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https://shareablecode.com/browse/tags/bfs | [
"Showing 20 of 46 from page 1\n\n## Minimum Number of Flips to Convert Binary Matrix to Zero Matrix - Python Solution @ LeetCode\n\nMinimum Number Of Flips To Convert Binary Matrix To Zero Matrix, is a LeetCode problem from Breadth First Search subdomain. In this post we will see how we can solve this challenge in Python You can\n\n## Minimum Moves to Reach Target with Rotations - Python Solution @ LeetCode\n\nMinimum Moves To Reach Target With Rotations, is a LeetCode problem from Breadth First Search subdomain. In this post we will see how we can solve this challenge in Python You can find the full detai\n\n## Minimum Moves to Move a Box to Their Target Location - Python Solution @ LeetCode\n\nMinimum Moves To Move A Box To Their Target Location, is a LeetCode problem from Breadth First Search subdomain. In this post we will see how we can solve this challenge in Python You can find the fu\n\n## Minimum Jumps to Reach Home - Python Solution @ LeetCode\n\nMinimum Jumps To Reach Home, is a LeetCode problem from Breadth First Search subdomain. In this post we will see how we can solve this challenge in Python You can find the full details of the problem\n\n## Minimum Cost to Make at Least One Valid Path in a Grid - Python Solution @ LeetCode\n\nMinimum Cost To Make At Least One Valid Path In A Grid, is a LeetCode problem from Breadth First Search subdomain. In this post we will see how we can solve this challenge in Python You can find the\n\n## Maximum Level Sum of a Binary Tree - Python Solution @ LeetCode\n\nMaximum Level Sum Of A Binary Tree, is a LeetCode problem from Breadth First Search subdomain. In this post we will see how we can solve this challenge in Python You can find the full details of the\n\n## Maximum Candies You Can Get from Boxes - Python Solution @ LeetCode\n\nMaximum Candies You Can Get From Boxes, is a LeetCode problem from Breadth First Search subdomain. In this post we will see how we can solve this challenge in Python You can find the full details of\n\n## Map of Highest Peak - Python Solution @ LeetCode\n\nMap Of Highest Peak, is a LeetCode problem from Breadth First Search subdomain. In this post we will see how we can solve this challenge in Python You can find the full details of the problem Map of\n\n## Lexicographically Smallest String After Applying Operations - Python Solution @ LeetCode\n\nLexicographically Smallest String After Applying Operations, is a LeetCode problem from Breadth First Search subdomain. In this post we will see how we can solve this challenge in Python You can find\n\n## K-Similar Strings - Python Solution @ LeetCode\n\nK Similar Strings, is a LeetCode problem from Breadth First Search subdomain. In this post we will see how we can solve this challenge in Python You can find the full details of the problem K Similar\n\n## Jump Game IV - Python Solution @ LeetCode\n\nJump Game IV, is a LeetCode problem from Breadth First Search subdomain. In this post we will see how we can solve this challenge in Python You can find the full details of the problem Jump Game IV a\n\n## Get Watched Videos by Your Friends - Python Solution @ LeetCode\n\nGet Watched Videos By Your Friends, is a LeetCode problem from Breadth First Search subdomain. In this post we will see how we can solve this challenge in Python You can find the full details of the\n\n## Find Nearest Right Node in Binary Tree - Python Solution @ LeetCode\n\nFind Nearest Right Node In Binary Tree, is a LeetCode problem from Breadth First Search subdomain. In this post we will see how we can solve this challenge in Python You can find the full details of\n\n## Even Odd Tree - Python Solution @ LeetCode\n\nEven Odd Tree, is a LeetCode problem from Breadth First Search subdomain. In this post we will see how we can solve this challenge in Python You can find the full details of the problem Even Odd Tree\n\n## Escape a Large Maze - Python Solution @ LeetCode\n\nEscape A Large Maze, is a LeetCode problem from Breadth First Search subdomain. In this post we will see how we can solve this challenge in Python You can find the full details of the problem Escape\n\n## Cut Off Trees for Golf Event - Python Solution @ LeetCode\n\nCut Off Trees For Golf Event, is a LeetCode problem from Breadth First Search subdomain. In this post we will see how we can solve this challenge in Python You can find the full details of the proble\n\n## Correct a Binary Tree - Python Solution @ LeetCode\n\nCorrect A Binary Tree, is a LeetCode problem from Breadth First Search subdomain. In this post we will see how we can solve this challenge in Python You can find the full details of the problem Corre\n\n## Coloring A Border - Python Solution @ LeetCode\n\nColoring A Border, is a LeetCode problem from Breadth First Search subdomain. In this post we will see how we can solve this challenge in Python You can find the full details of the problem Coloring\n\n## Closest Leaf in a Binary Tree - Python Solution @ LeetCode\n\nClosest Leaf In A Binary Tree, is a LeetCode problem from Breadth First Search subdomain. In this post we will see how we can solve this challenge in Python You can find the full details of the probl\n\n## Cheapest Flights Within K Stops - Python Solution @ LeetCode\n\nCheapest Flights Within K Stops, is a LeetCode problem from Breadth First Search subdomain. In this post we will see how we can solve this challenge in Python You can find the full details of the pro",
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https://number-word.calculators.ro/how-to-write-cardinal-numbers-out-in-words.php | [
"# How to Write Out Cardinal Numbers in Words in (US) American English, How to Convert Numbers to Words\n\n## 1. The basics: important numbers in English and how to combine them to write out longer compound numbers.\n\n### 1.1. What are the most important numerals and numbers in English?\n\n• 1 = one (the lowest cardinal number; half of two;) Ex: one nation, one car, one piece of the mechanism.\nIdioms containing one: at one = in a state of agreement; one and all = everyone; one by one = singly and successively; one for the road = a final alcoholic drink taken just before departing from a party (hopefully not drinking and driving).\n• 2 = two (equivalent to the sum of one and one; one less than three;) Ex: two cars, two pieces of the mechanism. Not to be confused with: to, too.\nIdioms containing two: in two = into two separate parts; put two and two together = draw a correct conclusion.\n• 3 = three (equivalent to the sum of one and two; one more than two;) Ex: three cars, three pieces of the mechanism. Not to be confused with: tree.\nIdioms containing three: three sheets in the wind = intoxicated.\n• 4 = four (equivalent to the sum of two and two; one more than three;) Ex: four cars, four pieces of the mechanism. Not to be confused with: for, fore.\nIdioms containing four: the four corners of the earth = the most distant or remote regions.\n• 5 = five (equivalent to the sum of two and three; one more than four;) Ex: five cars, five pieces of the mechanism.\nIdioms containing five: take five = take a brief respite; give me five = shake hands with me.\n• 6 = six (equivalent to the sum of three and three; one more than five;) Ex: six cars, six pieces of the mechanism.\nIdioms containing six: six feet under = dead and buried.\n• 7 = seven (equivalent to the sum of three and four; one more than six;) Ex: seven cars, seven pieces of the mechanism.\nIdioms containing seven: at sixes and sevens = in disorder or confusion.\n• 8 = eight (equivalent to the sum of four and four; one more than seven;) Ex: eight cars, eight pieces of the mechanism.\nIdioms containing eight: behind the eight ball (eightball) = in uncomfortable situation.\n• 9 = nine (equivalent to the sum of four and five; one more than eight;) Ex: nine cars, nine pieces of the mechanism.\nIdioms containing nine: dressed to the nines = looking one's best.\n• 10 = ten (equivalent to the sum of five and five; one more than nine;) Ex: ten cars, ten pieces of the mechanism.\nIdioms containing ten: count to ten = calm down.\n• - - - - -\n• 11 = eleven (one and ten)\n• 12 = twelve (two and ten)\n• 13 = thirteen (three and ten)\n• 14 = fourteen (four and ten)\n• 15 = fifteen (five and ten)\n• 16 = sixteen (six and ten)\n• 17 = seventeen (seven and ten)\n• 18 = eighteen (eight and ten)\n• 19 = nineteen (nine and ten)\n• - - - - -\n• 20 = twenty (two tens)\n• 30 = thirty (three tens)\n• 40 = forty (four tens)\n• 50 = fifty (five tens)\n• 60 = sixty (six tens)\n• 70 = seventy (seven tens)\n• 80 = eighty (eight tens)\n• 90 = ninety (nine tens)\n• - - - - -\n• 100 = one hundred\n• 200 = two hundred\n• 300 = three hundred\n• 400 = four hundred\n• 500 = five hundred\n• 600 = six hundred\n• 700 = seven hundred\n• 800 = eight hundred\n• 900 = nine hundred\n• - - - - -\n• 1,000 = one thousand\n• 10,000 = ten thousand\n• 100,000 = one hundred thousand\n• 1,000,000 = one million\n• 10,000,000 = ten million\n• 100,000,000 = one hundred million\n• 1,000,000,000 = one billion\n• 10,000,000,000 = ten billion\n• 100,000,000,000 = one hundred billion\n• 1,000,000,000,000 = one trillion, etc.\n\n### 1.2. Combine the words in the list above to construct English words of longer compound numbers\n\n• Let's see how to write 65 out:\n• 6 is in the tens place and 5 is in the ones place.\n• 65 = 60 + 5 = six tens + five ones = sixty + five = sixty-five.\n• Notice the hyphen (or the minus sign) between sixty and five.\n• Let's see how to write 1,765 out:\n• 1 is in the thousands place, 7 is in the hundreds place, 6 is in the tens place and 5 is in the ones place.\n• 1,765 = 1,000 + 700 + 60 + 5 = one thousands + seven hundreds + six tens + five ones = one thousand + seven hundred + sixty + five = one thousand seven hundred sixty-five.\n• Notice the hyphen (or the minus sign) between sixty and five.\n\n## 2. How to convert natural numbers (positive integers) to (US) American English words, how to write them out?\n\n### 2.1. To know how to write a number in words it's important to know the place value of each digit.\n\n• For example, the number 12,345 has a 1 in the ten thousands place, a 2 in the thousands place, a 3 in the hundreds place, a 4 in the tens place and a 5 in the ones place.\n• 12,345 in words =\n• = one ten thousands (10,000) + two thousands (2,000) + three hundreds (300) + four tens (40) + five ones\n• = ten thousands (10,000) + two thousands (2,000) + three hundreds (300) + four tens (40) + five ones\n• = ten thousand + two thousand + three hundred + forty + five\n• = (ten + two) thousand + three hundred + forty-five\n• = twelve thousand + three hundred + forty-five\n• = twelve thousand three hundred forty-five.\n\n### 2.2. Notes:\n\n• 1: Note the hyphen (or the minus sign) in \"thirty-four\" above. Technically, it's correct to hyphenate all compound numbers from twenty-one (21) through ninety-nine (99).\n• 2: In American English, when writing out natural numbers of three or more digits, the word \"and\" is not used after \"hundred\" or \"thousand\". So it is \"one hundred twenty-three\" and not \"one hundred and twenty-three\", though you may hear a lot of people using the last, informally.\nIn British English, the word \"and\" is used after \"hundred\" or \"thousand\" in numbers of three or more digits.\n• 3. Do not use commas when writing out numbers above 999: so it is \"one thousand two hundred thirty-four\" and not \"one thousand, two hundred thirty-four\". For clarity, use commas when writing figures of four or more digits: 1,234, 43,290,120, etc.\n\n## 3. How to convert decimals to (US) American English words?\n\n### To know how to write a decimal number in words it's important to know the place value of each digit, before and after the decimal point (decimal mark).\n\n• This task is a little bit more complicated than converting an integer, because with a decimal number we have to worry also about the names of the places after the decimal point (decimal mark).\n• Let's take an example: the decimal number 987.123456, made of numerals from 1 to 9. Notice that for this example's sake, every digit in this number is unique, so I can explain it better.\n\n## 4. Steps to take in order to convert decimal numbers to (US) American English words.\n\n### Step 1: What are the names of the places after the decimal mark:\n\n• 1 is in the tenths place\n• 2 is in the hundredths place\n• 3 is in the thousandths place\n• 4 is in the ten thousandths place\n• 5 is in the hundred thousandths place\n• 6 is in the millionths place;\n\n### Step 2: How to spell out the number after the decimal mark, as an integer: 123,456?\n\n• Using the explanations from the previous points above, 123,456 =\n• = one hundred thousands (100,000) + two ten thousands (20,000) + three thousands (3,000) + four hundreds (400) + five tens (50) + six ones (6)\n• = one hundred thousands + two ten thousands + three thousands + four hundreds + five tens + six\n• = one hundred thousand + twenty thousand + three thousand + four hundred + fifty + six\n• = (one hundred + twenty + three) thousand + four hundred + fifty + six\n• = one hundred twenty-three thousand four hundred fifty-six.\n\n### Step 3: What is the name of the smallest place (the place farthest to the right from the decimal mark)?\n\n• In our number, it's the millionths place.\n\n### Step 4: Spell out the whole number after the decimal, followed by the name of the smallest place:\n\n• 0.123456 = one hundred twenty-three thousand four hundred fifty-six millionths;\n\n### Step 5, final: Connect everything before and after the decimal mark with an \"and\":\n\n• 987 = nine hundreds + eight tens + seven ones = nine hundred + eighty + seven = nine hundred eighty-seven;\n• 987.123456 = nine hundred eighty-seven and one hundred twenty-three thousand four hundred fifty-six millionths.\n\n## 5. When to write numbers out using words?\n\n• Spell out all numbers beginning a sentence, \"Forty years ago today,...\" Not \"40 years ago today,...\".\n• The Chicago Manual of Style calls for the numbers zero through one hundred to be written out - this would include forms like \"one hundred million\".\n• Using words to write short numbers makes your writing look clean and classy. In handwriting, words are easy to read and hard to mistake for each other. Writing longer numbers as words isn't as useful, but it's good practice while you're learning.\n• Otherwise, clarity should matter, for example when two numbers are used in a row: \"They needed five 2-foot copper pipes to finish the job. \". \"There were 15 six-foot tall men on the basketball team roster. \".\n• Be consistent within a sentence. Do not write \"... one million people...\" but \"... 1,000,000 cars...\", stick to one or another, but not both."
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https://rdrr.io/cran/TeachingSampling/man/S.PO.html | [
"# S.PO: Poisson Sampling In TeachingSampling: Selection of Samples and Parameter Estimation in Finite Population\n\n## Description\n\nDraws a Poisson sample of expected size \\$n\\$ from a population of size \\$N\\$\n\n## Usage\n\n `1` ```S.PO(N, Pik) ```\n\n## Arguments\n\n `N` Population size `Pik` Vector of inclusion probabilities for each unit in the population\n\n## Details\n\nThe selected sample is drawn according to a sequential procedure algorithm based on a uniform distribution. The Poisson sampling design is not a fixed sample size one.\n\n## Value\n\nThe function returns a vector of size N. Each element of this vector indicates if the unit was selected. Then, if the value of this vector for unit k is zero, the unit k was not selected in the sample; otherwise, the unit was selected in the sample.\n\n## Author(s)\n\nHugo Andres Gutierrez Rojas [email protected]\n\n## References\n\nSarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.\nGutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas.\nTille, Y. (2006), Sampling Algorithms. Springer.\n\n`E.PO`\n ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30``` ```############ ## Example 1 ############ # Vector U contains the label of a population of size N=5 U <- c(\"Yves\", \"Ken\", \"Erik\", \"Sharon\", \"Leslie\") # Draws a Bernoulli sample without replacement of expected size n=3 # \"Erik\" is drawn in every possible sample becuse its inclusion probability is one Pik <- c(0.5, 0.2, 1, 0.9, 0.5) sam <- S.PO(5,Pik) sam # The selected sample is U[sam] ############ ## Example 2 ############ # Uses the Lucy data to draw a Poisson sample data(Lucy) attach(Lucy) N <- dim(Lucy) n <- 400 Pik<-n*Income/sum(Income) # None element of Pik bigger than one which(Pik>1) # The selected sample sam <- S.PO(N,Pik) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] data dim(data) ```"
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https://www.physicsforums.com/threads/using-jordan-curve-thm-to-show-h_n-r-n-trivial.521327/ | [
"# Using Jordan Curve Thm to Show H_n(R^n) Trivial?\n\nGold Member\nHi, All:\n\nI hope I am not missing something obvious: can't we use the Jordan Curve Thm. to show\nthat the homology H_n(R^n) of R^n is trivial ? How about showing that Pi_n(R^n) is trivial?\n\nIt seems like the def. of cycles in a space X is geenralized by continuous , injective maps f: S^n -->X . When X=R^n, JCT says that f(S^n) separates R^n into 2 regions, which can be seen as saying that f(S^n) bounds, so that every cycle bounds, and then the homology is trivial.\n\nUsing the generalized Jordan curve theorem is massively overcomplicating it. All the homology groups of R^n greater than the zeroth are trivial, because R^n is contractible and homology groups remain unchanged under homotopy equivalence. Likewise with the homotopy groups.\n\nGold Member\nI understand; I know R^n is contractible, and we can use homotopy equivalence, etc., but I am trying to see if all n-cycles can be represented as images of spheres, and if the JCT actually says that these cycles bound, i.e., the interior region into which the simple-closed curve separates R^n, is the(an) object being bounded.\n\nWell, obviously not all cycles can be represented as the image of a sphere. Just take the boundary of two disjoint n+1-simplices in the space -- that boundary is not even connected, hence cannot be the image of a sphere.\n\nAs for the other question -- yes, the image of the sphere is always the boundary of the inside, but the inside is not always homeomorphic to a ball. To see this, consider an Alexander horned sphere with the origin on the inside. The outside is not simply connected, but the inside is. Now consider the image of the horned sphere under the map v ↦ v/|v|². This exchanges the inside and the outside, so now the inside is not simply connected and hence is not homeomorphic to a ball.\n\nGold Member\nBut it seems like you could do away with the first objection by saying that a cycle is the\nunion of continuous images of S^n .\n\nGold Member\nI guess I am unclear about the geometric definition of a cycle; I guess this would\n\ndepend on the choice of homology we make, but, given that these theories are all\n\nequivalent ( i.e., they output isomorphic groups for the same space), the choice should\n\nbe independent of choice of homology.\n\nI think Citan just gave an example of a cycle that is not the image of S^n with\n\nAlexander's horned sphere, as a space that is bound by a 2-dimensional object\n\nthat is not the image of a sphere.\n\nAnd, with respect to cycles, I would say that , in the most general sense, an n- cycle would\nbe an n-dimensional subspace that can be oriented (if the subspace is triangulable and can be made into a simplicial complex, then the net boundary should be zero); maybe others here can double-check.\n\nFirst, check the dimensions on the jordan curve theorem. Second, maps from the sphere are most definitely not a generalization, since they're a very special case of maps from the n-simplex.\n\nThird, I'd be interested in seeing a proof of the generalized Jordan curve theorem for continuous maps that doesn't render this circular: I.e. Showing that it separates without knowing anything about the homology of the sphere or Euclidean space."
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https://everything.explained.today/Electrical_load/ | [
"An electrical load is an electrical component or portion of a circuit that consumes (active) electric power, such as electrical appliances and lights inside the home. The term may also refer to the power consumed by a circuit. This is opposed to a power source, such as a battery or generator, which produces power.\n\nThe term is used more broadly in electronics for a device connected to a signal source, whether or not it consumes power. If an electric circuit has an output port, a pair of terminals that produces an electrical signal, the circuit connected to this terminal (or its input impedance) is the load. For example, if a CD player is connected to an amplifier, the CD player is the source and the amplifier is the load.\n\nLoad affects the performance of circuits with respect to output voltages or currents, such as in sensors, voltage sources, and amplifiers. Mains power outlets provide an easy example: they supply power at constant voltage, with electrical appliances connected to the power circuit collectively making up the load. When a high-power appliance switches on, it dramatically reduces the load impedance.\n\nIf the load impedance is not very much higher than the power supply impedance, the voltages will drop. In a domestic environment, switching on a heating appliance may cause incandescent lights to dim noticeably.\n\n## A more technical approach\n\nWhen discussing the effect of load on a circuit, it is helpful to disregard the circuit's actual design and consider only the Thévenin equivalent. (The Norton equivalent could be used instead, with the same results.) The Thévenin equivalent of a circuit looks like this:\n\ncenter|thumb|322px|The circuit is represented by an ideal voltage source Vs in series with an internal resistance Rs.\n\nWith no load (open-circuited terminals), all of\n\nVS\n\nfalls across the output; the output voltage is\n\nVS\n\n. However, the circuit will behave differently if a load is added. We would like to ignore the details of the load circuit, as we did for the power supply, and represent it as simply as possible. If we use an input resistance to represent the load, the complete circuit looks like this:\n\ncenter|322px|thumb|The input resistance of the load stands in series with Rs.\n\nWhereas the voltage source by itself was an open circuit, adding the load makes a closed circuit and allows charge to flow. This current places a voltage drop across\n\nRS\n\n, so the voltage at the output terminal is no longer\n\nVS\n\n. The output voltage can be determined by the voltage division rule:\n\nVOUT=VS\n\n RL RL+RS\n\nIf the source resistance is not negligibly small compared to the load impedance, the output voltage will fall.\n\nThis illustration uses simple resistances, but similar discussion can be applied in alternating current circuits using resistive, capacitive and inductive elements."
]
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.90566796,"math_prob":0.9684328,"size":2338,"snap":"2023-40-2023-50","text_gpt3_token_len":486,"char_repetition_ratio":0.13838904,"word_repetition_ratio":0.0,"special_character_ratio":0.19375534,"punctuation_ratio":0.09767442,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.964528,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-21T08:34:40Z\",\"WARC-Record-ID\":\"<urn:uuid:333f2c7c-50a7-4cc5-abc9-f02049ca24a2>\",\"Content-Length\":\"13370\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d6c10454-5f0f-4776-98b1-00f438267a9b>\",\"WARC-Concurrent-To\":\"<urn:uuid:0dc0dab2-82a3-4162-8ffc-d124948b8c58>\",\"WARC-IP-Address\":\"85.25.210.18\",\"WARC-Target-URI\":\"https://everything.explained.today/Electrical_load/\",\"WARC-Payload-Digest\":\"sha1:ZJIOO64634K2XKPDQ2NLCK6TPUTY2ESP\",\"WARC-Block-Digest\":\"sha1:ZLWS4PUPYC42DDA7FJ74YDKU6JL2B6VU\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233505362.29_warc_CC-MAIN-20230921073711-20230921103711-00847.warc.gz\"}"} |
https://puzzling.stackexchange.com/questions/40435/the-toroidal-chessboard?noredirect=1 | [
"The Toroidal Chessboard!\n\nInspired by this awesome question, and this old-but-gold question:\n\nWhat is the minimum number of Chess pieces to dominate(attack all squares) a 8x8 chessboard in shape of a toroid.",
null,
"image courtesy: Tex.stackexchange.com\n\n• How many squares are on the major and minor radius? 16 in both directions? – Aza Aug 10 '16 at 19:16\n• exactly my thoughts @Emrakul – lois6b Aug 10 '16 at 19:16\n• @Emrakul Added that part :) – ABcDexter Aug 10 '16 at 19:17\n• It would be nice if this question could be self-contained — ie. include what dominate means without the link. – Shuri2060 Aug 10 '16 at 19:19\n• While the torus image is very pleasing, the puzzle is far better solved with a regular grid in 2D. Whenever you move \"outside\" the board on one end, just \"enter\" it at some height (if horizontal) or width (if vertical) on the other side. Far less mind-bending. – BmyGuest Aug 10 '16 at 19:57\n\nWe can do it with\n\n$4$ queens:\n\nQ . . . . . . .\n. . . . Q . . .\n. . . . . . . .\n. . . . . . . .\n. . . Q . . . .\n. . . . . . . Q\n. . . . . . . .\n. . . . . . . .\n\nCan we do it with less pieces?\n\nNo.\nPlacing the first piece on the board dominates the cell in which it is placed and the cells it attacks.\nPlacing a second (third) piece does the same, but only adds to the set of dominated cells those which were not already dominated by the first (first and second).\nThere are $64$ cells on the board.\nA queen dominates the most cells at $28$, next are rooks at $15$ then bishops at $14$, then kings and knights at $9$, and finally pawns at $2$.\nSo to perform total domination with $3$ pieces would require use of at least $2$ queens (since $28+15+15<64$)\nPlacing the first queen dominates $28$ cells including at least $2$ cells in each row and $2$ cells in each column.\nPlacing the second queen can, therefore, only ever hope to add at most $28-8=20$ freshly dominated cells to the set of dominated cells.\nSo the $3^\\text{rd}$ piece would have to be a queen too (since $28+20+15<64$)\nWe can then check all arrangements of $3$ queens to see that the most cells that they can dominate is $58<64$.\n\nHere is some code to build and check states\n\n(it's set up for knights too, but this was not necessary in the end - see above)\n\nQ = 1\nN = 2\nVALS = ' QN'\n\ndef initBoard():\nreturn [[0 for c in range(8)] for r in range(8)]\n\ndef place(board, piece, r, c):\nboard[r][c] = piece\n\ndef dominated(board, r, c, justTruth=True):\nif board[r][c]:\nreturn True\nfor d in range(1,8):\nif board[r-d][c] == Q or board[r][c-d] == Q or board[r-d][c-d] == Q or board[(r+d)%8][c-d] == Q:\nreturn justTruth or 'q'\nfor rd, cds in ((-2,(-1, 1)), (-1,(-2, 2)), (1,(-2, 2)), (2,(-1, 1))):\nfor cd in cds:\nif board[(r+rd)%8][(c+cd)%8] == N:\nreturn justTruth or 'n'\nif justTruth:\nreturn False\nreturn '.'\n\ndef printBoard(board):\ns = ''\nfor r in range(8):\nfor c in range(8):\nif board[r][c]:\ns += VALS[board[r][c]] + ' '\nelse:\ns += dominated(board, r, c, False) + ' '\ns += '\\n'\nprint(s)\n\nSo let's first check my suggestion works, adding one piece at a time...\n\n>>> b = initBoard()\n>>> place(b, Q, 0, 0)\n>>> printBoard(b)\nQ q q q q q q q\nq q . . . . . q\nq . q . . . q .\nq . . q . q . .\nq . . . q . . .\nq . . q . q . .\nq . q . . . q .\nq q . . . . . q\n\n>>> place(b, Q, 1, 4)\n>>> printBoard(b)\nQ q q q q q q q\nq q q q Q q q q\nq . q q q q q .\nq . q q q q q .\nq q . . q . . q\nq . . q q q . .\nq q q . q . q q\nq q q . q . q q\n\n>>> place(b, Q, 4, 3)\n>>> printBoard(b)\nQ q q q q q q q\nq q q q Q q q q\nq q q q q q q .\nq . q q q q q .\nq q q Q q q q q\nq . q q q q . .\nq q q q q q q q\nq q q q q . q q\n\n>>> place(b, Q, 5, 7)\n>>> printBoard(b)\nQ q q q q q q q\nq q q q Q q q q\nq q q q q q q q\nq q q q q q q q\nq q q Q q q q q\nq q q q q q q Q\nq q q q q q q q\nq q q q q q q q\n\nNow let's check for possible lesser placements as described\n\n>>> from itertools import combinations\n>>> rcs = [(r, c) for r in range(8) for c in range(8)]\n>>> m = 0\n>>> for locs in combinations(rcs, 3):\n... b = initBoard()\n... for r, c in locs:\n... place(b, Q, r, c)\n... d = sum(dominated(b, r, c) for r in range(8) for c in range(8))\n... if d > m:\n... m = d\n... printBoard(b)\n... print(d)\n... print()\n...\nQ Q Q q q q q q\nq q q q . . . q\nq q q q q . q q\nq q q q q q q q\nq q q . q q q .\nq q q q q q q q\nq q q q q . q q\nq q q q . . . q\n\n54\n\nQ Q q q q q q q\nq q q q Q q q q\nq q q q q q q q\nq q q q q q q .\nq q . . q q . q\nq q . q q q q .\nq q q q q . q q\nq q q . q . q q\n\n55\n\nQ Q q q q q q q\nq q q q . . q q\nq q q q . q q q\nq q q q q q q .\nq q q Q q q q q\nq q q q q q q .\nq q q q . q q q\nq q q q . . q q\n\n56\n\nQ q q q Q q q q\nq q . q q q q q\nq q q q q . q q\nq q q q q q . q\nq Q q q q q q q\nq q q q q q . q\nq q q q q . q q\nq q . q q q q q\n\n58\n\nIn fact\n\nThere are $832$ possible ways to choose $4$ of the $64$ cells such that placing queens in those cells would totally dominate the torus.\nIf we reduce this to the symmetry of the torus (we can shift rows or columns by any number and we can rotate the board in quarters) that yields $70$ possible arrangements.\n\n• Will add some code for double checking it shortly... – Jonathan Allan Aug 10 '16 at 20:46\n• Added code, this could be used to brute force the solution once extended to include other pieces – Jonathan Allan Aug 10 '16 at 20:59\n• Update: No lesser possible. – Jonathan Allan Aug 10 '16 at 22:59\n• Awesome. had to check you code again and again(on my system)... – ABcDexter Aug 12 '16 at 6:13\n\nTwo bishops?\n\nExplanation:\n\nIf you put on bishop on white and one on black, they should be able to spiral throughout the torus and eventually get every space.\n\n• This was my initial thought but I believe that the diagonals wrap. If you put a piece at A1 diagonal to H8 then wraps back to A1. Same with the other diagonals B1>H7>A8>B1 and around we go. – gtwebb Aug 10 '16 at 19:47\n• Nope, doesn't work. (Gray is the actual board, the others are just for visualization.) – Deusovi Aug 10 '16 at 19:53\n\nI believe the answer is\n\n5, the same as a regular chess board, see here for regular solution which has also been copied below\n\nBecause\n\nBasic trial and error seemed to suggest 4 was not even close to enough, Q1 can cover 22 squares (7 each row, column, diagonal plus standing cell), Q2 can cover 16 squares (5 each row, column, diagonal plus standing cell, since Q1 covers 2 in each of the rows, columns, diagonals), This leaves 2 queens to cover 26 cells and each queen can cover less then the last due to already covered cells so I don't think this is possible. (Incorrect as I started in the corner and was only looking at 1 diagonal)\n\nBelow\n\n-----------------------------------------------------------------------\n\nYes. The minimum number of pieces required is 5.\n\n5 queens can be places such that they cover every space on the board, as in the following example:",
null,
"",
null,
"There are 12 such arrangements, along with rotation and reflection of each of them.\nEdit: The above proves that 5 queens is enough, but it doesn't prove that 4 queens isn't enough. According to this MathOverflow question and its answers, there is no easy logical or mathematical proof, but it has been proven by completely evaluating all possible arrangements of queens on a board. See this list to see the minimum number of required queens for any square board from $1\\times1$ to $18\\times18$.\n\nSolution:\n\nYou need 2 queens.\n\nbecause:\n\nThe red queen covers horizontal and vertical. plus all the black tiles in diagonal.\nThe other queen covers all the white ones in diagonal.\nSince all sides are together, the diagonal are infinite",
null,
"• Nope, doesn't work. (Gray is the actual board, the others are just for visualization.) – Deusovi Aug 10 '16 at 19:52\n• This does not work link. Oh, @Deusovi again! :c( – BmyGuest Aug 10 '16 at 19:55\n• oh ... btw, how did you do the image, @deusovi? – lois6b Aug 10 '16 at 20:02\n• @lois6b: Google Sheets. – Deusovi Aug 10 '16 at 20:42"
]
| [
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"https://i.stack.imgur.com/DRJV2.png",
null,
"https://i.stack.imgur.com/3MsU5.gif",
null,
"https://i.stack.imgur.com/EKhvj.png",
null,
"https://i.stack.imgur.com/5mR7q.png",
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.8321512,"math_prob":0.99588656,"size":6408,"snap":"2019-43-2019-47","text_gpt3_token_len":1989,"char_repetition_ratio":0.2574953,"word_repetition_ratio":0.41063124,"special_character_ratio":0.3687578,"punctuation_ratio":0.18568103,"nsfw_num_words":1,"has_unicode_error":false,"math_prob_llama3":0.99784356,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,8,null,null,null,null,null,8,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-14T08:58:29Z\",\"WARC-Record-ID\":\"<urn:uuid:7fd65992-48c9-4e59-be32-e7a6e6c92a86>\",\"Content-Length\":\"177124\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1604d992-76f3-455d-b5d4-f7c6ebd74f3f>\",\"WARC-Concurrent-To\":\"<urn:uuid:acb0451d-668f-4683-81fa-171b38a47def>\",\"WARC-IP-Address\":\"151.101.193.69\",\"WARC-Target-URI\":\"https://puzzling.stackexchange.com/questions/40435/the-toroidal-chessboard?noredirect=1\",\"WARC-Payload-Digest\":\"sha1:Y7HASJD6CC63JQBF2MRDYCJ3RU7UPIDJ\",\"WARC-Block-Digest\":\"sha1:TGPZJ3HXBWWQXDI5EY2MPCU7LI4SVYMS\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570986649841.6_warc_CC-MAIN-20191014074313-20191014101313-00306.warc.gz\"}"} |
https://arturobaldo.com.ar/tag/sklearn/ | [
"Categories\n\n## Machine Learning – Weighted Train Data\n\nLast post talked about an introduction to Machine Learning and how outcomes can be predicted using sklearn’s LogisticReggression.\n\nSometimes, the input data could require additional processing to prefer certain classes of information, that it considered more valuable or more representative to the outcome.\n\nThe LogisticRegression model allows to set the preference, or weight, at the time of being created, or later when being fitted.\n\nThe data used on the previous entry had four main classes: DRAFT, ACT, SLAST and FLAST. Once it is encoded and fitted, it can be selected by its index. I prefer to initialize some mnemonics selectors to ease the coding and make the entire code more human friendly.\n\n``````x_columns_names = ['DRAFT', 'ACT', 'SLAST', 'FLAST']\ny_columns_names = ['PREDICTION']\n\n# Indexes for columns, used for weighting\nDRAFT = 0\nACT = 1\nSLAST = 2\nFLAST = 3\n\n# Weights\nDRAFT_WEIGHT = 1\nACT_WEIGHT = 1\nSLAST_WEIGHT = 1\nFLAST_WEIGHT = 1``````\n\nThe model can be initialized lated using the following method, where the class_weight parameter is used referencing the previous helpers.\n\n``````model = LogisticRegression(\nsolver='lbfgs',\nmulti_class='multinomial',\nmax_iter=5000,\nclass_weight={\nDRAFT: DRAFT_WEIGHT,\nACT: ACT_WEIGHT,\nSLAST: SLAST_WEIGHT,\nFLAST: FLAST_WEIGHT,\n})``````\n\nCategories\n\n## Machine Learning – Classification and Regression Analysis\n\nMachine Learning is the science and art of programming computers so they can learn from data.\n\nFor example, your spam filter is a Machine Learning program that can learn to flag spam given examples of spam emails (flagged by users, detected by other methods) and examples of regular (non-spam, also called “ham”) emails.\n\nThe examples that the system uses to learn are called the training set. The new ingested data is called the test set. The performance measure of the prediction model is called accuracy and it’s the objetive of this project.\n\nThe tools\n\nTo tackle this, Python (version 3) will be used, among the package scikit-learn. You can find more info about this package on the official page.\n\nhttps://scikit-learn.org/stable/tutorial/basic/tutorial.html\n\nSupervised learning\n\nIn general, a learning problem considers a set of n samples of data and then tries to predict properties of unknown data. If each sample is more than a single number and, for instance, a multi-dimensional entry (aka multivariate data), it is said to have several attributes or features.\n\nSupervised learning consists in learning the link between two datasets: the observed data X and an external variable y that we are trying to predict, usually called “target” or “labels”. Most often, y is a 1D array of length n_samples.\n\nAll supervised estimators in scikit-learn implement a fit(X, y) method to fit the model and a predict(X) method that, given unlabeled observations X, returns the predicted labels y.\n\nIf the prediction task is to classify the observations in a set of finite labels, in other words to “name” the objects observed, the task is said to be a classification task. On the other hand, if the goal is to predict a continuous target variable, it is said to be a regression task.\n\nWhen doing classification in scikit-learn, `y` is a vector of integers or strings.\n\nThe Models\n\nLinearRegression, in its simplest form, fits a linear model to the data set by adjusting a set of parameters in order to make the sum of the squared residuals of the model as small as possible.\n\nLogisticRegression, which has a very counter-intuitive model, is a better choice when linear regression is not the right approach as it will give too much weight to data far from the decision frontier. A linear approach is to fit a sigmoid function or logistic function.\n\nThe Data\n\nData is presented on a CSV file. It has around 2500 rows, with 5 columns. Correct formatting and integrity of values cannot be assured, so additional processing will be needed. The sample file is like this.\n\nThe Code\n\nWe need three main libraries to start:\n\n• numpy, which basically is a N-dimensional array object. It also has tools for linear algebra, Fourier transforms and random numbers.\nIt can be used as an efficient multi-dimensional container of generic data, where arbitrary data-types can be defined.\n• pandas, which provides high-performance and easy-to-use data structures and data analysis tools simple and efficient tools for data mining and data analysis\n• sklearn, the main machine learning library. It has capabilities for classification, regression, clustering, dimensionality reduction, model selection and data preprocessing.\n\nA non essential, but useful library is matplotlib, to plot sets of data.\n\nIn order to provide data for sklearn models to work, it has to be encoded first. As the sample data has strings, or labels, a LabelEncoder is needed. Next, the prediction model is declared, where a LogisticRegression model is used.\n\nThe input data file path is also declared, in order to be loaded with pandas.read_csv().\n\n``````import pandas as pd\nimport numpy as np\nimport matplotlib.pyplot as pyplot\n\nfrom sklearn.preprocessing import LabelEncoder\nfrom sklearn.linear_model import LogisticRegression\n\nencoder = LabelEncoder()\nmodel = LogisticRegression(\nsolver='lbfgs', multi_class='multinomial', max_iter=5000)\n\n# Input dataset\nfile = \"sample_data.csv\"``````\n\nThe CSV file can be loaded into a pandas dataframe in a single line. The library also provides a convenient method to remove any rows with missing values.\n\n``````# Use pandas to load csv. Pandas can eat mixed data with numbers and strings\ndata = pd.read_csv(file, header=0, error_bad_lines=False)\n# Remove missing values\ndata = data.dropna()\n\nprint(\"Valid data items : %s\" % len(data))``````\n\nOnce loaded, the data needs to be encoded in order to be fitted into the prediction model. This is handled by the previously declared LabelEncoder. Once encoded, the x and y datasets are selected. The pandas library provides a way to drop entire labels from a dataframe, which allows to easily select data.\n\n``````encoded_data = data.apply(encoder.fit_transform)\nx = encoded_data.drop(columns=['PREDICTION'])\ny = encoded_data.drop(columns=['DRAFT', 'ACT', 'SLAST', 'FLAST'])``````\n\nThe main objective is to test against different lengths of train and test data, to find out how much data provides the best accuracy. The lengths of data will be incremented in steps of 100 to get a broad variety of results.\n\n``````length = 100\nscores = []\nlenghts = []\nwhile length < len(x):\nx_train = x[:length]\ny_train = y[:length]\nx_test = x.sample(n=length)\ny_test = y.sample(n=length)\nprint(\"Fitting model for %s training values\" % length)\ntrained = model.fit(x_train, y_train.values.ravel())\nscore = model.score(x_test, y_test)\nprint(\"Score for %s training values is %0.6f\" % (length, score))\nlength = length + 100\nscores.append(score)\nlenghts.append(length)``````\n\nFinally, a plot is made with the accuracy scores.\n\n``````pyplot.plot(lenghts,scores)\npyplot.ylabel('accuracy')\npyplot.xlabel('values')\npyplot.show()``````"
]
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.86796135,"math_prob":0.9470093,"size":6015,"snap":"2021-04-2021-17","text_gpt3_token_len":1291,"char_repetition_ratio":0.104142405,"word_repetition_ratio":0.002105263,"special_character_ratio":0.21346633,"punctuation_ratio":0.122666664,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.995581,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-04-22T02:59:06Z\",\"WARC-Record-ID\":\"<urn:uuid:8d7c073d-d2b3-47e0-a56c-8f3a0ac08a64>\",\"Content-Length\":\"127842\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b09760cd-9d28-40f8-a9f3-9818296a2e8b>\",\"WARC-Concurrent-To\":\"<urn:uuid:33943c22-fdbf-4c5f-a519-22e4bb7ce71b>\",\"WARC-IP-Address\":\"157.245.248.143\",\"WARC-Target-URI\":\"https://arturobaldo.com.ar/tag/sklearn/\",\"WARC-Payload-Digest\":\"sha1:HG7QOCUI74HAIEREN26MCXIOD5CAWGUY\",\"WARC-Block-Digest\":\"sha1:X53PD254ANZE3VQIKY6QMEP775RQUY7X\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-17/CC-MAIN-2021-17_segments_1618039560245.87_warc_CC-MAIN-20210422013104-20210422043104-00148.warc.gz\"}"} |
https://softwareengineering.stackexchange.com/questions/tagged/operator-precedence?tab=Newest | [
"# Questions tagged [operator-precedence]\n\nThe tag has no usage guidance.\n\n14 questions\nFilter by\nSorted by\nTagged with\n610 views\n\n### What is the logic in the order of operator precedence? [closed]\n\nAbsolutely academic context question- I found countless articles listing the order of operator precedence in all languages, but what is the logical reasoning behind that specific order? For clarity ...\n1k views\n\n### Should I use parenthesis around every operators?\n\nThe facts This is a very similar question to this one, but here I am talking about a more general case the MISRA-C3 Rule 5.0.2 or the SEI CERT C EXP00-C rule (more permissive). Within MISRA-C3 I ...\n178 views\n\n### Operators precedence\n\nI have a code snippet in Java: int y = ++x * 5 / x-- + --x; So my confusion was since x--(postfix) has higher precedence than ++x(prefix) operator so x-- should be executed first then ++x.But a ...\n148 views\n\n### Operators precedence in java (unary plus and addition) [closed]\n\nI'm having trouble in figuring out why the output for theses two lines is different .. public static void main(String[] args) { System.out.println(\"6.0+1=\"+6.0+1); System.out.println(\"6.0+1=\"+(...\n1k views\n\n### Shunting-yard algorithm and unary minus\n\nI am attempting to implement a shunting-yard algorithm for a calculator following the rules laid out in https://en.wikipedia.org/wiki/Shunting-yard_algorithm . When programming the unary minus, ...\n1k views\n\n### Is order of arguments in an arithmetic expression important to achieve as most exact result as possible (speed is not necessary)?\n\nActually, in this question I do not ask about particular language or architecture, however I understand there might be some differences. In physics / engineering it is usually better to handle ...\n152 views\n\n### Proper way to interpret this dereference operation?\n\nI've seen this example in a text book and am a little confused how to interpret the operator precedence rules. Given this struct: typedef struct { char *data; size_t start, end; } ...\n4k views\n\n### Precedence of function in Shunting-yard algorithm\n\nI am working through the Shunting-yard algorithm, as described by wikipedia. The description of the algorithm when dealing with operators is as follows: If the token is an operator, o1, then: ...\n134 views\n\n### The difference between (-(a*b)) and ((-a)*b)\n\nOne of our teachers said that there is just one example that there is a difference between (-(a*b)) and ((-a)*b). He said by using two's complement you can find one. I am trying to find this example. ...\n270 views\n\n### Order of Operations Annoyance [duplicate]\n\nIn most programming languages (C#, JavaScript, Java) the order of operations precedence has that equality comparison come BEFORE bitwise comparisons. This means that if you have a bit operation and ...\n782 views\n\n### Should ** bind more tightly than !, ~?\n\nDesigning a programming language, I'm including the ** exponentiation operator. In Fortran and Python, the two languages I know of which have this operator, it binds more tightly than unary minus, ...\n53k views\n\n### Should I use parentheses in logical statements even where not necessary?\n\nLet's say I have a boolean condition a AND b OR c AND d and I'm using a language where AND has a higher order of operation precedent than OR. I could write this line of code: If (a AND b) OR (c AND d)..."
]
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.9041497,"math_prob":0.60629004,"size":4009,"snap":"2019-35-2019-39","text_gpt3_token_len":950,"char_repetition_ratio":0.1318352,"word_repetition_ratio":0.0,"special_character_ratio":0.2516837,"punctuation_ratio":0.15433674,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9507835,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-09-22T22:02:57Z\",\"WARC-Record-ID\":\"<urn:uuid:e372f870-1597-4998-99dd-a4c80d29a78d>\",\"Content-Length\":\"153898\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:cf5979f7-74f3-406e-8557-c4813f8a39a5>\",\"WARC-Concurrent-To\":\"<urn:uuid:8fa972ac-88b7-48ba-99f2-cc7899830632>\",\"WARC-IP-Address\":\"151.101.1.69\",\"WARC-Target-URI\":\"https://softwareengineering.stackexchange.com/questions/tagged/operator-precedence?tab=Newest\",\"WARC-Payload-Digest\":\"sha1:UWX3LR2AW456SH44I3YFQYOEPNL72RM2\",\"WARC-Block-Digest\":\"sha1:A6GDMMJV7ZVFFHZ6HFDQ5FYX6ZMMIHRO\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-39/CC-MAIN-2019-39_segments_1568514575674.3_warc_CC-MAIN-20190922201055-20190922223055-00184.warc.gz\"}"} |
https://docs.faculty.ai/user-guide/experiments/index.html | [
"# Experiments¶\n\nIncreasingly, data science projects do not simply end with a few key takeaway conclusions, but result in trained machine learning models going into production. With these models taking ever more critical roles in organisations’ services and tooling, it’s important for us to track how models were created, know why a particular model was selected over other candidates, and be able to reproduce them when necessary.\n\nExperiments in Faculty Platform makes it easy to keep track of this information. We’ve integrated MLflow, a popular open source project providing tooling for the data science workflow, into Faculty, requiring adding only minor annotations to your existing code.\n\nFor more information on why we introduced the experiment tracking feature, see our blog post on it.\n\n## Getting started¶\n\n### Start tracking¶\n\nAll you need to do to use MLflow and the experiment tracking feature in Faculty is to import the Python library and start logging experiment runs:\n\nimport mlflow\n\nwith mlflow.start_run():\nmlflow.log_param(\"gamma\", 0.0003)\nmlflow.log_metric(\"accuracy\", 0.98)\n\n\nThis will create a new run in the ‘Default’ experiment of the open project, which you can view in the Experiments screen:",
null,
"Clicking on the run will open a more detailed view:",
null,
"### Customising¶\n\nIn the run history screen, we can customise the displayed columns in the top right, and sort columns by clicking on a column label.\n\nWith multiple runs, the ‘Filter’ option allows to filter runs based on logged information:",
null,
"## What can I log?¶\n\n### Model parameters, tags, performance metrics¶\n\nMLflow and experiment tracking log a lot of useful information about the experiment run automatically (start time, duration, who ran it, git commit, etc.), but to get full value out of the feature you need to log useful information like model parameters and performance metrics during the experiment run.\n\nAs shown in the above example, model parameters, tags and metrics can be logged. These are shown both in the list of runs for an experiment and in the run detail screen. In the following, more complete example, we’re logging multiple useful metrics on the performance of a scikit-learn Support Vector Machine classifier:\n\nfrom sklearn import datasets, svm, metrics\nimport mlflow\n\n# Load and split training data\ndata_train, data_test, target_train, target_test = train_test_split(\ndigits.data, digits.target, random_state=221\n)\n\nwith mlflow.start_run():\n\ngamma = 0.01\nmlflow.log_param(\"gamma\", gamma)\nmlflow.set_tag(\"model\", \"svm\")\n\n# Train model\nclassifier = svm.SVC(gamma=gamma)\nclassifier.fit(data_train, target_train)\n\n# Evaluate model performance\npredictions = classifier.predict(data_test)\naccuracy = metrics.accuracy_score(target_test, predictions)\nprecision = metrics.precision_score(target_test, predictions, average=\"weighted\")\nrecall = metrics.recall_score(target_test, predictions, average=\"weighted\")\n\nmlflow.log_metric(\"accuracy\", accuracy)\nmlflow.log_metric(\"precision\", precision)\nmlflow.log_metric(\"recall\", recall)\n\n\nIf we then run the above code with different values of the gamma parameter, we can see and compare various runs and their metrics in the run history screen:",
null,
"We can also compare runs visually by selecting runs and clicking ‘Compare’:",
null,
"### Models¶\n\nIn addition to parameters and metrics, we can also log artifacts with experiment runs. These can be anything that can be stored in a file, including images and models themselves.\n\nLogging models is fairly straightforward: first import the module in MLflow that corresponds to the model type you’re using, and call its log_model function. In the above example:\n\nfrom sklearn import datasets, svm, metrics\nimport mlflow\nimport mlflow.sklearn\n\n# Load and split training data\n# ...\n\nwith mlflow.start_run():\n\ngamma = 0.01\nmlflow.log_param(\"gamma\", gamma)\n\n# Train model\nclassifier = svm.SVC(gamma=gamma)\nclassifier.fit(data_train, target_train)\n\n# Log model\nmlflow.sklearn.log_model(classifier, \"svm\")\n\n# Evaluate model performance\n# ...\n\n\nNote\n\nThe following model types are supported in MLflow:\n\n• Keras (see mlflow.keras.log_model)\n• TensorFlow (see mlflow.tensorflow.log_model)\n• Spark (see mlflow.spark.log_model)\n• scikit-learn (see mlflow.sklearn.log_model)\n• MLeap (see mlflow.mleap.log_model)\n• H2O (see mlflow.h2o.log_model)\n• PyTorch (see mlflow.pytorch.log_model)\n\nIt’s also possible to wrap arbitrary Python fuctions in an MLflow model with mlflow.pyfunc.\n\nThe model will then be stored as artifacts of the run in MLflow’s MLmodel serialisation format. Such models can be inspected and exported from the artifacts view on the run detail page:",
null,
"Context menus in the artifacts view provide the ability to download models and artifacts from the UI or load them into Python for further use.\n\n### Artifacts¶\n\nIt’s also possible to log any other kind of file as an artifact of a run. For example, to store a matplotlib plot in a run, first write it out as a file, then log that file as an artifact:\n\nimport os\nimport tempfile\nimport numpy\nfrom matplotlib import pyplot\nimport mlflow\n\nwith mlflow.start_run():\n\n# Plot the sinc function\nx = numpy.linspace(-10, 10, 201)\npyplot.plot(x, numpy.sinc(x))\n\n# Log as MLflow artifact\nwith tempfile.TemporaryDirectory() as temp_dir:\nimage_path = os.path.join(temp_dir, \"sinc.svg\")\npyplot.savefig(image_path)\nmlflow.log_artifact(image_path)\n\n\nThe plot is then stored with the run’s artifacts and can be previewed and exported from the UI:",
null,
"By the same mechanism, many types of files can be stored and previewed as part of an experiment run’s artifacts. A whole directory of artifacts can also be logged with mlflow.log_artifacts().\n\n## Multiple experiments¶\n\nEach Faculty project has a ‘Default’ experiment that runs will be stored in, unless configured otherwise. However, if you have a lot of experiment runs, you may wish to break them up into multiple experiments. To do this, just set the name of the experiment you wish to use in your notebook before starting any runs:\n\nimport mlflow\n\nmlflow.set_experiment(\"SVM classifier\")\n\nwith mlflow.start_run():\n# ...\n\n\nIf the experiment does not already exist, it will be created for you and appear as a new card in the run history screen:",
null,
"Tags can help to categorise runs within an experiment.\n\nTo make predictions using a logged model from an experiment, we can use MLFlow’s mlflow.pyfunc.load_model interface. To illustrate how to use this functionality in the context of an app, assume we have trained a logistic regression to use a person’s age to predict whether they earn more than £50k, and logged it with an experiment run. To use the model for making predictions via an app, just load the model:\n\nimport mlflow.pyfunc\nimport pandas as pd\n\n# Load logged model using model ID and run ID\nMODEL_URI = \"logistic_regression\"\nRUN_ID = \"f5121088-8b72-4fd7-a5fd-50653c988f4d\"\n\n# Interpret target values\nTARGET_LABELS = {0:\"< 50k\", 1:\"> 50k\"}\n\n# Use @app.route decorator to register run_prediction as endpoint on /\[email protected](\"/predict/<int:age>\")\ndef run_prediction(age):\ndf = pd.DataFrame({\"age\": [age]})\n\n# Run prediction\nprediction = MODEL.predict(df)\n\n# Interpret prediction value\nprediction_label = TARGET_LABELS[prediction]\n\nreturn jsonify({\"prediction\": prediction_label})\n\n# Run app\nif __name__ == \"__main__\":\napp.run(port=5000, debug=True)\n\n\nFinally, to get a prediction, send a GET request with a specific value for age, for example 55, to the server:\n\nimport requests\n\nage = 55\n\nrequests.get(\"http://127.0.0.1:5000/predict/{}\".format(age)).json()\n\n\nThis will decode the JSON response from the API and return a Python dictionary {'prediction': '< 50k'}.\n\n## Using experiment tracking from Faculty Jobs¶\n\nIt’s also possible to use experiment tracking with jobs. Just include the same MLflow tracking code as above in your Python script which gets run by the job, and experiments will be logged by the job automatically when run.\n\nExperiments run from jobs will display the job and job run number used to generate them. Clicking on the job / run displayed in the experiment run will take you to the corresponding job, where you can see its logs and other runtime information."
]
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"https://docs.faculty.ai/_images/first_run.png",
null,
"https://docs.faculty.ai/_images/first_run_detail.png",
null,
"https://docs.faculty.ai/_images/filter.png",
null,
"https://docs.faculty.ai/_images/run_view_metrics.png",
null,
"https://docs.faculty.ai/_images/compare_view_metrics.png",
null,
"https://docs.faculty.ai/_images/detail_view_svm_model.png",
null,
"https://docs.faculty.ai/_images/detail_view_artifact.png",
null,
"https://docs.faculty.ai/_images/svm_run_view.png",
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]
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https://www.cl.cam.ac.uk/~jrh13/papers/arith18.html | [
"# An Implementation of the IEEE 754R Decimal Floating-Point Arithmetic Using the Binary Encoding Format\n\nMarius Cornea, Cristina Anderson, John Harrison, Ping Tak Peter Tang, Eric Schneider, Charles Tsen. Proceedings of the 18th IEEE Symposium on Computer Arithmetic, Montpellier, France 2007, IEEE Computer Society Press, pp. 148-157 2003.\n\n## Abstract:\n\nThe IEEE Standard 754-1985 for Binary Floating-Point Arithmetic was revised, and an important addition is the definition of decimal floating-point arithmetic. This is aimed mainly to provide a robust, reliable framework for financial applications that are often subject to legal requirements concerning rounding and precision of the results, because the binary floating-point arithmetic may introduce small but unacceptable errors. Using binary floating-point calculations to emulate decimal calculations in order to correct the issue has led to the existence of numerous proprietary software packages, each with its own characteristics and capabilities. IEEE 754R decimal arithmetic should unify the ways decimal floating-point calculations are carried out on various platforms. New algorithms and properties are presented in this paper which were used in what is likely the first complete implementation in software of the IEEE 754R decimal floating-point arithmetic, with emphasis on using efficiently binary operations. Performance results are included, showing promise that our approach is viable for applications that require decimal floating-point calculations.\n\n## Bibtex entry:\n\n```@INPROCEEDINGS{harrison-arith18,\nauthor = \"Marius Cornea and Cristina Anderson and\nJohn Harrison and Ping Tak Peter Tang and\nEric Schneider and Charles Tsen\",\ntitle = \"An Implementation of the {IEEE} {754R} Decimal\nFloating-Point Arithmetic Using the Binary Encoding\nFormat\",\nbooktitle = \"Proceedings, 18th {IEEE} Symposium\non Computer Arithmetic\","
]
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https://datascience.stackexchange.com/questions/48169/naive-bayes-classifier-discriminant-function | [
"# Naive Bayes Classifier - Discriminant Function\n\nTo classify my samples, I decided to use Naive Bayes classifier, but I coded it, not used built-in library functions.\n\nIf I use this equality, I obtain nice classification accuracy: p1(x) > p2(x) => x belongs to C1\n\nHowever, I could not understand why discriminant functions produce negative values. If they are probability functions, I think they must generate a value between 0 and 1.\n\nIs there anyone who can explain the reason ?\n\nIn Naive Bayes, for the case of two classes, a discriminant function could be $$D(\\boldsymbol{x}) = \\frac{P(\\boldsymbol{x}, c=1)}{P(\\boldsymbol{x}, c=0)}$$ which can be anywhere in $$[0, +\\infty)$$, and decides $$c=1$$ if $$D(\\boldsymbol{x})>1$$, $$c=0$$ otherwise, or it could be the logarithm of that value\n$$d(\\boldsymbol{x}) = \\text{log}\\frac{P(\\boldsymbol{x}, c=1)}{P(\\boldsymbol{x}, c=0)}=\\text{log}P(\\boldsymbol{x}, c=1)-\\text{log}P(\\boldsymbol{x}, c=0)$$ which can be anywhere in $$(-\\infty, +\\infty)$$ (handling zero probability as a special case), and decides $$c=1$$ if $$d(\\boldsymbol{x})>0$$, $$c=0$$ otherwise.\nAs a side note, $$P(\\boldsymbol{x}, c=k)$$ in Naive Bayes is calculated as $$P(\\boldsymbol{x}, c=k)=P(c=k)\\prod_{i=1}^{d}P(x_i|c=k)$$ or equivalently for log probabilities as $$\\text{log}P(\\boldsymbol{x}, c=k)=\\text{log}P(c=k) + \\sum_{i=1}^{d}\\text{log}P(x_i|c=k)$$"
]
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http://zjtjxy.net/Item/15645.aspx | [
"# var myDate = new Date(); myDate.getYear(); //获取当前年份(2位) myDate.getFullYear(); //获取完整的年份(4位,1970-????) myDate.getMonth(); //获取当前月份(0-11,0代表1月) myDate.getDate(); //获取当前日(1-31) myDate.getDay(); //获取当前星期X(0-6,0代表星期天) myDate.getTime(); //获取当前时间(从1970.1.1开始的毫秒数) myDate.getHours(); //获取当前小时数(0-23) myDate.getMinutes(); //获取当前分钟数(0-59) myDate.getSeconds(); //获取当前秒数(0-59) myDate.getMilliseconds(); //获取当前毫秒数(0-999) myDate.toLocaleDateString(); //获取当前日期 var mytime=myDate.toLocaleTimeString(); //获取当前时间 myDate.toLocaleString( ); //获取日期与时间 var week; if(new Date().getDay()==0) week=\"星期日\" if(new Date().getDay()==1) week=\"星期一\" if(new Date().getDay()==2) week=\"星期二\" if(new Date().getDay()==3) week=\"星期三\" if(new Date().getDay()==4) week=\"星期四\" if(new Date().getDay()==5) week=\"星期五\" if(new Date().getDay()==6) week=\"星期六\" document.write( myDate.toLocaleDateString()+\" \"+ week +\" \"+mytime);\n\n 序号 课题名称 负责人 1 郑小忠 2 骆中慧\n\n20181225"
]
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https://eduladder.com/viewnotes/185/VTU-SYLLABUS-2010-Civil-FLUID-MECHANICS-10CV35-Engineering | [
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"This is designed to incentify community members as a proof of contribution token.\n\nUsing this You can,Buy courses,Reward others and exchange for real money.\n\nWHITE PAPER COURSES\n\nReal Problems! Real Experts!\n\nThe Eduladder is a community of students, teachers, and programmers. We help you to solve your academic and programming questions fast.\nWatch related videos of your favorite subject.\nConnect with students from different parts of the world.\nApply or Post Jobs, Courses ,Internships and Volunteering opportunity. For FREE\nSee Our team\nWondering how we keep quality?\nGot unsolved questions?\n\nYou are here:Open notes-->Syllabus-->VTU-SYLLABUS-2010-Civil-FLUID-MECHANICS-10CV35-Engineering\n\n# VTU SYLLABUS 2010 (Civil) FLUID MECHANICS [10CV35] Engineering\n\n10 CV 35 FLUID MECHANICS\nSub. Code: 10CV 35 IA Marks: 25\nHrs/Week : 04 Exam Hours: 03\nTotal Hrs: 52 Exam Marks: 100\nPART-A\nUNIT-1: BASIC PROPERTIES OF FLUIDS\nIntroduction, Definiton of Fluid, Systems of units, properties of\nfluid: Mass density, Specific weight, Specific gravity, Specific\nvolume, Viscosity, Cohesion, Adhesion, Surface tension,&\nCapillarity. Newton�s law of viscosity (theory &\nproblems).Capillary rise in a vertical tube and between two\nplane surfaces (theory & problems). 06 Hrs.\nUNIT-2: PRESSURE AND ITS MEASUREMENT\nDefinition of pressure, Pressure at a point, Pascal�s law,\nVariation of pressure with depth. Types of pressure. Vapour\npressre. Measurement of pressure using a simple, differential &\ninclined manometers (theory & problems). Introduction to\nMechanical and electronic pressure measuring devices.\n07 Hrs.\nUNIT-3: HYDROSTATIC PRESSURE ON SURFACES\nBasic definitions, equations for hydrostatic force and depth of\ncentre of pressure for Vertical and inclined submerged laminae\n(plane and curved )- Problems. 06 Hrs\nUNIT-4: KINEMATICS OF FLOW\nIntroduction, methods of describing fluid motion, definitions of\ntypes of fluid flow, streamline, pathline, streamtube. Three\ndimensional continuity equation in Cartesian Coordinates (\nderivation and problems ). General Continuity equation (\nproblems ). Velocity potential, Stream function, Equipotential\nline, Stream line- problems, Physical concepts of\nStreamfunction. Introduction to flow net.\n07 Hrs\nPART-B\nUNIT-5: DYNAMICS OF FLUID FLOW\nIntroduction, Energy possessed by a fluid body. Euler�s equation\nof motion along a streamline and Bernoulli�s equation.\nAssumptions and limitations of Bernoulli�s equation. Problems\non applications of Bernoulli�s equation (with and without\nlosses). Introduction to kinetic energy correction factor.\nMomentum equation problems on pipe bends.\n07 Hrs\nUNIT-6: PIPE FLOW\nIntroduction, losses in pipe flow,. Darcy-Weisbach equation for\nhead loss due to friction in a pipe. Pipes in series, pipes in\nparallel, equivalent pipe-problems. Minor losses in pipe flow,\nequation for head loss due to sudden expansion- problems.\nWater hammer in pipes, equation for pressure rise due to gradual\n12\nvalve closure & sudden closure for rigid and elastic pipesproblems.\n07 Hrs\nUNIT-7: DEPTH AND VELOCITY MEASUREMENTS\nIntroduction, Measurement of depth, point & hook gauges, self\nrecording gauges. Staff gauge, Weight gauge, float gauge.\nMeasurement of velocity- single and double gauges, pitot tube,\nCurrent meter- Problems.\n06 Hrs\nUNIT-8: DISCHARGE MEASUREMENTS\nIntroduction, Venturimeter, Orificemeter, Rotometer,\nVenturiflume, Triangular notch, Rectangular notch, Cipolletti\nnotch, Ogee weir and Broad crested weir, Small orifices-\nProblems. 06 Hrs\nTEXT BOOKS:\n1. �A TextBook of Fluid mechanics & Hydraulic\nMachines�- R.K.Rajput, S.Chand & Co, New Delhi,\n2006 Edition.\n2. �Principles of Fluid Mechanics and Fluid Machines�-\nN.Narayana Pillai, Universities Press(India),\n3. � Fluid Mechanics and Turbomachines�- Madan Mohan\nDas, PHI Learning Pvt. Limited, New Delhi. 2009\nEdition.\nREFERENCE BOOKS:\n1. � Fundamentals of Fluid Mechanics� � Bruce R. Munson,\nDonald F.Young, Theodore H. Okiishi, Wiley India, New\nDelhi, 2009 Edition.\n2. �Introduction To Fluid Mechanics� � Edward j.\nShaughnessy,jr; Ira m. Katz:; James p Schaffer, Oxford\nUniversity Press, New Delhi, 2005 Edition.\n3. � Text Book Of Fluid Mechanics& Hydralic Machines�-\nR.K.Bansal, Laxmi Publications, New Delhi, 2008\nEdition.\n4. �Fluid Mechanics� � Streeter, Wylie, Bedford New Delhi,\n2008(Ed)\n\n## Tool box\n\nEdit this note | Upvote | Down vote | Questions\n\n### Watch more videos from this user Here\n\nLearn how to upload a video over here"
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"https://i.imgur.com/cHidSVu.gif",
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https://stat.ethz.ch/CRAN/web/packages/nimbleSCR/vignettes/Point_Process.html | [
"# Point process Bayesian SCR models with nimbleSCR\n\n#### 2022-11-30\n\nIn this vignette, we demonstrate how to use the nimbleSCR (Bischof et al. 2020) and NIMBLE packages (de Valpine et al. 2017; NIMBLE Development Team 2020) to simulate spatial capture-recapture (SCR) data and fit flexible and efficient Bayesian SCR models via a set of point process functions. Users with real-life SCR data can use this vignette as a guidance for preparing the input data and fitting appropriate Bayesian SCR models in NIMBLE.\n\n## Load packages\nlibrary(nimble)\nlibrary(nimbleSCR)\nlibrary(basicMCMCplots)\n\n## 1. Simulate SCR data\n\n### 1.1 Habitat and trapping grid\n\nAs an example, we create a $$80 \\times 100$$ habitat grid with a resolution of 10 for each dimension. On the habitat, we center a $$60 \\times 80$$ trapping grid with also a resolution of 10 for each dimension, leaving an untrapped perimeter (buffer) with a width of 20 distance units on each side of the grid.\n\n## Create habitat grid\ncoordsHabitatGridCenter <- cbind(rep(seq(75, 5, by = -10), 10),\nsort(rep(seq(5, 100, by = 10), 8)))\ncolnames(coordsHabitatGridCenter) <- c(\"x\",\"y\")\n\n## Create trap grid\ncoordsObsCenter <- cbind(rep(seq(15, 65, by = 10), 8),\nsort(rep(seq(15, 85, by = 10), 6)))\ncolnames(coordsObsCenter) <- c(\"x\",\"y\")\n\n## Plot check\nplot(coordsHabitatGridCenter[,\"y\"] ~ coordsHabitatGridCenter[,\"x\"],\nxlim = c(0,80), ylim = c(0,100),\npch = 1, cex = 1.5)\npoints(coordsObsCenter[,\"y\"] ~ coordsObsCenter[,\"x\"], col=\"red\", pch=16 )\npar(xpd=TRUE)\nlegend(x = 7, y = 13,\nlegend=c(\"Habitat window centers\", \"Observation window centers\"),\npt.cex = c(1.5,1),\nhoriz = T,\npch=c(1,16),\ncol=c(\"black\", \"red\"),\nbty = 'n')",
null,
"### 1.2 Rescale coordinates\n\nTo implement the local evaluation approach when fitting the SCR model (see Milleret et al. (2019) and Turek et al. (2021) for further details), we need to rescale the habitat and trapping grid coordinates so that each habitat cell is of dimension $$1 \\times 1$$. We also need to identify the lower and upper coordinates of each habitat cell using the ‘getWindowCoords’ function.\n\n## Rescale coordinates\nscaledObjects <- scaleCoordsToHabitatGrid(\ncoordsData = coordsObsCenter,\ncoordsHabitatGridCenter = coordsHabitatGridCenter)\n\n## Get lower and upper cell coordinates\nlowerAndUpperCoords <- getWindowCoords(\nscaledHabGridCenter = scaledObjects$coordsHabitatGridCenterScaled, scaledObsGridCenter = scaledObjects$coordsDataScaled,\nplot.check = F)\n\n### 1.3 Model definition\n\nmodelCode <- nimbleCode({\n##---- SPATIAL PROCESS\n## Prior for AC distribution parameter\nhabCoeffSlope ~ dnorm(0, sd = 10)\n\n## Intensity of the AC distribution point process\nhabIntensity[1:numHabWindows] <- exp(habCoeffSlope * habCovs[1:numHabWindows])\nsumHabIntensity <- sum(habIntensity[1:numHabWindows])\nlogHabIntensity[1:numHabWindows] <- log(habIntensity[1:numHabWindows])\nlogSumHabIntensity <- log(sumHabIntensity)\n\n## AC distribution\nfor(i in 1:M){\nsxy[i, 1:2] ~ dbernppAC(\nlowerCoords = lowerHabCoords[1:numHabWindows, 1:2],\nupperCoords = upperHabCoords[1:numHabWindows, 1:2],\nlogSumIntensity = logSumHabIntensity,\nhabitatGrid = habitatGrid[1:numGridRows,1:numGridCols],\nnumGridRows = numGridRows,\nnumGridCols = numGridCols\n)\n}\n\n##---- DEMOGRAPHIC PROCESS\n## Prior for data augmentation\npsi ~ dunif(0,1)\n\n## Data augmentation\nfor (i in 1:M){\nz[i] ~ dbern(psi)\n}\n\n##---- DETECTION PROCESS\n## Priors for detection parameters\nsigma ~ dunif(0, 50)\ndetCoeffInt ~ dnorm(0, sd = 10)\ndetCoeffSlope ~ dnorm(0, sd = 10)\n\n## Intensity of the detection point process\ndetIntensity[1:numObsWindows] <- exp(detCoeffInt + detCoeffSlope * detCovs[1:numObsWindows])\n\n## Detection process\nfor (i in 1:M){\ny[i, 1:numMaxPoints, 1:3] ~ dpoisppDetection_normal(\nlowerCoords = obsLoCoords[1:numObsWindows, 1:2],\nupperCoords = obsUpCoords[1:numObsWindows, 1:2],\ns = sxy[i, 1:2],\nsd = sigma,\nbaseIntensities = detIntensity[1:numObsWindows],\nnumMaxPoints = numMaxPoints,\nnumWindows = numObsWindows,\nindicator = z[i]\n)\n}\n\n##---- DERIVED QUANTITIES\n## Number of individuals in the population\nN <- sum(z[1:M])\n})\n\n### 1.4 Set up parameter values\n\nWe set parameter values for the simulation as below.\n\nsigma <- 1\npsi <- 0.6\ndetCoeffInt <- 0.1\ndetCoeffSlope <- 0.5\nhabCoeffSlope <- -1.5\n\nWe use the data augmentation approach (Royle and Dorazio 2012) to estimate population size N. Thus, we need to choose a value M for the size of the superpopulation (detected + augmented individuals). Here we set M to be 150. The expected total number of individuals that are truly present in the population is M *psi.\n\nM <- 150\n\nWhen simulating individual detections using the Poisson point process function ‘dpoispp_Detection_normal’, all the information is stored in y, a 3D array containing i) the number of detections per individual, ii) the x- and y-coordinates of each detection, and iii) the index of the habitat grid cell for each detection (see ?dpoisppDetection_normal for more details):\n\n• ‘y[ ,1,1]’: number of detections for each individual\n\n• ‘y[ ,2:numDetections,1:2]’: x and y coordinates of the detections\n\n• ‘y[ ,2:numDetections,3]’: IDs of the cells (from lowerAndUpperCoords$habitatGrid) in which the detections fall. Cell IDs can be obtained using the ‘getWindowIndex()’ function. Next, we need to provide the maximum number of detections that can be simulated per individual. We set this to be 19 + 1 to account for the fact that the first element of the second dimension of the detection array (y[ ,1,1]) does not contain detection data but the total number of detections for each individual. numMaxPoints <- 19 + 1 In this simulation, we also incorporate spatial covariates on the intensity of the point processes for AC distribution and individual detections. Values of both covariates are generated under a uniform distribution: Unif[-1, 1]. detCovs <- runif(dim(lowerAndUpperCoords$lowerObsCoords),-1,1)\nhabCovs <- runif(dim(lowerAndUpperCoords$lowerHabCoords),-1,1) ### 1.5 Create data, constants and initial values Here we prepare objects containing data, constants, and initial values that are needed for creating the NIMBLE model below. nimConstants <- list( M = M, numObsWindows = dim(lowerAndUpperCoords$lowerObsCoords),\nnumMaxPoints = numMaxPoints,\nnumHabWindows = dim(lowerAndUpperCoords$upperHabCoords), habitatGrid = lowerAndUpperCoords$habitatGrid,\nnumGridRows = dim(lowerAndUpperCoords$habitatGrid), numGridCols = dim(lowerAndUpperCoords$habitatGrid))\n\nnimData <- list( obsLoCoords = lowerAndUpperCoords$lowerObsCoords, obsUpCoords = lowerAndUpperCoords$upperObsCoords,\nlowerHabCoords = lowerAndUpperCoords$lowerHabCoords, upperHabCoords = lowerAndUpperCoords$upperHabCoords,\ndetCovs = detCovs,\nhabCovs = habCovs)\n\nIn order to simulate directly from the NIMBLE model, we set the true parameter values as initial values. These will be used by the NIMBLE model object to randomly generate SCR data.\n\nnimInits <- list( psi = psi,\nsigma = sigma,\ndetCoeffInt = detCoeffInt,\ndetCoeffSlope = detCoeffSlope,\nhabCoeffSlope = habCoeffSlope)\n\n### 1.6 Create NIMBLE model\n\nWe can then build the NIMBLE model.\n\nmodel <- nimbleModel( code = modelCode,\nconstants = nimConstants,\ndata = nimData,\ninits = nimInits,\ncheck = F,\ncalculate = F)\n\n### 1.7 Simulate data\n\nIn this section, we demonstrate how to simulate data using the NIMBLE model code. Here, we want to simulate individual AC locations (‘sxy’), individual states (‘z’), and observation data (‘y’), based on the values provided as initial values. We first need to identify which nodes in the model need to be simulated, via the ‘getDependencies’ function in NIMBLE. Then, we can generate values for these nodes using the ‘simulate’ function in NIMBLE.\n\nnodesToSim <- model$getDependencies(names(nimInits), self = F) set.seed(1) model$simulate(nodesToSim, includeData = FALSE)\n\nAfter running the code above, simulated data are stored in the ‘model’ object. For example, we can access the simulated ‘z’ and check the number of individuals that are truly present in the population:\n\nN <- sum(model$z) We have simulated 89 individuals truly present in the population, of which 83 are detected. To check the simulate data, we can also plot the locations of the simulated activity center and detections for a particular individual. i = 7 ## Number of detections for individual i model$y[i,1,1]\n## 0\n## Plot of the habitat and trap grids\nplot( scaledObjects$coordsHabitatGridCenterScaled[,\"y\"] ~ scaledObjects$coordsHabitatGridCenterScaled[,\"x\"],\npch = 1, cex = 0.5)\nrect( xleft = lowerAndUpperCoords$lowerHabCoords[,1] , ybottom = lowerAndUpperCoords$lowerHabCoords[,2] ,\nxright = lowerAndUpperCoords$upperHabCoords[,1], ytop = lowerAndUpperCoords$upperHabCoords[,2],\ncol = adjustcolor(\"red\", alpha.f = 0.4),\nborder = \"red\")\n\nrect( xleft = lowerAndUpperCoords$lowerObsCoords[,1] , ybottom = lowerAndUpperCoords$lowerObsCoords[,2] ,\nxright = lowerAndUpperCoords$upperObsCoords[,1], ytop = lowerAndUpperCoords$upperObsCoords[,2],\nborder = \"blue\")\n\n## Plot the activity center of individual i\npoints( model$sxy[i, 2] ~ model$sxy[i, 1],\ncol = \"orange\", pch = 16)\n\n## Plot detections of individual i\ndets <- model$y[i,2:model$y[i,1,1], ]\npoints( dets[,2] ~ dets[,1],\ncol = \"green\", pch = 16)\n\npar(xpd = TRUE)\nlegend(x = -1, y = 13,\nlegend = c(\"Habitat windows\",\n\"Observation windows\",\n\"Simulated AC\",\n\"Detections\"),\npt.cex = c(1,1),\nhoriz = T,\npch = c(16, 16, 16, 16),\ncol = c(\"red\", \"blue\", \"orange\", \"green\"),\nbty = 'n')",
null,
"## 2. Fit model with data augmentation\n\n### 2.1. Prepare the input data\n\nWe have already defined the model above and now need to build the NIMBLE model again using the simulated data ‘y’. For simplicity, we use the simulated ‘z’ as initial values. When using real-life SCR data you will need to generate initial ‘z’ values for augmented individuals and initial ‘sxy’ values for all individuals.\n\nnimData1 <- nimData\nnimData1$y <- model$y\nnimInits1 <- nimInits\nnimInits1$z <- model$z\nnimInits1$sxy <- model$sxy\n\n## Create and compile the NIMBLE model\nmodel <- nimbleModel( code = modelCode,\nconstants = nimConstants,\ndata = nimData1,\ninits = nimInits1,\ncheck = F,\ncalculate = F)\n\n## Check the initial log-likelihood\nmodel$calculate() ## -1416.63 cmodel <- compileNimble(model) ### 2.2. Run MCMC with NIMBLE Now we can configure and run the MCMC in NIMBLE to fit the model. MCMCconf <- configureMCMC(model = model, monitors = c(\"N\",\"sigma\",\"psi\",\"detCoeffInt\", \"detCoeffSlope\",\"habCoeffSlope\"), control = list(reflective = TRUE), thin = 10) ## ===== Monitors ===== ## thin = 10: N, detCoeffInt, detCoeffSlope, habCoeffSlope, psi, sigma ## ===== Samplers ===== ## binary sampler (150) ## - z[] (150 elements) ## RW_block sampler (150) ## - sxy[] (150 multivariate elements) ## RW sampler (5) ## - habCoeffSlope ## - psi ## - sigma ## - detCoeffInt ## - detCoeffSlope MCMC <- buildMCMC(MCMCconf) cMCMC <- compileNimble(MCMC, project = model, resetFunctions = TRUE) ## Run MCMC MCMCRuntime <- system.time(samples <- runMCMC( mcmc = cMCMC, nburnin = 500, niter = 10000, nchains = 3, samplesAsCodaMCMC = TRUE)) ## Print runtime MCMCRuntime ## user system elapsed ## 136.356 0.328 137.179 ## Traceplots and density plots for the tracked parameters chainsPlot(samples, line = c(N, detCoeffInt, detCoeffSlope, habCoeffSlope, N/M, sigma))",
null,
"## 3. Fit model without data augmentation ### 3.1. Model definition We use the same simulated dataset to demonstrate how to fit a model using the semi-complete data likelihood (SCDL) approach (King et al. 2016). We first need to re-define the model. modelCodeSemiCompleteLikelihood <- nimbleCode({ #----- SPATIAL PROCESS ## Priors habCoeffInt ~ dnorm(0, sd = 10) habCoeffSlope ~ dnorm(0, sd = 10) ## Intensity of the AC distribution point process habIntensity[1:numHabWindows] <- exp(habCoeffInt + habCoeffSlope * habCovs[1:numHabWindows]) sumHabIntensity <- sum(habIntensity[1:numHabWindows]) logHabIntensity[1:numHabWindows] <- log(habIntensity[1:numHabWindows]) logSumHabIntensity <- log(sum(habIntensity[1:numHabWindows] )) ## AC distribution for(i in 1:nDetected){ sxy[i, 1:2] ~ dbernppAC( lowerCoords = lowerHabCoords[1:numHabWindows, 1:2], upperCoords = upperHabCoords[1:numHabWindows, 1:2], logIntensities = logHabIntensity[1:numHabWindows], logSumIntensity = logSumHabIntensity, habitatGrid = habitatGrid[1:numGridRows,1:numGridCols], numGridRows = numGridRows, numGridCols = numGridCols ) } ##---- DEMOGRAPHIC PROCESS ## Number of individuals in the population N ~ dpois(sumHabIntensity) ## Number of detected individuals nDetectedIndiv ~ dbin(probDetection, N) ##---- DETECTION PROCESS ## Probability that an individual in the population is detected at least once ## i.e. 1 - void probability over all detection windows probDetection <- 1 - marginalVoidProbNumIntegration( quadNodes = quadNodes[1:nNodes, 1:2, 1:numHabWindows], quadWeights = quadWeights[1:numHabWindows], numNodes = numNodes[1:numHabWindows], lowerCoords = obsLoCoords[1:numObsWindows, 1:2], upperCoords = obsUpCoords[1:numObsWindows, 1:2], sd = sigma, baseIntensities = detIntensity[1:numObsWindows], habIntensities = habIntensity[1:numHabWindows], sumHabIntensity = sumHabIntensity, numObsWindows = numObsWindows, numHabWindows = numHabWindows ) ## Priors for detection parameters sigma ~ dunif(0, 50) detCoeffInt ~ dnorm(0, sd = 10) detCoeffSlope ~ dnorm(0, sd = 10) ## Intensity of the detection point process detIntensity[1:numObsWindows] <- exp(detCoeffInt + detCoeffSlope * detCovs[1:numObsWindows]) ## Detection process ## Note that this conditions on the fact that individuals are detected (at least once) ## So, at the bottom of this model code we deduct log(probDetection) from the log-likelihood ## function for each individual for (i in 1:nDetected){ y[i, 1:numMaxPoints, 1:3] ~ dpoisppDetection_normal( lowerCoords = obsLoCoords[1:numObsWindows, 1:2], upperCoords = obsUpCoords[1:numObsWindows, 1:2], s = sxy[i, 1:2], sd = sigma, baseIntensities = detIntensity[1:numObsWindows], numMaxPoints = numMaxPoints, numWindows = numObsWindows, indicator = 1 ) } ## Normalization: normData can be any scalar in the data provided when building the model ## The dnormalizer is a custom distribution defined for efficiency, where the input data ## does not matter. It makes it possible to use the general dpoippDetection_normal function ## when either data augmentation or the SCDL is employed logDetProb <- log(probDetection) normData ~ dnormalizer(logNormConstant = -nDetected * logDetProb) }) ### 3.2. Prepare the input data We use the same simulated data as above. Since we do not use data augmentation here, we have to remove all individuals that are not detected from ‘y’ and ‘sxy’. idDetected <- which(nimData1$y[,1,1] > 0)\n## Subset data to detected individuals only\nnimData1$y <- nimData1$y[idDetected,,]\n## Provide the number of detected individuals as constant\nnimConstants$nDetected <- length(idDetected) ## With this model, we also need to provide the number of detected individuals as data for the estimation of population size. nimData1$nDetectedIndiv <- length(idDetected)\n## As mentioned above, \"normData\" can take any value.\nnimData1$normData <- 1 ## We also provide initial values for the new parameters that need to be estimated nimInits1$N <- 100\nnimInits1$habCoeffInt <- 0.5 nimInits1$sxy <- nimInits1$sxy[idDetected,] The values below are needed to calculate the void probability numerically (i.e. the probability that one individual is detected at least once) using the midpoint rule. ## Number of equal subintervals for each dimension of a grid cell nPtsPerDim <- 2 ## Number of points to use for the numerical integration for each grid cell nNodes <- nPtsPerDim^2 ## Generate midpoint nodes coordinates for numerical integration using the \"getMidPointNodes\" function nodesRes <- getMidPointNodes( nimData1$lowerHabCoords,\nnimData1$upperHabCoords, nPtsPerDim) ## Add this info to the data and constant objects nimData1$quadNodes <- nodesRes$quadNodes nimData1$quadWeights <- nodesRes$quadWeights nimData1$numNodes <- rep(nNodes,dim(nimData1$lowerHabCoords)) nimConstants$nNodes <- dim(nodesRes$quadNodes) ### 3.3. Run MCMC with NIMBLE Finally we can re-build the model and run the MCMC to fit the SCDL model. model <- nimbleModel(code = modelCodeSemiCompleteLikelihood, constants = nimConstants, data = nimData1, inits = nimInits1, check = F, calculate = F) model$calculate()\n## -1058.118\ncmodel <- compileNimble(model)\ncmodel\\$calculate()\nMCMCconf <- configureMCMC(model = model,\nmonitors = c(\"N\",\"sigma\",\"probDetection\",\"habCoeffInt\", \"detCoeffInt\",\"detCoeffSlope\",\"habCoeffSlope\"),\ncontrol = list(reflective = TRUE),\nthin = 10)\n## ===== Monitors =====\n## thin = 10: N, detCoeffInt, detCoeffSlope, habCoeffInt, habCoeffSlope, probDetection, sigma\n## ===== Samplers =====\n## slice sampler (1)\n## - N\n## RW_block sampler (83)\n## - sxy[] (83 multivariate elements)\n## RW sampler (5)\n## - habCoeffInt\n## - habCoeffSlope\n## - sigma\n## - detCoeffInt\n## - detCoeffSlope\nMCMC <- buildMCMC(MCMCconf)\ncMCMC <- compileNimble(MCMC, project = model, resetFunctions = TRUE)\n\n## Run MCMC\nMCMCRuntime1 <- system.time(samples1 <- runMCMC( mcmc = cMCMC,\nnburnin = 500,\nniter = 10000,\nnchains = 3,\nsamplesAsCodaMCMC = TRUE))\nMCMCRuntime1\n## user system elapsed\n## 594.192 1.807 598.858\n## Plot check\nchainsPlot(samples1, line = c(N, detCoeffInt, detCoeffSlope, NA, habCoeffSlope, NA, sigma))"
]
| [
null,
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",
null,
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",
null,
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",
null
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http://nikolavitas.blogspot.com/2017/03/k-means-clustering.html | [
"## Monday, 20 March 2017\n\n### K-means clustering\n\nThe problem of clustering is a rather general one: If one has $m$ observations or measurements in $n$ dimensional space, how to identify $k$ clusters (classes, groups, types) of measurements and their centroids (representatives)?\n\nThe k-means method is extremely simple, rather robust and widely used in it numerous variants. It is essentially very similar (but not identical) to Lloyd's algorithm (aka Voronoi relaxation or interpolation used in computer sciences).\n\nk-means\n\nLet's use the following indices: $i$ counts measurements, $i \\in [0, m-1]$; $j$ counts dimensions, $j \\in [0, n-1]$; $l$ counts clusters, $l \\in [0, k-1]$.\n\nEach measurement in $n$-dimensional space is represented by a vector $x_i = \\{x_{i, 0}, \\dots x_{i, n-1}\\}$, where index $i$ is counting different measurements ($i = 0, \\dots, m-1$). The algorithm can be summarized as:\n\n1. Choose randomly $k$ measurements as initial cluster centers: $c_0, ..., c_{k-1}$. Obviously, each of the clusters is also $n$-dimensional vector.\n\n2. Compute Euclidean distance $D_{i, l}$ between every measurement $x_i$ and every cluster center $c_l$:\n$$D_{i, l} = \\sqrt{\\sum_{j=0}^{n-1} (x_{i, j} - c_{l, j})^2}.$$\n3. Assign every measurement $x_i$ to the cluster represented by the closest cluster center $c_l$.\n\n4. Now compute new cluster centers by simply averaging all the measurements in each cluster.\n\n5. Go back to 2. and keep iterating until none of the measurements changes its cluster in two successive iterations.\n\nThis procedure is initiated randomly and the result will be slightly different in every run. The result of clustering (and the actual number of necessary iteration) significantly depends on the initial choice of cluster centers. The easiest way to improve the algorithm is to improve the initial choice, i.e. to alter only the step 1. and then to iterate as before. There are to simple alternatives for the initialization.\n\nFurthest point\n\nIn the furthest cluster variant, only the very fist cluster center $c_0$ is obtained randomly. Then the distances of all other measurements from $c_0$ are computed and the most distant measurement is selected as $c_1$. The next cluster is selected as the most distant from both $c_0$ and $c_1$, and so on until all initial cluster centers are set. An issue with this method of initialization is that it is very sensitive to outliers especially those on the edges of the measurement space.\n\nk-means++\n\nArthur and Vassilvitskii (2006) proposed an alternative method for the initial randomization. The first cluster center $c_0$ is purely random. Then the distances of all other measurements from $c_0$ are computed as before. Now this distances are used to define probability distribution,\n$$p = \\frac{D_{i, 0}^2}{\\sum_{i=0}^{m-1} D_{i, 0}^2}$$,\nand the next cluster is chosen again randomly, but now we used the probability distribution $p$ (instead of uniform). The idea is again to draw new clusters so that they are far from the previously chosen. The difference is that now the new clusters will not necessarily be at the very edges of the measurement space, so it is less likely that isolated outliers would be picked.\n\nExample of initialization\n\nI constructed a simple test data with 4 clearly separated sets with $m=2$ and then run the three variants for the k-means realization assuming $k=4$. The result is shown in the figure below. The first selected cluster-center is yellow.\n\nIn this trivial case, the 4 clusters are correctly identified already in the first iteration for the furthest-point and k-means++ initializations. In the random initialization, it takes 4 iteration steps. The following figure shows how does the solution propagates step-by-step.\n\nSilhouette\n\nRousseew (1987) proposed the concept of silhouette as an estimate how consistent are the clusters and how appropriate is clustering for a given dataset. He introduced a measure of dissimilarity as the mean distance between a measurement and all measurements in one cluster. Let's label with $a_j$ the dissimilarity between a measurement and the cluster to which this measurement is assigned, and with $b_j$ the mean dissimilarity between the same measurement and all other clusters. Then the silhouette is defined for every measurement as: $$s_j =\\frac{b_j - a_j}{\\mathrm{max}(a_j, b_j)}.$$ The value of silhouette averaged over the entire dataset tells us how well the data have been clustered. If the value is closed to 1, the clustering is well done. If it is close to 0, the clusters found by the method are not appropriate for the given data.\n\nIDL implementation\n\nIDL has its own implementation of k-means (CLUSTER, before it was called KMEANS). To be able to experiment and play with the method, I wrote my KMEANS function that includes the three initializations mentioned above. The result of the function is structure with three tags: clusters, frequencies (percentage of the measurements assigned to each cluster) and silhouette (for every measurement).\n\nExample:\nIDL> n = 100 ; Number of pointsIDL> m = 2 ; Number of dimensions, ie. length of vectors\nIDL> k = 4 ; Number of clusters\n\nIDL> x = REFORM(RANDOMU(10, m*n)/4., [m, n])\nIDL> x[0, 0:24] += 0.2\nIDL> x[1, 0:24] += 0.2\nIDL> x[0, 25:49] += 0.8\nIDL> x[1, 25:49] += 0.8\nIDL> x[0, 50:74] += 0.2\nIDL> x[1, 50:74] += 0.8\nIDL> x[0, 75:99] += 0.8\nIDL> x[1, 75:99] += 0.2\nIDL> y = KMEANS(x, k = k, initial = 'kmeanspp')\n\n; Show the initial data points\nIDL> PLOT, x[0, *], x[1, *], psym = 4\n\n; Show data points which are assigned to the cluster 2\nIDL> id = WHERE(y.clusters EQ 2)\nIDL> OPLOT, x[0, id], x[1, id], psym = -1\n\n\nDownload: kmeans.pro\n\nReferences:\nRousseeuw (1987), Silhouettes: a graphical aid to the interpretation and validation of cluster analysis\nSu & Dy (2004), A Deterministic Method for Initializing K-means Clustering\nArthur & Vassilvitskii (2007), k-means++ : The Advantages of Careful Seeding\nBahmani et al (2013), Scalable K-Means++\n\nApplication in solar physics:\nViticchié & Sánchez Almeida (2011), Asymmetries of the Stokes V profiles observed by HINODE SOT/SP in the quiet Sun\n\n#### 1 comment:\n\n1.",
null,
"Great post dear. It definitely has increased my knowledge on R Programming. Please keep sharing similar write ups of yours. You can check this too for R Programming tutorial as i have recorded this recently on R Programming. and i'm sure it will be helpful to you.https://www.youtube.com/watch?v=gXb9ZKwx29U"
]
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null,
"http://lh3.googleusercontent.com/zFdxGE77vvD2w5xHy6jkVuElKv-U9_9qLkRYK8OnbDeJPtjSZ82UPq5w6hJ-SA=s35",
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https://modelassist.epixanalytics.com/plugins/viewsource/viewpagesrc.action?pageId=1147779 | [
"The Hypergeometric Process",
null,
"Description\n\nThe hypergeometric process occurs when one is sampling randomly without replacement from some population (as opposed to sampling with replacement in the Binomial Process), and where one is counting the number in that sample that have some particular characteristic. This is a very common type of scenario. For example, population surveys, herd testing, and lotto are all hypergeometric processes. In many situations, the population is very large in comparison to the sample and we can assume that if a sample was put back into the population, the probability is very small that it would be picked again. In that case, each sample would have the same probability of picking an individual with a particular characteristic: in other words this becomes a binomial process. When the population is not very large compared to the sample (a good rule is that the population is less than ten times the size of the sample) we cannot make a binomial approximation to the hypergeometric. This section discusses the distributions associated with the hypergeometric process.",
null,
"The figure above demonstrates the four parameters of the Hypergeometric process: The population one is sampling from (M); the sub-population of interest (D), the number being randomly sampled from the population (n) and the number (s) in that sample that come from D. We recommend that you draw out a diagram like this when you are faced with a hypergeometric problem to keep that all clear!\n\nOnce you have reviewed the material in this section, you might like to test how much you have learned by taking the self-test quiz:\n\nA quiz on The hypergeometric process:",
null,
"Summary of results for the hypergeometric process\n\n Quantity Formula Notes Number of sub-population in the sample In Crystal Ball version 5.5-: s = Hypergeometric(D/M,n,M)In Crystal Ball version 7.0+: s = Hypergeometric(D,n,M) Number of samples to observe s from the sub-population n = InvHypergeo(s,D,M) Number of samples there were to have observed s from the sub-population n = InvHypergeo(s,D,M) Where the last sample is known to have been from the sub-population Number of samples n there were before having observed s from the sub-population",
null,
"Where the last sample is not known to have been from the sub-population. This uncertainty distribution needs to be normalized. Size of sub-population D",
null,
"This uncertainty distribution needs to be normalized. Size of population M",
null,
"This uncertainty distribution needs to be normalized.\n\nUseful Excel Functions:\n\n Use Function Explanation Hypergeometric probability =HYPGEOMDIST(x,n,D,M) The hypergeometric probability of observing exactly s in a sample of size n that come from sub-population D in a total population M. Combinations =COMBIN(n,x) The binomial coefficient nCx = n!/(s!(n-s)!) Factorial =FACT(x) x!"
