lme) returns the dataset array stats that includes the results of the F-tests for each fixed-effects term in the linear mixed-effects model lme. Here is a solution for an Anova table using the command capture. The following is an abbreviated example of a nested anova using the lmer function in the lme4 package. A very basic tutorial for performing linear mixed effects analyses (Tutorial 2) Bodo Winter1 University of California, Merced, Cognitive and Information Sciences Last updated: 01/19/2013; 08/13/2013 This tutorial serves as a quick boot camp to jump-start your own analyses with linear mixed effects models. Generalized Linear Mixed Models (illustrated with R on Bresnan et al. Another crucial advantage of mixed logit models over ANOVA for CDA is their greater power. One of the frequent questions by users of the mixed model function lmer of the lme4 package has been: How can I get p values for the F and t tests for objects returned by lmer? The lmerTest package extends the 'lmerMod' class of the lme4 package, by overloading the anova and summary functions by providing p values for tests for fixed effects. Repeated measures analysis with R Summary for experienced R users The lmer function from the lme4 package has a syntax like lm. ##### # # # STAT 599 Spring 2013 # # # # Example R code # # # # Chapter 8 # # # ##### ### Installing the add-on packages needed for this course: # If you haven't. We illustrate the use of the modular functions in lme4 to fit such a model. The former is the REML log likelihood, the latter the ML likelihood. Also, this uses ML/REML techniques, as above. Even ignoring the cheating and p-value chasing aspect of it, I think that using ANOVA is statistically problematic for the above reason alone. plot(partcount. statistics) submitted 22 days ago by ice_shadow I have a dataset where some biomarkers from Mice are measured at 4 different time points (call it 1/2/3/4) in response to 2 different drugs A and B. 7 Repeated measures ANOVA using the lme4 package. If you are not familiar with three-way interactions in ANOVA, please see our general FAQ on understanding three-way interactions in ANOVA. In contrast, afex focuses on tests of effects. PyData Singapore is a group for users and developers of data analysis tools to share ideas and learn from each other. It is important when discussing the behavior of lmer and other functions in the lme4 package to state the version of the package that you are using. The interpretation of the statistical output of a mixed model requires an. Experimental Designs - Between Subject ANOVA Models. ANOVA table with F-tests and p-values using Satterthwaite's or Kenward-Roger's method for denominator degrees-of-freedom and F-statistic. Working with orthogonal contrasts in R. The lme() and lmer() functions assume that the sampling variances are not exactly known, but again just up to a proportionality constant, namely the residual variance. homogeneity) and equal correlations between any pair of time points [e. Indeed, for a balanced design, the estimates and hypothesis for Factor A will be identical to that produced via nested ANOVA. Many research questions require comparisons of several groups of subjects representing different populations. subj_intercepts_mod <-lmer(Reaction ~ A + (1 \| Subject)) A model that allows intercepts to vary across subjects does just that: it does a great job of estimating overall Reaction for each subject, but it is. Homepage for the Language and Cognitive Dynamics Laboratory, headed by Dan Mirman in the Department of Psychology at Drexel University. This article describes how to compute manova in R. We really cannot work out why its > not working!!. ANOVA table and lmer. 1 Fitting Linear Mixed Models with a Varying Intercept We will now work through the same Ultimatum Game example from the regression section and the introduction using the lme4 package. Anova(lm(time ~ topic * sys, data=search, contrasts=list(topic=contr. ##### # # # STAT 599 Spring 2013 # # # # Example R code # # # # Chapter 8 # # # ##### ### Installing the add-on packages needed for this course: # If you haven't. The summary() method uses the REML estimates (the latter is clearly indicated in the output). An interaction term (presence of hiatus:preceding glottalization) was included because it improved the model’s fit (which was assessed by the anova function in R, following Baayen (2008)). The entire random-e ects expression should be enclosed in parentheses. For a simple completely balanced nested ANOVA, it is possible to pool together (calculate their mean) each of the sub-replicates within each nest (=site) and then perform single factor ANOVA on those aggregates. Note: the lmer function in the lme4 package also can be used for the same results. If we look at the different inputs for the LMER function we: have \"popular\", which indicates the dependent variable we want to predict. Compute an ANOVA-like table with tests of random-effect terms in the model. Model selection methods include step, drop1 and anova-like tables for random effects (ranova). nobody knows what is going on ? the \"Why do I recieve NaN's in the ANOVA table when I try to analyze my data using. Calculates type-II or type-III analysis-of-variance tables for model objects produced by lm, glm, multinom (in the nnet package), polr (in the MASS package), coxph (in the survival package), lmer in the lme4 package, lme in the nlme package, and for any model with a linear predictor and asymptotically normal coefficients that responds to. Because the multi-way ANOVA model is over-parameterised, it is necessary to choose a contrasts setting that sums to zero, otherwise the ANOVA analysis will give incorrect results with respect to the expected hypothesis. ANOVA/LMER vs paired t tests I have a dataset where some biomarkers from Mice are measured at 4 different time points (call it 1/2/3/4) in response to 2 different drugs A and B What is the appropriate analysis tool for this dataset?. These expressions are used to calculate the ANOVA table entries for the (fixed effects) two-way ANOVA. search(\"linear models\") A window will pop up that lists commands available and the packages that include them. But unlike an ANOVA a LMM does not have to be averaged over repetitions. This is Part 2 of a two part lesson. aov() uses ordinary least squares as the methodology for calculating the ANOVA table. lmer doesn't currently express uncertainty in the variance parameters In R2. I wrote several functions that handled it. example stats = anova( lme , Name,Value ) also returns the dataset array stats with additional options specified by one or more Name,Value pair arguments. 's datives data) Christopher Manning 23 November 2007 In this handout, I present the logistic model with ﬁxed and random eﬀects, a form of Generalized Linear. > Subject: Re: [R] anova statistics in lmer > > The issue is not unresolved within lmer, but with the > statistical model itself. Because this requires fitting as many models as there are terms in the formula, the function may take a while to complete its calculations. The following output results from fitting models using lmer and lm to data arising from a split-plot experiment (#320 from \"Small Data Sets\" by Hand et al. Three ways to get parameter-specific p-values from lmer How to get parameter-specific p -values is one of the most commonly asked questions about multilevel regression. In this design only one factor, C, is crossed with subjects (is a within-subjects factor), while the other two factors, A and B, are between-subjects factors. Lmer (formula, data, family='gaussian') [source] ¶ Model class to hold data outputted from fitting lmer in R and converting to Python object. 3) why the anova summary don't say if differences in classes are significance (or not significance)? 4) I'd like to perform a post-hoc test with the package \"multicomp\" but the lmer function give me a lmer object (and this kind of object is not read by the \"multicomp\" package). lme4 Luke Chang Last Revised July 16, 2010 1 Using lme4 1. Supplement Material Description (For publication) RGxE: An R Program for Genotype x Environment Interaction Analysis Description The supplemental material provides RGxE program, instructions for user enetered field needed in RGxE program, independent module of ANOVA model case 2 to 5 (Table 1), interpretation of univariate. Statistics 203: Introduction to Regression and Analysis of Variance Fixed vs. A good online presentation on ANOVA in R can be found in ANOVA section of the Personality Project. The issue is that in a major recent paper the authors did an ANOVA after they fail to get statistical significance with lmer. If > 1 verbose output is generated during the individual penalized iteratively reweighted least squares (PIRLS) steps. In this post, I want to take a quick look at how you would actually run a mixed-effects model, using the lmer() function furnished by the lme4 package, written by Doug Bates (Bates, 2010 - appears to a preprint of his presumed new book, see also Pinheiro & Bates, 2000). Also the difference between repeated measures ANOVA and ANOVA. R lmer ONE WAY ANOVA by horacio3miranda3varg. The following is an abbreviated example of a nested anova using the lmer function in the lme4 package. This requires the \"lme4\" package. If > 0 verbose output is generated during the optimization of the parameter estimates. Raccoon is Quantide’s third web book after “ Rabbit – Introduction to R ” and “ Ramarro – R for Developers “. It is also intented to prepare the reader to a more complicated model. This makes a comparison between the size of the differences between groups, as measured by a contrast and the accuracy with which that contrast can be measured by a given study or experiment. Statistics > ANOVA models > Repeated Measures. sum, sys=contr. Analysis of variance is merely regression when the predictive variables are qualitative -- more precisely, it refers to the tests one performs in that context. We really cannot work out why its > not working!!. As a result, this approach allows researchers to describe, specify, and interpret a wide range of effects in an LMER more easily. And, for future reference, when the experts ask you for a data example to work on, they do not mean a copy of your printout, although that may help. The e ects of Grand Mean Centering In the case of grand mean centering, we subtract the value of the independent variable for each \\i\" student from their grand. Here we'll introduce anova() and TukeyHSD() which help us understand our linear model in ways that complement the output from summary() ‹ 12. The stan_lmer approach just calls stan_glm but specifies a normal prior with mean zero for the deviations from $$\\alpha$$ across groups. However, I. Specifying a single object gives a sequential analysis of variance table for that fit. 485) for Variety is the same for aov, lme and lmer, but lmer's mean square for variety is 1. Need to load the library lme4. Notice that this model contains an additional term, (1\|id), which specifies a random effect for each subject. 485 times the subplot residual mean square. Models should be fitted with lmer from the lmerTest-package. The lme4 package is unique in that it allows for correlated random variance structures and also allows. It is intended to be very basic. example stats = anova( lme , Name,Value ) also returns the dataset array stats with additional options specified by one or more Name,Value pair arguments. Four different methods are available for estimating the variance components: minimum norm quadratic unbiased estimator (MINQUE), analysis of variance (ANOVA), maximum likelihood (ML), and restricted maximum likelihood (REML). Testing significance. lmer() One of the challenges with our previous analysis is that aov() ran the analysis and considered our block effect as a fixed effect. Repeated measures ANOVA is the equivalent of the one-way ANOVA, but for related, not independent groups, and is the extension of the dependent t-test. Basic Features; Notation for the Mixed Model. ANOVA table and lmer. Because of the balance in the data, the F-test requires no adjustment and the outcome is identical with that presented in the printed textbook. The ANOVA model is then fit using lmer(). 7 Repeated measures ANOVA using the lme4 package. To do this, you should use the lmer function in the lme4 package. For the second part go to Mixed-Models-for-Repeated-Measures2. 4 - Repeated Measures Using Mixed Effects II up 18. Unlike most statistical packages, the default assumes unequal variance and applies the Welsh df modification. Compare Likelihoods of Fitted Objects Description. However, afex involves many functions that support nice printing of the \"mixed\" objects returned from mixed. To begin with, we will use the example I had in class. Statistics Question ANOVA/LMER vs paired t tests (self. Compute for each pair of means, where M i is one mean, M j is the other mean, and n is the number of scores in each group. Simulations show that lmer's quasi-likelihood. • [gn]lmer now produces objects of class merMod rather than class mer as before •the new version uses a combination of S3 and reference classes (see ReferenceClasses, merPredD-class, and lmResp-class) as well as S4 classes; partly for this reason it is more interoperable with nlme. To illustrate, the figure below shows the output after loading the lmerTest package. VCs (in lme the corresponding standard deviations, i. 485) for Variety is the same for aov, lme and lmer, but lmer's mean square for variety is 1. That is, the reductions in the residual sum of squares as each term of the formula is added in turn are given in as the rows of a table, plus the residual sum of squares. If you wanted to see if Year is important for predicting Crime in Maryland, we can build a null model with only County as a random-effect and a year model that includes Year. To enter these data into SPSS we use the same procedure as the repeated measures ANOVA that we came across last week, except that we also need a variable (column) that codes whether the helper was an elf or a reindeer. (Degrees of freedom for the t -test is N-k-1 where k equals the number of predictor variables. So, let’s dive into the intersection of these three. sum','contr. • The model formula consists of two expressions separated by the ∼ symbol. √VC) are obtained by applying the function summary. The F-ratio (1. Mar 11 th, 2013. One of the frequent questions by users of the mixed model function lmer of the lme4 package has been: How can I get p values for the F and t tests for objects returned by lmer? The lmerTest package extends the 'lmerMod' class of the lme4 package, by overloading the anova and summary functions by providing p values for tests for fixed effects. In this post, I want to take a quick look at how you would actually run a mixed-effects model, using the lmer() function furnished by the lme4 package, written by Doug Bates (Bates, 2010 - appears to a preprint of his presumed new book, see also Pinheiro & Bates, 2000). The interpretation of the statistical output of a mixed model requires an. a \"~\", that we use to indicate that we now give the other variables of interest. As this post shows, it can detect multivariate patterns in the DVs that ANOVA is simply unable to detect at all. Extrusion and Wear ex8_3_15 has data on the relationship between extrusion pressure (x, in KPa) and wear (y, in mg). anova (reduced. lmer() One of the challenges with our previous analysis is that aov() ran the analysis and considered our block effect as a fixed effect. Simulations