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"https://modelassist.epixanalytics.com/plugins/servlet/latexmath/placeholder",
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https://answers.everydaycalculation.com/add-fractions/30-60-plus-50-21 | [
"Solutions by everydaycalculation.com\n\n1st number: 30/60, 2nd number: 2 8/21\n\n30/60 + 50/21 is 121/42.\n\n1. Find the least common denominator or LCM of the two denominators:\nLCM of 60 and 21 is 420\n2. For the 1st fraction, since 60 × 7 = 420,\n30/60 = 30 × 7/60 × 7 = 210/420\n3. Likewise, for the 2nd fraction, since 21 × 20 = 420,\n50/21 = 50 × 20/21 × 20 = 1000/420\n210/420 + 1000/420 = 210 + 1000/420 = 1210/420\n5. 1210/420 simplified gives 121/42\n6. So, 30/60 + 50/21 = 121/42\nIn mixed form: 237/42\n\nMathStep (Works offline)",
null,
"Download our mobile app and learn to work with fractions in your own time:"
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"https://answers.everydaycalculation.com/mathstep-app-icon.png",
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https://www.lin2j.tech/archives/3-1--zhan-de-ya-ru--dan-chu-xu-lie | [
"",
null,
"",
null,
"• 累计撰写 99 篇文章\n• 累计创建 43 个标签\n• 累计收到 5 条评论\n\n### 目 录CONTENT",
null,
"# 31 栈的压入、弹出序列",
null,
"2021-07-21 / 0 评论 / 0 点赞 / 168 阅读 / 1,450 字 / 正在检测是否收录...\n\n• 创建一个模拟栈 $S$，弹出元素的索引 $k$ 初始值为 $0$。\n• 遍历 $pushed$，用 $num$ 表示当前压入元素\n• 将 $num$ 压入 $S$ 中。\n• 循环检查，当 $S$ 不为空时，检查 $S$ 的栈顶元素是否等于 $popped[k]$\n• 如果相等，则 $S$ 弹出栈顶元素，$k$ 自增\n• 判断 $S$ 是否为空\n• $false$：$S$ 不为空，$popped$ 不合法；\n• $true$：$S$ 为空，$popped$ 合法\n\npublic boolean validateStackSequences(int[] pushed, int[] popped) {\nif (pushed == null || popped == null\n|| pushed.length == 0 || pushed.length != popped.length) {\nreturn true;\n}\n// helper 来模拟 pushed 的入栈\nint k = 0;\nfor (int num : pushed) {\n// 模拟入栈\nhelper.push(num);\n// 如果辅助栈不为空，检查辅助栈的栈顶元素，如果和弹出序列相等就弹出\nwhile (!helper.isEmpty() && helper.peek() == popped[k]) {\nhelper.pop();\nk++;\n}\n}\nreturn helper.isEmpty();\n}\n\n\n• 时间复杂度$O(N)$：$N$ 为 $pushed$ 的长度，每个元素最多出入栈 $2$ 次，即最多共 $2N$ 次出入栈操作。\n• 空间复杂度$O(N)$：$N$ 为 $pushed$ 的长度，辅助栈最多存储 $N$ 个元素。\n0"
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https://www.orderhive.com/knowledge-center/economic-order-quantity | [
"# EOQ Formula\n\nThe company’s reputation and profitability are always at stake if it has too much or too little inventory on hand. 43% of business owners have considered “overbuying inventory” as a challenge, whereas 36% said the same for “underbuying inventory”.\n\nTo provide a solution to this, in 1913, Ford W. Harris designed a model of “Economic Order Quantity (EOQ)” through an explanation. This was later turned to a mathematical equation by R.H. Wilson, a consultant who applied it extensively.\n\nThe Economic Order Quantity is a very good approach for efficient inventory management, though not the only step that a merchant can take, but can certainly make an impact.\n\n## The Derivation of EOQ Formula:\n\nVariables:\n\nT = Total annual inventory cost\nP = Purchase unit price, unit production cost\nQ = Order quantity\nQ* = Optimal order quantity\nD = Annual demand quantity\nK = Fixed cost per order, setup cost\nh = Annual holding cost per unit, also known to be carrying or storage cost\n\nThe single-item EOQ formula helps find the minimum point of the following cost function:\n\nTotal Cost = Purchase Cost or Production Cost + Ordering Cost + Holding Cost\n\nWhere,\n\n• Purchase cost: This is the variable cost of goods: purchase unit price × annual demand quantity. This is P × D\n• Ordering cost: This is the cost of placing orders: each order has a fixed cost K, and we need to order D/Q times per year. This is K × D/Q\n• Holding cost: the average quantity in stock (between fully replenished and empty) is Q/2, so this cost is h × Q/2",
null,
"To determine the minimum point of the total cost curve, calculate the derivative of the total cost with respect to Q (assume all other variables are constant) and set it equal to zero (0):",
null,
"Solving for Q gives Q* (the optimal order quantity):",
null,
"Therefore,",
null,
"Can also be written as,",
null,
"## Example of Economic Order Quantity (EOQ)\n\nLet’s assume, a retail clothing shop is into men’s jeans and sells roughly around 1000 pairs of jeans every year. It takes \\$5 for the shop to hold a pair of jeans for the entire year, and the fixed cost to place an order is \\$2.\n\nAs per the EOQ formula, the calculation of the above-mentioned scenario is below:\n\nEOQ = Sq. root [(2 * 1000 pairs * \\$2 order cost) / (\\$5 carrying cost)]\n\nTherefore, EOQ = 28.3 pairs.\n\nThe ideal order quantity for the shop will be 28 pairs of jeans. Simple!\n\n## Factors that affect Economic Order Quantity\n\n• Reorder Point\nIt is the time when there occurs a need to reorder another set of stock or replenish the existing stock. EOQ always assumes that you order the same quantity at each reorder point.\nThis is the time period from placing the order until the ordering is delivered. EOQ assumes that the lead time is understood.\nThe cost per unit never changes, over the period of time, even though the quantity of the order is changed. EOQ always assumes that you pay the same amount per product, every time.\n• Stockouts\nThere are no chances for stockouts. You have to always maintain enough inventory to avoid stockout costs. This clearly states that you always have to strictly monitor your customer demand along with your inventory levels, carefully.\n• Quality costs\nEOQ never focuses on the quality costs, rather the carrying costs.\n• Demand\nIt’s about how much the customer wants the product for a specific time period.\n• Relevant ordering cost\nThe cost per purchase order.\n• Relevant carrying cost\nThe cost involved in the entire maintenance and carrying the stock, for the specific period.\n\n## Importance of Economic Order Quantity (EOQ)\n\nThe Economic Order Quantity is a quantity designed to assist companies to not over- or under-stock their inventories and minimize their capital investments on the products that they are selling. The cost of ordering an inventory touches down with an increase in ordering in bulk. However, as the seller wishes to grow the size of the inventory, the carrying costs also increase.\n\nThe EOQ is exactly the point that optimizes both of these costs i.e. cost of ordering and the carrying costs which are inversely related.\n\nNow, with this…\n\n• The business owners can easily order the right quantities and reduce the ordering and carrying costs. This will eventually result in either profits or a balanced business.\n• Decision making can be made smoother, with less time and effort wasted.\n• Right vendors can be chosen, with the right packages to save costs and earn better profits.\n\n## Why should you be calculating EOQ?\n\nThere are several benefits of calculating EOQ that can impact your business. It shows and lets you maintain your supply chain while keeping the costs down.\n\n### Minimize Inventory Costs\n\nThere are high chances of booming storage costs if you plan to store any extra inventory. High inventory costs depend majorly on how you order, if there is anything that is damaged, the number of products that lie there not getting sold. If you are constantly re-ordering products that have a very low velocity, EOQ can help you analyze how much to order in a certain period.\n\n### Minimize Stockouts\n\nBy calculating how much inventory you need on how much you are planning to sell, EOQ will help you avoid stock-outs without having too much inventory on hand for too long. It can definitely be surprising enough to see that ordering in small quantities can be way more cost-effective, but this can turn the other way as well – calculating EOQ for your products can help.",
null,
"## Limitations of Economic Order Quantity (EOQ)\n\nThe EOQ formula always works on an assumption that the consumer demand is constant.\n\nIt becomes difficult or nearly impossible for the formula to work when it comes to business events such as changing consumer demand, seasonal changes in inventory costs, or purchase discounts a company might look out for at the time of buying larger quantities.\n\nNot at all designed to consider any fluctuation in the order quantity or carrying costs.\n\nThe basic EOQ model always assumes that you are selling just one product. So, as a seller, if you are selling multiple products, you need to calculate and track all your products separately.\n\n## Conclusion\n\nEconomic Order Quantity might not consider all the factors that affect business but is still a powerful tool if it sits right for you.",
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""
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"data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%20345%20105'%3E%3C/svg%3E",
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"data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%20303%20105'%3E%3C/svg%3E",
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"data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%20274%20116'%3E%3C/svg%3E",
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"data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%20264%20117'%3E%3C/svg%3E",
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"data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%20606%20123'%3E%3C/svg%3E",
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"data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%201024%20565'%3E%3C/svg%3E",
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"data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%200%200'%3E%3C/svg%3E",
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.92954606,"math_prob":0.93181366,"size":7114,"snap":"2020-45-2020-50","text_gpt3_token_len":1527,"char_repetition_ratio":0.13403657,"word_repetition_ratio":0.010673235,"special_character_ratio":0.2088839,"punctuation_ratio":0.09694258,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96789134,"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\":\"2020-10-22T07:06:49Z\",\"WARC-Record-ID\":\"<urn:uuid:c7dc42e6-71fa-4e91-982a-25ef0f468095>\",\"Content-Length\":\"178072\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4f33ee8b-c368-44dd-bed1-cd56107c95fa>\",\"WARC-Concurrent-To\":\"<urn:uuid:3fba261b-2307-4842-9e97-8ef74d4b2fc6>\",\"WARC-IP-Address\":\"104.26.11.107\",\"WARC-Target-URI\":\"https://www.orderhive.com/knowledge-center/economic-order-quantity\",\"WARC-Payload-Digest\":\"sha1:HL6Y4753WY4PFJU5LVPLLQF5IAFM5J7Y\",\"WARC-Block-Digest\":\"sha1:3GAJ36A3NIPCJBDKB75UTCRMPLRF45XO\",\"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-20201022053410-20201022083410-00524.warc.gz\"}"} |
https://www.quantel-laser.com/en/press-review/article/items/lidt-wavelength-scaling-rule-of-thumb-shown-to-be-inaccurate.html | [
"# LIDT wavelength-scaling rule of thumb shown to be inaccurate\n\n## by John Wallace - Laser Focus World\n\n06 August 2015 USABack",
null,
"",
null,
"Optical catalogs often specify the laser-damage threshold of an optic at only one or two wavelengths. This raises the question: What is the laser-induced damage threshold (LIDT) of that optic at other wavelengths? One rule of thumb that has been proposed is that the LIDT can be scaled by an inverse square-root relationship with wavelength: for example, a LIDT measured to be 10.0 J/cm2 at 1064 nm would scale to 7.07 J/cm2 at 532 nm.\n\nTo determine whether or not this rule of thumb is in fact accurate, engineers at Quantel USA (Bozeman, MT), an independent laser-damage testing facility, set out to measure the LIDT of a substrate at different wavelengths. They chose a sapphire substrate with a diameter large enough to allow multiple LIDT tests to be completed on a single surface. The sapphire, which was coated with a dual-band antireflection coating for 1064 nm and 1574 nm, was then subjected to LIDT measurements at both 1064 nm and 1574 nm (see test parameters in the table).",
null,
"Damage was defined as any permanent laser-induced change observable at 150X magnification with a Nomarski darkfield microscope. The resultant LIDT at 1064 nm was found to be 6.0 J/cm2 (see figure). Using the wavelength scaling equation above, this would correspond to 7.3 J/cm2 at 1574 nm. In fact, the actual measured LIDT at 1574 nm was 15.4 J/cm2, a factor of two higher that the predicted value. The inverse square root relationship was shown to predict a significantly lower LIDT than the actual measured value by more than a factor of two. The Quantel results show that, when needing to determine the LIDT at various wavelengths, the best approach is to measure the LIDT at the wavelengths of interest.\n\nContact Jason Yager at [email protected].\n\nTo determine whether or not this rule of thumb is in fact accurate, engineers at Quantel USA (Bozeman, MT), an independent laser-damage testing facility, set out to measure the LIDT of a substrate at different wavelengths. They chose a sapphire substrate with a diameter large enough to allow multiple LIDT tests to be completed on a single surface. The sapphire, which was coated with a dual-band antireflection coating for 1064 nm and 1574 nm, was then subjected to LIDT measurements at both 1064 nm and 1574 nm (see test parameters in the table).",
null,
"Damage was defined as any permanent laser-induced change observable at 150X magnification with a Nomarski darkfield microscope. The resultant LIDT at 1064 nm was found to be 6.0 J/cm2 (see figure). Using the wavelength scaling equation above, this would correspond to 7.3 J/cm2 at 1574 nm. In fact, the actual measured LIDT at 1574 nm was 15.4 J/cm2, a factor of two higher that the predicted value. The inverse square root relationship was shown to predict a significantly lower LIDT than the actual measured value by more than a factor of two. The Quantel results show that, when needing to determine the LIDT at various wavelengths, the best approach is to measure the LIDT at the wavelengths of interest.\n\nContact Jason Yager at [email protected].\n\nTo determine whether or not this rule of thumb is in fact accurate, engineers at Quantel USA (Bozeman, MT), an independent laser-damage testing facility, set out to measure the LIDT of a substrate at different wavelengths. They chose a sapphire substrate with a diameter large enough to allow multiple LIDT tests to be completed on a single surface. The sapphire, which was coated with a dual-band antireflection coating for 1064 nm and 1574 nm, was then subjected to LIDT measurements at both 1064 nm and 1574 nm (see test parameters in the table).",
null,
"Damage was defined as any permanent laser-induced change observable at 150X magnification with a Nomarski darkfield microscope. The resultant LIDT at 1064 nm was found to be 6.0 J/cm2 (see figure). Using the wavelength scaling equation above, this would correspond to 7.3 J/cm2 at 1574 nm. In fact, the actual measured LIDT at 1574 nm was 15.4 J/cm2, a factor of two higher that the predicted value. The inverse square root relationship was shown to predict a significantly lower LIDT than the actual measured value by more than a factor of two. The Quantel results show that, when needing to determine the LIDT at various wavelengths, the best approach is to measure the LIDT at the wavelengths of interest.\n\nContact Jason Yager at [email protected].\n\nGo back",
null,
""
]
| [
null,
"https://www.quantel-laser.com/en/press-review/article/items/tl_files/quantel_vf/img/coche-blanche-sans-fond.png",
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"https://www.quantel-laser.com/en/press-review/article/items/tl_files/client/ACTUALITES/1508LFW_9.jpg",
null,
"http://www.laserfocusworld.com/content/dam/lfw/print-articles/2015/08/1508LFW_nb_3.jpg",
null,
"http://www.laserfocusworld.com/content/dam/lfw/print-articles/2015/08/1508LFW_nb_3.jpg",
null,
"http://www.laserfocusworld.com/content/dam/lfw/print-articles/2015/08/1508LFW_nb_3.jpg",
null,
"https://www.quantel-laser.com/cron.php",
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.93154097,"math_prob":0.81188774,"size":4218,"snap":"2019-51-2020-05","text_gpt3_token_len":1019,"char_repetition_ratio":0.114143334,"word_repetition_ratio":0.94526625,"special_character_ratio":0.22593646,"punctuation_ratio":0.099386506,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9732846,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12],"im_url_duplicate_count":[null,1,null,1,null,3,null,3,null,3,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-12T15:10:33Z\",\"WARC-Record-ID\":\"<urn:uuid:d2b253c1-4956-4658-92c3-df2cfbbccbb0>\",\"Content-Length\":\"26861\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7dd25c1b-3f56-43f5-a00a-f3b289fb0371>\",\"WARC-Concurrent-To\":\"<urn:uuid:7619bd3e-122d-4757-848a-54ecc94c4245>\",\"WARC-IP-Address\":\"178.32.243.213\",\"WARC-Target-URI\":\"https://www.quantel-laser.com/en/press-review/article/items/lidt-wavelength-scaling-rule-of-thumb-shown-to-be-inaccurate.html\",\"WARC-Payload-Digest\":\"sha1:KKQZG7AIALW6J2T42DIMC3R25QBEC4MP\",\"WARC-Block-Digest\":\"sha1:2XVDSRLH3GLBIHARQMJOKQOUY7HYAICQ\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575540543850.90_warc_CC-MAIN-20191212130009-20191212154009-00338.warc.gz\"}"} |
https://www.ankitcodinghub.com/product/cmis102-lab7-functions-solved/ | [
"# CMIS102-Lab7- Functions Solved\n\n30.00 \\$\n\nCategory:\nClick Category Button to View Your Next Assignment | Homework\n\nYou'll get a download link with a: . ` zip` solution files instantly, after Payment\n\n## Description\n\n5/5 - (1 vote)\n\nWeek 7\nOverview This hands-on lab allows you to follow and experiment with the critical steps of developing a program including the program description, analysis, test plan, design, and implementation with C code. The example provided uses sequential, repetition, selection statements and user-defined functions.\nProgram Description\nWrite a program that will allow the user to select from a variety of mathematical functions, evaluate that function at a numerical value, and keep going until the user enters a selection indicating that the user is done with the program.\nThe program should be written in such a way that adding new functions to the source code is relatively easy.\nInteraction\nA menu will be presented to the user as a prompt. The exact menu will depend upon the actual functions currently available in the program. Here is one typical interaction, where a, b, c, etc. represent function selections.\n>Make a selection: a: a(x) = x*x b: b(x) = x*x*x c: c(x) = x^2 + 2*x + 7 q: quit Enter selection and value, or q: a 3.45 c(3.45) = 3.45^2 + 2*3.45 + 7 = 25.80 Analysis\n1. Use float data types for input, calculations and results. 2. Create a main input loop to select a function or quit. 3. Create a good prompt, including a list of possible selections to help the user. 4. Include appropriate printf functions within the math functions. 5. Make the main method simple by using a while loop, and a menu function which will return a special number if the user chooses the quit option. a. while (menu () == 0); b. if the menu function returns a 0 then continue c. returning any other value will end the program. 6. Use the ^ symbol in the display to indicate a power of x, i.e., x^4 means x*x*x*x. 7. Write a simple message when the program is over, such as “… bye …”.\n\n• lab7-10fwq9.zip"
]
| [
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.79594535,"math_prob":0.9176812,"size":1792,"snap":"2022-40-2023-06","text_gpt3_token_len":430,"char_repetition_ratio":0.15324385,"word_repetition_ratio":0.0,"special_character_ratio":0.25167412,"punctuation_ratio":0.15284973,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95793176,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-02-08T00:52:39Z\",\"WARC-Record-ID\":\"<urn:uuid:c9fa8681-4487-4644-a125-ba64c63e708f>\",\"Content-Length\":\"200614\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:8a4de494-5cc2-4ad7-9cd3-8700b3a59c57>\",\"WARC-Concurrent-To\":\"<urn:uuid:7663ab87-b79f-4f6c-86ad-170f7e565822>\",\"WARC-IP-Address\":\"104.21.40.150\",\"WARC-Target-URI\":\"https://www.ankitcodinghub.com/product/cmis102-lab7-functions-solved/\",\"WARC-Payload-Digest\":\"sha1:HJHMGTNUOMTZ5PUX3NS6RYQD4RJ6X4AI\",\"WARC-Block-Digest\":\"sha1:7FWLKY5BDQGXX2XTFDIH3N5AEAODHWLA\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-06/CC-MAIN-2023-06_segments_1674764500664.85_warc_CC-MAIN-20230207233330-20230208023330-00390.warc.gz\"}"} |
https://www.snapxam.com/problems/65957458/x-2-3x-20 | [
"Try now NerdPal! Our new app on iOS and Android\n\n# Solve the quadratic equation $x^2+3x+10=20$\n\n## Step-by-step Solution\n\nGo!\nMath mode\nText mode\nGo!\n1\n2\n3\n4\n5\n6\n7\n8\n9\n0\na\nb\nc\nd\nf\ng\nm\nn\nu\nv\nw\nx\ny\nz\n.\n(◻)\n+\n-\n×\n◻/◻\n/\n÷\n2\n\ne\nπ\nln\nlog\nlog\nlim\nd/dx\nDx\n|◻|\nθ\n=\n>\n<\n>=\n<=\nsin\ncos\ntan\ncot\nsec\ncsc\n\nasin\nacos\natan\nacot\nasec\nacsc\n\nsinh\ncosh\ntanh\ncoth\nsech\ncsch\n\nasinh\nacosh\natanh\nacoth\nasech\nacsch\n\n### Videos\n\n$x=2,\\:x=-5$\nGot another answer? Verify it here!\n\n## Step-by-step Solution \n\nProblem to solve:\n\n$x^2+3x+10=20$\n\nSpecify the solving method\n\n1\n\nGroup the terms of the equation by moving the terms that have the variable $x$ to the left side, and those that do not have it to the right side\n\n$x^2+3x=20-10$\n\nLearn how to solve quadratic equations problems step by step online.\n\n$x^2+3x=20-10$\n\nLearn how to solve quadratic equations problems step by step online. Solve the quadratic equation x^2+3x+10=20. Group the terms of the equation by moving the terms that have the variable x to the left side, and those that do not have it to the right side. Subtract the values 20 and -10. Rewrite the equation. To find the roots of a polynomial of the form ax^2+bx+c we use the quadratic formula, where in this case a=1, b=3 and c=-10. Then substitute the values of the coefficients of the equation in the quadratic formula: \\displaystyle x=\\frac{-b\\pm\\sqrt{b^2-4ac}}{2a}.\n\n$x=2,\\:x=-5$\n\n## Explore different ways to solve this problem\n\nSolving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more\n\nSolve for xFind the rootsSolve by factoringSolve by completing the squareSolve by quadratic formulaFind break even points\n\nSnapXam A2\n\nGo!\n1\n2\n3\n4\n5\n6\n7\n8\n9\n0\na\nb\nc\nd\nf\ng\nm\nn\nu\nv\nw\nx\ny\nz\n.\n(◻)\n+\n-\n×\n◻/◻\n/\n÷\n2\n\ne\nπ\nln\nlog\nlog\nlim\nd/dx\nDx\n|◻|\nθ\n=\n>\n<\n>=\n<=\nsin\ncos\ntan\ncot\nsec\ncsc\n\nasin\nacos\natan\nacot\nasec\nacsc\n\nsinh\ncosh\ntanh\ncoth\nsech\ncsch\n\nasinh\nacosh\natanh\nacoth\nasech\nacsch\n\n~ 0.09 s\n\n### Join 500k+ students in problem solving.\n\n##### Without automatic renewal.\nCreate an Account"
]
| [
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.8250945,"math_prob":0.9958249,"size":880,"snap":"2023-40-2023-50","text_gpt3_token_len":223,"char_repetition_ratio":0.1563927,"word_repetition_ratio":0.375,"special_character_ratio":0.25113636,"punctuation_ratio":0.07526882,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9996389,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-10-04T04:05:14Z\",\"WARC-Record-ID\":\"<urn:uuid:12168f3c-62fa-43be-8bef-36da7e654ea9>\",\"Content-Length\":\"62015\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a41d92af-db20-4290-bf8f-e28ff5dac45a>\",\"WARC-Concurrent-To\":\"<urn:uuid:bedf85fe-6103-4263-81bb-21baf2290747>\",\"WARC-IP-Address\":\"3.18.122.152\",\"WARC-Target-URI\":\"https://www.snapxam.com/problems/65957458/x-2-3x-20\",\"WARC-Payload-Digest\":\"sha1:XB33FUI46PRDMJYEORNXBASG43PVTFZF\",\"WARC-Block-Digest\":\"sha1:SQPOSX25XF4Y4G2FCINZUJUXGFT3RSGB\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233511351.18_warc_CC-MAIN-20231004020329-20231004050329-00224.warc.gz\"}"} |
https://stackoverflow.com/questions/33665241/is-opencv-matrix-data-guaranteed-to-be-continuous | [
"# Is opencv matrix data guaranteed to be continuous?\n\nI know that the data contained in an OpenCV matrix is not guaranteed to be continuous. To make myself clear, here is a paragraph from Opencv documentation:",
null,
"OpenCV provides a function called `isContinuous()` to test if the data of a given matrix is continuous. My questions are\n\n1. If I create a new matrix as follows\n``````cv::Mat img = cv::imread(img_name)\n``````\n\nIs the data in `img` guaranteed to be continuous?\n\n1. I know that creating a new matrix by borrowing data from the existing matrix would result in discontinuous data\n``````cv::Mat small_mat = large_mat.col(0);\n``````\n\nThe above code creates a new matrix `small_mat` by borrowing the 0th column of `large_mat`, leading to discontinuous data in `small_mat`. So the question is if I create a brand new matrix without borrowing data from the existing matrix, will the brand new matrix have continuous data or discontinuous data?\n\n1. Is the following code guaranteed to create a matrix with continuous data?\n``````cv::Mat mat(nRows, nCols, CV_32FC1);\n``````\n• I guess it is not guaranteed to be continuous if you use things like IPP with odd image dimensions. So it might depend on your speicific OpenCV build. Nov 12, 2015 at 9:45\n\nYou can see in the OpenCV doc for isContinuous:\n\nThe method returns true if the matrix elements are stored continuously without gaps at the end of each row. Otherwise, it returns false. Obviously, 1x1 or 1xN matrices are always continuous. Matrices created with Mat::create() are always continuous. But if you extract a part of the matrix using Mat::col(), Mat::diag() , and so on, or constructed a matrix header for externally allocated data, such matrices may no longer have this property.\n\nSo, as long as you are creating a new matrix (i.e. you're calling create), your matrix will be continuous.\n\n`create` works like:\n\n1. If the current array shape and the type match the new ones, return immediately. Otherwise, de-reference the previous data by calling Mat::release().\n3. Allocate the new data of total()*elemSize() bytes.\n4. Allocate the new, associated with the data, reference counter and set it to 1.\n\nThis means that when you (implicitly) call create, the matrix will be continuous (step 3).\n\nIf I create a new matrix with `imread` is the data guaranteed to be continuous\n\nYes, because `imread` internally calls `create`.\n\nI know that creating a new matrix by borrowing data from existing matrix would result in incontinuous data.\n\nCorrect, data will be non continuous. To make the new matrix continuous, you can call `clone()`, which calls `create` to create the new matrix.\n\nif I create a brand new matrix without borrowing data from existing matrix, will the brand new matrix have incontinuous data?\n\nYes, the constructor internally calls `create`.\n\nMatrix constructor is guaranteed to create a matrix with continuous data?\n\nYes, the constructor internally calls `create`.\n\nThis is a small example to summarize:\n\n``````#include <opencv2\\opencv.hpp>\n#include <iostream>\nusing namespace std;\nusing namespace cv;\n\nint main()\n{\ncout << \"img is continuous? \" << img.isContinuous() << endl;\n// Yes, calls create internally\n\n// Constructed a matrix header for externally allocated data\nMat small_mat = img.col(0);\ncout << \"small_mat is continuous? \" << small_mat.isContinuous() << endl;\n// No, you're just creating a new header.\n\n// Matrix (self) expression\nsmall_mat = small_mat + 2;\ncout << \"small_mat is continuous? \" << small_mat.isContinuous() << endl;\n// No, you're not even creating a new header\n\n// Matrix expression\nMat expr = small_mat + 2;\ncout << \"expr is continuous? \" << expr.isContinuous() << endl;\n// Yes, you're creating a new matrix\n\n// Clone\nMat small_mat_cloned = img.col(0).clone();\ncout << \"small_mat_cloned is continuous? \" << small_mat_cloned.isContinuous() << endl;\n// Yes, you're creating a new matrix\n\n// Create\nMat mat(10, 10, CV_32FC1);\ncout << \"mat is continuous? \" << mat.isContinuous() << endl;\n// Yes, you're creating a new matrix\n\nreturn 0;\n}\n``````\n\nWhen you create a `Mat` with `Mat::create`, it is continuous. Such operation like explicitly `Mat::create`, or implicitly `Mat::clone`, `Mat::Mat(...)`.\n\nData stored in OpenCV `cv::Mat`s are not always continuous in memory, which can be verified via API `Mat::isContinuous()`. Instead, it follows the following rules:\n\n1. Matrices created by `imread()`, `clone()`, or a constructor will always be continuous.\n2. The only time a matrix will not be continuous is when it borrows data from an existing matrix (i.e. created out of an ROI of a big mat), with the exception that the data borrowed is continuous in the big matrix, including\n• borrow a single row;\n• borrow multiple rows but with full original width.\n\nThe following code from my blog demonstrates this in a better way (see the inline comments for further explanation).\n\n``````std::vector<cv::Mat> mats(7);\n\n// continuous as created using constructor\nmats = cv::Mat::ones(1000, 800, CV_32FC3);\n\n// NOT continuous as borrowed data is not continuous (multiple rows and not full original width)\nmats = mats(cv::Rect(100, 100, 300, 200));\n\n// continuous as created using clone()\nmats = mats.clone();\n\n// continuous for single row always\nmats = mats.row(10);\n\n// NOT continuous as borrowed data is not continuous (multiple rows and not full original width)\nmats = mats(cv::Rect(5, 5, 100, 2));\n\n// continuous as borrowed data is continuous (multiple rows with full original width)\nmats = mats(cv::Rect(0, 5, mats.cols, 2));\n\n// NOT continuous as borrowed data is not continuous (multiple rows and not full original width)\nmats = mats.col(10);\n``````"
]
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null,
"https://i.stack.imgur.com/zv18U.jpg",
null
]
| {"ft_lang_label":"__label__en","ft_lang_prob":0.815368,"math_prob":0.9293698,"size":2829,"snap":"2023-40-2023-50","text_gpt3_token_len":662,"char_repetition_ratio":0.18477876,"word_repetition_ratio":0.1091314,"special_character_ratio":0.25733474,"punctuation_ratio":0.17953669,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.995222,"pos_list":[0,1,2],"im_url_duplicate_count":[null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-10-01T05:33:16Z\",\"WARC-Record-ID\":\"<urn:uuid:7e4cc2ba-c877-4643-98c9-aaf9bc02ec6e>\",\"Content-Length\":\"194996\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b4459a65-2eaa-450e-a61c-af2d9b7b0f01>\",\"WARC-Concurrent-To\":\"<urn:uuid:463ea330-0d4c-4bc8-9f17-f135772d3249>\",\"WARC-IP-Address\":\"104.18.22.201\",\"WARC-Target-URI\":\"https://stackoverflow.com/questions/33665241/is-opencv-matrix-data-guaranteed-to-be-continuous\",\"WARC-Payload-Digest\":\"sha1:R62E4ZB76KPKJUO4L6EXRD2YPQEDNPIW\",\"WARC-Block-Digest\":\"sha1:N62342TZOQJKOPQMKQ3KGTYDP653WVFQ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510781.66_warc_CC-MAIN-20231001041719-20231001071719-00179.warc.gz\"}"} |
https://edurev.in/course/quiz/attempt/18188_Test-Two-Port-Network-1-/24a85cca-6fdd-4095-abf6-fd24bdda48c0 | [
"Test: Two Port Network - 1\n\n# Test: Two Port Network - 1\n\nTest Description\n\n## 10 Questions MCQ Test Network Theory (Electric Circuits) | Test: Two Port Network - 1\n\nTest: Two Port Network - 1 for Electrical Engineering (EE) 2023 is part of Network Theory (Electric Circuits) preparation. The Test: Two Port Network - 1 questions and answers have been prepared according to the Electrical Engineering (EE) exam syllabus.The Test: Two Port Network - 1 MCQs are made for Electrical Engineering (EE) 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Two Port Network - 1 below.\nSolutions of Test: Two Port Network - 1 questions in English are available as part of our Network Theory (Electric Circuits) for Electrical Engineering (EE) & Test: Two Port Network - 1 solutions in Hindi for Network Theory (Electric Circuits) course. Download more important topics, notes, lectures and mock test series for Electrical Engineering (EE) Exam by signing up for free. Attempt Test: Two Port Network - 1 | 10 questions in 30 minutes | Mock test for Electrical Engineering (EE) preparation | Free important questions MCQ to study Network Theory (Electric Circuits) for Electrical Engineering (EE) Exam | Download free PDF with solutions\n 1 Crore+ students have signed up on EduRev. Have you?\nTest: Two Port Network - 1 - Question 1\n\n### [T] = ?",
null,
"Detailed Solution for Test: Two Port Network - 1 - Question 1\n\nLet I3 be the clockwise loop current in center loop",
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"Test: Two Port Network - 1 - Question 2\n\n### [h] = ?",
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"Detailed Solution for Test: Two Port Network - 1 - Question 2",
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"",
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"Test: Two Port Network - 1 - Question 3\n\n### [y] = ?",
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"Detailed Solution for Test: Two Port Network - 1 - Question 3",
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"",
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"Test: Two Port Network - 1 - Question 4\n\nThe y-parameters of a 2-port network are",
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"A resistor of 1 ohm is connected across as shown in fig. P.1.10.2 8. The new y –parameter would be",
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"Detailed Solution for Test: Two Port Network - 1 - Question 4\n\ny-parameter of 1Ω resistor network are",
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"New y-parameter =",
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"Test: Two Port Network - 1 - Question 5\n\nFor the 2-port of fig. P.1.10.29,",
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"",
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"The value of Vo/Vs is\n\nDetailed Solution for Test: Two Port Network - 1 - Question 5",
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"",
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"Test: Two Port Network - 1 - Question 6\n\nThe T-parameters of a 2-port network are",
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"If such two 2-port network are cascaded, the z –parameter for the cascaded network is\n\nDetailed Solution for Test: Two Port Network - 1 - Question 6",
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"",
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"",
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"Test: Two Port Network - 1 - Question 7\n\n[y] = ?",
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"Detailed Solution for Test: Two Port Network - 1 - Question 7",
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"",
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"Test: Two Port Network - 1 - Question 8\n\n[y] = ?",
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"Detailed Solution for Test: Two Port Network - 1 - Question 8",
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"",
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"",
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"",
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"Test: Two Port Network - 1 - Question 9\n\nh21 = ?",
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"Detailed Solution for Test: Two Port Network - 1 - Question 9",
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"",
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"Test: Two Port Network - 1 - Question 10\n\nIn the circuit shown in fig. P.1.10.34, when the voltage V1 is 10 V, the current I is 1 A. If the applied voltage at port-2 is 100 V, the short circuit current flowing through at port 1 will be",
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"Detailed Solution for Test: Two Port Network - 1 - Question 10",
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"Interchanging the port",
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"## Network Theory (Electric Circuits)\n\n23 videos|63 docs|61 tests\nInformation about Test: Two Port Network - 1 Page\nIn this test you can find the Exam questions for Test: Two Port Network - 1 solved & explained in the simplest way possible. Besides giving Questions and answers for Test: Two Port Network - 1 , EduRev gives you an ample number of Online tests for practice\n\n## Network Theory (Electric Circuits)\n\n23 videos|63 docs|61 tests",
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"(Scan QR code)"
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https://mathoverflow.net/questions/72978/radon-nikodym-derivative-as-a-measurable-function-in-a-product-space | [
"# Radon-Nikodym derivative as a measurable function in a product space.\n\nLet $X$ be a Polish space with the probability measure $P$ and the Borel sigma algebra. Suppose that $X$ is also a group and the probability $P$ is left and right quasiinvariant. Let $P_x$ denote the probability measure $P_x(A)=P(xA)$ for every $x$ in $X$ .Obviously, for each $x$ in $X$, the radon-nikodym derivative $dP_x/dP$ is borel measurable.\n\nI am traying to show that there is a measureable function $\\Phi:X \\times X\\rightarrow[0,\\infty )$ such that for every $x$ in $X$ , $\\Phi(x,y)=(dP_x/dP)(y)$ for a.e. $y$ (notice that $\\Phi$ needs to be measurable with respect to the borel sigma-algebra of the product space).\n\nI can show that there is a measurable function $\\Phi$ such that for $P$ - almost every $x$ in $X$, $\\Phi(x,y)=(dP_x/dP)(y)$ for a.e. $y$ , by taking the derivative $dm/dP\\times P$ , where $m=(P\\times P)\\circ S$ and $S:X \\times X\\rightarrow X\\times X$ is the function $S(x,y)=(x,x^{-1}y)$. But i need the eqaulity for every x in X.\n\nAny suggestions?\n\n• Concerning your last statement (I must have overlooked it first), you won't need equality for all $x \\in X$, but only for a.a. $x \\in X$, in order to show measurablity, so you argument is slicker than mine. Sets of measure $0$ are always $P$ measurable, by definition, and the completion wrt. to any quasiinvariant measure on a transitive $G$ space will coincide, so the completion do not depend upon the quasiinvariant measure chosen in the first place, and you should enrich your $\\sigma$ algebra by these sets. – Marc Palm Aug 17 '11 at 7:58\n• Asked and answered at MathSE: math.stackexchange.com/questions/58018/… – user6096 Aug 30 '11 at 15:27\n\nConsider a topological Hausdorff group $G$ with a quasi invariant measure, then the group is necessary locally compact. Now, since you assume implicitely that the transform of a measurable set by multiplication is measurbale, the action will be continuous, as measurable group isomorphisms are continuous. Hence we may assume that $X$ is a topological group. Now since your action is transitive, there is only one orbit and your quasi invariant measure is necesary continuous against the Haar measure $\\mu$. The function $d P_x / d P$ can writen as the product of two measurable functions $d P_x / d \\mu$ and $d \\mu / d P$ by the chain rule of the Radon Nykodym derivatives, hence is measurable.\nNote $\\mu_x = \\mu$: So in fact, your function $\\Phi(x,y) = \\frac{\\lambda(xy)}{\\lambda(y)}$ for $\\lambda =d P /d \\mu$.\n• Btw, $\\Phi$ is a cocycle and the data $P$, $\\lambda$ or $\\phi$ are all equivalent, and can be recovered from each other under some mild assumptions. And assuming right quasi invariance, or left quasi invariance, should be sufficient to get quasi invariance from both sides. – Marc Palm Aug 16 '11 at 15:09\n• One quick way to topologize $X$ is to use the quasi-invariant measure to produce an action of $X$ on $L^2(X)$ by unitaries. This embeds $X$ into the unitary group on a Hilbert space, which is a topological group if endowed with the strong operator topology. – Dima Shlyakhtenko Aug 16 '11 at 17:51"
]
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https://blender.stackexchange.com/questions/129302/how-to-update-blenders-naming-index-thing-001-002-etc-after-joining-obje | [
"# How to update Blender's naming index thing (.001, .002, etc.) after joining objects\n\nI've been trying to reuse certain parts of code as functions in my bpy scripts. But that means that the same bmesh will be created as 'my_bmesh.001' the next time I run that function. To deal with this, I join 'my_bmesh' with a different object, 'main_object' and then run the function again, hoping that it will notice that 'my_bmesh' doesn't exist anymore, because it was joined into 'main_object' thereby allowing me to avoid situations with .001 names. In one current case, where I make stairs using an add_stairs() function, that function makes 2 objects, 'stairs' and 'stairs_support'. At the end of the function, I join 'stairs_support' into 'stairs'. A different function runs that add_stairs() function twice, and here is where the problem happens. Since 'stairs_support' has already been joined to 'stairs', it no longer exists. Still, upon the next call to add_stairs(), instead of the new bmesh being named 'stairs_support', it would be named 'stairs_support.001' so when the script looks for 'stairs_support' to join it with 'stairs', it returns the error:\n\nFor now, I just have to check myself that the original object already exists, so it knows to go with the 'stairs_support.001' name, but I don't want to have to make something like a for-loop that goes until it figures out what number mesh the counter has gone up to. I know that the counter restarts when Blender starts up again, but I can't just restart Blender mid-script. How do I refresh this counter, after I join 'stairs_support' to 'stairs'? Or perhaps there is some other means of combating this issue without dealing with the naming counter?\n\nMy original script is full of 1AM math that somehow just works, so to keep the code as readable as possible, I created a new script in under 200 lines of code that demonstrates the issue I'm having.\n\nHere is the script:\n\nimport bpy\nimport bmesh\nfrom bpy_extras import object_utils\n\ndef add_box(width, height, depth, self, context):\n\nverts = [(+(width / 2.0), +(height / 2.0), -(depth / 2.0)),\n(+(width / 2.0), -(height / 2.0), -(depth / 2.0)),\n(-(width / 2.0), -(height / 2.0), -(depth / 2.0)),\n(-(width / 2.0), +(height / 2.0), -(depth / 2.0)),\n(+(width / 2.0), +(height / 2.0), +(depth / 2.0)),\n(+(width / 2.0), -(height / 2.0), +(depth / 2.0)),\n(-(width / 2.0), -(height / 2.0), +(depth / 2.0)),\n(-(width / 2.0), +(height / 2.0), +(depth / 2.0)),\n]\n\nfaces = [(0, 1, 2, 3),\n(4, 7, 6, 5),\n(0, 4, 5, 1),\n(1, 5, 6, 2),\n(2, 6, 7, 3),\n(4, 0, 3, 7),\n]\n\nmesh = bpy.data.meshes.new(\"Object1\")\n\nbm = bmesh.new()\n\nfor v_co in verts:\nbm.verts.new(v_co)\n\nbm.verts.ensure_lookup_table()\nfor f_idx in faces:\nbm.faces.new([bm.verts[i] for i in f_idx])\n\nbm.to_mesh(mesh)\nmesh.update()\n\n# add the mesh as an object into the scene with this utility module\n\nwidth += 1.0\nverts = [(+(width / 2.0), +(height / 2.0), -(depth / 2.0)),\n(+(width / 2.0), -(height / 2.0), -(depth / 2.0)),\n(-(width / 2.0), -(height / 2.0), -(depth / 2.0)),\n(-(width / 2.0), +(height / 2.0), -(depth / 2.0)),\n(+(width / 2.0), +(height / 2.0), +(depth / 2.0)),\n(+(width / 2.0), -(height / 2.0), +(depth / 2.0)),\n(-(width / 2.0), -(height / 2.0), +(depth / 2.0)),\n(-(width / 2.0), +(height / 2.0), +(depth / 2.0)),\n]\n\nfaces = [(0, 1, 2, 3),\n(4, 7, 6, 5),\n(0, 4, 5, 1),\n(1, 5, 6, 2),\n(2, 6, 7, 3),\n(4, 0, 3, 7),\n]\n\nmesh = bpy.data.meshes.new(\"Object2\")\n\nbm = bmesh.new()\n\nfor v_co in verts:\nbm.verts.new(v_co)\n\nbm.verts.ensure_lookup_table()\nfor f_idx in faces:\nbm.faces.new([bm.verts[i] for i in f_idx])\n\nbm.to_mesh(mesh)\nmesh.update()\n\n# add the mesh as an object into the scene with this utility module\n\n#THE WAY IT CURRENTLY FAILS:\nbpy.data.objects['Object1'].select=True\nbpy.data.objects['Object2'].select=True\nbpy.context.scene.objects.active = bpy.data.objects['Object1']\nbpy.ops.object.join()\nbpy.data.objects['Object1'].name = 'Final_object'\n\n#TO MAKE IT WORK, COMMENT OUT THE ABOVE (ALL LINES FROM 79 TO 83) AND UNCOMMENT THE SECTION BELOW:\n\"\"\"\n#Join them and rename them\nbpy.ops.object.select_all(action='DESELECT')\nif bpy.data.objects.get('Object1') is not None:\nbpy.data.objects['Object1'].select=True\nelse:\nbpy.data.objects['Object1.001'].select=True\nif bpy.data.objects.get('Object2') is not None:\nbpy.data.objects['Object2'].select=True\nelse:\nbpy.data.objects['Object2.001'].select=True\nif bpy.data.objects.get('Object1') is not None:\nbpy.context.scene.objects.active = bpy.data.objects['Object1']\nelse:\nbpy.context.scene.objects.active = bpy.data.objects['Object1.001']\n\nbpy.ops.object.join()\n\nif bpy.data.objects.get('Object1') is not None:\nbpy.data.objects['Object1'].name = 'Final_object'\nelse:\nbpy.data.objects['Object1.001'].name = 'Final_object'\n\"\"\"\n\nfrom bpy.props import (\nBoolProperty,\nBoolVectorProperty,\nFloatProperty,\nFloatVectorProperty,\n)\n\nbl_options = {'REGISTER', 'UNDO'}\n\nwidth = FloatProperty(\nname=\"Width\",\ndescription=\"Box Width\",\nmin=0.01, max=100.0,\ndefault=1.0,\n)\nheight = FloatProperty(\nname=\"Height\",\ndescription=\"Box Height\",\nmin=0.01, max=100.0,\ndefault=1.0,\n)\ndepth = FloatProperty(\nname=\"Depth\",\ndescription=\"Box Depth\",\nmin=0.01, max=100.0,\ndefault=1.0,\n)\nlayers = BoolVectorProperty(\nname=\"Layers\",\ndescription=\"Object Layers\",\nsize=20,\noptions={'HIDDEN', 'SKIP_SAVE'},\n)\n\n# generic transform props\nview_align = BoolProperty(\nname=\"Align to View\",\ndefault=False,\n)\nlocation = FloatVectorProperty(\nname=\"Location\",\nsubtype='TRANSLATION',\n)\nrotation = FloatVectorProperty(\nname=\"Rotation\",\nsubtype='EULER',\n)\n\ndef execute(self, context):\n\nreturn {'FINISHED'}\n\ndef register():\n\ndef unregister():\n\nif __name__ == \"__main__\":\nregister()\n\n\nAnd a test .blend file:",
null,
"• I'm using Blender 2.79, if that makes a difference. – Perregrinne Jan 20 '19 at 6:45\n• It would be far easier to help if you included your script rather than a description of your script. – batFINGER Jan 20 '19 at 8:09\n• Let me know if the link to the script doesn't work. I've never really had to do this before. – Perregrinne Jan 21 '19 at 15:59\n\nBased on your original script the following changes 4 lines to store your newly created mesh data in variables that can be accessed instead of the name. The other changes are primarily with regards to pep8 compliance and removal of alternative method from your original code. It is likely that this can be improved upon. Furthermore the use of join will create orphan data that will be removed on save/reload of file may become excessive after multiple uses of the command. Also it was unclear as to whether or not you intended to have the execute duplicate the command so that was left as found.\n\nimport bpy\nimport bmesh\nfrom bpy_extras import object_utils\nfrom bpy.props import (\nBoolProperty,\nBoolVectorProperty,\nFloatProperty,\nFloatVectorProperty,\n)\n\ndef add_box(width, height, depth, self, context):\n\nverts = [(+(width / 2.0), +(height / 2.0), -(depth / 2.0)),\n(+(width / 2.0), -(height / 2.0), -(depth / 2.0)),\n(-(width / 2.0), -(height / 2.0), -(depth / 2.0)),\n(-(width / 2.0), +(height / 2.0), -(depth / 2.0)),\n(+(width / 2.0), +(height / 2.0), +(depth / 2.0)),\n(+(width / 2.0), -(height / 2.0), +(depth / 2.0)),\n(-(width / 2.0), -(height / 2.0), +(depth / 2.0)),\n(-(width / 2.0), +(height / 2.0), +(depth / 2.0)),\n]\n\nfaces = [\n(0, 1, 2, 3),\n(4, 7, 6, 5),\n(0, 4, 5, 1),\n(1, 5, 6, 2),\n(2, 6, 7, 3),\n(4, 0, 3, 7),\n]\n\nmesh = bpy.data.meshes.new(\"Object1\")\n\nbm = bmesh.new()\n\nfor v_co in verts:\nbm.verts.new(v_co)\n\nbm.verts.ensure_lookup_table()\nfor f_idx in faces:\nbm.faces.new([bm.verts[i] for i in f_idx])\n\nbm.to_mesh(mesh)\nmesh.update()\n\n# add the mesh as an object into the scene with this utility module\n# and assign to variable\n\nwidth += 1.0\nverts = [(+(width / 2.0), +(height / 2.0), -(depth / 2.0)),\n(+(width / 2.0), -(height / 2.0), -(depth / 2.0)),\n(-(width / 2.0), -(height / 2.0), -(depth / 2.0)),\n(-(width / 2.0), +(height / 2.0), -(depth / 2.0)),\n(+(width / 2.0), +(height / 2.0), +(depth / 2.0)),\n(+(width / 2.0), -(height / 2.0), +(depth / 2.0)),\n(-(width / 2.0), -(height / 2.0), +(depth / 2.0)),\n(-(width / 2.0), +(height / 2.0), +(depth / 2.0)),\n]\n\nfaces = [\n(0, 1, 2, 3),\n(4, 7, 6, 5),\n(0, 4, 5, 1),\n(1, 5, 6, 2),\n(2, 6, 7, 3),\n(4, 0, 3, 7),\n]\n\nmesh = bpy.data.meshes.new(\"Object2\")\n\nbm = bmesh.new()\n\nfor v_co in verts:\nbm.verts.new(v_co)\n\nbm.verts.ensure_lookup_table()\nfor f_idx in faces:\nbm.faces.new([bm.verts[i] for i in f_idx])\n\nbm.to_mesh(mesh)\nmesh.update()\n\n# add the mesh as an object into the scene with this utility module\n# and assign to variable\n# by default obj2 is both selected and active\n\nobj1.select = True\n\nbpy.ops.object.join()\ncontext.active_object.name = 'Final_object'\n\nbl_options = {'REGISTER', 'UNDO'}\n\nwidth = FloatProperty(\nname=\"Width\",\ndescription=\"Box Width\",\nmin=0.01, max=100.0,\ndefault=1.0,\n)\nheight = FloatProperty(\nname=\"Height\",\ndescription=\"Box Height\",\nmin=0.01, max=100.0,\ndefault=1.0,\n)\ndepth = FloatProperty(\nname=\"Depth\",\ndescription=\"Box Depth\",\nmin=0.01, max=100.0,\ndefault=1.0,\n)\nlayers = BoolVectorProperty(\nname=\"Layers\",\ndescription=\"Object Layers\",\nsize=20,\noptions={'HIDDEN', 'SKIP_SAVE'},\n)\n\n# generic transform props\nview_align = BoolProperty(\nname=\"Align to View\",\ndefault=False,\n)\nlocation = FloatVectorProperty(\nname=\"Location\",\nsubtype='TRANSLATION',\n)\nrotation = FloatVectorProperty(\nname=\"Rotation\",\nsubtype='EULER',\n)\n\ndef execute(self, context):\n\nreturn {'FINISHED'}\n\ndef register():"
]
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null,
"https://blend-exchange.giantcowfilms.com/embedImage.png",
null
]
| {"ft_lang_label":"__label__en","ft_lang_prob":0.600965,"math_prob":0.9632381,"size":6191,"snap":"2021-21-2021-25","text_gpt3_token_len":1858,"char_repetition_ratio":0.1819945,"word_repetition_ratio":0.33089134,"special_character_ratio":0.3421095,"punctuation_ratio":0.28240407,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98131865,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-05-08T20:25:45Z\",\"WARC-Record-ID\":\"<urn:uuid:fcd1972c-b9b0-4fba-ba52-6ade1a9bdfec>\",\"Content-Length\":\"182747\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6bbc1231-a035-4459-a720-eb7713522b1b>\",\"WARC-Concurrent-To\":\"<urn:uuid:2bc5c796-3190-485d-9931-5f0b3a00d8df>\",\"WARC-IP-Address\":\"151.101.129.69\",\"WARC-Target-URI\":\"https://blender.stackexchange.com/questions/129302/how-to-update-blenders-naming-index-thing-001-002-etc-after-joining-obje\",\"WARC-Payload-Digest\":\"sha1:KQIJFH55FUTFWZEYHU7JOXO26WNOWMW2\",\"WARC-Block-Digest\":\"sha1:DVAVSCVMLR2V7PAEDY4LADOJO5EMLHIU\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-21/CC-MAIN-2021-21_segments_1620243988923.22_warc_CC-MAIN-20210508181551-20210508211551-00505.warc.gz\"}"} |
https://wisdomessays.com/true-or-false-true-or-false-a-set-is-any-collection-of-objects-true-or-false-a-proper-subset-of-a-set-is-itself-a-subset-of-the-set-but-not-vice-versa-true-or-false-the-empty-set-is-a-subset-of/ | [
"# True or False True or false. A set is any collection of objects. True or false. A proper subset of a set is itself a subset of the set, but not vice versa. True or false. The empty set is a subset of every set. True or false. If A ∪ B = ∅ , then A = ∅ a\n\nRate this post\n\nTrue or False True or false. A set is any collection of objects. True or false. A proper subset of a set is itself a subset of the set, but not vice versa. True or false. The empty set is a subset of every set. True or false. If A ∪ B = ∅ , then A = ∅ a\n\n1. True or false. A set is any collection of objects.\n2. True or false. A proper subset of a set is itself a subset of the set, but not vice versa.\n3. True or false. The empty set is a subset of every set.\n4. True or false. If A ∪ B = ∅ , then A = ∅ and B = ∅ .\n5. True or false. If A ∩ B = ∅ , then A = ∅ or B = ∅ or both A and B are empty sets.\n6. True or false. (A ∪ Ac)c = ∅ .\n7. True or false. [A ∩ (B ∪ C)]c = (A ∩ B)c (A C)c\n8. True or false. n(A) + n(B) = n(A ∪ B) + n(A B)\n9. True or false. If A ∈ B, then n(B) = n(A) + n(Ac B).\n10. True or false. The number of permutations of n distinct objects taken all together is n!\n11. True or false. P(nr) = rC(nr)."
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.7085671,"math_prob":0.93692964,"size":1699,"snap":"2023-40-2023-50","text_gpt3_token_len":554,"char_repetition_ratio":0.25545722,"word_repetition_ratio":0.60106385,"special_character_ratio":0.34196585,"punctuation_ratio":0.15274464,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9990658,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-02T21:11:59Z\",\"WARC-Record-ID\":\"<urn:uuid:f1278440-ebeb-459d-a1ff-5e3f312d766d>\",\"Content-Length\":\"64397\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:13800808-4cfd-41d1-80d0-5bcdaa56e579>\",\"WARC-Concurrent-To\":\"<urn:uuid:759ba11b-daea-4301-8ae8-754dd87d6d3f>\",\"WARC-IP-Address\":\"63.250.32.84\",\"WARC-Target-URI\":\"https://wisdomessays.com/true-or-false-true-or-false-a-set-is-any-collection-of-objects-true-or-false-a-proper-subset-of-a-set-is-itself-a-subset-of-the-set-but-not-vice-versa-true-or-false-the-empty-set-is-a-subset-of/\",\"WARC-Payload-Digest\":\"sha1:53JUML34PLZPJQLL7SQCZNVXCKD3KIUD\",\"WARC-Block-Digest\":\"sha1:QZV6WGOODQ66RC45MKIOBTJPUBTIZ7CY\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100452.79_warc_CC-MAIN-20231202203800-20231202233800-00127.warc.gz\"}"} |
http://makemathmore.com/members/category/common-core-standards/6th-grade/page/2/ | [
"### Dream House Project\n\nA rich task to discover and practice how to find like terms and then simplify expressions.\n\n### Integer Football\n\nAmerican Football is a game of positive and negative yards. This game simulates this experience. It shows students where negatives exist in real life (America’s favorite sport) and helps them to practice and further realize the rule for adding integers of different signs.\n\n### Describing The Speed Of A Car\n\nIn this lesson students will see why math is important in helping us describe things like the speed of a car. Without math describing how fast a car is going is much more difficult. Students will watch a video, make observations, and discover math to help them describe what is happening.\n\n### Geometry Walk\n\nIn this lesson students will take a walk and discover where geometric figures are around them. Please read the lesson plan fully as there is a lot of depth and variety that this lesson can provide which is all spelled out in the lesson plan.\n\n### Bar Graphing An Inquiry\n\nIn this lesson students will ask questions and answer questions about stuff they care about and then summarize their data in a single or double bar graph.\n\n### Life’s Order Of Operations\n\nIn this lesson students will cement understanding of order of operations while seeing how this often boring math subject can relate to the rules and order we have to follow in life to accomplish even the most basic tasks.\n\n### How Tall Is That?\n\nStudents will use proportions and proportional reasoning to accurately calculate how tall something is without actually measuring the height of that object – since it is really tall and they can’t!\n\n### Who is the better quarterback? (Algebra In Football)\n\nStudents will calculate quarterback passer ratings to determine which quarterback is better using algebraic substituting into equations.\n\n### Cellular Algebra\n\nStudents will discover an equation that will allow them to calculate the cost of a cell plan with variables involved using algebraic concepts. Students will have to do research to discover the costs.\n\n### Clothing Design And Pricing\n\nStudents will design clothing and then use substitution into a preset equation to determine how much they should charge for their clothing.\n\n### Analyzing Data\n\nStudents will create a question and ask that question to collect data and then analyze that data to pull as much meaning out of the numbers as possible."
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https://www.britannica.com/science/eigenvalue | [
"Science & Tech\n\n# eigenvalue\n\nmathematics\nAlso known as: characteristic value, latent root\nRelated Topics:\nroot\n\neigenvalue, one of a set of discrete values of a parameter, k, in an equation of the form = , in which P is a linear operator (that is, a symbol denoting a linear operation to be performed), for which there are solutions satisfying given boundary conditions. The symbol ψ (psi) represents an eigenfunction (proper or characteristic function) belonging to that eigenvalue. The totality of eigenvalues is a set. In quantum mechanics P is frequently a Hamiltonian, or energy, operator and the eigenvalues are energy values, but operators corresponding to other dynamical variables such as total angular momentum are also used. Experimental measurements of the proper dynamical variable will yield eigenvalues.\n\nThis article was most recently revised and updated by William L. Hosch."
]
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.8430789,"math_prob":0.9701191,"size":838,"snap":"2023-40-2023-50","text_gpt3_token_len":175,"char_repetition_ratio":0.117506,"word_repetition_ratio":0.0,"special_character_ratio":0.18735084,"punctuation_ratio":0.10958904,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9917105,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-01T13:48:59Z\",\"WARC-Record-ID\":\"<urn:uuid:2ade5f59-c526-4252-a2af-1be2040bbacf>\",\"Content-Length\":\"71516\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:74fe0560-b196-49fa-be30-daaab5952b95>\",\"WARC-Concurrent-To\":\"<urn:uuid:0104fc89-5c2a-4035-bbb5-a509488dc47c>\",\"WARC-IP-Address\":\"104.18.4.110\",\"WARC-Target-URI\":\"https://www.britannica.com/science/eigenvalue\",\"WARC-Payload-Digest\":\"sha1:WKOO27GJ2ZLFZM525GJKWOACOANAD2Q4\",\"WARC-Block-Digest\":\"sha1:W3CQPGDYTNCIY7NR3KR5MRIQLMA6OMZU\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100287.49_warc_CC-MAIN-20231201120231-20231201150231-00344.warc.gz\"}"} |
http://appddeevvmeanderings.blogspot.com/2014/02/scala-slick-and-sub-selects-for-max.html | [
"### scala slick and sub-selects for max value\n\nI am learning slick. A bit of tough road initially. The blogs and other posts out there really help. Thistutorial was especially helpful.\nMy domain was storing note objects in database and tracking revisions. Here's the table structure:\n``` class Notes(tag: Tag) extends Table[(Int, Int, java.sql.Timestamp, Boolean, Option[String])](tag, \"Notes\") {\n// some dbs cannot return compound primary key, so use a standard int\ndef id = column[Int](\"id\", O.AutoInc, O.PrimaryKey)\ndef docId = column[Int](\"docId\")\ndef createdOn = column[java.sql.Timestamp](\"createdOn\")\ndef content = column[Option[String]](\"content\")\ndef latest = column[Boolean](\"latest\")\ndef * = (id, docId, createdOn, latest, content)\n\ndef index1 = index(\"index1\", docId)\ndef index2 = index(\"index2\", createdOn)\ndef index3 = index(\"index3\", latest)\n}\nval Notes = TableQuery[Notes]\n```\nThere are more enhancements needed for this table, but you get the gist.\nSo we can query the table for a specific document id and obtain the latest document:\n``` def latestNote(docId: Int) =\nfor {\nn <- font=\"\" notes=\"\">\nif n.docId === docId;\nif n.latest === true\n} yield n\n```\nBut if we want to find it using just the timestamp, the first thing you can do is issue 2 queries:\n``` def latestFromTimestamp(docId: Int)(implicit session: Session) = {\nval maxTimestamp = Notes.groupBy(_.docId).map {\ncase (docId, note) => note.map(_.createdOn).max\n}\nmaxTimestamp.firstOption match {\ncase Some(ts) =>\n(for { n <- font=\"\" notes=\"\"> if n.createdOn === ts } yield n).firstOption\ncase _ => None\n}\n}\n```\nBut we would like to avoid issuing 2 queries because then we need a Session object. We want more of a query:\n``` def latestFromTimestamp2(docId: Int) = {\nfor {\nn <- font=\"\" notes=\"\">\nmaxTimestamp <- font=\"\" notes=\"\">.groupBy(_.docId).map { case (docId, note) => note.map(_.createdOn).max }\nif n.createdOn === maxTimestamp\n} yield n\n}\n```\n\nwhich generates:\n```query: select x2.\"id\", x2.\"docId\", x2.\"createdOn\", x2.\"latest\", x2.\"content\" from \"blah\" x2, (select max(x3.\"createdOn\") as x4 from \"blah\" x3 group by x3.\"docId\") x5 where x2.\"createdOn\" = x5.x4\n```\nand that's what we wanted.\nOf course, if we want to update a Note's latest flag, we do need to run 2 queries and hence need a session:\n``` def update(docId: Int, content: Option[String])(implicit session: Session) = {\nval note = latestNote(docId).firstOption\nnote match {\ncase Some(n) =>\n// Update old note\nNotes.filter(_.docId === docId).map(_.latest).update(false)\n// Add insert the new note\nval newNote = (n._1, n._2, now, true, content)\nval newId = (Notes returning Notes.map(_.id)) insert newNote\nSome((newId, n._2, n._3, n._4, n._5))\ncase _ => None\n}\n}```\n\nThis is on gisthub: gisthub"
]
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https://discuss.pytorch.org/t/why-using-linearfunction-in-extending-torch-nn/16227 | [
"# Why using LinearFunction in `Extending torch.nn`?\n\nHello everyone,\n\nI’m a bit confused with how to properly extend `torch.nn`.\n\nIn basically all code samples I’ve seen, custom modules are compositions of already existing modules. But after playing around with tensors and autograd, it is tempting (if one wants flexibility) to just define parameters in a custom module’s `__init__` and then perform some calculation in the `forward` function, similarly to how it is described here:\n\nhttp://pytorch.org/docs/0.3.1/notes/extending.html?highlight=extending#extending-torch-nn\n\n``````def forward(self, input):\n# See the autograd section for explanation of what happens here.\nreturn LinearFunction.apply(input, self.weight, self.bias)\n``````\n\nNow – is it o.k. to drop `LinearFunction` and perform the calculation directly like this:\n\n``````def forward(self, input):\noutput = input.mm(self.weight.t())\nif self.bias is not None:\noutput += self.bias.unsqueeze(0).expand_as(output)\nreturn output\n``````\n\nIt seem to work, but I’ve never seen this practice in code examples, so my question basically is whether there’s something wrong with this approach.\n\nThanks for clarification.\n\nHi,\n\nThe difference is that in the first case, you have a single Function in the computational graph: LinearFunction, and so the backward will just call the backward for that Function.\nIn the second case, the computational graph contain few Functions: mm, transpose, addition, unsqueeze, expand… This means that the backward pass will require to traverse all these functions and call the backward for each of them. Moreover to be able to perform this backward pass, all intermediary results in between them will be saved in memory.\n\nThe first one is thus more efficient both speed and memory wise, but it requires you to implement the `backward` method by hand. The second one pay the cost of using the autograd to get the gradients without implementing the backward method explicitly.\n\n1 Like\n\nThanks! That makes sense."
]
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https://apprize.best/science/algorithms/6.html | [
" Branch-and-Bound - Foundations of Algorithms (2015)\n\n# Foundations of Algorithms (2015)\n\n### Chapter 6 Branch-and-Bound",
null,
"We’ve provided our thief with two algorithms for the 0-1 Knapsack problem: the dynamic programming algorithm in Section 4.5 and the backtracking algorithm in Section 5.7. Because both these algorithms are exponential-time in the worst case, they could both take many years to solve our thief’s particular instance. In this chapter, we provide our thief with yet another approach, called branch-and-bound. As we shall see, the branch-and-bound algorithm developed here is an improvement on the backtracking algorithm. Therefore, even if the other two algorithms fail to solve our thief’s instance efficiently, the branch-and-bound algorithm might do so.\n\nThe branch-and-bound design strategy is very similar to backtracking in that a state space tree is used to solve a problem. The differences are that the branch-and-bound method (1) does not limit us to any particular way of traversing the tree and (2) is used only for optimization problems. A branch-and-bound algorithm computes a number (bound) at a node to determine whether the node is promising. The number is a bound on the value of the solution that could be obtained by expanding beyond the node. If that bound is no better than the value of the best solution found so far, the node is nonpromising. Otherwise, it is promising. Because the optimal value is a minimum in some problems and a maximum in others, by “better” we mean smaller or larger, depending on the problem. As is the case for backtracking algorithms, branch-and-bound algorithms are ordinarily exponential-time (or worse) in the worst case. However, they can be very efficient for many large instances.\n\nThe backtracking algorithm for the 0-1 Knapsack problem in Section 5.7 is actually a branch-and-bound algorithm. In that algorithm, the promising function returns false if the value of bound is not greater than the current value of maxprofit. A backtracking algorithm, however, does not exploit the real advantage of using branch-and-bound. Besides using the bound to determine whether a node is promising, we can compare the bounds of promising nodes and visit the children of the one with the best bound.\n\nFigure 6.1 A breadth-first search of a tree. The nodes are numbered in the order in which they are visited. The children of a node are visited from left to right.",
null,
"In this way we often can arrive at an optimal solution faster than we would by methodically visiting the nodes in some predetermined order (such as a depth-first search). This approach is called best-first search with branch-and-bound pruning. The implementation of the approach is a simple modification of another methodical approach called breadth-first search with branch-and-bound pruning. Therefore, even though this latter technique has no advantage over depth-first search, in Section 6.1 we will first solve the 0-1 Knapsack problem using a breadth-first search. This will enable us to more easily explain best-first search and use it to solve the 0-1 Knapsack problem. Sections 6.2 and 6.3 apply the best-first search approach to two more problems.\n\nBefore proceeding, we review breadth-first search. In the case of a tree, a breadth-first search consists of visiting the root first, followed by all nodes at level 1, followed by all nodes at level 2, and so on. Figure 6.1 shows a breadth-first search of a tree in which we proceed from left to right. The nodes are numbered according to the order in which they are visited.\n\nUnlike depth-first search, there is no simple recursive algorithm for breadth-first search. However, we can implement it using a queue. The algorithm that follows does this. The algorithm is written specifically for trees because presently we are interested only in trees. We insert an item at the end of the queue with a procedure called enqueue, and we remove an item from the front with a procedure called dequeue.",
null,
"If you are not convinced that this procedure produces a breadth-first search, you should walk through an application of this algorithm to the tree in Figure 6.1. In that tree, as mentioned previously, a node’s children are visited from left to right.\n\n6.1 Illustrating Branch-and-Bound with the 0-1 Knapsack problem\n\nWe show how to use the branch-and-bound design strategy by applying it to the 0-1 Knapsack problem. First we discuss a simple version called breadth-first search with branch-and-bound pruning. After that, we show an improvement on the simple version called best-first search with branch-and-bound pruning.\n\n6.1.1 Breadth-First Search with Branch-and-Bound Pruning\n\nLet’s demonstrate this approach with an example.\n\nExample 6.1\n\nSuppose we have the instance of the 0-1 Knapsack problem presented in Exercise 5.6. That is, n = 4, W = 16, and we have the following:",
null,
"As in Example 5.6, the items have already been ordered according to pi/wi. Using breadth-first search with branch-and-bound pruning, we proceed exactly as we did using backtracking in Example 5.6, except that we do a breadth-first search instead of a depth-first search. That is, we let weightand profit be the total weight and total profit of the items that have been included up to a node. To determine whether the node is promising, we initialize totweight and bound to weight and profit, respectively, and then greedily grab items, adding their weights and profits to totweight and bound, until we reach an item whose weight would bring totweight above W . We grab the fraction of that item allowed by the available weight, and add the profit of that fraction to bound. In this way, bound becomes an upper bound on the amount of profit we could obtain by expanding beyond the node. If the node is at level i, and the node at level k is the one whose weight would bring the weight above W , then",
null,
"and",
null,
"A node is nonpromising if this bound is less than or equal to maxprofit, which is the value of the best solution found up to that point. Recall that a node is also nonpromising if",
null,
"The pruned state space tree produced using a breadth-first search on the instance in this example, with branches pruned using the bounds indicated above, is shown in Figure 6.2. The values of profit, weight, and bound are specified from top to bottom at each node. The node shaded in color is where the maximum profit is found. The nodes are labeled according to their levels and positions from the left in the tree.\n\nBecause the steps are so similar to those in Example 5.6, we will not walk through them. We mention only a few important points. We refer to a node by its level and position from the left in the tree. First, notice that nodes (3, 1) and (4, 3) have bounds of \\$0. A branch-and-bound algorithm decides whether to expand beyond a node by checking whether its bound is better than the value of the best solution found so far. Therefore, when a node is nonpromising because its weight is not less than W, we set its bound to \\$0. In this way, we ensure that its bound cannot be better than the value of the best solution found so far. Second, recall that when backtracking (depth-first search) was used on this instance, node (1, 2) was found to be nonpromising and we did not expand beyond the node.\n\nFigure 6.2 The pruned state space tree produced using breadth-first search with branch-and-bound pruning in Example 6.1. Stored at each node from top to bottom are the total profit of the items stolen up to that node, their total weight, and the bound on the total profit that could be obtained by expanding beyond the node. The node shaded in color is the one at which an optimal solution is found.",
null,
"However, in the case of a breadth-first search, this node is the third node visited. At the time it is visited, the value of maxprofit is only \\$40. Because its bound \\$82 exceeds maxprofit at this point, we expand beyond the node. Last of all, in a simple breadth-first search with branch-and-bound pruning, the decision of whether or not to visit a node’s children is made at the time the node is visited. That is, if the branches to the children are pruned, they are pruned when the node is visited. Therefore, when we visit node (2, 3), we decide to visit its children because the value of maxprofit at that time is only \\$70, whereas the bound for the node is \\$82. Unlike a depth-first search, in a breadth-first search the value of maxprofit can change by the time we actually visit the children. In this case, maxprofit has a value of \\$90 by the time we visit the children of node (2, 3). We then waste our time checking these children. We avoid this in our best-first search, which is described in the next subsection.\n\nNow that we have illustrated the technique, we present a general algorithm for breadth-first search with branch-and-bound pruning. Although we refer to the state space tree T as the input to this general-purpose algorithm, in actual applications the state space tree exists only implicitly. The parameters of the problem are the actual inputs to the algorithm and determine the state space tree T .",
null,
"This algorithm is a modification of the breadth-first search algorithm presented at the beginning of this chapter. In this algorithm, however, we expand beyond a node (visit a node’s children) only if its bound is better than the value of the current best solution. The value of the current best solution (the variable best) is initialized to the value of the solution at the root. In some applications, there is no solution at the root because we must be at a leaf in the state space tree to have a solution. In such cases, we initialize best to a value that is worse than that of any solution. The functions bound andvalue are different in each application of breadth_first_branch_and_bound. As we shall see, we often do not actually write a function value. We simply compute the value directly.\n\nNext we present a specific algorithm for the 0-1 Knapsack problem. Because we do not have the benefit of recursion (which means we do not have new variables being created at each recursive call), we must store all the information pertinent to a node at that node. Therefore, the nodes in our algorithm will be of the following type:",
null,
"",
null,
"Algorithm 6.1\n\nThe Breadth-First Search with Branch-and-Bound Pruning Algorithm for the 0-1 Knapsack problem\n\nProblem: Let n items be given, where each item has a weight and a profit. The weights and profits are positive integers. Furthermore, let a positive integer W be given. Determine a set of items with maximum total profit, under the constraint that the sum of their weights cannot exceed W .\n\nInputs: positive integers n and W , arrays of positive integers w and p, each indexed from 1 to n, and each of which is sorted in nonincreasing order according to the values of p [i] /w [i].\n\nOutputs: an integer maxprofit that is the sum of the profits in an optimal set.",
null,
"We do not need to check whether u.profit exceeds maxprofit when the current item is not included because, in this case, u.profit is the profit associated with u’s parent, which means that it cannot exceed maxprofit. We do not need to store the bound at a node (as depicted in Figure 6.2) because we have no need to refer to the bound after we compare it with maxprofit.\n\nFunction bound is essentially the same as function promising in Algorithm 5.7. The difference is that we have written bound according to guidelines for creating branch-and-bound algorithms, and therefore bound returns an integer. Function promising returns a boolean value because it was written according to backtracking guidelines. In our branch-and-bound algorithm, the comparison with maxprofit is done in the calling procedure. There is no need to check for the condition i = n in function bound because in this case the value returned by bound is less than or equal to maxprofit, which means that the node is not put in the queue.\n\nAlgorithm 6.1 does not produce an optimal set of items; it only determines the sum of the profits in an optimal set. The algorithm can be modified to produce an optimal set as follows. At each node we also store a variable items, which is the set of items that have been included up to the node, and we maintain a variable bestitems, which is the current best set of items. When maxprofit is set equal to u.profit, we also set bestitems equal to u.items.\n\n6.1.2 Best-First Search with Branch-and-Bound Pruning\n\nIn general, the breadth-first search strategy has no advantage over a depth-first search (backtracking). However, we can improve our search by using our bound to do more than just determine whether a node is promising. After visiting all the children of a given node, we can look at all the promising, unexpanded nodes and expand beyond the one with the best bound. Recall that a node is promising if its bound is better than the value of the best solution found so far. In this way, we often arrive at an optimal solution more quickly than if we simply proceeded blindly in a predetermined order. The example that follows illustrates this method.\n\nExample 6.2\n\nSuppose we have the instance of the 0-1 Knapsack problem in Example 6.1. A best-first search produces the pruned state space tree in Figure 6.3. The values of profit, weight, and bound are again specified from top to bottom at each node in the tree. The node shaded in color is where the maximum profit is found. Next we show the steps that produced this tree. We again refer to a node by its level and its position from the left in the tree. Values and bounds are computed in the same way as in Examples 5.6 and 6.1. We do not show the computations while walking through the steps. Furthermore, we only mention when a node is found to be nonpromising; we do not mention when it is found to be promising.\n\nThe steps are as follows:\n\n1. Visit node (0, 0) (the root).\n\n(a) Set its profit and weight to \\$0 and 0.\n\n(b) Compute its bound to be \\$115. (See Example 5.6 for the computation.)\n\n(c) Set maxprofit to 0.\n\n2. Visit node (1, 1).\n\n(a) Compute its profit and weight to be \\$40 and 2.\n\n(b) Because its weight 2 is less than or equal to 16, the value of W, and its profit \\$40 is greater than \\$0, the value of maxprofit, set maxprofit to \\$40.\n\n(c) Compute its bound to be \\$115.\n\n3. Visit node (1, 2).\n\n(a) Compute its profit and weight to be \\$0 and 0.\n\n(b) Compute its bound to be \\$82.\n\nFigure 6.3 The pruned state space tree produced using best-first search with branch-and-bound pruning in Example 6.2. Stored at each node from top to bottom are the total profit of the items stolen up to the node, their total weight, and the bound on the total profit that could be obtained by expanding beyond the node. The node shaded in color is the one at which an optimal solution is found.",
null,
"4. Determine promising, unexpanded node with the greatest bound.\n\n(a) Because node (1, 1) has a bound of \\$115 and node (1, 2) has a bound of \\$82, node (1, 1) is the promising, unexpanded node with the greatest bound. We visit its children next.\n\n5. Visit node (2, 1).\n\n(a) Compute its profit and weight to be \\$70 and 7.\n\n(b) Because its weight 7 is less than or equal to 16, the value of W , and its profit \\$70 is greater than \\$40, the value of maxprofit, set maxprofit to \\$70.\n\n(c) Compute its bound to be \\$115.\n\n6. Visit node (2, 2).\n\n(a) Compute its profit and weight to be \\$40 and 2.\n\n(b) Compute its bound to be \\$98.\n\n7. Determine promising, unexpanded node with the greatest bound.\n\n(a) That node is node (2, 1). We visit its children next.\n\n8. Visit node (3, 1).\n\n(a) Compute its profit and weight to be \\$120 and 17.\n\n(b) Determine that it is nonpromising because its weight 17 is greater than or equal to 16, the value of W. We make it nonpromising by setting its bound to \\$0.\n\n9. Visit node (3, 2).\n\n(a) Compute its profit and weight to be \\$70 and 7.\n\n(b) Compute its bound to be \\$80.\n\n10. Determine promising, unexpanded node with the greatest bound.\n\n(a) That node is node (2, 2). We visit its children next.\n\n11. Visit node (3, 3).\n\n(a) Compute its profit and weight to be \\$90 and 12.\n\n(b) Because its weight 12 is less than or equal to 16, the value of W, and its profit \\$90 is greater than \\$70, the value of maxprofit, set maxprofit to \\$90.\n\n(c) At this point, nodes (1, 2) and (3, 2) become nonpromising because their bounds, \\$82 and \\$80 respectively, are less than or equal to \\$90, the new value of maxprofit.\n\n(d) Compute its bound to be \\$98.\n\n12. Visit node (3, 4).\n\n(a) Compute its profit and weight to be \\$40 and 2.\n\n(b) Compute its bound to be \\$50.\n\n(c) Determine that it is nonpromising because its bound \\$50 is less than or equal to \\$90, the value of maxprofit.\n\n13. Determine promising, unexpanded node with the greatest bound.\n\n(a) The only unexpanded, promising node is node (3, 3). We visit its children next.\n\n14. Visit node (4, 1).\n\n(a) Compute its profit and weight to be \\$100 and 17.\n\n(b) Determine that it is nonpromising because its weight 17 is greater than or equal to 16, the value of W . We set its bound to \\$0.\n\n15. Visit node (4, 2).\n\n(a) Compute its profit and weight to be \\$90 and 12.\n\n(b) Compute its bound to be \\$90.\n\n(c) Determine that it is nonpromising because its bound \\$90 is less than or equal to \\$90, the value of maxprofit. Leaves in the state space tree are automatically nonpromising because their bounds cannot exceed maxprofit.\n\nBecause there are now no promising, unexpanded nodes, we are done.\n\nUsing best-first search, we have checked only 11 nodes, which is 6 less than the number checked using breadth-first search (Figure 6.2) and 2 less than the number checked using depth-first search (see Figure 5.14). A savings of 2 is not very impressive; however, in a large state space tree, the savings can be very significant when the best-first search quickly hones in on an optimal solution. It must be stressed, however, that there is no guarantee that the node that appears to be best will actually lead to an optimal solution. In Example 6.2, node (2, 1) appears to be better than node (2, 2), but node (2, 2) leads to the optimal solution. In general, best-first search can still end up creating most or all of the state space tree for some instances.\n\nThe implementation of best-first search consists of a simple modification to breadth-first search. Instead of using a queue, we use a priority queue. Recall that priority queues were discussed in Section 4.4.2. A general algorithm for the best-first search algorithm follows. Again, the tree T exists only implicitly. In the algorithm, insert (PQ, v) is a procedure that adds v to the priority queue PQ, whereas remove (PQ, v) is a procedure that removes the node with the best bound and assigns its value to v.",
null,
"Besides using a priority queue instead of a queue, we have added a check following the removal of a node from the priority queue. The check determines if the bound for the node is still better than best. This is how we determine that a node has become nonpromising after visiting the node. For example, node (1, 2) in Figure 6.3 is promising at the time we visit it. In our implementation, this is when we insert it in PQ. However, it becomes nonpromising when maxprofit takes the value \\$90. In our implementation, this is before we remove it from PQ. We learn this by comparing its bound with maxprofit after removing it from PQ. In this way, we avoid visiting children of a node that becomes nonpromising after it is visited.\n\nThe specific algorithm for the 0-1 Knapsack problem follows. Because we need the bound for a node at insertion time, at removal time, and to order the nodes in the priority queue, we store the bound at the node. The type declaration is as follows:",
null,
"",
null,
"Algorithm 6.2\n\nThe Best-First Search with Branch-and-Bound Pruning Algorithm for the 0-1 Knapsack problem\n\nProblem: Let n items be given, where each item has a weight and a profit. The weights and profits are positive integers. Furthermore, let a positive integer W be given. Determine a set of items with maximum total profit, under the constraint that the sum of their weights cannot exceed W .\n\nInputs: positive integers n and W , arrays of positive integers w and p, each indexed from 1 to n, and each of which is sorted in nonincreasing order according to the values of p [i] /w [i].\n\nOutputs: an integer maxprofit that is the sum of the profits of an optimal set.",
null,
"Function bound is the one in Algorithm 6.1.\n\n6.2 The Traveling Salesperson Problem\n\nIn Example 3.12, Nancy won the sales position over Ralph because she found an optimal tour for the 20-city sales territory in 45 seconds using a Θ (n22n) dynamic programming algorithm to solve the Traveling Sales-person problem. Ralph used the brute-force algorithm that generates all 19! tours. Because the brute-force algorithm takes over 3,800 years, it is still running. We last saw Nancy in Section 5.6 when her sales territory was expanded to 40 cities. Because her dynamic programming algorithm would take more than six years to find an optimal tour for this territory, she became content with just finding any tour. She used the backtracking algorithm for the Hamiltonian Circuits problem to do this. Even if this algorithm did find a tour efficiently, that tour could be far from optimal. For example, if there were a long, winding road of 100 miles between two cities that were 2 miles apart, the algorithm could produce a tour containing that road even if it were possible to connect the two cities by a city that is a mile from each of them. This means Nancy could be covering her territory very inefficiently using the tour produced by the backtracking algorithm. Given this, she might decide that she better go back to looking for an optimal tour. If the 40 cities were highly connected, having the backtracking algorithm produce all the tours would not work, because there would be a worst-than-exponential number of tours. Let’s assume that Nancy’s instructor did not get to the branch-and-bound technique in her algorithms course (this is why Nancy settled for any tour in Section 5.6). After going back to her algorithms text and discovering that the branch-and-bound technique is specifically designed for optimization problems, Nancy decides to apply it to the Traveling Salesperson problem. She might proceed as follows.\n\nRecall that the goal in this problem is to find the shortest path in a directed graph that starts at a given vertex, visits each vertex in the graph exactly once, and ends up back at the starting vertex. Such a path is called an optimal tour. Because it does not matter where we start, the starting vertex can simply be the first vertex. Figure 6.4 shows the adjacency matrix representation of a graph containing five vertices, in which there is an edge from every vertex to every other vertex, and an optimal tour for that graph.\n\nAn obvious state space tree for this problem is one in which each vertex other than the starting one is tried as the first vertex (after the starting one) at level 1, each vertex other than the starting one and the one chosen at level 1 is tried as the second vertex at level 2, and so on. A portion of this state space tree, in which there are five vertices and in which there is an edge from every vertex to every other vertex, is shown in Figure 6.5. In what follows, the term “node” means a node in the state space tree, and the term “vertex” means a vertex in the graph. At each node in Figure 6.5, we have included the path chosen up to that node. For simplicity, we have denoted a vertex in the graph simply by its index. A node that is not a leaf represents all those tours that start with the path stored at that node. For example, the node containing [1, 2, 3] represents all those tours that start with the path [1, 2, 3]. That is, it represents the tours [1, 2, 3, 4, 5, 1] and [1, 2, 3, 5, 4, 1]. Each leaf represents a tour. We need to find a leaf that contains an optimal tour. We stop expanding the tree when there are four vertices in the path stored at a node because, at that time, the fifth one is uniquely determined. For example, the far-left leaf represents the tour [1, 2, 3, 4, 5, 1 ] because once we have specified the path [1, 2, 3, 4], the next vertex must be the fifth one.\n\nFigure 6.4 Adjacency matrix representation of a graph that has an edge from every vertex to every other vertex (left), and the nodes in the graph and the edges in an optimal tour (right).",
null,
"Figure 6.5 A state space tree for an instance of the Traveling Salesperson problem in which there are five vertices. The indices of the vertices in the partial tour are stored at each node.",
null,
"To use best-first search, we need to be able to determine a bound for each node. Because of the objective in the 0-1 Knapsack problem (to maximize profit while keeping the total weight from exceeding W), we computed an upper bound on the amount of profit that could be obtained by expanding beyond a given node, and we called a node promising only if its bound was greater than the current maximum profit. In this problem, we need to determine a lower bound on the length of any tour that can be obtained by expanding beyond a given node, and we call the node promising only if its bound is less than the current minimum tour length. We can obtain a bound as follows. In any tour, the length of the edge taken when leaving a vertex must be at least as great as the length of the shortest edge emanating from that vertex. Therefore, a lower bound on the cost (length of the edge taken) of leaving vertex v1 is given by the minimum of all the nonzero entries in row 1 of the adjacency matrix, a lower bound on the cost of leaving vertex v2 is given by the minimum of all the nonzero entries in row 2, and so on. The lower bounds on the costs of leaving the five vertices in the graph represented in Figure 6.4 are as follows:",
null,
"Because a tour must leave every vertex exactly once, a lower bound on the length of a tour is the sum of these minimums. Therefore, a lower bound on the length of a tour is",
null,
"This is not to say that there is a tour with this length. Rather, it says that there can be no tour with a shorter length.\n\nSuppose we have visited the node containing [1, 2] in Figure 6.5. In that case we have already committed to making v2 the second vertex on the tour, and the cost of getting to v2 is the weight on the edge from v1 to v2, which is 14. Any tour obtained by expanding beyond this node, therefore, has the following lower bounds on the costs of leaving the vertices:",
null,
"To obtain the minimum for v2 we do not include the edge to v1, because v2 cannot return to v1. To obtain the minimums for the other vertices we do not include the edge to v2, because we have already been at v2. A lower bound on the length of any tour, obtained by expanding beyond the node containing [1, 2], is the sum of these minimums, which is",
null,
"To further illustrate the technique for determining the bound, suppose we have visited the node containing [1, 2, 3] in Figure 6.5. We have committed to making v2 the second vertex and v3 the third vertex. Any tour obtained by expanding beyond this node has the following lower bounds on the costs of leaving the vertices:",
null,
"To obtain the minimums for v4 and v5 we do not consider the edges to v2 and v3, because we have already been to these vertices. The lower bound on the length of any tour we could obtain by expanding beyond the node containing [1, 2, 3] is",
null,
"In the same way, we can obtain a lower bound on the length of a tour that can be obtained by expanding beyond any node in the state space tree, and we use these lower bounds in our best-first search. The following example illustrates this technique. We will not actually do any calculations in the example. They would be done as just illustrated.\n\nExample 6.3\n\nGiven the graph in Figure 6.4 and using the bounding considerations outlined previously, a best-first search with branch-and-bound pruning produces the tree in Figure 6.6. The bound is stored at a nonleaf, whereas the length of the tour is stored at a leaf. We show the steps that produced the tree. We initialize the value of the best solution to (infinity) because there is no candidate solution at the root. (Candidate solutions exist only at leaves in the state space tree.) We do not compute bounds for leaves in the state space tree because the algorithm is written so as not to expand beyond leaves. When referring to a node, we refer to the partial tour stored at the node. This is different from the way we referred to a node when illustrating the 0-1 Knapsack problem.\n\nThe steps are as follows:\n\n1. Visit node containing (the root).\n\n(a) Compute bound to be 21.\n\n(b) Set minlength to .\n\n{This is a lower bound on the}\n\n{length of a tour.}\n\n2. Visit node containing [1, 2].\n\n(a) Compute bound to be 31.\n\n3. Visit node containing [1, 3].\n\n(a) Compute bound to be 22.\n\n4. Visit node containing [1, 4].\n\n(a) Compute bound to be 30.\n\n5. Visit node containing [1, 5].\n\n(a) Compute bound to be 42.\n\n6. Determine promising, unexpanded node with the smallest bound.\n\n(a) That node is the node containing [1, 3]. We visit its children next.\n\n7. Visit node containing [1, 3, 2].\n\n(a) Compute bound to be 22.\n\nFigure 6.6 The pruned state space tree produced using best-first search with branch-and-bound pruning in Example 6.3. At each node that is not a leaf in the state space tree, the partial tour is at the top and the bound on the length of any tour that could be obtained by expanding beyond the node is at the bottom. At each leaf in the state space tree, the tour is at the top and its length is at the bottom. The node shaded in color is the one at which an optimal tour is found.",
null,
"8. Visit node containing [1, 3, 4].\n\n(a) Compute bound to be 27.\n\n9. Visit node containing [1, 3, 5].\n\n(a) Compute bound to be 39.\n\n10. Determine promising, unexpanded node with the smallest bound.\n\n(a) That node is the node containing [1, 3, 2]. We visit its children next.\n\n11. Visit node containing [1,3,2,4].\n\n(a) Because this node is a leaf, compute tour length to be 37.\n\n(b) Because its length 37 is less than , the value of minlength, set minlength to 37.\n\n(c) The nodes containing [1, 5] and [1, 3, 5] become nonpromising because their bounds 42 and 39 are greater than or equal to 37, the new value of minlength.\n\n12. Visit node containing [1, 3, 2, 5].\n\n(a) Because this node is a leaf, compute tour length to be 31.\n\n(b) Because its length 31 is less than 37, the value of minlength, set minlength to 31.\n\n(c) The node containing [1, 2] becomes nonpromising because its bound 31 is greater than or equal to 31, the new value of minlength.\n\n13. Determine promising, unexpanded node with the smallest bound.\n\n(a) That node is the node containing [1, 3, 4]. We visit its children next.\n\n14. Visit node containing [1, 3, 4, 2].\n\n(a) Because this node is a leaf, compute tour length to be 43.\n\n15. Visit node containing [1, 3, 4, 5].\n\n(a) Because this node is a leaf, compute tour length to be 34.\n\n16. Determine promising, unexpanded node with the smallest bound.\n\n(a) The only promising, unexpanded node is the node containing [1, 4]. We visit its children next.\n\n17. Visit node containing [1, 4, 2].\n\n(a) Compute bound to be 45.\n\n(b) Determine that the node is nonpromising because its bound 45 is greater than or equal to 31, the value of minlength.\n\n18. Visit node containing [1, 4, 3].\n\n(a) Compute bound to be 38.\n\n(b) Determine that the node is nonpromising because its bound 38 is greater than or equal to 31, the value of minlength.\n\n19. Visit node containing [1, 4, 5].\n\n(a) Compute bound to be 30.\n\n20. Determine promising, unexpanded node with the smallest bound.\n\n(a) The only promising, unexpanded node is the node containing [1, 4, 5]. We visit its children next.\n\n21. Visit node containing [1, 4, 5, 2].\n\n(a) Because this node is a leaf, compute tour length to be 30.\n\n(b) Because its length 30 is less than 31, the value of minlength, set minlength to 30.\n\n22. Visit node containing [1, 4, 5, 3].\n\n(a) Because this node is a leaf, compute tour length to be 48.\n\n23. Determine promising, unexpanded node with the smallest bound.\n\n(a) There are no more promising, unexpanded nodes. We are done.\n\nWe have determined that the node containing [1, 4, 5, 2], which represents the tour [1,4, 5, 2, 3, 1], contains an optimal tour, and that the length of an optimal tour is 30.\n\nThere are 17 nodes in the tree in Figure 6.6, whereas the number of nodes in the entire state space tree is 1 + 4 + 4 × 3 + 4 × 3 × 2 = 41.\n\nWe will use the following data type in the algorithm that implements the strategy used in the previous example:",
null,
"The field path contains the partial tour stored at the node. For example, in Figure 6.6 the value of path for the far left child of the root is [1, 2]. The algorithm follows.",
null,
"Algorithm 6.3\n\nThe Best-First Search with Branch-and-Bound Pruning Algorithm for the Traveling Salesperson problem\n\nProblem: Determine an optimal tour in a weighted, directed graph. The weights are nonnegative numbers.\n\nInputs: a weighted, directed graph, and n, the number of vertices in the graph. The graph is represented by a two-dimensional array W , which has both its rows and columns indexed from 1 to n, where W [i] [j] is the weight on the edge from the ith vertex to the jth vertex.\n\nOutputs: variable minlength, whose value is the length of an optimal tour, and variable opttour, whose value is an optimal tour.",
null,
"You are asked to write functions length and bound in the exercises. Function length returns the length of the tour u.path, and function bound returns the bound for a node using the considerations discussed.\n\nA problem does not necessarily have a unique bounding function. In the Traveling Salesperson problem, for example, we could observe that every vertex must be visited exactly once, and then use the minimums of the values in the columns in the adjacency matrix instead of the minimums of the values in the rows. Alternatively, we could take advantage of both the rows and the columns by noting that every vertex must be entered and exited exactly once. For a given edge, we could associate half of its weight with the vertex it leaves and the other half with the vertex it enters. The cost of visiting a vertex is then the sum of the weights associated with entering and exiting it. For example, suppose we are determining the initial bound on the length of a tour. The minimum cost of entering v2 is obtained by taking 1/2 of the minimum of the values in the second column. The minimum cost of exiting v2 is obtained by taking 1/2 of the minimum of the values in the second row. The minimum cost of visiting v2 is then given by",
null,
"Using this bounding function, a branch-and-bound algorithm checks only 15 vertices in the instance in Example 6.3.\n\nWhen two or more bounding functions are available, one bounding function may produce a better bound at one node whereas another produces a better bound at another node. Indeed, as you are asked to verify in the exercises, this is the case for our bounding functions for the Traveling Sales-person problem. When this is the case, the algorithm can compute bounds using all available bounding functions, and then use the best bound. However, as discussed in Chapter 5, our goal is not to visit as few nodes as possible, but rather to maximize the overall efficiency of the algorithm. The extra computations done when using more than one bounding function may not be offset by the savings realized by visiting fewer nodes.\n\nRecall that a branch-and-bound algorithm might solve one large instance efficiently but check an exponential (or worse) number of nodes for another large instance. Returning to Nancy’s dilemma, what is she to do if even the branch-and-bound algorithm cannot solve her 40-city instance efficiently? Another approach to handling problems such as the Traveling Salesperson problem is to develop approximation algorithms. Approximation algorithms are not guaranteed to yield optimal solutions, but rather yield solutions that are reasonably close to optimal. They are discussed in Section 9.5. In that section we return to the Traveling Salesperson problem.",
null,
"6.3 Abductive Inference (Diagnosis)\n\nThis section requires knowledge of discrete probability theory and Bayes’ theorem.\n\nAn important problem in artificial intelligence and expert systems is determining the most probable explanation for some findings. For example, in medicine we want to determine the most probable set of diseases, given a set of symptoms. In the case of an electronic circuit, we want to find the most probable explanation for a failure at some point in the circuit. Another example is the determination of the most probable causes for the failure of an automobile to function properly. This process of determining the most probable explanation for a set of findings is called abductive inference.\n\nFor the sake of focus, we use medical terminology. Assume that there are n diseases, d1, d2, … , dn, each of which may be present in a patient. We know that the patient has a certain set of symptoms S. Our goal is to find the set of diseases that are most probably present. Technically, there could be two or more sets that are probably present. However, we often discuss the problem as if a unique set is most probably present.\n\nThe Bayesian network has become a standard for representing probabilistic relationships such as those between diseases and symptoms. It is beyond our scope to discuss belief networks here. They are discussed in detail in Neapolitan (1990, 2003) and Pearl (1988). For many Bayesian network applications, there exist efficient algorithms for determining the prior probability (before any symptoms are discovered) that a particular set of diseases contains the only diseases present in the patient. These algorithms are also discussed in Neapolitan (1990, 2003) and Pearl (1988). Here we will simply assume that the results of the algorithms are available to us. For example, these algorithms can determine the prior probability that d1, d3, and d6 are the only diseases present in the patient. We will denote this probability by",
null,
"where",
null,
"These algorithms can also determine the probability that d1, d3, and d6 are the only diseases present, conditional on the information that the symptoms in S are present. We will denote this conditional probability by",
null,
"Given that we can compute these probabilities (using the algorithms mentioned previously), we can solve the problem of determining the most probable set of diseases (conditional on the information that some symptoms are present) using a state space tree like the one in the 0-1 Knapsack problem. We go to the left of the root to include d1, and we go to the right to exclude it. Similarly, we go to the left of a node at level 1 to include d2, and we go to the right to exclude it, and so on. Each leaf in the state space tree represents a possible solution (that is, the set of diseases that have been included up to that leaf). To solve the problem, we compute the conditional probability of the set of diseases at each leaf, and determine which one has the largest conditional probability.\n\nTo prune using best-first search, we need to find a bounding function. The following theorem accomplishes this for a large class of instances.",
null,
"Theorem 6.1\n\nIf D and D’ are two sets of diseases such that",
null,
"Proof: According to Bayes’ theorem,",
null,
"The first inequality is by the assumption in this theorem, and the second follows from the fact that any probability is less than or equal to 1. This proves the theorem.\n\nFor a given node, let D be the set of diseases that have been included up to that node, and for some descendant of that node, let D’ be the set of diseases that have been included up to that descendant. Then D D. Often it is reasonable to assume that",
null,
"The reason is that usually it is at least as probable that a patient has a set of diseases as it is that the patient has that set plus even more diseases. (Recall that these are prior probabilities before any symptoms are observed.) If we make this assumption, by Theorem 6.1,",
null,
"Therefore, p (D) /p (S) is an upper bound on the conditional probability of the set of diseases in any descendant of the node. The following example illustrates how this bound is used to prune branches.\n\nExample 6.4\n\nSuppose there are four possible diseases d1, d2, d3, and d4 and a set of symptoms S. The input to this example would also include a Bayesian network containing the probabilistic relationships among the diseases and the symptoms. The probabilities used in this example would be computed from this Bayesian network using the methods discussed earlier. These probabilities are not computed elsewhere in this text. We assign arbitrary probabilities to illustrate the best-first search algorithm. When using the results from one algorithm (in this case, the one for doing inference in a belief network) in another algorithm (in this case, the best-first search algorithm), it is important to recognize where the first algorithm supplies results that can simply be assumed in the second algorithm.\n\nFigure 6.7 is the pruned state space tree produced by a best-first search. Probabilities have been given arbitrary values in the tree. The conditional probability is at the top and the bound is at the bottom in each node. The node shaded in color is the one at which the best solution is found. As was done in Section 6.1, nodes are labeled according to their depth and position from the left in the tree. The steps that produce the tree follow. The variable best is the current best solution, whereas p (best | S) is its conditional probability. Our goal is to determine a value of best that maximizes this conditional probability. It is also assumed arbitrarily that\n\nFigure 6.7 The pruned state space tree produced using best-first search with branch-and-bound pruning in Example 6.4. At each node, the conditional probability of the diseases included up to that node is at the top, and the bound on the conditional probability that could be obtained by expanding beyond the node is at the bottom. The node shaded in color is the one at which an optimal set is found.",
null,
"",
null,
"1. Visit node (0, 0) (the root).\n\n(a) Compute its conditional probability. {∅ is the empty set. This means that no diseases are present.}",
null,
"(b) Set",
null,
"(c) Compute its prior probability and bound.",
null,
"2. Visit node (1, 1).\n\n(a) Compute its conditional probability.",
null,
"(b) Because 0.4 > p (best|S), set",
null,
"(c) Compute its prior probability and bound.",
null,
"3. Visit node (1, 2).\n\n(a) Its conditional probability is simply that of its parent—namely, 0.1.\n\n(b) Its prior probability and bound are simply those of its parent— namely, 0.9 and 90.\n\n4. Determine promising, unexpanded node with the largest bound.\n\n(a) That node is node (1, 2). We visit its children next.\n\n5. Visit node (2, 3).\n\n(a) Compute its conditional probability.",
null,
"(b) Compute its prior probability and bound.",
null,
"6. Visit node (2, 4).\n\n(a) Its conditional probability is simply that of its parent—namely, 0.1.\n\n(b) Its prior probability and bound are simply those of its parent— namely, .9 and 90.\n\n7. Determine promising, unexpanded node with the largest bound.\n\n(a) That node is node (2, 4). We visit its children next.\n\n8. Visit node (3, 3).\n\n(a) Compute its conditional probability.",
null,
"(b) Compute its conditional probability and bound.",
null,
"(c) Determine that it is nonpromising because its bound .2 is less than or equal to .4, the value of p (best|S).\n\n9. Visit node (3, 4).\n\n(a) Its conditional probability is simply that of its parent—namely, 0.1.\n\n(b) Its prior probability and bound are simply those of its parent– namely, 0.9 and 90.\n\n10. Determine promising, unexpanded node with the largest bound.\n\n(a) That node is node (3, 4). We visit its children next.\n\n11. Visit node (4, 3).\n\n(a) Compute its conditional probability.",
null,
"(b) Because 0.6 > p (best|S), set",
null,
"(c) Set its bound to 0 because it is a leaf in the state space tree.\n\n(d) At this point, the node (2, 3) becomes nonpromising because its bound 0.5 is less than or equal to 0.6, the new value of p (best|S).\n\n12. Visit node (4, 4).\n\n(a) Its conditional probability is simply that of its parent—namely, 0.1.\n\n(b) Set its bound to 0 because it is a leaf in the state space tree.\n\n13. Determine promising, unexpanded node with the largest bound.\n\n(a) That node is node (1, 1). We visit its children next.\n\n14. Visit node (2, 1).\n\n(a) Compute its conditional probability.",
null,
"(b) Compute its prior probability and bound.",
null,
"(c) Determine that it is nonpromising because its bound 0.3 is less than or equal to 0.6, the value of p (best|S).\n\n15. Visit node (2, 2).\n\n(a) Its conditional probability is simply that its parent–namely, 0.4.\n\n(b) Its prior probability and bound are simply those of its parent–namely, 0.009 and 0.9.\n\n16. Determine promising, unexpanded node with the greatest bound.\n\n(a) The only promising, unexpanded node is node (2, 2). We visit its children next.\n\n17. Visit node (3, 1).\n\n(a) Compute its conditional probability.",
null,
"(b) Compute its prior probability and bound.",
null,
"(c) Determine that it is nonpromising because its bound 0.1 is less than or equal to 0.6, the value of p (best|S).\n\n18. Visit node (3, 2).\n\n(a) Its conditional probability is simply that of its parent—namely, 0.4.\n\n(b) Its prior probability and found are simply those of its parent— namely, 0.009 and 0.9.\n\n19. Determine promising, unexpanded node with the largest bound.\n\n(a) The only promising, unexpanded node is node (3, 2). We visit its children next.\n\n20. Visit node (4, 1).\n\n(a) Compute its conditional probability.",
null,
"(b) Because 0.65 > p (best|S), set",
null,
"(c) Set its bound to 0 because it is a leaf in the state space tree.\n\n21. Visit node (4, 2).\n\n(a) Its conditional probability is simply that of its parent—namely, 0.4.\n\n(b) Set its bound to 0 because it is a leaf in the state space tree.\n\n22. Determine promising, unexpanded node with the largest bound.\n\n(a) There are no more promising, unexpanded nodes. We are done.\n\nWe have determined that the most probable set of diseases is {d1, d4} and that p (d1, d4|S) = 0.65.\n\nA reasonable strategy in this problem would be to initially sort the diseases in nonincreasing order according to their conditional probabilities. There is no guarantee, however, that this strategy will minimize the search time. We have not done this in Example 6.4, and 15 nodes were checked. In the exercises, you establish that if the diseases were sorted, 23 nodes would be checked.\n\nNext we present the algorithm. It uses the following declaration:",
null,
"The field D contains the indices of the diseases included up to the node. One of the inputs to this algorithm is a Bayesian network BN. As mentioned previously, a Bayesian network represents the probabilistic relationships among diseases and symptoms. The algorithms referenced at the beginning of this section can compute the necessary probabilities from such a network.\n\nThe following algorithm was developed by Cooper (1984):",
null,
"Algorithm 6.4\n\nCooper’s Best-First Search with Branch-and-Bound Pruning Algorithm for Abductive Inference\n\nProblem: Determine a most probable set of diseases (explanation) given a set of symptoms. It is assumed that if a set of diseases D is a subset of a set of diseases D, then p (D) ≤ p (D).\n\nInputs: positive integer n, a Bayesian network BN representing the probabilistic relationships among n diseases and their symptoms, and a set of symptoms S.\n\nOutputs: a set best containing the indices of the diseases in a most probable set (conditional on S), and a variable pbest that is the probability of best given S.",
null,
"The notation p (D) stands for the prior probability of D, p (S) stands for the prior probability of S, and p (D|S) stands for the conditional probability of D given S. These values would be computed from the Bayesian network BN using the algorithms referenced at the beginning of this section.\n\nWe have written the algorithm strictly according to our guidelines for writing best-first search algorithms. An improvement is possible. There is no need to call function bound for the right child of a node. The reason is that the right child contains the same set of diseases as the node itself, which means that its bound is the same. Therefore, the right child is pruned only if, at the left child, we change pbest to a value greater than or equal to this bound. We can modify our algorithm to prune the right child when this happens and to expand to the right child when it does not happen.\n\nLike the other problems described in this chapter, the problem of Abductive Inference is in the class of problems discussed in Chapter 9.\n\nIf there is more than one solution, the preceding algorithm only produces one of them. It is straightforward to modify the algorithm to produce all the best solutions. It is also possible to modify it to produce the m most probable explanations, where m is any positive integer. This modification is discussed in Neapolitan (1990). Furthermore, Neapolitan (1990) analyzes the algorithm in detail.\n\nEXERCISES\n\nSection 6.1\n\n1. Use Algorithm 6.1 (The Breadth-First Search with Branch-and-Bound Pruning algorithm for the 0-1 Knapsack problem) to maximize the profit for the following problem instance. Show the actions step by step.",
null,
"2. Implement Algorithm 6.1 on your system and run it on the problem instance of Exercise 1.\n\n3. Modify Algorithm 6.1 to produce an optimal set of items. Compare the performance of your algorithm with that of Algorithm 6.1.\n\n4. Use Algorithm 6.2 (The Best-First Search with Branch-and-Bound Pruning algorithm for the 0-1 Knapsack problem) to maximize the profit for the problem instance of Exercise 1. Show the actions step by step.\n\n5. Implement Algorithm 6.2 on your system and run it on the problem instance of Exercise 1.\n\n6. Compare the performance of Algorithm 6.1 with that of Algorithm 6.2 for large instances of the problem.\n\nSection 6.2\n\n7. Use Algorithm 6.3 (The Best-First Search with Branch-and-Bound Pruning Algorithm for the Traveling Salesperson problem) to find an optimal tour and the length of the optimal tour for the graph below.",
null,
"Show the actions step by step.\n\n8. Use Algorithm 6.3 to find an optimal tour for the graph whose adjacency matrix is given by the following array. Show your actions step by step.",
null,
"9. Write functions length and bound used in Algorithm 6.3.\n\n10. Consider the Traveling Salesperson problem.\n\n(a) Write the brute-force algorithm for this problem that considers all possible tours.\n\n(b) Implement the algorithm and use it to solve instances of size 6, 7, 8, 9, 10, 15, and 20.\n\n(c) Compare the performance of this algorithm to that of Algorithm 6.3 using the instances developed in (b).\n\n11. Implement Algorithm 6.3 on your system, and run it on the problem instance of Exercise 7. Use different bounding functions and study the results.\n\n12. Compare the performance of your dynamic programming algorithm (see Section 3.6, Exercise 27) for the Traveling Salesperson problem with that of Algorithm 6.3 using large instances of the problem.\n\nSection 6.3\n\n13. Revise Algorithm 6.4 (Cooper’s Best-First Search with Branch-and-Bound Pruning algorithm for Abductive Inference) to produce the m most probable explanations, where m is any positive integer.\n\n14. Show that if the diseases in Example 6.4 were sorted in nonincreasing order according to their conditional probabilities, the number of nodes checked would be 23 instead of 15. Assume that p(d4) = 0.008 and p (d4, d1) = 0.007.\n\n15. A set of explanations satisfies a comfort measure p if the sum of the probabilities of the explanations is greater than or equal to p. Revise Algorithm 6.4 to produce a set of explanations that satisfies p, where 0 ≤ p ≤ 1. Do this with as few explanations as possible.\n\n16. Implement Algorithm 6.4 on your system. The user should be able to enter an integer m, as described in Exercise 11, or a comfort measure p, as described in Exercise 13.\n\n17. Can the branch-and-bound design strategy be used to solve the problem discussed in Exercise 34 in Chapter 3? Justify your answer.\n\n18. Write a branch-and-bound algorithm for the problem of scheduling with deadlines discussed in Section 4.3.2.\n\n19. Can the branch-and-bound design strategy be used to solve the problem discussed in Exercise 26 in Chapter 4? Justify your answer.\n\n20. Can the branch-and-bound design strategy be used to solve the Chained Matrix Multiplication problem discussed in Section 3.4? Justify your answer.\n\n21. List three more applications of the branch-and-bound design strategy.\n\n"
]
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https://writingessays750.blogspot.com/2019/09/macro-and-microeconomics-essay-example.html | [
"## Thursday, September 26, 2019\n\n### Macro and Microeconomics Essay Example | Topics and Well Written Essays - 1000 words\n\nMacro and Microeconomics - Essay Example The exchange rate is 5.5francs/dollar meaning that one dollar is equivalent to 5.5 francs. Therefore, a Chrysler Neon costing 14,300 dollars will have the frank price calculate below: 1dollar = 5.5 francs 14,300 dollars= Franc price of Neon Using the principle of cross-multiplication, Price of Chrysler Neon = (14,300 dollars x 5.5 francs)/1dollar = 78,650 francs Question three Given that the franc depreciates by 9% and the initial exchange rate was 5.5 francs/dollar, the franc price of the shirt and dollar price of Chrysler Neon will be affected by the depreciation. If the franc depreciates by 9% from its previous dollar value, the dollar price of the shirt will also change as depicted in the following calculations. Depreciation = 9% Taking the original exchange rate, 5.5 francs/dollar, to be 100%, then the value after depreciation must be higher than the initial value by exactly the same amount as depreciation. New value = (100 + 9) % = 109% Therefore, the new exchange rate = (109/1 00) x 5.5 francs/dollar = 5.995 francs/dollar Hence, the new price of the shirt = (220 francs x 1 dollar)/5.995 = 37 dollars. ... The reason is that as the products become cheaper, the domestic and foreign demand of the products will increase. As currency devaluation increases competitiveness, demand for the country’s export increases, resulting in an increase in aggregate demand. According to macroeconomic principles, an increase in aggregate demand will cause an increase in GDP (Boyes & Melvin, 2011, pg.273). On another monetary perspective, France receipt from foreigners might increase due to currency devaluation and exceed the outgoing payments hence leading to an improved balance of payments. The fact that increased supply of foreign money leads to low supply of domestic currency highlights that an upward pressure will be placed on the domestic currency. Together with expensive imports due to currency devaluation, this pressure results in high price levels as well as higher GDP and employment levels. On the other hand, the depreciation in French franc will decrease the aggregate demand in United Sta tes. The currency devaluation means that the dollar will be stronger against the franc. As a result, the US imports from France will increase as the products in the country become cheaper. Comparatively, US products will be expensive and unpopular in the domestic and foreign markets. Aggregate demand which is dependent on price levels will decrease as more people will be opting to buy from France (Boyes & Melvin, 2011, pg.273). In the meantime, the gross domestic production will decrease as demand decreases. In addition, the franc depreciation will lead to a fixed exchange rate that is lower than the equilibrium exchange rate. This makes it cheaper for Americans to buy French goods and expensive for French people to"
]
| [
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http://ixtrieve.fh-koeln.de/birds/litie/document/2746 | [
"# Document (#2746)\n\nAuthor\nTitle\nIntelligent agents on the Web\nSource\nManaging information. 6(1999) no.1, S.35-41\nYear\n1999\nTheme\nWeb-Agenten\n\n## Similar documents (author)\n\n1. Bradley, N.: SGML concepts (1992) 5.39\n```5.3864803 = sum of:\n5.3864803 = weight(author_txt:bradley in 5917) [ClassicSimilarity], result of:\n5.3864803 = fieldWeight in 5917, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n8.618368 = idf(docFreq=20, maxDocs=42740)\n0.625 = fieldNorm(doc=5917)\n```\n2. Bradley, C.: Public affairs project (1994) 5.39\n```5.3864803 = sum of:\n5.3864803 = weight(author_txt:bradley in 791) [ClassicSimilarity], result of:\n5.3864803 = fieldWeight in 791, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n8.618368 = idf(docFreq=20, maxDocs=42740)\n0.625 = fieldNorm(doc=791)\n```\n3. Bradley, P.: Towards a common user interface (1995) 5.39\n```5.3864803 = sum of:\n5.3864803 = weight(author_txt:bradley in 3202) [ClassicSimilarity], result of:\n5.3864803 = fieldWeight in 3202, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n8.618368 = idf(docFreq=20, maxDocs=42740)\n0.625 = fieldNorm(doc=3202)\n```\n4. Bradley, P.: ¬The relevance of underpants to searching the Web (2000) 5.39\n```5.3864803 = sum of:\n5.3864803 = weight(author_txt:bradley in 4030) [ClassicSimilarity], result of:\n5.3864803 = fieldWeight in 4030, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n8.618368 = idf(docFreq=20, maxDocs=42740)\n0.625 = fieldNorm(doc=4030)\n```\n5. Bradley, P.: UKOLUG quick guide to the Internet (1995) 5.39\n```5.3864803 = sum of:\n5.3864803 = weight(author_txt:bradley in 4316) [ClassicSimilarity], result of:\n5.3864803 = fieldWeight in 4316, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n8.618368 = idf(docFreq=20, maxDocs=42740)\n0.625 = fieldNorm(doc=4316)\n```\n\n## Similar documents (content)\n\n1. Haverkamp, D.S.; Gauch, S.: Intelligent information agents : review and challenges for distributed information sources (1998) 1.77\n```1.7673664 = sum of:\n1.7673664 = sum of:\n0.5168446 = weight(abstract_txt:intelligent in 3883) [ClassicSimilarity], result of:\n0.5168446 = score(doc=3883,freq=1.0), product of:\n0.66095626 = queryWeight, product of:\n6.2557187 = idf(docFreq=222, maxDocs=42740)\n0.105656326 = queryNorm\n0.78196484 = fieldWeight in 3883, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n6.2557187 = idf(docFreq=222, maxDocs=42740)\n0.125 = fieldNorm(doc=3883)\n1.2505218 = weight(abstract_txt:agents in 3883) [ClassicSimilarity], result of:\n1.2505218 = score(doc=3883,freq=4.0), product of:\n0.7504244 = queryWeight, product of:\n1.0655335 = boost\n6.665678 = idf(docFreq=147, maxDocs=42740)\n0.105656326 = queryNorm\n1.6664195 = fieldWeight in 3883, product of:\n2.0 = tf(freq=4.0), with freq of:\n4.0 = termFreq=4.0\n6.665678 = idf(docFreq=147, maxDocs=42740)\n0.125 = fieldNorm(doc=3883)\n```\n2. Wiedemann, D.: Helfer im Netz (1998) 1.71\n```1.7131582 = sum of:\n1.7131582 = sum of:\n0.7752669 = weight(abstract_txt:intelligent in 2257) [ClassicSimilarity], result of:\n0.7752669 = score(doc=2257,freq=1.0), product of:\n0.66095626 = queryWeight, product of:\n6.2557187 = idf(docFreq=222, maxDocs=42740)\n0.105656326 = queryNorm\n1.1729473 = fieldWeight in 2257, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n6.2557187 = idf(docFreq=222, maxDocs=42740)\n0.1875 = fieldNorm(doc=2257)\n0.93789136 = weight(abstract_txt:agents in 2257) [ClassicSimilarity], result of:\n0.93789136 = score(doc=2257,freq=1.0), product of:\n0.7504244 = queryWeight, product of:\n1.0655335 = boost\n6.665678 = idf(docFreq=147, maxDocs=42740)\n0.105656326 = queryNorm\n1.2498146 = fieldWeight in 2257, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n6.665678 = idf(docFreq=147, maxDocs=42740)\n0.1875 = fieldNorm(doc=2257)\n```\n3. Imam, I.F.; Kodratoff, Y.: Intelligent adaptive agents (1997) 1.62\n```1.615181 = sum of:\n1.615181 = sum of:\n0.73092854 = weight(abstract_txt:intelligent in 5017) [ClassicSimilarity], result of:\n0.73092854 = score(doc=5017,freq=2.0), product of:\n0.66095626 = queryWeight, product of:\n6.2557187 = idf(docFreq=222, maxDocs=42740)\n0.105656326 = queryNorm\n1.1058652 = fieldWeight in 5017, product of:\n1.4142135 = tf(freq=2.0), with freq of:\n2.0 = termFreq=2.0\n6.2557187 = idf(docFreq=222, maxDocs=42740)\n0.125 = fieldNorm(doc=5017)\n0.8842524 = weight(abstract_txt:agents in 5017) [ClassicSimilarity], result of:\n0.8842524 = score(doc=5017,freq=2.0), product of:\n0.7504244 = queryWeight, product of:\n1.0655335 = boost\n6.665678 = idf(docFreq=147, maxDocs=42740)\n0.105656326 = queryNorm\n1.1783365 = fieldWeight in 5017, product of:\n1.4142135 = tf(freq=2.0), with freq of:\n2.0 = termFreq=2.0\n6.665678 = idf(docFreq=147, maxDocs=42740)\n0.125 = fieldNorm(doc=5017)\n```\n4. Griswold, S.D.: Unleashing agents : the first wave of agent-enabled products hit the market (1996) 1.62\n```1.615181 = sum of:\n1.615181 = sum of:\n0.73092854 = weight(abstract_txt:intelligent in 5053) [ClassicSimilarity], result of:\n0.73092854 = score(doc=5053,freq=2.0), product of:\n0.66095626 = queryWeight, product of:\n6.2557187 = idf(docFreq=222, maxDocs=42740)\n0.105656326 = queryNorm\n1.1058652 = fieldWeight in 5053, product of:\n1.4142135 = tf(freq=2.0), with freq of:\n2.0 = termFreq=2.0\n6.2557187 = idf(docFreq=222, maxDocs=42740)\n0.125 = fieldNorm(doc=5053)\n0.8842524 = weight(abstract_txt:agents in 5053) [ClassicSimilarity], result of:\n0.8842524 = score(doc=5053,freq=2.0), product of:\n0.7504244 = queryWeight, product of:\n1.0655335 = boost\n6.665678 = idf(docFreq=147, maxDocs=42740)\n0.105656326 = queryNorm\n1.1783365 = fieldWeight in 5053, product of:\n1.4142135 = tf(freq=2.0), with freq of:\n2.0 = termFreq=2.0\n6.665678 = idf(docFreq=147, maxDocs=42740)\n0.125 = fieldNorm(doc=5053)\n```\n5. Williams, J.G.; Sochats, K.: Application of expert agents/assistants in library and information systems (1996) 1.56\n```1.5570219 = sum of:\n1.5570219 = sum of:\n0.7833009 = weight(abstract_txt:intelligent in 1678) [ClassicSimilarity], result of:\n0.7833009 = score(doc=1678,freq=3.0), product of:\n0.66095626 = queryWeight, product of:\n6.2557187 = idf(docFreq=222, maxDocs=42740)\n0.105656326 = queryNorm\n1.1851025 = fieldWeight in 1678, product of:\n1.7320508 = tf(freq=3.0), with freq of:\n3.0 = termFreq=3.0\n6.2557187 = idf(docFreq=222, maxDocs=42740)\n0.109375 = fieldNorm(doc=1678)\n0.7737209 = weight(abstract_txt:agents in 1678) [ClassicSimilarity], result of:\n0.7737209 = score(doc=1678,freq=2.0), product of:\n0.7504244 = queryWeight, product of:\n1.0655335 = boost\n6.665678 = idf(docFreq=147, maxDocs=42740)\n0.105656326 = queryNorm\n1.0310445 = fieldWeight in 1678, product of:\n1.4142135 = tf(freq=2.0), with freq of:\n2.0 = termFreq=2.0\n6.665678 = idf(docFreq=147, maxDocs=42740)\n0.109375 = fieldNorm(doc=1678)\n```"
]
| [
null
]
| {"ft_lang_label":"__label__en","ft_lang_prob":0.6963608,"math_prob":0.99731755,"size":6497,"snap":"2020-45-2020-50","text_gpt3_token_len":2479,"char_repetition_ratio":0.17926998,"word_repetition_ratio":0.4830097,"special_character_ratio":0.51531476,"punctuation_ratio":0.28720626,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9998062,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-10-30T01:35:17Z\",\"WARC-Record-ID\":\"<urn:uuid:d41a5928-0cfb-4bc5-88e2-61e5d61e5745>\",\"Content-Length\":\"14953\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6ca81427-eab5-422b-86c0-2f6f1c21247e>\",\"WARC-Concurrent-To\":\"<urn:uuid:40ecfdec-2eac-4668-ad24-574f389006f0>\",\"WARC-IP-Address\":\"139.6.160.6\",\"WARC-Target-URI\":\"http://ixtrieve.fh-koeln.de/birds/litie/document/2746\",\"WARC-Payload-Digest\":\"sha1:BZBCGXL2RYFVFQG3G4GVIPJ25YKCLQXL\",\"WARC-Block-Digest\":\"sha1:PGWIILMAIVRJ6IQC46QYWPCQQOJ5BMBS\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-45/CC-MAIN-2020-45_segments_1603107906872.85_warc_CC-MAIN-20201030003928-20201030033928-00509.warc.gz\"}"} |
http://semiticroots.net/index.php?r=root/search&%3BRoot_page=12&Root_page=35&Root_sort=id | [
"# Root Filter Search\n\nTo filter on radicals you must enter their index number, click the tabs below to see how the indexes map out in various scripts.\n\n 𐩱 = 0 𐩨 = 1 𐩩 = 2 𐩻 = 3 𐩴 = 4 𐩢 = 5 𐩭 = 6 𐩵 = 7 𐩹 = 8 𐩧 = 9 𐩸 = 10 𐩪 = 11 𐩦 = 12 𐩮 = 13 𐩳 = 14 𐩷 = 15 𐩼 = 16 𐩲 = 17 𐩶 = 18 𐩰 = 19 𐩤 = 20 𐩫 = 21 𐩡 = 22 𐩣 = 23 𐩬 = 24 𐩠 = 25 𐩥 = 26 𐩺 = 27 𐩯 = 28\n\nYou may optionally enter a comparison operator (<, <=, >, >=, <> or =) at the beginning of each of your search values to specify how the comparison should be done. To filter on more than one index for a radical, separate them with a comma (eg. 0,1,2)."
]
| [
null
]
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https://www.medcalc.org/manual/VHARMEAN-function.php | [
"MedCalc",
null,
"",
null,
"# VHARMEAN function\n\n## Description\n\nVHARMEAN(variable[,filter]) returns the harmonic mean of a variable.\n\nThe harmonic mean is calculated as follows:",
null,
"$$\\frac{n}{\\frac1{x_1} + \\frac1{x_2} + \\cdots + \\frac1{x_n}} = \\frac{n}{\\sum\\limits_{i=1}^n \\frac1{x_i}}$$\n\nThe harmonic mean is undefined for a data set that contains zero or negative values.\n\n## Note\n\nThis function calculates a statistic on a variable. Be careful when you use this function in cells of the columns that correspond to the variable, because this actually adds a value to the variable which can lead to unexpected and faulty results. You can exclude the cell to avoid this."