show that lmer's quasi-likelihood. I am trying to perform a mixed-model analysis using the lmer() function. ANOVA/LMER vs paired t tests I have a dataset where some biomarkers from Mice are measured at 4 different time points (call it 1/2/3/4) in response to 2 different drugs A and B What is the appropriate analysis tool for this dataset?. * glance puts model summary statistics into a data frame. The lme() and lmer() functions assume that the sampling variances are not exactly known, but again just up to a proportionality constant, namely the residual variance. start with the full model and then do stepwise removal. As a result, this approach allows researchers to describe, specify, and interpret a wide range of effects in an LMER more easily. Posts about lmer() written by robayedavies. First, you will run an anova() on it to see if group explains a significant amount of variability. com What actually the “P” value tells us in ANOVA table. The logic and computational details of the two-way ANOVA for independent samples are described in Chapter 16 of Concepts and Applications. Notice above: Two-point panels such as Panel 4 and Panel 11 have lines not going exactly through the two points. For linear mixed models with little correlation among predictors, a Wald test using the approach of Kenward and Rogers (1997) will be quite similar to LRT test results. Four different methods are available for estimating the variance components: minimum norm quadratic unbiased estimator (MINQUE), analysis of variance (ANOVA), maximum likelihood (ML), and restricted maximum likelihood (REML). Si nous ne comparons que deux moyennes, l'ANOVA nous donnera les mêmes résultats qu'un test t pour des échantillons indépendants (pour comparer deux groupes différents d'observations), ou qu'un test t pour des échantillons appariés (pour comparer. Note anova() for balanced designs. Contrast Coding in R: An Exploration of a Dataset Rachel Baker Phonatics, Sept. In other software packages like SAS, Type III tests of fixed effects are presented with the regression output. I know that the variance of counts can often be stabilized by square roots, so I'll try. lmer : For models with random eﬀects. The former is the REML log likelihood, the latter the ML likelihood. a random e ect is a linear model term conditional on the level of the grouping factor. rand is an alias for ranova. Beautiful Piano Music 24/7: Study Music, Relaxing Music, Sleep Music, Meditation Music Soothing Relaxation 2,324 watching Live now. The library lmerTest has functions lsmeans for testing the treatment eﬀects,. aov() uses ordinary least squares as the methodology for calculating the ANOVA table. This function is equivalent to ‘lme(fixed=formula,random=~1\|random)’, except that the block variance component is not constrained to be non-negative, but is faster and more accurate for small to moderate size data sets. ® Levels of repeated measures variables go in different columns of the SPSS data editor. If > 0 verbose output is generated during the optimization of the parameter estimates. xlsx dataset with a mixed effects model. mod) Book recommendations. The lmer package can be used for modeling, and the general syntax is as follows: ` modelname <- lmer (dv ~ 1 + IV +(randomeffects), data = data. # independent 2-group t-test. Whereas the factorial ANOVAs can have one or more independent variables, the one-way ANOVA always has only one dependent variable. To do this, you should use the lmer function in the lme4 package. This makes a comparison between the size of the differences between groups, as measured by a contrast and the accuracy with which that contrast can be measured by a given study or experiment. The last argument is optional. When only one fitted model object is present, a data frame with the numerator degrees of freedom, denominator degrees of freedom, F-values, and P-values for Wald tests for the terms in the model (when Terms and L are NULL), a combination of model terms (when Terms in not NULL), or linear combinations of the model coefficients (when L is not NULL). It is a generalization of two sample t-test. adjust=TRUE) - bootstrap - nonparametric method using ranks (Kruskal-Wallis) kruskal. singular vs. This page is intended to simply show a number of different programs, varying in the number and type of variables. • [gn]lmer now produces objects of class merMod rather than class mer as before •the new version uses a combination of S3 and reference classes (see ReferenceClasses, merPredD-class, and lmResp-class) as well as S4 classes; partly for this reason it is more interoperable with nlme. Roughly: restrict the data to n −p modiﬁed observations,. The lme4 package is unique in that it allows for correlated random variance structures and also allows. Experimental Designs - Between Subject ANOVA Models. The F-ratio (1. 9-0 VarCorr(mcmcsamp(lmerModel, 10), \"varcov\") works (OK, with >10 iterations). For lmer this can be a numeric vector or a list with one component named \"theta\". As for the choice between RM anova and mixed regression, I have a strong bias in favor of mixed regression because it is tolerant of missing data (though apparently you don't have this problem, as both models ran with the same N), and because it dispenses with stringent assumptions such as compound symmetry (sphericity), and therefore does not. The last argument is optional. To compare the fits of two models, you can use the anova() function with the regression objects as two separate arguments. Assumptions. The SSCC does not recommend the use of Wald tests for generalized models. Home › forums › Mixed Models › Sum coding for ANOVA style results with unbalanced lmer data Tagged: lmer anova sum coding treatment coding This topic contains 1 reply, has 2 voices, and was last updated by henrik 1 year, 9 months ago. ANOVA (CRD) · General format of ANOVA in R · Testing the assumption of homogeneity of variances using Levene's Test · One-way ANOVA of nested design · Obtaining and interpreting Components of Variance Linear Models in R The primary R function for the analysis of variance of a fixed-effects model is the linear model (lm()) function. You are interested in seeing if tutorial performance is related to final grade. Because the multi-way ANOVA model is over-parameterised, it is necessary to choose a contrasts setting that sums to zero, otherwise the ANOVA analysis will give incorrect results with respect to the expected hypothesis. Do we still > need > to worry about the interaction as a whole, and if yes, how would we > evaluate > it? If you want to follow ANOVA logic, do model comparison. So, let's dive into the intersection of these three. Supplement Material Description (For publication) RGxE: An R Program for Genotype x Environment Interaction Analysis Description The supplemental material provides RGxE program, instructions for user enetered field needed in RGxE program, independent module of ANOVA model case 2 to 5 (Table 1), interpretation of univariate. 3 - Regression Assumptions in ANOVA ›. 1 Fitting Linear Mixed Models with a Varying Intercept We will now work through the same Ultimatum Game example from the regression section and the introduction using the lme4 package. The 95% prediction interval of the eruption duration for the waiting time of 80 minutes is between 3. For a simple completely balanced nested ANOVA, it is possible to pool together (calculate their mean) each of the sub-replicates within each nest (=site) and then perform single factor ANOVA on those aggregates. plot command is going to make four plots, one for each explicit random effect and two for residuals. interceptonlymodel<-lmer(popular~1 + (1\|class), data=popular2data) #to run the model. The default in lmer is to fit models using the REML (REstricted Maximum Likelihood) criterion. 6 - Using anova() to Compare Models ›. adjust=TRUE) - bootstrap - nonparametric method using ranks (Kruskal-Wallis) kruskal. On Oct 8, 2012, at 1:57 AM PDT, Holger Mitterer wrote: > Dear Fotis, > > All the points aside that Florian alreadly addressed, part of your message > reflects a typical problem in interpreting the output of an lmer > in comparison with the output of an ANOVA. 2-0 Date 2012-01-09 Author Alexandra Kuznetsova, Per Bruun Brockhoff, Rune Haubo Bojesen Christensen Maintainer Alexandra Kuznetsova Depends Matrix, stats. Many designs involve the assignment of participants into one of several groups (often denoted as treatments) where one is interested in differences between those treatments. 9788 for the mixed model vs 227. Random effects in models for paired and repeated measures As an example, if we are measuring the left hand and right of several individuals, the measurements are paired within each individual. library (lmerTest) anova (lmer. If you are not familiar with three-way interactions in ANOVA, please see our general FAQ on understanding three-way interactions in ANOVA. Rather, we explain only the proper way to report an F-statistic. MODEL SELECTION: To compare different lmer models it's best to avoid REML when the fixed effects are different between models. The following output results from fitting models using lmer and lm to data arising from a split-plot experiment (#320 from \"Small Data Sets\" by Hand et al. singular vs. A Kenward-Roger method is also available via the pbkrtest package. Posts about lmer() written by robayedavies. Lmer in the above table gives you (some of) the > contrasts, but doesn't evaluate the interaction as a whole. In this case, the random fertility level of each field. The last argument is optional. We can also test the main effect terms although we are not able to exactly reproduce the results in the text because we must frame the test as model comparisons in contrast to the ANOVA table in text. Horses are mainly housed in individual boxes. Nested ANOVA - Replication vs. The LRT is generally preferred over Wald tests of fixed effects in mixed models. Statistics 203: Introduction to Regression and Analysis of Variance Fixed vs. To illustrate this, we can again factor in that constant into the sampling variances and refit the model with rma() :. Kyle Roberts A Brief History of Multilevel Models • Nested ANOVA designs • Problems with the ANCOVA design – “Do schools differ” vs. R lmer ONE WAY ANOVA by horacio3miranda3varg. See the previous example in this chapter for explanation and model-checking. We can also compare the AIC values and note that the model with the lowest AIC value is the one with no fixed effects at all, which fits with our understanding that sex and social. Journal of Clinical Medicine Article The E ect of Tapered Abutments on Marginal Bone Level: A Retrospective Cohort Study Simone Marconcini 1,*, Enrica Giammarinaro 2, Ugo Covani 1, Eitan Mijiritsky 3, Xavier Vela 4. 0954) 0. plot(partcount. 1564 minutes. Each random-effect term is reduced or removed and likelihood ratio tests of model reductions are presented in a form similar to that of drop1. The chapter begins by reviewing paired t-tests and repeated measures ANOVA. Statistics Question ANOVA/LMER vs paired t tests (self. For example, we may conduct an experiment where we give two treatments (A and B) to two groups of mice, and we are interested in the weight and height of. lmer - lmer(mathgain ~ 1. P-value in ANOVA table – iSixSigma Isixsigma. In this tutorial, I’ll cover how to analyze repeated-measures designs using 1) multilevel modeling using the lme package and 2) using Wilcox’s Robust Statistics package (see Wilcox, 2012). lmer : For models with random eﬀects. To begin with, we will use the example I had in class. Repeated Measures and Mixed Models - m-clark. The lmer_out model you build in the previous exercise has been loaded for you. Select two of the levels and run the one-way ANOVA. There are three schools, with two students nested in each school. As for the choice between RM anova and mixed regression, I have a strong bias in favor of mixed regression because it is tolerant of missing data (though apparently you don't have this problem, as both models ran with the same N), and because it dispenses with stringent assumptions such as compound symmetry (sphericity), and therefore does not. The following information is a best approximation of how to test assumptions of mixed and multilevel models as of November 2016. Using the \"Repeated-measures / within-subjects ANOVA in R\", \"repeated measure anova using regression models (LM, LMER)\", and \"How to convert Afex or car ANOVA models to lmer? Observed variables \" questions and Chapter 4 of the lme4 book , I created the following code that uses the CO2 sample data. Analysis of variance using distance matrices — for partitioning distance matrices among sources of variation and fitting linear models (e. And random (a. Lmer in the above table gives you (some of) the > contrasts, but doesn't evaluate the interaction as a whole. This function is equivalent to 'lme(fixed=formula,random=~1\|random)', except that the block variance component is not constrained to be non-negative, but is faster and more accurate for small to moderate size data sets. The following is an abbreviated example of a nested anova using the lmer function in the lme4 package. The following output results from fitting models using lmer and lm to data arising from a split-plot experiment (#320 from \"Small Data Sets\" by Hand et al. One of the frequent questions by users of the mixed model function lmer of the lme4 package has been: How can I get pvalues for the F and ttests for objects returned by lmer? The lmerTest package extends the 'lmerMod' class of the lme4 package, by overloading the anova and summary functions by providing pvalues for tests for xed e ects. In this case, the random fertility level of each field. Compute an ANOVA-like table with tests of random-effect terms in the model. • In lmer the model is speciﬁed by the formula argument. 's datives data) Christopher Manning 23 November 2007 In this handout, I present the logistic model with ﬁxed and random eﬀects, a form of Generalized Linear. lme4 Luke Chang Last Revised July 16, 2010 1 Using lme4 1. One of the advantages of lmerTest and afex is that all one has to do is load the package in R, and the output of lmer is automatically updated to include the p values. While I could get lmer() to work, I can't seem to get the anova t. In the simplest form you test the mean of one set of numbers against the mean of another set of numbers (one-way ANOVA). anova anova method for lmer model ﬁts produces type I, II, and III anova tables for ﬁxed-effect terms with Satterthwaite and Kenward-Roger methods for denominator degrees of freedom for F-tests. You are interested in seeing if tutorial performance is related to final grade. poly\")) lmod - aov(bright ~ operator, pulp) summary(lmod) coef(lmod) options(op) (0. MODEL SELECTION: To compare different lmer models it's best to avoid REML when the fixed effects are different between models. Package 'lme4' November 10, 2010 Version. Speaker and word were included as random intercepts. The data is given at the bottom of this message. We will use the following simulated dataset for illustration:. Assumptions. Recall that the likelihood function is the function links the model parameters to the data and is found by taking the probability density function and interpreting it as a function of the parameters instead of the a function of the data. Using Mixed-Effects Models for Confirmatory Hypothesis Testing (FAQ) This FAQ is intended for people using linear mixed effects models (LMEMs) as a replacement for the statistical techniques that are more traditionally used for confirmatory hypothesis testing, such as ANOVA or t-tests. Contrast Coding in R: An Exploration of a Dataset Rachel Baker Phonatics, Sept. Nested Designs in R Example 1. In a repeated-measures design, each participant provides data at multiple time points. Two-Way ANOVA Example: Data An evaluation of a new coating applied to 3 different materials was conducted at 2 different laboratories. ANOVA; One-way ANOVA; Two-way ANOVA; Analysis of covariance; One-way repeated-measures ANOVA; Two-way repeated-measures ANOVA; Two-way split-plot ANOVA; Three-way split-plot ANOVA; Mixed effects models; Sum of squares type I, II, and III; General Topics; Assess normality; Assess variance homogeneity. How to predict and graph non-linear varying slopes in lmer or glmer? r,ggplot2,lme4,mixed-models,lmer. You are interested in seeing if tutorial performance is related to final grade. Statistics Question ANOVA/LMER vs paired t tests (self. 