]
| [
null,
"https://www.medcalc.org/gif/wait20trans.gif",
null,
"https://www.medcalc.org/svg/hamburger_icon.svg",
null,
"https://www.medcalc.org/manual/formula/harmonicmean.png",
null
]
| {"ft_lang_label":"__label__en","ft_lang_prob":0.7632226,"math_prob":0.99503833,"size":627,"snap":"2021-43-2021-49","text_gpt3_token_len":161,"char_repetition_ratio":0.1364366,"word_repetition_ratio":0.0,"special_character_ratio":0.24720894,"punctuation_ratio":0.071428575,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99823874,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,null,null,null,null,6,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-22T00:16:39Z\",\"WARC-Record-ID\":\"<urn:uuid:1175d4c7-5998-430a-bd76-f80102626557>\",\"Content-Length\":\"27017\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:62116b9a-7cd7-4e7f-8694-84d44bf11c7e>\",\"WARC-Concurrent-To\":\"<urn:uuid:000fecab-e8a2-4eaa-bfbc-ca006c6b19f6>\",\"WARC-IP-Address\":\"104.26.2.186\",\"WARC-Target-URI\":\"https://www.medcalc.org/manual/VHARMEAN-function.php\",\"WARC-Payload-Digest\":\"sha1:CJRA4LEULFPT6NA2RHOUWJAIVJASMQ7C\",\"WARC-Block-Digest\":\"sha1:N73HZYBYHZLBBKORYHEMKRC2OLBMA7T4\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323585449.31_warc_CC-MAIN-20211021230549-20211022020549-00365.warc.gz\"}"} |
http://cloud-map.org/?q=node/27 | [
"# Variogram Analysis\n\nThough the processes influencing the spatial variation of a measured variable in the atmosphere obey physical laws, the number of forces acting on the measured variable can make it appear random. There is still, however, an underlying structure relative to its location. Such as variable is known as a regionalized variable and is best described using a random function. A single realization of a regionalized variable Z for all locations in x (x1, x2…xn) constitutes the random function which is defined as\n\nZ(x) = µ + ε(x)\n\nwhere µ is a stationary mean and ε(x) consists of both spatially autocorrelated residuals and a random noise component. The expected difference between Z at location x and x + h is zero\n\nE [ Z(x) - Z(x+h) ] = 0\n\nwhere h is a spatial separation vector. This means that the variance of Z measured at two locations in x is a function of distance h\n\nvar [ Z(x) - Z(x+h) ] = 2γ(h)\n\nwhere the quantity 2γ(h) is the variogram.\n\nPlotting the variogram reveals characteristics of the spatial nature of the random variable. Typically, as the spatial separation distance h increases, as does the variance until a point to where the variance levels off. This is known as the sill. It is at this point that spatial autocorrelation between samples dissipates. The distance h at which the sill occurs is known as the range. The range component of the variogram is important as it speaks to the spatial dependence of the random variable. Such information can lead to better informed sampling of the random variable, or used to assign weights for spatial interpolation.\n\nReferences:\n\nCressie, N., 1993. Statistics for spatial data, New York, Wiley.\nBurrough, P.A., McDonnell, R., McDonnell, R.A., & Lloyd, C.D. 2015. Principles of geographical information systems, New York, Oxford.",
null,
""
]
| [
null,
"http://cloud-map.org/sites/default/files/variogram.jpeg",
null
]
| {"ft_lang_label":"__label__en","ft_lang_prob":0.91825026,"math_prob":0.9945358,"size":1782,"snap":"2020-24-2020-29","text_gpt3_token_len":399,"char_repetition_ratio":0.14735658,"word_repetition_ratio":0.013468013,"special_character_ratio":0.22109988,"punctuation_ratio":0.13142857,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9944113,"pos_list":[0,1,2],"im_url_duplicate_count":[null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-05-29T16:37:34Z\",\"WARC-Record-ID\":\"<urn:uuid:170560ad-df9d-48aa-aae8-52fd2d579944>\",\"Content-Length\":\"9529\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:3ef44933-678a-4dc2-8702-efa122afd056>\",\"WARC-Concurrent-To\":\"<urn:uuid:a9baec57-e359-49b1-a7f0-3e7a3ed91053>\",\"WARC-IP-Address\":\"69.90.66.100\",\"WARC-Target-URI\":\"http://cloud-map.org/?q=node/27\",\"WARC-Payload-Digest\":\"sha1:UFM2Q6X7Q2XCPPNDVZ5VNC6M7IQW2VHY\",\"WARC-Block-Digest\":\"sha1:ZK3RHECE6VIYMU2QERZZ7OFQUWX3XEOT\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-24/CC-MAIN-2020-24_segments_1590347405558.19_warc_CC-MAIN-20200529152159-20200529182159-00285.warc.gz\"}"} |
https://www.iodraw.com/en/blog/220797265 | [
"Hear something , Obviously irrelevant, I will turn several corners in my heart and think of you .\n\nThe moon meets clouds , Flowers meet the wind , The night sky is beautiful tonight , I miss you again .\n\nAround the galaxy , Can't find a star brighter than you .\n\nSaid the little prince , There are tens of thousands of roses in this world , But this one is my own rose .\n\nTomorrow is 520 Yes , Bring you a code suitable for novice programmers to confess ：\n\nLet's take a look at the renderings first ：\n\nFirst one 321 count down\nvoid countdown(void) // Countdown function { int temp, i, j; char Word = \" Limited time , Talk about your feelings ~\";\nfor (i = 0; Word[i] != NULL; i++) { cout << Word[i]; Sleep(50); } Sleep(1000);\nsystem(\"cls\"); void printchar(); for (temp = 3; temp >= 1; temp--) { switch\n(temp) { case 1: for (i = 2; i <= 15; i++) { for (j = wide / 2; j <= wide / 2 +\n1; j++)str[i][j] = 1; }break; case 2: for (i = 2; i <= 15; i++) { switch (i) {\ncase 2:case 3:case 8:case 9:case 14:case 15: for (j = wide / 2 - 7; j <= wide /\n2 + 8; j++)str[i][j] = 1; break; case 4:case 5:case 6:case 7: for (j = wide / 2\n+ 7; j <= wide / 2 + 8; j++)str[i][j] = 1; break; default: for (j = wide / 2 -\n7; j <= wide / 2 - 6; j++)str[i][j] = 1; break; } }break; case 3: for (i = 2; i\n<= 15; i++) { switch (i) { case 2:case 3:case 8:case 9:case 14:case 15: for (j\n= wide / 2 - 7; j <= wide / 2 + 8; j++)str[i][j] = 1; break; default: for (j =\nwide / 2 + 7; j <= wide / 2 + 8; j++)str[i][j] = 1; break; } }break; }\nprintchar(); Sleep(1000); for (i = 0; i < gao; i++) { for (j = 0; j < wide;\nj++)str[i][j] = 0; } system(\"cls\"); } Sleep(500); //system(\"cls\");// Clean screen }\nCome out, all of them ta Love of name\n\nThen a Winnie the Pooh will be drawn\n\nvoid bear_display(void) { system(\"cls\");// Clean screen int i; char Word = \" Send\nyou a Teddy Bear\"; for (i = 0; Word[i] != NULL; i++) { cout << Word[i];\nSleep(50); } cout << endl; cout << endl; cout << endl; cout << \" ┴┬┴┬／￣＼＿／￣＼\"\n<< endl; cout << \" ┬┴┬┴▏ ▏▔▔▔▔＼ \" << endl; cout << \" ┴┬┴／＼ ／ ﹨ \" << endl;\ncout << \" ┬┴∕ ／ ） \" << endl; cout << \" ┴┬▏ ● ▏ \" << endl; cout\n<< \" ┬┴▏ ▔█ \" << endl; cout << \" ┴◢██◣ ＼＿＿＿／ \" << endl; cout <<\n\" ┬█████◣ ／ \" << endl; cout << \" ┴█████████████◣ \" << endl; cout << \"\n◢██████████████▆▄ \" << endl; cout << \" █◤◢██◣◥█████████◤＼ \" << endl; cout << \"\n◥◢████ ████████◤ ＼ \" << endl; cout << \" ┴█████ ██████◤ ﹨ \" << endl; cout\n<< \" ┬│ │█████◤ ▏ \" << endl; cout << \" ┴│ │ ▏ \" <<\nendl; cout << \" ┬ ∕ ∕ ／▔▔▔＼ ∕ \" << endl; cout << \"\n┴/＿＿＿／﹨ ∕ ﹨ ／＼ \" << endl; cout << \" ┬┴┬┴┬┴＼ ＼ ﹨／ ﹨ \" << endl;\ncout << \" ┴┬┴┬┴┬┴ ＼＿＿＿＼ ﹨／▔＼﹨ ▔＼ \" << endl; cout << \" ▲△▲▲╓╥╥╥╥╥╥╥╥＼ ∕\n／▔﹨／▔﹨ \" << endl; cout << \" ＊＊╠╬╬╬╬╬╬╬╬＊﹨ ／ ／／ \" << endl; Sleep(1000); for\n(float y = 1.3; y >= -1.1; y -= 0.06) { for (float x = -1.1; x <= 1.1; x +=\n0.025) if (x * x + pow(5.0 * y / 4.0 - sqrt(fabs(x)), 2) - 1 <= 0.0) cout <<\n'*'; else cout << ' '; cout << endl; } Sleep(3000); }\n\nFinally, draw a rose for her\n\nSee the previous article for the complete rose code !\nvoid rose_display(void) { system(\"cls\");// Clean screen int i; char Word = \"\nThere are also 5000 identical flowers in the world , But only you are my unique rose \"; for (i = 0; Word[i] != NULL; i++) { cout <<\nWord[i]; Sleep(50); } puts(\"\\033[91m\"); for (int y = 0; y < 80; y++) { for (int\nx = 0; x < 160; x++) putchar(\" .-:;+=*#@\"[(int)(f(make2((x / 160.0f - 0.5f) *\n2.0f, (y / 80.0f - 0.5f) * -2.0f)) * 12.0f)]); putchar('\\n'); } }\n\nPartners who need this complete source code can enter the penguin skirt 【8060】【41599】 Get it from the administrator\n\nTechnology"
]
| [
null
]
| {"ft_lang_label":"__label__en","ft_lang_prob":0.50595593,"math_prob":0.98229575,"size":3564,"snap":"2023-14-2023-23","text_gpt3_token_len":1553,"char_repetition_ratio":0.2030899,"word_repetition_ratio":0.2849741,"special_character_ratio":0.46380472,"punctuation_ratio":0.22994652,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9882812,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-03-27T01:38:01Z\",\"WARC-Record-ID\":\"<urn:uuid:03704530-fcfd-4b89-ada5-3af1c83ee09d>\",\"Content-Length\":\"13377\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b4532f27-4a07-45d1-b403-d4d2b6a109fc>\",\"WARC-Concurrent-To\":\"<urn:uuid:c32f49b4-6d67-4afd-8a8c-5e4f877f3c0a>\",\"WARC-IP-Address\":\"129.226.56.201\",\"WARC-Target-URI\":\"https://www.iodraw.com/en/blog/220797265\",\"WARC-Payload-Digest\":\"sha1:FH7LDRMIBLY6J5PH74VVTVXMGVZCJ5IK\",\"WARC-Block-Digest\":\"sha1:IFXLUY2QD6AMGJ2P5UQ7QBEJQ3JGJGJ3\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-14/CC-MAIN-2023-14_segments_1679296946584.94_warc_CC-MAIN-20230326235016-20230327025016-00474.warc.gz\"}"} |
https://www.wangzhanchengxu.com/wangzhanbj/316.html | [
"# javascript 作为值的函数\n\n0\n\n```function callSomeFunction(someFunction, someArgument){\nreturn someFunction(someArgument);\n}```\n\n```function add10(sum){\nreturn num+10;\n}\nLS.log.write(result1);\n\nfunction getGreeting(name){\nreturn \"Hello \"+name;\n}\nvar result2=callSomeFunction(getGreeting, \"Nicholas\");\nLS.log.write(result2);```\n\n```function createComparisonFunction(propertyName){\nreturn function(object1, object2){\nvar value1=object1[propertyName];\nvar value2=object2[propertyName];\nif(value1 < value2){\nreturn -1;\n}else if(value1 > value2){\nreturn 1;\n}else{\nreturn 0;\n}\n};\n}```\n\n```var data=[{name:\"Zachary\",age:28}, {name:\"Nicholas\",age:29}];\ndata.sort(createComparisonFunction(\"name\"));\nLS.log.write(data.name);\n\ndata.sort(createComparisonFunction(\"age\"));\nLS.log.write(data.name);\n```\n\n137 1731 25507×24小时服务热线",
null,
"终于等到你，还好我没放弃"
]
| [
null,
"https://www.wangzhanchengxu.com/statics/limages/ygshop/leftewm.png",
null
]
| {"ft_lang_label":"__label__zh","ft_lang_prob":0.861967,"math_prob":0.8432832,"size":1760,"snap":"2021-21-2021-25","text_gpt3_token_len":949,"char_repetition_ratio":0.13952164,"word_repetition_ratio":0.0,"special_character_ratio":0.19147727,"punctuation_ratio":0.2,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9664436,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-05-16T06:43:40Z\",\"WARC-Record-ID\":\"<urn:uuid:2e40df06-1118-4b42-be31-a3e5e35df857>\",\"Content-Length\":\"15225\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:97b3c52b-5750-4a3c-b299-8e35edc4f6ce>\",\"WARC-Concurrent-To\":\"<urn:uuid:15e6302a-43fa-43a8-b993-198fa4c6f052>\",\"WARC-IP-Address\":\"116.255.186.88\",\"WARC-Target-URI\":\"https://www.wangzhanchengxu.com/wangzhanbj/316.html\",\"WARC-Payload-Digest\":\"sha1:2ZOJITLBVZVSJS7NXVXLSSM4AG6M3EEJ\",\"WARC-Block-Digest\":\"sha1:JWZCLXCJLS7QR3TTKP2ZD2BE5J4YWGAW\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-21/CC-MAIN-2021-21_segments_1620243989690.55_warc_CC-MAIN-20210516044552-20210516074552-00223.warc.gz\"}"} |
https://www.mathworks.com/matlabcentral/answers/1603540-why-do-i-get-the-error-array-indices-must-be-positive-integers-or-logical-values?s_tid=prof_contriblnk | [
"# Why do i get the error: Array indices must be positive integers or logical values?\n\n3 views (last 30 days)\nSebastian Sunny on 5 Dec 2021\nEdited: Stephen23 on 10 Dec 2021\nHi, ive been trying to plot 3 sets of data on the same graph plot and i keep getting this error message :Array indices must be positive integers or logical values in my for loop\nStephen23 on 10 Dec 2021\nWhy do i get the error: Array indices must be positive integers or logical values?\nHi, ive been trying to plot 3 sets of data on the same graph plot and i keep getting this error message :Array indices must be positive integers or logical values in my for loop\nWindSpeeds = linspace(0,30,300);%m/s\ndeltaT = 0.01;\ntime = 0:deltaT:300;\n%preallocation\nrotorTorque = zeros(length(WindSpeeds),1); %Nm\nturbinePower = zeros(length(WindSpeeds),1);\ngeneratorTorque = zeros(length(WindSpeeds),1);\nomegaRotor = zeros(length(WindSpeeds),1);\n%eulers method\nfor i = 2:length(time)\nomegaRotor(i) = omegaRotor(i-1) + deltaT((windTurbineRotorModel(WindSpeeds,Ct,D,Vcutout,Vrated,Vcutin))-(k*omegaRotor(i-1).^2)/j);\nend\nthis is the code ive written at the moment\nThank you\n\n_ on 5 Dec 2021\nThis expression in the loop:\ndeltaT((windTurbineRotorModel(WindSpeeds,Ct,D,Vcutout,Vrated,Vcutin))-(k*omegaRotor(i-1).^2)/j)\nsays to get the elements of deltaT with index (or indices) equal to the value of:\n(windTurbineRotorModel(WindSpeeds,Ct,D,Vcutout,Vrated,Vcutin))-(k*omegaRotor(i-1).^2)/j\nI don't know what the value of that expression is because most of those variables are undefined, but given that deltaT is a scalar variable, I would guess that indexing it like that is not what you mean to be doing.\nSebastian Sunny on 5 Dec 2021\nForgot the multiplication sign thank you"
]
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.7472012,"math_prob":0.9805671,"size":2251,"snap":"2022-05-2022-21","text_gpt3_token_len":620,"char_repetition_ratio":0.108144194,"word_repetition_ratio":0.31698114,"special_character_ratio":0.2447801,"punctuation_ratio":0.15022421,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96980566,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-25T06:07:09Z\",\"WARC-Record-ID\":\"<urn:uuid:86f80b33-bfb8-4251-9122-ff7a9968f763>\",\"Content-Length\":\"126672\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0839406b-62f9-43ac-b1b8-fa2d6c004e63>\",\"WARC-Concurrent-To\":\"<urn:uuid:6f2fb048-8f02-44e4-a50e-65dcd101295c>\",\"WARC-IP-Address\":\"104.69.217.80\",\"WARC-Target-URI\":\"https://www.mathworks.com/matlabcentral/answers/1603540-why-do-i-get-the-error-array-indices-must-be-positive-integers-or-logical-values?s_tid=prof_contriblnk\",\"WARC-Payload-Digest\":\"sha1:YWELO3MB4IOIGRL3OX4KTXJH53ZBIFFN\",\"WARC-Block-Digest\":\"sha1:XMW7ZTR6VUOMJ7FB6QQBHI2IVUSLPYA6\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662580803.75_warc_CC-MAIN-20220525054507-20220525084507-00766.warc.gz\"}"} |
https://tex.stackexchange.com/questions/53061/insert-image-and-list-inside-a-table | [
"# Insert image and list inside a table\n\nI am trying to add both an image and list inside a table but I face various problems. As shown in the picture, the image is above the first horizontal line and also the lists are not properly oriented, they are located at the end of the table, not in the same line with the image. Can anybody help me with that? Thanks a lot\n\n \\begin{table}[h!]\n\\begin{center}\n\\begin{tabular}{ | c | p{5cm} | p{5cm} | }\n\\hline\n\\includegraphics[width=0.3\\textwidth, height=60mm]{images/myLboro.png}\n&\n\\begin{itemize}\n\\item Accessibility\n\\item Up to date information\n\\item Fulfil students needs and wants \\ldots\n\\end{itemize}\n&\n\\begin{itemize}\n\\item Accessibility\n\\item Up to date information\n\\item Fulfil students needs and wants \\ldots\n\\end{itemize}\n\\\\ \\hline\n\\end{tabular}\n\\caption{my.Lboro Analysis}\n\\label{tbl:myLboro}\n\\end{center}\n\\end{table}",
null,
"You can use \\raisebox to adjust the vertical positioning of the image:\n\n\\documentclass{memoir}\n\\usepackage[demo]{graphicx}% delete the demo option in your actual code\n\\usepackage{enumitem}\n\\usepackage{booktabs}\n\n\\begin{document}\n\n\\begin{table}[h!]\n\\begin{center}\n\\begin{tabular}{ c p{5cm} p{5cm} }\n\\toprule\n\\cmidrule(r){1-1}\\cmidrule(lr){2-2}\\cmidrule(l){3-3}\n\\raisebox{-\\totalheight}{\\includegraphics[width=0.3\\textwidth, height=60mm]{images/myLboro.png}}\n&\n\\begin{itemize}[topsep=0pt]\n\\item Accessibility\n\\item Up to date information\n\\item Fulfil students needs and wants \\ldots\n\\end{itemize}\n&\n\\begin{itemize}[topsep=0pt]\n\\item Accessibility\n\\item Up to date information\n\\item Fulfil students needs and wants \\ldots\n\\end{itemize}\n\\\\ \\bottomrule\n\\end{tabular}\n\\caption{my.Lboro Analysis}\n\\label{tbl:myLboro}\n\\end{center}\n\\end{table}\n\n\\end{document}",
null,
"I also made some changes to your code (as suggestions, of course):\n\n1. I used the booktabs package to improve the table design (in particular, no vertical rules).\n2. I used the enumitem package to suppress some vertical spacing before the lists.\n• You are amazing man, great solution. Thanks a lot, 10000 likes!!!! ;) Apr 23, 2012 at 23:29\n\nThe array package provides the m{<len>} column type which vertically aligns content in rows:",
null,
"\\documentclass{article}\n\\usepackage{graphicx}% http://ctan.org/pkg/graphicx\n\\usepackage{array}% http://ctan.org/pkg/array\n\\begin{document}\n\n\\begin{table}[h!]\n\\centering\n\\begin{tabular}{ | c | m{5cm} | m{5cm} | }\n\\hline\n\\begin{minipage}{.3\\textwidth}\n\\includegraphics[width=\\linewidth, height=60mm]{tiger}\n\\end{minipage}\n&\n%\\begin{minipage}[t]{5cm}\n\\begin{itemize}\n\\item Accessibility\n\\item Up to date information\n\\item Fulfil students needs and wants \\ldots\n\\end{itemize}\n%\\end{minipage}\n&\n%\\begin{minipage}{5cm}\n\\begin{itemize}\n\\item Accessibility\n\\item Up to date information\n\\item Fulfil students needs and wants \\ldots\n\\end{itemize}\n%\\end{minipage}\n\\\\ \\hline\n\\end{tabular}\n\\caption{my.Lboro Analysis}\\label{tbl:myLboro}\n\\end{table}\n\n\\end{document}\n\n\n\nThen, additionally, you can place the image inside a minipage of equivalent size (box it) to obtain the correct alignment. The adjustbox package provides a similar alignment modification for controlling boxes.\n\n• I like the flexibility of this approach - thanks\n– Alec\nMar 30, 2018 at 9:45"
]
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null,
"https://i.stack.imgur.com/TOjsK.png",
null,
"https://i.stack.imgur.com/jnBuP.png",
null,
"https://i.stack.imgur.com/uwJYR.png",
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.60304135,"math_prob":0.6932522,"size":3103,"snap":"2022-05-2022-21","text_gpt3_token_len":937,"char_repetition_ratio":0.13423686,"word_repetition_ratio":0.27173913,"special_character_ratio":0.2497583,"punctuation_ratio":0.08102767,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9536363,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,2,null,2,null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-26T15:16:24Z\",\"WARC-Record-ID\":\"<urn:uuid:f6a97687-eddf-458b-bedd-bafcafd2e064>\",\"Content-Length\":\"226553\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:8dfbe2b8-363e-4e0b-9d23-7eb9a24c8054>\",\"WARC-Concurrent-To\":\"<urn:uuid:6a42e51d-218b-438c-a3c5-adafd0e1731d>\",\"WARC-IP-Address\":\"151.101.1.69\",\"WARC-Target-URI\":\"https://tex.stackexchange.com/questions/53061/insert-image-and-list-inside-a-table\",\"WARC-Payload-Digest\":\"sha1:7B2ROF3G34R4JPEVOU7CZMFSGJQBRTDL\",\"WARC-Block-Digest\":\"sha1:VIMQETT2BTNCAOPTZ6LIHBGZ6RHRJ7ML\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662606992.69_warc_CC-MAIN-20220526131456-20220526161456-00272.warc.gz\"}"} |
https://ncatlab.org/schreiber/show/Equivariant+cohomology+of+M2%2FM5-branes | [
"# Schreiber Equivariant cohomology of M2/M5-branes\n\nContents",
null,
"Abstract. While it is well-known that the charges of F1/Dp-branes in type II string theory need to be refined from de Rham cohomology to certain twisted generalized differential cohomology theories, it is an open problem to determine the generalized cohomology theory for M2-brane/M5-branes in 11 dimensions. I discuss how a careful re-analysis of the old brane scan (arXiv:1308.5264 , arXiv:1506.07557, joint with Fiorenza and Sati) shows that rationally and unstably, the M2/M5 brane charge is in degree-4 cohomotopy. While this does not integrate to the generalized cohomology theory called stable cohomotopy, it does integrate to $G$-equivariant stable cohomotopy, for $G$ a non-cyclic finite group of ADE type. On general grounds, such an equivariant cohomology theory needs to be evaluated on manifolds with ADE orbifold singularities, and picks up contributions from the orbifold fixed points. Both of these statements are key in the hypothesized but open problem of gauge enhancement in M/F-theory.\n\nAcknowledgement. This note profited from discussion with David Barnes, Domenico Fiorenza, Thomas Nikolaus, Charles Rezk, David Roberts, Hisham Sati. It is adapted from a previous talk “Generalized cohomology of M2/M5-branes” at Higher Structures in String Theory, ESI Vienna, 11 Dec 2015.\n\n$\\,$\n\nFor details see:\n\n$\\,$\n\n# Contents\n\n## Background\n\nWe are going to analyze an open problem in the mathematical theory of super p-branes. Before even stating the open problem and its analysis, we do need to briefly recall what super $p$-branes are, mathematically. Lecture notes with more details on the following are in (Schreiber 15). Full details are in (dcct).\n\n### $L_\\infty$-algebras and Rational homotopy theory\n\nRationally, what we are going to be concerned with is all enoced in L-∞ algebra cohomology for super L-∞ algebras. We briefly recall this, following (Sati-Schreiber-Stasheff 09). For more exposition see at super Cartan geometry. All algebras here are over $\\mathbb{R}$.\n\nThe operation of sending finite dimensional Lie algebras? to their Chevalley-Eilenberg algebras is a fully faithful functor\n\n\\begin{aligned} LieAlg &\\stackrel{}{\\hookrightarrow} dgAlg^{op} \\\\ (\\mathfrak{g}, [-,-]) & \\mapsto CE(\\mathfrak{g}) \\coloneqq (\\wedge \\mathfrak{g}^\\ast, d_{CE} = [-,-]^\\ast) \\end{aligned}\n\nfrom the category of Lie algebras to the opposite category of dg-algebras.\n\nGeneralizing the image of this functor to those dg-algebras of the form $(\\wedge^\\bullet \\mathfrak{g}^\\ast, d)$ for $\\mathfrak{g}$ an $\\mathbb{N}$-graded vector space of finite type yields the opposite of the category of (connective) L-∞ algebras of finite type:\n\n\\begin{aligned} L_\\infty Alg & \\hookrightarrow dgAlg^{op} \\\\ (\\mathfrak{g}, [-], [-,-], [-,-,-], \\cdots) & \\mapsto CE(\\mathfrak{g}) \\coloneqq (\\wedge \\mathfrak{g}^\\ast, d_{CE} = [-]^\\ast + [-,-]^\\ast + [-,-,-]^\\ast + \\cdots) \\end{aligned} \\,.\n\nAccordingly, super L-∞ algebras are given by generalizing this further to $\\mathfrak{g}$ being an $\\mathbb{N}$-graded super vector space of finite type and regarding the Grassmann algebra $\\wedge^\\bullet \\mathfrak{g}^\\ast$ as $(\\mathbb{Z},\\mathbb{Z}_2)$-bigraded (see at signs in supergeometry).\n\n$CE \\colon sL_\\infty Alg \\hookrightarrow sdgAlg^{op} \\,.$\n\nThe category $sL_\\infty Alg$ carries a canonical homotopical structure whose weak equivalences are the quasi-isomorphisms on the underlying chain complexes $(\\mathfrak{g},[-])$ (Pridham 07).\n\nFor $\\mathbf{B}^{p+1} \\mathbb{R}$ denoting the line Lie (p+2)-algebra (whose Chevalley-Eilenberg algebra is generated in degree $(p+2)$ with vanishing differential) then an $L_\\infty$-algebra homomorphism\n\n$\\mathfrak{g} \\stackrel{\\mu}{\\longrightarrow} \\mathbf{B}^{p+1}\\mathbb{R}$\n\nis equivalently a $(p+2)$-cocycle in L-infinity algebra cohomology. Its homotopy fiber is the L-∞ algebra extension $\\hat \\mathfrak{g}$ that it classifies\n\n$\\array{ \\hat \\mathfrak{g} \\\\ \\downarrow^{\\mathrlap{hofib(\\mu)}} \\\\ \\mathfrak{g} &\\stackrel{\\mu}{\\longrightarrow}& \\mathbf{B}^{p+1}\\mathbb{R} } \\,.$\n###### Proposition\n\nFor $\\mathfrak{g} \\in sL\\infty Alg$, the homotopy fiber $\\hat {\\mathfrak{g}}$ of a cocycle $\\mu \\colon \\mathfrak{g} \\longrightarrow \\mathbf{B}^{p+1} \\mathbb{R}$ is given by\n\n$CE(\\hat {\\mathfrak{g}}) \\simeq CE(\\mathfrak{g})[b_{p+1}]/(d b_{p+1} = \\mu) \\,.$\n###### Example\n\nFor $\\mathfrak{g}$ a semisimple Lie algebra and $\\mathfrak{g} \\stackrel{\\langle-,[-,-]\\rangle}{\\longrightarrow} \\mathbf{B}^2 \\mathbb{R}$ the canonical 3-cocycle, its homotopy fiber is the string Lie 2-algebra.\n\nThis $L_\\infty$-extension will in general carry new cocycles, so that towers and bouquets of higher extensions emanate from any one super $L_\\infty$-algebra\n\n$\\array{ \\widehat{\\hat \\mathfrak{g}} \\\\ \\downarrow^{\\mathrlap{hofib(\\mu_2)}} \\\\ \\hat \\mathfrak{g} &\\stackrel{\\mu_2}{\\longrightarrow}& \\mathbf{B}^{p_2 + 1} \\mathbb{R} \\\\ \\downarrow^{\\mathrlap{hofib(\\mu_1)}} \\\\ \\mathfrak{g} &\\stackrel{\\mu_1}{\\longrightarrow}& \\mathbf{B}^{p_1+1}\\mathbb{R} } \\,.$\n\nThis reminds one of Whitehead towers in homotopy theory. And indeed, there is Lie integration of $L_\\infty$-algebras, which connects them both to smooth ∞-groups and to rational homotopy theory:\n\nFor $\\mathfrak{g}$ a Lie algebra, then the 2-coskeleton of the simplicial set\n\n$\\flat \\exp(\\mathfrak{g}) \\;\\colon\\; [k] \\mapsto Hom(CE(\\mathfrak{g}), \\Omega_{dR}^\\bullet(\\Delta^k))$\n\nis the simplicial nerve of the simply connected Lie group $G$ corresponding to $\\mathfrak{g}$:\n\n$cosk_2 \\flat \\exp(\\mathfrak{g}) \\simeq N G \\,.$\n\nTo remember the smooth structure on $G$ we simply parameterize this over smooth manifolds $U$. Then the simplicial presheaf\n\n$\\exp(\\mathfrak{g}) \\;\\colon\\; (U,[k]) \\mapsto Hom(CE(\\mathfrak{g}), \\Omega_{vert}^\\bullet(\\U \\times Delta^k))$\n\ngives the smooth stack delooping of the Lie group $G$:\n\n$cosk_2 \\exp(\\mathfrak{g}) \\simeq \\mathbf{B}G \\,.$\n\nThis generalizes verbatim to a Lie integration functor\n\n$\\exp \\;\\colon\\; sL_\\infty Alg \\longrightarrow PSh(SuperMfd, sSet)$\n\nfrom (super-)L-∞ algebras $\\mathfrak{g}$ to simplicial presheaves over supermanifolds, hence (super-)smooth ∞-stacks.\n\nNotice that for $CE(\\mathfrak{g})$ a Sullivan model, then over the point this is the Sullivan construction of rational homotopy theory. For instance the Eilenberg-MacLane spaces\n\n$\\flat \\exp( \\mathbf{B}^{p+1} \\mathbb{R} ) \\simeq K(\\mathbb{R}, p+2)$\n\nThis will be key in the following: $L_\\infty$-theory allows to derive the cohomological nature of the charges of super p-branes, but only in rational homotopy theory. The open problem to be discussed below is concerned with the ambiguity of lifting this to genuine (non-rational) homotopy theory.\n\n### Higher WZW-type sigma-models\n\nPhysics is all encoded in nonlinear functionals on moduli stacks of configurations of a physical system, called action functionals. We now review how every super $L_\\infty$-cocycle as above canonically induces an action functional called a higher WZW term. The super $p$-branes below are then determined by exceptional examples of this general construction.\n\n###### Proposition\n\nThere is a differential Lie integration functor that sends an $L_\\infty$-cocycle\n\n$\\mu \\;\\colon\\; \\mathfrak{g} \\stackrel{}{\\longrightarrow} \\mathbf{B}^{p+1}\\mathbb{R}$\n\nto a smooth ∞-group $\\tilde G$ equipped with a circle n-bundle with connection modulated by a map into the Deligne complex $\\mathbf{B}^{p+1}(\\mathbb{R}/\\Gamma)_{conn}$\n\n$\\mathbf{L}_\\mu \\;\\colon\\; \\tilde G \\stackrel{}{\\longrightarrow} \\mathbf{B}^{p+1}(\\mathbb{R}/\\Gamma)_{conn}$\n\nsuch that\n\n• it lifts the plain Lie integration $\\exp(\\mu) \\colon \\exp(\\mathfrak{g})\\to \\mathbf{B}^{p+1}\\mathbb{R}$ from above;\n\n• the curvature is $\\mu(\\theta)$, for $\\theta$ the Maurer-Cartan form on the smooth ∞-group $\\tilde G$.\n\n###### Proposition\n\nFor $\\Sigma_k$ an oriented closed manifold of dimension $k$, fiber integration in ordinary differential cohomology lifts to a morphism of smooth stacks\n\n$\\int_{\\Sigma_k} \\;\\colon\\; [\\Sigma_k, \\mathbf{B}^{p+1}(\\mathbb{R}/\\Gamma)_{conn}] \\longrightarrow \\mathbf{B}^{p+1-k}(\\mathbb{R}/\\Gamma)_{conn}$\n\nand the transgression of $\\mathbf{L}_\\mu$ to the mapping stack $[\\Sigma_k, \\tilde G]$ is simply the composition\n\n$\\int_{\\Sigma_k} [\\Sigma_k, \\mathbf{L}_\\mu] \\;\\colon\\; [\\Sigma_k, \\tilde G] \\stackrel{[\\Sigma_k, \\mathbf{L}]}{\\longrightarrow} [\\Sigma_k, \\mathbf{B}^{p+1}(\\mathbb{R}/\\Gamma)_{conn}] \\stackrel{\\int_{\\Sigma_k}}{\\longrightarrow} \\mathbf{B}^{p+1-k}(\\mathbb{R}/\\Gamma)_{conn}$\n\nFor $k = p+1$ this yields a functional\n\n$\\exp(i S_\\mu) \\;\\colon\\; [\\Sigma_{p+1}, \\tilde G] \\longrightarrow \\mathbb{R}/\\Gamma$\n\nwhich in physics one regards as the “gauge interactionaction functional of a local field theory of “higher WZW sigma-model”-type, describing the propagation of a “$p$-brane” with worldvolume $\\Sigma_{p+1}$ in $\\tilde G$.\n\n###### Example\n\nThe archetypical sigma-model for our purposes is that for the electron (a “0-brane”). On spacetime $X$ an electromagnetic field is represented by a circle group principal connection\n\n$\\mathbf{L}_{EM} \\colon X \\longrightarrow \\mathbf{B} (\\mathbb{R}/\\mathbb{Z})_{conn} \\,.$\n\nFor $\\Sigma_1 = S^1$ the abstract worldline of the electron, its electromagnetic interaction is encoded in the functional\n\n$\\int_{S^1}[S^1,\\mathbf{L}_{EM}] \\;\\colon\\; [S^1,X] \\longrightarrow \\mathbb{R}/\\mathbb{Z} \\,,$\n\nnamely the holonomy. The equations of motion that this induces by variation gives the Lorentz force exerted by the electromagnetic field on the electron.\n\nBy a fundamental phenomenon called Dirac charge quantization, the first Chern class\n\n$[\\mathbf{L}_{EM}] \\in \\mathbf{H}^2(X,\\mathbb{Z})$\n\nof $\\mathbf{L}_{EM}$ is identified with the total magnetic charge in the spacetime $X$. Put the other way around:\n\nThe action functional for the 0-brane is the transgression of the lift of the background charge to a cocycle in differential cohomology.\n\nThis is the blueprint for the $p$-brane charges that we are considering.\n\n###### Example\n\nFor $\\mathfrak{g}$ an ordinary Lie algebra then $\\tilde G$ is its ordinary simply-connected Lie group. For $\\mathfrak{g}$ semisimple, then the differential Lie integration, prop. , of the string 3-cocycle from example is the original WZW gerbe\n\n$\\mathbf{L}_{WZW} \\;\\colon\\; G \\longrightarrow \\mathbf{B}^2 U(1)_{conn} \\,.$\n\nIts transgression, prop. , is its surface holonomy and this is the interaction term of the action functional for the WZW sigma model describing propagation of a string in $G$, subject to the force exerted by a background “B-field charge”.\n\nNotice that this process of differential Lie integration produces coefficients in ordinary differential cohomology whose curvatures are the (left-translation) of the $B^{p+1} \\mathbb{R}$-values $L_\\infty$-cocycles. Below we will find cocycles taking values in more complicated $L_\\infty$-algebras, and then the construction of a Lagrangian from them is less immediate.\n\n### Green-Schwarz functionals for Super $p$-branes\n\nBy the above, each $(p+2)$-cocycle in higher Lie theory defines a p-brane sigma-model. Particularly interesting will be exceptional cocycles. Such happen to appear when passing from Minkowski-Poincaré spacetime symmetry to supersymmetry:\n\nPerturbativestring theory on geometric backgrounds is defined by the Neveu-Schwarz-Ramond model, namely by sigma-model 2d super conformal field theories (of central charge 15) on worldsheets $\\Sigma$ that are super Riemann surfaces, with target spaces $X$ that are ordinary (i.e. “bosonic”) spacetime manifolds.\n\nThese worldsheet field theories are induced from action functionals, namely variants of the standard energy functional (Polyakov action) on the space $[\\Sigma,X]$ of smooth functions\n\n$\\phi \\;\\colon\\; \\Sigma \\longrightarrow X \\,.$\n\nThe central theorem of perturbative superstring theory says that the spectrum of such a 2d SCFT are the quanta of the perturbations of a higher dimensional effective supergravity field theory on target spacetime, hence transforms under supersymmetry on target spacetime.\n\nThis is the fundamental prediction of the assumption of fundamental strings: assuming 1) that the particles that run in Feynman diagrams are fundamentally strings, and demanding 2) that there are fermionic particles among these, first implies that the strings must be spinning strings (have fermions on their worldsheet), which implies that they are superstrings (worldsheet supersymmetry mixes the worldsheet bosons and fermions), which then in addition implies that their target space effective field theory is supergravity, hence that also the effective target space fields exhibit local supersymmetry.\n\n$\\underset{spinning\\; string}{\\underbrace{fermions \\;+\\; strings}} \\;=\\; superstring \\;\\Rightarrow\\; supergravity \\,.$\n\nThe first step in this implications (spinning string is superstring) is straightforward, but the second step appears as a miracle from the point of view of the NSR string. It comes out this way by non-trivial computation, but is not manifest in the theory.\n\nIn order to improve on this situation, Green and Schwarz searched and found (Green-Schwarz 81, Green-Schwarz 82 Green-Schwarz 84) a suitably equivalent string action functional that would manifestly exhibit spacetime supersymmetry. This is now called the Green-Schwarz action functional.\n\naction functional for superstringmanifest supersymmetry\nRamond-Neveu-Schwarz stringon worldsheet\nGreen-Schwarz stringon target spacetime\n\nThe basic idea is to pass to the evident supergeometric analogue of the bosonic string action:\n\nLet $\\Sigma$ be a closed manifold of dimension 2 – representing the abstract worldsheet of a string. Let $(X,g)$ be a pseudo-Riemannian manifold – representing a purely gravitational spacetime background. Then the action functional governing the bosonic string propagating in this spacetime is the functional\n\n$\\exp(\\tfrac{i}{\\hbar} S_{bos}) \\;\\colon\\; [\\Sigma,X] \\longrightarrow \\mathbb{R}/_{\\hbar}\\mathbb{Z}$\n\non the smooth mapping space $[\\Sigma,X]$ of smooth functions $\\Sigma \\to X$, that simply assigns the proper relativistic volume of the image of the worldsheet $\\Sigma$ in spacetime:\n\n$(\\Sigma\\overset{\\phi}{\\longrightarrow} X) \\;\\mapsto\\; \\int_\\Sigma vol_{\\phi^\\ast g} \\,.$\n\n(This is the Nambu-Goto action. It is classically equivalently to the Polyakov action which is the genuine starting point for the quantum Neveu-Schwarz-Ramond string. Howver, since, as we discuss below, the Green-Schwarz action naturally generalizes to that of other $p$-branes it is more natural to consider the Nambu-Goto form of the action here.)\n\nWhen here $(X,g)$ is generalized to a superspacetime supermanifold with orthogonal structure encoded by a super-vielbein $e$ (see at super Cartan geometry for details), then the same form of the action functional still makes sense and produces a functional on the supergeometric mapping space $[\\Sigma,X]$. Moreover, by construction this action functional is invariant under the superisometry group of $(X,g)$, hence under spacetime supersymmetry.\n\n$\\array{ \\text{symmetry of worldsheet theory} \\\\ \\array{ && \\Sigma \\\\ & {}^{\\mathllap{\\phi}}\\swarrow && \\searrow^{\\mathrlap{\\phi'}} \\\\ X &&\\underset{\\simeq}{\\longrightarrow}&& X } \\\\ \\text{super-isometry of target spacetime} }$\n\nHowever, Green and Schwarz noticed that this kinetic action functional $\\phi \\mapsto \\int_\\Sigma vol_{\\phi^\\ast e}$ does not quite yield dynamics that is equivalent to that of the NSR string: when the equations of motion hold (“on shell”) it has more fermionic degrees of freedom than present in the NSR string. The key insight of Green and Schwarz was that one may add an extra summand to the action functional to the plain super-Nambu-Goto action, such that the resulting functional enjoys a further 1-parameter symmetry, called kappa-symmetry, and such that restricting to the $\\kappa$-symmetric states, then the action functionals do become classically equivalent.\n\nMoreover, they showed that in light-cone gauge the resulting quantum dynamics is equivalent to that of the NSR string, thus providing a conceptual proof for the observed local spacetime supersymmetry for backgrounds that admit two lightlike Killing vectors. (The quantization of the GS-string away from lightcone gauge however remains an open problem.)\n\nGreen-Schwarz’s extra kappa-symmetry term serves a clear purpose, but originally its geometrically meaning was mysterious. However, in (Henneaux-Mezincescu 85) it was observed (expanded on in (Rabin 87, Azcarraga-Townsend 89, Azcarraga-Izqierdo 95,chapter 8)), that the Green-Schwarz-action functional describing the string in $d+1$-dimensions has a neat geometrical interpretation: it is simply the (parameterized) WZW-model for\n\n1. target space being locally super Minkowski spacetime $\\mathbb{R}^{d-1,1|\\mathbf{N}}$ regarded as the coset supergroup\n\n$\\mathbb{R}^{d-1,1\\vert \\mathbf{N}} \\;\\simeq\\; Iso(\\mathbb{R}^{d-1,1\\vert \\mathbf{N}}) / Spin(d-1,1)$\n\nfor $\\mathbf{N}$ a real spin representation (the “number of supersymmetries”), $Iso(\\mathbb{R}^{d-1,1\\vert \\mathbf{N}})$ the corresponding super Poincaré group and $Spin(d-1,1)$ its Lorentz-signature Spin subgroup;\n\n2. WZW-term being a local potential for the the unique (up to rescaling, if it exists) $Spin(d-1,1)$-invariant group 3-cocycle $\\mu_3$ on $Iso(\\mathbb{R}^{d-1,1\\vert \\mathbf{N}})$, with component locally given by the Gamma-matrices of the given Clifford algebra representation.\n\nMore in detail, just as ordinary Minkowski spacetime $\\mathbb{R}^{d-1,1}$ may be identified with the translation group with canonical basis of left invariant 1-forms given by the canonical vielbein field\n\n$\\{e^a \\coloneqq \\mathbf{d}x^a\\}_{a = 0}^{d-1} \\,,$\n\nwhere $\\{x^a\\}$ are the canonical coordinates on $\\mathbb{R}^{d-1,1}$, so super Minkowski spacetime $\\mathbb{R}^{d-1,1\\vert \\mathbf{N}}$ for some real spin representation $\\mathbf{N}$ is characterized as the supergroup whose left invariant 1-forms consitute the $\\mathbb{Z} \\times \\mathbb{Z}/2\\mathbb{Z}$-bigraded differential with generators the super-vielbein\n\n$\\underset{deg = (1,even)}{\\underbrace{e^a}} \\;\\coloneqq\\; \\mathbf{d}x^a + \\tfrac{i}{2}\\overline{\\theta}\\Gamma^a \\mathbf{d} \\theta \\;\\;\\;\\,,\\;\\;\\;\\;\\;\\;\\;\\;\\;\\; \\underset{deg = (1,odd)}{\\underbrace{\\psi^\\alpha}} \\;\\coloneqq\\; \\mathbf{d}\\theta^\\alpha \\,,$\n\nwhere $(x^a, \\theta^\\alpha)$ are the canonical coordinates on $\\mathbb{R}^{d-1,1\\vert \\mathbf{N}}$, with the odd-graded elements $\\{\\theta^\\alpha\\}$ spanning the given real Spin(d-1,1)-representation $\\mathbf{N}$ with Clifford algebra generators $\\{\\Gamma^a\\}$.\n\nNow while ordinary Minkowski spacetime $\\mathbb{R}^{d-1,1}$ is an abelian group, reflected by the fact that its left-invariant 1-forms are all closed\n\n$\\mathbf{d}e^a = 0 \\;\\;\\;\\;\\;\\; on \\; \\mathbb{R}^{d-1,1} \\,,$\n\nthe key phenomenon of supersymmetry (that two fermions pair to a bosons) means that $\\mathbb{R}^{d-1,1\\vert \\mathbf{N}}$ is slightly non-abelian, reflected by the fact that the super-vielbein is not closed\n\n$\\mathbf{d} e^a = \\tfrac{i}{2} \\overline{\\psi} \\Gamma^a \\psi \\;\\,,\\;\\;\\;\\;\\;\\; \\mathbf{d} \\psi^\\alpha = 0 \\,.$\n\nThis is the source of all the rich structure seen in Green-Schwarz theory.\n\nIn particular, for special combinations of spacetime dimension $d$ and number of supersymmetries $\\mathbf{N}$ the 3-form\n\n$\\mu_3 \\;\\coloneqq\\; \\overline{\\psi} \\wedge \\Gamma_a \\psi \\wedge e^a$\n\nis a non-trivial super Lie algebra cocycle on $\\mathbb{R}^{d-1,1\\vert \\mathbf{N}}$, in that $\\mathbf{d}\\mu_3 = 0$ and so that there is no left invariant differential form $b$ with $\\mathbf{d}b = \\mu_3$.\n\nThis happens notably for $d = 10$ and $\\mathbf{N} = (1,0)$ (heterotic string) or $\\mathbf{N} = (2,0)$ (type IIB superstring) and $\\mathbf{N} = (1,1)$ (type IIA superstring). (It also happens in some lower dimensions, where however the corresponding NSR-string develops a conformal anomaly after quantization (“non-critical strings”). This classification of cocycles is part of what has come to be known as the brane scan in superstring theory, see below.)\n\nIn this equivalent formulation, the Green-Schwarz action functional for the superstring has the following simple form:\n\nLet $(X,e)$ be a superspacetime, hence a supermanifold $X$ equipped with a super-vielbein $e$ (super-orthogonal structure) which is locally modeled on $\\mathbb{R}^{d-1,1\\vert \\mathbf{N}}$ (technically: a torsion-free super-Cartan geometry modeled on $Spin(d-1,1) \\hookrightarrow Iso(\\mathbb{R}^{d-1,1\\vert \\mathbf{N}})$). Write $\\mu_3^X \\in \\Omega^3(X)$ be the super differential form on $X$ which is the induced definite globalization of the cocycle $\\mu_3$ over $X$. For $U \\subset X$ any contractible subspace, then the restriction of $\\mu^X_3|_{U} \\in \\Omega^3(U)$ of $\\mu_3^X$ to $U$ is exact, and hence admits a potential $B_U \\in \\Omega^2(U)$, i.e. such that $d B = \\mu^X_3|_U$.\n\nThen for $\\Sigma$ a 2-dimensional closed manifold, the Green-Schwarz action functional\n\n$\\exp(\\tfrac{i}{\\hbar} S_{GS}) \\;\\colon\\; [\\Sigma,X]_U \\longrightarrow \\mathbb{R}/_{\\hbar} \\mathbb{Z}$\n\nis the function on the super-smooth space $[\\Sigma,X]_U$ of smooth maps of supermanifolds $\\phi \\colon \\Sigma \\to X$ which factor through $U$, given by\n\n$\\phi \\;\\mapsto\\; \\int_\\Sigma vol_{\\phi^\\ast e} \\;+\\; \\int_\\Sigma \\phi^\\ast B_U \\;\\;\\;\\,,\\;\\;\\;\\;\\;\\;\\;\\;\\; \\mathbf{d} B_U = \\mu^X_3|_U \\,.$\n\nIn order to get rid of the restriction to some $U \\subset X$ one needs to add global data. The need for this is at least mentioned briefly in (Witten 86, p. 261 (17 of 20)), but had otherwise been ignored in the physics literature. The general solution is to promote the local potentials $B$ to the connection $\\hat B$ on a super gerbe (Fiorenza-Sati-Schreiber 13). This is a choice of higher prequantization\n\n$\\array{ && \\mathbf{B}^{2}(\\mathbb{R}/_\\hbar \\mathbb{Z}) & \\text{prequantization} \\\\ & {}^{\\mathllap{\\hat B}}\\nearrow & \\downarrow^{\\mathrlap{curv}} \\\\ X &\\underset{\\mu^X_3}{\\longrightarrow}& \\mathbf{\\Omega}^3 & \\text{3-form curvature} } \\,.$\n\nWriting $\\int_\\Sigma \\phi^\\ast \\hat B$ for the volume holonomy of a circle 2-bundle with connection $\\hat B$, then the globally defined Green-Schwarz sigma model\n\n$\\exp(\\tfrac{i}{\\hbar} S_{GS}) \\;\\colon\\; [\\Sigma, X] \\longrightarrow \\mathbb{R}/_\\hbar\\mathbb{Z}$\n\nis given by\n\n$\\phi \\;\\mapsto\\; \\int_\\Sigma vol_{\\phi^\\ast} + \\int_\\Sigma \\phi^\\ast \\hat B \\;\\;\\,, \\;\\;\\;\\;\\;\\;\\; curv(\\hat B) = \\mu_3^X \\,.$\n\nThis form of the Green-Schwarz action functional for the string has evident generalization to other $p$-branes. Whenever there is a Lorentz-invariant $(p+2)$-cocycle $\\mu_{p+2}$ on $\\mathbb{R}^{d-1,1\\vert \\mathbf{N}}$, then one may ask for a higher gerbe (higher prequantum line bundle) $\\hat C$ with curvature $\\mu^X_{p+2}$ and consider the analogous functional.\n\nThe triples $(d,\\mathbf{N},p)$ (spacetime dimension, number of supersymmetries, dimension of brane) such that\n\n$\\mu_{p+2} \\;\\coloneqq\\; \\overline{\\psi} \\wedge \\Gamma^{a_1 \\cdots a_p} \\psi \\wedge e_{a_1} \\wedge \\cdots \\wedge e_{a_p}$\n\nis a nontrivial cocycle, hence for which there is such a Green-Schwarz action functional for $p$-branes on $\\mathbb{R}^{d-1,1\\vert \\mathbf{N}}$ may be classified and form what is called the brane scan (Achúcarro-Evans-TownsendWiltshire 87, Brandt 12-13):",
null,
"The grapics on the left is from (Duff 87). The diagonal lines indicate double dimensional reduction, taking a $(p+1)$-brane in $(d+1)$ dimensions to a $p$-brane in $d$-dimensions.\n\nFor instance for $(d = 11, \\; \\mathbf{N} = \\mathbf{32}, \\; p = 2)$ one finds a cocycle, and the corresponding GS-action functional is that of the fundamental M2-brane.\n\nThis was a striking confluence of brane physics and classification of super Lie algebra cohomology. But just as striking as the matching, was what it lacked to match: the D-branes and the M5-brane ($d = 11$, $p = 5$) are lacking from the old brane scan. Incidentally, these lacking branes are precisely those branes on which the branes that do appear on the brane scan may end, equivalently those branes that have higher gauge fields on their worldvolume (tensor multiplets).\n\nAn action functional for the M5-brane vaguely analogous to a Green-Schwarz action functional was found in (BLNPST 97, APPS 97). It is again the sum of a kinetic term and a WZW-like term, but the WZW-like term does not come from a cocycle on a (super-)group.\n\nIn order to deal with this, it was suggested in (CAIB 99, Sakaguchi 00, Azcarraga-Izquierdo 01) that there is an algebraic structure called “extended super-Minkowski spacetimes” that generalizes super Minkowski spacetime and serves to unify the Green-Schwarz-like models for the D-branes and the M5-brane with the original Green-Schwarz models for the string and the M2-brane.\n\nThese extended super-Minkowski spacetimes carry algebraic analogs of super Lie algebra cocycles, such that the relevant terms for the D-branes and the M5-brane do appear after all, hence such that all the branes in string theory/M-theory are unified. In fact these “extended super-Minkowski spacetimes” are precisely the “FDA”s that have been introduced before in the D'Auria-Fré formulation of supergravity and what became identified as the 7-cocycle for the M5-brane this way had earlier been recognized algebraically as an stepping stone for an elegant re-derivation of 11-dimensional supergravity (D’Auria-Fré 82).\n\nThe (higher) geometric meaning of these constructions was found in (Fiorenza-Sati-Schreiber 13): these algebraic structures of “extended super-Minkowski spacetimes”/FDAs are precisely the Chevalley-Eilenberg algebras of super Lie n-algebra-extensions of super-Minkowski spacetime which are classified by the cocycles that serve as the GS-WZW terms of the $p_1$-branes that may end on those $p_2$-branes whose cocycles are carried by the extended super-Minkowski spacetime.\n\nHence the missing $p$-branes in the old brane scan (classifying just cocycles on super Lie algebras) do appear as one generalizes (super) Lie algebras to (super) strong homotopy Lie algebras = L-infinity algebras. Moreover, each brane intersection law (one brane species may end on another) is now matched to a super $L_\\infty$-algebra extension and so the old brane scan is generalized to a tree of branes The brane bouquet:",
null,
"Each item in this bouquet denotes a super L-infinity algebra and each arrow denotes an L-infinity extension classified by a cocycle which encodes the GS-WZW term of the brane named by the domain of the arrow.\n\nIn (Fiorenza-Sati-Schreiber 13) it is shown that all these super L-infinity algebras Lie integrate to smooth super-n-groups, and all the cocycles Lie integrate to super-gerbes on these, such that the induced volume holonomy is the relevant generalized GS-WZW term. For detailed exposition see at Structure Theory for Higher WZW Terms.\n\nWith this generalized perspective, now the Green-Schwarz-type action functionals describe all the p-branes in string theory/M-theory.\n\nAgain, in order to make this generally true one needs to apply a higher prequantization – a choice of line (p+1)-bundle with connection – in order to globalize the WZW-terms (Fiorenza-Sati-Schreiber 13)\n\n$\\array{ && \\mathbf{B}^{p+1}(\\mathbb{R}/_\\hbar \\mathbb{Z}) & \\text{prequantization} \\\\ & {}^{\\mathllap{\\hat A_{p+1}}}\\nearrow & \\downarrow^{\\mathrlap{curv}} \\\\ X &\\underset{\\mu^X_{p+2}}{\\longrightarrow}& \\mathbf{\\Omega}^{p+2} & (p+2)\\text{-form curvature} } \\,.$\n\nHence $\\hat A_{p+1}$ is the actual background field that the $p$-brane couples to. There is considerably more information in $\\hat A_p$ than in its curvature $curv(\\hat A_{p+1}) = \\mu_{p+2}$. For instance for the M2-brane one may find the local super moduli space for local choices of $\\hat A_{p+1}$ for the given $\\mu_{4}$ on KK-compactifications to $d = 4$. It turns out that the bosonic body of this moduli space is the exceptional tangent bundle on which the U-duality group E7 has a canonical action (see at From higher to exceptional geometry).\n\nThis highlights that Green-Schwarz functionals capture fundamental (“microscopic”) aspects of $p$-branes. In contrast, often $p$-branes are discussed in their solitonic incarnation as black branes. These solitonic branes sit at asymptotic boundaries of anti-de Sitter spacetime and carry conformal field theories, related to the ambient supergravity by AdS-CFT duality.\n\nThis phenomenon is indeed a consequence of the fundamental Green-Schwarz branes:\n\nConsider a 1/2-BPS state solution of type II supergravity or 11-dimensional supergravity, respectively. These solutions locally happen to have the same classification as the Green-Schwarz branes. Hence we may consider a configuration $\\phi \\colon \\Sigma \\to X$ of the corresponding fundamental $p$-brane which embeds $\\Sigma$ into the asymptotic AdS boundary of the given 1/2 BPS spacetime $X$. Then it turns out that restricting the Green-Schwarz action functional to small fluctuations around this configuration, and applying a diffeomorphism gauge fixing, then the resulting action functional is that of a supersymmetric conformal field theory on $\\Sigma$ as in the AdS-CFT dictionary:\n\nfundamental $p$-brane-fluctuations about asymptotic AdS configuration$\\to$solitonic $p$-brane\nGreen-Schwarz action functionalsuper-conformal field theory\n\nIn fact the BPS-state condition itself is neatly encoded in the Green-Schwarz action functionals: by construction they are invariant under the spacetime superisometry group. Hence the Noether theorem implies that there are corresponding conserved currents, whose Dickey bracket forms a super-Lie algebra extension of the Lie algebra of supersymmetries.\n\n$\\array{ \\left\\{ \\array{ X && \\overset{=}{\\longrightarrow} && X \\\\ & {}_{\\mathllap{\\hat C}}\\searrow &\\swArrow& \\swarrow_{\\mathrlap{\\hat C}} \\\\ && \\mathbf{B}^{p+1}(\\mathbb{R}/_{\\hbar} \\mathbb{Z}) } \\right\\} &\\longrightarrow& \\left\\{ \\array{ X && \\overset{\\simeq}{\\longrightarrow} && X \\\\ & {}_{\\mathllap{\\hat C}}\\searrow &\\swArrow& \\swarrow_{\\mathrlap{\\hat C}} \\\\ && \\mathbf{B}^{p+1}(\\mathbb{R}/_{\\hbar} \\mathbb{Z}) } \\right\\} &\\longrightarrow& \\left\\{ \\array{ X && \\overset{\\simeq}{\\longrightarrow} && X } \\right\\} \\\\ \\text{topological currents} && \\text{Noether currents} && \\text{symmetries} }$\n\nHere the “$\\swArrow$” filling the triangles is the non-trivial gauge transformation by which the WZW term (as any WZW term) is preserved under the symmetries (instead of being fixed identically). It is the information in this transformations which makes the currents form an extension of the symmetries.\n\nHere this yields the famous brane charge extensions of the super-isometry super Lie algebra of the schematic form\n\n$\\{Q_\\alpha, Q_\\beta\\} \\;=\\; (C \\Gamma^a_{\\alpha \\beta}) P_a \\;+\\; (C \\Gamma^{a_1 \\cdots a_p})_{\\alpha \\beta} Z_{a_1, \\cdots, a_p}$\n\n(for $Q$ a Killing spinor and $P$ its corresponding Killing vector) known as the type II supersymmetry algebra and the M-theory supersymmetry algebra, respectively (Azcárraga-Gauntlett-Izquierdo-Townsend 89). In fact it yields super-Lie n-algebra extensions of which the familiar super Lie algebra extensions are the 0-truncation (Sati-Schreiber 15, Khavkine-Schreiber 16).\n\nIn summary, the nature and classification of Green-Schwarz action functionals captures in a mathematically precise way a good deal of the core structure of string/M-theory.\n\nIn fact, the super L-infinity algebraic perspective on the Green-Schwarz functionals via The brane bouquet also solves the following open problem on M-branes:\n\nit is famously known from Freed-Witten anomaly-cancellation that the D-brane charges are not in fact just in de Rham cohomology in every second degree, but are in twisted K-theory, hence rationally in twisted de Rham cohomology, with the twist being the F1-brane charge (from the fundamental). It is an open problem to determine what becomes of these twisted K-theory charge groups as one lifts F1/D$p$-branes in string theory to M2/M5-branes in M-theory.\n\nintersecting branescharges in generalized cohomology theory\nstring theoryF1/Dp-branestwisted K-theory\nM-theoryM2/M5-branes???\n\nNotice that there are “microscopic degrees of freedom” of the theory encoded by the choice of generalized cohomology theory here, generalizing the extra degrees of freedom in the choice of a WZW-term already mentioned above. In general for $E$ a cohomology theory and $E \\longrightarrow E \\otimes \\mathbb{Q}$ its Chern character map (for instance from topological K-theory to ordinary cohomology in every second degree), then a choice of genuine charges is the extra information encoded in a lift\n\n$\\array{ && E \\\\ & {}^{\\mathllap{\\text{true charge}}}\\nearrow & \\downarrow^{\\mathrlap{ch}} \\\\ X &\\underset{\\text{rational} \\atop \\text{charge}}{\\longrightarrow}& E \\otimes \\mathbb{Q} }$\n\nBut rationally The brane bouquet allows to derive this from first principles:\n\nAbove we saw that the naive cocycles of the D-branes and of the M5-brane are not defined on the actual spacetime, but on some “extended” spacetime, which is really a smooth super infinity-groupoid extension of spacetime. Hence we should ask if these cocycles descend to the actual super-spacetime while picking up some twists.\n\nOne may prove that:\n\n• the F1/D$p$-brane GS-WZW cocycles descend to 10d type II superspacetime to form a single cocycle in rational twisted K-theory, just as the traditional lore reqires (Fiorenza-Sati-Schreiber 16);\n\n• the M2/M5 GS-WZW cocycles descent to 11d superspacetime to form a single cocycle with values in the rational 4-sphere (Fiorenza-Sati-Schreiber 16).\n\nThis we turn to now.\n\n## The open problem\n\nWe are now ready to state the open problem to be analyzed. We first give its purely mathematical content.\n\n### Twisted generalized cohomology from prescribed rationalization\n\nGiven one stage in the brane bouqet\n\n$\\array{ \\hat \\mathfrak{g} & \\stackrel{\\mu_2}{\\longrightarrow} & \\mathbf{B}\\mathfrak{h}_2 \\\\ {}^{\\mathllap{hofib(\\mu_1)}}\\downarrow \\\\ \\mathfrak{g} \\\\ & {}_{\\mathllap{\\mu_1}}\\searrow \\\\ && \\mathbf{B}\\mathfrak{h}_1 }$\n\nthen $\\hat \\mathfrak{g}$ is a $\\mathfrak{h}_1$-principal ∞-bundle over $\\mathfrak{g}$.\n\nThis and the following statements all are the general theorems of (Nikolaus-Schreiber-Stevenson 12) specified to $L_\\infty$-algebras regarded as infinitesimal $\\infty$-stacks (aka “formal moduli problems”) according to dcct.\n\nHence it is natural to ask whether the second cocycle $\\mu_2$, defined on the total space (stack) of this bundle is equivariant under the ∞-action of $\\mathfrak{h}_1$. If $\\mu_2$ does not itself already come from the base space, then it can at best be equivariant with respect to an $\\mathfrak{h}_1$-∞-action on $\\mathbf{B}\\mathfrak{h}_2$.\n\nFirst, specifying such ∞-action $\\rho$ is equivalent to specifying a second homotopy fiber sequence of the form as on the right of this completed diagram:\n\n$\\array{ \\hat \\mathfrak{g} && \\stackrel{\\mu_2}{\\longrightarrow} && \\mathbf{B}\\mathfrak{h}_2 \\\\ {}^{\\mathllap{hofib(\\mu_1)}}\\downarrow && && \\downarrow^{\\mathrlap{hofib(p_\\rho)}} \\\\ \\mathfrak{g} && && (\\mathbf{B}\\mathfrak{h}_2)/\\mathfrak{h}_1 \\\\ & {}_{\\mathllap{\\mu_1}}\\searrow && \\swarrow_{\\mathrlap{p_\\rho}} \\\\ && \\mathbf{B}\\mathfrak{h}_1 } \\,.$\n\nSecond, given $\\rho$, then the $\\infty$-equivariance of $\\mu_2$ is equivalent to it descending down the homotopy fibers on both sides to an $L_\\infty$-homomorphism of the form\n\n$\\mu_2/\\mathfrak{h}_1 \\;\\colon\\; \\mathfrak{g} \\longrightarrow (\\mathbf{B}\\mathfrak{h}_2)/\\mathfrak{h}_1$\n\nmaking this diagram commute in the homotopy category:\n\n$\\array{ \\hat \\mathfrak{g} && \\stackrel{\\mu_2}{\\longrightarrow} && \\mathbf{B}\\mathfrak{h}_2 \\\\ {}^{\\mathllap{hofib(\\mu_1)}}\\downarrow && && \\downarrow^{\\mathrlap{hofib(p_\\rho)}} \\\\ \\mathfrak{g} && \\stackrel{\\mu_2/\\mathfrak{h}_1}{\\longrightarrow} && (\\mathbf{B}\\mathfrak{h}_2)/\\mathfrak{h}_1 \\\\ & {}_{\\mathllap{\\mu_1}}\\searrow && \\swarrow_{\\mathrlap{p_\\rho}} \\\\ && \\mathbf{B}\\mathfrak{h}_1 } \\,.$\n\nIn conclusion:\n\n###### Remark\n\nThe resulting triangle diagram\n\n$\\array{ \\mathfrak{g} && \\stackrel{\\mu_2/\\mathfrak{h}_1}{\\longrightarrow} && (\\mathbf{B}\\mathfrak{h}_2)/\\mathfrak{h}_1 \\\\ & {}_{\\mathllap{\\mu_1}}\\searrow && \\swarrow_{\\mathrlap{p_\\rho}} \\\\ && \\mathbf{B}\\mathfrak{h}_1 }$\n\nregarded as a morphism\n\n$\\mu_2/\\mathfrak{h}_1 \\;\\colon\\; \\mu_{1} \\longrightarrow p_rho$\n\nin the slice over $\\mathbf{B}\\mathfrak{h}_1$ exhibits $\\mu_2/\\mathfrak{h}_1$ as a cocycle in (rational) $\\mu_1$-twisted cohomology with respect to the local coefficient bundle $p_\\rho$.\n\nNotice that a priori this is (twisted) nonabelian cohomology, though it may happen to land in abelian-, i.e. stable-cohomology.\n\nSuch descent is what one needs to find for The brane bouquet above, in order to interpret each of its branches as encoding $p$-brane model on spacetime itself. This is a purely algebraic problem which has been solved (Fiorenza-Sati-Schreiber 15). We discuss the solution in a moment.\n\nBut then the open problem is this: now the new rational coefficients is $p_\\rho$ (in the slice over $\\mathbf{B}\\mathfrak{h}_1$). This is no longer of the simple abelian form for which there exists the differential Lie integration functro from above. So:\n\nOpen problem: Find twisted differential cohomology theories which lifts the rational situation of remark through its Chern character map. In particular its curvature forms are to be in $Hom(CE((\\mathbf{B}\\mathfrak{h}_2)/\\mathfrak{h}_1, \\Omega^\\bullet(-))$.\n\nTo illustrate this problem in a situation where the solution is something well-known, we first discuss below how to derive from super $L_\\infty$-cohomology the famous statement that F1/Dp-brane charges are in twisted K-theory.\n\nThen further below we finally turn to the analogous but open case of M2/M5-brane charges.\n\n### M-brane charges\n\nHere is a comment on the significance of the above for physics. This is not needed for the mathematical discussion below, but it may help to motivate it.\n\nInspection shows that what is known for sure about M-theory (Witten 95) is all encoded in the prequantum Green-Schwarz-type sigma-models describing the propagation of M2-branes and M5-branes on super-spacetimes. In particular:\n\n1. The BPS charges of such spacetimes – which are traditionally argued to probe properties of the full quantum regime of the elusive theory – are identified with the charges of the Noether currents of these sigma-models.\n\nIn fact the Heisenberg Lie n-algebra (Fiorenza-Rogers-Schreiber 13) of these prequantum field theories is The M-Theory BPS charge super Lie 6-algebra, whose 0-truncation is the M-theory super Lie algebra$\\{Q_\\alpha, Q_\\beta\\} = (C \\Gamma^a_{\\alpha \\beta}) P_a + (\\Gamma^{a_1 a_2}_{\\alpha \\beta}) Z_{a_1 a_2} + \\Gamma^{a_1 a_2 \\cdots a_5}_{\\alpha \\beta} Z_{a_1 a_2 \\cdots a_5}$” (Sati-Schreiber 15, Schreiber-Khavkine 16).\n\n2. The membrane instanton contributions – which are argued to detect further non-perturbative effects – are the volume holonomy, i.e. the magnetic flux, of the complexified higher WZW term of the M2-brane over supersymmetric cycles (Schreiber 15).\n\n3. The definite globalization of the M2-WZW term over a superspacetime implies the equations of motion of 11-dimensional supergravity (hence in particular the Hodge duality between the rational M-brane charges) together with the classical anomaly cancellation that makes the M2-sigma model be globally well defined on this target (Schreiber 15).",
null,
"Moreover:\n\nTherefore, for making progress with the open question of formulating M-theory proper, a key issue is a precise understanding of the cohomological nature of M-brane charges (Sati 10) as twisted differential cohomology along the lines above.\n\nIn most of the existing literature, these charges are being regarded in de Rham cohomology. But it is well known (see (Distler-Freed-Moore 09) for the state of the art) that in the small coupling limit where the perturbation theory of type II string theory applies, the brane charges are not just in (twisted, self-dual) de Rham cohomology, but instead in a (twisted, self-dual) equivariant generalized cohomology theory, namely in real ($\\mathbb{Z}/2$-equivariant) topological K-theory, of which de Rham cohomology is only the rational shadow under the Chern character map. This makes a crucial difference (Maldacena-Moore-Seiberg 01, Evslin-Sati 06): the differentials in the Atiyah-Hirzebruch spectral sequence for K-theory describe how de Rham cohomology classes receive corrections as they are lifted to K-theory: some charges may disappear, others may appear.\n\nBut the lift of this situation to M-branes had been missing. The open question is: Which equivariant generalized cohomology theory $E_G$ do M-brane charges take values in?\n\nThe answer needs to satisfy (at least) the following two consistency conditions:\n\n1. the rationalization $E_G(X_{11})\\otimes \\mathbb{Q}$ of the generalized cohomology classes has to reproduce the correct rational brane charges, we analyze these below in The rational cohomology of M2/M5-brane charges;\n\n2. the $G$-equivariant Atiyah-Hirzebruch spectral sequence for $E_G(X_{11})$ along an M-theory circle fibration\n\n$\\array{ S^1 &\\to& X_{11} \\\\ && \\downarrow \\\\ && X_{10} }$\n\nneeds to be a suitable higher order correction to the AHSS for topological KR-theory $KU_{\\mathbb{Z}/2}(X_{10})$.\n\nHere we are concerned with the first item. By the analysis in (Sati-Varghese 03, section 4), at the rational level the second item is implied by the first, see the conclusion below.\n\n## Warmup: Generalized cohomology of F1/Dp-brane charges\n\nTo illustrate the general approach, we give a re-derivation from super $L_\\infty$-cohomology of the famous identification of F1/D$p$-brane charges in twisted K-theory (Fiorenza-Sati-Schreiber 16).\n\nThe super Minkowski spacetime $\\mathbb{R}^{9,1\\vert \\mathbf{16} + \\overline{\\mathbf{16}}}$ – locally modeling super spacetimes in 10d type IIA supergravity – carries super $L_\\infty$-extensions of the following form (FSS 13):\n\n$\\array{ \\widehat{\\mathbb{R}^{9,1\\vert \\mathbf{16}+ \\overline{\\mathbf{16}}}} && \\stackrel{\\underset{p=0,2,4,6}{\\oplus} \\mu_{D p}}{\\longrightarrow} && \\underset{p = 0,2,4,6}{\\oplus} \\mathbf{B}^{p+1}\\mathbb{R} \\\\ \\downarrow^{\\mathrlap{hofib(\\mu_{F1})}} \\\\ \\mathbb{R}^{9,1\\vert \\mathbf{16}+ \\overline{\\mathbf{16}}} \\\\ & {}_{\\mathllap{\\mu_{F1}}}\\searrow \\\\ && \\mathbf{B}^2 \\mathbb{R} } \\,.$\n\nHere the homotopy fiber $\\widehat{\\mathbb{R}^{9,1\\vert \\mathbf{16}+ \\overline{\\mathbf{16}}}}$ is the $\\mathbf{B}\\mathbb{R}$-principal ∞-bundle classified by the 3-cocycle $\\mu_{F1}$ for the F1-brane (the type IIA superstring), just like the string Lie 2-algebra-extension of example , but now for the super-part of the symmetry group. Therefore this has sometimes been called the “superstring super Lie 2-algebra”.\n\nBy the above (Nikolaus-Schreiber-Stevenson 12), asking whether the cocycles $\\mu_{D p}$ for the D-branes are $\\mathbf{B}\\mathbb{R}$-equivariant and descend as twisted cocycles down to super-Minkowski spacetime is equivalent to asking whether there is a homotopy fiber sequence $\\underset{p = 0,2,4,6}{\\oplus} \\mathbf{B}^{p+1}\\mathbb{R} \\to something \\to \\mathbf{B}^2\\mathbb{R}$ and a homotopy-commuting diagram of the form\n\n$\\array{ \\widehat{\\mathbb{R}^{9,1\\vert \\mathbf{16}+ \\overline{\\mathbf{16}}}} && \\stackrel{\\underset{p=0,2,4,6}{\\oplus} \\mu_{D p}}{\\longrightarrow} && \\underset{p = 0,2,4,6}{\\oplus} \\mathbf{B}^{2p+1}\\mathbb{R} \\\\ \\downarrow^{\\mathrlap{hofib(\\mu_{F1})}} && && \\downarrow^{\\mathrlap{hofib(\\phi)}} \\\\ \\mathbb{R}^{9,1\\vert \\mathbf{16}+ \\overline{\\mathbf{16}}} && \\stackrel{}{\\longrightarrow} && something \\\\ & {}_{\\mathllap{\\mu_{F 1}}}\\searrow && \\swarrow_{\\mathrlap{\\phi}} \\\\ && \\mathbf{B}^2 \\mathbb{R} } \\,.$\n\nInspection shows that this indeed exists: write $\\left(\\underset{p = 0,2,4,6}{\\oplus}\\mathbf{B}^{2p+1}\\mathbb{R}\\right)/\\mathbf{B} \\mathbb{R}$ for the L-∞ algebra whose Chevalley-Eilenberg algebra has generators $\\omega_2, \\omega_4, \\omega_6, \\omega_8$ and $h_3$ in the indicated degrees, with non-trivial differential given by $d(\\omega_{2(k+1)}) = h_3 \\wedge \\omega_{2k}$:\n\n$CE \\left( \\left(\\underset{p = 0,2,4,6}{\\oplus}\\mathbf{B}^{2p+1}\\mathbb{R}\\right)/\\mathbf{B} \\mathbb{R} \\right) \\coloneqq \\left\\{ \\{ \\omega_{p+2}, h_3\\}_{p = 0,2,4,6}, d \\omega_{2(k+1)} = h_3 \\wedge \\omega_{2k} \\right\\} \\,.$\n\nMoreover write $\\mathbb{R}^{9,1\\vert \\mathbf{16} + \\overline{\\mathbf{16}}}_{res}$ for the super $L_\\infty$-algebra whose Chevalley-Eilenberg algebra is that of $\\mathbb{R}^{9,1\\vert \\mathbf{16} + \\overline{\\mathbf{16}}}$ with generators $f_2$ and $h_3$ added, subject to $d f_2 = \\mu_{F1} + h_3$. This is a resolution\n\n$\\mathbb{R}^{9,1\\vert \\mathbf{16} + \\overline{\\mathbf{16}}}_{res} \\stackrel{\\simeq}{\\longrightarrow} \\mathbb{R}^{9,1\\vert \\mathbf{16} + \\overline{\\mathbf{16}}}$\n\nof type IIA super-Minkowski spacetime which serves to represent morphisms in the homotopy theory for super L-infinity algebras in the following. Because with this, the above descent problem indeed has a solution as follows:\n\n$\\array{ \\left\\{ {{d e^a = \\overline{\\psi}\\Gamma^a \\wedge \\psi } \\atop {d \\psi^\\alpha = 0}} \\atop { d f_2 = \\mu_{F1}} \\right\\} && \\widehat{ \\mathbb{R}^{ 9,1\\vert \\mathbf{16} + \\overline{\\mathbf{16}} } } && \\stackrel{\\underset{p=0,2,4,6}{\\oplus} \\mu_{D p}}{\\longrightarrow} && \\underset{p = 0,2,4,6}{\\oplus} \\mathbf{B}^{2p+1}\\mathbb{R} && \\left\\{ d \\omega_{2 k} = 0 \\right\\} \\\\ && \\downarrow^{\\mathrlap{hofib(\\mu_{F1})}} && && \\downarrow \\\\ \\left\\{ {{d e^a = \\overline{\\psi}\\Gamma^a \\wedge \\psi } \\atop {d \\psi^\\alpha = 0}} \\atop { d f_2 = \\mu_{F1} + h_3 } \\right\\} & & \\mathbb{R}_{res}^{9,1\\vert \\mathbf{16}+ \\overline{\\mathbf{16}}} && \\stackrel{ \\left( \\omega_{p+2} \\mapsto \\mu_{D p} \\right) }{\\longrightarrow} && \\left( \\underset{p = 0,2,4,6}{\\oplus} \\mathbf{B}^{2p+1}\\mathbb{R} \\right)/\\mathbf{B} \\mathbb{R} && \\left\\{ d\\omega_{2(k+1)} = h_3\\wedge \\omega_{2k} \\right\\} \\\\ && & {}_{\\mathllap{\\mu_{F 1}}}\\searrow && \\swarrow \\\\ && && \\mathbf{B}^2 \\mathbb{R} \\\\ && && \\left\\{ d h_3 = 0 \\right\\} } \\,.$\n\nThis says that the type IIA F1-brane and D-brane cocycles with $\\mathbb{R}$-coefficients do descent to super-Minkowski spacetime as one single cocycle with coefficients in the homotopy quotient $\\left( \\underset{p = 0,2,4,6}{\\oplus} \\mathbf{B}^{2p+1}\\mathbb{R} \\right)/\\mathbf{B} \\mathbb{R}$.\n\nBut these rational coefficients are precisely the rational image of twisted topological K-theory.\n\nAccordingly, the Lie integration of this rational situation to twisted K-theory, and its globalization over a 10-dimensional IIA super spacetime $X_{10}$, yields a diagram of parameterized spectra in smooth infinity-stacks of the form\n\n$\\array{ X_{10} && \\stackrel{RR_{/B}}{\\longrightarrow} && KU / \\mathbf{B} U(1) \\\\ & {}_{\\mathllap{B}}\\searrow && \\swarrow \\\\ && \\mathbf{B}^2 U(1) }$\n\nAccording to (Sati-Schreiber-Stasheff 09, Nikolaus-Schreiber-Stevenson 12) here the morphism denoted $B$ represents the Kalb-Ramond B-field under which the F1-brane is charged and the morphism denoted $RR_{/B}$ represents the RR-field under which the D-branes are charged.\n\nThis is how one may re-discover the familiar cohomological nature of the F1/Dp-brane charges in type II string theory from an analysis of the super $L_\\infty$-cohomology embodied in the brane bouquet-refinement of the old brane scan.\n\n## The rational cohomology of M2/M5-brane charges\n\nWe now consider the analogue of this re-derivation, but up in 11-dimensions, where it provides a previously missing derivation of the rational cohomology of M-brane charges.\n\nFor the 11-dimensional super Minkowski spacetime on which 11-dimensional supergravity is locally modeled (via super Cartan geometry) the iterative extension of $L_\\infty$-cocycles in the brane bouquet looks like so (Fiorenza-Sati-Schreiber 13):\n\n$\\array{ \\widehat{\\mathbb{R}^{10,1\\vert \\mathbf{32}}} &\\stackrel{\\mu_{M5}}{\\longrightarrow}& \\mathbf{B}^6 \\mathbb{R} \\\\ \\downarrow^{\\mathrlap{hofib(\\mu_{M2})}} \\\\ \\mathbb{R}^{10,1\\vert \\mathbf{32}} & \\stackrel{\\mu_{M2}}{\\longrightarrow} & \\mathbf{B}^3 \\mathbb{R} \\\\ \\downarrow^{\\mathrlap{hofib(\\mu_{D 0})}} \\\\ \\mathbb{R}^{9,1\\vert \\mathbf{16} + \\overline{\\mathbf{16}}} }$\n\nHence the M5-brane WZW term exists on the $\\mathbf{B}^2 \\mathbb{R}$-principal infinity-bundle that is classified by the M2-brane WZW term. Again using (Nikolaus-Schreiber-Stevenson 12), we may ask if this is equivariant and descends back to 11-dimensional super-Minkowski spacetime.\n\nAnd it does (Fiorenza-Sati-Schreiber 15):\n\nwrite $\\mathbf{B}^6 \\mathbb{R}/\\mathbf{B}^2 \\mathbb{R}$ for the L-infinity algebra whose Chevalley-Eilenberg algebra is generated from elements $\\omega_4$ and $\\omega_7$, in degrees 4 and 7 as indicated, and whose differential is given by $d \\omega_4 = 0$ and $d \\omega_7 = \\omega_4 \\wedge \\omega_4$. This sits in a homotopy fiber sequence of L-infinity algebras of the form\n\n$\\mathbf{B}^6 \\mathbb{R} \\longrightarrow \\mathbf{B}^6\\mathbb{R}/\\mathbf{B}^2 \\mathbb{R} \\longrightarrow \\mathbf{B}^3 \\mathbb{R} \\,.$\n\nNotice that if we think of the Chevalley-Eilenberg algebras of these $L_\\infty$-algebras as being Sullivan models in rational homotopy theory, then this homotopy fiber sequence is the rational image of the quaternionic Hopf fibration\n\n$S^7 \\longrightarrow S^4 \\to \\mathbf{B}SU(2) \\stackrel{\\mathbf{c_2}}{\\to} \\mathbf{B}^3 U(1) \\,.$\n\nNow computation shows (Fiorenza-Sati-Schreiber 15) that indeed the WZW term for the M5-brane does descend back to super-Minkowski spacetime as a cocycle with coefficients in this rational 4-sphere:\n\n$\\array{ \\left\\{ { { d e^a = \\overline{\\psi}\\wedge \\Gamma^a \\wedge \\psi } \\atop { d \\psi^\\alpha = 0 } } \\atop d h_3 = - \\mu_{M2} \\right\\} && \\widehat{\\mathbb{R}^{10,1\\vert \\mathbf{32}}} && \\stackrel{h_3 \\wedge \\mu_4 + \\frac{1}{15}\\mu_{M5} }{\\longrightarrow} && \\mathbf{B}^6 \\mathbb{R} && \\left\\{ d \\omega_7 = 0 \\right\\} \\\\ && \\downarrow^{\\mathrlap{hofib(\\mu_{M2})}} && && \\downarrow \\\\ \\left\\{ { { d e^a = \\overline{\\psi}\\wedge \\Gamma^a \\wedge \\psi } \\atop { d \\psi^\\alpha = 0 } } \\atop d h_3 = g_4 - \\mu_{M2} \\right\\} && \\mathbb{R}_{res}^{10,1\\vert\\mathbf{32}} && \\stackrel{h_3 \\wedge (g_4 + \\mu_4) + \\frac{1}{15}\\mu_7 }{\\longrightarrow} && \\mathbf{B}^6 \\mathbb{R}/\\mathbf{B}^2 \\mathbb{R} && \\left\\{ {d g_4 = 0} \\atop {d g_7 = g_4 \\wedge g_4} \\right\\} \\\\ && & {}_{\\mathllap{\\mu_{M2}}}\\searrow && \\swarrow \\\\ && && \\mathbf{B}^3 \\mathbb{R} \\\\ && && \\left\\{ d g_4 = 0\\right\\} }$\n\nHence we read off from this computation that, rationally, M2-brane charge is in degree-4 ordinary cohomology and it twists M5-brane charge which is, rationally, in unstable degree-4 cohomotopy. This confirms a statement made earlier in (Sati 10, section 6.3, Sati 13, section 2.5).\n\nAn unstable Lie integration of this situation, in direct analogy to the above situation for twisted K-theory, would be given by maps into the quaternionic Hopf fibration\n\n$\\array{ && && S^7 \\\\ && && \\downarrow \\\\ X && \\stackrel{G_7_{/G_4}}{\\longrightarrow} && S^4 \\\\ & {}_{\\mathllap{G_4}} \\searrow && \\swarrow & \\downarrow \\\\ && \\mathbf{B}^3 U(1) &\\stackrel{\\mathbf{c2}}{\\longleftarrow}& \\mathbf{B}SU(2) }$\n\nwhere the left map $G_4$ would represent the magnetic M2-brane charge and the horizontal map the $G_4$-twisted magnetic M5-brane charge. (Here we are displaying a diagram of smooth infinity-stacks, there is a further refinement of these cocycles to nonabelian differential cohomology (FSS 15)).\n\nNotice that, unstably, the 4-sphere is just the space whose non-torsion homotopy groups (hence those that are visible rationally) are in degrees 4 and 7\n\nk1234567\n$\\pi_k(S^4)$000$\\mathbb{Z}$$\\mathbb{Z}_2$$\\mathbb{Z}_2$$\\mathbb{Z} \\oplus \\mathbb{Z}_{12}$\n\nHence, unstably, the 4-sphere $S^4$ may be thought of as the coefficient which is just right for detecting integral M2-brane charge and M5-brane charge. For instance the near-horizon limit of a black M2-brane is the spacetime $X_{11} = AdS_4 \\times S^7$ and the degree-4 cohomotopy classes\n\n$[AdS_4 \\times S^7, S^4] \\simeq [S^7,S^4] \\simeq \\mathbb{Z} \\oplus \\mathbb{Z}_12$\n\ndetect the integral charge of these (the M2 being the magnetic source for M5-brane charge), with the unit of charge being represented by the quaternionic Hopf fibration. Similarly the near-horizon limit of a black M5-brane is $AdS_7 \\times S^4$ and again the degree-4 cohomotopy classes are\n\n$[AdS_7 \\times S^4 , S^4] \\simeq [S^4, S^4] \\simeq \\mathbb{Z}$\n\ndetecting the integral charge of these branes.\n\nBut unstable cohomotopy – which may be thought of as a very nonabelian cohomology theory – is unlikely to satisfy consistency condition 2 of reproducing topological K-theory in a suitable limit, for that we need an actual “abelian” cohomology theory represented by a spectrum. This we turn to now.\n\n## Lift to ADE-equivariant stable cohomotopy\n\nIt follows that the first of our two consistency conditions is to be solved by finding a (possibly equivariant) generalized cohomology theory whose rational image is 4-shifted cohomotopy.\n\nThe immediate guess might be that this is 4-shifted stable cohomotopy, i.e. the generalized cohomology theory which is represented by the suspension spectrum of the 4-sphere, hence by the 4-suspended sphere spectrum $\\mathbb{S}$:\n\n$\\Sigma^\\infty S^4 = \\Sigma^4 \\mathbb{S} \\,.$\n\nHowever, this does not work: the non-torsion element in $\\pi_7(S^4) = \\mathbb{Z} \\oplus \\mathbb{Z}/12$, which is the one represented by the quaternionic Hopf fibration, becomes torsion after stabilization – since the third stable homotopy group of spheres is the cyclic group $\\pi_3^S = \\mathbb{Z}/24$ – and hence disappears rationally:\n\n$\\array{ \\pi_7(S^4) &\\longrightarrow& \\pi_3(\\mathbb{S}) \\\\ \\mathbb{Z}\\oplus \\mathbb{Z}_{12} && \\mathbb{Z}_{24} } \\,.$\n\nA natural way to evade this problem is to ask for a finite group $G$ acting on the quaternionic Hopf fibration and to consider $G$-equivariant stable cohomotopy. Since this forces all homotopies to exist $G$-equivariantly, it potentially makes some unstable non-torsion elements remain stably non-torsion.\n\nMore concretely, there is “genuine” $G$-equivariant cohomology theory, motivated as follows. The traditional suspension isomorphism\n\n$H^n(X,E) \\simeq H^{n+k}(S^k \\wedge X, E)$\n\nrelates the integer grading of cohomology groups with $k$-fold suspensions of base spaces given by smash product with the $k$-sphere. In a context where all spaces and coefficients are equipped with $G$-action, then one may consider not just plain spheres $S^k$ but representation spheres $S^V$ given by one-point compactification of linear $G$-representations $V$. The usual spheres are subsumed by this as coming from the trivial representations: $S^k \\simeq S^{\\mathbb{R}^k}$. This gives rise to a generalized grading of cohomology groups not just by integers, but by linear $G$-representations – called RO(G)-grading – such that an equivariant suspension isomorphism holds\n\n$H^W_G(X,E) \\simeq H^{W+V}_G(S^V\\wedge X, E)$\n\nfor any linear $G$-representations $W$ and $V$.\n\nAn equivariant version of the Brown representability theorem states that every RO(G)-graded equivariant cohomology theory is represented by what is called a genuine G-spectrum. Where an ordinary spectrum $E$ is a system of pointed topological spaces $E_n$ indexed by the integers, hence by the ordinary spheres $S^n$, and equipped with compatible comparison maps\n\n$S^{n-k}\\wedge E_k \\longrightarrow E_{n} \\,,$\n\na genuine G-spectrum is a system of pointed topological spaces $E_V$ indexed by representation spheres $S^V$ and equipped with compatible comparison maps of the form\n\n$S^{V-W} \\wedge E_W \\longrightarrow E_V \\,.$\n\nIn particular for $X$ any pointed topological G-space, there is the corresponding $G$-equivariant suspension spectrum $\\Sigma^\\infty_G X$ whose value on a representation sphere $S^V$ is the smash product $S^V \\wedge X$.\n\nHence the problem that $\\pi_7(\\Sigma^\\infty S^4)$ is torsion may potentially be fixed by finding a finite group $G$ and a $G$-action on the quaternionic Hopf fibration, $S^7_G \\to S^4_G$, such that $S^7_G \\simeq S^{\\mathbb{R}^7_G}$ is a representation sphere for a 7-dimensional linear $G$-representation, and such that the $G$-equivariant quaternonic Hopf fibration represents a non-torsion element in\n\n$H^{-\\mathbb{R}^7_G}(\\ast, \\Sigma^\\infty_G S^4) = [\\Sigma^\\infty_G S^7, \\Sigma^\\infty_G S^4] \\,.$\n\nNow, by the way the quaternionic Hopf fibration is obtained, via the Hopf construction, from the product operation on the quaternions $\\mathbb{H}$, it is equivariant under the induced action of the automorphism group of the quaternions. This automorphism group is the special orthogonal group $SO(3)$, acting on the imaginary quaternions by rotation:\n\n$Aut_{\\mathbb{R}}(\\mathbb{H}) \\simeq SO(3) \\,.$\n\nSince we need equivariance under a finite group, our options are finite subgroups of $SO(3)$\n\n$G \\hookrightarrow SO(3) \\,.$\n\nThese finite subgroups have an ADE classification. In the A-series they are the cyclic groups, sitting in the inclusion $SO(2) \\hookrightarrow SO(3)$. In the D-series these are the dihedral groups which are those subgroups generated from a cyclic subgroup rotating in some plane and a reflection at that plane. Finally there are three exceptional finite subgroups: the tetrahedral group, the octahedral group and the icosahedral group\n\nRegard both $S^7$ and $S^4$ as pointed topological G-spaces via the $SO(3)$-action induced via automorphisms of the quaternions. Write\n\n$\\Sigma^\\infty_G S^7, \\Sigma^\\infty_G S^4 \\in G Spectra$\n\nfor the corresponding equivariant suspension spectra.\n\n###### Remark\n\nThe 4-sphere with this action is manifestly a representation sphere\n\n$S^4 = \\mathbb{H}\\mathbb{P}^1 \\simeq \\mathbb{H} \\cup \\{\\infty\\} \\simeq S^{\\mathbb{H}} \\,.$\n\nWe will write $S^{\\mathbb{R}^4_G}$ for this representation sphere.\n\nMoreover, the 7-sphere with this action is also a representation sphere, via stereographic projection\n\n\\begin{aligned} S^7 & =_G S(\\mathbb{H} \\times \\mathbb{H}) \\\\ & \\simeq_G S( \\mathbb{R} \\oplus (Im(\\mathbb{H} \\oplus \\mathbb{H})) ) \\\\ & \\simeq_G S^{Im(\\mathbb{H} \\oplus \\mathbb{H})} \\end{aligned} \\,.\n\nWe will write $S^{\\mathbb{R}^7_G}$ for this.\n\nRecall again that if we took trivial $G$, then in the stable homotopy category\n\n$[\\Sigma^\\infty S^7, \\Sigma^\\infty S^4] \\simeq \\mathbb{Z}_{24}$\n\nby the above. In contrast:1\n\n###### Theorem",
null,
"Let $G \\hookrightarrow SO(3)$ be a non-cyclic finite subgroup, hence a dihedral group or one of the three exceptionals: the tetrahedral group, the octahedral group, the icosahedral group.\n\nThen in $G$-equivariant homotopy theory the quaternionic Hopf fibration $S^7 \\to S^4$ represents a non-torsion group, i.e.\n\n$H_G^{-\\mathbb{R}^7_G}(\\ast, \\Sigma^\\infty_G S^4) \\;\\coloneqq\\; [\\Sigma^\\infty_G S^7, \\Sigma^\\infty_G S^4]_G \\;\\simeq\\; \\mathbb{Z} \\oplus \\cdots$\n\nwith the quaternionic Hopf fibration, regarded as a $G$-equivariant map, representing the element $2 \\in \\mathbb{Z}$.\n\n###### Proof\n\nFirst use the Greenlees-May decomposition which says that for any two $G$-equivariant spectra $X,Y$ and writing $\\pi_\\bullet(X), \\pi_\\bullet(Y)$ for their equivariant homotopy groups, organized as Mackey functors $H \\mapsto \\pi_n^H(X)$ for all subgroups $H \\subset G$, then the canonical map\n\n$[X,Y]_G \\longrightarrow \\underset{n}{\\oplus} Hom_{\\mathcal{M}[G]}(\\pi_n(X), \\pi_n(Y))$\n\nWith this we are reduced to showing that there exists $n \\in \\mathbb{Z}$ and a morphism of Mackey functors of equivariant homotopy groups $\\pi_n(\\Sigma^\\infty_G S^7) \\to \\pi_n(\\Sigma^\\infty_G S^4)$ which is not a torsion element in the abelian hom-group of Mackey functors.\n\nTo analyse this, we use the tom Dieck splitting which says that the equivariant homotopy groups of equivariant suspension spectra $\\Sigma^\\infty_G X$ contain a direct summand which is simply the ordinary stable homotopy groups of the naive fixed point space $X^H$:\n\n$\\pi_n^G(\\Sigma^\\infty_G X) \\;\\simeq\\; \\pi_n(\\Sigma^\\infty (X^G)) \\; \\underset{{[H \\subset G]} \\atop {H \\neq G}}{\\oplus} \\pi_\\bullet(\\Sigma^\\infty (E (W_G H)_+ \\wedge_{W_G H} X^H))$\n\n(here $W_G H \\coloneqq (N_G H)/H$ denotes the Weyl group, the quotient group of the normalizer subgroup (of $H$ in $G$) by $H$).\n\nNow observe that the fixed points of the $SO(3)$-action on the quaternionic Hopf fibration that we are considering is just the real Hopf fibration:\n\n$(p_{\\mathbb{H}})^{SO(3)} = p_{\\mathbb{R}} \\;\\colon\\; S^1 \\longrightarrow S^1$\n\nsince $SO(3)$ acts transitively on the imaginary quaternions and fixes the real quaternions. By our assumption that $G \\subset SO(3)$ does not come through $SO(2) \\hookrightarrow SO(3)$ it follows that this statment is still true for $G$:\n\n$(p_{\\mathbb{H}})^{G} = p_{\\mathbb{R}} \\;\\colon\\; S^1 \\longrightarrow S^1 \\,.$\n\nBut the real Hopf fibration represents the non-torsion element $2 \\in \\pi_0^S \\simeq \\mathbb{Z}$.\n\nIn conclusion then, at $n = 1$ and $H = G$ we find that the $G$-equivariant quaternionic Hopf fibration contributes a non-torsion element in\n\n$Hom_{Ab}(\\pi_1^G(\\Sigma^\\infty_G S^7), \\pi_1^G(\\Sigma^\\infty_G S^4))$\n\nwhich appears as a non-torsion element in\n\n$Hom_{\\mathcal{M}[G]}( \\pi_1(\\Sigma^\\infty_G S^7), \\pi_1(\\Sigma^\\infty_G S^4) )$\n\nand hence in $[\\Sigma^\\infty_G S^7, \\Sigma^\\infty_G S^4]_G$.\n\n## Conclusion and outlook\n\nIn conclusion, a consistent possibility for the equivariant generalized cohomology theory in which M2/M5-brane charges take value is 4-shifted DE-equivariant stable cohomotopy in RO(G)-degree\n\n$\\mathbb{R}^7 - \\mathbb{R}^7_G \\;\\; \\in Rep(G)$\n\n(in the notation of remark ), hence the cohomology theory\n\n$H^{\\mathbb{R}^{7}-\\mathbb{R}^{7}_G }_G( -,\\; \\Sigma^\\infty_G S^4 ) \\simeq H(- , [\\Sigma^\\infty_G S^7, \\Sigma^7 \\Sigma^\\infty_G S^4]) \\,.$\n\nThe ADE-equivariance (or rather: DE-equivariance) which we discovered this way from the mathematics is a pleasant surprise:\n\nThe key conjecture (Sen 97) on the nature of the elusive “microscopic degrees of freedom” of M-theory states (see Acharya-Gukov 04 for review) that\n\n1. its spacetimes are ADE orbifolds;\n\n2. the theory is non-degenerate – in that it exhibits the nonabelian gauge enhancement – only at the ADE singularities, i.e. at the fixed points of the ADE-action.\n\nThis comes form the following physical heuristics (Sen 97):",
null,
"The de-singularization of an ADE singularity via blow-up is a system of touching spheres forming the corresponding Dynkin diagram. Under double dimensional reduction the M2-brane wrapped on this configuration becomes the type IIA string stretched between non-coincident D6-branes in the form of the Dynkin diagram. Here type IIA string theory applies and yields that the quiver gauge theory on these D-branes exhibits gauge enhancement to the corresponding ADE-simple gauge group as the D-branes are brought together again. But this end result must be the same as applying double dimensional reduction to the original ADE-singular M-theory configuration. Hence there must be nonabelian ADE-simple gauge group degrees of freedom hidden in M-theory on ADE-orbifolds, waiting to be mathematically identified.\n\nNow observe that both items above follow at least qualitatively from our mathematical analysis:\n\n1. a $G$-equivariant cohomology theory is to be evaluated on topological G-spaces;\n\n2. it picks up its contributions from the fixed points – by the tom Dieck splitting principle (as in the proof of theorem ) .\n\nThis gauge enhancement in M-theory at these fixed points is to be the M-theory lift of the familiar appearance of Chan-Paton gauge fields with nonabelian structure group on coincident D-branes. But mathematically the Chan-Paton gauge fields are just elements in the twisted topological K-theory in which the D-brane charges take values, as above. Hence it seems that in order to mathematically exhibit the conjectured gauge enhancement in M-theory at ADE-singularities, it is now sufficient to show that DE-equivariant stable cohomotopy on an 11-dimensional circle fibration reduces to twisted K-theory on the 10-dimensional base. But that is just the second consistency check already mentioned at the beginning.\n\nTo check this, one may run the Serre spectral sequence/Atiyah-Hirzebruch spectral sequence for $G$-equivariant stable cohomotopy theory on circle fibrations\n\n$\\array{ S^1 &\\to& X_{11} \\\\ && \\downarrow \\\\ && X_{10} } \\,.$\n\nWe may check this rationally: By Greenlees-May decomposition our equivariant cohomology theory rationally decomposes as a direct sum of equivariant Eilenberg-MacLane spectra on the equivariant homotopy group Mackey functors\n\n$H^{\\mathbb{R}^{7}-\\mathbb{R}^{7}_G }_G( -,\\; \\Sigma^\\infty_G S^4 ) \\simeq_{\\mathbb{Q}} \\underset{n}{\\prod} \\Sigma^n H(\\pi_n(\\Sigma^\\infty_G S^4))$\n\nand for each of the EM-summands there is a Serre-Atiyah-Hirzebruch spectral sequence (Kronholm 10, theorem 3.1)\n\n$E_2^{p,q} \\;=\\; H^p(X_{10}, H^{(\\mathbb{R}^{7}-\\mathbb{R}^{7}_G) + q}(S^1,\\pi_{p+q}(\\Sigma^\\infty_G S^4))) \\;\\;\\Rightarrow\\;\\; H^{\\mathbb{R}^{7}-\\mathbb{R}^{7}_G + \\bullet}_G(X_{11} , \\pi_\\bullet(\\Sigma^\\infty_G S^4)) \\,.$\n\nBut by the above analysis the $E_2$-page here rationally reduces to the Gysin sequence analysis in (Sati-Varghese 03, section 4).\n\nFor instance for $p + q = 6 - 5$ there is the following contribution that gives the correct double dimensional reduction of the charge seen by the M5-brane to the charge seen by the D4-brane, rationally:\n\n\\begin{aligned} H^6(X_{10}, H^{(\\mathbb{R}^{7}-\\mathbb{R}^{7}_G) -5}( S^1,\\pi_{1}(\\Sigma^\\infty_G S^4) ) ) & = H^6(X_{10}, H^{-\\mathbb{R}^{7}_G + 2}( S^1, \\pi_{1}(\\Sigma^\\infty_G S^4) ) ) \\\\ & \\simeq H^6( X_{10}, Hom_{\\mathcal{M}[G]}( \\pi_2(\\Sigma^1 \\Sigma^\\infty_G S^7),\\pi_{1}(\\Sigma^\\infty_G S^4)) ) \\\\ & \\simeq H^6( X_{10}, Hom_{\\mathcal{M}[G]}( \\pi_1(\\Sigma^\\infty_G S^7),\\pi_{1}(\\Sigma^\\infty_G S^4)]_G ) \\\\ & \\simeq H^6( X_{10}, \\mathbb{Z} ) \\oplus torsion \\end{aligned} \\,.\n\nHere in the second step we unraveled the definition of cohomology with values in a Mackey for the case of the domain being a sphere, in the third step we used stability of the stable equivariant homotopy groups and in the fourth we used the proof of theorem .\n\n$\\,$\n\n$\\,$\n\n$\\,$\n\n$\\,$\n\n$\\,$\n\n$\\,$\n\n$\\,$\n\n$\\,$\n\n$\\,$\n\n$\\,$\n\n$\\,$\n\n$\\,$\n\n$\\,$\n\n$\\,$\n\nReferences\n\n1. The proof of theorem profited crucially from Charles Rezk, who suggested here that the reduction to fixed points will make the real Hopf fibration give a non-torsion contribution; and from David Barnes who amplified the use of the Greenless-May decomposition theorem.\n\nLast revised on September 27, 2019 at 04:11:22. See the history of this page for a list of all contributions to it."