's datives data) Christopher Manning 23 November 2007 In this handout, I present the logistic model with ﬁxed and random eﬀects, a form of Generalized Linear. tutorial 1 pdf tutorial 2 pdf dataset for tutorial 2 Please cite as: Winter, B. To do this, you should use the lmer function in the lme4 package. The last argument is optional. integer scalar. Here's the thing many don't realize is that the anytime you use (1\|x) in lmer it is basically like there is an as. aov() uses ordinary least squares as the methodology for calculating the ANOVA table. Running a repeated measures analysis of variance in R can be a bit more difficult than running a standard between-subjects anova. creates both treatment (a. If you wanted to see if Year is important for predicting Crime in Maryland, we can build a null model with only County as a random-effect and a year model that includes Year. Extrusion and Wear ex8_3_15 has data on the relationship between extrusion pressure (x, in KPa) and wear (y, in mg). The term Analysis of Variance (ANOVA) refers to a number of different concepts, but here use it to describe experimental designs that are based on one or more discrete-valued variables called factors, where the unique values of each factor are called levels. 's datives data) Christopher Manning 23 November 2007 In this handout, I present the logistic model with ﬁxed and random eﬀects, a form of Generalized Linear. Interactions and Contrasts. The key issue is that the degrees of freedom are not trivial to compute for multilevel regression. Type library(lme4) to ensure it is active. This is Part 2 of a two part lesson. Non-nested (crossed) Random Effects in R June 13, 2015 Technical mixed-effects , nonlinear , R , statistics BioStatMatt The R script below illustrates the nested versus non-nested (crossed) random effects functionality in the R packages lme4 and nlme. However, we can use contrast and ANOVA-type commands to extract these effects. singular vs. Statistics Question ANOVA/LMER vs paired t tests (self. The factorial ANOVA is closely related to both the one-way ANOVA (which we already discussed) and the MANOVA (Multivariate Analysis of Variance). Each laboratory tested 3 samples from each of the treated materials. I wrote several functions that handled it. We really cannot work out why its > not working!!. Mixed Models Analysis of a psycholinguistic experiment Ruggero Montalto Seminar in Statistics and Methodology 17/05/2011. The library lmerTest has functions lsmeans for testing the treatment eﬀects,. integer scalar. Nested ANOVA - Replication vs. In the situation where there multiple response variables you can test them simultaneously using a multivariate analysis of variance (MANOVA). Mar 11 th, 2013. lmer) And now we see a problem. anova anova method for lmer model ﬁts produces type I, II, and III anova tables for ﬁxed-effect terms with Satterthwaite and Kenward-Roger methods for denominator degrees of freedom for F-tests. Once you´ve done an Analysis of Variance (ANOVA), you may reach a point where you want to know: What levels of the factor of interest were significantly different from one another?. This article describes how to compute manova in R. A good online presentation on ANOVA in R can be found in ANOVA section of the Personality Project. Nested Designs in R Example 1. ANOVA assumes (1) errors are normally distributed, (2) variances are homogeneous, and (3) observations are independent of each other. You are interested in seeing if tutorial performance is related to final grade. Each random-effect term is reduced or removed and likelihood ratio tests of model reductions are presented in a form similar to that of drop1. Formula lmer() A random-e ects term in lmer() is speci ed by a linear model term and a grouping factor separated by ’j’; i. How to Calculate the Least Significant Difference (LSD): Overview. In the previous post, we ran through an example of a mixed-effects analysis completed using the lmer() function from the lme4 package (Bates, 2005; Bates, Maelchler & Bolker, 2013). com What actually the “P” value tells us in ANOVA table. lme4) via Satterthwaite's degrees of freedom method. The last argument is optional. 1 Fitting Linear Mixed Models with a Varying Intercept We will now work through the same Ultimatum Game example from the regression section and the introduction using the lme4 package. The goal is to test if the group means are different (at some significance level). 36-463/663: Hierarchical Linear Models Lmer model selection and residuals Brian Junker 132E Baker Hall [email protected] library (lmerTest) anova (lmer." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8889297,"math_prob":0.81276286,"size":37121,"snap":"2020-10-2020-16","text_gpt3_token_len":8537,"char_repetition_ratio":0.1402053,"word_repetition_ratio":0.35619578,"special_character_ratio":0.21462245,"punctuation_ratio":0.09848485,"nsfw_num_words":1,"has_unicode_error":false,"math_prob_llama3":0.98360485,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-03-29T06:08:54Z\",\"WARC-Record-ID\":\"<urn:uuid:bb8cfc56-42b1-4421-ba8a-afc4a60f550a>\",\"Content-Length\":\"41183\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:aee3aabb-cbc2-409b-9875-7f1966b487cb>\",\"WARC-Concurrent-To\":\"<urn:uuid:acd01716-0e28-437f-8055-87aa720fd0d2>\",\"WARC-IP-Address\":\"104.27.162.1\",\"WARC-Target-URI\":\"http://npvw.xhrh.pw/anova-lmer.html\",\"WARC-Payload-Digest\":\"sha1:QFBIYBVUIDMQYJ77SWMUCCOSZSOIQUT2\",\"WARC-Block-Digest\":\"sha1:Z7W5JWL2AZXXO7ZMGSC7CCQ6EQWFTDCK\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-16/CC-MAIN-2020-16_segments_1585370493818.32_warc_CC-MAIN-20200329045008-20200329075008-00497.warc.gz\"}"}
http://rohitapte.com/2017/04/24/	[ "## Convolutions\n\nIn the previous post we discussed using Convolutional Neural Networks for Image Recognition. In order to better understand what the algorithms are doing we need to explore convolutions in more detail.\n\n#### Definition\n\nA convolution of f and g, denoted f*g, is the integral of the product of 2 functions after one is reversed and shifted. Mathematically", null, "One way of thinking about convolutions is an integral that expresses the amount of overlap of g as it is shifted over f. It “blends” one function with another. The below image courtesy of Wikipedia demonstrates this.", null, "Some more intuitive explanations of convolutions (and more applicable to machine learning):\n\nThink about a time series. Say we look at the fed funds rate over time.", null, "One way to smooth data is to convolve it against a smaller list. For example, to calculate the weekly moving average we convolve it against [1,1,1,1,1]. For a monthly moving average we would convolve it with a list of 25 ones (assuming 25 business days in a month).\n\nAs another example, consider rolling 2 six sided dice. The probability distribution looks as follows.", null, "This can be represented as a convolution… For example to get a 4 we have", null, "So what does the “Convolution” in Convolutional Neural Networks (aka Deep Learning) do to images? Convolutions (called Kernels in image processing) work as feature detectors. Lets look at a few convolutions on 2 images below.\n\n Convolution Matrix Image 1 Image 2 Original Image", null, "", null, "Average", null, "", null, "", null, "Sharpen", null, "", null, "", null, "Edge Detection 1", null, "", null, "", null, "Edge Detection 2", null, "", null, "", null, "Edge Detection 3", null, "", null, "", null, "Edge Detection 4", null, "", null, "", null, "Box Blur", null, "", null, "", null, "Gaussian Blur", null, "", null, "", null, "Gradient Detection 1", null, "", null, "", null, "Gradient Detection 2", null, "", null, "", null, "The amazing part about Deep Learning is we don’t have to teach the algorithm the convolutions to use. It learns them as part of the hyperparameter tuning!" ]	[ null, "http://rohitapte.com/wp-content/ql-cache/quicklatex.com-5666b1a2e839b520cd4395a5a421c3fe_l3.png", null, "http://rohitapte.com/wp-content/uploads/2017/04/Convolution_of_box_signal_with_itself2.gif", null, "http://rohitapte.com/wp-content/uploads/2017/04/Federal_funds_rate_history_and_recessions-1024x410.png", null, "http://rohitapte.com/wp-content/uploads/2017/04/DiceRolls-300x202.png", null, "http://rohitapte.com/wp-content/uploads/2017/04/DiceRollConvolution.gif", null, "http://rohitapte.com/wp-content/uploads/2017/04/HKskyline.jpg", null, "http://rohitapte.com/wp-content/uploads/2017/04/HuskyBW-2.jpg", null, "http://rohitapte.com/wp-content/uploads/2017/04/Average.png", null, "http://rohitapte.com/wp-content/uploads/2017/04/HKskyline-Average.jpg", null, "http://rohitapte.com/wp-content/uploads/2017/04/HuskyBW-Average.jpg", null, "http://rohitapte.com/wp-content/uploads/2017/04/Sharpen.png", null, "http://rohitapte.com/wp-content/uploads/2017/04/HKskyline-Sharpen.jpg", null, "http://rohitapte.com/wp-content/uploads/2017/04/HuskyBW-Sharpen.jpg", null, "http://rohitapte.com/wp-content/uploads/2017/04/EdgeDetection1.png", null, "http://rohitapte.com/wp-content/uploads/2017/04/HKskyline-Edge-Detection-1.jpg", null, "http://rohitapte.com/wp-content/uploads/2017/04/HuskyBW-Edge-Detection-1.jpg", null, "http://rohitapte.com/wp-content/uploads/2017/04/EdgeDetection2.png", null, "http://rohitapte.com/wp-content/uploads/2017/04/HKskyline-Edge-Detection-2.jpg", null, "http://rohitapte.com/wp-content/uploads/2017/04/HuskyBW-Edge-Detection-2.jpg", null, "http://rohitapte.com/wp-content/uploads/2017/04/EdgeDetection3.png", null, "http://rohitapte.com/wp-content/uploads/2017/04/HKskyline-Edge-Detection-3.jpg", null, "http://rohitapte.com/wp-content/uploads/2017/04/HuskyBW-Edge-Detection-3.jpg", null, "http://rohitapte.com/wp-content/uploads/2017/04/EdgeDetection4.png", null, "http://rohitapte.com/wp-content/uploads/2017/04/HKskyline-Edge-Detection-4.jpg", null, "http://rohitapte.com/wp-content/uploads/2017/04/HuskyBW-Edge-Detection-4.jpg", null, "http://rohitapte.com/wp-content/uploads/2017/04/BoxBlur.png", null, "http://rohitapte.com/wp-content/uploads/2017/04/HKskyline-Box-Blur.jpg", null, "http://rohitapte.com/wp-content/uploads/2017/04/HuskyBW-Box-Blur.jpg", null, "http://rohitapte.com/wp-content/uploads/2017/04/GaussianBlur.png", null, "http://rohitapte.com/wp-content/uploads/2017/04/HKskyline-Gaussian-Blur.jpg", null, "http://rohitapte.com/wp-content/uploads/2017/04/HuskyBW-Gaussian-Blur.jpg", null, "http://rohitapte.com/wp-content/uploads/2017/04/GradientDetection1.png", null, "http://rohitapte.com/wp-content/uploads/2017/04/HKskyline-Gradient-Detection-1.jpg", null, "http://rohitapte.com/wp-content/uploads/2017/04/HuskyBW-Gradient-Detection-1.jpg", null, "http://rohitapte.com/wp-content/uploads/2017/04/GradientDetection2.png", null, "http://rohitapte.com/wp-content/uploads/2017/04/HKskyline-Gradient-Detection-2.jpg", null, "http://rohitapte.com/wp-content/uploads/2017/04/HuskyBW-Gradient-Detection-2.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8901443,"math_prob":0.9698058,"size":1761,"snap":"2023-40-2023-50","text_gpt3_token_len":406,"char_repetition_ratio":0.13716562,"word_repetition_ratio":0.0,"special_character_ratio":0.20954004,"punctuation_ratio":0.083076924,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9928676,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74],"im_url_duplicate_count":[null,5,null,5,null,5,null,5,null,5,null,5,null,5,null,5,null,5,null,5,null,5,null,5,null,5,null,5,null,5,null,5,null,5,null,5,null,5,null,5,null,5,null,5,null,5,null,5,null,5,null,5,null,5,null,5,null,5,null,5,null,5,null,5,null,5,null,5,null,5,null,5,null,5,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-10-03T14:31:24Z\",\"WARC-Record-ID\":\"<urn:uuid:520109c4-e482-4e8e-9017-6fcd0235b9a8>\",\"Content-Length\":\"45980\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9212595f-93ba-40b5-8367-4b04ceebf76c>\",\"WARC-Concurrent-To\":\"<urn:uuid:60fb54e1-7394-46b5-8ddc-985c0d01908f>\",\"WARC-IP-Address\":\"23.235.223.233\",\"WARC-Target-URI\":\"http://rohitapte.com/2017/04/24/\",\"WARC-Payload-Digest\":\"sha1:VEXFYPMRL7RSOAKZKE5FPIRDNGGKZ6CD\",\"WARC-Block-Digest\":\"sha1:3RR3JQY2ANIJHMF4FJGJMNG6F4I7O2KD\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233511106.1_warc_CC-MAIN-20231003124522-20231003154522-00474.warc.gz\"}"}
http://oak.go.kr/central/journallist/journaldetail.do?article_seq=13110	[ "•", null, "• #### ABSTRACT\n\nThis paper presents a zero-IF CMOS RF receiver, which supports three channel bandwidths of 5/10/40MHz for LTE-Advanced systems. The receiver operates at IMT-band of 2,500 to 2,690MHz. The simulated noise figure of the overall receiver is 1.6 dB at 7MHz (7.5 dB at 7.5 kHz). The receiver is composed of two parts: an RF front-end and a baseband circuit. In the RF front-end, a RF input signal is amplified by a low noise amplifier and Gm with configurable gain steps (41/35/29/23 dB) with optimized noise and linearity performances for a wide dynamic range. The proposed baseband circuit provides a -1 dB cutoff frequency of up to 40MHz using a proposed wideband OP-amp, which has a phase margin of 77° and an unit-gain bandwidth of 2.04 GHz. The proposed zero-IF CMOS RF receiver has been implemented in 0.13-μm CMOS technology and consumes 116 (for high gain mode)/106 (for low gain mode) mA from a 1.2 V supply voltage. The measurement of a fabricated chip for a 10-MHz 3G LTE input signal with 16-QAM shows more than 8.3 dB of minimum signal-to-noise ratio, while receiving the input channel power from -88 to -12 dBm.\n\n• #### KEYWORD\n\nCMOS , LTE , LTE Advanced , RF Receiver , Passive Mixer , Wideband OP-Amp.\n\n• ### Ⅰ. INTRODUCTION\n\nCurrently, smartphone use continues to increase and is now an essential part of people’s daily lives. Mobile applications that utilize long-term evolution (LTE) of 3rd generation partnership project (3GPP) are now popular because of highly responsive mobile voice and data services. However, the development of new mobile communication systems such as LTE-Advanced is required to satisfy demands for high-speed multimedia data communications such as real-time video streaming. The LTE-Advanced system offers a peak data-rate of 1 Gbps downlink, which is 10 times higher than 100 Mbps of the 3G LTE systems . Accordingly, many RF receivers for LTE-Advanced systems have been reported in [2-4]. A high data-rate can be achieved by increasing the modulation level and expanding the signal bandwidth as effective techniques .", null, "This paper presents a zero-IF CMOS RF receiver for LTE-Advanced system, which can support up to a 40MHz channel bandwidth for high data-rate applications. The proposed RF receiver operates at an IMT-band of 2,500 to 2,690MHz and provides a gain from 25 dB (low gain mode) to 99 dB (high gain mode). The simulated noise figure of the receiver is 1.6 dB in channel bandwidth from 5 to 40 MHz and 7.5 dB at 7.5MHz. Since the sub-carrier channel bandwidth is 15 kHz and a null-tone has been allocated in the LTE-Advanced system, the baseband signal power is located from 7.5 kHz to 10/20/40MHz.\n\nFig. 1 shows a block diagram of the proposed zero-IF RF receiver, which consists of two parts: the RF front-end and the baseband circuit. The RF front-end is composed of a narrow-band low noise amplifier (LNA), a Gm (transconductor), a current-driven passive mixer, and transimpedance amplifiers (TIAs). The baseband circuit is composed of several variable gain amplifiers (VGAs), low-pass filters (LPFs), and DC-offset cancellation (DCOC) circuits. Here, a local oscillator (LO) signal for the passive mixer is externally provided from a signal generator.\n\n### Ⅱ. RF FRONT-END DESIGN\n\nAs shown in Fig. 2, the proposed LNA is a differential common-source amplifier with an inductive source degeneration to achieve a low noise characteristic and a high voltage gain versus power consumption. The LNA has an RLC resonant load centered at 2.6 GHz and provides a voltage gain of 29/35/41 dB by controlling the load resistors R1 and R2.\n\nIn Fig. 2, the current-driven passive mixer architecture , which is composed of the Gm, the quadrature passive mixer core, and the quadrature TIAs, is adopted to overcome a trade-off between signal-to-noise ratio (SNR) and linearity. The Gm has adopted a differential common-source topology and uses inductive loads (L3 and L4) to eliminate input parasitic capacitance of the passive mixer . This inductive load provides high impedance to the following TIA through the passive mixer’s on-resistor Ron so that 1/f noise from the TIAs can be mitigated.", null, "In the passive mixer, a trade-off between linearity and noise figure occurs directly, depending on the LO bias levels. In this work, the on-overlap LO biasing level has been chosen for the proposed passive mixer considering noise figure, conversion gain, and linearity.\n\nThe proposed TIA is a common-gate amplifier with low input impedance for the current-to-voltage conversion. It has the 1st-order RC load for filtering unwanted spurious noise from the mixing operation and LO leakage. In the TIA, long-channel NMOS devices (L = 5 μm) for M11-M18 have been used to suppress 1/f noise.\n\nIn order to ensure a wide dynamic range of the overall RF receiver, the gain of the RF front-end should be in the range of 41 to 23 dB with a step of 6 dB for the incoming input signal. The gain control from 41 to 29 dB has been achieved in the LNA load by adjusting the value of the resistors (R1 and R2). However, even though the LNA has a gain of 23 dB, the following Gm is saturated by the LNA output voltage swing. Thus, a minimum gain mode switch (M5 and M6) is added between the LNA and the Gm . As shown in Fig. 2, in order to achieve minimum voltage gain of 23 dB, the cascode transistors (M3 and M4) in the LNA and input transistors (M7 and M8) in the Gm turn off and the switches (M5 and M6) simultaneously turn on. Thus, the LNA’s input stage (M1 and M2) and the Gm’s cascode stage (M9 and M10) are operated as another new cascode amplifier. Using this method, the RF front-end can achieve the minimum gain of 23 dB without severe distortion for the high input signal of -18 dBm.\n\n### Ⅲ. BASE-BAND CIRCUIT DESIGN\n\nFig. 3 shows the proposed analog baseband circuit (only I-path), comprising a VGA1, a channel-selection LPF, a VGA chain (VGA2), and a DCOC circuit. A lower noise figure of the receiver is achieved by locating the LPF between VGA1 and VGA2. The gain of the VGA1 suppresses noise from the LPF. The proposed analog baseband circuit provides a voltage gain from -23 to 79 dB in a 0.25 dB gain step.", null, "", null, "In general, since active RC LPF shows higher linearity than Gm-C LPF, a 5th-order active RC Chebyshev LPF is adopted in this work [9-11]. The LPF provides a -1 dB cutoff frequency of 5MHz, 10MHz, and 40MHz with a frequency compensation circuit. The -1 dB cutoff bandwidth of the channel-selection LPF is given by 1/(RS۰C1-5) and can be changed by varying the capacitance of C1-5. An insertion loss of the LPF is given by K/2 where K is a proportionality constant, which is implemented in input resistance of the LPF. In this work, the K of 2 was chosen to make an insertion loss of 0 dB.\n\nFig. 4 shows the simulated frequency response of the proposed channel-selection LPF, where the cutoff frequencies of 5, 10, and 40MHz are not much changed for corner states of SS (-80℃), TT (27℃), and FF (40℃) mode. In Fig. 4, the peaking at 40MHz channel bandwidth comes from the deficient unit-gain bandwidth (UGBW) of 2.04 GHz in the proposed OP-amp. However, from the overall receiver measurements, the receiver does not show any oscillation problem or performances degradation.\n\nThe proposed VGAs (VGA1 and VGA2), which are composed of a fully differential OP-amp with a negative feedback resistor for high linearity, are designed to achieve -1 dB cutoff frequency of 50MHz for the maximum channel bandwidth of 40MHz .\n\nIn Fig. 3, the VGA1 provides a voltage gain from -12 to 12 dB with a 6 dB step. The VGA2 provides voltage gain from -11 to 67 dB with a 0.25 dB fine gain step to compensate I-Q gain mismatch. To provide the total gain of 67 dB, the VGA2 consists of 7 stages; the 1st, 3rd, and 5th amplifiers have a voltage gain from -12 to 12 dB with a 6 dB step respectively, the 2nd and 7th amplifiers provide a fixed voltage gain of 12 dB, the 4th amplifier provides a voltage gain from 1 to 6 dB with a 1 dB step, and the 6th amplifier provides a voltage gain from 0 to 1 dB with a 0.25 dB step.\n\nA DCOC in a zero-IF receiver is inevitable, since an unexpected DC-offset may saturate the baseband output. The DC-offset problem is solved by building a DCOC loop based on voltage-current negative-feedback, as shown in Fig. 3. The high-pass cutoff frequency of the DCOC circuits is set to less than 1 kHz to ensure active sub-carriers around DC. However, due to this cutoff frequency of 1 kHz, the required capacitances Cf are 2 μF, which cannot be integrated on a chip. Thus, they are externally implemented at the cost of extra pads. The constant cutoff frequency in the DCOC circuit has been achieved by digital control of the value of input resistor RD1 in the DCOC circuit as the variation of voltage gain in the feed-forward path. The post-layout simulation shows that the analog baseband output can be tolerated for up to 700 mV input DC-offset.\n\nFig. 5 shows the frequency response of the baseband circuit with a cutoff frequency of 10MHz. The baseband circuit provides a voltage gain from -23 to 79 dB, and the high pass cutoff frequency of less than 1 kHz. The simulated results of the proposed baseband circuit are summarized in Table 1.\n\nTo achieve the channel bandwidth of up to 40MHz, the LPF and VGAs need a wideband OP-amp. Fig. 6 shows the proposed wideband two-stage OP-amp, which uses a crossconnected PMOS load (M3 to M6) at the first stage . The cross-connected PMOS load provides a very wideband characteristic of the OP-amp by putting the second pole far away from the dominant pole. However, the cross-connected PMOS load generates nonlinear components such as evenorder harmonics. To eliminate this problematic effect, a diode-connected PMOS load (M9 and M10) is added at the second stage. The even-order harmonics from the first stage can be eliminated after combining with another even-order harmonic from the diode-connected PMOS load (M9 and M10) of the second stage. Additionally, for immunity of common-mode signals, a diode-connected NMOS load (M11 and M12) with a high value of the resistor, which has high common-mode rejection ratio, is used at the second stage. To secure an enough phase-margin of the OP-amp, an RC compensation circuit (RZ, CC) is adopted between the first and the second stage .", null, "", null, "", null, "", null, "Fig. 7 shows simulated results of the proposed wideband OP-amp. The proposed OP-amp provides a phase margin 77° and a UGBW of 2.04 GHz, which is about 50 times the maximum channel bandwidth (40MHz). An OP-amp consumes 3.47 mA from a 1.2 V supply.\n\n### Ⅳ. MEASUREMENT RESULTS\n\nThe proposed zero-IF CMOS RF receiver for LTE-Advanced systems has been implemented in 0.13-μm CMOS technology, as shown in Fig. 8. The receiver consumes 116 (high gain mode)/106 (low gain mode) mA from a 1.2 V supply.\n\nFigs. 9-11 show the measured results of the fabricated chip. A 10-MHz 3G LTE signal only is applied to the input of the chip for measurements, even though the receiver supports multi-channels of 5, 10, and 40MHz.\n\nFigs. 9 and 10 show the measured an input 1- dB gain compression point (P1dB) of the proposed RF receiver with the high and low gain modes, respectively. Due to the sufficient linearity for all the signal paths, the proposed RF receiver achieves P1dB of -92 dBm (high gain mode) and -18 dBm (low gain mode) for a fixed output power of 6 dBm for 50 Ω loading. At the high and the low gain mode, a simulated overall gain of the RF receiver is 103/29 dB but the measurements show the 99/25 dB because of unexpected parasitic capacitances in the RF paths.\n\nFig. 11 shows the measured SNR for the 10-MHz 3G LTE input signal with 16-QAM. The proposed RF receiver provides more than 8.3 dB of minimum SNR , while receiving the input channel power from -88 to -12 dBm.", null, "", null, "Table 2 summarizes the measured results and compares them with the state-of-the-art measurements [12,13]. The proposed RF receiver achieves the widest channel bandwidth, the highest gain, and the lowest noise figure.\n\n### Ⅴ. CONCLUSION\n\nThis paper has presented a zero-IF CMOS RF receiver for LTE-Advanced systems, which is implemented in 0.13-μm CMOS technology. The simulated and the measurement results demonstrate that the proposed RF receiver can favorably support the LTE-Advance systems.", null, "", null, "", null, "• [Fig. 1.] Simplified block diagram of the proposed RF receiver.", null, "• [Fig. 2.] Schematic of the proposed RF front-end receiver. LNA=low noise amplifier, Gm=transconductor, TIA=transimpedance amplifier.", null, "• [Fig. 3.] Block diagram of the proposed base-band circuit (I-path). VGA = variable gain amplifier, LPF = low-pass filter, DCOC = DC-offset cancellation circuit.", null, "• [Fig. 4.] Frequency response of the proposed low-pass filter.", null, "• [Fig. 5.] Frequency response of the proposed baseband circuits.", null, "• [Table 1.] Performance summary of the baseband circuit", null, "• [Fig. 6.] Schematic of the proposed operational amplifier.", null, "• [Fig. 7.] Phase and gain curve of the operational amplifier. UGBW = unit-gain bandwidth.", null, "• [Fig. 8.] Chip micrograph. LNA = low noise amplifier, Gm = transconductor, TIA = transimpedance amplifier, LPF = lowpass filter, DCOC = DC-offset cancellation circuit, VGA = variable gain amplifier.", null, "• [Fig. 9.] Measured P1dB at the high gain mode.", null, "• [Fig. 10.] Measured P1dB at the low gain mode.", null, "• [Fig. 11.] Measured SNR of the proposed RF receiver using a 10-MHz LTE signal. SNR = signal-to-noise ratio, LTE = long-term evolution.", null, "• [Table 2.] Performance comparison", null, "" ]	[ null, "http://oak.go.kr/central/images/2015/cc_img.png", null, "http://oak.go.kr//repository/journal/13110/E1ELAT_2014_v14n2_61_f0001.jpg", null, "http://oak.go.kr//repository/journal/13110/E1ELAT_2014_v14n2_61_f0002.jpg", null, "http://oak.go.kr//repository/journal/13110/E1ELAT_2014_v14n2_61_f0003.jpg", null, "http://oak.go.kr//repository/journal/13110/E1ELAT_2014_v14n2_61_f0004.jpg", null, "http://oak.go.kr//repository/journal/13110/E1ELAT_2014_v14n2_61_f0005.jpg", null, "http://oak.go.kr//repository/journal/13110/E1ELAT_2014_v14n2_61_t0001.jpg", null, "http://oak.go.kr//repository/journal/13110/E1ELAT_2014_v14n2_61_f0006.jpg", null, "http://oak.go.kr//repository/journal/13110/E1ELAT_2014_v14n2_61_f0007.jpg", null, "http://oak.go.kr//repository/journal/13110/E1ELAT_2014_v14n2_61_f0008.jpg", null, "http://oak.go.kr//repository/journal/13110/E1ELAT_2014_v14n2_61_f0009.jpg", null, "http://oak.go.kr//repository/journal/13110/E1ELAT_2014_v14n2_61_f0010.jpg", null, "http://oak.go.kr//repository/journal/13110/E1ELAT_2014_v14n2_61_f0011.jpg", null, "http://oak.go.kr//repository/journal/13110/E1ELAT_2014_v14n2_61_t0002.jpg", null, "http://oak.go.kr/repository/journal/13110/E1ELAT_2014_v14n2_61_f0001.jpg", null, "http://oak.go.kr/repository/journal/13110/E1ELAT_2014_v14n2_61_f0002.jpg", null, "http://oak.go.kr/repository/journal/13110/E1ELAT_2014_v14n2_61_f0003.jpg", null, "http://oak.go.kr/repository/journal/13110/E1ELAT_2014_v14n2_61_f0004.jpg", null, "http://oak.go.kr/repository/journal/13110/E1ELAT_2014_v14n2_61_f0005.jpg", null, "http://oak.go.kr/repository/journal/13110/E1ELAT_2014_v14n2_61_t0001.jpg", null, "http://oak.go.kr/repository/journal/13110/E1ELAT_2014_v14n2_61_f0006.jpg", null, "http://oak.go.kr/repository/journal/13110/E1ELAT_2014_v14n2_61_f0007.jpg", null, "http://oak.go.kr/repository/journal/13110/E1ELAT_2014_v14n2_61_f0008.jpg", null, "http://oak.go.kr/repository/journal/13110/E1ELAT_2014_v14n2_61_f0009.jpg", null, "http://oak.go.kr/repository/journal/13110/E1ELAT_2014_v14n2_61_f0010.jpg", null, "http://oak.go.kr/repository/journal/13110/E1ELAT_2014_v14n2_61_f0011.jpg", null, "http://oak.go.kr/repository/journal/13110/E1ELAT_2014_v14n2_61_t0002.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9067761,"math_prob":0.9101858,"size":14203,"snap":"2020-45-2020-50","text_gpt3_token_len":3654,"char_repetition_ratio":0.1447285,"word_repetition_ratio":0.11120401,"special_character_ratio":0.24769415,"punctuation_ratio":0.112469435,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96184486,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54],"im_url_duplicate_count":[null,null,null,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,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\":\"2020-10-20T05:35:11Z\",\"WARC-Record-ID\":\"<urn:uuid:c84df048-d7c8-4d33-b5c7-83a899571d7a>\",\"Content-Length\":\"236871\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:bde8ad67-f3de-4374-b7ac-ba3b7ef3a8fe>\",\"WARC-Concurrent-To\":\"<urn:uuid:14d20622-93db-46af-b6f4-0a5fde49a0d8>\",\"WARC-IP-Address\":\"124.137.58.153\",\"WARC-Target-URI\":\"http://oak.go.kr/central/journallist/journaldetail.do?article_seq=13110\",\"WARC-Payload-Digest\":\"sha1:P3BOMX54Q3QQ6IDYHIRIP2PDPESZPRRK\",\"WARC-Block-Digest\":\"sha1:URZ2BC2VMPZFGCYNYF35JQALPYUNMGKW\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-45/CC-MAIN-2020-45_segments_1603107869933.16_warc_CC-MAIN-20201020050920-20201020080920-00085.warc.gz\"}"}