]
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"https://ncatlab.org/schreiber/files/MPIBonnHigherStructuresSeminar.JPG",
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"https://ncatlab.org/nlab/files/DuffBraneScan.jpg",
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"https://dl.dropboxusercontent.com/u/12630719/BraneBouquet.JPG",
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"https://dl.dropboxusercontent.com/u/12630719/branecharges.JPG",
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"https://upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Icosahedron.jpg/621px-Icosahedron.jpg",
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"http://ncatlab.org/nlab/files/ADE2Cycle.jpeg",
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https://dsp.stackexchange.com/questions/24364/filters-hilbert-transform-and-absolute-value-of-magnitude-response | [
"# Filters - Hilbert Transform and Absolute Value of Magnitude Response\n\nFollowing relationship between magnitude response and phase response for minimum phase:",
null,
"I have implemented in C++ code using the Hilbert Transform C code from file found online ht.c. However, I am not getting the phase response as expected. My magnitude response follows raised cosine formula:",
null,
"Essentially I provide $|H(j\\omega)| = \\text{Gain}(f)$ to be all real values as per this cosine formula. The phase response is not as expected. Also, how am I suppose to handle $\\log(|H(i\\omega)|)$ when $|H(i\\omega)| = 0$? Am I missing any steps to obtain phase response in this process?\n\nHere is how phase and magnitude response should look like:",
null,
"• What did you expect the phase to look like? Also note that there is no problem with zero values because (at least from the figure) the magnitude never becomes zero. Furthermore, the phase is not defined when the magnitude is zero, so this is not a relevant problem. (What phase does the value $0$ have?) But now comes the most important question: what are you going to do with the phase response if you manage to compute it from the given magnitude response? In what way are you expecting it to help you when designing the filter? – Matt L. Jun 25 '15 at 13:14\n• I'm not sure what you're after but I think you might be on the wrong track. – Matt L. Jun 25 '15 at 13:14\n• Can your code demonstrate the Hilbert transform of $\\cos$ is $\\sin$? That's the first step. Then test your code satisfies $\\left<x,Hx\\right> = 0$ and $\\left<Hx,Hx\\right> = \\left<x,x\\right>$. – user14717 Jun 25 '15 at 13:17\n• @MattL. In the definition of filters magnitude response it specifies Gain(f) = 0 (otherwise). Correct me if I am wrong but magnitude is zero there. As for the phase, it should look like as in this question but I am getting different kind of curve. My filter needs to have this kind minimum phase response, that's the design objective. – Nebojsa Jun 25 '15 at 13:22\n• you have real problems with your definition. in your figure the raised cosine is drawn on a log-frequency scale, not a linear-frequency scale. there is symmetry in log-frequency, not linear-frequency. so your mathematical definition is inconsistent with that. (your $W$ and $f$ terms do not have the same dimensions. you'll likely have to replace $f$ with $\\log_2(f)$ somehow, somewhere.) – robert bristow-johnson Jun 25 '15 at 15:23\n\nNeb, i dunno where you got that frequency response expression from, but it's flawed. from the description (of parameters like $W$ in \"octaves\"), it should be like this:\n$$Gain(f) = \\begin{cases} 10^{Boost/20} \\times \\frac{1}{2}\\left\\{1 + \\cos\\left(\\pi \\frac{\\log_2(f/F_c)}{W} \\right) \\right\\}, & \\text{if }|\\log_2(f/F_c)|<W \\\\ 0, & \\text{otherwise } \\end{cases}$$"
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"https://i.stack.imgur.com/y9MTy.jpg",
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"https://i.stack.imgur.com/sqeLY.jpg",
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"https://i.stack.imgur.com/0Rmor.jpg",
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.9066461,"math_prob":0.97055817,"size":639,"snap":"2020-45-2020-50","text_gpt3_token_len":145,"char_repetition_ratio":0.16377953,"word_repetition_ratio":0.0,"special_character_ratio":0.23004694,"punctuation_ratio":0.09836066,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9977086,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,6,null,6,null,6,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-10-20T20:16:30Z\",\"WARC-Record-ID\":\"<urn:uuid:331c0f4c-42f2-47ec-9890-1bd873cca9b9>\",\"Content-Length\":\"158043\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f7aa06a1-9032-471c-ad21-2b3b3cabc704>\",\"WARC-Concurrent-To\":\"<urn:uuid:b07d3927-be59-4f95-8b47-40cbc6340ced>\",\"WARC-IP-Address\":\"151.101.129.69\",\"WARC-Target-URI\":\"https://dsp.stackexchange.com/questions/24364/filters-hilbert-transform-and-absolute-value-of-magnitude-response\",\"WARC-Payload-Digest\":\"sha1:5MUEOXGYJ7P57XUP7T6IMTCNAFNGR2KB\",\"WARC-Block-Digest\":\"sha1:I6FM4J7Z6GZZ7MQCXDU7DCXLHIK6CMLC\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-45/CC-MAIN-2020-45_segments_1603107874135.2_warc_CC-MAIN-20201020192039-20201020222039-00248.warc.gz\"}"} |
https://exploringtm1.com/calculating-as-at-values-in-a-tm1-rule/ | [
"# Calculating “As At” Values in a TM1 Rule\n\nHave you ever needed to calculate the value “as at” a point in time? For example, you have an inventory cube and want to show the volume of stock at the end of a quarter, or end of the year. You might have values in each month, but if you use a regular consolidation for months, it won’t work for you. You will end up with each month aggregated and a total for the 12 months, rather than the last value.\n\n## Calculating As At Values\n\nIn the example below we have a continuous time dimension. we have values for FTE and Average Annual Salary for each week. We needed our rule to populate the month value with the value for the last week.\n\nTo do this we created the following rule:\n\n`['FTE'] = C: DB('Labour Plan', ELCOMP( 'Time', !Time, ELCOMPN( 'Time', !Time)), !Version, !Department , !Location, !Labour Role, !Measures - Labour Plan);`\n\nWhat this is saying is the measure FTE at a consolidation level is equal to the last child element of a parent. In other words, put the as at value into the parent!\n\nNote that we have not (yet) calculated the rule for the Annual Base Salary. So this is showing \\$440,000 for the first period, which is somewhat more than a person loading trucks is likely to earn!\n\n## Explanation of the Rule\n\nSo, for example we have the following structure:\n\n• 2021\n• 2021 Period 1\n• 2021 Week 1\n• 2021 Week 2\n• 2021 Week 3\n• 2021 Week 4\n\nWhen evaluating 2021 Period 1, the ELCOMPN returns 4 children. Then ELCOMP then goes and gets the 4th element from the structure, which in this case is 2021 Week 4. Therefore the value for 2021 Period 1 will equal the contents of 2021 Week 4.\n\nIf, alternatively, we had the following:\n\n• 2021\n• 2021 Period 1\n• 2021 Period 2\n• 2021 Period n\n• 2021 Period 12\n\nThen, assuming there were 12 periods, the ELCOMPN would return 12 and the twelfth period is 2021 Period 12. Therefore the as at value would be the number in period 12.\n\nPretty clever, huh!"
]
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.91239864,"math_prob":0.9394633,"size":1943,"snap":"2023-40-2023-50","text_gpt3_token_len":531,"char_repetition_ratio":0.15420319,"word_repetition_ratio":0.021857923,"special_character_ratio":0.28924343,"punctuation_ratio":0.13106796,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9827491,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-10-02T17:38:09Z\",\"WARC-Record-ID\":\"<urn:uuid:e1c4233c-0362-4722-8af0-b4af854251b4>\",\"Content-Length\":\"102713\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:44cd4b3a-c7ee-4d77-b514-a68e0edc1e0f>\",\"WARC-Concurrent-To\":\"<urn:uuid:400ca914-10b3-4278-b2f2-1e500a52042c>\",\"WARC-IP-Address\":\"162.159.130.73\",\"WARC-Target-URI\":\"https://exploringtm1.com/calculating-as-at-values-in-a-tm1-rule/\",\"WARC-Payload-Digest\":\"sha1:Q2T2XGGYC5BXH4QP7R5HZNSBJTECQGVW\",\"WARC-Block-Digest\":\"sha1:IRLUWNH7LUB4P7NP3PWZRO66M5ZO4QHR\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233511002.91_warc_CC-MAIN-20231002164819-20231002194819-00416.warc.gz\"}"} |
https://celestrak.com/columns/v02n01/ | [
"",
null,
"## Orbital Coordinate Systems, Part I\n\nBy Dr. T.S. Kelso",
null,
"September/October 1995\n\n By this point, I hope to have helped you develop an understanding of two key aspects of practical orbital mechanics. The first has to do with why we use the orbital models we do for predicting the position of earth-orbiting artificial satellites. As with any computer model, orbital models must trade off accuracy for computational speed. Which model you decide to use will depend upon which of these factors is most important to you. Of course, from a practical perspective, the choice of orbital model is also strongly influenced by the availability of data (element sets). Knowing that orbital element sets are generated by fitting observations to a trajectory based upon a particular orbital model is the second of our key aspects. Accuracy of our predictions will depend upon using that same orbital model. Up to now, however, all we've really talked about are orbital element sets. But how do we get from the data in these orbital element sets to something we can use, such as knowing where to look (or point an antenna) when a satellite passes over? To answer this question requires an understanding of the various coordinate systems involved and how to transform coordinates (typically position and velocity) from one system to another. The correct application of these coordinate transformations is every bit as important to our overall accuracy as the selection of the orbital model itself. Where do we start? Let's start with the orbital element sets themselves and discuss some terminology. The two most common forms of orbital element sets are state vectors and Keplerian orbital elements (e.g., the NORAD two-line element sets). A state vector is a collection of values (states) that if known, together with the state transformation rules (how the state vector changes over time), the state vector for any past or future time can be computed. For a satellite in Earth orbit, if we ignore atmospheric drag and maneuvering, the state vector would be comprised of the satellite's position and velocity. Knowing the position alone would not be sufficient, since a satellite with zero velocity would fall to Earth while one with orbital velocity would not, even if the satellites start at the same physical location. We cannot, however, talk about position and velocity without discussing the coordinate system that these values are measured relative to. For most state vectors, this is the Earth-Centered Inertial (ECI) coordinate system. The first part of this designation should seem fairly obvious. That is, since we're studying objects that revolve around the center of the Earth, it seems natural to have the center (origin) of our coordinate system at the center of the Earth. Inertial, in this context, simply means that the coordinate system is not accelerating (rotating). In other words, it is 'fixed' in space relative to the stars. We shall see that this is an ideal definition of the ECI coordinate system, but we won't worry about the slight rotations involved until later. The ECI coordinate system (see Figure 1) is typically defined as a Cartesian coordinate system, where the coordinates (position) are defined as the distance from the origin along the three orthogonal (mutually perpendicular) axes. The z axis runs along the Earth's rotational axis pointing North, the x axis points in the direction of the vernal equinox (more on this in a moment), and the y axis completes the right-handed orthogonal system. As seen in Figure 1, the vernal equinox is an imaginary point in space which lies along the line representing the intersection of the Earth's equatorial plane and the plane of the Earth's orbit around the Sun or the ecliptic. Another way of thinking of the x axis is that it is the line segment pointing from the center of the Earth towards the center of the Sun at the beginning of Spring, when the Sun crosses the Earth's equator moving North. The x axis, therefore, lies in both the equatorial plane and the ecliptic. These three axes defining the Earth-Centered Inertial coordinate system are 'fixed' in space and do not rotate with the Earth.",
null,
"Figure 1. Earth-Centered Inertial (ECI) Coordinate System Now, while state vectors are normally used with numerical integration models for highly accurate calculations, Keplerian orbital elements are used for the vast majority of orbital predictions. But, the ECI coordinate system is still often used as the common coordinate system when performing coordinate transformations. For example, before a calculation can be made of the distance between a satellite and an observer on the ground, both the satellite and the observer's position must be defined in a common coordinate system. Since the satellite's position is typically represented by a Keplerian orbital element set and the observer's position is given in latitude, longitude, and altitude above the Earth's surface, we cannot perform the calculation directly without first converting to a common coordinate frame. As it turns out, the NORAD SGP4 orbital model takes the standard two-line orbital element set and the time and produces an ECI position and velocity for the satellite. In particular, it puts it in an ECI frame relative to the \"true equator and mean equinox of the epoch\" of the element set. This specific distinction is necessary because the direction of the Earth's true rotation axis (the North Pole) wanders slowly over time, as does the true direction of the vernal equinox. Since observations of satellites are made by stations fixed to the Earth's surface, the elements generated will be referenced relative to the true equator. However, since the direction of vernal equinox is not tied to the Earth's surface, but rather to the Earth's orientation in space, an approximation must be made of its true direction. The approximation made in this case is to account for the precession of the vernal equinox but to ignore the nutation (nodding) of the Earth's obliquity (the angle between the equatorial plane and the ecliptic). We'll address how to use this level of detail in a future column. So, we now know that whether we're using state vectors or Keplerian orbital element sets, our calculations will likely yield ECI position and velocity. Let's begin working now to answer two common questions in satellite tracking. The first question is: Where do I look or point my antenna to acquire a particular satellite? The second question is: What is the latitude, longitude, and altitude of that satellite? These questions come up frequently, whether the goal is to watch the US Space Shuttle and Russian Mir Space Station pass overhead, to acquire an amateur radio satellite, or to determine the longitude of a geostationary TVRO satellite. But, to be able to answer these questions, we will need to determine either the position of an observer on the Earth relative to the ECI coordinate frame or the position of a satellite relative to the Earth. In either case, we will need to know the rotation angle between the Greenwich Meridian (zero degrees longitude) and the vernal equinox and, hence, the orientation of the Earth relative to the ECI coordinate frame. Let's start by calculating the position of an observer in the ECI coordinate frame. For our initial discussions, we'll assume a spherical Earth. This assumption is not a particularly good one, as we'll see in our next column, but will make the initial development easier to follow. The calculation of the z coordinate is straightforward, as can be seen in Figure 2. This figure shows a side cutaway of the Earth with North up. For an observer at latitude φ, the z coordinate is shown in Figure 2, where Re is the Earth's equatorial radius. To calculate the x and y coordinates, we will also need the value of R from Figure 2. If we wanted to calculate z and R for distances above mean sea level, we would simply replace Re with Re + h, where h is the distance above mean sea level.",
null,
"Figure 2. Latitude to ECI Conversion Computing the x and y coordinates requires a bit more work. Since the Earth rotates in the x-y plane (i.e., about the z axis), the x and y coordinates of a point on the Earth's surface will vary with time, unlike the z coordinate. However, if we know the angle between the observer's longitude and the x axis (the vernal equinox), we can specify the x and y coordinates as a function of time. In fact, if we designate the angle between the x axis and the observer's longitude as θ(τ), where τ is the time of interest, x(τ) and y(τ) are given in Figure 3. This figure shows a slice through the Earth, parallel to the equatorial plane and through the observer's location.",
null,
"Figure 3. Longitude to ECI Conversion Upon first inspection, these equations would seem straightforward enough. But just what is θ(τ) and how is it calculated? The function θ(τ) is what astronomers refer to as the local sidereal time. Sidereal time is simply time measured relative to the stars. In our day-to-day lives, we are used to measuring time relative to the position of the Sun because of its obvious position in the heavens. This time scale is referred to as mean solar time. As with any time system, time is defined as the angle between the observer and some reference direction. With mean solar time, the reference direction is the direction of the mean sun; with sidereal time, the direction is the vernal equinox—just the direction we need for our calculation. So what causes the difference between these two time scales? As seen in Figure 4, the position of the Sun moves with respect to the stars because of the Earth's orbit around it. Let's say we noted the position of the Sun relative to the stars when it crosses our meridian (longitude) on one day. By definition, that passage is called local noon. However, when that same position relative to the stars crosses our meridian on the following day, the Sun will not yet have reached our meridian. That is to say, the position will cross our meridian before local noon. The interval of time between two successive meridian crossings of a fixed position in inertial space is referred to as one sidereal day. Sidereal midnight occurs when the vernal equinox crosses the meridian. The interval of time between two successive meridian crossings of the mean sun is referred to as one mean solar day. As seen in Figure 4, the Earth must rotate a bit more for a mean solar day than for a sidereal day. In fact, a sidereal day is only 23h56m04s.09054 of mean solar time. This difference, while small, is extremely important.",
null,
"Figure 4. Sidereal versus Solar Time Now, since all of our common time measurements are based on UTC (Coordinated Universal Time) which is mean solar time, how do we calculate our local sidereal time? Well, as shown in Figure 3, the local sidereal time can be calculated by adding the observer's east longitude, λE, to the Greenwich sidereal time (GST), θg(τ). Oftentimes, GST (or more specifically, Greenwich Mean Sidereal Time or GMST), can be found in references such as the US Naval Observatory's Astronomical Almanac. If GMST is known for 0h UTC, θg(0h), on a particular date, then θg(Δτ) = θg(0h) + ωe·Δτ, where Δτ is the UTC time of interest and ωe = 7.29211510 × 10-5 radians/second is the Earth's rotation rate. Unfortunately, this approach requires a table of reference times to do the calculations. Another approach is to calculate θg(0h) using the equation from Page 50 of the Explanatory Supplement to the Astronomical Almanac: θg(0h) = 24110s.54841 + 8640184s.812866 Tu + 0s.093104 Tu2 - 6.2 × 10- 6 Tu3 where Tu = du/36525 and du is the number of days of Universal Time elapsed since JD 2451545.0 (2000 January 1, 12h UT1). While we've covered a lot of ground in this column, we obviously still have a bit more to go before we can answer the questions raised above. For our computer implementation, we will first need to develop a procedure for calculating the Julian Date in our last equation. Then, we will need to refine our conversion from latitude, longitude, and altitude to ECI coordinates to incorporate an oblate (flattened) Earth. When we make this refinement, we will also see the magnitude of error which can occur if this factor is ignored. At this point, we will have finished our first coordinate transformation and will be able to calculate the vector from the Earth observer to the satellite. We will then begin the process of developing our second coordinate transformation, that from ECI to the topocentric-horizon or azimuth-elevation coordinate system. It is this system which will allow us to measure the position of a satellite relative to the Earth's surface. We will also begin to include snippets of computer code to illustrate the theory we're developing here. If you'd like to look ahead, these routines can be found in the file sgp4-plb26a.zip on the CelesTrak WWW site. As always, if you have questions or comments on this column, feel free to send me e-mail at [email protected] or write care of Satellite Times. Until next time, keep looking up!",
null,
"TLE Data Space Data",
null,
"Current GPS\nArchives EOP\nDocumentation Space Weather\nSATCAT Columns\nBoxscore Software\nSOCRATES\nWe do not use cookies on CelesTrak and we do not collect any personal information, other than IP addresses, which are used to detect and block malicious activity and to assess system performance. We do not use IP addresses for tracking or any other purposes. No personal data is shared with third parties. For further details, see AGI's privacy policy.\n\nDr. T.S. Kelso [[email protected]]"
]
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https://briefencounters.ca/42655/fractions-and-percentages-worksheets/ | [
"# Fractions and Percentages Worksheets\n\nPosted on\n\nComparing percentages and fractions worksheets, example and lesson plans: two lesson plans (ones suitable for beginners) to compare percentages and fractions. Three differentiated asking questions on the fraction types: Fraction by numbers or percentage by quantities. The last one has a special feature in that the numbers can be printed in the small print to indicate which fractions are to be used. Fraction types on the fraction toolbar are also shown as a table, allowing you to easily see which types are applicable in your current situation. Each question has a detail explanation for the reason why it is relevant and how it can best be used. Fraction practice questions for each type are available as separate downloads from the teaching site.",
null,
"Worksheet search result by word Fractions revision worksheet year 7 from fractions and percentages worksheets , source:ftxs8.com\n\nFractions and percentage units of measure are a fundamental part of teaching and learning about fractions. Teaching resources are available for comparing fractions and teaching students how to use them in their own lives. The first two lesson plan sets, teach students how to compare fractions and percentages in units of measurement. Using a table to display the units, they can learn to make sense of the units of measure.\n\nThe second set of two lesson plans to teach students how to compare fractions by quantities. Students learn to do the same kind of thinking as they would when asked to compare two fractions. Using a table to display the units, they can see which fraction is larger and thus easier to work out. Some teachers supply charts with this lesson, but the teaching resources I found online provide graphs too.",
null,
"How to Convert Fractions Decimals and Percents Worksheets Lovely from fractions and percentages worksheets , source:roofinginhoumala.com\n\nFractions and percentage units of measure are again a fundamental part of teaching and learning about fractions. A great many resources to offer units of measurement for all the major units of measurement. Fractions units for each major unit can be compared with other units of measure in tables that are also shown on the lesson plan. This sets up the basis for further teaching on the subject.\n\nFractions may not seem like they are all that important when only taught in elementary school. In fact, many teachers do not use fraction lessons until higher education levels. That is not surprising, since higher education degrees require learning to use several different types of measurement. But anyone who has ever taught a class in elementary school knows that the usefulness of a fraction is fundamental. Teachers need to use the tools of the fraction in order to teach other subjects at a high school, college, and beyond.",
null,
"fraction sheet Erkalnathandedecker from fractions and percentages worksheets , source:erkal.jonathandedecker.com\n\nThe Fractions and Percentages Worksheet are a great teaching tool because it enables the teacher to compare a fraction with another. It can show a fraction is bigger, smaller, or more or less than another unit. Because they are so closely related, the comparison becomes almost automatic. It only takes a few seconds to compare Fractions and Percentages Worksheets side-by-side in a lesson plan, which is useful, especially when the teacher is trying to teach an entire class about fractions.\n\nFractions and Percentages worksheets enable teachers to also show how different units of measurement relate to one another. For example, by using the fraction, a teacher can show that inches are less than five-hundredths of a degree. Or, she can show that a centimeter is less than one-eighth of an inch. Using these teaching aids allows students to learn about fractions quickly and easily, which helps them develop a better understanding and memory skills when they begin high school.",
null,
"Product from fractions and percentages worksheets , source:hope-education.co.uk\n\nFractions and percentages not only make learning easier, but they also help the students understand the relationship between the fraction, its percentages, and other units of measurement. Educators can find out which types of Fractions and Percentages are most common by using teaching resources that include Fractions and Percentages worksheet packs and other lesson aids. Fractions and percentages can be a great teaching tool, as they make learning fun for students and easy for the teacher. If teachers integrate them into their lessons, they can help their students to succeed.",
null,
"Math worksheets number line decimals from fractions and percentages worksheets , source:myscres.com",
null,
"Numbers Worksheets Fractions Worksheets Fresh Fractions A Number from fractions and percentages worksheets , source:sblomberg.com",
null,
"Worksheet Decimal Fraction Percent Beautiful Fraction Decimal from fractions and percentages worksheets , source:penlocalmag.com",
null,
"Line Plots With Fractions 5Th Grade Worksheets Worksheets for all from fractions and percentages worksheets , source:bonlacfoods.com",
null,
"Worksheets by Math Crush Fractions from fractions and percentages worksheets , source:mathcrush.com",
null,
"Worksheets by Math Crush Fractions from fractions and percentages worksheets , source:mathcrush.com"
]
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null,
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"https://briefencounters.ca/wp-content/uploads/2018/11/fractions-and-percentages-worksheets-and-how-to-convert-fractions-decimals-and-percents-worksheets-lovely-of-fractions-and-percentages-worksheets.jpg",
null,
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null,
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null,
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null,
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null,
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https://pureportal.spbu.ru/en/publications/confluent-heun-equation-and-confluent-hypergeometric-equation | [
"# Confluent Heun Equation and Confluent Hypergeometric Equation\n\nS. Yu Slavyanov, A. A. Salatich\n\nResearch output: Contribution to journalArticleResearch\n\n### Abstract\n\nThe confluent Heun equation and the confluent hypergeometric equation are studied in scalar and vector forms with particular emphasis on the role of apparent singularities. A relation to the Painlevé equation is established.\n\nOriginal language English 157-163 7 Journal of Mathematical Sciences (United States) 232 2 https://doi.org/10.1007/s10958-018-3865-2 Published - 1 Jul 2018\n\n### Scopus subject areas\n\n• Statistics and Probability\n• Mathematics(all)\n• Applied Mathematics\n\n### Cite this\n\n@article{f384681edc084451900e261a71b132e2,\ntitle = \"Confluent Heun Equation and Confluent Hypergeometric Equation\",\nabstract = \"The confluent Heun equation and the confluent hypergeometric equation are studied in scalar and vector forms with particular emphasis on the role of apparent singularities. A relation to the Painlev{\\'e} equation is established.\",\nauthor = \"Slavyanov, {S. Yu} and Salatich, {A. A.}\",\nyear = \"2018\",\nmonth = \"7\",\nday = \"1\",\ndoi = \"10.1007/s10958-018-3865-2\",\nlanguage = \"English\",\nvolume = \"232\",\npages = \"157--163\",\njournal = \"Journal of Mathematical Sciences\",\nissn = \"1072-3374\",\npublisher = \"Springer\",\nnumber = \"2\",\n\n}\n\nIn: Journal of Mathematical Sciences (United States), Vol. 232, No. 2, 01.07.2018, p. 157-163.\n\nResearch output: Contribution to journalArticleResearch\n\nTY - JOUR\n\nT1 - Confluent Heun Equation and Confluent Hypergeometric Equation\n\nAU - Slavyanov, S. Yu\n\nAU - Salatich, A. A.\n\nPY - 2018/7/1\n\nY1 - 2018/7/1\n\nN2 - The confluent Heun equation and the confluent hypergeometric equation are studied in scalar and vector forms with particular emphasis on the role of apparent singularities. A relation to the Painlevé equation is established.\n\nAB - The confluent Heun equation and the confluent hypergeometric equation are studied in scalar and vector forms with particular emphasis on the role of apparent singularities. A relation to the Painlevé equation is established.\n\nUR - http://www.scopus.com/inward/record.url?scp=85047390281&partnerID=8YFLogxK\n\nU2 - 10.1007/s10958-018-3865-2\n\nDO - 10.1007/s10958-018-3865-2\n\nM3 - Article\n\nVL - 232\n\nSP - 157\n\nEP - 163\n\nJO - Journal of Mathematical Sciences\n\nJF - Journal of Mathematical Sciences\n\nSN - 1072-3374\n\nIS - 2\n\nER -"
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https://stocksbeat.com/which-pair-of-financial-statements-show-depreciation-expense/ | [
"8.8 C\nNew York\nTuesday, February 7, 2023\nMore\n\n# Which Pair of Financial Statements Show Depreciation Expense?\n\nDepreciation expense is a key component of a company’s financial statements, as it reflects the gradual wear and tear of a company’s fixed assets over time. There are two main financial statements that show depreciation expense: the balance sheet and the income statement.\n\nThe balance sheet is a snapshot of a company’s financial position at a specific point in time. It lists the company’s assets, liabilities, and equity. Depreciation expense is shown on the balance sheet as a reduction in the value of a company’s fixed assets. This is done through the process of depreciation, which is the allocation of the cost of a fixed asset over its useful life.",
null,
"The income statement, also known as the profit and loss statement, shows a company’s revenues, expenses, and net income over a specific period of time. Depreciation expense is shown on the income statement as a reduction in the value of a company’s fixed assets. This is done through the process of depreciation, which is the allocation of the cost of a fixed asset over its useful life.\n\n## How Depreciation Expense is Calculated\n\nThere are several methods that can be used to calculate depreciation expense, including the straight-line method, the declining balance method, and the sum-of-the-years’-digits method. The choice of method depends on the nature of the asset and the company’s accounting policies.\n\nThe straight-line method is the most commonly used method for calculating depreciation expense. It involves dividing the cost of the asset by its useful life to determine the annual depreciation expense. For example, if a company buys a machine for \\$100,000 and estimates its useful life to be 10 years, the annual depreciation expense would be \\$10,000.",
null,
"The declining balance method involves calculating the depreciation expense for an asset at a higher rate in the earlier years of its useful life and a lower rate in the later years. The sum-of-the-years’-digits method involves calculating the depreciation expense for an asset based on the fraction of its useful life that has passed.\n\nConclusion:\n\nIn conclusion, depreciation expense is an important component of a company’s financial statements, as it reflects the gradual wear and tear of a company’s fixed assets over time. The two main financial statements that show depreciation expense are the balance sheet and the income statement. There are several methods that can be used to calculate depreciation expense, including the straight-line method, the declining balance method, and the sum-of-the-years’-digits method.\n\n### Stay in touch\n\nTo be updated with all the latest news, offers and special announcements."
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https://maths.olympiadsuccess.com/class-3-numerals | [
"Alert: You are not allowed to copy content or view source\nIMO Result Declared Check here | IMO Level 2 Exam Timing & Guidelines Check here | Register for Maths, Science, English, GK Olympiad Exam Click here | Check Olympiad Exam Dates here | Buy Practice Papers for IMO, IOM, HEO, IOEL etc here | Login here to participate in all India free mock test on every Saturday\n\n# Numerals",
null,
"What are numerals? We all come across various kinds of values which include numbers, characters, alphabets, symbols etc. But here we will specially learn about those magical figures called numbers which is the base of Mathematics and have made this subject so much interesting. Let’s find out.\n\n• Any figure or symbol representing a number is a numeral.\n• The numbers from 0 to 9 when combined and written in a specific order creates a numeral.\n• The numeral can be single digit like 5 or 2 digits like 12 or 3 digits like 564 and 4 digits like 5854.\n\nThere are two Types of numerals which we should learn\n\n• The western Arabic numerals\n\nExample is 0,1,2,3,4,5,6,7,8,9\n\n• The Roman Numerals",
null,
"Western Arabic Numerals\n\nThe numbers from 0-9 are the base of the western Arabic numerals and then their combinations which results in the formation of more numbers also come under this category.\n\n• The numbers 0 – 9 are called as digit.\n• The numbers created by their combination is numeral.\n\nWe all know two and three digit numbers and how to read and write them so here we are going to learn about the four digit numbers and how to read and write them.\n\nFour Digit Numbers\n\nThe numeral containing four digits is called as a four digit number. For example 4586 is a four digit number.\n\n• To identify the numbers, count the digits and hence you can predict if it is a four digit number or any other number.\n\nPlace Values\n\nIn our number system the value of a digit completely depends on its position and that position helps us to write the expanded form of that number and hence helps in identifying the number.\n\n• Each and every number has a place value.\n• We start assigning the place values from right to left.\n• The place values starts from Ones then Tens, Hundreds, Thousands, Ten Thousands,\n\nExample 1: Determine the place values of the number 24 and write its expanded form.\n\nSolution: We will start from right most digit and then we will go to left.\n\nHere, the right most digit is 4, hence its place value is One.\n\nNext is 2 and hence its place value is Tens.\n\nTherefore we can write the number as\n\n24 = (2 x 10) + (4 x 1) = Twenty + Four = Twenty four.\n\nHence the expanded form is Twenty Four.\n\nExample 2: Determine the place values of the number 789 and write its expanded form.\n\nSolution: Here the right most digit is 9 so its place value is Ones.\n\nNext is 8 so its place value is Tens.\n\nNext is 7 so its place value is Hundreds.\n\nTherefor we can write the number as\n\n789 = (7 x 100) + (8 x 10) + (9 x 1) = 700 + 80 + 9\n\nWhich will be Seven Hundred + Eighty + Nine which makes it Seven hundred eighty nine.\n\nLet us learn how to write these four digits numbers:\n\nLet’ s take any 4 digit number for example we will take 1234.\n\nNow here we know that 4 is called at ones place and 3 is at tens, 2 is at hundreds and 1 is at thousands.\n\nSo the number 1234 can be written as\n\n1234 = (1 x 1000) + (2 x 100) + (3 x 10) + (4 x 1)\n\n= One thousand + Two hundred + Thirty + Four\n\nHence the number is One thousand two hundred thirty four.\n\n• The smallest 4 digit number is 1000 = One thousand\n• The Largest 4 digit number is 9999 = Nine thousand nine hundred ninety nine.",
null,
"Roman Numerals\n\nThe numbers from 0 – 9 and also their magical combinations can also represented using certain alphabets and this representation is called Roman Numerals.\n\nLet us learn how to write and read roman Numerals from this table:",
null,
"Here we have to learn the representations of the numbers and then we can write the roman numerals also.\n\nExample 3: Write 23 in Roman numeral form.\n\nSolution: Now in 23, 3 is at ones place and 2 is at tens place.\n\nSo, 23 = (2 x 10) + (3 x 1) = 20 + 3 = XXIII\n\nFrom here we learnt that we can write the roman form of any number if we know the place values and roman forms of initial numbers.\n\nExample 4: Write the roman form of 2356.\n\nSolution: Here 6 is at ones place, 5 is at tens, 3 is at hundreds, 2 is at thousands.\n\n2356 = (2 x 1000) + (2 x 100) + (5 x 10) + (6 x 1)\n\n= Two thousand + two hundred + fifty + six = MMCCLVI\n\nIsn’t it interesting to find roman numbers and place values so let’s practice a few more questions.",
null,
"Practice Questions\n\nQ1) Count the number of 4 digit numbers among the following:\n\n784, 45, 1235, 6547, 7895, 564, 1254, 56879, 45641, 454, 6985.\n\nQ2) Write the expanded form of following numbers:\n\n1. 124\n2. 1654\n3. 7100\n4. 1100\n5. 78\n\nQ3) Find the place values of the following numbers:\n\n1. 456\n2. 523\n3. 1569\n4. 2307\n\nQ4) Write the roman representation of the following numbers:\n\n1. 145\n2. 325\n3. 894\n4. 1006\n5. 4589\n\nQ5) State True or False:\n\n1. Every digit has a place value.\n2. We start from left most digit while assigning the place values\n3. Hundreds then tens then ones.\n4. 10000 is a 4 digit number\n5. Largest 3 digit number is 999.\n\nRecap\n\n• Any figure representing a number is a numeral.\n• While assigning the place values we start from right to left.\n• First comes ones then tens, then hundreds, then thousands.\n• By counting the digits we can predict whether the number is two or three for digit number.\n• In roman numerals the numbers are just represented using the alphabets.\n• The numbers from 0 to 9 are called western Arabic numerals.\n\n## Quiz for Numerals\n\n Q.1 Fill in the blank. 445, 452, 459, ______, 473. a) 445 b) 480 c) 460 d) 466\n Q.2 In 7,86,452 which number is present in hundreds place? a) 4 b) 5 c) 6 d) 7\n Q.3 In 45,782 which number is present in thousands place? a) 4 b) 5 c) 7 d) 8\n Q.4 Which number has 8 in its hundreds place? a) 6,008 b) 46,782 c) 3,65,888 d) 8,88, 567\n Q.5 Find the greatest number we can make using digits 3, 2, 6 and 7. a) 7263 b) 6723 c) 7362 d) 7632\n Q.6 Find the lowest number we can make using the digits 4, 5, 2 and 8. a) 2548 b) 2458 c) 2854 d) 2845\n Q.7 Find the greatest number we can make using digits 9 and 7. (Each number is allowed to be repeated maximum twice) a) 797 b) 977 c) 997 d) 979\n Q.8 Find the lowest number we can make using digits 4 and 5. (Each number is allowed to be repeated maximum twice) a) 545 b) 544 c) 454 d) 445\n Q.9 In morning a man noticed he has 789 messages in his phone. At the end of the day he noticed he has 1008 messages. How many new messages he has received in that day? a) 199 b) 219 c) 329 d) 209\n Q.10 In a farm there are 7000 hens, the owner brings 2567 new hens. Total how many hens are there now? a) 9567 b) 7567 c) 10567 d) 2567"
]
| [
null,
"https://maths.olympiadsuccess.com/assets/images/maths_square/maths_topic_118.jpg",
null,
"https://maths.olympiadsuccess.com/assets/images/maths_square/M03NUM01.jpg",
null,
"https://maths.olympiadsuccess.com/assets/images/maths_square/M03NUM02.jpg",
null,
"https://maths.olympiadsuccess.com/assets/images/maths_square/M03NUM03.jpg",
null,
"https://maths.olympiadsuccess.com/assets/images/maths_square/M03NUM04.jpg",
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]
| {"ft_lang_label":"__label__en","ft_lang_prob":0.86058176,"math_prob":0.99586236,"size":5099,"snap":"2019-51-2020-05","text_gpt3_token_len":1337,"char_repetition_ratio":0.17291462,"word_repetition_ratio":0.07185629,"special_character_ratio":0.29182193,"punctuation_ratio":0.09770115,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9962625,"pos_list":[0,1,2,3,4,5,6,7,8,9,10],"im_url_duplicate_count":[null,3,null,5,null,5,null,5,null,5,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-01-17T23:05:32Z\",\"WARC-Record-ID\":\"<urn:uuid:45fdad8b-d7d9-4f84-9c52-92c68f173c5d>\",\"Content-Length\":\"142506\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d2b25475-d040-4e3b-b120-1e2f25a4ad55>\",\"WARC-Concurrent-To\":\"<urn:uuid:0a1759bd-42e3-4d6d-90f5-ab16f5a7bcb7>\",\"WARC-IP-Address\":\"104.26.11.203\",\"WARC-Target-URI\":\"https://maths.olympiadsuccess.com/class-3-numerals\",\"WARC-Payload-Digest\":\"sha1:DV2FIVOQIMCXPBA6IVFL4XWVVYDHEAAP\",\"WARC-Block-Digest\":\"sha1:UKDMLSO4F3KP5C7URSWRQO2VX6T4X2CB\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-05/CC-MAIN-2020-05_segments_1579250591234.15_warc_CC-MAIN-20200117205732-20200117233732-00541.warc.gz\"}"} |
https://stackoverflow.com/questions/53527844/liquid-haskell-error-with-proof-combinators-and-types-refined-by-predicates/53562300 | [
"# Liquid Haskell: Error with Proof Combinators and Types Refined by Predicates\n\nAs a minimal example of the problem I'm having, here's a definition of natural numbers, a doubling function, and a type refined by an even-ness predicate:\n\n``````data Nat' = Z | S Nat' deriving Show\n\n{-@ reflect double' @-}\ndouble' :: Nat' -> Nat'\ndouble' Z = Z\ndouble' (S x) = (S (S (double' x)))\n\n{-@ type Even' = {v:Nat' | even' v} @-}\n\n{-@ reflect even' @-}\neven' :: Nat' -> Bool\neven' Z = True\neven' (S Z) = False\neven' (S (S x)) = even' x\n``````\n\nI'd like to first declare `{-@ double' :: Nat' -> Even' @-}` and then prove this to be true, but I'm under the impression that I instead must first write the proof and then use `castWithTheorem` (which itself has worked for me) as such:\n\n``````{-@ even_double :: x:Nat' -> {even' (double' x)} @-}\neven_double Z = even' (double' Z)\n==. even' Z\n==. True\n*** QED\neven_double (S x) = even' (double' (S x))\n==. even' (S (S (double' x)))\n==. even' (double' x)\n? even_double x\n==. True\n*** QED\n\n{-@ double :: Nat' -> Even' @-}\ndouble x = castWithTheorem (even_double x) (double' x)\n``````\n\nHowever, this gives fairly illegible errors like:\n\n``````:1:1-1:1: Error\nelaborate solver elabBE 177 \"lq_anf\\$##7205759403792806976##d3tK\" {lq_tmp\\$x##1556 : (GHC.Types.\\$126\\$\\$126\\$ (GHC.Prim.TYPE GHC.Types.LiftedRep) (GHC.Prim.TYPE GHC.Types.LiftedRep) bool bool) | [(lq_tmp\\$x##1556 = GHC.Types.Eq#)]} failed on:\nlq_tmp\\$x##1556 == GHC.Types.Eq#\nwith error\nCannot unify (GHC.Types.\\$126\\$\\$126\\$ (GHC.Prim.TYPE GHC.Types.LiftedRep) (GHC.Prim.TYPE GHC.Types.LiftedRep) bool bool) with func(0 , [(GHC.Prim.\\$126\\$\\$35\\$ @(42) @(43) @(44) @(45));\n(GHC.Types.\\$126\\$\\$126\\$ @(42) @(43) @(44) @(45))]) in expression: lq_tmp\\$x##1556 == GHC.Types.Eq#\nbecause\nElaborate fails on lq_tmp\\$x##1556 == GHC.Types.Eq#\nin environment\nGHC.Types.Eq# := func(4 , [(GHC.Prim.\\$126\\$\\$35\\$ @(0) @(1) @(2) @(3));\n(GHC.Types.\\$126\\$\\$126\\$ @(0) @(1) @(2) @(3))])\n\nlq_tmp\\$x##1556 := (GHC.Types.\\$126\\$\\$126\\$ (GHC.Prim.TYPE GHC.Types.LiftedRep) (GHC.Prim.TYPE GHC.Types.LiftedRep) bool bool)\n``````\n\nWhat am I doing wrong? From my experiments, it seems to be caused by trying to prove that some predicate function is true of some argument.\n\n## 1 Answer\n\nThe issue was that I should have been using `NewProofCombinators` instead of `ProofCombinators`. Then replacing `==.` with `===` and `castWithTheorem (even_double x) (double' x)` with `(double' x) `withProof` (even_double x)` fixes the problem: http://goto.ucsd.edu:8090/index.html#?demo=permalink%2F1543595949_5844.hs\n\nAll the online resources I've found use `ProofCombinators` so hopefully this saves someone some pain."
]
| [
null
]
| {"ft_lang_label":"__label__en","ft_lang_prob":0.7211718,"math_prob":0.83609796,"size":2069,"snap":"2021-04-2021-17","text_gpt3_token_len":721,"char_repetition_ratio":0.17627119,"word_repetition_ratio":0.035369776,"special_character_ratio":0.40985984,"punctuation_ratio":0.20930232,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98811847,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-04-11T07:36:30Z\",\"WARC-Record-ID\":\"<urn:uuid:ba2ea0fe-5a13-4a71-ba38-b264b7f3063d>\",\"Content-Length\":\"162821\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:dd33a347-e6db-4747-8295-2533faf49a52>\",\"WARC-Concurrent-To\":\"<urn:uuid:255e0d82-c149-40b5-a754-ab4c1aabc33f>\",\"WARC-IP-Address\":\"151.101.193.69\",\"WARC-Target-URI\":\"https://stackoverflow.com/questions/53527844/liquid-haskell-error-with-proof-combinators-and-types-refined-by-predicates/53562300\",\"WARC-Payload-Digest\":\"sha1:E4JDBSLHJKJF7PHMJQQIJSKTMEVFFO5L\",\"WARC-Block-Digest\":\"sha1:LQK27ONBS6EMTYLMF6IHSIHJM44LHHP4\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-17/CC-MAIN-2021-17_segments_1618038061562.11_warc_CC-MAIN-20210411055903-20210411085903-00419.warc.gz\"}"} |
http://www.physicsmynd.com/?page_id=580 | [
"IIT JEE Physics Mechanics : 2005 -2010 Questions & Answers\n\nIn this festive season of crackers and sparklers , let us get a crack at the previous mechanics questions asked in the IIT JEE Physics paper during the last 5 years. It’s also a sneak preview of the kind of mechanics questions you can expect in the upcoming exam. We begin with questions asked in this year and the portions covered are up to Simple Harmonic Motion. In the second part of this post, the answers will be given.\n\nIIT JEE Advanced & Mains Physics 2018 : Mechanics : Rank file / expected questions / Physicsmynd Elite Series\n\nP U B L I S H I N G S O O N\n\nA block of mass m is on an inclined plane of angle θ. The coefficient of friction between the plane and the block is μ and tanθ > μ. The block is held stationary by applying a force P parallel to the plane. The direction of force pointing up the plane is taken to be positive. As P is varied from P1 = mg( sinθ – μcosθ ) to P2 = mg( sinθ+ μcosθ ), the frictional force f versus P graph will look like –",
null,
"A thin uniform annular disc ( see figure ) of mass M has outer radius 4R and inner radius 3R . The work required to take a unit mass from point P on its axis to infinity is",
null,
"• (a) 2GM/7g ( 4√2 – 5 ) (b) 2GM/7g ( 4√2 – 5 (c) GM/4R (d) 2GM/5R ( √2 – 1 )\n\nA point mass of 1 kg collides elastically with a stationary point mass of 5 kg.After their collision , the 1 kg mass reverses its direction and moves with a speed of 2 m/s. Which of the following statement(s) is (are) correct for the system of these two masses ?\n\n1. (a) Total momentum of the system is 3 kgm/s\n2. (b) Momentum of 5 kg mass after collision is 4 kg m/s.\n3. (c) Kinetic energy of the centre of mass is 0.75 J\n4. (d) Total kinetic energy of the system is 4 J.\n\nA student uses a simple pendulum of exactly 1 m length to determine g, the acceleration due to gravity. He uses a stop watch with the least count of 1 sec for this and records 40 seconds for 20 oscillations. For this observation, which of the following statement(s) is (are) true ?\n\n1. (a) Error ΔT in measuring T . the time period , is 0.05 seconds .\n2. (b) Error ΔT in measuring T , the time period , is 1 second.\n3. (c) Percentage error in the determination of g is 5 %.\n4. (d) Perecntage error in the determination of g is 2.5 %.\n• Paragraph basedWhen a particle of mass m moves on the x -axis in a potential of thev form F(x) – kx² it performs SHM. The corresponding time period is proportional to √ m/k ,as can be easily during dimensional analysis.However, the motion of a particle can be periodic even when its potential energy increases on both sides of x = 0 in a way different from kx² and its total energy is such that the particle does not escape to infinity. Consider a particle of mass m moving on the x – axis.Its potential energy is F(x) = αx4 ( α > o) for |x| near the origin and becomes a constant equal to V0 for |x| ≥ Xo ( see figure )",
null,
"If the total energy of the particle is E , it will perform periodic motion only if –\n\n• (a) E < o (b) E > o (c) Vo > E > o (d) E > Vo\n\nFor periodic motion of small amplitude A, the time period T of this particle is proportional to\n\n• (a) A√m/α (b) 1/A √m/α (c) A√α/m (d) A√\n\nThe acceleration of this particle for |x| > Xo is\n\n1. (a) proportional to Vo\n2. (b) proportional to Vo/mXo\n3. (c) proportional to √Vo/mXo\n4. (d) zero\n\nGravitational acceleration on the surface of a planet is √6/11 g, where g is the gravitational acceleration on the surface of the earth.The average mass density of the planet is 2/3 times thet of the earth. If the escape speed on the surface of the earth is taken to be 11 km/s , the escape speed on the surface of the planet in km/s will be\n\nA 0.1 kg mass is suspended from a wire of negligible mass . The length of the wire is 1m and its cross sectional area is 4.9 x 10-7 m².If the mass is pulled by a little in the vertically downward direction and released , it performs SHM of angular frequency 140 rad /s.If the Young’s modulus of the material of the wire is η x 109 Nm², the value of η is\n\nA binary star consists of two stars A ( mass =2.2Ms) and B ( mass = 11Ms), where Ms is the mass of the sun.They are separated by distance d and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binary star to the angular momentum of star B about the centre of mass is-\n\nA block of mass 2 kg is free to move along the x – axis. It is at rest and from t = 0 onwards it is subjected to a time dependent force F(t) in the x direction.The force F(t) varies witht as shown in the figure. The kinetic energy of the block after 4.5 seconds is-",
null,
"1 ) The given graph shows the variation of velocity with displacement. W hich one of the graph below correctly represents the variation of acceleration with displacement. ( IIT JEE 2005 2M )",
null,
"",
null,
"• 2) Assertion and Reason – Mark your answer as (a) If statement I is true , statement II is true and statement II is the correct explanation of Statement I (b) If statement I is true , statement II is true , but statement II is not a correct explanation of statement I. (c) If statement I is true, statement II is false , (d) If statement I is false , statement II is true.\n• Statement I : For an observer looking out through the window of a fast moving train , the nearby objects appear to move in the opposite direction to the train , while the distant objects appear to be stationary. ( IIT JEE 2008 3M )\n• Statement II : If the observer and the object are moving at velocities | v1 | and |v2| respectively , with reference to a laboratory frame , the velocity of the object with respect to the observer is |v2| – |v1| .\n• Statement I : A cloth covers a table. Some dishes are kept on it . The cloth can be pulled out without dislodging the dishes from the table.(IIT JEE 2007 3M )\n• Statement II : For every action there is an equal and opposite reaction.\n• Statement I : It is easier to pull a heavy object than to push it on a level ground. ( IIT JEE 2008 3M )\n• Statement II: The magnitude of frictional force depends on the nature of the two surfaces in contact.\n\nSystem shown in figure is in equilibrium and at rest.The spring and string are massless , now the string is cut.The acceleration of mass 2m and m , just after string is cut will be.. ( IIT JEE 2006 3M )",
null,
"1. (a) g/2 upwards , g downwards\n2. (b) g upwards , g/2 downwards.\n3. (c) g upwards , 2g downwards.\n4. (d) 2g upwards , g downwards.\n\nTwo particles of mass m each are tied at the ends of a light string of length 2a. The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance a from the centre P . Now ,the midpoint of the string is pulled vertically upwards with a small but constant force F. As a result , the particles move towards each other on the surface. The magnitude of acceleration , when the separation between them becomes 2 x , is ( IIT JEE 2007 3 M )",
null,
"Two identical ladders are arranged as shown in the figure. Mass of each ladder is M and length L . The system is in equilibrium. Find direction and magnitude of frictional force acting at A or B . ( IIT JEE 2005 3 M )",
null,
"A circular disc with a groove along its diameter is placed horizontally . A block of mass 1 kg is placed as shown.The coefficient of friction between the block and all surfaces of groove in contact is μ = 2/5 .The disc has an acceleration of 25 m/s². Find the acceleration of the block with respect to disc. ( IIT JEE 2006 6 M )",
null,
"A bob of mass M is suspended by a massless string of length L . The horizontal velocity v at position A is just sufficient to make it reach the point B . The angle θ at which the speed of the bob is half of that at A , satisfies – ( IIT JEE 2008 3M )",
null,
"1. (a) θ = π / 4\n2. (b) π/4 < θ < π /2\n3. (c) π/2 < θ < 3π/4\n4. (d) 3π/4 <θ < π\n\nA Block B is atteched to two unstreched springs S1 and S2 with spring constants k and 4k respectively.The other ends are attached to two supports M1 and M2 , not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere.The block B is displaced towards wall 1 by a small distance x and released. The block returns and moves a maximum distance y towards wall 2 . Displacements x and y are measured with respect to the equilibrium position of the block B. The ratio y/x is ( IIT JEE 2008 3M)",
null,
"• Statement I : A block of mass m starts moving on a rough horizontal surface with a velocity v .It stops due to friction between the block and the surface after moving through a certain distance. The surface is now tilted to an angle of 30° with the horizontal and the same block is made to go up on the surface with the same intial velocity v . The decrease in the mechanical energy in the second situation is smaller that that in the first situation. ( IIT JEE 2007 3M )\n• Statement II : The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination.\n• Statement I : In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision. ( IIT JEE 2007 3M )\n• Statement II: In an elastic collision , the linear momentum of the system is conserved.\n\nPassage based problemA small block of mass M moves on a frictionless surface of an inclined plane. The angle of the incline suddenly changes from 60º to 30º at point B. The block is initially at rest at A. Assume that collisions between the block and the incline are totally inelastic ( g = 10 m/s² ) ( IIT JEE 2008 4M each )",
null,
"1] The speed of the block at point B immediately after it strikes the second incline is –\n\n(a) √60m/s (b) √45 m/s (c) √30 m/s (d) √15 m/s .\n\n2] The speed of the block at point C , immediately before it leaves the second incline is –\n\n(a) √120 m/s (b) √105 m/s (c) √90 m/s (d) √75 m/s .\n\n3] If collision between the block and the incline is completely elastic , then the vertical ( upward ) component of the velocity of the block at point B , immediately after itb strikes the second incline is\n\n(a) √30 m/s (b) √15 m/s (c) zero (d) -√ 15 m/s .\n\nThere is a rectangular plate of mass M kg of dimensions ( a xb ) . The plate is held in horizontal position by striking n small balls uniformily each of mass m per unit area per unit time. These are striking in the shaded half region of the plate. The balls are colliding elastically with velocity v . What is v ? [ n = 100, M =3kg, m = 0.01 kg, b= 2m, a=1m, g=10 m/s² ] ( IIT JEE 2006 6M )",
null,
"A particle moves in a circular path with decreasing speed . Choose the correct statement – ( IIT JEE 2005 )\n\n1. (a) Angular momentum remains constant.\n2. (b) Acceleration is towards the centre.\n3. (c) Particle moves in a spiral path with decreasing radius.\n4. (d) The direction of angular momentum remains constant.\n\nFrom a circular disc of radius R and mass 9M , a small disc of radius R/3 is removed from the disc.The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through O is ( IIT JEE 2005 )",
null,
"(a) 4 MR² (b) 40/9 MR² (c) 10 MR² (d) 37/9 MR²\n\nA solid sphere of radius R has moment of inertia I about it’s geometrical axis. It is melted into a disc of radius r and thickness t. If it’s moment of inertia about the tangential axis ( which is perpendicular to plane of the disc ), is also equal to I , then the value of r is equal to-( IIT JEE 2006 3M)",
null,
"(a) 2/√15 R (b) 2/√5 R (c) 3/√15 R (d) √3 /√15 R\n\nA ball moves over a fixed track as shown in the figure.From A to B the ball rolls without slipping.If surface BC is frictionless and Ka , Kb, and Kc are kinetic energies of the ball at A,B and C respectively, then – ( IIT JEE 2006 5M)",
null,
"1. (a) ha > hc ; Kb > Kc\n2. (b) ha > hc : Kc > Ka\n3. (c) ha = hc ; Kb = Kc\n4. (d) ha < hc ; Kb > Kc\n\nA small object with uniform density rolls up a curved surface with an initial velocity v.It reaches up to a maximum height of 3v²/4g with respect to the initial position.The object is- ( IIT JEE 2007 3M)",
null,
"(a) ring (b) solid sphere (c) hollow sphere (d) disc.\n\n• Statement I : Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the inclined plane first. ( IIT JEE 2008 3M )\n• Statement II : By the principle of conservation of energy , the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline.\n\nPassage basedTwo discs A and B are mounted coaxially on a vertical axle. The discs have moment of inertia I and 2I respectively about the common axis. Disc A is imparted an initial angular velocity 2 ω using the entire potential energy of a spring compressed by a distance x1. Disc B is imparted an angular velocity ω by a spring having the same spring constant and compressed by a distance x2. Both the discs rotate in the clockwise direction. ( IIT JEE 2007 4M each )\n\n1.The ratio x1/x2 is\n\n(a) 2 (b) 1/2 (c) √2 (d) 1/√2\n\n2.When disc B is brought in contact with disc A, they aquire a common angular velocity in time t. The average frictional torque on one disc by the other during this period is\n\n(a) 2Iω/3t (b) 9Iω/2t (c) 9Iω/4t (d) 3Iω/2t\n\n3.The loss of kinetic energy during the above process is\n\n(a) Iω²/2 (b) Iω²/3 (c) Iω²/4 (d) Iω²/6\n\nPassage basedA uniform thin cylindrical disk of mass M and radius R is attached to two identical massless springs of spring constant k which are fixed to the wall as shown in the figure.The springs are attached to the axle of the of the disk diammetrically on either side at a distance d from its centre. The axle is massless and both the springs and the axle are in a horizontal plane.The unstretched length of each spring is L. The disk is initially at its equilibrium position with its centre of mass ( CM ) at a distance L from the wall. The disk rolls without slipping with velocity |vo| = |voiˆ|. The coefficient of friction is μ. ( IIT JEE 2008 4M each )",
null,
"1.The net external force acting on the disk when its centre of mass is at displacement x with respect to its equilibrium position is\n\n(a) -kx (b) -2kx (c) -2kx/3 (d) -4kx/3\n\n2.The centre of mass of the disk undergoes simple harmonic motion with angular frequency ω equal to\n\n(a) √k/M (b) √2k/M (c) √2k/3M (d) √4k/3M\n\n3.The maximum value of v0 for which the disc will roll without slipping is\n\n(a) μg√M/k (b) μg√M/2k (c) μg√3M/k (d) μg √5M/2k\n\nA solid sphere is in pure rolling motion on an inclined surface having inclination θ ( IIT JEE 2006 2 M )\n\n1. (a) frictional force acting on the sphere is f = μmg cos θ\n2. (b) f is dissipative force\n3. (c) friction will increase its angular velocity and decrease its linear velocity.\n4. (d) if θ decreases , friction will decrease.\n\nA rod of length L and mass M is hinged at point O. A small bullet of mass m hits the rod as shown in the figure.The bullet gets embedded in the rod.Find the angular velocity of the system just after impact. ( IIT JEE 2005 2M ).\n\nA solid cylinder rolls without slipping on an inclined plane inclined at an angle θ . Find the linear acceleration of the cylinder.Mass of the cylinder is M. ( IIT JEE 2005 4 M )\n\nA double star system consists of two stars A and B which have time periods Ta and Tb, radius Ra and Rb and mass Ma and Mb. Choose the correct option. ( IIT JEE 2006 3M )\n\n1. (a) If Ta > Tb, then Ra > Rb.\n2. (b) If Ta > Tb, then Ma >Mb.\n3. (c) [ Ta/Tb]² = [ Ra/Rb]².\n4. (d) Ta = Tb.\n\nA spherically symmentric gravitational system of particles has a mass density ρ = { ρo for r ≤ R , o for r > R. where ρo is a constant. A test mass can undergo circular motion under the influence of the gravitational feild particles.Its speed v as a function of distance r from the centre of the system is represented by– ( IIT JEE 2008 3M )",
null,
"• Statement I : An astronaut in an orbiting space station above the earth experiences weightlessness. ( IIT JEE 2008 3M )\n• Statement IIAn object moving around the earth under the influence of earth’s gravitational force is in a state of ‘ free-fall ‘.\n\nA simple pendulum has time period T1 . The point of suspension is now moved upward according to the relation y = kt², ( y= 1 m/s² ) where y is the vertical displacement. The time period now becomes T2. The ratio of T1²/T2² is- ( IIT JEE 2005 2M )\n\n(a) 6/5 (b) 5/6 (c) 1 (d) 4/5\n\nA mass m is undergoing SHM in the verical direction about the mean position y0 with amplitude A and angular frequency ω. At a distance y from the mean position , the mass detaches from the spring. Assume thet the spring contracts and does not obstruct the motion of m. Find the distance y ( measured from the mean position ) such that the height h attained by the block is maximum. ( Aω ² > g ) (IIT JEE 2005 )",
null,
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https://www.tutoringhour.com/worksheets/integers/subtraction-number-line/ | [
"# Subtracting Integers on a Number Line Worksheets\n\nDive into our printable worksheets for subtracting integers on a number line to rack up practice in finding the difference between positive and negative integers. Remind students that while they subtract integers having opposite signs in these pdfs, they should subtract the smaller number from the larger number and use the sign of the latter. Although there are no sticking points while subtracting +ve integers, kids must write the sum with a (-) sign when subtracting -ve integers. Our free practice tools are equipped with answer keys to keep track of how many answers they get right.\n\nThese pdf worksheets are suitable for students in 6th grade and 7th grade.\n\nCCSS: 6.NS\n\nYou are here: Pre-Algebra >> Integers >> Subtraction >> Number Line"
]
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http://umj-old.imath.kiev.ua/article/?lang=en&article=9688 | [
"2019\nТом 71\n№ 11\n\n# On primarily factorable groups\n\nGогсhаkоv Y. M.\n\nAbstract\n\nIn the present paper the author solves the question of the structure of groups with complemented $p$-subgroups (a subgroup $\\mathfrak{U}$ of a group $\\mathfrak{G}$ is said to be complemented in $\\mathfrak{G}$ if there exists in $\\mathfrak{G}$ such a subgroup $\\mathfrak{B}$ that $\\mathfrak{UB} = \\mathfrak{G}$ and $\\mathfrak{U} \\bigcap \\mathfrak{B} = 1$ which was suggested to the author by S. N. Chernikov. If the group is periodical, the necessary and sufficient conditions are given for the p-subgroups of the group to be complemented in it. It is also shown that in general not every subgroup of a periodical group is complemented if all its $p$-subgroups are complemented.\n\nCitation Example: Gогсhаkоv Y. M. On primarily factorable groups // Ukr. Mat. Zh. - 1962. - 14, № 1. - pp. 3-9.\n\nFull text"
]
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.8836966,"math_prob":0.99530333,"size":788,"snap":"2021-04-2021-17","text_gpt3_token_len":240,"char_repetition_ratio":0.20408164,"word_repetition_ratio":0.0,"special_character_ratio":0.26649746,"punctuation_ratio":0.11333334,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9965877,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-01-23T14:18:08Z\",\"WARC-Record-ID\":\"<urn:uuid:f0ea53f4-67b0-4611-a4c4-9284d3372f4a>\",\"Content-Length\":\"20353\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7c9c57f2-fb52-4cef-98b0-30c8e6dcdb78>\",\"WARC-Concurrent-To\":\"<urn:uuid:ddf4db89-7a17-4d29-9986-b625e6259bb7>\",\"WARC-IP-Address\":\"194.44.31.54\",\"WARC-Target-URI\":\"http://umj-old.imath.kiev.ua/article/?lang=en&article=9688\",\"WARC-Payload-Digest\":\"sha1:NNO5F56JO54JRTOZLW64X333YESGGJV4\",\"WARC-Block-Digest\":\"sha1:PQ44VRYN55BIJIH52IR76WX32WKFUCGA\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-04/CC-MAIN-2021-04_segments_1610703538082.57_warc_CC-MAIN-20210123125715-20210123155715-00324.warc.gz\"}"} |
https://cs.stackexchange.com/questions/39622/designing-a-dfa-and-the-reverse-of-it | [
"# Designing a DFA and the reverse of it\n\nThere is a theorem that says if a language is regular, its reverse is regular as well. How can I draw a DFA that shows if a language is regular, it's regular as well?\n\n• I'm assuming by reverse, you mean its complement. Just change every accepting state in a DFA to rejecting, and every rejecting to accepting. – Daniil Agashiyev Feb 21 '15 at 17:02\n• What do you mean by a DFA which does all the things itself? – babou Feb 22 '15 at 10:49\n\n$$L^R$$ is the reverse of the language $$L$$ and for designing $$L^R$$ you must:"
]
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https://wtmaths.com/ratios.html | [
"Ratios\n\n## Ratios\n\nA ratio describes the relationship between parts of an amount.\n\nIf a sum of money - £100 - is split into two sums of £30 and £70, then the sum has been split into a ratio of 30:70. Note that in describing the ratio, there is a colon : between the two amounts, and that the order of the numbers is important.\n\nThe ratio can also be shown as a part: whole. The sum of the money can be shown as 30:100 which is showing the irst amount as a ratio to the whole amount.\n\nRatios can be simplified. The ratio 30:70 is simplified by dividing both sides by 10; a ratio of 30:70 is the same as a ratio of 3:7. Ratios are fully simplified when both numbers are integers, and have been reduced in value as much as possible.\n\n## Example 1\n\nA bag contains 40 red and blue balls. there are 10 red balls. What is the ratio of red to blue balls?\n\nThe number of blue balls is 40 - 10 = 30.\n\nTherefore there are 10 red balls and 30 blue balls, or 10:30.\n\nThis simplifies to 1:3. Note that the order of numbers is important."
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https://physics.stackexchange.com/questions/503627/what-physical-interpretation-can-we-derive-from-this-experimental-step-up | [
"# What physical interpretation can we derive from this experimental step up?",
null,
"(This is not a homework question!) An experimental set up shows 2 rigidly placed stands, with pieces of metal links joining with each other forming a chain. The chain is hung from the top point to point of the stand. If we were to plot a graph, with $$d$$ being the dependent variable and the number of links we put into the chain to make the overall length of the chain longer, ie the length of the chain is considered the independent variable. We get a graph:",
null,
"From here we see, we get a non-linear increasing trend line. What would be the physical reasoning for such non-linear trend.\n\nAttempt to answer: With the increase of links to the chain, ie by increasing the length of the chain, the links at some point stack on top of each other, which may lead to increase of mass therefore more gravitational pull, therefore leading to equal increments in giving rise to unequal increments in d.\n\n• – Gert Sep 19 at 13:50\n• Hint: the chain's shape changes when you add more links. – probably_someone Sep 19 at 13:52"
]
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null,
"https://i.stack.imgur.com/Dba1W.png",
null,
"https://i.stack.imgur.com/0pysi.png",
null
]
| {"ft_lang_label":"__label__en","ft_lang_prob":0.9481572,"math_prob":0.9730434,"size":889,"snap":"2019-51-2020-05","text_gpt3_token_len":185,"char_repetition_ratio":0.13898306,"word_repetition_ratio":0.0,"special_character_ratio":0.208099,"punctuation_ratio":0.09392265,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9587051,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,2,null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-12T03:00:16Z\",\"WARC-Record-ID\":\"<urn:uuid:bad7e55a-4564-4300-8b99-8db6048aa630>\",\"Content-Length\":\"127362\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c2eb42b0-4eef-463a-96a4-60b999c9b3fc>\",\"WARC-Concurrent-To\":\"<urn:uuid:20f02aa3-5d23-430d-8224-3fc59b3319ac>\",\"WARC-IP-Address\":\"151.101.1.69\",\"WARC-Target-URI\":\"https://physics.stackexchange.com/questions/503627/what-physical-interpretation-can-we-derive-from-this-experimental-step-up\",\"WARC-Payload-Digest\":\"sha1:MDWXOYGE7TECVIBW2X2FO7RYJXRZAOEF\",\"WARC-Block-Digest\":\"sha1:EO6A7RZIDM7K7XNQY2DNB3ULKS52ENRN\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575540536855.78_warc_CC-MAIN-20191212023648-20191212051648-00093.warc.gz\"}"} |
https://donabategolfclub.com/club-foursomes-championship-2023/ | [
"# Club Foursomes Championship 2023\n\nHandicap Rules:\nUnder WHS, all players in the match will individually calculate a course handicap (CH). To calculate your CH, why not use our WHS Handicap Calculator. The pair receives 50% of their combined total of their CHs. The full difference between the calculated handicaps of each pair will determine the number of shots given/received.\n\nFor example:\n1) Tom calculates his CH as 6, his partner John calculates his CH as 10\n2) Their combined CH is 6 + 10 = 16, and they received 50% which is 8\n3) Michael calculates his CH as 15, his partner Frank calculates his CH as 20\n4) Their combined CH is 15 + 20 = 35, and they received 50% which is 17.5, then rounded to 18\n5) The difference between the team allocations is 18 – 8 = 10, which means Michael and Frank receive 10 shots\n\nDraw:"
]
| [
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https://percent.info/decrease/645/how-to-calculate-the-percent-decrease-from-645-to-492.html | [
"Percent decrease from 645 to 492",
null,
"This page will answer the question \"What is the percent decrease from 645 to 492?\" and also show you how to calculate the percent decrease from 645 to 492.\n\nBefore we continue, note that the percent decrease from 645 to 492 is the same as the percentage decrease from 645 to 492. Furthermore, we will refer to 645 as the initial value (n) and 492 as the final value (f).\n\nSo what exactly are we calculating? The initial value is 645 and then a percent is used to decrease the initial value to the final value of 492. We want to calculate what that percent is!\n\nHere are step-by-step instructions showing you how to calculate the percent decrease from 645 to 492.\n\nFirst, we calculate the amount of decrease from 645 to 492 by subtracting the final value from the initial value, like this:\n\n645 - 492\n= 153\n\nTo calculate the percent of any number, you multiply the value (n) by the percent (p) and then divide the product by 100 to get the answer, like this:\n\n(n × p) / 100 = Answer\n\nIn our case, we know that the initial value (n) is 645 and that the answer (amount of decrease) is 153 to get the final value of 492. Therefore, we fill in what we know in the equation above to get the following equation:\n\n(645 × p) / 100 = 153\n\nNext, we solve the equation above for percent (p) by first multiplying each side by 100 and then dividing both sides by 645 to get percent (p):\n\n(645 × p) / 100 = 153\n((645 × p) / 100) × 100 = 153 × 100\n645p = 15300\n645p / 645 = 15300 / 645\np = 23.7209302325581\nPercent ≈ 23.7209\n\nThat's all there is to it! The percentage decrease from 645 to 492 is 23.7209%. In other words, if you take 23.7209% of 645 and subtract it from 645, then the difference will be 492.\n\nThe step-by-step instructions above were made so we could clearly explain exactly what a percent decrease from 645 to 492 means. For future reference, you can use the following percent decrease formula to calculate percent decreases:\n\n((n - f)/n) × 100 = p\n\nf = Final Value\nn = Initial Value\np = Percent decrease\n\nOnce again, here is the math and the answer to calculate the percent decrease from 645 to 492 using the percent decrease formula above:\n\n((n - f)/n) × 100\n= ((645 - 492)/645) × 100\n= (153/645) × 100\n= 0.237209302325581 × 100\n≈ 23.7209\n\nPercent Decrease Calculator\nGo here if you need to calculate another percent decrease.\n\nPercent decrease from 645 to 493\nHere is the next percent decrease tutorial on our list that may be of interest.\n\nCopyright | Privacy Policy | Disclaimer | Contact"
]
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"https://percent.info/images/percent-decrease.png",
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https://discuss.codechef.com/t/cheffa-editorial/15925?page=2 | [
"",
null,
"# CHEFFA - Editorial\n\n#21\n\n@dpraveen thanks now it’s clear to me",
null,
"#22\n\n`The number ∑i≥1ϕiai∑i≥1ϕiai won't change, where ϕ=1+5√2ϕ=1+52 is a solution of ϕ2=ϕ+1ϕ2=ϕ+1.`\n\nWhat is this?!???\n\n#23\n\ncan you link editorials with questions It will be easy to search\n\n#24\n\nYes this is interesting, can you please elaborate?\n\n#25\n\nyes its correct now\n\n#26\n\nI understood one thing that these two arrays of length N - [0 0…1] and [1 0…0 0] are different. The f() for the first one will be phi^1 while for the second one will be phi^N. For the array of size N will have a non-zero element at nth pos. So, to minimise it make all element 0 and put 1 at the Nth element. This will ensure that the f() is calculated for an array of length N.\n\n#27\n\nAny operation on array a doesnt change the value of f(a). I think it means that you cannot change the length of the array ‘a’ more than log(f(a)).\nlog(f(a)) - gives a number which is the max length possible for the given array.\n\n#28\n\n“on the subarray starting from the element having index pos assuming that this element was changed by deltapos and the next element to the right was changed by deltanxt.” Can somebody please explain this to me?\n\n#29\n\n@underdog_eagle: I don’t have a specific set of problems. If you see Topcoder Div 2 hard problems, you will set a lot of such examples of dp problems, which require multiple dimensions in the state.\n\n#30\n\nSleek trick! I love it even more because it uses phi and the problem is called Fibonacci Array.\n\n#31\n\nThere is a reason for the problem to be called “Fibonacci Array” - if all n members of the initial array are equal to 1 then the answer will be the n-th fibonacci number.\n\n#32\n\ndiv2 hard mean div2 1000 pointers or anything else?\n\n#33\n\nYes, div 2 1000 level problems.\n\n#34\n\nCan you please tell me, how do you approach such a DP problems with such a lenient solution in one go?\n\nI mean what type of technique do you follow in solving these ones?\n\n#35\n\nShoudn’t it be: dp[pos][deltapos][deltanxt] += dp[pos+1][deltanxt-op][op]?\n\n#36\n\nAlso, I think there shouldn’t be a +1 here: 0 ≤ op ≤ min(arrpos+deltapos , arrnxt+deltanxt) + 1 (in the two places where it appears).\n\n#37\n\nwhat does f(a) represent wrt array that we have? and how did you come up with this function and what is the general idea about this function?"