https://svi.nl/BytesAndBits	[ "# Bits and bytes (Image sizes)\n\nbit (b)\nOne bit is the smallest unit of information. In a binary numerical system it is what you can represent with a one or a zero. (more).\n\nbyte (B)\nNowadays one byte is always 8 bits. Therefore, in a 16 bit image every PiXel intensity is represented by 2 bytes. (more).\n\nThe size of an image in bits (b) can be computed multiplying:\n\n• the total number of PiXels or VoXels in the image by\n• the number of bits per pixel by\n• the total number of channels\n\nThis number divided by 8 expresses the file size in bytes (B).\n\nIf you divide the size in bytes by 2^10> = 1024, you obtain the size in kilo-bytes (kB). If you divide it again by 1024 you obtain mega-bytes (MB).\n\n### Example\n\nA Two Channel, 16 bit, 3D image that is 512 × 512 × 100 large will need\n\n2 × 16 × 512 × 512 × 100 = 838860800 bits\n\nof storage size only for the intensity values, plus some extra space if metadata exists describing the image. This is at least\n\n838860800 bits / 8 = 104857600 bytes\n\nor\n\n104857600 / 1024 = 102400 kB\n\nor\n\n102400 / 1024 = 100 MB" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8171454,"math_prob":0.9895798,"size":1045,"snap":"2021-31-2021-39","text_gpt3_token_len":306,"char_repetition_ratio":0.12199808,"word_repetition_ratio":0.009569378,"special_character_ratio":0.35502392,"punctuation_ratio":0.07582939,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99894994,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-27T23:15:25Z\",\"WARC-Record-ID\":\"<urn:uuid:fdc7179f-4837-4541-a40c-5f534cff2581>\",\"Content-Length\":\"85938\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1c4994bf-b653-4b66-954a-829b3b36afe4>\",\"WARC-Concurrent-To\":\"<urn:uuid:13ebdf62-ae80-455b-aba6-24da8351a271>\",\"WARC-IP-Address\":\"185.27.175.64\",\"WARC-Target-URI\":\"https://svi.nl/BytesAndBits\",\"WARC-Payload-Digest\":\"sha1:KRFBDAEAPU77POW6ITQF4D6I2PNCRHA3\",\"WARC-Block-Digest\":\"sha1:NQR3C63PL7WSXFJXM23UDD2HC4YQJDVR\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780058552.54_warc_CC-MAIN-20210927211955-20210928001955-00667.warc.gz\"}"}
https://openhome.cc/Gossip/Scala/ShadowOverride.html	[ "``val x = 10{ val x = 20 println(x) // 顯示 20}println(x) // 顯示 10``\n\nScala支援區塊可視範圍，在上例中，{}區塊外宣告了一個x變數，而區塊內也宣告了一個x變數，在區塊中x的變數定義遮蔽了區塊外的x定義。\n\nclass A {\nprotected int x = 10;\n}\n\nclass B extends A {\npublic int x = 20; // 這邊 x 遮蔽了 A 類別中的 x\n}\n\npublic class Main {\npublic static void main(String[] args) {\nB b = new B();\nA a = b;\nSystem.out.println(b.x); // 顯示 20\nSystem.out.println(a.x); // 顯示 10\n}\n}\n\nclass Parent {\nprotected val x = 10\n}\n\nclass Child extends Parent {\nval x = 20\n}\n\nerror: error overriding value x in class Parent of type Int; value x needs `override' modifier\nval x = 20\n^\n\n``class Parent { protected val x = 10}class Child extends Parent { override val x = 20}val c = new Childprintln(c.x) // 顯示為 20``\n\n``class Parent { private val x = 10}class Child extends Parent { val x = 20 // 因為 Parent 的 x 在這邊不可視，所以不用 override}val c = new Childprintln(c.x)``\n\nclass Parent {\nval x = 10\n}\n\nclass Child extends Parent {\noverride protected val x = 20 // error, value x has weaker access privileges\n}\n\n``class Parent { val x = 10}class Child extends Parent { private[this] val x = 20 def getX = x}val c = new Childprintln(c.x) // 顯示 10println(c.getX) // 顯示 20``\n\nclass Parent {\nvar x = 10\n}\n\nclass Child extends Parent {\noverride val x = 10 // error, value x cannot override a mutable variable\n}" ]	[ null ]	{"ft_lang_label":"__label__zh","ft_lang_prob":0.6639021,"math_prob":0.9913098,"size":2558,"snap":"2022-40-2023-06","text_gpt3_token_len":1497,"char_repetition_ratio":0.19929522,"word_repetition_ratio":0.6492537,"special_character_ratio":0.2928069,"punctuation_ratio":0.08018868,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9696088,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-01-30T07:54:46Z\",\"WARC-Record-ID\":\"<urn:uuid:e81086a8-9b52-4320-b0c4-afdc8e232ba0>\",\"Content-Length\":\"12182\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:46f8afde-5ff3-4967-aeee-fd7608f3a97f>\",\"WARC-Concurrent-To\":\"<urn:uuid:b79c6cfc-a31f-4ccc-bc8e-c46961d5c12d>\",\"WARC-IP-Address\":\"203.98.64.6\",\"WARC-Target-URI\":\"https://openhome.cc/Gossip/Scala/ShadowOverride.html\",\"WARC-Payload-Digest\":\"sha1:Q66UVRY3GMSXRO5MS72CU3YE3VH3HCPK\",\"WARC-Block-Digest\":\"sha1:WBB4XLQODU2KWIB35JRNLXYLPNDHWJFT\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-06/CC-MAIN-2023-06_segments_1674764499804.60_warc_CC-MAIN-20230130070411-20230130100411-00270.warc.gz\"}"}
https://www.carvadia.com/how-do-you-identify-influential-observations/	[ "• September 27, 2022\n\n### How Do You Identify Influential Observations?\n\n•", null, "How do you identify influential observations? If the predictions are the same with or without the observation in question, then the observation has no influence on the regression model. If the predictions differ greatly when the observation is not included in the analysis, then the observation is influential.\n\n## What is the difference between an outlier and an influential observation?\n\nAn outlier is a data point that diverges from an overall pattern in a sample. An influential point is any point that has a large effect on the slope of a regression line fitting the data. They are generally extreme values.\n\n## Are there any outliers or influential observations?\n\nAll outliers are influential data points. The correct answer is (E). Data sets with influential points can be linear or nonlinear. For example, when the data set is very large, a single outlier may not have a big effect on the regression equation.\n\n## How do you identify influential data points?\n\nAn influential data point has two key properties: It has properties that are not representative of the other data points. It doesn't follow the general trend, and it's dependent variable value is unexpected given values you would get from predictor variables.\n\n## Why outliers are sometimes called influential observations?\n\nSometimes outliers can be called influential observations since they can significantly tilt a regression line towards them. When an outlier is included in a regression of Y versus a single X, the slope of the line is greatly tilted towards the outlier. This change in slope normally leads to a shift in the y-intercept.\n\n## Related faq for How Do You Identify Influential Observations?\n\n### Which of the following measures are used for identifying influential observations in the data?\n\nIn this section, we learn the following two measures for identifying influential data points: Difference in fits (DFFITS) Cook's distance.\n\n### What makes a point influential?\n\nAn influential point is an outlier that greatly affects the slope of the regression line. The slope is larger when the outlier is present, so this outlier would be considered an influential point.\n\n### What are influential points in acupuncture?\n\nThe Influential Points are eight important points where qi of the respective body tissues is infused into the body surface, namely zang, fu, qi, blood, tendons, vessels, bones and marrow. \"Hui\" means influential in particular.\n\n### How do you find influential points in R?\n\nThere are two common measures for identifying influential data points: difference in fits (DFFITS), and Cook's distance.\n\n### What is an influential case in statistics?\n\nAn influential case is any case that significantly alters the value of a regression coefficient whenever it is deleted from an analysis. If the deletion of particular cases in an analysis alters the parameters of the regression equation significantly, then these cases represent influential cases.\n\n### When one has influential points in their data How should regression and correlation be done?\n\nWhen one has influential points in their data, how should regression and correlation be done? When one has influential points in their data, they should do the regression and correlation with and without these points and comment on the differences.\n\n### What are influence statistics?\n\nInfluence statistics measure the effects of individual data points or groups of data points on a statistical analysis. The effect of individual data points on an analysis can be profound, and so the detection of unusual or aberrant data points is an important part of nearly every analysis.\n\n### What is influential data?\n\nInfluential data points are observations that exert an unusually large effect on the results of regression analysis. Influential data might be classified as outliers, as leverage points, or as both. An outlier is an anomalous response value, whereas a leverage point has atypical values of one or more of the predictors.\n\n### What is an influential observation in a linear regression setting?\n\nIn statistics, an influential observation is an observation for a statistical calculation whose deletion from the dataset would noticeably change the result of the calculation. In particular, in regression analysis an influential observation is one whose deletion has a large effect on the parameter estimates.\n\n### What is an influential point quizlet?\n\nAn influential point is a point that changes the regression by a large amount. The coefficient of determination, or r2, is a measure of how well the regression line summarizes the data.\n\n### How do outliers affect correlation?\n\nInfluence Outliers\n\nIn most practical circumstances an outlier decreases the value of a correlation coefficient and weakens the regression relationship, but it's also possible that in some circumstances an outlier may increase a correlation value and improve regression.\n\n### How do you identify outliers?\n\nDetermining Outliers\n\nMultiplying the interquartile range (IQR) by 1.5 will give us a way to determine whether a certain value is an outlier. If we subtract 1.5 x IQR from the first quartile, any data values that are less than this number are considered outliers.\n\n### How Dffits are used to detect influential observations?\n\nDFFITS Plot\n\nDFFIT - difference in fits, is used to identify influential data points. It quantifies the number of standard deviations that the fitted value changes when the ith data point is omitted. Steps to compute DFFITs: delete observations one at a time.\n\n### How do you read an influence plot?\n\nAn influence plot shows the outlyingness, leverage, and influence of each case. The plot shows the residual on the vertical axis, leverage on the horizontal axis, and the point size is the square root of Cook's D statistic, a measure of the influence of the point.\n\n### What does a high CovRatio mean?\n\nDelete-1 change in covariance ( CovRatio ) identifies the observations that are influential in the regression fit. Values of CovRatio larger than 1 + 3p/n or smaller than 1 – 3p/n indicate influential points, where p is the number of regression coefficients, and n is the number of observations.\n\n### Do residual plots identify influential points?\n\nYou can't see influence in the usual residual plot.\n\n### Does an influential point affect correlation?\n\nOutliers and high-leverage points can be influential to different measurements in least-squares regression like the slope, y-intercept, and correlation coefficient (r).\n\n### How do you read Dffits?\n\nThe DFFITS statistic is a scaled measure of the change in the predicted value for the ith observation and is calculated by deleting the ith observation. A large value indicates that the observation is very influential in its neighborhood of the X space. , where n and p are as defined previously.\n\n### What does joy do to Qi?\n\nJoy relaxes and slows the movement of Qi. Symptoms from a Heart or Joy imbalance can result in: Palpitations. Restlessness.\n\n### What are Luo connecting points?\n\nThe Luo (connecting) points are locations at which the qi of the twelve regular meridians converges. All of the fifteen collaterals are the passages through which qi and blood are transported into the zangfu organs and tissues of the body.\n\n### What are front mu points?\n\nFront-Mu points are located at the chest and abdomen where the Qi of Zang-Fu organs is infused. These points are named according to corresponding zang-fu organs. When a Zang-Fu organ is diseased , there is an abnormal sensation (tenderness or a sensitive spot) in the corresponding Back-Shu points.\n\n### What is influence plot in R?\n\nInfluence Index Plots for Multivariate Linear Models. Description. Provides index plots of some diagnostic measures for a multivariate linear model: Cook's distance, a generalized (squared) studentized residual, hat-values (leverages), and Mahalanobis squared dis- tances of the residuals. Usage.\n\n### Are high leverage points always influential?\n\nNot all leverage points are influential, unless they have large residuals. Observations with large values of hii and large residuals are likely to be influential.\n\n### What does Studentized residuals measure?\n\nIn statistics, a studentized residual is the quotient resulting from the division of a residual by an estimate of its standard deviation. It is a form of a Student's t-statistic, with the estimate of error varying between points. This is an important technique in the detection of outliers.\n\n### What is Homoscedasticity in statistics?\n\nHomoskedastic (also spelled \"homoscedastic\") refers to a condition in which the variance of the residual, or error term, in a regression model is constant. That is, the error term does not vary much as the value of the predictor variable changes.\n\n### What are observations in regression?\n\nRegression analysis is the method of using observations (data records) to quantify the relationship between a target variable (a field in the record set), also referred to as a dependent variable, and a set of independent variables, also referred to as a covariate." ]	[ null, "https://secure.gravatar.com/avatar/5767204be390fb840d83adb63addaff2", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.90334445,"math_prob":0.9567982,"size":8973,"snap":"2022-40-2023-06","text_gpt3_token_len":1753,"char_repetition_ratio":0.19645445,"word_repetition_ratio":0.027464788,"special_character_ratio":0.18444222,"punctuation_ratio":0.1020025,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9921669,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-09-27T01:21:13Z\",\"WARC-Record-ID\":\"<urn:uuid:354b7e11-d020-460f-ac17-30997c02e408>\",\"Content-Length\":\"50455\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:555d9fd3-537e-4041-b63b-91c37a3e16e1>\",\"WARC-Concurrent-To\":\"<urn:uuid:e005da38-5837-4d94-aee3-09d8e3f5ada7>\",\"WARC-IP-Address\":\"172.67.153.75\",\"WARC-Target-URI\":\"https://www.carvadia.com/how-do-you-identify-influential-observations/\",\"WARC-Payload-Digest\":\"sha1:DQPXMPUBTTLIQ5ZMERMEYWTA7F7PBUW7\",\"WARC-Block-Digest\":\"sha1:KORKYTFGR5RIEAQAMXPWAK45GQT2OGAA\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030334974.57_warc_CC-MAIN-20220927002241-20220927032241-00744.warc.gz\"}"}
https://users.rust-lang.org/t/error-t-might-need-a-bound-for-std-partialeq-in-singly-linked-list/41867	[ "# Error `T` might need a bound for `std::cmp::PartialEq` in singly linked list\n\nWhile doing the Rust track in Exercism, I came accross the singly linked list exercise. Once my compilation passed the tests, I continued to work on the code to add some more functionality and train myself.\nThe error I get while compiling is error[E0369]: binary operation `==` cannot be applied to type `T`\n\nThe code is something like this:\n\n``````#[derive(Default)]\nstruct Node<T>{\ndata: T,\nnext: Option<Box<Node<T>>>,\n}\n\nimpl<T: PartialEq> PartialEq for Node<T> {\nfn eq(&self, other: &Self) -> bool {\nself.data == other.data\n}\n}\n\n#[derive(Default)]\nlength: usize,\n}\n``````\n\nSome implementation and then the problem\n\n``````pub fn find(&self, value: T) -> bool {\n\nwhile let Some(node) = head {\nmatch node.next {\nNone => return false,\nSome(a) => {if a.data == value { return true }},\n}\n}\nfalse\n}\n``````\n\nThe error happens when comparing a.data with value.\nI thought that the PartialEq implementation for Node should take care of that.\nIf possible, I would like some assistance in that matter.\n\nThanks\n\nCould you share the full code which reproduces an error? I wasn't able to get it in your current variant - playground.\n\n``````use std::iter::FromIterator;\n\n#[derive(Default)]\nstruct Node<T>{\ndata: T,\nnext: Option<Box<Node<T>>>,\n}\n\nimpl<T: PartialEq> PartialEq for Node<T> {\nfn eq(&self, other: &Self) -> bool {\nself.data == other.data\n}\n}\n\n#[derive(Default)]\nlength: usize,\n}\n\npub fn new() -> Self {\nlength: 0\n}\n}\n\npub fn len(&self) -> usize {\nself.length\n}\n\npub fn push(&mut self, _element: T) {\nlet node = Box::new(Node {\ndata: _element,\n});\nself.length += 1;\n}\n\npub fn pop(&mut self) -> Option<T> {\nNone => None,\nSome(node) => {\nself.length -= 1;\nSome(node.data)\n}\n}\n}\n\npub fn peek(&self) -> Option<&T> {\nNone => None,\nSome(node) => Some(&node.data),\n}\n}\n\npub fn find(&self, value: T) -> bool {\nself.head.iter().find(\| node \| node.data == value).is_some()\n}\n\npub fn rev(mut self) -> SimpleLinkedList<T> {\nlet mut previous = None;\n\nwhile let Some(mut node) = current_node {\nlet next = node.next;\nnode.next = previous;\nprevious = Some(node);\ncurrent_node = next;\n}\nself\n}\n\npub fn is_empty(&self) -> bool {\nself.len() == 0\n}\n}\n\nfn from_iter<I: IntoIterator<Item = T>>(_iter: I) -> Self {\nfor i in _iter {\nc.push(i);\n}\nc\n}\n}\n\n// In general, it would be preferable to implement IntoIterator for SimpleLinkedList<T>\n// instead of implementing an explicit conversion to a vector. This is because, together,\n// FromIterator and IntoIterator enable conversion between arbitrary collections.\n// Given that implementation, converting to a vector is trivial:\n//\n// let vec: Vec<_> = simple_linked_list.into_iter().collect();\n//\n// The reason this exercise's API includes an explicit conversion to Vec<T> instead\n// of IntoIterator is that implementing that interface is fairly complicated, and\n// demands more of the student than we expect at this point in the track.\n\nfn into(mut self) -> Vec<T> {\nlet mut vec = vec![];\n\nwhile let Some(element) = self.pop() {\nvec.push(element);\n}\nvec.reverse();\nvec\n}\n}``````\n\nSorry, wrong version. This is the version that uses the iterator\n\nJust use the find method from the code I sent before. The rest is identical\n\n``````error[E0599]: no method named `borrow` found for enum `std::option::Option<std::boxed::Box<Node<T>>>` in the current scope\n--> src/lib.rs:30:34\n\|\n\|\n= help: items from traits can only be used if the trait is in scope\nhelp: the following trait is implemented but not in scope; perhaps add a `use` for it:\n\|\n1 \| use std::borrow::Borrow;\n\|\n``````\n\nAre you sure that the structure is correct?\n\n``````use std::borrow::Borrow;\n``````\n\nat the top of your module, and changing\n\n``````match node.next {\n``````\n\nwith\n\n``````match &node.next {\n``````\n\nSince you can't move out of node since it's under a reference.\n\nThanks, but those are only there due to the change in the find function from the two versions I sent. That's my fault.\nBut still, the error I mentioned in the post about comparing T values is still there.\nPlayground\n\nOh, add a bound to `T` on the `find` method:\n\n``````pub fn find(&self, value: T) -> bool\nwhere T: PartialEq<T> { /* / }\n``````\n\nOr, make another impl block:\n\n``````impl<T: PartialEq<T>> SimpleLinkedList<T> {\npub fn find(&self, value: T) -> bool {\n/ */\n}\n}\n``````\n2 Likes\n\nHere you didn't specify that you're only implementing these methods if `T: PartialEq`, so you can't rely on that in the body of `find()`.\n\nThank you very much.\n\nThis topic was automatically closed 90 days after the last reply. New replies are no longer allowed." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6561428,"math_prob":0.81333673,"size":5090,"snap":"2022-27-2022-33","text_gpt3_token_len":1323,"char_repetition_ratio":0.113055445,"word_repetition_ratio":0.103406325,"special_character_ratio":0.30117878,"punctuation_ratio":0.19864342,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9868075,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-07-07T04:11:08Z\",\"WARC-Record-ID\":\"<urn:uuid:cd50047a-9a32-4b35-bb55-6dbffde6862e>\",\"Content-Length\":\"46578\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:eb01b692-24c6-450b-9bd3-c9329c86327e>\",\"WARC-Concurrent-To\":\"<urn:uuid:4bcd4fc5-a8ab-4d00-a76c-e648131c9963>\",\"WARC-IP-Address\":\"64.71.144.205\",\"WARC-Target-URI\":\"https://users.rust-lang.org/t/error-t-might-need-a-bound-for-std-partialeq-in-singly-linked-list/41867\",\"WARC-Payload-Digest\":\"sha1:QCN2CDOOS566XHOGYSWRLHDSJD7HDRS4\",\"WARC-Block-Digest\":\"sha1:YM6KFJWUZDN4YLQ2HMPC4ASP6ESP2YPF\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656104683683.99_warc_CC-MAIN-20220707033101-20220707063101-00509.warc.gz\"}"}
https://dsp.stackexchange.com/questions/22945/root-locus-for-a-system	[ "# Root Locus for a system\n\nI know this subject tends more to control theory but I am certain its part of the global knowledge basis for engineers, thus I believe I can find the answer here. I'm trying to draw Root Locus for $K<0$, but can't understand how the system behaves.\n\nI have this open loop system:\n\n$$\\frac{20(1+s)^2}{(1+\\frac{s}{10})(1+\\frac{s}{2})}$$\n\nI know it has no asymptotes, but yet by one of the drawing rules for $k<0$, it tends to $\\pm \\infty$ in the real axis. How is it possible?\n\n• Is $s10$ a typo, or is that \"s times 10\"? Apr 23 '15 at 15:56\n• it is an s/10 sir. Apr 23 '15 at 15:58\n• @minimalrisk do you know how to get the closed loop transfer function and how to get its poles? Apr 23 '15 at 17:07\n• yes, its $$1+K(s)*G(s)$$ and the poles are -2, -10, and the two zeroes are in -1 Apr 23 '15 at 17:17\n\nI will denote the given system as,\n\n$$G(s) = \\frac{20(1+s)^2}{(1+\\frac{s}{2})(1+\\frac{s}{10})}$$\n\nThe input or reference signal to the closed loop will be denoted by $R(s)$ and the output by $Y(s)$. The controller will initially be denoted by $H(s)$, while in this case it is equal to $K$. The block diagram of the closed loop system can then be drawn as,", null, "With its transfer function from input to output equal to,\n\n$$\\frac{Y(s)}{R(s)} = \\frac{G(s)}{1 + H(s) G(s)}.$$\n\nFor root locus analysis you want to find the poles of this transfer function as function of $H(s)$. The poles can be found by solving when the denominator is equal to zero. However the denominator (and numerator) are polynomials of $s$, so can't be fractions themselves. In order to ensure this I will slit $G(s)$ up in to two parts, its numerator, $G_n(s)$, and denominator, $G_d(s)$. The same can be done for $H(s)$. The resulting transfer function can then be written as,\n\n$$\\frac{Y(s)}{R(s)} = \\frac{\\frac{G_n(s)}{G_d(s)}}{1 + \\frac{H_n(s)}{H_d(s)} \\frac{G_n(s)}{G_d(s)}} = \\frac{H_d(s) G_n(s)}{H_d(s) G_d(s) + H_n(s) G_n(s)}.$$\n\nAs stated before, in this case $H(s)$ is equal to $K$, thus $H_d(s)$ is equal to one. By substituting in $K$ for $H_n(s)$ and the two polynomials, from this first equation, for $G_n(s)$ and $G_d(s)$, then the following expression can be obtained,\n\n$$\\frac{Y(s)}{R(s)} = \\frac{20(1+s)^2}{(1+\\frac{s}{2})(1+\\frac{s}{10}) + 20K(1+s)^2}.$$\n\nThe resulting denominator is a second order polynomial, so solving for the poles yields two solutions, which can be simplified to,\n\n$$p=-\\frac{400 K \\pm 4 \\sqrt{1 - 225 K} + 6}{400 K + 1}.$$\n\nFor $K=-\\frac{1}{400}$ the limits of both $p$ are $\\pm\\infty$ depending if you approach that value from the left or the right. Thus near $K=-\\frac{1}{400}$ there will be values for the poles of the closed loop transfer function which will have a positive real values.\n\n• Nice answer; welcome to the site. Apr 24 '15 at 0:34\n• Thanks, but I think it missed my question. Lets have a look at the denominator We got 2 poles,2 zeros, thus we conclude that each pole has its zero buddy that it tends to as K goes to negative infinity. We have no asymptotes, so no pole is going to infinity. Here comes the But, for the negative K, root locus diagram, by rule number 5, the portion of the real axis of the right of the -1 zeroes and the portion of the real axis of the left of the -10 poles belongs to the $$RL$$, plus we have no breach/escape points beyond these points, so a loop is out of consideration. Apr 24 '15 at 6:05\n• @minimalrisk Could you maybe elaborate what you mean by rule number 5, because not all literature uses the same (order of) rules for drawing root locus. And these rules are mainly useful to estimate it for higher order systems. For a second order system you can calculate it analytically. Apr 24 '15 at 9:41\n• Rule number 5 states that the portion of the real axis is part of the RL if and only if the number of open loop poles and zeroes to its right is an even number. Apr 24 '15 at 10:38\n• @minimalrisk I added an expression for the poles of the closed loop system, from which it will become obvious why it tends $\\pm\\infty$. For simple second order systems like this it can be worth it to finding the analytical solution for the poles. Apr 24 '15 at 11:55" ]	[ null, "https://i.stack.imgur.com/wYXPH.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.83974725,"math_prob":0.9995315,"size":1898,"snap":"2021-43-2021-49","text_gpt3_token_len":602,"char_repetition_ratio":0.12143611,"word_repetition_ratio":0.0,"special_character_ratio":0.35458377,"punctuation_ratio":0.08108108,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9998957,"pos_list":[0,1,2],"im_url_duplicate_count":[null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-12-05T21:19:43Z\",\"WARC-Record-ID\":\"<urn:uuid:bc93f6f1-f606-4d5e-b850-c112c54031cf>\",\"Content-Length\":\"148574\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:cd171724-15f9-4e3e-b386-2448a3a97c2a>\",\"WARC-Concurrent-To\":\"<urn:uuid:2bdb2be0-dacb-46a2-b023-5408dca8d62d>\",\"WARC-IP-Address\":\"151.101.129.69\",\"WARC-Target-URI\":\"https://dsp.stackexchange.com/questions/22945/root-locus-for-a-system\",\"WARC-Payload-Digest\":\"sha1:OEVDLQBQKHNQFICOZCAAZDLOL6WEPYKD\",\"WARC-Block-Digest\":\"sha1:KPGU3P3KWUZ7G2KLB24VKGF5TAYOFTNZ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964363216.90_warc_CC-MAIN-20211205191620-20211205221620-00212.warc.gz\"}"}
https://explain.depesz.com/s/qQGl	[ "# Result: qQGl\n\nSettings\n# exclusive inclusive rows x rows loops node\n1. 0.000 0.000 ↓ 0.0\n\n(cost=8,087.04..8,087.04 rows=2 width=592) (actual rows= loops=)\n\n• Sort Key: o_e.partner_reporting_date\n2. 0.000 0.000 ↓ 0.0\n\n(cost=8,070.75..8,087.03 rows=2 width=592) (actual rows= loops=)\n\n3. 0.000 0.000 ↓ 0.0\n\n(cost=8,070.60..8,070.64 rows=2 width=476) (actual rows= loops=)\n\n4.\n\nCTE reasons_cte\n\n5. 0.000 0.000 ↓ 0.0\n\n(cost=2,505.29..2,505.31 rows=1 width=35) (actual rows= loops=)\n\n6. 0.000 0.000 ↓ 0.0\n\n(cost=2,505.29..2,505.30 rows=1 width=35) (actual rows= loops=)\n\n• Sort Key: obligation_reasons.id, obligation_reasons.kind, obligation_reasons.external_id\n7. 0.000 0.000 ↓ 0.0\n\n(cost=9.17..2,505.28 rows=1 width=35) (actual rows= loops=)\n\n8. 0.000 0.000 ↓ 0.0\n\n(cost=8.88..2,504.89 rows=1 width=4) (actual rows= loops=)\n\n9. 0.000 0.000 ↓ 0.0\n\n(cost=8.60..2,504.56 rows=1 width=4) (actual rows= loops=)\n\n10. 0.000 0.000 ↓ 0.0\n\n(cost=8.31..2,498.67 rows=19 width=8) (actual rows= loops=)\n\n• Hash Cond: (obligations_2.from_party_id = from_parties_2.id)\n11. 0.000 0.000 ↓ 0.0\n\nSeq Scan on obligations obligations_2 (cost=0.00..2,216.49 rows=104,249 width=12) (actual rows= loops=)\n\n12. 0.000 0.000 ↓ 0.0\n\n(cost=8.30..8.30 rows=1 width=4) (actual rows= loops=)\n\n13. 0.000 0.000 ↓ 0.0\n\nIndex Scan using parties_idx_uniq on parties from_parties_2 (cost=0.28..8.30 rows=1 width=4) (actual rows= loops=)\n\n• Index Cond: ((external_id = '5bec27212440da00050000df'::bpchar) AND ((kind)::text = 'partner'::text))\n14. 0.000 0.000 ↓ 0.0\n\nIndex Scan using parties_pkey on parties to_parties_2 (cost=0.28..0.31 rows=1 width=4) (actual rows= loops=)\n\n• Index Cond: (id = obligations_2.to_party_id)\n• Filter: (((kind)::text = 'driver'::text) AND (external_id = '5bebe344b344be0010aa42db'::bpchar))\n15. 0.000 0.000 ↓ 0.0\n\nIndex Scan using obligation_events_pkey on obligation_events o_e_2 (cost=0.29..0.33 rows=1 width=8) (actual rows= loops=)\n\n• Index Cond: (id = obligations_2.event_id)\n• Filter: ((partner_reporting_date >= '2017-01-01 00:00:00'::timestamp without time zone) AND (partner_reporting_date < '2020-01-01 00:00:00'::timestamp without time zone) AND ((event_kind)::text = 'create'::text))\n16. 0.000 0.000 ↓ 0.0\n\nIndex Scan using obligation_reasons_pkey on obligation_reasons (cost=0.28..0.40 rows=1 width=35) (actual rows= loops=)\n\n• Index Cond: (id = o_e_2.reason_id)\n17. 0.000 0.000 ↓ 0.0\n\n(cost=5,565.29..5,565.30 rows=2 width=476) (actual rows= loops=)\n\n• Sort Key: from_parties.external_id, to_parties.external_id, o_e.event_kind, reasons_cte.cte_reason_external_id, reasons_cte.cte_reason_kind, obligations.kind_id, o_e.partner_reporting_date, obligations.amount\n18. 0.000 0.000 ↓ 0.0\n\n(cost=285.18..5,565.28 rows=2 width=476) (actual rows= loops=)\n\n19. 0.000 0.000 ↓ 0.0\n\n(cost=285.18..2,782.63 rows=1 width=299) (actual rows= loops=)\n\n• Hash Cond: (o_e.reason_id = reasons_cte.cte_id)\n20. 0.000 0.000 ↓ 0.0\n\n(cost=285.15..2,782.53 rows=15 width=81) (actual rows= loops=)\n\n21. 0.000 0.000 ↓ 0.0\n\n(cost=284.86..2,777.71 rows=15 width=66) (actual rows= loops=)\n\n• Hash Cond: (obligations.to_party_id = to_parties.id)\n22. 0.000 0.000 ↓ 0.0\n\n(cost=142.20..2,632.55 rows=950 width=44) (actual rows= loops=)\n\n• Hash Cond: (obligations.from_party_id = from_parties.id)\n23. 0.000 0.000 ↓ 0.0\n\nSeq Scan on obligations (cost=0.00..2,216.49 rows=104,249 width=22) (actual rows= loops=)\n\n24. 0.000 0.000 ↓ 0.0\n\n(cost=141.57..141.57 rows=50 width=30) (actual rows= loops=)\n\n25. 0.000 0.000 ↓ 0.0\n\nSeq Scan on parties from_parties (cost=0.00..141.57 rows=50 width=30) (actual rows= loops=)\n\n• Filter: ((kind)::text = 'partner'::text)\n26. 0.000 0.000 ↓ 0.0\n\n(cost=141.57..141.57 rows=87 width=30) (actual rows= loops=)\n\n27. 0.000 0.000 ↓ 0.0\n\nSeq Scan on parties to_parties (cost=0.00..141.57 rows=87 width=30) (actual rows= loops=)\n\n• Filter: ((kind)::text = 'driver'::text)\n28. 0.000 0.000 ↓ 0.0\n\nIndex Scan using obligation_events_pkey on obligation_events o_e (cost=0.29..0.32 rows=1 width=23) (actual rows= loops=)\n\n• Index Cond: (id = obligations.event_id)\n29. 0.000 0.000 ↓ 0.0\n\n(cost=0.02..0.02 rows=1 width=226) (actual rows= loops=)\n\n30. 0.000 0.000 ↓ 0.0\n\nCTE Scan on reasons_cte (cost=0.00..0.02 rows=1 width=226) (actual rows= loops=)\n\n31. 0.000 0.000 ↓ 0.0\n\n(cost=285.18..2,782.63 rows=1 width=299) (actual rows= loops=)\n\n• Hash Cond: (o_e_1.reason_id = reasons_cte_1.cte_id)\n32. 0.000 0.000 ↓ 0.0\n\n(cost=285.15..2,782.53 rows=15 width=81) (actual rows= loops=)\n\n33. 0.000 0.000 ↓ 0.0\n\n(cost=284.86..2,777.71 rows=15 width=66) (actual rows= loops=)\n\n• Hash Cond: (obligations_1.from_party_id = from_parties_1.id)\n34. 0.000 0.000 ↓ 0.0\n\n(cost=142.20..2,632.55 rows=950 width=44) (actual rows= loops=)\n\n• Hash Cond: (obligations_1.to_party_id = to_parties_1.id)\n35. 0.000 0.000 ↓ 0.0\n\nSeq Scan on obligations obligations_1 (cost=0.00..2,216.49 rows=104,249 width=22) (actual rows= loops=)\n\n36. 0.000 0.000 ↓ 0.0\n\n(cost=141.57..141.57 rows=50 width=30) (actual rows= loops=)\n\n37. 0.000 0.000 ↓ 0.0\n\nSeq Scan on parties to_parties_1 (cost=0.00..141.57 rows=50 width=30) (actual rows= loops=)\n\n• Filter: ((kind)::text = 'partner'::text)\n38. 0.000 0.000 ↓ 0.0\n\n(cost=141.57..141.57 rows=87 width=30) (actual rows= loops=)\n\n39. 0.000 0.000 ↓ 0.0\n\nSeq Scan on parties from_parties_1 (cost=0.00..141.57 rows=87 width=30) (actual rows= loops=)\n\n• Filter: ((kind)::text = 'driver'::text)\n40. 0.000 0.000 ↓ 0.0\n\nIndex Scan using obligation_events_pkey on obligation_events o_e_1 (cost=0.29..0.32 rows=1 width=23) (actual rows= loops=)\n\n• Index Cond: (id = obligations_1.event_id)\n41. 0.000 0.000 ↓ 0.0\n\n(cost=0.02..0.02 rows=1 width=226) (actual rows= loops=)\n\n42. 0.000 0.000 ↓ 0.0\n\nCTE Scan on reasons_cte reasons_cte_1 (cost=0.00..0.02 rows=1 width=226) (actual rows= loops=)\n\n43. 0.000 0.000 ↓ 0.0\n\nIndex Scan using obligation_kinds_pkey on obligation_kinds o_k (cost=0.15..8.17 rows=1 width=120) (actual rows= loops=)\n\n• Index Cond: (id = obligations.kind_id)" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.5063066,"math_prob":0.9966579,"size":4817,"snap":"2019-51-2020-05","text_gpt3_token_len":2136,"char_repetition_ratio":0.3230833,"word_repetition_ratio":0.44444445,"special_character_ratio":0.5864646,"punctuation_ratio":0.27524307,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9867651,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-01-27T15:54:40Z\",\"WARC-Record-ID\":\"<urn:uuid:60da3f71-3057-468d-ae77-66d02e403ee8>\",\"Content-Length\":\"82410\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1345c639-63ab-4f15-a0db-08d01d03c29a>\",\"WARC-Concurrent-To\":\"<urn:uuid:b4397edf-6546-4351-a3cb-31d5a464672f>\",\"WARC-IP-Address\":\"88.198.49.178\",\"WARC-Target-URI\":\"https://explain.depesz.com/s/qQGl\",\"WARC-Payload-Digest\":\"sha1:ON5TU543GKGYNCINMY4R75LKNYZIHNSE\",\"WARC-Block-Digest\":\"sha1:2NRSQTH5OV53D3HA2C3QBZLE5HOMRHR6\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-05/CC-MAIN-2020-05_segments_1579251700988.64_warc_CC-MAIN-20200127143516-20200127173516-00217.warc.gz\"}"}