]
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null,
"https://s3.amazonaws.com/discourseproduction/original/2X/5/5a0884438a044b037255f4e65309549719f222a3.png",
null,
"https://discusslive.codechef.com/images/emoji/twitter/slight_smile.png",
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https://www.codespeedy.com/program-to-find-the-area-of-the-parallelogram-in-cpp/ | [
"# Program to find the area of the parallelogram in C++\n\nIn this c++ program, we will calculate the area of the parallelogram. Before going to the program let us know what is a parallelogram. A parallelogram is a four-sided quadrilateral with both the opposite sides to parallel to each other and equal. So let’s start learning how to find the area of a parallelogram in C++.",
null,
"To calculate the area of the parallelogram we need the length of base and height. From the figure, we can see AB||CD and AC|| BD. Consider CD as the base then height is the perpendicular distance between the base and it’s opposite side. Here AE is the height of the parallelogram.\n\nFORMULA FOR AREA OF THE PARALLELOGRAM:\n\nArea of the parallelogram=base * height.\n\nFrom the figure CD i.e.’b’ is the base and AE i.e, ‘h’ is the height of the parallelogram.\n\nArea=b*h.\n\n## C++ program to find area of a parallelogram\n\nThere are 2 ways to initialise the variables in the program.\n\nCompile time and Run time\n\nSyntax for compile time initialisation:\n\nfloat base=13.5;\n\nfloat height=12.7;\n\nfloat area=base * height;\n\nSource code:\n\n```int main()\n{\nfloat base=13.5;\nfloat height=12.7;\nfloat area =base * height;\ncout<<\"area of the parallelogram is \"<<area;\nreturn 0;\n}\n\n```\n\nOutput:\n\n```area of the parallelogram is 171.450000.\n\n```\n\nSyntax for run time initialisation:\n\nfloat base,height,area;\n\ncin>>base>>height;\n\narea=base*height;\n\nSource code:\n\n```int main()\n{\nfloat base,height,area;\ncout<<\"enter base value:\";\ncin>>base;\ncout<<\"\\n enter height value:\";\ncin>>height;\narea=base*height;\ncout<<\"\\n area of parallelogram is \"<<area;\nreturn 0;\n}\n\n```\n\nOutput:\n\n```enter base value:13.5\nenter height value:12.7\narea of parallelogram is 171.45000.```"
]
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"data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI5NjAiIGhlaWdodD0iNzIwIiB2aWV3Qm94PSIwIDAgOTYwIDcyMCI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgc3R5bGU9ImZpbGw6I2NmZDRkYjtmaWxsLW9wYWNpdHk6IDAuMTsiLz48L3N2Zz4=",
null
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https://www.adaic.org/resources/add_content/docs/95style/html/sec_2/2-1-3.html | [
"Ada 95 Quality and Style Guide Chapter 2\n\n### Chapter 2: Source Code Presentation - TOC - 2.1 CODE FORMATTING\n\n2.1.3 Alignment of Operators\n\nguideline\n\n• Align operators vertically to emphasize local program structure and semantics.\n• example\n\n``` if Slot_A >= Slot_B then\nTemporary := Slot_A;\nSlot_A := Slot_B;\nSlot_B := Temporary;\nend if;\n----------------------------------------------------------------\nNumerator := B**2 - 4.0 * A * C;\nDenominator := 2.0 * A;\nSolution_1 := (B + Square_Root(Numerator)) / Denominator;\nSolution_2 := (B - Square_Root(Numerator)) / Denominator;\n----------------------------------------------------------------\n:= A * B +\nC * D +\nE * F;\nY := (A * B + C) + (2.0 * D - E) - -- basic equation\n3.5; -- account for error factor\n```\n\nrationale\n\nAlignment makes it easier to see the position of the operators and, therefore, puts visual emphasis on what the code is doing.\n\nThe use of lines and spacing on long expressions can emphasize terms, precedence of operators, and other semantics. It can also leave room for highlighting comments within an expression.\n\nexceptions\n\nIf vertical alignment of operators forces a statement to be broken over two lines, especially if the break is at an inappropriate spot, it may be preferable to relax the alignment guideline.\n\nautomation notes\n\nThe last example above shows a kind of \"semantic alignment\" that is not typically enforced or even preserved by automatic code formatters. If you break expressions into semantic parts and put each on a separate line, beware of using a code formatter later. It is likely to move the entire expression to a single line and accumulate all the comments at the end. However, there are some formatters that are intelligent enough to leave a line break intact when the line contains a comment. A good formatter will recognize that the last example above does not violate the guidelines and would, therefore, preserve it as written.\n\n < Previous Page Search Contents Index Next Page >\n 1 2 3 4 5 6 7 8 9 10 11 TOC TOC TOC TOC TOC TOC TOC TOC TOC TOC TOC\n Appendix References Bibliography"
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http://mathandmultimedia.com/tag/line-symmetry/ | [
"## Understanding Point Symmetry\n\nIn the previous post, we have learned about line symmetry. In this post, we are going to learn about point symmetry, another type of symmetry.\n\nIf a figure is rotated 180 degrees about a point and it coincides with its original position, then it is said that the figure has point symmetry. The point of rotation is called the point of symmetry.\n\nThe figure below shows the point symmetric polygon ABCDEF rotated clockwise about P, its point of symmetry. The polygon outlined by the dashed line segments shows its original position. » Read more\n\n## Understanding Line Symmetry\n\nMany people believe that symmetry is beauty. Nature is full of symmetric objects. There are many man-made structures that are also symmetric. In this post, we are going to discuss some of the basic mathematical properties of symmetric objects. We will limit our discussion to line symmetric objects.\n\nLine Symmetry\n\nA figure is line symmetrical when it can be folded along a straight line such that the folded shapes fit exactly on top of each other. The fold line is called the line of symmetry.\n\nWhen a symmetric figure is folded along its line of symmetry, the parts that are on top of each other are called the corresponding parts. In the polygon below with line of symmetry AB, points C and D are corresponding points, segments GB and HB are corresponding sides, and angle G and angle H are corresponding angles. Since the folded shapes fit exactly on top of each other, the corresponding angles are congruent and their corresponding sides are also congruent. » Read more",
null,
""
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"http://www.linkwithin.com/pixel.png",
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https://davidmichaelhairsalon.com/qa/how-did-einstein-prove-e-mc2.html | [
"",
null,
"# How Did Einstein Prove E Mc2?\n\n## Does light have mass?\n\nDoes light have mass.\n\nLight is composed of photons, so we could ask if the photon has mass.\n\nThe answer is then definitely “no”: the photon is a massless particle.\n\nAccording to theory it has energy and momentum but no mass, and this is confirmed by experiment to within strict limits..\n\n## Why does E MC squared?\n\nThe equation — E = mc2 — means “energy equals mass times the speed of light squared.” It shows that energy (E) and mass (m) are interchangeable; they are different forms of the same thing. … The only reason light moves at the speed it does is because photons, the quantum particles that make up light, have a mass of zero.\n\n## Who came up with E mc2?\n\nAlbert EinsteinAccording to scientific folklore, Albert Einstein formulated this equation in 1905 and, in a single blow, explained how energy can be released in stars and nuclear explosions. This is a vast oversimplification.\n\n## What did Einstein mean when he said God does not play dice?\n\nEinstein had his personal views about religion and he believed in what he called “cosmic religion” where God’s presence was evident in the order and rationality of nature and the universe in all its aspects and expressions. Chaos and randomness are, therefore, not part of nature (“God does not play dice”).\n\n## What was Einstein’s theory of time?\n\nGeneral relativity is a theory of gravitation developed by Einstein in the years 1907–1915. … To resolve this difficulty Einstein first proposed that spacetime is curved. In 1915, he devised the Einstein field equations which relate the curvature of spacetime with the mass, energy, and any momentum within it.\n\n## How did Einstein prove relativity?\n\nSince Einstein believed that the laws of physics were local, described by local fields, he concluded from this that spacetime could be locally curved. This led him to study Riemannian geometry, and to formulate general relativity in this language.\n\n## Is E mc2 true?\n\nSend this by. It’s taken more than a century, but Einstein’s celebrated formula e=mc2 has finally been corroborated, thanks to a heroic computational effort by French, German and Hungarian physicists. … The e=mc2 formula shows that mass can be converted into energy, and energy can be converted into mass.\n\n## What does C stand for in E mc2?\n\nE = mc2. An equation derived by the twentieth-century physicist Albert Einstein, in which E represents units of energy, m represents units of mass, and c2 is the speed of light squared, or multiplied by itself. (See relativity.)\n\n## How do we use E mc2 today?\n\nThey are metamorphosing mass into energy in direct accordance with Einstein’s equation. We take advantage of that realization today in many technologies. PET scans and similar diagnostics used in hospitals, for example, make use of E = mc2.\n\n## What does E mc2 calculate?\n\nE = mc2. It’s the world’s most famous equation, but what does it really mean? “Energy equals mass times the speed of light squared.” On the most basic level, the equation says that energy and mass (matter) are interchangeable; they are different forms of the same thing.\n\n## How did Einstein come up with E mc2?\n\nSo he took this assumption–that the speed of light was a constant–and he returned to the mathematical and electromagnetic equations that were worked out years before. He then plugged in the letter “C” (a constant) to represent the fixed speed of light (whatever it might be) and low and behold… Out Popped E=MC2 !!\n\n## What E mc2 means?\n\nE = mc2. It’s the world’s most famous equation, but what does it really mean? “Energy equals mass times the speed of light squared.” On the most basic level, the equation says that energy and mass (matter) are interchangeable; they are different forms of the same thing.\n\n## What is the meaning of Einstein’s famous equation E mc2?\n\nE = mc2. An equation derived by the twentieth-century physicist Albert Einstein, in which E represents units of energy, m represents units of mass, and c2 is the speed of light squared, or multiplied by itself.\n\n## What is the derivation of E mc2?\n\nIn the equation, the increased relativistic mass (m) of a body times the speed of light squared (c2) is equal to the kinetic energy (E) of that body. In physical theories prior to that of special relativity, mass and energy were viewed as distinct entities."
]
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null,
"https://mc.yandex.ru/watch/65696350",
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https://metanumbers.com/559527 | [
"## 559527\n\n559,527 (five hundred fifty-nine thousand five hundred twenty-seven) is an odd six-digits composite number following 559526 and preceding 559528. In scientific notation, it is written as 5.59527 × 105. The sum of its digits is 33. It has a total of 3 prime factors and 8 positive divisors. There are 363,840 positive integers (up to 559527) that are relatively prime to 559527.\n\n## Basic properties\n\n• Is Prime? No\n• Number parity Odd\n• Number length 6\n• Sum of Digits 33\n• Digital Root 6\n\n## Name\n\nShort name 559 thousand 527 five hundred fifty-nine thousand five hundred twenty-seven\n\n## Notation\n\nScientific notation 5.59527 × 105 559.527 × 103\n\n## Prime Factorization of 559527\n\nPrime Factorization 3 × 41 × 4549\n\nComposite number\nDistinct Factors Total Factors Radical ω(n) 3 Total number of distinct prime factors Ω(n) 3 Total number of prime factors rad(n) 559527 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 559,527 is 3 × 41 × 4549. Since it has a total of 3 prime factors, 559,527 is a composite number.\n\n## Divisors of 559527\n\n8 divisors\n\n Even divisors 0 8 4 4\nTotal Divisors Sum of Divisors Aliquot Sum τ(n) 8 Total number of the positive divisors of n σ(n) 764400 Sum of all the positive divisors of n s(n) 204873 Sum of the proper positive divisors of n A(n) 95550 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 748.015 Returns the nth root of the product of n divisors H(n) 5.85586 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors\n\nThe number 559,527 can be divided by 8 positive divisors (out of which 0 are even, and 8 are odd). The sum of these divisors (counting 559,527) is 764,400, the average is 95,550.\n\n## Other Arithmetic Functions (n = 559527)\n\n1 φ(n) n\nEuler Totient Carmichael Lambda Prime Pi φ(n) 363840 Total number of positive integers not greater than n that are coprime to n λ(n) 45480 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 45931 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 363,840 positive integers (less than 559,527) that are coprime with 559,527. And there are approximately 45,931 prime numbers less than or equal to 559,527.\n\n## Divisibility of 559527\n\n m n mod m 2 3 4 5 6 7 8 9 1 0 3 2 3 3 7 6\n\nThe number 559,527 is divisible by 3.\n\n## Classification of 559527\n\n• Arithmetic\n• Deficient\n\n• Polite\n\n• Square Free\n\n### Other numbers\n\n• LucasCarmichael\n• Sphenic\n\n## Base conversion (559527)\n\nBase System Value\n2 Binary 10001000100110100111\n3 Ternary 1001102112020\n4 Quaternary 2020212213\n5 Quinary 120401102\n6 Senary 15554223\n8 Octal 2104647\n10 Decimal 559527\n12 Duodecimal 22b973\n16 Hexadecimal 889a7\n20 Vigesimal 39ig7\n36 Base36 bzqf\n\n## Basic calculations (n = 559527)\n\n### Multiplication\n\nn×i\n n×2 1119054 1678581 2238108 2797635\n\n### Division\n\nni\n n⁄2 279764 186509 139882 111905\n\n### Exponentiation\n\nni\n n2 313070463729 175171377358896183 98013115259491104585441 54840984341797279275378046407\n\n### Nth Root\n\ni√n\n 2√n 748.015 82.4025 27.3499 14.1112\n\n## 559527 as geometric shapes\n\n### Circle\n\nRadius = n\n Diameter 1.11905e+06 3.51561e+06 9.8354e+11\n\n### Sphere\n\nRadius = n\n Volume 7.33756e+17 3.93416e+12 3.51561e+06\n\n### Square\n\nLength = n\n Perimeter 2.23811e+06 3.1307e+11 791291\n\n### Cube\n\nLength = n\n Surface area 1.87842e+12 1.75171e+17 969129\n\n### Equilateral Triangle\n\nLength = n\n Perimeter 1.67858e+06 1.35563e+11 484565\n\n### Triangular Pyramid\n\nLength = n\n Surface area 5.42254e+11 2.06441e+16 456852\n\n## Cryptographic Hash Functions\n\nmd5 25157450aab80d5e6992f73fdada1a0f 5ca66bb5175bc9bec658ea3fe7860c5488788e4b 1e5cc7fd82cef0349b50201ca989fccb34cc3b012a42b6a02216ae41ea549b11 b5bd326b439533db6e8dae113ac7f600de5486f27880b89930402f0d731e2f4d8b3520e017d461705650e18e86043a8cd058a9add1d56c702467e4d4160511c0 e6e1ca8b6f2b03aad164c8c7e290bf17e8293917"
]
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https://socratic.org/calculus/graphing-with-the-first-derivative/classifying-critical-points-and-extreme-values-for-a-function | [
"# Classifying Critical Points and Extreme Values for a Function\n\n## Key Questions\n\n• Here is how to find and classify a critical point of $f$.\n\nRemember that $x = c$ is called a critical value of $f$ if $f ' \\left(c\\right) = 0$ or $f ' \\left(c\\right)$ is undefined.\n\n$f ' \\left(x\\right) = 3 {x}^{2} = 0 R i g h t a r r o w x = 0$ is a critical number.\n\n(Note: $f '$ is defined everywhere, $0$ is the only critical value.)\n\nObserving that $f ' \\left(x\\right) = 3 {x}^{2} \\ge 0$ for all $x$,\n\n$f '$ does not change sign around the critical value $0$.\n\nHence, $f \\left(0\\right)$ is neither a local maximum nor a local minimum by First Derivative Test."
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https://freezingblue.com/flashcards/208810/preview/precal-word-problems | [
"# PreCal Word Problems\n\n Interest Equation I = Prt Compound Interest Formula A=P(1+r/n)^(nt) Continuous Compounding A=Pe^(rt) Effective Rate of Interest: Compounding formula re=(1+r/n)^(n) -1 Effective Rate of Interest: Continous Compounding formula re= e^(r) -1 Authoresmer.710 ID208810 Card SetPreCal Word Problems Descriptionword problems Updated2013-03-22T01:10:32Z Show Answers"
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https://www.bartleby.com/solution-answer/chapter-7r-problem-64e-calculus-mindtap-course-list-8th-edition/9781285740621/use-a-the-trapezoidal-rule-b-the-midpoint-rule-and-c-simpsons-rule-with-n10-to-approximate-the/dc3595bb-9407-11e9-8385-02ee952b546e | [
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"Chapter 7.R, Problem 64E\n\nChapter\nSection\nTextbook Problem\n\n# Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson’s Rule with n = 10 to approximate the given integral. Round your answers to six decimal places. ∫ 1 4 x cos x d x\n\nTo determine\n\n( a)\n\nTo approximate:\n\nThe given integral using Trapezoidal Rule.\n\nExplanation\n\nGiven:\n\n14xcosxdx\n\nFormulae used:\n\nThe integration by using Trapezoidal Rule.\n\nConsider 14xcosxdx for n=10\n\nHence, use the integration by using Trapezoidal rule\n\nNow according to the given expression, the value of the given expression 14xcosxdx is\n\nInterval width\n\nΔx=ban=4110=0.3\n\nTrapezoidal rule has n+1=11 terms\n\nT10=Δx2[f(1)+2f(1.3)+2f(1.6)+2f(1.9)+2f(2.2)+2f(2.5)+2f(2\n\nTo determine\n\n(b)\n\nTo approximate:\n\nThe given integral using Midpoint Rule.\n\nTo determine\n\n(c)\n\nTo approximate:\n\nThe given integral using by Simpson's Rule.\n\n### Still sussing out bartleby?\n\nCheck out a sample textbook solution.\n\nSee a sample solution\n\n#### The Solution to Your Study Problems\n\nBartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!\n\nGet Started\n\n#### Evaluate the expression sin Exercises 116. (32)3\n\nFinite Mathematics and Applied Calculus (MindTap Course List)\n\n#### (916)1/2\n\nApplied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach\n\n#### It does not exist.\n\nStudy Guide for Stewart's Multivariable Calculus, 8th",
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.64685446,"math_prob":0.977971,"size":2350,"snap":"2019-43-2019-47","text_gpt3_token_len":513,"char_repetition_ratio":0.16922422,"word_repetition_ratio":0.12,"special_character_ratio":0.16425532,"punctuation_ratio":0.09763314,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9931544,"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\":\"2019-11-19T08:03:52Z\",\"WARC-Record-ID\":\"<urn:uuid:ffcba105-4403-4387-9ab6-017b092ae31f>\",\"Content-Length\":\"868412\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9a69c679-dd91-4257-9489-1f6406485a26>\",\"WARC-Concurrent-To\":\"<urn:uuid:3aa8c905-e422-4407-b855-a931b35c82df>\",\"WARC-IP-Address\":\"99.86.230.91\",\"WARC-Target-URI\":\"https://www.bartleby.com/solution-answer/chapter-7r-problem-64e-calculus-mindtap-course-list-8th-edition/9781285740621/use-a-the-trapezoidal-rule-b-the-midpoint-rule-and-c-simpsons-rule-with-n10-to-approximate-the/dc3595bb-9407-11e9-8385-02ee952b546e\",\"WARC-Payload-Digest\":\"sha1:YYFZS4XHZ4EW6CEOEZ33HSLM2I6YTI7A\",\"WARC-Block-Digest\":\"sha1:P43GXEIAMZQKSBW6NGZOZRIJSLDRBULJ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-47/CC-MAIN-2019-47_segments_1573496670036.23_warc_CC-MAIN-20191119070311-20191119094311-00353.warc.gz\"}"} |
https://quant67.com/post/C/bit-hack.html | [
"# 一些常用位运算技巧\n\n## 1 整数的符号\n\nint v; // 需要获得 v 的符号\nint sign; // 结果\n\n// CHAR_BIT 是一个字节的比特数\n// v < 0 则是 -1，否则 0\nsign = -(v < 0);\n// 使用位运算更快\nsign = -(int)((unsigned int)v >> sizeof(int) * CHAR_BIT - 1);\n// 或者更简单的写法\nsign = v >> (sizeof(int) * CHAR_BIT - 1);\n\n// 如果想要得到 -1 或 +1，只需要在最低位或 1\nsign = 1 | (v >> sizeof(int) * CHAR_BIT -1);\n\n// 如果想要 -1, 0 或 1， 则需要根据情况或 1 或 0\nsign = (v != 0) | (v >> (sizeof(int) * CHAR_BIT - 1));\n// 或者更简单的写法\nsign = (v > 0) - (v < 0);\n\n// 如果要判断一个值是不是非负的\nsign = 1 ^ ((unsigned int)v >> (sizeof(int) * CHAR_BIT - 1)); // v < 0 则 0, 否则 1\n\n// 判断两个整数是不是符号相反，只需要将最高位异或\nint x, y; // 两个整数\nbool f = ((x ^ y) < 0); // 符号相反就是真，否则为假\n\n// 获得绝对值\nunsigned int r; // 绝对值\nint const mask = v >> sizeof(int) * CHAR_BIT - 1;\n// 或者\n\n\n## 2 最大值和最小值\n\nint x;\nint y;\nint r; // 结果\n\n// 最小值\nr = y ^ ((x ^ y) & -(x < y));\n// 最大值\nr = x ^ ((x ^ y) & -(x < y));\n\n\nr = y + ((x - y) & ((x - y) >> (sizeof(int) * CHAR_BIT - 1))); // min(x, y)\nr = x - ((x - y) & ((x - y) >> (sizeof(int) * CHAR_BIT - 1))); // max(x, y)\n\n\n## 3 判断是不是 2 的幂\n\nunsigned int v;\nbool f; // 结果\n\nf = (v & (v - 1)) == 0;\n\n// 注意到 0 不是 2 的倍数，所以修正如下\nf = v && !(v & (v - 1));\n\n\n## 4 b 比特位的数值转换为整数\n\nunsigned b; // 整数 x 的比特位\nint x; // 低 b 位保存需要读取的整数值\nint r; // 结果\nint const m = 1U << (b - 1); // 原整数符号位\n\nx = x & ((1U << b) - 1); // 将无关比特清零\nr = (x ^ m) - m;\n\n\n## 5 如果满足条件将第 b 位置 0 或 1\n\nbool f; // 条件\nint b; // 设置第 b 位\nunsigned int m = 1 << b;\n\n// if (f) w |= m; else w &= ~m;\nw ^= (-f ^ w) & m;\n\n\n## 6 条件满足取相反数\n\nbool fDontNegate; // 为假时取反\nint v;\nint r;\n\nr = (fDontNegate ^ (fDontNegate - 1)) * v;\n\n\nbool fNegate;\nint v;\nint r;\n\nr = (v ^ -fNegate) + fNegate;\n\n\n## 7 统计 1 的数量，也就是 Hamming weight\n\n00010110001011010011110110110011\n0 1 1 1 0 1 2 1 0 2 2 1 1 2 0 2\n1 2 1 3 2 3 3 2\n3 4 5 5\n7 10\n17\n\n\nconst uint64_t m1 = 0x5555555555555555; //binary: 0101...\nconst uint64_t m2 = 0x3333333333333333; //binary: 00110011..\nconst uint64_t m4 = 0x0f0f0f0f0f0f0f0f; //binary: 4 zeros, 4 ones ...\nconst uint64_t m8 = 0x00ff00ff00ff00ff; //binary: 8 zeros, 8 ones ...\nconst uint64_t m16 = 0x0000ffff0000ffff; //binary: 16 zeros, 16 ones ...\nconst uint64_t m32 = 0x00000000ffffffff; //binary: 32 zeros, 32 ones\nconst uint64_t hff = 0xffffffffffffffff; //binary: all ones\nconst uint64_t h01 = 0x0101010101010101; //the sum of 256 to the power of 0,1,2,3...\n\n\nint popcount64a(uint64_t x)\n{\nx = (x & m1 ) + ((x >> 1) & m1 ); //put count of each 2 bits into those 2 bits\nx = (x & m2 ) + ((x >> 2) & m2 ); //put count of each 4 bits into those 4 bits\nx = (x & m4 ) + ((x >> 4) & m4 ); //put count of each 8 bits into those 8 bits\nx = (x & m8 ) + ((x >> 8) & m8 ); //put count of each 16 bits into those 16 bits\nx = (x & m16) + ((x >> 16) & m16); //put count of each 32 bits into those 32 bits\nx = (x & m32) + ((x >> 32) & m32); //put count of each 64 bits into those 64 bits\nreturn x;\n}\n\n\nint popcount64b(uint64_t x)\n{\nx -= (x >> 1) & m1; //put count of each 2 bits into those 2 bits\nx = (x & m2) + ((x >> 2) & m2); //put count of each 4 bits into those 4 bits\nx = (x + (x >> 4)) & m4; //put count of each 8 bits into those 8 bits\nx += x >> 8; //put count of each 16 bits into their lowest 8 bits\nx += x >> 16; //put count of each 32 bits into their lowest 8 bits\nx += x >> 32; //put count of each 64 bits into their lowest 8 bits\nreturn x & 0x7f;\n}\n\n\nm1 行与上一个实现的 m1 行做的是一样的事情，这需要一点解释：\n\n\\begin{eqnarray*} x &=& a + 2b + 2^{2}c + 2^{3}d + 2^{4}e + \\cdots \\\\ (x >> 1) &=& b + 2c + 2^{2}d + 2^{3}e + 2^{4}f + \\cdots \\\\ (x >> 1) \\& m1 &=& b + 2^{2}d + 2^{4}f + \\cdots \\\\ x-((x>>1)\\&m1) &=& a + b + 2{2}c + 2^{2}d + \\cdots \\end{eqnarray*}\n\nm2 行和上一个实现是一样的，下面看 m4 行。因为 8 比特的 Hamming weigth 绝对不会超过 8，所以最后累加只会存储到最多 4 比特的空间内，所以直接移位相加取后四位就是这个分组的累加和。\n\nint popcount64c(uint64_t x)\n{\nx -= (x >> 1) & m1; //put count of each 2 bits into those 2 bits\nx = (x & m2) + ((x >> 2) & m2); //put count of each 4 bits into those 4 bits\nx = (x + (x >> 4)) & m4; //put count of each 8 bits into those 8 bits\nreturn (x * h01) >> 56; //returns left 8 bits of x + (x<<8) + (x<<16) + (x<<24) + ...\n}\n\n\n## 8 交换两个整数值\n\nint a, b;\na ^= b;\nb ^= a;\na ^= b;\n\n\n## 9 判断整数中有没有某个字节全 0\n\n#define ahszero(v) v - 0x01010101UL & ~v & 0x80808080UL\n\n\n## 10 枚举整数位图表示的集合的子集\n\nt = s;\ndo {\nt = (t - 1) & t;\n} while (t != s);\n\n\ncomb = (1 << k) - 1\nwhile (comb < 1 << n) {\nx = comb & -comb;\ny = comb + x;\ncomb = ((comb & ~y) / x >> 1) | y;\n// comb 就是大小为 k 的子集\n}"
]
| [
null
]
| {"ft_lang_label":"__label__zh","ft_lang_prob":0.5730411,"math_prob":0.9999453,"size":5372,"snap":"2022-27-2022-33","text_gpt3_token_len":3105,"char_repetition_ratio":0.15443368,"word_repetition_ratio":0.2091562,"special_character_ratio":0.4670514,"punctuation_ratio":0.12107209,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.999716,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-08-19T05:55:34Z\",\"WARC-Record-ID\":\"<urn:uuid:19fd2b9a-09fa-43ca-b364-a5f55f3c2f61>\",\"Content-Length\":\"24935\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:45b55721-c912-4adc-a2a3-404436d71a22>\",\"WARC-Concurrent-To\":\"<urn:uuid:164958e8-3513-4171-9299-da9a29b4aa89>\",\"WARC-IP-Address\":\"104.21.4.89\",\"WARC-Target-URI\":\"https://quant67.com/post/C/bit-hack.html\",\"WARC-Payload-Digest\":\"sha1:HT67LSR6FKIPO3JRQTD6B4S4YI4E5R2H\",\"WARC-Block-Digest\":\"sha1:KMO3UDXINBMF2EIBOFYXS232LS22XW4N\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-33/CC-MAIN-2022-33_segments_1659882573623.4_warc_CC-MAIN-20220819035957-20220819065957-00581.warc.gz\"}"} |
http://interview.fyicenter.com/799_What_Is_the_Scope_of_a_Local_Variable.html | [
"What Is the Scope of a Local Variable\n\nQ\n\nWhat Is the Scope of a Local Variable? - Oracle DBA FAQ - Creating Your Own PL/SQL Procedures and Functions\n\n✍: FYIcenter.com\n\nA",
null,
"The scope of a variable can be described with these rules:\n\n• A variable is valid within the procedure or function where it is defined.\n• A variable is also valid inside a sub procedure or function defined.\n• If a variable name is collided with another variable in a sub procedure or function, this variable becomes not visible in that sub procedure or function.\n\nHere is a sample script to show you those rules:\n\nThe script below illustrates how to use named parameters:\n\n```SQL> CREATE OR REPLACE PROCEDURE PARENT AS\n2 X CHAR(10) := 'FYI';\n3 Y NUMBER := 999999.00;\n4 PROCEDURE CHILD AS\n5 Y CHAR(10) := 'CENTER';\n6 Z NUMBER := -1;\n7 BEGIN\n8 DBMS_OUTPUT.PUT_LINE('X = ' || X); -- X from PARENT\n9 DBMS_OUTPUT.PUT_LINE('Y = ' || Y); -- Y from CHILD\n10 DBMS_OUTPUT.PUT_LINE('Z = ' || TO_CHAR(Z));\n11 END;\n12 BEGIN\n13 DBMS_OUTPUT.PUT_LINE('X = ' || X); -- X from PARENT\n14 DBMS_OUTPUT.PUT_LINE('Y = ' || TO_CHAR(Y));\n15 -- DBMS_OUTPUT.PUT_LINE('Z = ' || TO_CHAR(Z));\n16 CHILD;\n17 END;\n18 /\n\nSQL> EXECUTE PARENT;\nX = FYI\nY = 999999\nX = FYI\nY = CENTER\nZ = -1\n```\n\n2007-04-21, 5276👍, 0💬"
]
| [
null,
"http://interview.fyicenter.com/z/_icon_Oracle.png",
null
]
| {"ft_lang_label":"__label__en","ft_lang_prob":0.6074242,"math_prob":0.9002971,"size":1785,"snap":"2022-05-2022-21","text_gpt3_token_len":545,"char_repetition_ratio":0.10836609,"word_repetition_ratio":0.06097561,"special_character_ratio":0.3764706,"punctuation_ratio":0.15079366,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97848547,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-24T05:46:59Z\",\"WARC-Record-ID\":\"<urn:uuid:d743d56e-85f7-4aa0-9a77-1588426a8dd4>\",\"Content-Length\":\"25327\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a7f5c90b-b44d-46e3-a930-180406d3c832>\",\"WARC-Concurrent-To\":\"<urn:uuid:349aee35-60d1-4e24-a9bb-14c2380d3e92>\",\"WARC-IP-Address\":\"74.208.236.35\",\"WARC-Target-URI\":\"http://interview.fyicenter.com/799_What_Is_the_Scope_of_a_Local_Variable.html\",\"WARC-Payload-Digest\":\"sha1:WS2XSRTI4WE4PZSWNX7BYBNLM6NVWFMT\",\"WARC-Block-Digest\":\"sha1:PRRBKLJRVMBWBK5KY4AID3RKFZ72NTW4\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662564830.55_warc_CC-MAIN-20220524045003-20220524075003-00269.warc.gz\"}"} |
https://access-excel.tips/excel-covariance-s-covariance-b/ | [
"# Excel calculate covariance using COVARIANCE.S and COVARIANCE.P\n\nThis Excel tutorial explains how to calculate sample covariance using COVARIANCE.S and calculate population covariance using COVARIANCE.P\n\n## Covariance\n\nCovariance is a measure of how much two random variables change together.\n\nThe below formula is for calculation of Population Covariance. For Sample Covariance, divide n-1 instead of N.",
null,
"While σx is denoted as standard variation of x, σxy is denoted as Covariance.\n\nAfter we calculate the covariance, we can check the sign whether it is negative or positive. Positive covariance means positive relationship (y increases as x increases), negative covariance means a negative relationship (y decreases as x increases). However, we cannot see the strength of relationship.\n\n## Covariance – Manual calculation\n\nAssume B2 to B4 are the source data of variable x and y, when x increases, y also increases.",
null,
"The gray cells are Excel formula, you can easily create a table as above. The final figure we need from the above table is the yellow cell.\n\nNow we can apply the formula to calculate sample covariance and population covariance\n\nPopulation covariance = 35/N = 35/3 =11.7\n\nSample covariance = 35/n-1 = 35/2 =17.5\n\nIf we invert the y data so that y decreases with x, then",
null,
"Population covariance = -35/N = -35/3 =-11.7\n\nSample covariance = -35/n-1 = -35/2 =-17.5\n\nIf y is constant, then",
null,
"Population covariance = 0\n\nSample covariance = 0\n\nWe can tell from the sign of covariance that positive covariance is a positive relationship, negative covariance is negative relationship, zero covariance is no relationship, but we cannot tell the strength of the relationship by looking at the number.\n\n## COVARIANCE.S and COVARIANCE.P Functions\n\nCalculating covariance using Excel formula is very straight forward.\n\nCovariance.S is to calculate sample covariance, while Covariance.P is to calculate population covariance. Both functions have two parameters\n\n```Covariance.S(array1, array2)\nCovariance.P(array1, array2)```\n\narray1 is the variable x data set, while array2 is the variable y data set. Using the below dataset as an example",
null,
"Formula Result Population Covariance =COVARIANCE.P(B2:B4,C2:C4) 11.66667 Sample Covariance =COVARIANCE.S(B2:B4,C2:C4) 17.5\n\nWyman is a Human Resources professional based in Hong Kong, specialized in business analysis, project management, data transformation with Access and Excel.\n\nHe is also a:\n- Microsoft Most Valuable Professional (Excel)\n- Microsoft Community Contributor\n- Microsoft Office Specialist in Access / Excel\n- Microsoft Specialist in MS Project\n- Microsoft Technical Associate\n- Microsoft Certified Professional\n- IBM SPSS Specialist"
]
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"http://access-excel.tips/wp-content/uploads/2015/09/population-covariance.png",
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"http://access-excel.tips/wp-content/uploads/2016/04/COVARIANCE.S-and-COVARIANCE.B-01.jpg",
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"http://access-excel.tips/wp-content/uploads/2016/04/COVARIANCE.S-and-COVARIANCE.B-02.jpg",
null,
"http://access-excel.tips/wp-content/uploads/2016/04/COVARIANCE.S-and-COVARIANCE.B-03.jpg",
null,
"http://access-excel.tips/wp-content/uploads/2016/04/COVARIANCE.S-and-COVARIANCE.B-01.jpg",
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.85577124,"math_prob":0.9953212,"size":2170,"snap":"2019-13-2019-22","text_gpt3_token_len":515,"char_repetition_ratio":0.2156048,"word_repetition_ratio":0.0,"special_character_ratio":0.22949308,"punctuation_ratio":0.12990196,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9992861,"pos_list":[0,1,2,3,4,5,6,7,8,9,10],"im_url_duplicate_count":[null,2,null,2,null,1,null,1,null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-03-20T07:21:05Z\",\"WARC-Record-ID\":\"<urn:uuid:181df07a-52ec-4476-a696-36e6732a5bde>\",\"Content-Length\":\"80759\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:bfa56515-9fcb-4b75-a48a-98e162b6a783>\",\"WARC-Concurrent-To\":\"<urn:uuid:14372b2d-d64e-4ee6-aaab-8888c4967999>\",\"WARC-IP-Address\":\"50.17.94.88\",\"WARC-Target-URI\":\"https://access-excel.tips/excel-covariance-s-covariance-b/\",\"WARC-Payload-Digest\":\"sha1:VAGLQGHO63CPBONVYCAEQUMFNEM44D3W\",\"WARC-Block-Digest\":\"sha1:C3JVIJQYW2EBQ2IW4FMNNDR5RFG33UKA\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-13/CC-MAIN-2019-13_segments_1552912202303.66_warc_CC-MAIN-20190320064940-20190320090940-00432.warc.gz\"}"} |
https://fr.maplesoft.com/support/help/errors/view.aspx?path=Optimization/General/AlgebraicForm&L=F | [
"",
null,
"Algebraic - Maple Help\n\nAlgebraic Form of Input for Optimization Package Commands\n\n This help page describes the algebraic form of input for commands in the Optimization package. For general information on all the input forms accepted by the Optimization package commands, see the Optimization/InputForms help page. For more information about options mentioned below, see the Optimization/Options help page.",
null,
"Objective Function\n\n • The objective function of the optimization problem must be an algebraic expression in the problem variables, for example, exp(tan(x)) and ${x}^{2}+{y}^{2}-3x+3y+3$. The problem variables are the indeterminates in the objective function and, if provided, the constraints. They can also be specified using the variables option.\n • Some commands impose additional restrictions. For example, Optimization[QPSolve] requires the objective function to be quadratic in the problem variables.\n • The Optimization[LSSolve] command accepts an objective function in least-squares form. This objective function is specified as a list of algebraic expressions $[{r}_{1},{r}_{2},...,{r}_{q}]$, where ${r}_{1}$, ${r}_{2}$, ..., ${r}_{q}$ represent the residuals to be minimized in a least-squares sense. Thus, the objective function is $\\left(\\frac{1}{2}\\right)\\left({\\left({r}_{1}\\right)}^{2}+{\\left({r}_{2}\\right)}^{2}+...+{\\left({r}_{q}\\right)}^{2}\\right)$.",
null,
"Constraints\n\n • The constraints must be a set or list of relations. Only relations of type <= and = are allowed. An example is $\\left\\{w=1,2\\le {y}^{2}+z,x\\le 5\\right\\}$.\n • Some commands impose additional restrictions. For example, Optimization[LPSolve] requires all relations in the constraint set to be linear in the problem variables.",
null,
"Bounds\n\n • Specify the bounds as a sequence of arguments of the form $\\mathrm{vname}=\\mathrm{vrange}$, where vname is the name of a problem variable and vrange is its range, for example $y=-1..2$.\n • Bounds can be included with the general constraints. For example, adding the inequalities $1.5\\le x$ and $x\\le 3.2$ to the constraint set is equivalent to specifying $x=1.5..3.2$. Bounds are not required to be specified separately, though this usually leads to more efficient computation.\n • The problem variables are not assumed to be non-negative by default, but the $\\mathrm{assume}=\\mathrm{nonnegative}$ option can be used to specify this.",
null,
"Initial Values\n\n • Specify the initial values using the option $\\mathrm{initialpoint}=p$, where p is a set or list of equalities in the form $\\mathrm{varname}=\\mathrm{value}$. Each varname is one of the problem variables and value is the value to which it is initially set. An example is $\\mathrm{initialpoint}=\\left\\{x=-1.2,y=5.7\\right\\}$.",
null,
"Solution\n\n • Maple returns the solution as a list containing the final minimum (or maximum) value and a point (the computed extremum). The point is a list containing elements of the form $\\mathrm{varname}=\\mathrm{value}$, where varname is a problem variable and value is its value.",
null,
"Examples\n\n > $\\mathrm{with}\\left(\\mathrm{Optimization}\\right):$\n\nSolve a linear program, quadratic program, and nonlinear program, all expressed in algebraic form.\n\n > $\\mathrm{LPSolve}\\left(-4x-5y,\\left\\{0\\le x,0\\le y,x+2y\\le 6,5x+4y\\le 20\\right\\}\\right)$\n $\\left[{-19.}{,}\\left[{x}{=}{2.66666666666667}{,}{y}{=}{1.66666666666667}\\right]\\right]$ (1)\n > $\\mathrm{QPSolve}\\left(2x+5y+3{x}^{2}+3xy+2{y}^{2},\\left\\{2\\le x-y\\right\\}\\right)$\n $\\left[{-3.53333333333333}{,}\\left[{x}{=}{0.466666666666667}{,}{y}{=}{-1.60000000000000}\\right]\\right]$ (2)\n > $\\mathrm{NLPSolve}\\left(\\frac{\\mathrm{sin}\\left(x\\right)}{x},x=1..10\\right)$\n $\\left[{-0.217233628211222}{,}\\left[{x}{=}{4.49340945753529}\\right]\\right]$ (3)"
]
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null,
"https://bat.bing.com/action/0",
null,
"https://fr.maplesoft.com/support/help/errors/arrow_down.gif",
null,
"https://fr.maplesoft.com/support/help/errors/arrow_down.gif",
null,
"https://fr.maplesoft.com/support/help/errors/arrow_down.gif",
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null,
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https://www.scribd.com/document/256767093/SM-Horngren-Cost-Accounting-14e-Ch17 | [
"You are on page 1of 48\n\ncom\n\nCHAPTER 17\nPROCESS COSTING\n17-1 Industries using process costing in their manufacturing area include chemical processing,\noil refining, pharmaceuticals, plastics, brick and tile manufacturing, semiconductor chips,\nbeverages, and breakfast cereals.\n17-2 Process costing systems separate costs into cost categories according to the timing of\nwhen costs are introduced into the process. Often, only two cost classifications, direct materials\nand conversion costs, are necessary. Direct materials are frequently added at one point in time,\noften the start or the end of the process. All conversion costs are added at about the same time,\nbut in a pattern different from direct materials costs. Conversion costs are often added\nthroughout the process, which can of any length of time, lasting from seconds to several months.\n17-3 Equivalent units is a derived amount of output units that takes the quantity of each input\n(factor of production) in units completed or in incomplete units in work in process, and converts\nthe quantity of input into the amount of completed output units that could be made with that\nquantity of input. Each equivalent unit is comprised of the physical quantities of direct materials\nor conversion costs inputs necessary to produce output of one fully completed unit. Equivalent\nunit measures are necessary since all physical units are not completed to the same extent at the\nsame time.\n17-4 The accuracy of the estimates of completion depends on the care and skill of the\nestimator and the nature of the process. Semiconductor chips may differ substantially in the\nfinishing necessary to obtain a final product. The amount of work necessary to finish a product\nmay not always be easy to ascertain in advance.\n17-5 The five key steps in process costing follow:\nStep 1: Summarize the flow of physical units of output.\nStep 2: Compute output in terms of equivalent units.\nStep 3: Summarize total costs to account for.\nStep 4: Compute cost per equivalent unit.\nStep 5: Assign total costs to units completed and to units in ending work in process.\n17-6\n\n## Three inventory methods associated with process costing are:\n\nWeighted average.\nFirst-in, first-out.\nStandard costing.\n\n17-7 The weighted-average process-costing method calculates the equivalent-unit cost of all\nthe work done to date (regardless of the accounting period in which it was done), assigns this\ncost to equivalent units completed and transferred out of the process, and to equivalent units in\nending work-in-process inventory.\n\n17-1\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n17-8 FIFO computations are distinctive because they assign the cost of the previous\naccounting periods equivalent units in beginning work-in-process inventory to the first units\ncompleted and transferred out of the process and assign the cost of equivalent units worked on\nduring the current period first to complete beginning inventory, next to start and complete new\nunits, and finally to units in ending work-in-process inventory. In contrast, the weighted-average\nmethod costs units completed and transferred out and in ending work in process at the same\naverage cost.\n17-9 FIFO should be called a modified or departmental FIFO method because the goods\ntransferred in during a given period usually bear a single average unit cost (rather than a distinct\nFIFO cost for each unit transferred in) as a matter of convenience.\n17-10 A major advantage of FIFO is that managers can judge the performance in the current\nperiod independently from the performance in the preceding period.\n17-11 The journal entries in process costing are basically similar to those made in job-costing\nsystems. The main difference is that, in process costing, there is often more than one work-inprocess accountone for each process.\n17-12 Standard-cost procedures are particularly appropriate to process-costing systems where\nthere are various combinations of materials and operations used to make a wide variety of similar\nproducts as in the textiles, paints, and ceramics industries. Standard-cost procedures also avoid\nthe intricacies involved in detailed tracking with weighted-average or FIFO methods when there\nare frequent price variations over time.\n17-13 There are two reasons why the accountant should distinguish between transferred-in\ncosts and additional direct materials costs for a particular department:\n(a) All direct materials may not be added at the beginning of the department process.\n(b) The control methods and responsibilities may be different for transferred-in items and\n17-14 No. Transferred-in costs or previous department costs are costs incurred in a previous\ndepartment that have been charged to a subsequent department. These costs may be costs\nincurred in that previous department during this accounting period or a preceding accounting\nperiod.\n17-15 Materials are only one cost item. Other items (often included in a conversion costs pool)\ninclude labor, energy, and maintenance. If the costs of these items vary over time, this variability\ncan cause a difference in cost of goods sold and inventory amounts when the weighted-average\nor FIFO methods are used.\nA second factor is the amount of inventory on hand at the beginning or end of an\naccounting period. The smaller the amount of production held in beginning or ending inventory\nrelative to the total number of units transferred out, the smaller the effect on operating income,\ncost of goods sold, or inventory amounts from the use of weighted-average or FIFO methods.\n\n17-2\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n1.\n\n## Direct materials cost per unit (\\$750,000 10,000)\n\nConversion cost per unit (\\$798,000 10,000)\nAssembly Department cost per unit\n\n\\$ 75.00\n79.80\n\\$154.80\n\n2a. Solution Exhibit 17-16A calculates the equivalent units of direct materials and conversion\ncosts in the Assembly Department of Nihon, Inc. in February 2012.\nSolution Exhibit 17-16B computes equivalent unit costs.\n2b. Direct materials cost per unit\nConversion cost per unit\nAssembly Department cost per unit\n\n\\$ 75\n84\n\\$159\n\n3. The difference in the Assembly Department cost per unit calculated in requirements 1 and\n2 arises because the costs incurred in January and February are the same but fewer equivalent\nunits of work are done in February relative to January. In January, all 10,000 units introduced are\nfully completed resulting in 10,000 equivalent units of work done with respect to direct materials\nand conversion costs. In February, of the 10,000 units introduced, 10,000 equivalent units of\nwork is done with respect to direct materials but only 9,500 equivalent units of work is done with\nrespect to conversion costs. The Assembly Department cost per unit is, therefore, higher.\nSOLUTION EXHIBIT 17-16A\nSteps 1 and 2: Summarize Output in Physical Units and Compute Output in Equivalent Units;\nAssembly Department of Nihon, Inc. for February 2012.\n(Step 1)\nPhysical\nUnits\n0\n10,000\n10,000\n\nFlow of Production\nWork in process, beginning (given)\nStarted during current period (given)\nTo account for\nCompleted and transferred out\nduring current period\nWork in process, ending* (given)\n1,000 100%; 1,000 50%\nAccounted for\nEquivalent units of work done in current period\n\n9,000\n1,000\n\n(Step 2)\nEquivalent Units\nDirect\nConversion\nMaterials\nCosts\n\n9,000\n1,000\n\n9,000\n500\n\n10,000\n10,000\n\n9,500\n\n*Degree of completion in this department: direct materials, 100%; conversion costs, 50%.\n\n17-3\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n## SOLUTION EXHIBIT 17-16B\n\nCompute Cost per Equivalent Unit,\nAssembly Department of Nihon, Inc. for February 2012.\n\n## (Step 3) Costs added during February\n\nDivide by equivalent units of work done\nin current period (Solution Exhibit 17-l6A)\nCost per equivalent unit\n\nTotal\nProduction\nDirect\nConversion\nCosts\nMaterials\nCosts\n\\$1,548,000\n\\$750,000\n\\$798,000\n\n10,000\n75\n\\$\n\n9,500\n84\n\n## 17-17 (20 min.) Journal entries (continuation of 17-16).\n\n1.\n\n2.\n\n3.\n\nWork in ProcessAssembly\nAccounts Payable\nTo record \\$750,000 of direct materials\npurchased and used in production during\nFebruary 2012\nWork in ProcessAssembly\nVarious accounts\nTo record \\$798,000 of conversion costs\nfor February 2012; examples include energy,\nmanufacturing supplies, all manufacturing\nlabor, and plant depreciation\nWork in ProcessTesting\nWork in ProcessAssembly\nTo record 9,000 units completed and\ntransferred from Assembly to Testing\nduring February 2012 at\n\\$159 9,000 units = \\$1,431,000\n\n750,000\n750,000\n\n798,000\n798,000\n\n1,431,000\n1,431,000\n\n## Postings to the Work in ProcessAssembly account follow.\n\nWork in Process Assembly Department\nBeginning inventory, Feb. 1\n0\n3. Transferred out to\n1. Direct materials\n750,000\nWork in ProcessTesting\n2. Conversion costs\n798,000\nEnding inventory, Feb. 29\n117,000\n\n1,431,000\n\n17-4\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n17-18 (25 min.) Zero beginning inventory, materials introduced in middle of process.\n1.\nSolution Exhibit 17-18A shows equivalent units of work done in the current period of\nChemical P, 50,000; Chemical Q, 35,000; Conversion costs, 45,000.\n2.\nSolution Exhibit 17-18B summarizes the total Mixing Department costs for July 2012,\ncalculates cost per equivalent unit of work done in the current period for Chemical P, Chemical\nQ, and Conversion costs, and assigns these costs to units completed (and transferred out) and to\nunits in ending work in process.\nSOLUTION EXHIBIT 17-18A\nSteps 1 and 2: Summarize Output in Physical Units and Compute Output in Equivalent Units;\nMixing Department of Roary Chemicals for July 2012.\n(Step 1)\n\nFlow of Production\nWork in process, beginning (given)\nStarted during current period (given)\nTo account for\nCompleted and transferred out\nduring current period\nWork in process, ending* (given)\n15,000 100%; 15,000 0%;\n15,000 66 2/3%\nAccounted for\nEquivalent units of work done\nin current period\n\n(Step 2)\nEquivalent Units\n\nPhysical\nUnits\nChemical P\n0\n50,000\n50,000\n35,000\n15,000\n\n35,000\n\n15,000\n\nChemical Q\n\nConversion\nCosts\n\n35,000\n\n35,000\n\n10,000\n\n50,000\n50,000\n\n35,000\n\n45,000\n\n*Degree of completion in this department: Chemical P, 100%; Chemical Q, 0%; conversion costs, 66 2/3%.\n\n17-5\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n## SOLUTION EXHIBIT 17-18B\n\nSteps 3, 4, and 5: Summarize Total Costs to Account For, Compute Cost per Equivalent Unit,\nand Assign Total Costs to Units Completed and to Units in Ending Work in Process;\nMixing Department of Roary Chemicals for July 2012.\nTotal\nProduction\nCosts\n(Step 3) Costs added during July\nTotal costs to account for\n\n\\$455,000\n\\$455,000\n\n## (Step 4) Costs added in current period\n\nDivide by equivalent units of work\ndone in current period\n(Solution Exhibit 17-l8A)\nCost per equivalent unit\n(Step 5) Assignment of costs:\nCompleted and transferred out\n(35,000 units)\nWork in process, ending\n(15,000 units)\nTotal costs accounted for\n\nChemical P\n\nChemical Q\n\nConversion\nCosts\n\n\\$250,000\n\\$250,000\n\n\\$70,000\n\\$70,000\n\n\\$135,000\n\\$135,000\n\n\\$250,000\n\n\\$70,000\n\n\\$135,000\n\n\\$350,000 (35,000*\n\n50,000\n5\n\n\\$5)\n\n+ (35,000*\n\n## 105,000 (15,000 \\$5) +\n\n\\$250,000\n+\n\\$455,000\n\n35,000\n2\n\n(0 \\$2)\n\\$70,000\n\n45,000\n3\n\n\\$2) + (35,000*\n\n\\$3)\n\n+ (10,000 \\$3)\n+\n\\$135,000\n\n*Equivalent units completed and transferred out from Solution Exhibit 17-18A, Step 2.\n\nEquivalent units in ending work in process from Solution Exhibit 17-18A, Step 2.\n\n## 17-19 (15 min.) Weighted-average method, equivalent units.\n\nUnder the weighted-average method, equivalent units are calculated as the equivalent units of\nwork done to date. Solution Exhibit 17-19 shows equivalent units of work done to date for the\nAssembly Division of Fenton Watches, Inc., for direct materials and conversion costs.\nSOLUTION EXHIBIT 17-19\nSteps 1 and 2: Summarize Output in Physical Units and Compute Output in Equivalent Units;\nWeighted-Average Method of Process Costing, Assembly Division of Fenton Watches, Inc., for\nMay 2012.\n(Step 2)\n(Step 1)\nEquivalent Units\nPhysical\nDirect Conversion\nFlow of Production\nUnits\nMaterials\nCosts\nWork in process beginning (given)\n80\nStarted during current period (given)\n500\nTo account for\n580\nCompleted and transferred out during current period\n460\n460\n460\nWork in process, ending* (120 60%; 120 30%)\n120\n72\n36\nAccounted for\n580\n___\n___\nEquivalent units of work done to date\n532\n496\n*Degree of completion in this department: direct materials, 60%; conversion costs, 30%.\n\n17-6\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n## 17-20 (20 min.) Weighted-average method, assigning costs (continuation of 17-19).\n\nSolution Exhibit 17-20 summarizes total costs to account for, calculates cost per equivalent unit\nof work done to date in the Assembly Division of Fenton Watches, Inc., and assigns costs to\nunits completed and to units in ending work-in-process inventory.\nSOLUTION EXHIBIT 17-20\nSteps 3, 4, and 5: Summarize Total Costs to Account For, Compute Cost per Equivalent Unit,\nand Assign Total Costs to Units Completed and to Units in Ending Work in Process;\nWeighted-Average Method of Process Costing, Assembly Division of Fenton Watches, Inc., for\nMay 2012.\nTotal\nProduction\nCosts\n\\$ 584,400\n4,612,000\n\\$5,196,400\n\n(Step 3)\n\n## Work in process, beginning (given)\n\nCosts added in current period (given)\nTotal costs to account for\n\n(Step 4)\n\n## Costs incurred to date\n\nDivide by equivalent units of work done to date\n(Solution Exhibit 17-19)\nCost per equivalent unit of work done to date\n\n(Step 5)\n\nAssignment of costs:\nCompleted and transferred out (460 units)\nWork in process, ending (120 units)\nTotal costs accounted for\n\nDirect\nMaterials\n\\$ 493,360\n3,220,000\n\\$3,713,360\n\nConversion\nCosts\n\\$ 91,040\n1,392,000\n\\$1,483,040\n\n\\$3,713,360\n\n\\$1,483,040\n\n\\$4,586,200\n610,200\n\\$5,196,400\n\n532\n6,980\n\n496\n2,990\n\n## (460* \\$6,980) + (460* \\$2,990)\n\n(72 \\$6,980) + (36 \\$2,990)\n\\$3,713,360 +\n\\$1,483,040\n\nEquivalent units completed and transferred out from Solution Exhibit 17-19, Step 2.\nEquivalent units in work in process, ending from Solution Exhibit 17-19, Step 2.\n\n17-7\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n## 17-21 (15 min.) FIFO method, equivalent units.\n\nUnder the FIFO method, equivalent units are calculated as the equivalent units of work done in\nthe current period only. Solution Exhibit 17-21 shows equivalent units of work done in May\n2012 in the Assembly Division of Fenton Watches, Inc., for direct materials and conversion\ncosts.\nSOLUTION EXHIBIT 17-21\nSteps 1 and 2: Summarize Output in Physical Units and Compute Output in Equivalent Units;\nFIFO Method of Process Costing, Assembly Division of Fenton Watches, Inc., for May 2012.\n\nFlow of Production\nWork in process, beginning (given)\nStarted during current period (given)\nTo account for\nCompleted and transferred out during current\nperiod:\nFrom beginning work in process\n80 (100% 90%); 80 (100% 40%)\nStarted and completed\n380 100%, 380 100%\nWork in process, ending* (given)\n120 60%; 120 30%\nAccounted for\nEquivalent units of work done in current period\n\n(Step 1)\nPhysical\nUnits\n80\n500\n580\n\n(Step 2)\nEquivalent Units\nDirect\nConversion\nMaterials\nCosts\n(work done before current period)\n\n80\n380\n\n120\n___\n580\n\n48\n\n380\n\n380\n\n72\n\n36\n\n460\n\n464\n\nDegree of completion in this department: direct materials, 90%; conversion costs, 40%.\n460 physical units completed and transferred out minus 80 physical units completed and transferred out from\nbeginning work-in-process inventory.\n*Degree of completion in this department: direct materials, 60%; conversion costs, 30%.\n\n17-8\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n## 17-22 (20 min.) FIFO method, assigning costs (continuation of 17-21).\n\nSolution Exhibit 17-22 summarizes total costs to account for, calculates cost per equivalent unit\nof work done in May 2012 in the Assembly Division of Fenton Watches, Inc., and assigns total\ncosts to units completed and to units in ending work-in-process inventory.\nSOLUTION EXHIBIT 17-22\nSteps 3, 4, and 5: Summarize Total Costs to Account For, Compute Cost per Equivalent Unit,\nand Assign Total Costs to Units Completed and to Units in Ending Work in Process;\nFIFO Method of Process Costing, Assembly Division of Fenton Watches, Inc., for May 2012.\nTotal\nProduction\nCosts\n\\$ 584,400\n4,612,000\n\\$5,196,400\n\n## (Step 3) Work in process, beginning (given)\n\nCosts added in current period (given)\nTotal costs to account for\n(Step 4) Costs added in current period\nDivide by equivalent units of work done in\ncurrent period (Solution Exhibit 17-21)\nCost per equiv. unit of work done in current period\n(Step 5) Assignment of costs:\nCompleted and transferred out (460 units):\nWork in process, beginning (80 units)\nCosts added to beginning work in process\nin current period\nTotal from beginning inventory\nStarted and completed (380 units)\nTotal costs of units completed and\ntransferred out\nWork in process, ending (120 units)\nTotal costs accounted for\n\n\\$ 584,400\n\nDirect\nMaterials\n\\$ 493,360\n3,220,000\n\\$3,713,360\n\nConversion\nCosts\n\\$ 91,040\n1,392,000\n\\$1,483,040\n\n\\$3,220,000\n460\n\n\\$1,392,000\n464\n\n7,000\n\n\\$493,360\n\n3,000\n\n\\$91,040\n\n## 200,000 (8* \\$7,000) + (48* \\$3,000)\n\n784,400\n3,800,000 (380 \\$7,000) + (380 \\$3,000)\n4,584,400\n612,000 (72# \\$7,000) + (36# \\$3,000)\n\\$5,196,400\n\\$3,713,360 +\n\\$1,483,040\n\nEquivalent units used to complete beginning work in process from Solution Exhibit 17-21, Step 2.\nEquivalent units started and completed from Solution Exhibit 17-21, Step 2.\n#\nEquivalent units in work in process, ending from Solution Exhibit 17-21, Step 2.\n\n17-9\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n## 17-23 (20-25 min.) Operation costing.\n\n1. To obtain the conversion-cost rates, divide the budgeted cost of each operation by the number\nof packages that are expected to go through that operation.\n\nMixing\nShaping\nCutting\nBaking\nSlicing\nPackaging\n\nBudgeted\nConversion\nCost\n\\$ 9,040\n1,625\n720\n7,345\n650\n8,475\n\nBudgeted\nnumber of\npackages\n11,300\n6,500\n4,800\n11,300\n6,500\n11,300\n\nConversion\nCost per\nPackage\n\\$0.80\n0.25\n0.15\n0.65\n0.10\n0.75\n\n2.\nWork Order\n#215\nDinner Roll\n1,200\n\\$ 660\n960\n0\n180\n780\n0\n900\n\\$3,480\n\nQuantity:\nDirect Materials\nMixing\nShaping\nCutting\nBaking\nSlicing\nPackaging\nTotal\n\nWork Order\n#216\nMultigrain Loaves\n1,400\n\\$1,260\n1,120\n350\n0\n910\n140\n1,050\n\\$4,830\n\nThe direct materials costs per unit vary based on the type of bread (\\$2,640 4,800 = \\$0.55 for\nthe dinner rolls, and \\$5,850 6,500 = \\$0.90 for the multi-grain loaves). Conversion costs are\ncharged using the rates computed in part (1), taking into account the specific operations that each\ntype of bread actually goes through.\n3.\n\n## Work order #216 (Mulit-grain loaves):\n\nTotal cost\nDivided by number of\npackages:\nCost per package\nof dinner rolls:\n\nTotal cost:\nDivided by number of\npackages:\nCost per package\nof multigrain loaves:\n\n\\$3,480\n1,200\n\\$ 2.90\n\n\\$4,830\n1,400\n\\$ 3.45\n\n17-10\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n## 17-24 (25 min.) Weighted-average method, assigning costs.\n\n1. & 2.\nSolution Exhibit 17-24A shows equivalent units of work done to date for Bio Doc Corporation\nfor direct materials and conversion costs.\n\nSolution Exhibit 17-24B summarizes total costs to account for, calculates the cost per equivalent\nunit of work done to date for direct materials and conversion costs, and assigns these costs to\nunits completed and transferred out and to units in ending work-in-process inventory.\n\n## SOLUTION EXHIBIT 17-24A\n\nSteps 1 and 2: Summarize Output in Physical Units and Compute Output in Equivalent Units;\nWeighted-Average Method of Process Costing, Bio Doc Corporation for July 2011.\n\nFlow of Production\nWork in process, beginning (given)\nStarted during current period (given)\nTo account for\nCompleted and transferred out\nduring current period\nWork in process, ending* (given)\n10,500 100%; 10,500 60%\nAccounted for\nEquivalent units of work done to date\n\n(Step 1)\nPhysical\nUnits\n8,500\n35,000\n43,500\n33,000\n10,500\n\n(Step 2)\nEquivalent Units\nDirect\nConversion\nMaterials\nCosts\n\n33,000\n\n33,000\n\n10,500\n\n6,300\n\n43,500\n\n39,300\n\n43,500\n\n## *Degree of completion: direct materials, 100%; conversion costs, 60%.\n\n17-11\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n## SOLUTION EXHIBIT 17-24B\n\nSteps 3, 4, and 5: Summarize Total Costs to Account For, Compute Cost per Equivalent Unit,\nand Assign Total Costs to Units Completed and to Units in Ending Work in Process;\nWeighted-Average Method of Process Costing, Bio Doc Corporation for July 2011.\nTotal\nProduction\nCosts\n\\$108,610\n769,940\n\\$878,550\n\n(Step 3)\n\n## Work in process, beginning (given)\n\nCosts added in current period (given)\nTotal costs to account for\n\n(Step 4)\n\n## Costs incurred to date\n\nDivide by equivalent units of work done to\ndate (Solution Exhibit 17-24A)\nCost per equivalent unit of work done to date\n\n(Step 5)\n\nAssignment of costs:\nCompleted and transferred out (33,000 units)\nWork in process, ending (10,500 units)\nTotal costs accounted for\n\nDirect\nMaterials\n\\$ 63,100\n284,900\n\\$348,000\n\nConversion\nCosts\n\\$ 45,510\n485,040\n\\$530,550\n\n\\$348,000\n\n\\$530,550\n\n\\$709,500\n169,050\n\\$878,550\n\n43,500\n8.00\n\n39,300\n13.50\n\n## (33,000* \\$8.00) + (33,000* \\$13.50)\n\n(10,500 \\$8.00) + (6,300 \\$13.50)\n\\$348,000\n+\n\\$530,550\n\n## Equivalent units in ending work in process (given).\n\n17-12\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n## 17-25 (30 min.) FIFO method, assigning costs.\n\n1. & 2. Solution Exhibit 17-25A calculates the equivalent units of work done in the current\nperiod. Solution Exhibit 17-25B summarizes total costs to account for, calculates the cost per\nequivalent unit of work done in the current period for direct materials and conversion costs, and\nassigns these costs to units completed and transferred out and to units in ending work-in-process\ninventory.\nSOLUTION EXHIBIT 17-25A\nSteps 1 and 2: Summarize Output in Physical Units and Compute Output in Equivalent Units;\nFIFO Method of Process Costing, Bio Doc Corporation for July 2011.\n(Step 2)\nEquivalent Units\nDirect\nConversion\nMaterials\nCosts\n8,500(work done before current period)\n\n(Step 1)\nPhysical\nUnits\n\nFlow of Production\n\n## Work in process, beginning (given)\n\nStarted during current period (given)\nTo account for\nCompleted and transferred out during current period:\nFrom beginning work in process\n8,500 (100% 100%); 8,500 (100% 20%)\nStarted and completed\n24,500 100%, 24,500 100%\nWork in process, ending* (given)\n10,500 100%; 10,500 60%\nAccounted for\nEquivalent units of work done in current period\n\n35,000\n43,500\n\n6,800\n\n24,500\n\n24,500\n\n24,500\n\n10,500\n43,500\n\n10,500\n\n6,300\n\n35,000\n\n37,600\n\n8,500\n\nDegree of completion in this department: direct materials, 100%; conversion costs, 20%.\n33,000 physical units completed and transferred out minus 8,500 physical units completed and transferred out from\nbeginning work-in-process inventory.\n*Degree of completion in this department: direct materials, 100%; conversion costs, 60%.\n\n17-13\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n## SOLUTION EXHIBIT 17-25B\n\nSteps 3, 4, and 5: Summarize Total Costs to Account For, Compute Cost per Equivalent Unit, and Assign Total Costs to Units\nCompleted and to Units in Ending Work in Process;\nFIFO Method of Process Costing, Bio Doc Corporation for July 2011.\n\n## (Step 3) Work in process, beginning (given)\n\nCosts added in current period (given)\nTotal costs to account for\n\nTotal\nProduction\nCosts\n\\$108,610\n769,940\n\nDirect\nMaterials\n\\$ 63,100\n284,900\n\nConversion\nCosts\n\\$ 45,510\n485,040\n\n\\$878,550\n\n\\$348,000\n\n\\$530,550\n\n\\$284,900\n\n\\$485,040\n\n35,000\n\n37,600\n\n## (Step 4) Costs added in current period\n\nDivide by equivalent units of work done in\ncurrent period (Solution Exhibit 17-25A)\nCost per equivalent unit of work done in current period\n(Step 5) Assignment of costs:\nCompleted and transferred out (33,000 units):\nWork in process, beginning (8,500 units)\nCost added to beginning work in process in current period\nTotal from beginning inventory\nStarted and completed (24,500 units)\nTotal costs of units completed and transferred out\nWork in process, ending (10,500 units)\nTotal costs accounted for\n\n8.14\n\n12.90\n\n\\$108,610\n\\$63,100\n+\n\\$45,510\n*\n87,720 (0 \\$8.14)\n+ (6,800* \\$12.90)\n196,330\n515,480 (24,500 \\$8.14) + (24,500 \\$12.90)\n711,810\n166,740 (10,500# \\$8.14) + (6,300# \\$12.90)\n\\$878,550\n\\$348,000\n+ \\$530,550\n\n*Equivalent units used to complete beginning work in process from Solution Exhibit 17-25A, Step 2.\n\nEquivalent units started and completed from Solution Exhibit 17-25A, Step 2.\n#\nEquivalent units in ending work in process from Solution Exhibit 17-25A, Step 2.\n\n17-14\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n## 17-26 (30 min.) Standard-costing method, assigning costs.\n\n1.\nThe calculations of equivalent units for direct materials and conversion costs are identical\nto the calculations of equivalent units under the FIFO method. Solution Exhibit 17-25A shows\nthe equivalent unit calculations for standard costing and computes the equivalent units of work\ndone in July 2011. Solution Exhibit 17-26 uses the standard costs (direct materials, \\$8.25;\nconversion costs, \\$12.70) to summarize total costs to account for, and to assign these costs to\nunits completed and transferred out and to units in ending work-in-process inventory.\n2.\n\nSolution Exhibit 17-26 shows the direct materials and conversion costs variances for\nDirect materials\nConversion costs\n\n\\$3,850 F\n\\$7,520 U\n\n## SOLUTION EXHIBIT 17-26\n\nSteps 3, 4, and 5: Summarize Total Costs to Account For, Compute Cost per Equivalent Unit,\nand Assign Total Costs to Units Completed and to Units in Ending Work in Process;\nStandard Costing Method of Process Costing, Bio Doc Corporation for July 2011.\n\n## (Step 3) Work in process, beginning\n\nCosts added in current period at standard costs\nTotal costs to account for\n(Step 4) Standard cost per equivalent unit (given)\n(Step 5) Assignment of costs at standard costs:\nCompleted and transferred out (33,000 units):\nWork in process, beginning (8,500 units)\nCosts added to beg. work in process in current period\nTotal from beginning inventory\nStarted and completed (24,500 units)\nTotal costs of units transferred out\nWork in process, ending (10,500 units)\nTotal costs accounted for\nSummary of variances for current performance:\nCosts added in current period at standard costs (see Step 3 above)\nActual costs incurred (given)\nVariance\n\nTotal\nProduction\nDirect\nConversion\nCosts\nMaterials\nCosts\n\\$ 91,715 (8,500 \\$8.25) + (1,700 \\$12.70)\n766,270 (35,000 \\$8.25) + (37,600 \\$12.70)\n\\$857,985\n\\$358,875\n+\n\\$499,110\n\\$ 8.25\n\n\\$ 12.70\n\n## \\$91,715 (8,500 \\$8.25) + (1,700 \\$12.70)\n\n86,360\n(0* \\$8.25) + (6,800* \\$12.70)\n178,075\n513,275 (24,500 \\$8.25) + (24,500 \\$12.70)\n691,350\n166,635 (10,500# \\$8.25) + (6,300# \\$12.70)\n\\$857,985\n\\$358,875\n+\n\\$499,110\n\\$288,750\n284,900\n\\$ 3,850 F\n\n*Equivalent units to complete beginning work in process from Solution Exhibit 17-25A, Step 2.\n\nEquivalent units started and completed from Solution Exhibit 17-25A, Step 2.\n#\nEquivalent units in ending work in process from Solution Exhibit 17-25A, Step 2.\n\n17-15\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n\\$477,520\n485,040\n\\$ 7,520 U\n\n## 17-27 (3540 min.) Transferred-in costs, weighted-average method.\n\n1, 2. & 3. Solution Exhibit 17-27A calculates the equivalent units of work done to date.\nSolution Exhibit 17-27B summarizes total costs to account for, calculates the cost per equivalent\nunit of work done to date for transferred-in costs, direct materials, and conversion costs, and\nassigns these costs to units completed and transferred out and to units in ending work-in-process\ninventory.\nSOLUTION EXHIBIT 17-27A\nSteps 1 and 2: Summarize Output in Physical Units and Compute Output in Equivalent Units\nWeighted-Average Method of Process Costing;\nFinishing Department of Asaya Clothing for June 2012.\n(Step 1)\n\nFlow of Production\n\n## Work in process, beginning (given)\n\nTransferred in during current period (given)\nTo account for\nCompleted and transferred out\nduring current period\nWork in process, ending* (given)\n60 100%; 60 0%; 60 75%\nAccounted for\nEquivalent units of work done to date\n\nPhysical\nUnits\n\n(Step 2)\nEquivalent Units\nTransferredDirect\nConversion\nin Costs\nMaterials\nCosts\n\n75\n135\n210\n150\n60\n\n150\n\n150\n\n150\n\n60\n\n45\n\n210\n\n150\n\n195\n\n210\n\n*Degree of completion in this department: transferred-in costs, 100%; direct materials, 0%; conversion costs, 75%.\n\n17-16\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n## SOLUTION EXHIBIT 17-27B\n\nSteps 3, 4, and 5: Summarize Total Costs to Account For, Compute Cost per Equivalent Unit, and Assign Total Costs to Units\nCompleted and to Units in Ending Work in Process;\nWeighted-Average Method of Process Costing,\nFinishing Department of Asaya Clothing for June 2012.\n\n(Step 3)\n\n## Work in process, beginning (given)\n\nCosts added in current period (given)\nTotal costs to account for\n\n(Step 4)\n\n## Costs incurred to date\n\nDivide by equivalent units of work done to date\n(Solution Exhibit 17-27A)\nCost per equivalent unit of work done to date\n\n(Step 5)\n\na\nb\n\nAssignment of costs:\nCompleted and transferred out (150 units)\nWork in process, ending (60 units):\nTotal costs accounted for\n\nTotal\nProduction\nCosts\n\\$105,000\n258,000\n\\$363,000\n\n\\$275,934\n87,066\n\\$363,000\n\nTransferred-in\nCosts\n\\$ 75,000\n142,500\n\\$ 217,500\n\nDirect\nMaterials\n\\$\n0\n37,500\n\\$37,500\n\nConversion\nCosts\n\\$ 30,000\n78,000\n\\$108,000\n\n\\$ 217,500\n\n\\$37,500\n\n\\$108,000\n\n210\n\\$1,035.71\n\n195\n\\$ 553.85\n\n150\n250\n\n## (150 a \\$1,035.71) + (150 a \\$250) + (150a \\$553.85)\n\n(60b \\$1,035.71) + (0b \\$250) + (45b \\$553.85)\n\n\\$ 217,500\n\n\\$37,500\n\nEquivalent units completed and transferred out from Sol. Exhibit 17-27, step 2.\nEquivalent units in ending work in process from Sol. Exhibit 17-27A, step 2.\n\n17-17\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n\\$108,000\n\n## 17-28 (3540 min.) Transferred-in costs, FIFO method.\n\nSolution Exhibit 17-28A calculates the equivalent units of work done in the current period (for\ntransferred-in costs, direct-materials, and conversion costs) to complete beginning work-inprocess inventory, to start and complete new units, and to produce ending work in process.\nSolution Exhibit 17-28B summarizes total costs to account for, calculates the cost per equivalent\nunit of work done in the current period for transferred-in costs, direct materials, and conversion\ncosts, and assigns these costs to units completed and transferred out and to units in ending workin-process inventory.\nSOLUTION EXHIBIT 17-28A\nSteps 1 and 2: Summarize Output in Physical Units and Compute Output in Equivalent Units\nFIFO Method of Process Costing;\nFinishing Department of Asaya Clothing for June 2012.\n\n(Step 1)\n\nFlow of Production\nWork in process, beginning (given)\nTransferred-in during current period (given)\nTo account for\nCompleted and transferred out during current period:\nFrom beginning work in processa\n[75 (100% 100%); 75 (100% 0%); 75 (100% 60%)]\nStarted and completed\n(75 100%; 75 100%; 75 100%)\nWork in process, endingc (given)\n(60\n100%; 60\n0%; 60\n75%)\nAccounted for\nEquivalent units of work done in current period\n\n(Step 2)\nEquivalent Units\n\nPhysical Transferred-in\nDirect\nConversion\nUnits\nCosts\nMaterials\nCosts\n75\n(work done before current period)\n135\n210\n75\n0\n\n75\n\n30\n\n75\n\n75\n\n75\n\n60\n___\n135\n\n0\n___\n150\n\n45\n___\n150\n\n75b\n60\n___\n210\n\nDegree of completion in this department: Transferred-in costs, 100%; direct materials, 0%; conversion costs, 60%.\n150 physical units completed and transferred out minus 75 physical units completed and transferred out from beginning\n\nwork-in-process inventory.\nDegree of completion in this department: transferred-in costs, 100%; direct materials, 0%; conversion costs, 75%.\n\n17-18\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n## SOLUTION EXHIBIT 17-28B\n\nSteps 3, 4, and 5: Summarize Total Costs to Account For, Compute Cost per Equivalent Unit, and Assign Total Costs to Units\nCompleted and to Units in Ending Work in Process;\nFIFO Method of Process Costing,\nFinishing Department of Asaya Clothing for June 2012.\n\n(Step 3)\n\n## Work in process, beginning (given)\n\nCosts added in current period (given)\nTotal costs to account for\n\n(Step 4)\n\n## Costs added in current period\n\nDivide by equivalent units of work done in current period\n(Solution Exhibit 17-28A)\nCost per equivalent unit of work done in current period\n\n(Step 5)\n\nTotal\nProduction\nCosts\n\\$ 90,000\n246,300\n\\$336,300\n\nAssignment of costs:\nCompleted and transferred out (150 units)\nWork in process, beginning (75 units)\nCosts added to beginning work in process in current period\nTotal from beginning inventory\nStarted and completed (75 units)\nTotal costs of units completed and transferred out\nWork in process, ending (60 units):\nTotal costs accounted for\n\n\\$ 90,000\n34,350\n124,350\n130,416\n254,766\n81,534\n\\$336,300\n\nTransferred-in\nCosts\nDirect Materials Conversion Costs\n\\$ 60,000\n\\$\n0\n\\$ 30,000\n130,800\n37,500\n78,000\n\\$190,800\n\\$37,500\n\\$108,000\n\n(0a\n(75b\n(60c\n\n\\$130,800\n\n\\$37,500\n\n\\$ 78,000\n\n135\n\\$ 968.89\n\n\\$ 60,000\n\\$968.89)\n\n150\n250\n\n\\$\n0\n+ (75a \\$250)\n\n\\$968.89) + (75b\n\n\\$250)\n\n## \\$968.89) + (0c \\$250)\n\n\\$190,800 +\n\\$37,500\n\nEquivalent units used to complete beginning work in process from Solution Exhibit 17-28A, step 2.\nEquivalent units started and completed from Solution Exhibit 17-28A, step 2.\nc\nEquivalent units in ending work in process from Solution Exhibit 17-28A, step 2.\nb\n\n17-19\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n150\n520\n\n\\$ 30,000\n+ (30 a \\$520)\n+ (75b\n\n\\$520)\n\n+ (45c \\$520)\n+ \\$108,000\n\n1.\n\n## Vitamin A Vitamin B Multi-vitamin\n\nBudgeted 200-unit bottles\n12,000\n9,000\n18,000\na\nBudgeted labor hours\n300\n225\n450\nb\nBudgeted machine hours\n200\n150\n300\na\n12,000 1.5 minutes 60 minutes/hour = 300 hours\nb\n12,000 1 minute 60 minutes/hour = 200 hours\n\nMixing\nTableting\nEncapsulating\nBottling\n2.