https://bravelearn.com/tag/probability/	[ "# Tag: probability\n\n## Problems for Cumulative Distribution Function\n\nEarlier we discussed the introduction of a continuous random variable and cumulative distribution...\n\n## Continuous Random Variables and Cumulative Distribution Function\n\nThe problem with Discrete random variables was they can’t be used for continuous data. In...\n\n## Practice Problems (Introduction to Probability Theory)\n\nA few practice problems related to Probability theory are given here. These problems are adapted...\n\n## Random Variables\n\nA random variable is a real valued function of the elements of sample space S which maps each...\n\n## Assigning Probability and its Building Blocks", null, "" ]	[ null, "https://bravelearn.com/wp-content/themes/Extra/images/pagination-loading.gif", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.90665656,"math_prob":0.924288,"size":1010,"snap":"2022-40-2023-06","text_gpt3_token_len":188,"char_repetition_ratio":0.16003977,"word_repetition_ratio":0.13793103,"special_character_ratio":0.18217821,"punctuation_ratio":0.18041237,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99760646,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-02-03T03:39:18Z\",\"WARC-Record-ID\":\"<urn:uuid:91b35e9a-c9cb-41d8-a721-02301f747f4e>\",\"Content-Length\":\"106023\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b1a5f919-4c55-408f-b897-e02aff01665f>\",\"WARC-Concurrent-To\":\"<urn:uuid:6c25d093-5c38-4503-9145-535ba3614ce0>\",\"WARC-IP-Address\":\"198.54.114.240\",\"WARC-Target-URI\":\"https://bravelearn.com/tag/probability/\",\"WARC-Payload-Digest\":\"sha1:GESOQF3BNTVXGVNMDDLXSYLQRWWOVDYZ\",\"WARC-Block-Digest\":\"sha1:XJEZIRQS7E7GZN5UDFUOE6G3F7DD5T7Z\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-06/CC-MAIN-2023-06_segments_1674764500042.8_warc_CC-MAIN-20230203024018-20230203054018-00119.warc.gz\"}"}
https://mediatum.ub.tum.de/node?id=1632607&change_language=en	[ "User: Guest", null, "Login\nmediaTUM Gesamtbestand", null, "Einrichtungen", null, "Schools und Fakultäten", null, "Fakultät für Mathematik", null, "Zentrum Mathematik", null, "Arbeitsgruppe Mathematische Statistik", null, "Abschlussarbeiten", null, "Masterarbeiten", null, "2021", null, "Document type:\nMasterarbeit\nAuthor(s):\nMatthieu Bulté\nTitle:\nHigher-order statistics for high-dimensional problems with applications to graphical models\nAbstract:\nA Gaussian graphical model is a statistical model, where the data follows a multivariate Normal distribution in which conditional independence relations of the random vector are encoded in a graph. Testing the hypothesis that a Gaussian graphical model is associated to either a graph or a speciﬁc subgraph corresponds to a composite hypothesis test in the Normal model. However, the standard likelihood ratio test for this problem has both poor power and size, and is only suitable if the sample siz... »\n\nSubject:\nMAT Mathematik\nDDC:\n510 Mathematik\nMathias Drton\nDate of acceptation:\n27.05.2021\nYear:\n2021\nQuarter:\n2. Quartal\nYear / month:\n2021-05\nMonth:\nMay\nPages:\n71\nLanguage:\nen\nUniversity:\nTechnische Universität München\nFaculty:\nFakultät für Mathematik\nTUM Institution:\nLehrstuhl für Mathematische Statistik\nOccurrences:" ]	[ null, "https://mediatum.ub.tum.de/img/login.gif", null, "https://mediatum.ub.tum.de/img/breadcrumb-arrow.gif", null, "https://mediatum.ub.tum.de/img/breadcrumb-arrow.gif", null, "https://mediatum.ub.tum.de/img/breadcrumb-arrow.gif", null, "https://mediatum.ub.tum.de/img/breadcrumb-arrow.gif", null, "https://mediatum.ub.tum.de/img/breadcrumb-arrow.gif", null, "https://mediatum.ub.tum.de/img/breadcrumb-arrow.gif", null, "https://mediatum.ub.tum.de/img/breadcrumb-arrow.gif", null, "https://mediatum.ub.tum.de/img/breadcrumb-arrow.gif", null, "https://mediatum.ub.tum.de/img/breadcrumb-arrow.gif", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9293859,"math_prob":0.6720424,"size":1531,"snap":"2022-05-2022-21","text_gpt3_token_len":284,"char_repetition_ratio":0.12180746,"word_repetition_ratio":0.6333333,"special_character_ratio":0.17374265,"punctuation_ratio":0.07224335,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97626764,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-25T01:14:59Z\",\"WARC-Record-ID\":\"<urn:uuid:589fbd65-15ef-465e-ae56-b5102362906a>\",\"Content-Length\":\"31718\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0f8b579a-bb22-43f6-859b-d5047ed6d594>\",\"WARC-Concurrent-To\":\"<urn:uuid:ae6f00b9-edc8-432e-a59f-9273bb21d64d>\",\"WARC-IP-Address\":\"138.246.224.249\",\"WARC-Target-URI\":\"https://mediatum.ub.tum.de/node?id=1632607&change_language=en\",\"WARC-Payload-Digest\":\"sha1:3SMMARZKDTJOOXAKS3KZMRQ2EPPHSHNG\",\"WARC-Block-Digest\":\"sha1:O7J4NQWBIGFFMLU6VABYIEFNOTL723DU\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662577757.82_warc_CC-MAIN-20220524233716-20220525023716-00466.warc.gz\"}"}
https://www.codingninjas.com/codestudio/problems/swap-two-numbers_1112577	[ "Problem title\nDifficulty\nAvg time to solve\n\nSet Matrix Zeros\nEasy\n30 mins\nBeautiful String\nEasy\n18 mins\nYogesh And Primes\nModerate\n20 mins\nSwap Two Numbers\nEasy\n10 mins\nFirst Missing Positive\nModerate\n18 mins\nLongest Univalue Path\nModerate\n10 mins\nFind Unique\nEasy\n--\nValid Sudoku\nModerate\n40 mins\nReverse Nodes in k-Group\nHard\n56 mins\nSum Of Max And Min\nEasy\n10 mins", null, "235\n\n# Swap Two Numbers\n\nDifficulty: EASY\nAvg. time to solve\n10 min\n\nProblem Statement\n\n#### Take two numbers as input and swap them and print the swapped values.\n\n##### Input Format:\n``````The first line of input contains a single integer 't', representing the total number of test cases.\n\nThe second line of input contains two integers 'a' and 'b', representing the second number.\n``````\n##### Output Format:\n``````The first line of output prints the swapped value of 'a' and 'b'.\n``````\n##### Note:\n``````You do not need to print anything, it has already been taken care of. Just implement the given function.\n``````\n##### Constraints:\n``````1 <= 'T' <= 10^2\n-10^5 <= 'a', 'b' <= 10 ^ 5\n\nTime Limit: 1 sec\n``````\n##### Sample Input 1:\n``````2\n1 2\n3 4\n``````\n##### Sample Output 1:\n``````2 1\n4 3\n``````\n##### Explanation For Sample Input 1:\n``````The output of the above test case is 2 1 for the first test case.\nThe output of the 2nd test case is 4 3.\n``````\n##### Sample Input 2:\n``````2\n5 6\n7 8\n``````\n##### Sample Output 2:\n``````6 5\n8 7\n``````\n##### Explanation For Sample Input 2:\n``````The output of the above test case is 6 5 for the first test case.\nThe output of the 2nd test case is 8 7.\n``````", null, "", null, "", null, "Console" ]	[ null, "https://s3-ap-southeast-1.amazonaws.com/codestudio.codingninjas.com/codestudio/assets/images/ps_upvote.svg", null, "https://s3-ap-southeast-1.amazonaws.com/codestudio.codingninjas.com/codestudio/assets/icons/reset-code-dark.svg", null, "https://s3-ap-southeast-1.amazonaws.com/codestudio.codingninjas.com/codestudio/assets/icons/full-screen-dark.svg", null, "https://s3-ap-southeast-1.amazonaws.com/codestudio.codingninjas.com/codestudio/assets/icons/copy-code.svg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7500465,"math_prob":0.8991674,"size":1058,"snap":"2022-27-2022-33","text_gpt3_token_len":305,"char_repetition_ratio":0.14611006,"word_repetition_ratio":0.1352657,"special_character_ratio":0.2920605,"punctuation_ratio":0.11111111,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9868564,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-07-03T12:25:17Z\",\"WARC-Record-ID\":\"<urn:uuid:7acf585f-69bd-4c18-addc-15128bbc966f>\",\"Content-Length\":\"234782\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:14a26a98-0fd0-4f5d-9281-8950d1b268d7>\",\"WARC-Concurrent-To\":\"<urn:uuid:aadfcc06-20a2-4f4e-9e3b-d4fd09cd5592>\",\"WARC-IP-Address\":\"99.84.191.101\",\"WARC-Target-URI\":\"https://www.codingninjas.com/codestudio/problems/swap-two-numbers_1112577\",\"WARC-Payload-Digest\":\"sha1:KSVCG2S76I6Z7VWJEZIFFSWCVZ2QYPLZ\",\"WARC-Block-Digest\":\"sha1:BPMABDETMNQUXVHK5F3TITSOZQMABU32\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656104240553.67_warc_CC-MAIN-20220703104037-20220703134037-00373.warc.gz\"}"}
https://groupprops.subwiki.org/wiki/Amalgamated_free_product_of_Z_and_Z_over_2Z	[ "# Amalgamated free product of Z and Z over 2Z\n\nView a complete list of particular groups (this is a very huge list!)[SHOW MORE]\n\n## Definition\n\n### Definition as an amalgamated free product\n\nThe group is defined as the amalgamated free product", null, "$\\mathbb{Z} *_{2\\mathbb{Z}} \\mathbb{Z}$, i.e., we take two copies of the group of integers, take their free product, and then take the quotient group by the identification of the subgroup", null, "$2\\mathbb{Z}$.\n\n### Definition by presentation\n\nThe group can be defined by the presentation:", null, "$\\langle x,y \\mid x^2 = y^2 \\rangle$\n\n## Group properties\n\nProperty Meaning Satisfied? Explanation\nabelian group any two elements commute No", null, "$x,y$ do not commute\nnilpotent group upper central series reaches the whole group in finitely many steps No The quotient group by the center", null, "$\\langle x^2 \\rangle$ is isomorphic to the infinite dihedral group, which is centerless.\nsolvable group has a normal series where all the quotients are abelian Yes The quotient by the center is infinite dihedral group, which is a metacyclic group." ]	[ null, "https://groupprops.subwiki.org/w/images/math/5/b/4/5b4db2b5433d187718ddbee3cd5ec700.png ", null, "https://groupprops.subwiki.org/w/images/math/8/7/7/8770b58453583833d5ce47f41656919b.png ", null, "https://groupprops.subwiki.org/w/images/math/5/9/a/59af9d1b312f39e6d2ff31f43aa16990.png ", null, "https://groupprops.subwiki.org/w/images/math/f/1/0/f10bc3c94b77e1d6b9f98106daf335c1.png ", null, "https://groupprops.subwiki.org/w/images/math/3/0/6/306b57262f298538ce6f5824ec43c189.png ", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.87050474,"math_prob":0.9625574,"size":1138,"snap":"2020-34-2020-40","text_gpt3_token_len":258,"char_repetition_ratio":0.13844797,"word_repetition_ratio":0.011363637,"special_character_ratio":0.19507909,"punctuation_ratio":0.09950249,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97539383,"pos_list":[0,1,2,3,4,5,6,7,8,9,10],"im_url_duplicate_count":[null,7,null,null,null,3,null,null,null,5,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-10-01T06:56:57Z\",\"WARC-Record-ID\":\"<urn:uuid:cff90bda-c537-406c-9521-6acc4537817c>\",\"Content-Length\":\"33384\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6b73a0d7-58e8-44b5-a5cd-3ce33e402e2e>\",\"WARC-Concurrent-To\":\"<urn:uuid:b030bd80-bb61-4f48-ae2a-ea4f5439f1c2>\",\"WARC-IP-Address\":\"96.126.114.7\",\"WARC-Target-URI\":\"https://groupprops.subwiki.org/wiki/Amalgamated_free_product_of_Z_and_Z_over_2Z\",\"WARC-Payload-Digest\":\"sha1:VAH6T7IX7AARARTQJIQW4RHEEUYHVHJV\",\"WARC-Block-Digest\":\"sha1:P47ONHD6GVSLNWTKYROMQXIXV32EER4Y\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600402124756.81_warc_CC-MAIN-20201001062039-20201001092039-00290.warc.gz\"}"}
https://www.autoswiat-polska.pl/2021-apr-16/9203.html	[ "[email protected]\n\nNews Center\n\nHere, we will provide you with fresh corporate dynamics, industry information, and market focus, allowing you to grasp the dynamics of the mining machinery industry at any time, grasp the forefront of the market, and grasp the opportunities for entrepreneurship!\n\n1. Home\n2. Qtty Of Sand In 1 Cubic Metre Of Concrete", null, "Qtty Of Sand In 1 Cubic Metre Of Concrete\n\n•", null, "Quantities of Materials Per Cubic Meter of Concrete Mix\n\nQuantity of materials such as cement, sand, coarse aggregates and water required per cubic meter of concrete and mortar for different mix proportions varies with the mix design of the concrete and mortar respectively. Following table gives the estimated quantity of materials required per cubic meter of mortar and concrete for various nominal mixes.\n\n•", null, "Quantities of Materials Per Cubic Meter of Concrete Mix\n\n24 rows Oct 16, 2014 Quantity of materials such as cement, sand, coarse aggregates and water required per cubic ...\n\n•", null, "Sand and Aggregate Quantity In 1 Cubic metre Concrete\n\nDec 29, 2020 Tagged Sand and Aggregate Quantity In 1 Cubic metre Concrete . 1. Civil Topics. December 29, 2020. What is Retrofitting of Structures Its Types amp Benefits. ... Self Healing Concrete and Asphalt, Civil Drawing. 20 X 40 House Plan and Structure CAD Drawing CAD Blocks For Architect, Draftsman, designers\n\n•", null, "How many bags of cement do I need to make 1 cubic metre\n\nDec 30, 2011 1 Cement 2 Sand 3 Aggregate gravel is too strong. 16bags costly 1 Cement 2.5 Sand 4 Aggregate is OK for fence posts. 13bags of cement per cubic metre. The more cement the more costly of course so dont over do it. Note These are 20kg bags of General Purpose cement.\n\n•", null, "Rate Analysis of RCC Reinforcement Cement Concrete\n\nAssume of reinforcement 2 of the total volume of concrete. so, 1 cu.m. concrete for reinforcement 1.0 x 2 0.02 ton of steel this 2 only assumse as per exprience Her, 10 Cu.m concrete requirement 0.02 ton x 10 co.m. 0.20 ton 200 kg for 10 cu.m. Also, read What is Bitumen And Bitumens Types. Labour for Rate Analysis of Concrete\n\n•", null, "Quantities of Cement Sand and Aggregate in Cubic Meter\n\nJan 17, 2021 Hello, friends in this article you will learn to calculate the Quantity of Cement, Sand, and Aggregate In Kilograms, Cubic Meter and Cubic Feet. Also, you find the Table where you will get the Quantity of Cement, sand, and aggregate of different Grade of Concrete\n\n•", null, "How much cement sand amp aggregate required for M20 concrete\n\nAns. -0.42 m3 quantity of sand is required for 1 cubic metre of M20 concrete. How much sand required for M20 concrete in Kgs step 8 -calculate sand required for 1 cubic metre of M20 concrete in kgs kilogram is equal to 1.55.5 1.54m3 1620 Kgm3 680Kgs. Ans. -680 Kgs quantity of sand is required for 1 cubic metre of M20 concrete\n\n•", null, "How much cement sand amp aggregate required for m25 concrete\n\nAns. -624 Kgs quantity of sand is required for 1 cubic metre of M25 concrete. How much sand required for M25 concrete in cft step 9 -calculate sand required for 1 cubic metre of M25 concrete in cft cubic feet is equal to 14 1.54m335.3147 1620 Kgm3 18 cft. Ans.