\n\nBudgeted\nConversion\nCost\n\\$ 8,190\n24,150\n25,200\n3,510\n\nCost Driver\nLabor hours\nNumber of bottles\nNumber of bottles\nMachine hours\n\nBudgeted\nQuantity of\nCost Driver\n975\n21,000\n18,000\n650\n\n## Conversion Cost Rate\n\n\\$8.40 per labor hour\n1.15 per bottle\n1.40 per bottle\n5.40 per machine hour\n\n## Budgeted cost of goods manufactured:\n\nVitamin A\nVitamin B\nDirect Materials\n\\$23,040\n\\$21,600\nc\n2,520\n1,890\nMixing\nd\n13,800\n10,350\nTableting\n0\n0\nEncapsulating\ne\n1,080\n810\nBottling\nTotal\n\\$40,440\n\\$34,650\nc\n\\$8.40 per labor hour 300 labor hours = \\$2,520\nd\n\\$1.15 per bottle 12,000 bottles = \\$13,800\ne\n\\$5.40 per machine hour 200 machine hours = \\$1,080\n\n3.\n\nTotal\n39,000\n975\n650\n\nMulti-vitamin\n\\$47,520\n3,780\n0\n25,200\n1,620\n\\$78,120\n\n## Total budgeted costs\n\nNumber of bottles\nBudgeted cost per bottle\n\nVitamin A\n\\$40,440\n12,000\n\\$ 3.37\n\nVitamin B\n\\$34,650\n9,000\n\\$ 3.85\n\nMulti-vitamin\n\\$78,120\n18,000\n\\$ 4.34\n\n17-20\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n## 17-30 (25 min.) Weighted-average method.\n\n1.\nSince direct materials are added at the beginning of the assembly process, the units in this\ndepartment must be 100% complete with respect to direct materials. Solution Exhibit 17-30A\nshows equivalent units of work done to date:\nDirect materials\nConversion costs\n\n## 25,000 equivalent units\n\n24,250 equivalent units\n\n2. & 3. Solution Exhibit 17-30B summarizes the total Assembly Department costs for October\n2012, calculates cost per equivalent unit of work done to date, and assigns these costs to units\ncompleted (and transferred out) and to units in ending work in process using the weightedaverage method.\nSOLUTION EXHIBIT 17-30A\nSteps 1 and 2: Summarize Output in Physical Units and Compute Output in Equivalent Units;\nWeighted-Average Method of Process Costing, Assembly Department of Larsen Company, for\nOctober 2012.\n(Step 1)\n\nFlow of Production\nWork in process, beginning (given)\nStarted during current period (given)\nTo account for\nCompleted and transferred out\nduring current period\nWork in process, ending* (given)\n2,500 100%; 2,500 70%\nAccounted for\nEquivalent units of work done to date\n\nPhysical\nUnits\n5,000\n20,000\n25,000\n22,500\n2,500\n\n(Step 2)\nEquivalent Units\nDirect\nConversion\nMaterials\nCosts\n\n22,500\n\n22,500\n\n2,500\n\n1,750\n\n25,000\n\n24,250\n\n25,000\n\n*Degree of completion in this department: direct materials, 100% (since they are added at the start of the process);\nconversion costs, 70%.\n\n17-21\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n## SOLUTION EXHIBIT 17-30B\n\nSteps 3, 4, and 5: Summarize Total Costs to Account For, Compute Cost per Equivalent Unit,\nand Assign Total Costs to Units Completed and to Units in Ending Work in Process;\nWeighted-Average Method of Process Costing, Assembly Department of Larsen Company,\nfor October 2012.\nTotal\nProduction\nCosts\n\\$1,652,750\n6,837,500\n\\$8,490,250\n\n(Step 3)\n\n## Work in process, beginning (given)\n\nCosts added in current period (given)\nTotal costs to account for\n\n(Step 4)\n\n## Costs incurred to date\n\nDivide by equivalent units of work done to date\n(Solution Exhibit 17-30A)\nCost per equivalent unit of work done to date\n\n(Step 5)\n\nAssignment of costs:\nCompleted and transferred out (22,500 units)\nWork in process, ending (2,500 units)\nTotal costs accounted for\n\nDirect\nMaterials\n\\$1,250,000\n4,500,000\n\\$5,750,000\n\nConversion\nCosts\n\\$ 402,750\n2,337,500\n\\$2,740,250\n\n\\$5,750,000\n\n\\$2,740,250\n\n25,000\n230\n\n24,250\n113\n\n## \\$7,717,500 (22,500* \\$230) + (22,500* \\$113)\n\n772,750 (2,500 \\$230) + (1,750 \\$113)\n\\$8,490,250\n\\$5,750,000 +\n\\$2,740,250\n\nEquivalent units completed and transferred out from Solution Exhibit 17-30A, Step 2.\nEquivalent units in work in process, ending from Solution Exhibit 17-30A, Step 2.\n\n1.\n\n2.\n\n3.\n\n## Work in ProcessAssembly Department\n\nAccounts Payable\nDirect materials purchased and used in\nproduction in October.\n\n4,500,000\n\n## Work in ProcessAssembly Department\n\nVarious accounts\nConversion costs incurred in October.\n\n2,337,500\n\n4,500,000\n\n## Work in ProcessTesting Department\n\n7,717,500\nWork in ProcessAssembly Department\nCost of goods completed and transferred out\nin October from the Assembly Department to the Testing Department.\nWork in ProcessAssembly Department\nBeginning inventory, October 1\n1,652,750 3. Transferred out to\n1. Direct materials\n4,500,000\nWork in ProcessTesting\n2. Conversion costs\n2,337,500\nEnding Inventory, October 31\n772,750\n\n2,337,500\n\n7,717,500\n\n7,717,500\n\n17-22\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n## 17-32 (20 min.) FIFO method (continuation of 17-30).\n\n1.\nThe equivalent units of work done in the current period in the Assembly Department in\nOctober 2012 for direct materials and conversion costs are shown in Solution Exhibit 17-32A.\n2.\nThe cost per equivalent unit of work done in the current period in the Assembly\nDepartment in October 2012 for direct materials and conversion costs is calculated in Solution\nExhibit 17-32B.\n3.\nSolution Exhibit 17-32B summarizes the total Assembly Department costs for October\n2012, and assigns these costs to units completed (and transferred out) and units in ending work in\nprocess under the FIFO method.\nThe cost per equivalent unit of beginning inventory and of work done in the current\nperiod differ:\n\nDirect materials\nConversion costs\nTotal cost per unit\n\nBeginning\nInventory\n\\$250.00 (\\$1,250,000 5,000 equiv. units)\n134.25 (\\$ 402,750 3,000 equiv. units)\n\\$384.25\nDirect\nMaterials\n\n## Cost per equivalent unit (weighted-average)\n\nCost per equivalent unit (FIFO)\n\n\\$230*\n\\$225**\n\nWork Done in\nCurrent Period\n\\$225.00\n110.00\n\\$335.00\nConversion\nCosts\n\\$113*\n\\$110**\n\n## from Solution Exhibit 17-30B\n\nfrom Solution Exhibit 17-32B\n\n**\n\nThe cost per equivalent unit differs between the two methods because each method uses different\ncosts as the numerator of the calculation. FIFO uses only the costs added during the current\nperiod whereas weighted-average uses the costs from the beginning work-in-process as well as\ncosts added during the current period. Both methods also use different equivalent units in the\ndenominator.\nThe following table summarizes the costs assigned to units completed and those still in\nprocess under the weighted-average and FIFO process-costing methods for our example.\nWeighted\nAverage\nFIFO\n(Solution\n(Solution\nExhibit 17-30B) Exhibit 17-32B) Difference\nCost of units completed and transferred out\n\\$7,717,500\n\\$7,735,250 + \\$17,750\nWork in process, ending\n772,750\n755,000\n\\$17,750\nTotal costs accounted for\n\\$8,490,250\n\\$8,490,250\n\n17-23\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\nThe FIFO ending inventory is lower than the weighted-average ending inventory by\n\\$17,750. This is because FIFO assumes that all the higher-cost prior-period units in work in\nprocess are the first to be completed and transferred out while ending work in process consists of\nonly the lower-cost current-period units. The weighted-average method, however, smoothes out\ncost per equivalent unit by assuming that more of the lower-cost units are completed and\ntransferred out, while some of the higher-cost units in beginning work in process are placed in\nending work in process. So, in this case, the weighted-average method results in a lower cost of\nunits completed and transferred out and a higher ending work-in-process inventory relative to the\nFIFO method.\nSOLUTION EXHIBIT 17-32A\nSteps 1 and 2: Summarize Output in Physical Units and Compute Output in Equivalent Units;\nFIFO Method of Process Costing,\nAssembly Department of Larsen Company for October 2012.\n(Step 1)\n\nFlow of Production\nWork in process, beginning (given)\nStarted during current period (given)\nTo account for\nCompleted and transferred out during current\nperiod:\nFrom beginning work in process\n5,000 (100% 100%); 5,000 (100% 60%)\nStarted and completed\n17,500 100%, 17,500 100%\nWork in process, ending* (given)\n2,500 100%; 2,500 70%\nAccounted for\nEquivalent units of work done in current period\n\n(Step 2)\nEquivalent Units\nDirect\nConversion\nMaterials\nCosts\n\nPhysical\nUnits\n5,000 (work done before current period)\n20,000\n25,000\n\n5,000\n\n2,000\n\n17,000\n2,500\n\n17,500\n\n17,500\n\n2,500\n\n1,750\n\n20,000\n\n______\n21,250\n\n25,000\n\nDegree of completion in this department: direct materials, 100%; conversion costs, 60%.\n22,500 physical units completed and transferred out minus 5,000 physical units completed and transferred out from\nbeginning work-in-process inventory.\n*Degree of completion in this department: direct materials, 100%; conversion costs, 70%.\n\n17-24\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n## SOLUTION EXHIBIT 17-32B\n\nSteps 3, 4, and 5: Summarize Total Costs to Account For, Compute Cost per Equivalent Unit, and Assign Total Costs to\nUnits Completed and to Units in Ending Work in Process;\nFIFO Method of Process Costing, Assembly Department of Larsen Company for October 2012.\nTotal\nProduction\nCosts\n\\$1,652,750\n6,837,500\n\\$8,490,250\n\n## (Step 3) Work in process, beginning (given)\n\nCosts added in current period (given)\nTotal costs to account for\n(Step 4) Costs added in current period\nDivide by equivalent units of work done in\ncurrent period (Solution Exhibit 17-32A)\nCost per equivalent unit of work done in current period\n\nDirect\nMaterials\n\\$1,250,000\n4,500,000\n\\$5,750,000\n\nConversion\nCosts\n\\$ 402,750\n2,337,500\n\\$2,740,250\n\n\\$4,500,000\n\n\\$2,337,500\n\n## (Step 5) Assignment of costs:\n\nCompleted and transferred out (22,500 units):\nWork in process, beginning (5,000 units)\nCosts added to beg. work in process in current period\nTotal from beginning inventory\nStarted and completed (17,500 units)\nTotal costs of units completed & transferred out\nWork in process, ending (2,500 units)\nTotal costs accounted for\n\n20,000\n225\n\n\\$1,652,750\n\\$1,250,000\n220,000\n(0* \\$225)\n1,872,750\n5,862,500 (17,500 \\$225)\n7,735,250\n755,000 (2,500# \\$225)\n\\$8,490,250\n\\$5,750,000\n\n21,250\n110\n\n+ \\$ 402,750\n+ (2,000* \\$110)\n+ (17,500 \\$110)\n+ (1,750# \\$110)\n+ \\$2,740,250\n\n*Equivalent units used to complete beginning work in process from Solution Exhibit 17-32A, Step 2.\n\nEquivalent units started and completed from Solution Exhibit 17-32A, Step 2.\n#\nEquivalent units in ending work in process from Solution Exhibit 17-32A, Step 2.\n\n17-25\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n17-33 (30 min.) Transferred-in costs, weighted-average method (related to 17-30 to 17-32).\n1.\nTransferred-in costs are 100% complete, and direct materials are 0% complete in both\nbeginning and ending work-in-process inventory. The reason is that transferred-in costs are\nalways 100% complete as soon as they are transferred in from the Assembly Department to the\nTesting Department. Direct materials in beginning or ending work in process for the Testing\nDepartment are 0% complete because direct materials are added only when the testing process is\n90% complete and the units in beginning and ending work in process are only 70% and 60%\ncomplete, respectively.\n2.\nSolution Exhibit 17-33A computes the equivalent units of work done to date in the\nTesting Department for transferred-in costs, direct materials, and conversion costs.\n3.\nSolution Exhibit 17-33B summarizes total Testing Department costs for October 2012,\ncalculates the cost per equivalent unit of work done to date in the Testing Department for\ntransferred-in costs, direct materials, and conversion costs, and assigns these costs to units\ncompleted and transferred out and to units in ending work in process using the weighted-average\nmethod.\n4.\n\nJournal entries:\na. Work in ProcessTesting Department\nWork in ProcessAssembly Department\nCost of goods completed and transferred out\nduring October from the Assembly\nDepartment to the Testing Department\nb. Finished Goods\nWork in ProcessTesting Department\nCost of goods completed and transferred out\nduring October from the Testing Department\nto Finished Goods inventory\n\n7,717,500\n7,717,500\n\n23,459,600\n23,459,600\n\n17-26\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n## SOLUTION EXHIBIT 17-33A\n\nSteps 1 and 2: Summarize Output in Physical Units and Compute Output in Equivalent Units;\nWeighted-Average Method of Process Costing,\nTesting Department of Larsen Company for October 2012.\n(Step 1)\nPhysical\nFlow of Production\nUnits\nWork in process, beginning (given)\n7,500\nTransferred in during current period (given) 22,500\nTo account for\n30,000\nCompleted and transferred out\nduring current period\n26,300\n26,300\nWork in process, ending* (given)\n3,700\n3,700 100%; 3,700 0%; 3,700 60%\n2,220\nAccounted for\n30,000\nEquivalent units of work done to date\n28,520\n\n(Step 2)\nEquivalent Units\nTransferred-in\nDirect\nConversion\nCosts\nMaterials\nCosts\n\n26,300\n\n26,300\n\n3,700\n\n30,000\n\n26,300\n\n*Degree of completion in this department: transferred-in costs, 100%; direct materials, 0%; conversion costs, 60%.\n\n17-27\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n## SOLUTION EXHIBIT 17-33B\n\nSteps 3, 4, and 5: Summarize Total Costs to Account For, Compute Cost per Equivalent Unit, and Assign Total Costs to Units Completed\nand to Units in Ending Work in Process;\nWeighted-Average Method of Process Costing,\nTesting Department of Larsen Company for October 2012.\n\n## (Step 3) Work in process, beginning (given)\n\nCosts added in current period (given)\nTotal costs to account for\n\nTotal\nProduction\nCosts\n\\$ 3,767,960\n21,378,100\n\\$25,146,060\n\n## (Step 4) Costs incurred to date\n\nDivide by equivalent units of work done to date\n(Solution Exhibit 17-33A)\nEquivalent unit costs of work done to date\n(Step 5) Assignment of costs:\nCompleted and transferred out (26,300 units)\nWork in process, ending (3,700 units)\nTotal costs accounted for\n\nTransferred\n-in Costs\n\\$ 2,932,500\n7,717,500\n\\$10,650,000\n\nDirect\nMaterials\n\\$\n0\n9,704,700\n\\$9,704,700\n\nConversion\nCosts\n\\$ 835,460\n3,955,900\n\\$4,791,360\n\n\\$10,650,000\n\n\\$9,704,700\n\n\\$4,791,360\n\n30,000\n355\n\n26,300\n369\n\n28,520\n168\n\n\\$23,459,600\n1,686,460\n\\$25,146,060\n\n## (26,300* \\$355) + (26,300* \\$369)\n\n(3,700 \\$355) + (0 \\$369)\n\\$10,650,000\n+ \\$9,704,700\n\n*Equivalent units completed and transferred out from Solution Exhibit 17-33A, Step 2.\n\nEquivalent units in ending work in process from Solution Exhibit 17-33A, Step 2.\n\n17-28\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n+ (26,300* \\$168)\n+ (2,220 \\$168)\n+\n\\$4,791,360\n\n## 17-34 (30 min.) Transferred-in costs, FIFO method (continuation of 17-33).\n\n1.\nAs explained in Problem 17-33, requirement 1, transferred-in costs are 100% complete\nand direct materials are 0% complete in both beginning and ending work-in-process inventory.\n2.\nThe equivalent units of work done in October 2012 in the Testing Department for\ntransferred-in costs, direct materials, and conversion costs are calculated in Solution Exhibit 1734A.\n3.\nSolution Exhibit 17-34B summarizes total Testing Department costs for October 2012,\ncalculates the cost per equivalent unit of work done in October 2012 in the Testing Department\nfor transferred-in costs, direct materials, and conversion costs, and assigns these costs to units\ncompleted and transferred out and to units in ending work in process using the FIFO method.\n4.\n\nJournal entries:\na. Work in ProcessTesting Department\nWork in ProcessAssembly Department\nCost of goods completed and transferred out\nduring October from the Assembly Dept. to\nthe Testing Dept.\nb. Finished Goods\nWork in ProcessTesting Department\nCost of goods completed and transferred out\nduring October from the Testing Department\nto Finished Goods inventory.\n\n7,735,250\n7,735,250\n\n23,463,766\n23,463,766\n\n17-29\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n## SOLUTION EXHIBIT 17-34A\n\nSteps 1 and 2: Summarize Output in Physical Units and Compute Output in Equivalent Units;\nFIFO Method of Process Costing,\nTesting Department of Larsen Company for October 2012.\n\nFlow of Production\nWork in process, beginning (given)\nTransferred-in during current period (given)\nTo account for\nCompleted and transferred out during current\nperiod:\nFrom beginning work in process\n7,500 (100% 100%); 7,500 (100% 0%);\n7,500 (100% 70%)\nStarted and completed\n18,800 100%; 18,800 100%; 18,800 100%\nWork in process, ending* (given)\n3,700 100%; 3,700 0%; 3,700 60%\nAccounted for\nEquivalent units of work done in current period\n\n(Step 2)\n(Step 1)\nEquivalent Units\nPhysical TransferredDirect\nConversion\nUnits\nin Costs\nMaterials\nCosts\n7,500\n(work done before current period)\n22,500\n30,000\n\n7,500\n18,800\n3,700\n_____\n30,000\n\n7,500\n\n2,250\n\n18,800\n\n18,800\n\n18,800\n\n3,700\n\n2,220\n\n22,500\n\n26,300\n\n23,270\n\nDegree of completion in this department: Transferred-in costs, 100%; direct materials, 0%; conversion costs, 70%.\n26,300 physical units completed and transferred out minus 7,500 physical units completed and transferred out from\nbeginning work-in-process inventory.\n*Degree of completion in this department: transferred-in costs, 100%; direct materials, 0%; conversion costs, 60%.\n\n17-30\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n## SOLUTION EXHIBIT 17-34B\n\nSteps 3, 4, and 5: Summarize Total Costs to Account For, Compute Cost per Equivalent Unit, and Assign Total Costs to\nUnits Completed and to Units in Ending Work in Process;\nFIFO Method of Process Costing,\nTesting Department of Larsen Company for October 2012.\n\n## (Step 3) Work in process, beginning (given)\n\nCosts added in current period (given)\nTotal costs to account for\n\nTotal\nProduction\nCosts\n\\$ 3,717,335\n21,395,850\n\\$25,113,185\n\nTransferred-in\nCosts\n\\$ 2,881,875\n7,735,250\n\\$10,617,125\n\nDirect\nMaterials\n\\$\n0\n9,704,700\n\\$9,704,700\n\nConversion\nCosts\n\\$ 835,460\n3,955,900\n\\$4,791,360\n\n\\$ 7,735,250\n\n\\$9,704,700\n\n\\$3,955,900\n\n## (Step 4) Costs added in current period\n\nDivide by equivalent units of work done in\ncurrent period (Solution Exhibit 17-34A)\nCost per equiv. unit of work done in current period\n(Step 5) Assignment of costs:\nCompleted and transferred out (26,300 units):\nWork in process, beginning (7,500 units)\nCosts added to beg. work in process in current period\nTotal from beginning inventory\nStarted and completed (18,800 units)\nTotal costs of units completed & transferred out\nWork in process, ending (3,700 units)\nTotal costs accounted for\n\n\\$ 3,717,335\n3,150,000\n6,867,335\n16,596,431\n23,463,766\n1,649,419\n\\$25,113,185\n\n22,500\n343.79\n\n\\$2,881,875\n(0* \\$343.79)\n\n26,300\n369.00\n\n23,270\n170.00\n\n+\n\\$0\n+\n\\$835,460\n+ (7,500* \\$369.00) + (2,250* \\$170.00)\n\n## (3,700# \\$343.79) + (0# \\$369.00)\n\n\\$10,617,125\n+ \\$9,704,700\n\n*Equivalent units used to complete beginning work in process from Solution Exhibit 17-34A, Step 2.\n\nEquivalent units started and completed from Solution Exhibit 17-34A, Step 2.\n#\nEquivalent units in ending work in process from Solution Exhibit 17-34A, Step 2.\n\n17-31\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n+ (2,220# \\$170.00)\n+ \\$4,791,360\n\n## 17-35 (25 min.) Weighted-average method.\n\nSolution Exhibit 17-35A shows equivalent units of work done to date of:\nDirect materials\nConversion costs\n\n## 625 equivalent units\n\n525 equivalent units\n\nNote that direct materials are added when the Assembly Department process is 10%\ncomplete. Both the beginning and ending work in process are more than 10% complete and\nhence are 100% complete with respect to direct materials.\nSolution Exhibit 17-35B summarizes the total Assembly Department costs for April\n2012, calculates cost per equivalent unit of work done to date for direct materials and conversion\ncosts, and assigns these costs to units completed (and transferred out), and to units in ending\nwork in process using the weighted-average method.\nSOLUTION EXHIBIT 17-35A\nSteps 1 and 2: Summarize Output in Physical Units and Compute Output in Equivalent Units;\nWeighted-Average Method of Process Costing, Assembly Department of Ashworth Handcraft\nfor April 2012.\n(Step 1)\n\nFlow of Production\nWork in process, beginning (given)\nStarted during current period (given)\nTo account for\nCompleted and transferred out\nduring current period\nWork in process, ending* (given)\n130 100%; 130 30%\nAccounted for\nEquivalent units of work done to date\n\nPhysical\nUnits\n95\n490\n585\n455\n130\n\n(Step 2)\nEquivalent Units\nDirect\nConversion\nMaterials\nCosts\n\n455\n\n455\n\n130\n\n39\n\n585\n\n494\n\n585\n\nDegree of completion in this department: direct materials, 100%; conversion costs, 30%.\n\n17-32\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n## SOLUTION EXHIBIT 17-35B\n\nSteps 3, 4, and 5: Summarize Total Costs to Account For, Compute Cost per Equivalent Unit,\nand Assign Total Costs to Units Completed and to Units in Ending Work in Process;\nWeighted-Average Method of Process Costing, Assembly Department of Ashworth, April 2012.\nTotal\nProduction\nCosts\n\n## (Step 3) Work in process, beginning (given)\n\nCosts added in current period (given)\nTotal costs to account for\n\n\\$ 2,653\n29,496\n\\$32,149\n\n## (Step 4) Costs incurred to date\n\nDivide by equivalent units of work done to\ndate (Solution Exhibit 17-35A)\nCost per equivalent unit of work done to date\n(Step 5) Assignment of costs:\nCompleted and transferred out (455 units)\nWork in process, ending (130 units)\nTotal costs accounted for\n*\n\nDirect\nMaterials\n\n\\$ 1,665\n17,640\n\\$19,305\n\nConversion\nCosts\n\n\\$19,305\n\n\\$26,845\n5,304\n\\$32,149\n\n585\n33\n\n988\n11,856\n\\$12,844\n\\$12,844\n\n494\n26\n\n## (455* \\$33) + (455* \\$26)\n\n(130 \\$33) + (39 \\$26)\n\\$19,305\n+ \\$12,844\n\nEquivalent units completed and transferred out from Solution Exhibit 17-35A, Step 2.\nEquivalent units in ending work in process from Solution Exhibit 17-35A, Step 2.\n\n17-33\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n## 1. Work in Process Assembly Department\n\nAccounts Payable\nTo record direct materials purchased and\nused in production during April\n\n17,640\n\n## 2. Work in Process Assembly Department\n\nVarious Accounts\nTo record Assembly Department conversion\ncosts for April\n\n11,856\n\n## 3. Work in ProcessFinishing Department\n\nWork in Process Assembly Department\nTo record cost of goods completed and transferred\nout in April from the Assembly Department\nto the Finishing Department\n\n26,845\n\n17,640\n\n11,856\n\n## Work in Process Assembly Department\n\nBeginning inventory, April 1\n2,653\n3. Transferred out to\n1. Direct materials\n17,640\nWork in ProcessFinishing\n2. Conversion costs\n11,856\nEnding inventory, April 30\n5,304\n\n26,845\n\n26,845\n\n17-34\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n## 17-37 (20 min.) FIFO method (continuation of 17-35).\n\nThe equivalent units of work done in April 2012 in the Assembly Department for direct materials\nand conversion costs are shown in Solution Exhibit 17-37A.\nSolution Exhibit 17-37B summarizes the total Assembly Department costs for April 2012,\ncalculates the cost per equivalent unit of work done in April 2012 in the Assembly Department\nfor direct materials and conversion costs, and assigns these costs to units completed (and\ntransferred out) and to units in ending work in process under the FIFO method.\nThe equivalent units of work done in beginning inventory is: direct materials, 95 100% =\n95; and conversion costs 95 40% = 38. The cost per equivalent unit of beginning inventory and\nof work done in the current period are:\n\nDirect materials\nConversion costs\n\nBeginning\nInventory\n\\$17.53 (\\$1,665 95)\n\\$26.00 (\\$988 38)\n\nWork Done in\nCurrent Period\n(Calculated Under\nFIFO Method)\n\\$36\n\\$26\n\nThe following table summarizes the costs assigned to units completed and those still in\nprocess under the weighted-average and FIFO process-costing methods for our example.\n\n## Cost of units completed and transferred out\n\nWork in process, ending\nTotal costs accounted for\n\nWeighted\nAverage\nFIFO\n(Solution\n(Solution\nExhibit 17-35B) Exhibit 17-37B) Difference\n\\$26,845\n\\$26,455\n\\$390\n5,304\n5,694\n+\\$390\n\\$32,149\n\\$32,149\n\nThe FIFO ending inventory is higher than the weighted-average ending inventory by \\$390.\nThis is because FIFO assumes that all the lower-cost prior-period units in work in process are the\nfirst to be completed and transferred out while ending work in process consists of only the\nhigher-cost current-period units. The weighted-average method, however, smoothes out cost per\nequivalent unit by assuming that more of the higher-cost units are completed and transferred out,\nwhile some of the lower-cost units in beginning work in process are placed in ending work in\nprocess. Hence, in this case, the weighted-average method results in a higher cost of units\ncompleted and transferred out and a lower ending work-in-process inventory relative to the FIFO\nmethod.\n\n17-35\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n## SOLUTION EXHIBIT 17-37A\n\nSteps 1 and 2: Summarize Output in Physical Units and Compute Output in Equivalent Units;\nFIFO Method of Process Costing, Assembly Department of Ashworth Handcraft for April 2012.\n(Step 1)\nPhysical\nUnits\n95\n490\n585\n\nFlow of Production\nWork in process, beginning (given)\nStarted during current period (given)\nTo account for\nCompleted and transferred out during current period:\nFrom beginning work in process\n95 (100% 100%); 95 (100% 40%)\nStarted and completed\n455 100%; 455 100%\nWork in process, ending* (given)\n130\n100%; 130\n30%\nAccounted for\nEquivalent units of work done in current period\n\n(Step 2)\nEquivalent Units\nDirect\nConversion\nMaterials\nCosts\n(work done before current period)\n\n95\n0\n\n57\n\n360\n\n360\n\n130\n\n39\n\n490\n\n456\n\n360\n130\n585\n\nDegree of completion in this department: direct materials, 100%; conversion costs, 40%.\n455 physical units completed and transferred out minus 95 physical units completed and transferred out from\nbeginning work-in-process inventory.\n*Degree of completion in this department: direct materials, 100%; conversion costs, 20%.\n\n## SOLUTION EXHIBIT 17-37B\n\nSteps 3, 4, and 5: Summarize Total Costs to Account For, Compute Cost per Equivalent Unit,\nand Assign Total Costs to Units Completed and to Units in Ending Work in Process;\nFIFO Method of Process Costing, Assembly Department of Ashworth Handcraft for April 2012.\n\n## (Step 3) Work in process, beginning (given)\n\nCosts added in current period (given)\nTotal costs to account for\n(Step 4) Costs added in current period\nDivide by equivalent units of work done in\ncurrent period (Exhibit 17-37A)\nCost per equivalent unit of work done in current\nperiod\n(Step 5) Assignment of costs:\nCompleted and transferred out (455 units):\nWork in process, beginning (95 units)\nCosts added to begin. work in process in\ncurrent period\nTotal from beginning inventory\nStarted and completed (360 units)\nTotal costs of units completed & tsfd. out\nWork in process, ending (130 units)\nTotal costs accounted for\n\nTotal\nProduction\nCosts\n\\$ 2,653\n29,496\n\\$32,149\n\nDirect\nMaterials\n\\$ 1,665\n17,640\n\\$19,305\n\\$17,640\n\nConversion\nCosts\n\\$ 988\n11,856\n\\$12,844\n\\$11,856\n\n490\n\\$\n\n\\$ 2,653\n1,482\n4,135\n22,320\n26,455\n5,694\n\\$32,149\n\n36\n\n\\$1,665\n(0*\n\n456\n\\$\n\n\\$988\n\n(57*\n\n\\$36)\n\n(360\n\n(130# \\$36)\n\\$19,305\n\n+\n+\n\n(360\n\n\\$36)\n\n26\n\n\\$26)\n\\$26)\n\n(39# \\$26)\n\\$12,844\n\n*Equivalent units used to complete beginning work in process from Solution Exhibit 17-37A, Step 2.\n\nEquivalent units started and completed from Solution Exhibit 17-37A, Step 2.\n#\nEquivalent units in ending work in process from Solution Exhibit 17-37A, Step 2.\n\n17-36\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n## 17-38 (30 min.) Transferred-in costs, weighted average.\n\n1.\nSolution Exhibit 17-38A computes the equivalent units of work done to date in the\nBinding Department for transferred-in costs, direct materials, and conversion costs.\nSolution Exhibit 17-38B summarizes total Binding Department costs for April 2012,\ncalculates the cost per equivalent unit of work done to date in the Binding Department for\ntransferred-in costs, direct materials, and conversion costs, and assigns these costs to units\ncompleted and transferred out and to units in ending work in process using the weighted-average\nmethod.\n2.\n\nJournal entries:\na. Work in Process Binding Department\nWork in ProcessPrinting Department\nCost of goods completed and transferred out\nduring April from the Printing Department\nto the Binding Department\nb. Finished Goods\nWork in Process Binding Department\nCost of goods completed and transferred out\nduring April from the Binding Department\nto Finished Goods inventory\n\n129,600\n129,600\n\n220,590\n220,590\n\n## SOLUTION EXHIBIT 17-38A\n\nSteps 1 and 2: Summarize Output in Physical Units and Compute Output in Equivalent Units;\nWeighted-Average Method of Process Costing,\nBinding Department of Bookworm, Inc. for April 2012.\n(Step 1)\n\nFlow of Production\nWork in process, beginning (given)\nTransferred-in during current period (given)\nTo account for\nCompleted and transferred out during current period:\nWork in process, endinga (given)\n(750 100%; 750 0%; 750 70%)\nAccounted for\nEquivalent units of work done to date\na\n\n(Step 2)\nEquivalent Units\nPhysical Transferred- Direct Conversion\nUnits\nin Costs Materials Costs\n1,050\n2,400\n3,450\n2,700\n2,700\n2,700\n2,700\n750\n750\n0\n525\n3,450\n3,450\n2,700\n3,225\n\nDegree of completion in this department: transferred-in costs, 100%; direct materials, 0%; conversion costs, 70%.\n\n17-37\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n## SOLUTION EXHIBIT 17-38B\n\nSteps 3, 4, and 5: Summarize Total Costs to Account For, Compute Cost per Equivalent Unit, and Assign Total Costs to\nUnits Completed and to Units in Ending Work in Process;\nWeighted-Average Method of Process Costing,\nBinding Department of Bookworm, Inc. for April 2012.\n\n(Step 3)\n\n## Work in process, beginning (given)\n\nCosts added in current period (given)\nTotal costs to account for\n\n(Step 4)\n\n## Costs incurred to date\n\nDivide by equivalent units of work done to date\n(Solution Exhibit 17-38A)\nCost per equivalent unit of work done to date\n\n(Step 5)\n\na\nb\n\nAssignment of costs:\nCompleted and transferred out (2,700 units)\nWork in process, ending (750 units):\nTotal costs accounted for\n\nTotal\nProduction\nCosts\n\\$ 46,200\n223,290\n\\$269,490\n\n\\$220,590\n48,900\n\\$269,490\n\nTransferred-in\nCosts\n\\$ 32,550\n129,600\n\\$162,150\n\nDirect\nMaterials\n\\$\n0\n23,490\n\\$23,490\n\n\\$162,150\n\n\\$23,490\n\n\\$83,850\n\n2,700\n\\$ 8.70\n\n3,225\n\\$ 26.00\n\n3,450\n47.00\n\nConversion\nCosts\n\\$13,650\n70,200\n\\$83,850\n\n## (2,700a \\$47.00) + (2,700a \\$8.70) +\n\n(750b \\$47.00) + (0b \\$8.70) +\n\n\\$162,150\n\n+ \\$23,490\n\nEquivalent units completed and transferred out from Sol. Exhibit 17-38A, step 2.\nEquivalent units in ending work in process from Sol. Exhibit 17-38A, step 2.\n\n17-38\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n(2,700a \\$26)\n(525b \\$26)\n\n\\$83,850\n\n## 17-39 (30 min.) Transferred-in costs, FIFO method (continuation of 17-38).\n\n1.\nSolution Exhibit 17-39A calculates the equivalent units of work done in April 2012 in the\nBinding Department for transferred-in costs, direct materials, and conversion costs.\nSolution Exhibit 17-39B summarizes total Binding Department costs for April 2012,\ncalculates the cost per equivalent unit of work done in April 2012 in the Binding Department for\ntransferred-in costs, direct materials, and conversion costs, and assigns these costs to units\ncompleted and transferred out and to units in ending work in process using the FIFO method.\nJournal entries:\na. Work in Process Binding Department\nWork in ProcessPrinting Department\nCost of goods completed and transferred out\nduring April from the Printing Department to\nthe Binding Department.\nb.\n\nFinished Goods\nWork in Process Binding Department\nCost of goods completed and transferred out\nduring April from the Binding Department\nto Finished Goods inventory.\n\n124,800\n124,800\n\n216,240\n216,240\n\n2.\n\nThe equivalent units of work done in beginning inventory is: Transferred-in costs, 1,050\n100% = 1,050; direct materials, 1,050 0% = 0; and conversion costs, 1,050 50% = 525. The\ncost per equivalent unit of beginning inventory and of work done in the current period are:\nBeginning\nInventory\nTransferred-in costs (weighted average) \\$31.00 (\\$32,550 1,050)\nTransferred-in costs (FIFO)\n\\$35.00 (\\$36,750 1,050)\nDirect materials\n\nConversion costs\n\\$26.00 (\\$13,650 525)\n\nWork Done in\nCurrent Period\n\\$54.00 (\\$129,600 2,400)\n\\$52.00 (\\$124,800 2,400)\n\\$ 8.70\n\\$26.00\n\nThe following table summarizes the costs assigned to units completed and those still in\nprocess under the weighted-average and FIFO process-costing methods for the Binding\nDepartment.\n\n## Cost of units completed and transferred out\n\nWork in process, ending\nTotal costs accounted for\n\nWeighted\nAverage\nFIFO\n(Solution\n(Solution\nExhibit 17-38B) Exhibit 17-39B)\n\\$220,590\n\\$216,240\n48,900\n52,650\n\\$269,490\n\\$268,890\n\nDifference\n\\$4,350\n+\\$3,750\n\n17-39\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\nThe FIFO ending inventory is higher than the weighted-average ending inventory by\n\\$3,750. This is because FIFO assumes that all the lower-cost prior-period units in work in\nprocess (resulting from the lower transferred-in costs in beginning inventory) are the first to be\ncompleted and transferred out while ending work in process consists of only the higher-cost\ncurrent-period units. The weighted-average method, however, smoothes out cost per equivalent\nunit by assuming that more of the higher-cost units are completed and transferred out, while\nsome of the lower-cost units in beginning work in process are placed in ending work in process.\nHence, in this case, the weighted-average method results in a higher cost of units completed and\ntransferred out and a lower ending work-in-process inventory relative to FIFO. Note that the\ndifference in cost of units completed and transferred out (\\$4,350) does not exactly offset the\ndifference in ending work-in-process inventory (+\\$3,750). This is because the FIFO and\nweighted-average methods result in different values for transferred-in costs with respect to both\nbeginning inventory and costs transferred in during the period.\nSOLUTION EXHIBIT 17-39A\nSteps 1 and 2: Summarize Output in Physical Units and Compute Output in Equivalent Units;\nFIFO Method of Process Costing,\nBinding Department of Bookworm, Inc. for April 2012.\n(Step 1)\n\nFlow of Production\nWork in process, beginning (given)\nTransferred-in during current period (given)\nTo account for\nCompleted and transferred out during current period:\nFrom beginning work in processa\n[1,050 (100% 100%); 1,050\n(100% 0%); 1,050\nStarted and completed\n(1,650 100%; 1,650 100%; 1,650 100%)\nWork in process, endingc (given)\n(750 100%; 750 0%; 750 70%)\nAccounted for\nEquivalent units of work done in current period\n\n(Step 2)\nEquivalent Units\n\nPhysical Transferred-in\nDirect\nConversion\nUnits\nCosts\nMaterials\nCosts\n1,050\n(work done before current period)\n2,400\n3,450\n1,050\n(100% 50%)]\n\n1,050\n\n525\n\n1,650\n\n1,650\n\n1,650\n\n750\n____\n2,400\n\n0\n____\n2,700\n\n525\n____\n2,700\n\n1,650b\n750\n____\n3,450\n\nDegree of completion in this department: Transferred-in costs, 100%; direct materials, 0%; conversion costs, 50%.\n2,700 physical units completed and transferred out minus 1,050 physical units completed and transferred out from beginning\nwork-in-process inventory.\nc\nDegree of completion in this department: transferred-in costs, 100%; direct materials, 0%; conversion costs, 70%.\nb\n\n17-40\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n## SOLUTION EXHIBIT 17-39B\n\nSteps 3, 4, and 5: Summarize Total Costs to Account For, Compute Cost per Equivalent Unit, and Assign Total Costs to Units\nCompleted and to Units in Ending Work in Process;\nFIFO Method of Process Costing,\nBinding Department of Bookworm, Inc. for April 2012.\nTotal\nProduction\nCosts\n\\$ 50,400\n218,490\n\\$268,890\n\n## (Step 3) Work in process, beginning (given)\n\nCosts added in current period (given)\nTotal costs to account for\n(Step 4) Costs added in current period\nDivide by equivalent units of work done in current period (Sol.\nExhibit 17-39A)\nCost per equivalent unit of work done in current period\n(Step 5) Assignment of costs:\nCompleted and transferred out (2,700 units)\nWork in process, beginning (1,050 units)\nCosts added to beginning work in process in current period\nTotal from beginning inventory\nStarted and completed (1,650 units)\nTotal costs of units completed and transferred out\nWork in process, ending (750 units):\nTotal costs accounted for\n\n\\$ 50,400\n22,785\n73,185\n143,055\n216,240\n52,650\n\\$268,890\n\nDirect\nMaterials\n\\$\n0\n23,490\n\\$23,490\n\nTransferred-in Costs\n\\$ 36,750\n124,800\n\\$161,550\n\nConversion\nCosts\n\\$13,650\n70,200\n\\$83,850\n\n\\$124,800\n\n\\$23,490\n\n\\$70,200\n\n2,400\n\\$ 52.00\n\n2,700\n\\$ 8.70\n\n2,700\n\\$ 26.00\n\n\\$36,750\n(0a \\$52.00)\n(1,650b \\$52.00)\n(750c \\$52.00)\n\\$161,550\n\n+\n\\$0\n+\n+ (1,050a \\$8.70) +\n\n\\$13,650\n(525a \\$26)\n\n## + (1,650b \\$8.70) + (1,650b \\$26)\n\n+\n+\n\nEquivalent units used to complete beginning work in process from Solution Exhibit 17-39A, step 2.\nEquivalent units started and completed from Solution Exhibit 17-39A, step 2.\nc\nEquivalent units in ending work in process from Solution Exhibit 17-39A, step 2.\nb\n\n17-41\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n(0c \\$8.70)\n\\$23,490\n\n+\n+\n\n(525c \\$26)\n\\$83,850\n\n## 17-40 (45 min.) Transferred-in costs, weighted-average and FIFO methods.\n\n1.\nSolution Exhibit 17-40A computes the equivalent units of work done to date in the\nDrying and Packaging Department for transferred-in costs, direct materials, and conversion\ncosts. Solution Exhibit 17-40B summarizes total Drying and Packaging Department costs for\nweek 37, calculates the cost per equivalent unit of work done to date in the Drying and\nPackaging Department for transferred-in costs, direct materials, and conversion costs, and\nassigns these costs to units completed and transferred out and to units in ending work in process\nusing the weighted-average method.\n2.\nSolution Exhibit 17-40C computes the equivalent units of work done in week 37 in the\nDrying and Packaging Department for transferred-in costs, direct materials, and conversion\ncosts. Solution Exhibit 17-40D summarizes total Drying and Packaging Department costs for\nweek 37, calculates the cost per equivalent unit of work done in week 37 in the Drying and\nPackaging Department for transferred-in costs, direct materials, and conversion costs, and\nassigns these costs to units completed and transferred out and to units in ending work in process\nusing the FIFO method.\nSOLUTION EXHIBIT 17-40A\nSteps 1 and 2: Summarize Output in Physical Units and Compute Output in Equivalent Units;\nWeighted-Average Method of Process Costing,\nDrying and Packaging Department of Frito-Lay Inc. for Week 37.\n(Step 1)\nPhysical\nFlow of Production\nUnits\nWork in process, beginning (given)\n1,200\nTransferred in during current period (given)\n4,200\nTo account for\n5,400\nCompleted and transferred out\nduring current period\n4,000\nWork in process, ending* (given)\n1,400\n1,400 100%; 1,400 0%; 1,400 50%\nAccounted for\n5,400\nEquivalent units of work done to date\n\n(Step 2)\nEquivalent Units\nTransferredDirect\nConversion\nin Costs\nMaterials\nCosts\n\n4,000\n\n4,000\n\n4,000\n\n1,400\n\n700\n\n5,400\n\n4,000\n\n4,700\n\n*Degree of completion in this department: transferred-in costs, 100%; direct materials, 0%; conversion costs, 50%.\n\n17-42\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n## SOLUTION EXHIBIT 17-40B\n\nSteps 3, 4, and 5: Summarize Total Costs to Account For, Compute Cost per Equivalent Unit, and Assign Total\nCosts to Units Completed and to Units in Ending Work in Process;\nWeighted-Average Method of Process Costing,\nDrying and Packaging Department of Frito-Lay Inc. for Week 37.\n\n(Step 3)\n\n## Work in process, beginning (given)\n\nCosts added in current period (given)\nTotal costs to account for\n\n(Step 4)\n\n## Costs incurred to date\n\nDivide by equivalent units of work done\nto date (Solution Exhibit 17-40A)\nEquivalent unit costs of work done to date\n\n(Step 5)\n\na\nb\n\nTotal\nProduction\nCosts\n\\$ 30,770\n142,450\n\\$173,220\n\nTransferred\nDirect\n-in Costs\nMaterials\n\\$ 26,750\n\\$\n0\n91,510\n23,000\n\\$118,260\n\\$23,000\n\nAssignment of costs:\nCompleted and transferred out (4,000 units)\nWork in process, ending (1,400 units)\nTotal costs accounted for\n\n\\$137,800\n35,420\n\\$173,220\n\nConversion\nCosts\n\\$ 4,020\n27,940\n\\$31,960\n\n\\$118,260\n\n\\$23,000\n\n\\$31,960\n\n5,400\n21.90\n\n4,000\n5.75\n\n4,700\n\n6.80\n\n## (4,000a \\$21.90) + (4,000a \\$5.75) + (4,000a \\$6.80)\n\n(1,400b \\$21.90) +\n\n\\$118,260\n\n(0b \\$5.75)\n\n\\$23,000\n\nEquivalent units completed and transferred out from Solution Exhibit 17-40A, Step 2.\nEquivalent units in ending work in process from Solution Exhibit 17-40A, Step 2.\n\n17-43\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n+ (700b \\$6.80)\n\n\\$31,960\n\n## SOLUTION EXHIBIT 17-40C\n\nSteps 1 and 2: Summarize Output in Physical Units and Compute Output in Equivalent Units;\nFIFO Method of Process Costing,\nDrying and Packaging Department of Frito-Lay Inc. for Week 37.\n\nFlow of Production\nWork in process, beginning (given)\nTransferred-in during current period (given)\nTo account for\nCompleted and transferred out during current period:\nFrom beginning work in process\n1,200 (100% 100%); 1,200 (100% 0%);\n1,200 (100% 25%)\nStarted and completed\n2,800 100%; 2,800 100%; 2,800 100%\nWork in process, ending* (given)\n1,400 100%; 1,400 0%; 1,400 50%\nAccounted for\nEquivalent units of work done in current period\n\n(Step 2)\n(Step 1)\nEquivalent Units\nPhysical TransferredDirect\nConversion\nUnits\nin Costs\nMaterials\nCosts\n1,200\n(work done before current period)\n4,200\n5,400\n1,200\n2,800\n\n1,200\n\n2,800\n\n2,800\n\n1,400\n\n4,200\n\n4,000\n\n900\n2,800\n\n1,400\n700\n\n5,400\n4,400\n\nDegree of completion in this department: Transferred-in costs, 100%; direct materials, 0%; conversion costs, 25%.\n4,000 physical units completed and transferred out minus 1,200 physical units completed and transferred out from\nbeginning work-in-process inventory.\n*Degree of completion in this department: transferred-in costs, 100%; direct materials, 0%; conversion costs, 50%.\n\n17-44\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n## SOLUTION EXHIBIT 17-40D\n\nSteps 3, 4, and 5: Summarize Total Costs to Account For, Compute Cost per Equivalent Unit, and Assign Total Costs to\nUnits Completed and to Units in Ending Work in Process;\nFIFO Method of Process Costing,\nDrying and Packaging Department of Frito-Lay Inc. for Week 37.\nTotal\nProduction\nCosts\n\n## (Step 3) Work in process, beginning (given)\n\nCosts added in current period (given)\nTotal costs to account for\n\nTransferred-in\nCosts\n\n\\$ 32,940\n144,600\n\\$177,540\n\n\\$ 28,920\n93,660\n\\$122,580\n\n## (Step 4) Costs added in current period\n\nDivide by equivalent units of work done in current period\n(Solution Exhibit 17-40C)\nCost per equivalent unit of work done in current period\n\nDirect\nMaterials\n\n0\n23,000\n\\$23,000\n\n\\$ 4,020\n27,940\n\\$31,960\n\n\\$ 93,660\n\n\\$23,000\n\n\\$27,940\n\n4,200\n\n4,000\n\n4,400\n\n22.30\n\nConversion\nCosts\n\n5.75\n\n6.35\n\n## (Step 5) Assignment of costs:\n\nCompleted and transferred out (5,40 units):\nWork in process, beginning (1,200 units)\nCosts added to beg. work in process in current period\nTotal from beginning inventory\nStarted and completed (2,800 units)\nTotal costs of units completed & transferred out\nWork in process, ending (1,400 units)\nTotal costs accounted for\n\n\\$28,290\n+\n\\$0\n+\n\\$4,020\n\\$ 32,940\na\na\na\n(0\n\\$22.30)\n+\n(1,200\n\\$5.75)\n+\n(900\n\\$6.35)\n12,615\n45,555\n96,320 (2,800b \\$22.30) + (2,800b \\$5.75) + (2,800b \\$6.35)\n141,875\nc\nc\nc\n35,665 (1,400 \\$22.30) + (0 \\$5.75) + (700 \\$6.35)\n\\$177,540\n\\$122,580 +\n\\$23,000 +\n\\$31,960\n\nEquivalent units used to complete beginning work in process from Solution Exhibit 17-40C, Step 2.\nEquivalent units started and completed from Solution Exhibit 17-40C, Step 2.\nc\nEquivalent units in ending work in process from Solution Exhibit 17-40C, Step 2\nb\n\n17-45\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n## 17-41 (30-35 min.) Weighted-average and standard-costing method.\n\n1.\nSolution Exhibit 17-41A computes the equivalent units of work done in November 2010\nby Penelopes Pearls Company for direct materials and conversion costs.\n2. and 3.\nSolution Exhibit 17-41B summarizes total costs of the Penelopes Pearls\nCompany for November 30, 2012 and, using the standard cost per equivalent unit for direct\nmaterials and conversion costs, assigns these costs to units completed and transferred out and to\nunits in ending work in process. The exhibit also summarizes the cost variances for direct\nmaterials and conversion costs for November 2012.\nSOLUTION EXHIBIT 17-41A\nSteps 1 and 2: Summarize Output in Physical Units and Compute Output in Equivalent Units;\nStandard Costing Method of Process Costing,\nPenelopes Pearls Company for the month ended November 30, 2012.\n(Step 2)\nEquivalent Units\nDirect\nConversion\nMaterials\nCosts\n24,000(work done before current period)\n\n(Step 1)\nPhysical\nUnits\n\nFlow of Production\n\n## Work in process, beginning (given)\n\nStarted during current period (given)\nTo account for\nCompleted and transferred out during current period:\nFrom beginning work in process\n24,000 (100% 100%); 24,000 (100% 70%)\nStarted and completed\n99,000 100%, 99,000 100%\nWork in process, ending* (given)\n25,400 100%; 25,400 50%\nAccounted for\nEquivalent units of work done in current period\n\n124,400\n148,400\n24,000\n0\n\n7,200\n\n99,000\n\n99,000\n\n25,400\n_______\n148,400 _______\n124,400\n\n12,700\n\n99,000\n25,400\n\n_______\n118,900\n\nDegree of completion in this department: direct materials, 100%; conversion costs, 70%.\n\n123,000 physical units completed and transferred out minus 24,000 physical units completed and transferred out\nfrom beginning work-in-process inventory.\n\n*Degree of completion in this department: direct materials, 100%; conversion costs, 50%.\n\n17-46\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n## SOLUTION EXHIBIT 17-41B\n\nSteps 3, 4, and 5: Summarize Total Costs to Account For, Compute Cost per\nEquivalent Unit, and Assign Total Costs to Units Completed and to Units in\nEnding Work in Process;\nStandard-Costing Method of Process Costing,\nPenelopes Pearls Company for the month ended November 30, 2012.\n\n## (Step 3) Work in process, beginning (given)\n\nCosts added in current period at standard costs\nTotal costs to account for\n(Step 4) Standard cost per equivalent unit (given)\n(Step 5) Assignment of costs at standard costs:\nCompleted and transferred out (123,000 units):\nWork in process, beginning (24,000 units)\nCosts added to beg. work in process in current period\nTotal from beginning inventory\nStarted and completed (99,000 units)\nTotal costs of units transferred out\nWork in process, ending (25,400 units)\nTotal costs accounted for\nSummary of variances for current performance:\nCosts added in current period at standard costs (see Step 3 above)\nActual costs incurred (given)\nVariance\n\nTotal\nProduction\nDirect\nCosts\nMaterials\n\\$ 248,400\n\\$ 72,000\n1,621,650 (124,400 3.00)\n\\$1,870,050\n\\$445,200\n\\$\n\nConversion\nCosts\n+\n\\$ 176,400\n+ (118,900 \\$10.50)\n+\n\\$1,424,850\n\n3.00\n\n10.50\n\n\\$72,000\n+\n\\$176,400\n\\$ 248,400\n(0* \\$3.00) + (7,200* \\$10.50)\n75,600\n324,000\n1,336,500 (99,000 \\$3.00) + (99,000 \\$10.50)\n1,660,500\n209,550 (25,400# \\$3.00) + (12,700# \\$10.50)\n\\$1,870,050\n\\$445,200\n+\n\\$1,424,850\n\\$373,200\n329,000\n\\$ 44,200 F\n\n*Equivalent units to complete beginning work in process from Solution Exhibit 17-41A, Step 2.\n\nEquivalent units started and completed from Solution Exhibit 17-41A, Step 2.\nEquivalent units in ending work in process from Solution Exhibit 17-41A, Step 2.\n\n17-47\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren\n\n\\$1,248,450\n1,217,000\n\\$ 31,450 F\n\n## 17-42 (30 min.) Standard-costing method.\n\n1. Since there was no additional work needed on the beginning inventory with respect to\nmaterials, the initial mulch must have been 100% complete with respect to materials.\nFor conversion costs, the work done to complete the opening inventory was 434,250\n965,000 = 45%. Therefore, the unfinished mulch in opening inventory must have\nbeen 55% complete with respect to conversion costs.\n2. It is clear that the ending WIP is also 100% complete with respect to direct materials\n(1,817,000 1,817,000), and it is 60% (1,090,200 1,817,000) complete with regard\nto conversion costs.\n3. We can first obtain the total standard costs per unit. The number of units started and\ncompleted during August is 845,000, and a total cost of \\$6,717,750 is attached to\nthem. The per unit standard cost is therefore (\\$6,717,750 845,000) = \\$7.95. If x\nand y represent the per unit cost for direct materials and conversion costs,\nrespectively, we know that:\nx + y = 7.95\nWe also know that the ending inventory is costed at \\$12,192,070 and contains\n1,817,000 equivalent units of materials and 1,090,200 equivalent units of conversion\ncosts. This provides a second equation:\n1,817,000 x + 1,090,200 y = 12,192,070.\nSolving these two equations reveals that the direct materials cost per unit, x, is \\$4.85,\nwhile the conversion cost per unit, y, is \\$3.10.\n4. The opening WIP inventory contained 965,000 equivalent units of materials and\n(965,000 434,250) = 530,750 equivalent units of conversion costs. Applying the\nstandard costs computed in step (3), the cost of the opening inventory must have been:\n(965,000 \\$4.85) + (530,750 \\$3.10) = \\$6,325,575.\n\n17-48\n2012 Pearson Education, Inc. Publishing as Prentice Hall. SM Cost Accounting 14/e by Horngren"
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https://cstheory.stackexchange.com/questions/27268/data-structure-that-allows-moving-groups-of-elements-into-buckets | [
"# Data structure that allows moving groups of elements into buckets\n\nI'm looking for a data structure that can do the following geometric operation:\n\nSuppose there are a set of buckets $b_0, b_1..., b_n$ each of which contains some elements. Suppose I want to move all the elements in buckets $b_i$ where $i > k$ one bucket forward. So the elements in bucket $b_{k+1}$ would be moved to bucket $b_k$ and the elements in bucket $b_{k+2}$ would be moved to bucket $b_{k+1}$ and so on. The obvious way to move these elements is to go to each bucket and shift all the elements into the previous bucket. But is there a data structure that will allow me to move the buckets all at once?\n\nI used buckets in the description because it's easier to formulate the question in terms of buckets. But the data structure doesn't necessarily have to be buckets. All I need is a data structure that can allow me to move \"chunks\" of elements in one go (for example shifting consecutive the buckets $x$ number of buckets forward all at once) and then allow me to query the structure as normal (for example, allow me to query $b_{k}$ now with all the elements shifted.\n\nEDIT: I'm mainly interested in whether an already existing data structure that I'm not aware of does this.\n\n• What happens to bucket b0? – Ryan Oct 30 '14 at 18:27\n• if there are no buckets less than bucket $b_k$, then all the elements stay in the current bucket $b_k$. So all elements in bucket $b_0$ if it's moved down would stay in bucket $b_0$. – Quanquan Liu Oct 30 '14 at 18:40\n\nI don't quite know if this is what you were looking for since it is not a single data structure that has a name - but what you are asking for is easily implementable using just a linked list and a binary search tree:\n\nKeep a single linked list where all the elements of bucket $i$ come before the elements of bucket $i+1$. On every link you can have a boolean flag - is this the same bucket or next bucket. Now doing the shift corresponds to setting the flag to \"same bucket\" from \"next bucket\".\n\nOf course you probably also want to maintain some way to see the first element of each bucket. A way to do this is to store the pointers to the first element of each bucket in a balanced binary search tree, such that the key of the pointer to bucket $i$ is $i$. The search tree should be able to: (a) given $i$, output the entry with the $i$'th lowest key and (b) delete entries from the search tree.\n\nMerging bucket $i$ and $i+1$ now reduces to finding the entry in the search tree with the $i+1$'st lowest key, deleting this entry from the search tree, going to where it points in the list, and setting the flag of the arc pointing into this node in the list to \"same bucket\". Thus all operations take $O(\\log n)$ time.\n\nNote that after some \"shift\" operations are performed the key of the $i$'th bucket is no longer $i$, but it is the $i$'th lowest key stored in the search tree.\n\n• Not totally sure because I just skimmed this answer. But it doesn't allow moving a bucket more than once? Ie. if I wanted to move a set of buckets one down. Then I want to move another set of buckets one down but the sets of buckets have intersections so a subset of both sets could move more than once down. I'm not sure if this solution solves this problem? – Quanquan Liu Oct 30 '14 at 22:05\n• The solution handles this: suppose we start with 6 buckets and 15 elements: $1,2,3|4,5|6,7|8,9,10|11,12|13,14,15$. The binary search tree stores: $1,4,6,8,11,13$ (and pointers to them in the list). Then you merge bucket 3 and 4 - then you get: $1,2,3|4,5|6,7,8,9,10|11,12|13,14,15$ with $1,4,6,11,13$. Merge $3$ and $4$ again to get $1,2,3|4,5|6,7,8,9,10,11,12|13,14,15$ with $1,4,6,13$. – daniello Oct 30 '14 at 22:11\n• Ah thanks for the explanation. Looked at it more closely now, and I think it can handle up to one merge in $O(log n)$ time. If you have multiple merges, you potentially do $O(n \\log n)$ work right? – Quanquan Liu Oct 31 '14 at 20:38\n• Each merge takes $O(\\log)$ time. So $t$ merges take $O(t \\log n)$ time. – daniello Oct 31 '14 at 21:56"
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http://ebook3000.com/Introduction-to-Cryptography-with-Java-Applets_89399.html | [
"# Introduction to Cryptography with Java Applets",
null,
"Introduction to Cryptography with Java Applets By David Bishop\nPublisher: Jones Bartlett Learning 2002 | 384 Pages | ISBN: 0763722073 | File type: PDF | 10 mb\n\nIntroduction to Cryptography with Java Applets covers the mathematical basis of cryptography and cryptanalysis, like linear diophantine equations, linear congruences, systems of linear congruences, quadratic congruences, and exponential congruences. The chapters present theorems and proofs, and many mathematical examples.\nCryptography with Java Applets also covers programming ciphers, and cryptanalytic attacks on ciphers. In addition, many other types of cryptographic applications, like digest functions, shadows, database encryption, message signing, establishing keys, large integer arithmetic, pseudo-random bit generation, and authentication. The author has developed various Java crypto classes to perform these functions, and many programming exercises are assigned to the reader. The reader should be someone with a basic working knowledge of Java, but having Follow Rules!\n\n[Fast Download] Introduction to Cryptography with Java Applets",
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"",
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"http://ebook3000.com/upimg/201009/05/05004910604.jpeg",
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https://www.colorhexa.com/156f0d | [
"# #156f0d Color Information\n\nIn a RGB color space, hex #156f0d is composed of 8.2% red, 43.5% green and 5.1% blue. Whereas in a CMYK color space, it is composed of 81.1% cyan, 0% magenta, 88.3% yellow and 56.5% black. It has a hue angle of 115.1 degrees, a saturation of 79% and a lightness of 24.3%. #156f0d color hex could be obtained by blending #2ade1a with #000000. Closest websafe color is: #006600.\n\n• R 8\n• G 44\n• B 5\nRGB color chart\n• C 81\n• M 0\n• Y 88\n• K 56\nCMYK color chart\n\n#156f0d color description : Very dark lime green.\n\n# #156f0d Color Conversion\n\nThe hexadecimal color #156f0d has RGB values of R:21, G:111, B:13 and CMYK values of C:0.81, M:0, Y:0.88, K:0.56. Its decimal value is 1404685.\n\nHex triplet RGB Decimal 156f0d `#156f0d` 21, 111, 13 `rgb(21,111,13)` 8.2, 43.5, 5.1 `rgb(8.2%,43.5%,5.1%)` 81, 0, 88, 56 115.1°, 79, 24.3 `hsl(115.1,79%,24.3%)` 115.1°, 88.3, 43.5 006600 `#006600`\nCIE-LAB 40.503, -43.733, 42.198 6.066, 11.557, 2.292 0.305, 0.58, 11.557 40.503, 60.772, 136.023 40.503, -35.59, 47.379 33.995, -27.641, 19.8 00010101, 01101111, 00001101\n\n# Color Schemes with #156f0d\n\n• #156f0d\n``#156f0d` `rgb(21,111,13)``\n• #670d6f\n``#670d6f` `rgb(103,13,111)``\nComplementary Color\n• #466f0d\n``#466f0d` `rgb(70,111,13)``\n• #156f0d\n``#156f0d` `rgb(21,111,13)``\n• #0d6f36\n``#0d6f36` `rgb(13,111,54)``\nAnalogous Color\n• #6f0d46\n``#6f0d46` `rgb(111,13,70)``\n• #156f0d\n``#156f0d` `rgb(21,111,13)``\n• #360d6f\n``#360d6f` `rgb(54,13,111)``\nSplit Complementary Color\n• #6f0d15\n``#6f0d15` `rgb(111,13,21)``\n• #156f0d\n``#156f0d` `rgb(21,111,13)``\n• #0d156f\n``#0d156f` `rgb(13,21,111)``\n• #6f670d\n``#6f670d` `rgb(111,103,13)``\n• #156f0d\n``#156f0d` `rgb(21,111,13)``\n• #0d156f\n``#0d156f` `rgb(13,21,111)``\n• #670d6f\n``#670d6f` `rgb(103,13,111)``\n• #082b05\n``#082b05` `rgb(8,43,5)``\n• #0c4108\n``#0c4108` `rgb(12,65,8)``\n• #11580a\n``#11580a` `rgb(17,88,10)``\n• #156f0d\n``#156f0d` `rgb(21,111,13)``\n• #198610\n``#198610` `rgb(25,134,16)``\n• #1e9d12\n``#1e9d12` `rgb(30,157,18)``\n• #22b315\n``#22b315` `rgb(34,179,21)``\nMonochromatic Color\n\n# Alternatives to #156f0d\n\nBelow, you can see some colors close to #156f0d. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #2e6f0d\n``#2e6f0d` `rgb(46,111,13)``\n• #256f0d\n``#256f0d` `rgb(37,111,13)``\n• #1d6f0d\n``#1d6f0d` `rgb(29,111,13)``\n• #156f0d\n``#156f0d` `rgb(21,111,13)``\n• #0d6f0d\n``#0d6f0d` `rgb(13,111,13)``\n• #0d6f15\n``#0d6f15` `rgb(13,111,21)``\n• #0d6f1d\n``#0d6f1d` `rgb(13,111,29)``\nSimilar Colors\n\n# #156f0d Preview\n\nThis text has a font color of #156f0d.\n\n``<span style=\"color:#156f0d;\">Text here</span>``\n#156f0d background color\n\nThis paragraph has a background color of #156f0d.\n\n``<p style=\"background-color:#156f0d;\">Content here</p>``\n#156f0d border color\n\nThis element has a border color of #156f0d.\n\n``<div style=\"border:1px solid #156f0d;\">Content here</div>``\nCSS codes\n``.text {color:#156f0d;}``\n``.background {background-color:#156f0d;}``\n``.border {border:1px solid #156f0d;}``\n\n# Shades and Tints of #156f0d\n\nA shade is achieved by adding black to any pure hue, while a tint is created by mixing white to any pure color. In this example, #010601 is the darkest color, while #f4fef3 is the lightest one.\n\n• #010601\n``#010601` `rgb(1,6,1)``\n• #041703\n``#041703` `rgb(4,23,3)``\n• #082905\n``#082905` `rgb(8,41,5)``\n• #0b3a07\n``#0b3a07` `rgb(11,58,7)``\n• #0e4c09\n``#0e4c09` `rgb(14,76,9)``\n• #125d0b\n``#125d0b` `rgb(18,93,11)``\n• #156f0d\n``#156f0d` `rgb(21,111,13)``\n• #18810f\n``#18810f` `rgb(24,129,15)``\n• #1c9211\n``#1c9211` `rgb(28,146,17)``\n• #1fa413\n``#1fa413` `rgb(31,164,19)``\n• #22b515\n``#22b515` `rgb(34,181,21)``\n• #26c717\n``#26c717` `rgb(38,199,23)``\n• #29d819\n``#29d819` `rgb(41,216,25)``\n• #30e520\n``#30e520` `rgb(48,229,32)``\n• #41e732\n``#41e732` `rgb(65,231,50)``\n• #51e943\n``#51e943` `rgb(81,233,67)``\n• #61eb55\n``#61eb55` `rgb(97,235,85)``\n• #72ed67\n``#72ed67` `rgb(114,237,103)``\n• #82ef78\n``#82ef78` `rgb(130,239,120)``\n• #92f18a\n``#92f18a` `rgb(146,241,138)``\n• #a2f39b\n``#a2f39b` `rgb(162,243,155)``\n``#b3f5ad` `rgb(179,245,173)``\n• #c3f7be\n``#c3f7be` `rgb(195,247,190)``\n• #d3f9d0\n``#d3f9d0` `rgb(211,249,208)``\n• #e4fce2\n``#e4fce2` `rgb(228,252,226)``\n• #f4fef3\n``#f4fef3` `rgb(244,254,243)``\nTint Color Variation\n\n# Tones of #156f0d\n\nA tone is produced by adding gray to any pure hue. In this case, #3d3f3d is the less saturated color, while #0d7903 is the most saturated one.\n\n• #3d3f3d\n``#3d3f3d` `rgb(61,63,61)``\n• #394438\n``#394438` `rgb(57,68,56)``\n• #354933\n``#354933` `rgb(53,73,51)``\n• #314e2e\n``#314e2e` `rgb(49,78,46)``\n• #2d522a\n``#2d522a` `rgb(45,82,42)``\n• #295725\n``#295725` `rgb(41,87,37)``\n• #255c20\n``#255c20` `rgb(37,92,32)``\n• #21611b\n``#21611b` `rgb(33,97,27)``\n• #1d6517\n``#1d6517` `rgb(29,101,23)``\n• #196a12\n``#196a12` `rgb(25,106,18)``\n• #156f0d\n``#156f0d` `rgb(21,111,13)``\n• #117408\n``#117408` `rgb(17,116,8)``\n• #0d7903\n``#0d7903` `rgb(13,121,3)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #156f0d is perceived by people affected by a color vision deficiency. This can be useful if you need to ensure your color combinations are accessible to color-blind users.\n\nMonochromacy\n• Achromatopsia 0.005% of the population\n• Atypical Achromatopsia 0.001% of the population\nDichromacy\n• Protanopia 1% of men\n• Deuteranopia 1% of men\n• Tritanopia 0.001% of the population\nTrichromacy\n• Protanomaly 1% of men, 0.01% of women\n• Deuteranomaly 6% of men, 0.4% of women\n• Tritanomaly 0.01% of the population"
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https://bydokelyqogy.elizrosshubbell.com/symplectic-methods-in-harmonic-analysis-and-in-mathematical-physics-book-42914ls.php | [
"Last edited by Zulkijin\nSaturday, July 18, 2020 | History\n\n2 edition of Symplectic Methods in Harmonic Analysis and in Mathematical Physics found in the catalog.",
null,
"# Symplectic Methods in Harmonic Analysis and in Mathematical Physics\n\n## by Maurice A. Gosson\n\nWritten in English\n\nSubjects:\n• Global differential geometry,\n• Mathematics,\n• Operator theory,\n• Partial Differential equations\n\n• Edition Notes\n\nThe Physical Object ID Numbers Statement by Maurice A. Gosson Series Pseudo-Differential Operators, Theory and Applications -- 7 Contributions SpringerLink (Online service) Format [electronic resource] / Open Library OL25546020M ISBN 10 9783764399917, 9783764399924\n\n24 Chapter 2. The Symplectic Group where f∗σ is the pull-back of the two-form σ by the diffeomorphism f: f∗σ(z 0)(z,z)=σ(f(z 0))Df(z 0)z,Df(z 0)z). (Df(z0) the Jacobian matrix at z 0.) In particular one immediately sees that a symplectomorphism is volume-preserving since we then also have f∗ Vol = Vol in view of (). The language of differential form allows an elegant . Harmonic and Applied Analysis: From Groups to Signals is aimed at graduate students and researchers in the areas of harmonic analysis and applied mathematics, as well as at other applied scientists interested in representations of multidimensional data. It can also be used as a textbook. for graduate courses in applied harmonic analysis.\n\nSince then it has grown to a powerful machine which is used in global analysis, spectral theory, mathematical physics and other fields, and its further development is a lively area of current mathematical research. In this book extended abstracts of the conference 'Microlocal Methods in Mathematical Physics and Global Analysis', which was held Brand: Springer Basel. Open Math Notes. AMS Open Math Notes is a repository of freely downloadable mathematical works in progress hosted by the American Mathematical Society as a service to researchers, teachers and students. Bestsellers Sale. Enjoy 40% off .\n\nHusimi Parametric Oscillator in Frame of Symplectic Group Q-oscillators; Analysis and Mathematical Physics. Physics ' Geometrical Theory of Dynamical Systems and Fluid Flows. 伍连德研究：经验、认同、书写. A Guide to Mathematical Methods . The topics discussed at the meetings, while within the broad area of differential geometric methods in physics, have focused around quantization, coherent states, infinite dimensional systems, symplectic geometry, spectral theory and harmonic : Hardcover.\n\nYou might also like\n\n### Symplectic Methods in Harmonic Analysis and in Mathematical Physics by Maurice A. Gosson Download PDF EPUB FB2\n\nThis book is primarily directed towards students or researchers in harmonic analysis (in the broad sense) and towards mathematical physicists working in quantum mechanics.\n\nIt can also be read with profit by researchers in time-frequency analysis, providing a valuable complement to the existing literature on the topic. Symplectic Methods in Harmonic Analysis and in Mathematical Physics by Maurice de Gosson,available at Book Depository with free delivery worldwide.\n\nGet this from a library. Symplectic methods in harmonic analysis and in mathematical physics. [Maurice de Gosson] -- The aim of this book is to give a rigorous and complete treatment of various topics from harmonic analysis with a strong emphasis on symplectic invariance properties, which are often ignored or.\n\nFrom the reviews:\"The book under review presents new developments in harmonic analysis that have been inspired by research in quantum mechanics and time-frequency analysis. The book is well-written and the author has done a great job in.\n\nspringer, The aim of this book is to give a rigorous and complete treatment of various topics from harmonic analysis with a strong emphasis on symplectic invariance properties, which are often ignored or underestimated in the time-frequency literature. The topics that are addressed include (but are not limited to) the theory of the Wigner transform, the uncertainty principle (from the.\n\nHome» MAA Publications» MAA Reviews» Symplectic Methods in Harmonic Analysis and in Mathematical Physics. Symplectic Methods in Harmonic Analysis and in Mathematical Physics. Maurice A. de Gosson. Publisher: Springer. Publication Date: Number of Pages: Harmonic Analysis.\n\nLog in to post comments; Dummy View - NOT TO BE. 4 Most Efficient reference books for Mathematical Physics (preferably at Post graduate level, but these are equally good for undergraduates) 1) Mathematical methods in Physical sciences - Mary L Boas.\n\n(A great book with concise concepts, highligh. Symplectic geometry is very useful for clearly and concisely formulating problems in classical physics and also for understanding the link between classical problems and their quantum counterparts.\n\nIt is thus a subject of interest to both mathematicians and physicists, though they have approached the subject from different view points. This is the first book that attempts to 5/5(1). Properties. Every symplectic matrix is invertible with the inverse matrix given by − = −. Furthermore, the product of two symplectic matrices is, again, a symplectic matrix.\n\nThis gives the set of all symplectic matrices the structure of a exists a natural manifold structure on this group which makes it into a (real or complex) Lie group called the symplectic group.\n\nSymplectic Methods in Harmonic Analysis and in Mathematical Physics written by Maurice A. de Gosson This is an other great mathematics book cover the following topics. Part I Symplectic Mechanics Hamiltonian Mechanics in a Nutshell.\n\nThe theory of partial differential equations (and the related areas of variational calculus, Fourier analysis, potential theory, and vector analysis) are perhaps most closely associated with mathematical were developed intensively from the second half of the 18th century (by, for example, D'Alembert, Euler, and Lagrange) until the s.\n\nSymplectic Methods in Harmonic Analysis and in Mathematical Physics The novel approach to deformation quantization outlined in this text makes use of established tools in time-frequency Analysis. As one of the first volumes to discuss mathematical physics using Feichtinger's modulation spaces, this is a valuable reference.\n\nThis contemporary graduate-level text in harmonic analysis introduces the reader to a wide array of analytical results and techniques. Category: Mathematics Symplectic Methods In Harmonic Analysis And In Mathematical Physics. Fibre bundles, now an integral part of differential geometry, are also of great importance in modern physics--such as in gauge theory.\n\nThis book, a succinct introduction to the subject by renown mathematician Norman Steenrod, was the Harmonic Analysis (PMS), Volume Real-Variable Methods, Orthogonality, and Oscillatory Integrals.\n\n(PMS). de Gosson M.A. () Symplectic Capacities. In: Symplectic Methods in Harmonic Analysis and in Mathematical Physics. Pseudo-Differential. Applications of symplectic geometry now range from differential equations and dynamical systems to algebraic geometry, topology, representations of Lie groups, mathematical physics and more.\n\nThe current book originated with lectures given by Koszul in China inwritten and translated by Zou. The book introduces some methods of global analysis which are useful in various problems of mathematical physics.\n\nThe author wants to make use of ideas from geometry to shed light on problems in analysis which arise in mathematical physics. ( views) Elements for Physics: Quantities, Qualities, and Intrinsic Theories. Maurice A. de Gosson (born 13 March ), (also known as Maurice Alexis de Gosson de Varennes) is an Austrian mathematician and mathematical physicist, born in in Berlin.\n\nHe is currently a Senior Researcher at the Numerical Harmonic Analysis Group (NuHAG) of the University of mater: University of Nice, University of Paris 6. Group Theoretical Methods in Physics: Proceedings of the Fifth International Colloquium provides information pertinent to the fundamental aspects of group theoretical methods in physics.\n\nThis book provides a variety of topics, including nuclear collective motion, complex Riemannian geometry, quantum mechanics, and relativistic Edition: 1. April Applied and Computational Harmonic Analysis Maurice A de Gosson Gabor frames can advantageously be redefined using the Heisenberg–Weyl operators familiar from.\n\nGroup Theoretical Methods in Physics: Proceedings of the Fifth International Colloquium provides information pertinent to the fundamental aspects of group theoretical methods in physics.\n\nThis book provides a variety of topics, including nuclear collective motion, complex Riemannian geometry, quantum mechanics, and relativistic symmetry. Operator Theory, Analysis And Mathematical Physics Symplectic Methods In Harmonic Analysis And In Mathematical Physics Computer Algebra Recipes For Mathematical Physics Mathematical Physics.\n\nNorth.Fischer decomposition in symplectic harmonic analysis. Fischer Decomposition in Symplectic Harmonic Analysis. F aculty of Mathematics and Physics, Mathematical Institute."