- 18 cft quantity of sand is required for 1 cubic metre of M25 concrete.\n\n•", null, "How to Calculate Cement Sand amp Aggregate Quantity in Concrete\n\nFor M25 1 part of cement, 1 part of sand and 2 part of aggregate. Density of materials. Cement 1440 kgm 3. Dry Sand 1540 to 1600 kgm 3. Aggregate 1560 to 1600 kgm 3. Wet to Dry Conversion. Dry Volume Wet Volume 54 of wet volume Dry Volume Wet Volume x 1.54. How to calculate quantity for 10 cubic meter concrete.\n\n•", null, "Metric calculator for concrete cement sand gravel etc\n\nBoth of these concrete calculators make an allowance for the fact that material losses volume after being mixed to make concrete. Calculator are provided for a general mix and a paving mix, the different ratio of materials are General mix - 15 cementall-in ballast or 12 3 cementsharp sandgravel. Paving mix - 13 cementall-in ...\n\n•", null, "How to Calculate Quantities of Cement Sand and Aggregate\n\nSo 1.54 Cum of dry materials cement, sand and aggregate is required to produce 1 Cum of concrete. Volume of Cement required 1124 X 1.54 17 X 1.54 0.22 Cum. Volume of Sand required 27 X 1.54 0.44 Cum or 15.53 cft. Volume of Aggregate required 47 X 1.54 0.88 Cum or 31.05 cft. Note 1 cubic meter 35.29 cubic feet\n\n•", null, "How To Calculate Cement Bags In 1 Cubic Meter\n\nDec 21, 2016 Procedure To Calculate Cement Bags In 1 Cubic Meter To achieve 1 cum output, we need 10.67 1.49 say 1.50 cum dry mix. Now add the wastage of 2, i.e 1.50 0.02 1.52 cum. Weight of 1 bag cement 50 kg. 6.25 bags. Note You can use the same formula for calculating cement for other nominal mixes.\n\n•", null, "Calculate Quantities of Materials for Concrete Cement\n\nWe have considered an entrained air of 2. Thus the actual volume of concrete for 1 cubic meter of compacted concrete construction will be 1 -0.02 0.98 m 3. Thus, the quantity of cement required for 1 cubic meter of concrete 0.980.1345 7.29 bags of cement. The quantities of materials for 1 m3 of concrete production can be calculated as ...\n\n•", null, "How to Calculate Cement Sand and Aggregate required for\n\nMar 18, 2017 Density of concrete 2400 kgcum. So, 1 bag of cement produces 4002400 0.167 cum. No. of bags required for 01 cum of concrete 10.167 5.98 bags 6 bags. From above, if the concrete mix is 124 , to get a cubic meter of concrete we require. 1.Cement 6 bags 300 kgs. 2.Fine Aggregate 1150.167 689 kg.\n\n•", null, "Calculate Quantities of Materials for Concrete Cement\n\nApr 01, 2015 Thus, the quantity of cement required for 1 cubic meter of concrete 0.980.1345 7.29 bags of cement. The quantities of materials for 1 m3 of concrete production can be calculated as follows The weight of cement required 7.29 x 50 364.5 kg. Weight of fine aggregate sand 1.5 x 364.5\n\n•", null, "How to calculate quantity of cement sand amp aggregate in\n\nThere are two main ways to design the concrete mix. Design mix method - In this method, materials are proportioned based on the procedure and rules given in IS 456 2000 and IS 10262 code . In this method, cement, sand and aggregates are always batched in terms of weight, and concrete can be designed for different environmental conditions and different needs.\n\n•", null, "Sand Calculator how much sand do you need in tons\n\nHow much does a cubic meter of sand weigh A cubic meter of typical sand weighs 1,600 kilograms 1.6 tonnes. A square meter sandbox with a depth of 35 cm weighs about 560 kg or 0.56 tonnes. The numbers are obtained using this sand calculator. How much is a ton of sand A ton of sand is typically about 0.750 cubic yards 34 cu yd, or 20 cubic feet.\n\n•", null, "what is the cement quantity of nominal mix 124 for 1\n\nMay 14, 2009 7 cubic meters of loose mix will give 5 cubic meters of solid concrete. 136, 1 cubic meter of cement 3 c.m. of sand 6 c.m. of aggregate will give 10 cubic meters of loose material. when mixed in a mixture will give 10 x 57 7.143 cubic meters of solid containing 1440 Kg of cement. So 1 cubic meter will have 1440 7.143 201.59 Kg ...\n\n•", null, "How to Calculate Cement Sand and Coarse Aggregate\n\nConcrete Ingredients Calculation. For Cement, Sand and Coarse Aggregate. This is a Volumetric Calculation. Assuming we need 2 m 3 of concrete for M20 Concrete Mix, Mix Ratio, M20 1 1.5 3 Total Part of the Concrete 11.53 5.5 Parts. Therefore, Cement Quantity Cement Part Concrete Parts Concrete Volume\n\n•", null, "How to Calculate Brick Cement and Sand in Brickwork\n\nCement 0.043 28.8 1.238 bags Numbers of cement bags in 1 Cum 28.8 Sand 0.043 6 0.258 cum. But as the cement will go to fill up the voids in the sand, 0.045 cum of cement and 0.27 cum of sand may be taken. I hope now you understood how to calculate quantity of materials in brickwork.\n\n•", null, "How much cement sand amp aggregate required for M15\n\nJul 26, 2020 Ans. - 713 Kgs quantity of sand is required for 1 cubic metre of M15 concrete. How much sand required for M15 concrete in cft step 9 - calculate sand required for 1 cubic metre of M15 concrete in cft cubic feet is equal to 27 1.54m335.3147 1620 Kgm3 20 cft. Ans. - 20 cft quantity of sand is required for 1 cubic metre of M15 ...\n\n•", null, "How much cement sand amp aggregate required for M20\n\nJul 26, 2020 We have given dry volume of concrete is equal to 1.54 cubic metre and part of sand in concrete mix is equal to 1.55.5, density of sand is equal to 1620 Kgm3 and one cubic metre is equal to 35.3147 cu ft. How much sand required for M20 concrete in cubic metre.\n\n•", null, "How To Calculate the Quantity of Materials Sand and\n\nJul 20, 2016 Therefore, if we were to render a cubic meter of Mortar 1m3 with a mix ratio 16 Meaning One Bag Of Cement for 6 Parts Of sand, The quantity of sand needed here would be 1.371m 3 Volume of sand needed\n\n•", null, "Calculate Cement Sand amp Aggregate M20 M15 M10 M5\n\nCalculate the concrete quantity required in cubic meter and then multiply the quantity with the cement sand and aggregate for 1 cubic meter of concrete. In your case Volume of concrete 1.7 x 1.7 x 0.5 1.4 cu.m It looks like you are using m20 grade mix with extra sand. If you follow that mix proportion then to calculate use this following ...\n\n•", null, "How much Cement Sand Quantity in Brickwork Civil\n\nOct 13, 2018 You can add mortar if width of wall is more than 1 brick. Required Number of Bricks 2.140.00245 873 Bricks. So Actual Number of Bricks for 1 Cubic metre in field 8732.14 408 Bricks. Actual number varies from meson to meson because some one use less mortar and some one use more mortar. so it is mainly 390 to 430.\n\n•", null, "Cement Mortar Estimation of Cement Sand amp Water in\n\nJul 09, 2019 Estimation of Water, Cement amp Sand quantity for Cement Mortar. Let us assume a standard quantity of 1m 3 Cement mortar and a mix proportion of CM 16 1 part Cement amp 6 parts Sand. The quantity can calculated in two ways, one is by weight and the other by volume. Let us consider the volume method for the calculation of cement amp sand quantity.\n\n•", null, "Calculate Cement Sand amp Aggregate M20 M15 M10 M5\n\nSep 08, 2015 Calculate the concrete quantity required in cubic meter and then multiply the quantity with the cement sand and aggregate for 1 cubic meter of concrete. In your case Volume of concrete 1.7 x 1.7 x 0.5 1.4 cu.m It looks like you are using m20 grade mix with extra sand. If you follow that mix proportion then to calculate use this following method.\n\n•", null, "Tutorial How Many WheelBarrows Of Cement Sand And\n\nJul 12, 2017 ASSUMEConcrete Density is 2400kgm3 and a head pan is 25kg max carrying weight. A ratio of 124 gives 7 parts. Cement is 1 part therefore 17 of 2400 342kg 6.8 x 50kg bags. Sand is 2 parts, therefore 27 of 2400 684kg. 27 head pans Stone is 4 parts, therefore 47 of 2400 1368kg.55 head pans THIS IS ALL TO MAKE 1 meter cube of ...\n\n•", null, "Cement Concrete Calculator PCC Calculator RCC\n\nStrength of PCC is defined as compressive strength after 28 days, expressed as M15, M20, where M stands for Mix and 15 stands for 15 Nmm 2 nmm 2 must be read as Newtons per millimeter Cubic compressive strength at 28 days. The proportions of materials cement, sand, coarse aggregate for nominal mixdesign mix concrete that are normally used are 136 or 148.\n\n•", null, "How to Calculate Cement Sand and Aggregate required for 1\n\nDensity of concrete 2400 kgcum. So, 1 bag of cement produces 4002400 0.167 cum. No. of bags required for 01 cum of concrete 10.167 5.98 bags 6 bags. From above, if the concrete mix is 124 , to get a cubic meter of concrete we require. 1.Cement 6 bags 300 kgs. 2.Fine Aggregate 1150.167 689 kg\n\n•", null, "SAND CALCULATOR How Much Sand do I Need\n\nOur sand calculator can be used to work out how much sand your next landscaping project will require. Work out the total volume, weight and cost of the sand." ]	[ null, "https://www.autoswiat-polska.pl/image450/sand/56.jpg", null, "https://www.autoswiat-polska.pl/image450/sand/56.jpg", null, "https://www.autoswiat-polska.pl/image450/sand/14.jpg", null, "https://www.autoswiat-polska.pl/image450/sand/9.jpg", null, "https://www.autoswiat-polska.pl/image450/sand/40.jpg", null, "https://www.autoswiat-polska.pl/image450/sand/12.jpg", null, "https://www.autoswiat-polska.pl/image450/sand/20.jpg", null, "https://www.autoswiat-polska.pl/image450/sand/25.jpg", null, "https://www.autoswiat-polska.pl/image450/sand/36.jpg", null, "https://www.autoswiat-polska.pl/image450/sand/38.jpg", null, "https://www.autoswiat-polska.pl/image450/sand/44.jpg", null, "https://www.autoswiat-polska.pl/image450/sand/57.jpg", null, "https://www.autoswiat-polska.pl/image450/sand/21.jpg", null, "https://www.autoswiat-polska.pl/image450/sand/7.jpg", null, "https://www.autoswiat-polska.pl/image450/sand/6.jpg", null, "https://www.autoswiat-polska.pl/image450/sand/42.jpg", null, "https://www.autoswiat-polska.pl/image450/sand/39.jpg", null, "https://www.autoswiat-polska.pl/image450/sand/30.jpg", null, "https://www.autoswiat-polska.pl/image450/sand/22.jpg", null, "https://www.autoswiat-polska.pl/image450/sand/17.jpg", null, "https://www.autoswiat-polska.pl/image450/sand/37.jpg", null, "https://www.autoswiat-polska.pl/image450/sand/52.jpg", null, "https://www.autoswiat-polska.pl/image450/sand/16.jpg", null, "https://www.autoswiat-polska.pl/image450/sand/5.jpg", null, "https://www.autoswiat-polska.pl/image450/sand/19.jpg", null, "https://www.autoswiat-polska.pl/image450/sand/24.jpg", null, "https://www.autoswiat-polska.pl/image450/sand/28.jpg", null, "https://www.autoswiat-polska.pl/image450/sand/18.jpg", null, "https://www.autoswiat-polska.pl/image450/sand/32.jpg", null, "https://www.autoswiat-polska.pl/image450/sand/34.jpg", null, "https://www.autoswiat-polska.pl/image450/sand/1.jpg", null, "https://www.autoswiat-polska.pl/image450/sand/11.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8328844,"math_prob":0.986354,"size":10079,"snap":"2022-05-2022-21","text_gpt3_token_len":2746,"char_repetition_ratio":0.2026799,"word_repetition_ratio":0.20519762,"special_character_ratio":0.294176,"punctuation_ratio":0.13955556,"nsfw_num_words":6,"has_unicode_error":false,"math_prob_llama3":0.9820953,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64],"im_url_duplicate_count":[null,2,null,2,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-27T15:29:03Z\",\"WARC-Record-ID\":\"<urn:uuid:39812b62-b1f8-435c-959b-9a0305b24cd7>\",\"Content-Length\":\"30629\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:42ac8cf5-8457-4483-bf19-1ebfc1746117>\",\"WARC-Concurrent-To\":\"<urn:uuid:c9d78a9b-0df6-4c38-a192-2006b8f55f62>\",\"WARC-IP-Address\":\"104.21.45.120\",\"WARC-Target-URI\":\"https://www.autoswiat-polska.pl/2021-apr-16/9203.html\",\"WARC-Payload-Digest\":\"sha1:NU7MMOPYAS6AHWAZTRUONVHQAKDRXEGL\",\"WARC-Block-Digest\":\"sha1:EEERNEUFHBCR4HEZ356VUR2NAOJTH3ZY\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320305266.34_warc_CC-MAIN-20220127133107-20220127163107-00209.warc.gz\"}"}
https://hsm.stackexchange.com/questions/11624/what-is-the-origin-of-the-term-non-derogatory-matrix	[ "# What is the origin of the term (non-)derogatory matrix?\n\nA non-derogatory matrix $$A$$ is one, whose minimal polynomial $$m(z)$$ equals its characteristic polynomial $$p(z)$$, where we apply the convention $$p(z) = det(zI-A)$$, while a matrix is derogatory, if they do not coincide. I have certainly never felt particularly offended when dealing with the identity matrix $$I$$, so seriously I wonder, where that strange name has its origin.\n\nSome background:\n\nI would like to know about it, because I teach some advanced pupils at a german gymnasium school, who will be considering a field of study in the STEM-area, some linear algebra using examples from polynomial geometry. In that context, certain polynomials generate matrices with a double eigenvalue, which are either non-derogatory or diagonalizable, and where the non-derogatory ones are indeed preferable to the diagonalizable ones due to the particular application.\n\nIn order to make the rather involved notion more palatable to the audience, it is always good to have a story to tell about it, even if it turns out to be rather dull in the end.\n\nMy native language is german and I know of only one place in the german literature, where non-derogatory matrices get a special name. That is in E.Brieskorn \"Lineare Algebra und analytische Geometrie II\", where they are called \"regular\", which the author immediately distinguishes from another use of that word as invertible.\n\nOn the contrary, the english denomination sems to be well-established when refering to Google and I found it already mentioned in the first chapter of J.H. Wilkinson \"The Algebraic Eigenvalue Problem\" from 1965 without further comment, so it seems to have been established by then.\n\n• The term seems self-explanatory (=deficient matrix, non-diagonalizable matrix). And the question on historical usage is better to ask in History of Science and Maths SE. – Alexandre Eremenko Apr 5 at 19:37" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9364611,"math_prob":0.8566798,"size":1645,"snap":"2020-45-2020-50","text_gpt3_token_len":357,"char_repetition_ratio":0.09993906,"word_repetition_ratio":0.0,"special_character_ratio":0.2006079,"punctuation_ratio":0.1009772,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9658492,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-10-22T07:20:16Z\",\"WARC-Record-ID\":\"<urn:uuid:7d9f1490-626a-475a-88c2-e3df7f50d92e>\",\"Content-Length\":\"146570\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2d15d366-b10d-4c61-89c6-23583a451178>\",\"WARC-Concurrent-To\":\"<urn:uuid:2c193b85-a4c5-43e8-b753-f1821ce40303>\",\"WARC-IP-Address\":\"151.101.1.69\",\"WARC-Target-URI\":\"https://hsm.stackexchange.com/questions/11624/what-is-the-origin-of-the-term-non-derogatory-matrix\",\"WARC-Payload-Digest\":\"sha1:SDF2DRINDW23AQNCHPRX3UPOIYHTF24H\",\"WARC-Block-Digest\":\"sha1:GHBZQX7GY7WEUEN4SH3NN6AWKCJAGG2Y\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-45/CC-MAIN-2020-45_segments_1603107878921.41_warc_CC-MAIN-20201022053410-20201022083410-00442.warc.gz\"}"}