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https://cs.stackexchange.com/questions/29698/homomorphism-erasing-information | [
"# Homomorphism erasing information\n\nI would be grateful if anyone could help me with the tricky exerciese *7.52 from Sipser's Introduction to the Theory of Computation 3rd ed.\n\nI got stuck in proving that, if P is closed under nonerasing homomorphism (replacing all characters with nonempty string), then P = NP. With nonerasing homomorphism I cannot delete the characters, but I can get rid off the information by overwriting it e.g. with 0s.\n\nI'm trying to complete the following idea:\n\n1. Checking whether a given assignment to propositional formula makes it true is in P class.\n\nLet s be the 0-1 string encoding both the formula and particular assignement.\n\n2. I'm trying to find such nonerasing homomorphism H over 0-1 alphabet that H applied to string s will erease (overwrite with something that will destroy information) the particular variables assignment but I must be able to read off the formula.\n\nHave anyone the idea how such a homomorphism could look like? (only 2 letter alphabet is allowed).\n\n• Why is the two letter restriction important for you? It is not explicitly in the exercise. – Hendrik Jan Sep 6 '14 at 10:28\n• Yes, there's no such restriction in the book, but without it the whole exercise is rather trivial. I thought the whole difficulty lies in it, but maybe you have right and I'm exaggerating. By the way, that is suspicious why the 0-1 alphabet introduce such limitation. – Adam Przedniczek Sep 6 '14 at 11:11\n\n## 1 Answer\n\nDenote the closure of a class C of languages under log-space many-one reductions by Closure( under log-space many-one reduction of, C), and the closure of a class C of languages under e-free homomorphisms by Closure( under e-free homomorphisms of, C). So for example\n\n• NP=Closure( under log-space many-one reduction of, NP)\n• NP=Closure( under e-free homomorphisms of, NP)\n\nWe want to show:\n\nIf P=Closure( under e-free homomorphisms of, P) then P=NP.\n\nFor this, it is sufficient to show\n\n1. P=Closure( under log-space many-one reduction of, P)\n2. NP=Closure( under log-space many-one reduction of,\nClosure( under e-free homomorphisms of, P))\n\nbecause if P=Closure( under e-free homomorphisms of, P) then\nNP=Closure( under log-space many-one reduction of,\nClosure( under e-free homomorphisms of, P))\n=Closure( under log-space many-one reduction of, P)=P\n\nIt is well known how to show (1). For showing (2), it is sufficient to show\n\n1. NP=Closure( under log-space many-one reduction of, {SAT})\n2. SAT $\\in$ Closure( under e-free homomorphisms of, P)\n\nbecause if X$\\subset$Y then Closure( under ... of, X)$\\subset$Closure( under ... of, Y).\n\nIt is well known how to show (3), which says that SAT is NP-complete under log-space many-one reductions. For showing (4), note that certificates of length O(n) are sufficient for SAT, where n is the length of the input. So we need to show that e-free homomorphisms can erase a certificate of length O(n) from the input, if the certificate is encoded suitably. This is straightforward in a certain sense, but we have to change the alphabet. The letters of the larger alphabet contain both an original input letter, and an additional certificate letter. To \"erase the certificate\", the homomorphism replaces this pair of \"(original letter, certificate letter)\" by the \"original letter\".\n\nIf you want to stay with the 0-1 alphabet, then homomorphisms from the free monoid over 0-1 can't erase information selectively enough, because such a homomorphism is already uniquely determined by the image of 0 and 1. But if you look instead at the submonoid of words whose length is a multiple of some number k, then you can easily find suitable homomorphisms."
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http://infomutt.com/e/eu/euclidean_space.html | [
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"Main Page | See live article | Alphabetical index\n\nEuclidean space is the usual n-dimensional mathematical space, a generalization of the 2- and 3-dimensional spaces studied by Euclid. Formally, for any non-negative integer n, n-dimensional Euclidean space is the set Rn (where R is the set of real numbers) together with the distance function obtained by defining the distance between two points (x1, ..., xn) and (y1, ...,yn) to be the square root of Σ (xi-yi)2, where the sum is over i = 1, ..., n. This distance function is based on the Pythagorean Theorem and is called the Euclidean metric.\n\nThe term \"n-dimensional Euclidean space\" is usually abbreviated to \"Euclidean n-space\", or even just \"n-space\". Euclidean n-space is denoted by E n, although Rn is also used (with the metric being understood). E 2 is called the Euclidean plane.\n\nBy definition, E n is a metric space, and is therefore also a topological space. It is the prototypical example of an n-manifold, and is in fact a differentiable n-manifold. For n ≠ 4, any differentiable n-manifold that is homeomorphic to E n is also diffeomorphic to it. The surprising fact that this is not also true for n = 4 was proved by Simon Donaldson in 1982; the counterexamples are called exotic (or fake) 4-spaces.\n\nMuch could be said about the topology of E n, but that will have to wait until a later revision of this article. One important result, Brouwer's invariance of domain, is that any subset of E n which is homeomorphic to an open subset of E n is itself open. An immediate consequence of this is that E m is not homeomorphic to E n if mn -- an intuitively \"obvious\" result which is nonetheless not easy to prove.\n\nEuclidean n-space can also be considered as an n-dimensional real vector space, in fact a Hilbert space, in a natural way. The inner product of x = (x1,...,xn) and y = (y1,...,yn) is given by\n\nx · y = x1y1 + ... + xnyn.",
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https://testbook.com/learn/maths-profit-and-loss/ | [
"# Profit and Loss: Concepts, Solved Examples, & Preparation Strategies\n\n0\n\nSave\n\nWe all are somewhat familiar with the concepts of profit and loss, when a person runs a business, he or she either faces loss or earns profits. When a person sells a product at a higher rate than the cost price, the difference of both amounts is called profit. On the other hand, when a person sells a product at a lower rate than the cost price, then the difference of both amounts is called loss.\n\nIn this article, we are going to cover the key concepts of Profit and Loss along with the various types of questions, and tips and tricks. We have also added a few solved examples, which candidates will find beneficial in their exam preparation. Read the article thoroughly to clear all the doubts regarding the same.\n\nAlso check Ratio and Proportion concepts here once you are through with Profit and Loss concepts!\n\n## What is Profit and Loss?\n\n### Profit\n\nWhen a person sells a product at a higher rate than the cost price, the difference of both amounts is called profit.\n\nProfit = Selling price – Cost price\n\n### Loss\n\nWhen a person sells a product at a lower rate than the cost price, then the difference of both amounts is called loss.\n\nLoss = Cost Price – Selling Price\n\n## Important Definitions of Profit and Loss\n\nLet us know some of the important definitions related to the profit and loss.\n\n### Cost Price\n\nCost price is the price at which a person purchases a product.\n\n### Selling Price\n\nSelling price is the price at which a person sells a product.\n\n### Market Price\n\nIt is the price that is marked on an article or commodity. It is also known as list price or tag price. If there is no discount on the marked price, then the selling price is equal to marked price.\n\n### Markup\n\nIt is the amount by which cost price is increased to reach market price. Markup = market price – cost price\n\n### Discount\n\nThe reduction offered by a merchant on marked price is called discount.\n\n### Successive Discount\n\nIf an article is sold at two discounts then it is said that it is sold after two successive discounts.\n\n### Dishonest Dealing\n\nIn it a person/shopkeeper sells any product at the wrong weight and earns profit. This can be done either by using false weight or by false reading.\n\n1) A shopkeeper claims to sell rice at cost price but uses a false weight of 900gm instead of 1000gm.\n\n2) A person sells cloth to the customer but uses false reading and gives 90 meters cloth instead of 100 meters.\n\n### Successive Selling\n\nIn it a product is sold for more than one time from one person to another person at some profit or loss. For example – A sold a pen to B at 10% profit and then B sold the pen to C at 20% profit.\n\n### Sales Tax\n\nDuring purchasing any product we have to give certain tax to the government. This additional payment is known as sales tax. Tax is always calculated on the selling price of a product.\n\nWhen you’ve finished with Profit and Loss, you can learn about Problem on Ages concepts in depth here!\n\n### How to Solve Question-Based on Profit and Loss – Know all Tips and Tricks\n\nCandidates can find different tips and tricks from below for solving the questions related to profit and loss.\n\nTip # 1: Candidates need to make sure that they know all the important formulas related to profit and loss which are mentioned below.\n\n• Profit % = profit x 100 / cost price\n• Loss % = loss x 100 / cost price\n• Markup % = (markup / cost price) x 100\n• Discount % = (discount / market price) x 100\n• If ath part of items are sold at x% loss, then for making no profit no loss, Required gain percentage in selling rest items = ax/(1-a)\n• If two objects are sold at same selling price, one at x% profit and other at x% loss, then Loss % = X^2/100\n• If the cost price of x articles is equal to selling price of y articles, then Profit percentage = {(x-y)/y} x 100\n\nTip # 2: If there are two successive profits or losses at x% and y% respectively, then the result- ant profit or loss% = x + y + xy/100\n\n• For profit, we take x and/or y as +ve value\n• For loss, we take x and/or y as –ve value\n\nTip # 3: Profit percentage and loss percentage are always calculated on C.P. unless stated otherwise.\n\nIf you’ve learned Profit and Loss, you can move on to learn Simplification and Approximation concepts.\n\n## Profit and Loss Solved Sample Questions\n\nQuestion 1: Marked price of a cricket bat is Rs 1000 and it is sold at Rs 800. Find the discount percentage.\n\nSolution: Discount = MP – SP = 1000 – 800 = Rs 200\n\nDiscount Percentage = (D/MP) × 100 = (200/1000) × 100 = 20%.\n\nQuestion 2: Marked price of a product is Rs 240 and 25% of discount is provided on it. Find the selling price.\n\nSolution: Discount = SP × 25% = 240 × (25/100) = Rs 60\n\nSelling price = MP – Discount = 240 – 60 = Rs 180.\n\n### Alternate Method:\n\nSelling Price = (100 – D %) × MP/100 = (100 – 25) × 240/100 = Rs 180.\n\nQuestion 3: A T-shirt is sold after providing two successive discounts of 20%. If marked price of a T-shirt is Rs 200 then find the selling price.\n\nSolution:\n\nDiscount 1 = 200 × 20/100 = Rs 40\n\nSelling price after 1st discount = 200 – 40 = Rs 160 Discount 2 = 160 × 20/100 = Rs 32\n\nSelling price after 2nd discount = 160 – 32 = Rs 128\n\n### Alternate Method:\n\nEffective discount = 20 + 20 – (20 × 20)/100 = 36% Discount = 200 × 36/100 = Rs 72\n\nSelling price = 200 – 72 = Rs 128.\n\nQuestion 4: A man gains 30% by selling an article for a certain price. If he sells it at double the current selling price, then what will be the profit percentage?\n\nSolution:\n\nLet, the cost price be Rs. x.\n\n∴ Selling price = Rs. 1.3x\n\nNow, new SP = Rs. 2.6x\n\n∴ Profit % = [(2.6x− x )] × 100 = 160%\n\nQuestion 5: If A bought an article at Rs.200 and sold it to B at 20% profit. Again B sold the article at 10% profit to C. Find the amount paid by C.\n\nSolution:\n\nPrice paid by B = 200 + (200/100 × 20) = 200 + 40 = Rs. 240\n\n∴ Price paid by C = 240 + (240/100 × 10) = 240 + 24 = Rs. 264\n\n### Alternate Method:\n\nNet profit = 20 + 10 + 20 × 10/100 = 32%\n\nHence, amount paid by C = 200 + (200/100 × 32) = Rs. 264.\n\nQuestion 6: A man sold 2 bicycles at the same selling price. One at 20% loss and other at 20% profit. Find overall profit and loss percentage.\n\nSolution: Let selling price be 300x\n\nThen, CP for 1st bicycle = 250x Then, CP of 2nd bicycle = 375x\n\nHence, Net CP = 625x and net SP = 600x\n\n∴ Net loss % = (25x/625x) × 100 = 4%\n\nQuestion 7: If the cost price of 5 oranges is equal to the selling price of 4 oranges, then find a profit percentage?\n\nSolution: Let cost price of an orange is Rs. 4 and selling price of an orange is Rs. 5 (we can assume it as it satisfies the given condition of the cost price of 5 oranges is equal to selling price of 4 oranges)\n\nHence, profit percentage = [(5 – 4)/4] × 100 = 25%\n\nQuestion 8: 10 pens costs Rs. 100 each. If half of the pens are sold at 10% loss then find at what price remaining each pens should be sold for making no loss and no profit.\n\nSolution: Total cost price of 10 pens = 10 × 100 = Rs. 1000\n\nSelling price of 1 pen = 100 – (100 × 10%) = Rs. 90 Hence, selling price of 5 pens = Rs. 450\n\nNow, selling price of remaining 5 pens = 1000 – 450 = Rs. 550 Hence, selling price of 1 pen = Rs. 110\n\n∴ Profit % = [(110 – 100)/100] = 10%\n\nQuestion 9: Ram purchased a bicycle for Rs. 5954. He had paid a VAT of 14.5%. Find the list price of the bicycle.\n\nSolution: Let the list price be Rs. a. VAT = 14.5%\n\nSo, a × (114.5/100) = 5954\n\n⇒ a = (5954 × 100)/114.5\n\n⇒ a = 5200\n\n∴ The list price of the bicycle was Rs. 5200.\n\nQuestion 10: Rajesh bought accessories worth Rs. 150. Out of the amount spent for buying accessories, Rs. 10 were spent on sales tax due to taxable purchases. If the tax rate was 10%, calculate the price of the tax free items.\n\nSolution: Total Price = 150 Tax paid = Rs. 10 Tax = 10%\n\nLet the taxable purchases = Rs x\n\n⇒ 10% of x = 10\n\n⇒ 0.1x = 10\n\n∴ x = 100\n\n∴ Tax free items = 150 – 100 – 10 = Rs.40\n\n## Exams where Profit and Loss is Part of Syllabus\n\nQuestions based on profit and loss come up often in various prestigious government exams some of them are as follows.\n\nWe hope you found this article regarding Profit and Loss was informative and helpful, and please do not hesitate to contact us for any doubts or queries regarding the same. You can also download the Testbook App, which is absolutely free and start preparing for any government competitive examination by taking the mock tests before the examination to boost your preparation.\n\n## Profit and Loss FAQs\n\nQ.1 What is profit and loss?\nAns.1 When a person runs a business, he or she either faces loss or earns profits. When a person sells a product at a higher rate than the cost price, the difference of both amounts is called profit. On the other hand, when a person sells a product at a lower rate than the cost price, then the difference of both amounts is called loss.\n\nQ.2 Where to find the important terms related to profit and loss?\nAns.2 Important terms related to profit and loss can be found above in the article.\n\nQ.3 How to solve the problem related to profit and loss?\nAns.3 Tips and tricks to solve the problems related to profit and loss are given above in the article. Kindly go through the article for the same.\n\nQ.4 Where I will find some of the sample questions related to profit and loss?\nAns.4 Various example questions along with their solutions are given above in the article. Kindly go through the article for the same.\n\nQ.5 In which exam questions from profit and loss come up?\nAns.5 Profit and Loss based questions come in various government competitive examinations on a regular basis. The names of such examinations are given above in the article."
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https://en.b-ok.org/book/440872/4e27d4 | [
"Main Mathematical logic with special reference to natural numbers\n\nMathematical logic with special reference to natural numbers\n\nThis book presents a comprehensive treatment of basic mathematical logic. The author's aim is to make exact the vague, intuitive notions of natural number, preciseness, and correctness, and to invent a method whereby these notions can be communicated to others and stored in the memory. He adopts a symbolic language in which ideas about natural numbers can be stated precisely and meaningfully, and then investigates the properties and limitations of this language. The treatment of mathematical concepts in the main body of the text is rigorous, but, a section of 'historical remarks' traces the evolution of the ideas presented in each chapter. Sources of the original accounts of these developments are listed in the bibliography.\nCategories: Mathematics\nYear: 2008\nEdition: 1\nPublisher: Cambridge University Press\nLanguage: english\nPages: 327\nISBN 13: 9780521090582\nISBN: 052109058X\nFile: DJVU, 5.29 MB\n\nMost frequently terms\n\nPost a Review",
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"You can write a book review and share your experiences. Other readers will always be interested in your opinion of the books you've read. Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them.\n1\n\nCombinators,lambda-terms and proof theory\n\nYear: 1972\nLanguage: english\nFile: DJVU, 1.44 MB\n2\n\nRecursion Theory for Metamathematics\n\nYear: 1993\nLanguage: english\nFile: DJVU, 4.70 MB\nMathematical Logic with special reference to the natural numbers S. W. P. STEEN Sometime Cayley Lecturer in pure mathematics in the University of Cambridge Cambridge at the University Press 1972\n\nPublished by the Syndics of the Cambridge University Press Bentley House, 200 Euston Road, London, NW1 2DB American Branch: 32 East 57th Street, New York, N.Y.10022 © Cambridge University Press 1972 Library of Congress Catalogue Card Number: 77-152636 IS B N: 0 521 08053 3 rp0 my Printed in Great Britain at the University Printing House, Cambridge (Brooke Crutchley, University Printer) u\n\nContents Preface p. xv Introduction 1 Chapter 1. Formal systems 10 1.1 Nature of a formal system p. 10 1.2 The signs and symbols p. 10 1.3 The formulae p. 12 1.4 Occurrences p. 13 1.5 Rules of formation p. 13 1.6 Parentheses p. 16 1.7 Abstracts p. 18 1.8 The rules of consequence p. 18 1.9 Corresponding and related occurrences p. 21 1.10 The \"K-rules p. 22 1.11 Definitions and abbreviations p. 23 1.12 Omission of parentheses p. 24 1.13 Formal systems p. 27 1.14 Extensions of formal systems p. 28 1.15 Truth definitions p. 29 1.16 Negation p. 29 Historical ebmaeks to Chapter 1 p. 30 Examples 1 p. 32 Chapter 2. Propositional calculi 34 2.1 Definition of a propositional calculus p. 34 2.2 Equivalence of propositional calculi p. 35 2.3 Dependence and independence p. 36 2-4 Models of propositional calculi p. 36 2.5 Deductions p. 39 2.6 The classical propositional calculus p. 42 2.7 Some properties of the remodelling and building schemes p. 43 2.8 Deduction theorem p. 48 2.9 Modus Ponens p. 49 [vii]\n\nviii Contents Contents a.10 Regularity p. 51 a.n Duality p. 52 2.12 Independence of symbols, axioms and rules p. 53 2.13 Consistency and completeness of ?PO p. 55 2.14 Decidability p. 57 2.15 Truth-tables p. 58 2-i6 Boolean Algebra p. 61 2-17 Normal forms p. 64 HlSTOBICAL EBMABKS TO ChAPTBE 2 p. 65 Examples 2 p. 68 3.27 Ordinals p. 175 3.28 Transfinite induction p. 178 3.29 Cardinals p. 180 3.30 Elimination of the e-symbol p. 184 3.31 Complete Boolean Algebras p. 192 3.32 Truth-definitions for set theory p. 193 3.33 Predicative and impredicative properties p. 198 3.34 Topology p. 199 HlSTOBICAL BBMABKS TO CHAPTEB 3 p. 201 Examples 3 p. 205 Chapter 3. Predicate calculi 3.1 Definition of a predicate calculus p. 72 3.2 Models p. 76 3.3 Predicative and impredicative predicate calculi p. 77 3.4 The classical predicate calculus of the first order p. 78 3.5 Properties of the system ^c p. 79 3.6 Modus Ponens p. 84 3.7 Regularity p. 88 3.8 The system !F\"C p. 90 3.9 Prenex normal form p. 91 3.10 H-disjunctions p. 99 3.11 Validity and satisfaction p. 108 3.12 Independence p. Ill 3.13 Consistency p. 113 3.14 !FC with functors p. 113 3.15 Theories p. 114 3.16 Many-sorted predicate calculi p. 115 3.17 Equality p. 119 3.18 Predicate calculus with equality and functors p. 123 3.19 Elimination of axiom schemes p. 126 3.20 Special cases of the decision problem p. 130 3.21 The reduction problem p. 136 3.22 Method of semantic tableaux p. 149 3.23 An application of the method of semantic tableaux p. 154 3.24 Resolved 1FC p. 160 3.25 The system 38^c p. 166 3.26 Set theory p. 171 72 213 Chapter 4. A complete, decidable arithmetic. The system Aoo 4.1 The system Aoo p. 213 4.2 The A00-rules of formation p. 213 4.3 The A00-rules of consequence p. 215 4.4 Definition of A00-truth p. 218 4.5 Definition of A00-falsity p. 219 4.6 Exclusiveness of Aaa-truth and A00-falsity p. 219 4.7 Consistency of Aoo with respect to A00-truth p. 224 4.8 Completeness and decidability of Aoo with respect to AQQ-truth p. 225 4.9 Negation in the system AOo P- 227 4.10 The system Boo (the anti-Ago-system) p. 228 HlSTOBICAL BEMABKS TO CHAPTEB 4 p. 229 Examples 4 p. 230 Chapter 5. A00-Definable functions 5.1 Calculable functions p. 232 5.2 Primitive recursive functions p. 233 5.3 Definitions of particular primitive recursive functions p. 235 5.4 Characteristic functions p. 243 5.5 Other schemes for generating calculable functions p. 246 5.6 Course of value recursion p. 247 5.7 Simultaneous recursion p. 247 5.8 Recursion with substitution in parameter p. 248 5.9 Double recursion p. 250 5.10 Simple nested recursion p. 252 5.11 Alternative definitions of primitive recursive functions p. 254 5.12 Existence of a calculable function which fails to be primitive recursive p. 258 232\n\nContents 5.13 Enumeration of primitive recursive functions p. 260 5.14 Definition of the proof-predicate for Aoo p. 265 5.15 The function Val p. 270 HlSTOEICAL EBMAEKS TO ChAPTBB 5 p. 273 Examples 5 p. 275 Chapter 6. A complete, undecidable arithmetic. The system Ao 278 6.1 The system Ao p. 278 6.2 A0-truth p. 279 6.3 Undefinability of A0-falsity in Ao p- 283 6.4 Enumeration of Ao-theorems p. 284 HlSTOEICAL EBMAKKS TO ChAPTBB 6 p. 286 Examples 6 p. 286 Chapter 7. A0-Definable functions. Recursive function theory 288 7.1 Turing machines and Church's Thesis p. 288 7.2 Some simple tables p. 300 7.3 Equivalence of partially calculable and partially recursive functions p. 304 7.4 The S-6-6' proposition p. 313 7.5 The undecidability of the classical predicate calculus ^c p. 314 7.6 Various undecidability results p. 316 7.7 Lattice points p. 318 7.8 Complete sets p. 323 7.9 Simple sets p. 323 7.10 Hypersimple sets p. 324 7.11 Creative sets p. 327 7.1a Productive sets p. 330 7.13 Isomorphism of creative sets p. 332 7.14 Fixed point proposition p. 334 7.15 Completely productive sets p. 335 7.16 Oracles p. 336 7.17 Degrees of unsolvability p. 343 7.18 Structure of the upper semi-lattice of degrees of unsolvability p. 346 7.19 Example of the priority method. Solution of Post's problem p. 352 7.20 Complete degrees p. 356 7.21 Sequences of degrees p. 361 Contents 7.22 Non-recursively separable recursively enumerable sets p. 364 7-23 Cohesive sets p. 365 7.24 Maximal sets p. 366 7.25 Minimal degrees p. 368 7.26 Degrees of theories p. 372 7.27 Chains of degrees p. 374 7.28 Recursive real numbers p. 375 HlSTOEICAL EBMAEKS TO CHAPTBK 7 p. 378 Examples 7 p. 382 Chapter 8. An incomplete undecidable arithmetic. The system A 387 8.1 The system A p. 387 8.2 Definition of A-truth p. 388 8.3 Incompleteness and undecidability of the system A p. 390 8.4 Various properties of the system A p. 391 8.5 Modus Ponens p. 396 8.6 Consistency p. 398 8.7 Truth-definitions p. 401 8.8 Axiomatizable sets of statements p. 403 HlSTOBICAL EBMAEKS TO CHAPTER 8 p. 407 Examples 8 p. 408 Chapter 9. A-Definable sets of lattice points 409 9.1 The hierarchy of A-definable sets of lattice points p. 409 9.2 Assets p. 413 9.3 Sets undefinable in A p. 416 9.4 f-definable sets of lattice points p. 417 9.5 Computing degrees of unsolvability p. 419 HlSTOEICAL EBMAEKS TO CHAPTER 9 p. 421 Examples 9 p. 421 Chapter 10. Induction 423 10.i Limitations of the system A p. 423 10.2 Possible ways of extending the system Ao p. 425 10.3 The system E p. 430 10.4 The system AT p. 438 10.5 Definition of an Aj-proof p 440 10.6 Theorem induction p. 445 10.7 The Aj-prooj'-predicate p. 448\n\nContents Contents 10.8 An example of an Arproof p. 451 10.9 Relations between Ao-theorems and ^-correctness p. 455 10.10 Properties of the system Aj p. 459 10.n Reversibility of rules p. 463 io.iz Deduction theorem p. 469 10.13 Cuts with an Aoo cut formula p. 470 10.14 ^ut removal with a weaker form of RZ p. 484 10.15 Cut removal in general p. 487 10.16 Further properties of the system A7 p. 497 10.17 The consistency of AT p. 500 Historical ebmabks to Chapter 10 p. 507 Examples 10 p. 509 Chapter 11. Extensions of the system A7 11.1 The system A' p. 511 11.2 Remarks p. 516 11.3 The hierarchy of systems Am p. 518 11.4 Properties of the systems A'\"' p. 518 11.5 The systems A<\">* p. 519 11.6 The definition of A-truth in A'* p. 521 11.7 Consistency of AT p. 530 11.8 Definition of Am-truth p. 535 11.9 Scheme for an Am-truth-definition p. 538 11.10 Truth-definitions in impredicative systems p. 540 11.11 Further extensions of the systems Am p. 541 11.12 Incompleteness of extended systems p. 543 11.13 Real numbers p. 544 11.14 The analytical hierarchy p. 553 11.15 On the length of proofs p. 558 Historical ebmabks to Chapteb 11 p. 559 Examples 11 p. 560 Chapter 12. Models 12.1 Models and truth-definitions p. 563 12-2 Models for Aoo p. 565 12.3 Models for Ao p. 566 12.4 Models for AIt Am p. 567 12.5 General models p. 567 12.6 Satisfaction p. 568 511 12.7 Examples p. 570 12.8 Non-standard models p. 571 12.9 A non-standard model for Ar p. 575 12.10 Induction p. 577 12.11 S-models p. 580 12.12 Ultraproducts p. 581 12.13 H-models p. 585 12.14 Satisfaction by ^-predicates p. 590 12.15 He-models p. 593 12.16 Completeness of higher order Predicate Calculi p. 594 12-17 Independence proofs p. 599 Historical bemarks to Chapter 12 p. 606 Examples 12 p. 607 Epilogue Glossary of special symbols Note on references References Index 609 611 619 621 631 563\n\nIntroduction gets a similar thought to the writer is a philosophical question which we do not discuss. Our first task then will be to construct a language suitable for our purposes; but we also want to teach it to other persons. There are two methods of doing this. The first method is to take advantage of the fact that we all already know a language of sorts, namely the imprecise language of daily use. This language has been invented over the ages for the purposes of descrip- descriptions, commands, instructions, explanations, excuses, deceits, lies, warnings, songs, etc., it is imprecise in that it is impossible to give a precise definition of 'sentence', 'word', 'noun' and many other syntactic terms. For instance, try and give a definition of 'word in the English language' and then test this definition against the works of Shakespeare and see if it is satisfactory. Such a definition to be of any use must be applicable to all writers at all times and not to a particular writer. For instance a definition such as ' any consecutive set of letters (i.e. without a blank between them) written by Shakespeare and printed in the first folio edition is a word and these are all the words' though a precise definition would be quite unacceptable. Since we know the English language, or at any rate some part of it, then we can use it to describe what we are constructing and this will be quite satisfactory; we are quite accustomed to doing this sort of thing. It is unsatisfactory in that it makes our development of arithmetic depend on the English language or at any rate on part of the English language, and we wish our development to be independent of imprecise concepts. This method is the usual method used for teaching a language. But there is another method which is quite satisfactory because if we use it then our development does not depend on any thing outside itself. This method could be used in a modified form for inter-planetary com- communication, and is a modification of the method by which we learnt English in the first place. It consists of teaching the language by repeatedly writing down the signs of the language (its alphabet) until the pupil has understood which are the correct signs and which are foreign, for instance foreign shapes could be put down from time to time and immediately obliterated. Then repeatedly writing down correctly formed sequences of correct signs and others which are incorrectly formed and immediately erasing these latter; continue them until the pupil has understood which sequences of signs are correctly formed Introduction (meaningful sentences). This process would be possible, but lengthy and boring in the extreme. We shall employ the first method in this book. It would be quite possible to use part of the English language instead of inventing a new language to deal with the matter treated in this book. But the result would be impossibly lengthy and much of the matter treated here would hardly have been thought of in the first place if we restricted ourselves entirely to the English language. For example in the English language there is (except for idiomatic variations such as gender, plurals, etc.) only one pronoun namely 'it'. In our language variables correspond to pronouns and we require an unending list of them. In the English language with its one pronoun we have to introduce lengthy circumlocutions such as the 'first', 'the second', etc. to obviate the lack of different pronouns. This has the obvious disadvantage of introducing natural numbers before one has defined them. But the main advantage in a symbolic language is that it makes the metamathematical investiga- investigations far simpler and the whole subject far easier to handle. Without it very little headway would ever have been made. The language we shall construct will only be suitable for expressing our thoughts on natural numbers. If we wanted to construct a language for some other purpose, say chemistry, then we should want many more new signs standing for further undefined concepts. The main difficulty in constructing a language for extramathematical purposes is that we are unable to give precise definitions of the concepts used. For instance the solution of the problem 'which came first the egg or the hen ?' is that we are as yet unable .to give a precise definition of egg or of hen which would be applicable to all times and places; thus the ancestors of a given present day hen if pursued far enough back into geological times would ultimately contain creatures that no one would now call hen, in between such a creature and the given live hen of today Would be a series of creatures changing by imperceptible degrees. Maybe at some future date we shall be able to define 'hen' as a creature with such and such a protein molecule in its genetic code. In other words all extramathematical concepts have furry edges. Thus to count the grains of sand on a beach (i) it is not clear where the boundaries of the beach are (ii) it is not clear what objects are grains of sand, they range from minute pebbles to impalpable dust. We do not want any vagueness of this sort which is inherent in all colloquial languages. Again, words in a colloquial language are used differently as\n\nIntroduction Introduction then we should be unable to distinguish between every pair and reading would be impossible, in this case there would be two signs which differed so little from each other that even an electron microscope would be unable to detect any difference. For instance if the symbols were circles ^gth inch in diameter lying in a one inch square and with centres at the rational points. Certain sequences of signs will be called well-formed, the rest are called ill-formed. Our language must be constructive, that is to say it must be possible to decide by a terminating process whether a given formula is well-formed or is ill-formed. It is plain that if this was otherwise then our language would be unreadable. The well-formed formulae in our language corre- correspond to the words and sentences of a conversational language. If we were teaching a conversational language then we should stop at this place. Having listed and explained a certain set of words and told how they can be formed into sentences we would then use the language for descriptions, instructions, etc. But in our case our motive is different, we want to obtain the true statements about natural numbers. Truth is a property of statements. The statement ' it snows' is true if and only if it snows. The inverted commas round a statement give us a name of that statement. We wish to give a truth definition for our language which will make precise our vague intuitive conception of arithmetic truth. This we do by noting that our statements are built up from atomic statements by connectives (often called logical connectives, because they can be used in any language). Our atomic statements are equations and inequations. For these we can give a simple and intuitively satisfying truth-definition. The truth of compound statements is then determined in a perfectly precise manner from the truth-values of the statements from which it is compounded. Unfortunately we are some- sometimes unable to find the truth-value of a statement because we are referred to an unbounded set of more elementary statements. But per- perhaps this is fortunate because if we had a method which would tell us the truth-value of any statement then all the interest would have gone from mathematics, we could turn the whole thing over to a computer which would tell us the answer. The theory of truth for arithmetic is a very difficult and complicated business. We shudder to think what difficulties we should encounter if we attempted to deal with truth in such disciplines as theology, law or politics, even if we had a suitable language for them, these disciplines make considerable use of the concept of truth; judging by history both ancient and modern it appears that the only way the human race has found of settling the question of truth in any of these disciplines is by the use of force. Even a truth-definition for physics would be extremely difficult to handle. Since our motive is to find true arithmetic statements and since we are without a terminating method of testing a given arithmetic statement for truth then we proceed by what is called the deductive method. We first display a class of statements which we accept as true, these we call axioms, they are statements that anyone studying arithmetic would be bound to accept as true. Then we list certain methods whereby from true statements we can obtain other true statements. These methods are usually expressed as figures, the given true statements are called the premisses and the one that is obtained from them is called the conclusion. They and the axioms virtually play the part of implicit definitions of our primitive signs and logical connectives. Thus starting with the axioms and applying the figures repeatedly we continue to produce more and more true statements. The statements produced in this way are called theorems. But we shall see that in all except the simplest languages some true statement will always elude us, i.e. theorems will be a proper subset of true statements. Our intuition makes us believe that a given meaningful statement is either true or false, that we are without a third possibility. This belief comes from the examination of testable cases-usually reducible to bounded sets. But when we come to deal with unbounded sets then a third possibility arises namely when we are unable to decide between truth and falsity. It seems rather useless to believe that each sentence is either true or false when we are unable to decide which is the case. Anyway we desire our language to be free from all beliefs. The theory of truth belongs to semantics, this is the theory of meaning. The structure of a language belongs to syntax, this includes the signs and the rules which tell us which sequences of signs are well-formed and which figures are deductions. From syntax alone we obtain a language without meaning. Meaning will be given to the languages which we construct, in that, for the arithmetic languages (without going into details) each statement will give rise to a structure consisting of pairs of sequences of tallies and according as these pairs of sequences of tallies are the same or are different\n\n8 Introduction Introduction then the statement will be true or false. A true statement will then corre- correspond to a possible situation as regards these sets of pairs of tallies and a false statement will correspond to an impossible situation as regards these sets of pairs of sequences of tallies. In this way our language will have meaning and the true statements will correspond to possible con- constructions involving sequences of tallies. The full details of this sketch will become apparent as the book proceeds, but we omit them here. We have just said that our motive is to obtain true arithmetic state- statements. But we shall only obtain a few of the most elementary such state- statements. Our interest is in what our languages can do and what their limitations are. That is to say we are interested in the metatheory of our languages. If we were interested in obtaining true arithmetic statements then we would be writing a book on arithmetic, it would differ from an ordinary book on arithmetic because we should begin with a very full syntactic introduction. Frequently we want to show that each formula which has one property also has another property. We do this by showing outright that the shortest formulae with the first property also have the second property, then we show that if each formula having the first property and shorter than a given formula having the first property also has the second property then the given formula also has the second property. In this way we give sufficient instructions to obtain for a given formula having the first property a detailed demonstration that it also has the second property. This method we call formula iTiduction, it is distinct from mathematical induction. It has often been said that a formal system is just a meaningless game with symbols. In our case this is not so, we have something definite to say and have invented a language in which to say it. It is of course easy to invent a formal system void of meaning, sometimes such systems are useful to investigate, some like Post's productions are obtained by formalizing the essential properties of formal systems such as ours. course is due to Freudental A960). The terms 'object language' and 'metalanguage' are due to Carnap A957). The idea of using a tape divided into squares with only one symbol on a square is due to Turing A936, 1967), who used it in his machines. Russell once said 'no two x's are alike'. The term ' new' in the sense in which we have used it is due to Quine A951). Turing makes remarks A936,1967) about the unfeasibility of using an unbounded set of distinct symbols by making a definition of 'neighbourhood' for a symbol. Tarski A933-56) exhaustively discusses the concept of truth in formalized languages. Brouwer in his intuitionism -ably expounded by Heyting A956)-discards the hypothesis that a statement is either true or false. This is commonly called T.N.D. (Tertium non datur). Lorenzen A955) has a useful discussion about formula induc- induction and various other kinds of induction, which are used in the metalanguage. Historical remarks Brouwer A947) suggested that our concept of number derives from our perception of our own heartbeats. Progressions are discussed in Principia Mathematica, Whitehead & Russell. For remarks on formal and informal languages see Carnap A957). The method suggested for planetary inter-\n\nChapter 1 Formal systems i. i Nature of a formal system A. formal system is constructed by choosing a set of signs and laying down rules for their manipulation. We have a tape marked into consecutive squares which can always be lengthened, so that we always have vacant squares at the right. The signs are placed on consecutive squares of the tape from left to right, at most one sign to a square. We use capital ell in script type (=??) with or without superscripts or subscripts to denote an undetermined formal system. 1.2 The signs and symbols The signs of a formal system =??, called =??-signs, must be displayed by representative figures and it must be possible to distinguish between them and to recognise them on different occasions and to decide of an object whether it is intended to represent an j??-sign or whether it is irrelevant. These conditions are required in order that reading the system be possible. We lack means of displaying an unending list of distinct signs and if we make a list of distinct signs we shall have to stop at some place. Moreover at any stage in our work we shall only require a set of signs that can be displayed, so that the restriction to an initial displayed list of signs is without restriction on our work. The judgement whether a given mark or figure is intended to represent an j??-sign must be left to the reader. The =S?-signs in the initial displayed list are called primitive ?f-signs. In some formal systems we require a method whereby we can always obtain a new sign of a certain kind, that is a sign which is distinct from any sign of that kind, used up to that place. In order to be able to do this, starting with an initial displayed list, we use what we call compound JiC-signs, that is certain sequences of o??-signs which can be generated according to some fixed plan. If the scheme of generation can be carried 1.2 The signs and symbols 11 as far as we wish we can generate a new compound =S?-sign according to the scheme at any place we desire. The method we shall adopt is to select a primitive =S?-sign and obtain compound J?-signs by continually adding superscript primes to the right. For example, in this book we shall only need one scheme of generation, we shall use the sequence which begins as follows: x x to obtain an unlimited supply of compound =S?-'signs which we shall call variables. We can describe this scheme of generation thus: (i) 'x' is a variable, (ii) if ? is a variable then so is ?\"', (iii) a sequence of primitive =S?-signs is a variable if and only if it is obtained from (i) and (ii). Here ? stands for an undetermined primitive or compound =S?-sign and ?\"' stands for the result of superscripting a prime at the end (in the next square on the tape) of that undetermined primitive or compound JSf-sign. The clause (ii) could have been worded 'the result of attaching a superscript prime at the end of a variable is a variable'. The sign between capital sigma and the prime is called the concatenation sign. It is to be distinct from the =S?-signs, it is used to augment the English language when we talk about a formal system. A primitive =S?-sign used like the prime above is called a generating sign. The symbols of a formal system, called =??'-symbols, are the primitive & -signs other than any generating signs together with the compound 3?-signs which are obtained by a scheme of generation. Thus the set of primitive =S?-signs is limited and can be displayed, but if there are any schemes of generation then the ^-symbols can only be generated as far as desired. We shall use capital sigma with or without superscripted primes or subscripts to denote an undetermined =S?-symbol. Thus ?' will stand for an undetermined =S?-symbol, ?\"' will stand for the result of superscripting a prime at the right of an undetermined =S?-symbol. We use the notation (v) to stand for an undetermined succession of generating signs and {Sv) for the result of adding another generating sign at the end. Similarly for (k), F), (A), and (/i). Thus ?',?\",?'\", ...,?<\">, will stand for a sequence of undetermined ^-symbols. We shall frequently use Greek\n\n12 Ch. 1 Formal systems letters and the concatenation sign in this way, it will make our descrip- descriptions and instructions easier to follow. There is one further requirement: any linear sequence of ^-symbols must be uniquely constructed from =S?-symbols. For instance if 1 00 10 01 were ^-symbols obtained from the primitive =S?-signs 0 and 1 then the linear sequence 1001 could be constructed from ^-symbols in two dif- different ways. Similarly a linear sequence of generating signs must be uniquely constructed. For instance if ' and \" were different generating signs then x'\" would be ambiguous. Again if we allowed the same gene- generating sign to be used fore and aft so that '\"x, \"x, and 'x were ^-symbols as well as x', x\" and x'\" then x'\"x could be constructed in several ways. 1.3 The formulae An ^-formula is a terminating sequence of =S?-symbols. Thus an =S?-symbol standing alone is an =S?-formula. The null ^-formula is the empty terminating sequence of =§?-symbols. A non-null terminating sequence of generating signs (if JSP contains any such signs) fails to be an =S?-formula. Given a terminating sequence of signs (whether =S?-signs or other signs) it is possible to decide whether it is an ^-formula or contains signs foreign to the system ?? or contains generating signs incorrectly placed. It is possible to decide of an ^-symbol whether it is the end symbol of a given ^-formula or is the initial =S?-symbol of that =??-formula and if neither is the case then it is possible to find the =S?-symbol which precedes it and the =??-symbol which follows it, our device of the tape divided into consecutive squares does this. We shall use capital phi, psi, chi and omega with or without super- superscripts or subscripts to denote undetermined =S?-formulae. If O and T are ^-formulae then <3>nxF shall denote that =??-formula which is obtained by extending the ^-formula <E> by the addition of the ^-symbols of the =S?-formula T to the right of O in the order in which they occur in T. Similarly if S is an =S?-formula then OnvFnS shall denote that =S?-formula which is obtained from the =S?-formula OnxF by addition of the =S?-symbols of S to the right of the =S?-formula OnvF in the order in which they occur in S. Clearly the same =S?-formula is obtained if we attach Y to the right of the =S?-formula O. O is called an initial segment of OnxF, 3 is called an end segment of OnTnS, T is called a consecutive part of OnxF, here O or Y or 3 may be null. OT without concatenation sign denotes the 1.3 The formulae 13 sequence of separate formulae O and T in that order, there is then at least one blank square between them on the tape. The absence of con- concatenation sign denotes that we are dealing with a sequence of separate formulae rather than with a single formula. Usually written OTorO,T. 1.4 Occurrences An occurrence of an S?'-symbol ? in an ^-formula O is an initial segment of <E> which ends with the j??-symbol S. Note that by definition of initial segment the part of O which is left when the initial segment is removed is an =S?-formula, the end segment may be null. Thus if O' is an =S?-formula and ? is an =S?-symbol belonging to a scheme of generation with the prime as generating sign then O'n? fails to be an occurrence of the ^-symbol ? in the =S?-formula O'n?n/ because by definition of initial segment O'n? fails to be an initial segment of the ^-formula O'\"?n', the part left when <E>'n2 is removed is only the prime which fails to be an =S?-formula. A given =S?-symbol may have several distinct occurrences in a given ^-formula. If the last ^-symbol of the ^-formula O is S then O itself is an occurrence of S in O. The null formula fails to be an occurrence of any =S?-symbol in any =S?-formula. Similarly an occurrence of a non-null ^-formula T in an i?-formula O is an initial segment 0' of O which has the end segment T. Note that by definition the remainder of 0 when O' is removed is an =S?-formula. The remainder may be null. 1.5 Rules of formation Any formal system that has been constructed till the present time can be modified so that it uses the rules of formation that we are now going to give. Thus we say that the rules of formation are the same for all formal systems. The symbols of a formal system are of two kinds: proper symbols and improper symbols. The improper symbols are: X abstraction symbol, ( left parenthesis, ) right parenthesis. The abstraction symbol may be absent. There must be some proper symbols. The proper symbols are of two species at most; variables and constants. Each proper symbol has a type associated with it, the improper\n\n14 Ch. 1 Formal systems symbols are type-less. If 2 is a variable and' is a generating symbol then 2\"' has the same type as 2. We use small alpha, beta with or without superscript primes for undetermined type symbols. The type symbols are generated according to the following scheme: (i) omicron is a type symbol, (ii) iota with or without superscript primes is a type symbol, (iii) if a, /? are type symbols then so is (nan/?n), (iv) these are the only type symbols. Some of these type symbols may be absent from a given formal system. Thus a formal system might have type symbols only of the types o, (oo), ((oo) o). In writing type symbols we frequently omit the outer pair of parenthesis and omit other parentheses by association to the left. The omitted parentheses can then be replaced uniquely so that the result is a correctly formed type symbol. Thus we sometimes write: ooo for ((oo)o), o(oo) for (o{oo)), and so on. The rules of formation uniquely associate a type to certain =S?-formulae and enable us to find it or to decide that the =??-formula is without type. The =S?-formulae which have a type according to the rules of formation are called well-formed formulae (w.f .f.). The rules of formation also define a status (free or bound) for each occurrence of each variable in a well-formed formula and enable us to find it. In this way each occurrence of each variable in a well-formed formula is classified as a free occurrence or as a bound occurrence. When a type symbol is a suffix to a symbol then that symbol stands for an object of that type. The rules of formation are: (i) A symbol 2a of type a standing alone is a formula of type a. (ii) If 2 is a variable of type a then its occurrence in the formula 2 is free. (iii) If O(nary,) is a formula of type (nan/?n) and T» is a formula of type /? (fl*GG \\ , , I occur- occurrence of a variable 2 in the formula O^iyi) then (\"<!>' is a I, , I 1.5 Rules of formation 15 occurrence of the variable 2 in the formula (nO(naryn)nxF?), if T' is a I, ,1 occurrence of the variable 2 in the formula T» then \\bound/ p ( fCGG \\ (n<E>m n«n\\nvF' is a (, ,1 occurrence of the variable 2 in the v (a P' \\bound/ formula (\"^ (iv) If 2» is a variable of type ft and Oa is a formula of type a then (nXn2^,O\") is a formula of type (\"a\"/?\"). Each occurrence of the variable 2^ in the formula (nXn2?Oa) is a bound occurrence of the variable 2^ in the formula (nXn2?O. If O' is a (bound) occur- occurrence of a variable 2, distinct from the variable 2^, in the formula , - I occurrence of the variable 2 in the bound/ formula (nXn2^C). (v) A formula has a type if and only if a type is given to it by (i), (iii) and (iv). An occurrence of a variable is I. ,1 if and only if it v ' \\bound/ / free \\ is I, A according to (i), (ii), (iii) and (iv). \\bound/ An ^-formula which fails to be well-formed is said to be ill-formed. Given an ^-formula we can discover whether it is well-formed or ill- formed and if it is well-formed then we can find its associated type, the details will be given shortly. According to these rules the null formula is without type. The formation of the formula (\"Op^TJ) from the formulae O(nan»n) and T» is called application. A formula O(naryi) of the type (\"a\"/?\") is called a. functor of type (na\"/?n). In the application process a functor of type (\"a\"/?\") is given an argument of type /? and the resulting formula of type a is called the value of the functor for that argument. The formula (nXn2^Oa) formed from the formula Oa and the variable 2^ is called the abstract of Oa with respect to the variable 2^. The abstract is a functor, by application it can be given an argument of type /? and the resulting formula is of type a, thus (n(nXn2^O«)nY^) is of type a. If the formula O' is a free occurrence of the variable 2^ in the well- formed formula Oa then the occurrence (\"Xn2? O' of the variable 2^ in the well-formed formula (nX?<!>?), which by (iv) is a bound occurrence, is said to be bound by the occurrence of (nXnSA in (nXn2?O. The well-\n\n16 Ch. 1 Formal systems 1.6 Parentheses 17 formed part Oa of the well-formed formula (nXn21^ O?) is called the scope of the abstraction of the variable X^. If O'n(nXn2nSn) is an occurrence of (nXn2n3n) in Oa then each free occurrence of the variable 2 in S is bound by the occurrence O'n(nXnS of (nX\"S in <E>a. A bound occurrence O' of a variable 2 in a well-formed formula O is bound by an occurrence 0\" of (nXnS in O', and O\" is such that the scope of the occurrence O\" of (nX\"S in O' is the shortest well-formed formula *F such that O' is an occurrence of 2 in O\"nT. We also say that any well-formed part of S that contains a free occurrence of the variable 2 is bound by the occurrence <E>'n(nX of (nX in Oa. We say that a well-formed part S of Oa is free for 2 in Oa if it fails to be bound by any occurrence of (nXn2 in Oa. Thus the occurrence (nan/jn)\"S/5 °f the variable 2^ in the well-formed formula (nXnS^(nXnS;(n3(nan/,n)nS^)n)n) is bound by the occurrence (\"X^VS, of (\"X\"!)^ in that formula. i.6 Parentheses Suppose that En(nO(naIy,/nFj5)n3' is a well-formed formula where the parts 3 or S' or both may be null. Then the occurrence 3n( of the left parenthesis is said to correspond to the occurrence SXfy'V'v\")\"^) of the right parenthesis, and vice versa. These occurrences of parentheses are called mates. Similarly, if 3\"(nXnS^OS)n3' is a well-formed formula in which the parts 3 or 3' or both may be null, then the occurrences 3n( and 3\"(nX\"S?O?) Q? parentheges are caue(j mates. Each occurrence of a parenthesis in a well-formed formula has a unique mate. If <E>'\"( is an occurrence of a left parenthesis in a well-formed formula O then the occurrence of its mate is O'n(nO\"n) where (nO\"n) is a well-formed formula and O'n(\"O\"n) is an occurrence of a right parenthesis in O. Similarly for the mate of a right parenthesis. Lemma (i). // <E> is well-formed SC-formula then each occurrence of a left parenthesis in O has a unique mate, similarly for right parenthesis. The mate of a mate of the occurrence of a parenthesis is that occurrence of that parenthesis itself. Any proper initial segment O' of O contains an excess of occurrences of left parentheses, each occurrence of a right parenthesis in O' has its mate in <E>' but some occurrences of left parenthesis in O' lack mates in O'. Similarly a proper end segment <E>\" of <E> contains an excess of occur- occurrences of right parentheses, each occurrence of a left parenthesis in O\" has its mate in O\" but some occurrences of right parentheses in O\" lack mates in O\". The mates of a consecutive well-formed part of O are mates in O. If O is a single =S?-symbol then O is well-formed and is without paren- parentheses and the lemma follows trivially, otherwise O is of one of the forms: HTwrfE}) or (nXn3^\"a). Suppose the lemma has been demonstrated for well-formed formulae of shorter length than O, then the lemma holds for T(naiyi), 3^ and Ta. Clearly the lemma then holds for O. Given an ^-formula O we can discover whether it is well-formed or is ill-formed and find its type if it is well-formed as follows: if O is a single symbol then it is well-formed and its type is known. Otherwise O, if well- formed, must be of one of the forms: (\"Y^^a}) or (nXnS^TS), the associated types are a, (V/) respectively. In either case 0 must begin with a left parenthesis and end with a right parenthesis, otherwise it is ill-formed. Suppose the former, then remove the outer pair of paren- parentheses obtaining an =S?-formula O', if O' is null then O is ill-formed. If O is well-formed then O' must begin with X, (or a proper =S?-symbol of type (\"a\"/?\")) for some a, ft, otherwise 0 is ill-formed. If O' begins with X then the next symbol must be a variable if O is well-formed, otherwise O is ill-formed. Suppose O' begins with X\"!)^, where 2^ is a variable, remove this, we are left with an =S?-formula O\", 0 is well-formed if and only if 0\" is well-formed, hence O\" fails to be null if O is well-formed. Thus in this case we are referred to an =S?-formula shorter than O. The next case is when O' begins with a left parenthesis. Find the least initial segment of <[>' which fails to contain an excess of either kind of parenthesis. If we fail to find such a proper initial segment then, by the lemma, O is ill- fonned. Suppose we find this initial segment T then O' is of the form Tn3. Now 0 is well-formed if and only if T and 3 are both well-formed and of respective types (nan/?n), /?. The ^-formulae T and 3 are shorter than O. The last case is when O' begins with the =S?-symbol W(n^n), remove it and we are left with an i?-formula O\". Now O is well-formed if and only if 0\" is a well-formed =S?-formula of type ft also O\" is shorter than 0. Thus again we are referred to =S?-formulae shorter than <E>. Clearly the process will terminate and we shall discover whether O is well-formed or is ill- formed and if it is well-formed then we shall find its type. We say that the formulae <t> and *F overlap if some non-null proper\n\n18 Ch. 1 Formal systems end segment of O is a non-null proper initial segment of T, similarly with O and T interchanged. Lemma (ii). // O and W are well-formed ^-formulae then either O is a consecutive part of Y or T is a consecutive part of <E> or O and W fail to overlap. The first two alternatives arise in application and in abstraction. Suppose O is O'nS and T is S'T', where S, S', O' and T' are non-null. Since S is a proper end segment of O it will contain occurrences of right parentheses which lack their mates, but every occurrence of a left parenthesis in H will have its mate in 3, since S' is a proper initial segment of T it will contain occurrences of left parentheses which lack their mates, but every occurrence of a right parenthesis in S' will have its mate in S'. Hence S is distinct from S' and so O and W fail to overlap. Corollary. // O is a well-formed SC-formula then the scopes of the various occurrences of X in O, if any, fail to overlap, but the scope of an occurrence may be contained in the scope of another occurrence. i.y Abstracts Suppose that (j>{?) is of type /?, where ? is of type a, then X?. <{>{?] is of type (/?a). Given an argument 8 of the type a, the result, by the X-rules becomes <f>{8}, which depends on the formula d of type a. Thus the abstract X?. <f>{?] depends on all formulae of type a. Now consider the following situation: Let i/r{r], ?} be of type /?, where 7] is of type (/?a), and ? is of type a, then X?/. \\${>}, ?}, call this K, is of type /?(/?#) and depends on all formulae of type (/?a). Let A be of type /?(/?(/?a)), then AX?/. ijr{i], ?} is of type /?. Let \\${C> ?} be of type /?, where ? is of type /?, then X?. 0{AX?/. ijr{i], ?},?}, call this H, is of type (/?a), and since it contains K then it depends on all formulae of type (/?a) including itself! This form of circularity is known as predicativity, and H is called a, predicative formula. This circularity seems unsatisfactory, to avoid it we have to make complicated changes in type theory. The situation will be reopened later. i.8 The rules of consequence Well-formed formulae of a formal system ?(? of type o (for some systems further effectively testable structural conditions are required) will be 1.8 The rules of consequence 19 called ^C-statements, if there are any further conditions then it must be possible to decide if they are fulfilled or if they are violated. An ^-state- ^-statement will be called closed if every occurrence of each variable in the jSf-statement is a bound occurrence, otherwise the =S?-statement will be called open. In some formal systems it is required that an =S?-statement be closed. Certain =??-statements may be called SC-axioms, and if there are jSf-axioms then there must be a method whereby we can decide of an jSf-statement whether it is an =S?-axiom or is distinct from every=S?-axiom. Thus we could display the =S?-axioms or we could give a description of them by laying down that any =S?-statement satisfying such and such structural conditions is an =S?-axiom (provided we have a method whereby we can decide of an =S?-statement whether it satisfies the condi- conditions or fails to do so). Such a description is called an SC-axiom scheme. There may also be given some rules of procedure called SC-rules, these are relations between ^-statements whereby given a set of =S?-statements satisfying certain structural conditions we may by applying one of the JSf-rules produce another =S?-statement whose structure depends in some definite manner on the structure of the members of the given set. The given set of =S?-statements is called the premisses (or premiss if there is only one in the given set) and the =S?-statement produced by application of the rule is called the conclusion of that rule. It must be possible to decide whether a given =??-statement is the result of an application of an JSf-rule to given premisses or whether this fails to be the case. The JSf-rules are depicted as follows: 77 ' and so on. There may be conditions on O, T or on O, W, S, if so then it must be possible to decide if these conditions are satisfied or are violated. The conditions must be checked before using the rule. The =S?-statements above the line are called the premisses or upper formulae, the ^-state- ^-statement below the line is called the conclusion or lower formula. The •SP-axioms and the =S?-statements which result from applications of the •S^-rules are called ^-theorems. A partially ordered set of =S?-statements Which contains a unique last ^-statement and is such that each ^-state- ^-statement in the set is either an J5f-axiom or results from previous\n\n20 Ch. 1 Formal systems 1.8 The rules of consequence 21 =??-statements in the set by application of an »??-rule is called an &-proof of the last =??-statement in the set. In particular cases the partially ordered set might be linearly ordered. A connected tree-like figure consisting of columns of =??-statements with an =S?-axiom at the head of each column and an application of an =S?-rule between each consecutive vertical pair of members of a column or at a place where two or more columns termi- terminate and are replaced by a single column and which finally ends in a single =S?-statement 0 is called an SC-proof of O in tree-form or an ?f-proof-tree of O. The =??-statement <E> is called the base of the tree. The portion of the tree which can be reached by proceeding upwards from a given .??- statement T in the tree is an =S?-proof of T in tree-form and is called the branch of the tree ending in T. An ?f-proof thread is a linear column of =S?-statements which forms a consecutive part of an =S?-proof-tree. An =S?-proof can be checked since it is possible to decide if a sequence of signs is an ^-formula and to decide the type of a well-formed =S?-formula and so decide whether it is an ^-statement and to decide whether an ^-statement is an =S?-axiom and to decide applications of =S?-rules. The set of ^-axioms and =S?-rules are collectively known as the 3?-rules of consequence. An ?? -theorem-scheme is a description of a set of =S?-theorems together with instructions for obtaining the ,S?-proof of any member of the set. =??-theorem-schemes are frequently stated when a set of =??-theorems have =S?-proofs on the same general pattern, we then describe the pattern. In a formal system the =S?-rules are normally ??'-rule-schemes, that is to say they are descriptions applicable to a variety of cases. O \\$\\$' We use the notation — *, -™— *, etc. to denote that from an =S?-proof of O (of O and O', etc.) we can find an =S?-proof of T. We use the notation O O O' = , , etc. to denote that T can be obtained from O (from O and O', etc.) by the =S?-rules. In this case if the upper formula (formulae) are ir -theorems then so is the lower formula. ^ *, *, = , etc. are *, = called derived ?f-rules. The demonstration of™ * consists in giving instruc- O tions to find an =??-proof of T from an =S?-proof of O. For = we must give the =S?-rules used to transform 0 to W. We also use the notation ;==^ to denote that each of Y', ...,YM may be obtained from O', ...,OOT by the =S?-rules. Similarly we use the notation \"' k)* to denote that from the =??-proofs of O',..., Ow we can effectively find jSf-proofs for each of T', .,.,W If Q = 0 the above notations reduce to f^TrW and T'...TW* respectively. These mean that T' TW are jSf-theorems. Note that — whenever S is an ^-theorem, in this case <[> is unused. Also if ^ then „ here again T is unused. 1.9 Corresponding and related occurrences Let capital gamma with or without superscripts or subscripts be signs foreign to a formal system =??. Then O{F} shall denote a terminating linear succession of =??-symbols and F's, O{F, F'} shall denote a termi- terminating linear succession of =S?-symbols F's and F\"s, here O{F'} is to be without occurrences of F, O{F\", F'\"} without occurrences of F, F', and so on. The terminating linear successions 0{F}, 0{F, F'}, and so on, are called =??-formula-forms. If T, W are non-null ^-formulae then 0{T}, O{T, T'} shall denote the results of everywhere replacing F, F' by T, T' respectively in the =S?-formula-form 0{F}, and so on. This is done by inserting a piece of tape which exactly contains the =S?-formula T in place of the square which contains F, this is to be done for each occur- occurrence of F, in O{F}. Similarly each square containing F' is replaced by a piece of tape which exactly contains W. Thus if O{F, F'} is <&'TnO\"TO\"'TnO\"\" where O', O\", O'\" and O\"\" are ^-formulae, hence Tidthout occurrences of F, F', then O{T,T'} is OTnO\"nT'nO'\"nTnO'\"'. The ^-formulae O{T}, O{T,T'} are without occurrences of F or F'. The ^-formulae T, T' might be single ^-symbols, the ^-formulae V, T' might be identical. O{\\$} denotes one of O{F}, O{F, F'}, etc. when it occurs the context will show which is intended. Let O{F} be an =S?-formula-form and let T^H be an occurrence of the ^-formula 3 in the ^-formula T, and let O'{F}T be an occurrence of F in the ^-formula-form O{F}. Then O^T}^'^ is called an occurrence °f E in O{T} which corresponds to the occurrence of T'nS of 3 in T by Substitution of T for F in O{F}. The =S?-formula-form must be specified\n\n22 Ch. 1 Formal systems 1.10 The X-rules 23 because there might be occurrences of S or of T in O{F}. Suppose O\"{F} is an occurrence of 3 in O{F} then O\"{T}nS is distinct from any occurrence of H in OIT} which corresponds to the occurrence of m\"\"E of 3 in Y by substitution of T for F in O{F}. We require the notion of corresponding occurrences because we shall build up ^-formula by certain rules and shall require to trace =S?-symbols or ^-formulae through the build up. Sometimes we build up an i?-formula by certain rules and in the process transform some consecutive parts by other rules, and we may wish to trace these changing parts through the build up and transformation process. In this case we shall speak of related occurrences, which we now define. Let <E>{F,\\$'} be an i?-formula-form, let W{&'}nE{&'} be an occurrence of S{®'} in T{®'}. Let O'{Y{®'}, ®'}nx?\"{®'}na{®'} be an occurrence of 3{©'} in O{Y{©'}, &'} corresponding to the occurrence W{&'}nE{&'} of 3{\\$'} in Y{®'} by substitution of Y{F'} for T in O{F, &'}. Then O'{Y{2B'}, 2B'}nY'{2B'}n3{2B'} is called an occurrence of 3{2B'} in O{T{2B'}, 2B'} related to the occurrence Y'{2B}n3{2B} of 3{2B} in Y{38} by substitution of T{©'} for F in O{F, ©'} and the substitution of SB' for 3\\$ in O{Y{®'}; &'}. If <&x{rfi} is an ^-formula form and if O^V,,} is a well-formed ^-formula of type a whenever T^ is of type /? then we shall say that OJT^} is an =??-formula-form of type a. Similarly if 0A^, F^} is an ^-formula-form and if O^T^, T^} is an ^-formula of type a whenever T^ is of type /? and Wp, is of type /?', then <S>{Tfi, F^} is called ani?-formula- form of type a, and so on. If a is omicron we sometimes omit the suffix a and speak of an =??'statement-form, similarly we use the term 'functor- form', etc. We define 'free', 'bound', 'open', 'closed', etc. for formula- forms as for formulae. Thus if \\${1^} is a closed J?-statement-form and 2^ is a variable new to 0A^} then \\${1^} has S^ as sole free variable provided that some occurrence of F^ in ^{r^} is outside the scope of any occurrence of XF^ in i.io The \"k-rules If lambda is an ^-symbol then =?? may contain the \\-rules applicable to =S?-variables and =S?-formulae of certain types. The \\-rules for =S?-variables of type /? and =S?-formulae of type a are: (i) If S^ is an =??-variable of type /? and T^ is an ^-formula of type /? and O^Y^} is an ^-formula of type a whose =S?-formula-form Oa{F/S} lacks occurrences of the ^-variable S^ then is a rule of procedure provided that each occurrence of an ?P- variable 2 in QJ^V^ which corresponds to a free occurrence of that variable in T^ is a free occurrence of 2 in ^{T^}. (ii) Conversely with the same proviso and the same notation is a rule of procedure. (iii) Let O{F} be an ^-formula-form, ? an ^-variable. Let O{?} be the scope of an occurrence of (nXnS in an ^-formula vF{(nXn?nO{?}\")}. Let ?' be an oS?-variable distinct from and of the same type as the invariable 2. Let 0{F} lack free occurrences of the ^-variables S, ?'. Let each occurrence of F in O{F} be outside the scope of any occurrence of (nXn21' or of (\"XnS that there may be in T{(nXnS\"O{S}n)} O{F} then is a rule of procedure. It is called change of bound variable. If each occurrence of F in O{F} lies outside any scope of XnS then we say that F is free for 2 in O{F}. x.iz Definitions and abbreviations We shall frequently introduce new symbols to abbreviate closed formulae of a given formal system =??. The new symbol is to be considered as everywhere replaced by the =S?-formula it abbreviates. This device is adopted merely to prevent ^-formulae becoming of unmanageable length; it also facilitates reading, and enables one more clearly to see certain aspects of the structure of an =S?-formula. An ^-formula occu- occupying a few pages of print would be difficult to assess; such a formula might begin with several lines consisting entirely of left parentheses; but if broken up into parts and new symbols used as abbreviations for the different parts we might arrive at a formula which could be printed on ft line and certain features of its construction would be apparent at\n\n24 Ch. 1 Formal systems 1.12 Omission of parentheses 25 a glance. If the new symbol abbreviates a well-formed =??-formula then it can be given a type. Sometimes we shall introduce formulae containing new symbols to stand for certain other structurally related ^-formulae. When this is done the new symbol itself fails to stand for an ^-formula but certain formulae containing the new symbol stand for certain =S?-formulae. This device is usually adopted if S? fails to contain the abstraction symbol and its rules. Thus 'N' could be introduced by (niVnOn) for (n(n?nOn)nOn), where 0 is of type o and '8' is of type ooo, so that 'N' is of type oo. But if abstraction is present together with the X-rules then we could define N for (nXnSn(T<SnSn)nSn)n)> where ? is a variable of type o. Another case of this type of definition which occurs in Ch. 4 is: ^\"[\"\"\"O\"\"\"], for the formula which results when we everywhere replace * by = = by * V by & & by V Here N,[,],\" and \" are new symbols. Sometimes we replace an =S?-formula by another one containing the same proper symbols but in a different order. This rearrangement of the order of ^-symbols in a well-formed =S?-formula will sometimes be used when the order required by the =S?-rules of formation is different from that to which we have been accustomed. This again makes for easier reading. Thus (x = y) will often be written instead of ((= x)y), = is of type ou. 1.12 Omission of parentheses Lastly we shall frequently omit parentheses according to the following: (i) The outer pair of parentheses may be omitted, (ii) Parentheses may be omitted by association to the left. Thus ctfiyS will stand for (((afi)y)8). afi(y8) will stand for ((afi)(yS)). This device is adopted because it soon becomes difficult to see the structure of a formula on account of a multitude of parentheses. Parentheses round applications could be entirely omitted without affecting the use of a formal system. Lemma (iii). // all parentheses round applications in a well-formed jSf'-formula are struck out then there is a unique method of restoring them so that the result is a well-formed ^-formula. Let O be a well-formed =S?-formula and let O' be the result of removing parentheses round those applications which are outside abstracts. The only parentheses left in O' will then be round or inside abstracts; each abstract is a well-formed =??-formula, replace it by a new symbol of the same type. Let this transform O' into O\". Then O\" is a formula void of parentheses, it is a linear sequence of symbols each having a type. We know that it is possible to replace the parentheses so that <E>\" is con- converted into a well-formed =S?-formula O1\" (O'\" is obtained from O by replacing abstracts by new symbols of the same type). We want to show that there is a unique way of replacing the parentheses in <E>\" so that the resulting formula is well-formed. The procedure we give is effective and will also tell us of any linear sequence of proper symbols whether it derives from a well-formed formula by omission of parentheses or whether this fails to be the case. For brevity we omit concatenation signs in type symbols. If <E>\" consists of a single symbol then it is well-formed as it stands and we have finished. If O\" consists of several symbols let the left-most symbol be S(a/J) of type (a/?). If the type of the left-most symbol fails to be compound then it is impossible to replace parentheses so that the result is well-formed. If the next symbol is S. of type /? (case (a)), then parentheses are put in as (n?(a/J)n??). This is a well-formed formula of type a, replace it by a new symbol of type a. This converts O\" into a shorter formula Oiv. We then proceed with Olv. If the symbol after Sfey?) in O\" is 2r where y is a type symbol which must be (...(fid')...) d(sS)), where /?,8', ...,8{se) are type symbols, (case (&)), because it must be possible to insert parentheses so that S(a^ is followed by a well-formed formula of type /?. If y fails to be the above type symbol then it is impos- impossible to insert parentheses in O\" so that the result is well-formed. If y is the above type symbol then we insert parentheses as follows: (nv fi/n n/nv1 ^(afi) ( ¦¦¦ (*r (S0)-times\n\n26 Ch. 1 Formal systems 1.12 Omission of parentheses 27 The symbol next to Sy must be of type #S(?) or (...(S^r}')... ^Sn\\ where tj',..., r/(s\") are type symbols, otherwise it is impossible to replace paren- parentheses in O\" so that the result is well-formed. If it is S^j of type S<se) then parentheses go back as (n2MT... n(nS; 2*«w (case (a)). (SO) -times Here B?SJcs*) is a well-formed formula of type (... (fiS')... S^). Replace it by a new symbol of this type. This converts O\" into a shorter formula Olv; we then proceed with Olv. If the next symbol is of type (,..(8<-sehi')...ifS7')), call this y', then parentheses are inserted as follows: (nS?a0(n...TS;(n...T2y (case F)). (SO) -times (Sir) -times So we continue, but the process will terminate with case (a) occurring, we can then put in a right parenthesis and replace a part (nS\"a.^)S^) by a new symbol of type a'. This converts O\" into a shorter formula Ov, we then proceed with Ov. The whole process terminates in at most as many steps as there are proper symbols in O. Thus given a linear sequence of proper symbols we can either insert parentheses uniquely so that the result is a well-formed formula or we can discover that it is impossible to do so. In a similar manner we can deal with parentheses inside abstracts. But if we omit parentheses round abstracts in a well- formed formula then there may be several ways of replacing them so that the result is a well-formed formula. Consider the formula where 2^ and 2^ are distinct variables of type /?. This arises from either of the well-formed formulae, both of type (a/5): 3 2 T 12 2 3 1 1 32 by omission of parentheses round abstractions, and omission of the outer pair of parentheses. Mates are shown by subscript signs. Using the X-rules these two formulae may be replaced respectively by: (VS? *,{?,, S>}n) and fX^cD^Y^), provided that the proviso of the X-rules is satisfied. After this chapter we shall usually omit the concatenation sign. We shall usually write (XS^.OJ for (XIl^OJ, the dot before the scope of X2« makes for easier reading. Also we shall usually write J for (XS,.(XS,.<I>a)), a formula of type ((afi')fi). 1.13 Formal systems To sum up, a formal system is an ordered quartet (SP, IF, stf, 3P), !? is a display of signs, some of which may be designated as generating signs, \\$F is a description of rules of formation, stf is a display of axioms or a description of axiom schemes, 0* is a description of rules of procedure. It must be possible to decide of an object whether it comes under one of these cases or is foreign to them, only then is it possible to read the formal system and to check proofs. Thus we say that a formal system is constructive. A formal system =§? may be without rules of procedure, in this case the J§f-theorems are just the =§?-axioms. A formal system =§? may lack axioms, in this case the formal system =§? is without theorems and we are then only interested in transforming =§?-statements into other =S?-state- ments by the =S?-rules. Usually we then speak of transforming^? -formulae of a certain type into other .^-formulae, and the formal system =§? is then often used as a system of calculations, say of the value of functors. If we know a procedure which will decide whether an =§?-statement is an J§f-theorem, we can omit the .Sf-rules and take as .Sf-axioms the =??-theorems, because the requirement that it be possible to decide whether an 3?-statement is an =Sf-axiom remains satisfied. Thus =S?-rules are only required when we lack a procedure to decide whether an .^-statement is an =§?-theorem. A formal system =§? is called decidable if we have a procedure to decide if an .Sf-statement is an .Sf-theorem. But we can write down the .Sf-theorems one after the other, so that if we continue long enough any .Sf-theorem will appear in the list. To do this we select a new symbol, say Q. We then denote a sequence of ^-formulae O' O\" ... T by the formula O'n ?\"(!>\"\" ?\"...n \\J\"Y of a system •2\" obtained from the system =§? by adding the typeless symbol ?• We then give an order of preference, called the alphabetical order, to the \"ymbols, we then order the ^'-formulae first by length and lexico-\n\n28 Ch. 1 Formal systems 1.15 Truth definitions 29 graphically for those of equal length. In this manner we can generate the ^'-formulae one after the other. When an =§?'-formula has been generated we test it whether it is of the form (^\"?\"^\"\"?\"•••\"?'T where the sequence O' O\"... Y is an .Sf-proof of Y. If the test is affirmative we write *F down in a list. In this manner we generate the =Sf-theorems one after the other without omissions but with repetitions. 1.14 Extensions of formal systems A formal system =§?' is called a primary extension of a formal system =§? if the =§?-symbols are ^'-symbols of the same type and if the =§?-axioms and .Sf-rules are ^'-axioms and .Sf'-rules respectively. Thus a primary extension of a formal system =§? is obtained by doing some of the following operations: adding new symbols to =§?, adding new axioms, adding new rules of procedure. If =§?' is a primary extension of =§? then =§? is called a sub-system of =§?'. =§? is an improper primary extension and an improper subsystem of itself. Two formal systems =§? and =2\" are equivalent when their variables are of the same type (by a trivial adjustment we can then use the same symbols for variables in both systems) and when the constants of the one system can respectively be replaced by suitable formulae of the other system of the same respective types in such a way that the theorems of the one system translate via the replacements into theorems of the other system. If the formal system =§? is equivalent to the formal system =§?' and if jSf\" is a primary extension of =§?' then J§?\" is a secondary extension of =§?. Two formal systems, =??, =5?', can be equivalent merely because of different shapes in the choice of primitive symbols, or because though they both have exactly the same primitive symbols and each symbol has the same type in both systems yet the =§?-axioms are ^'-theorems and the =Sf-rules are derived =§?'-rules and vice versa. =§?, =§?' can be equivalent when the variables are the same and of the same types in the two systems yet the proper constants are different and perhaps of different types. For instance some symbols introduced into =§? by definitional abbreviation might be primitive =2\"-symbols of the same type as the =Sf-defined symbol. This, in general, would require that the =§?-axioms and =S?-rules be distinct from the =S?'-axioms and =S?'-rules respectively. 1.15 Truth definitions Let J§? be a formal system and let an ^-statement be of type o. A truth- definition for =§? is a set of conditions ^~x applicable to closed =§?-state- ments. We say that a closed .^-statement O is ^\"^-true if the conditions y<g tested on O lead to an affirmative result. It may happen that it is impossible to test the conditions &~g on some closed ^-statements. (For instance consider the intuitive definition of truth for arithmetic state- statements and then ask if Goldbach's conjecture is true.) We shall say that a closed J§f-statement O is ^x-false if the conditions Fg applied to O lead to a result which fails to be affirmative. It may happen that for a formal system =§? the conditions &~cg can be applied to each closed J§f-statement and yield a result. In such a case we have an effective truth-definition. We say that a formal system =§? is consistent with respect to a truth- definition 3~cg if each closed .^-theorem is =^.-true. We say that a formal system 3? is complete with respect to a truth definition «^> if each =^.-true =§?-statement is an =§?-theorem. It may be possible to give several distinct truth-definitions for a given formal system =§?. A trivial truth-definition for a formal system =§? is to say that a closed =§?-statement is true if and only if it is an =§?-theorem. The concepts of truth and provability then coincide. A useless truth- definition for a formal system =§? containing conjunction is to say that an J§f-statement is true if and only if it is of the form (c.f. 'The hunting of the shark', 'what I say three times is true'). In a similar manner we can define a falsity-definition (denoted by J^) for a formal system ??. If we define STX and J*> for a formal system <? then we require that they be exclusive. n6 Negation Let ?? be a formal system and let .Sf-statements be of type o. Let N be f-n ^-symbol of type 00 and let O be a closed ^-statement then (niVnOn) is an =Sf-statement. Let ^ be a truth-definition for S? and let J*> be a falsity-definition for J§? and let (nN\"\\$n) satisfy J^ when O satisfies 3TX and CWn(pn) satisfy ^ when O satisfies 3FX. Then we say that N is a two-valued ^-negation symbol. If a formal system ?? contains a two-"
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https://devtut.github.io/vbnet/declaring-variables.html | [
"# # Declaring variables\n\n## # Declaring and assigning a variable using a primitive type\n\nVariables in Visual Basic are declared using the `Dim` keyword. For example, this declares a new variable called `counter` with the data type `Integer`:\n\n``````Dim counter As Integer\n\n``````\n\nA variable declaration can also include an access modifier, such as `Public`, `Protected`, `Friend`, or `Private`. This works in conjunction with the variable's scope to determine its accessibility.\n\nAccess Modifier Meaning\nPublic All types which can access the enclosing type\nProtected Only the enclosing class and those that inherit from it\nFriend All types in the same assembly that can access the enclosing type\nProtected Friend The enclosing class and its inheritors, or the types in the same assembly that can access the enclosing class\nPrivate Only the enclosing type\nStatic Only on local variables and only initializes once.\n\nAs a shorthand, the `Dim` keyword can be replaced with the access modifier in the variable's declaration:\n\n``````Public TotalItems As Integer\nPrivate counter As Integer\n\n``````\n\nThe supported data types are outlined in the table below:\n\nType Alias Memory allocation Example\nSByte N/A 1 byte `Dim example As SByte = 10`\nInt16 Short 2 bytes `Dim example As Short = 10`\nInt32 Integer 4 bytes `Dim example As Integer = 10`\nInt64 Long 8 bytes `Dim example As Long = 10`\nSingle N/A 4 bytes `Dim example As Single = 10.95`\nDouble N/A 8 bytes `Dim example As Double = 10.95`\nDecimal N/A 16 bytes `Dim example As Decimal = 10.95`\nBoolean N/A Dictated by implementing platform `Dim example As Boolean = True`\nChar N/A 2 Bytes `Dim example As Char = \"A\"C`\nString N/A",
null,
"source `Dim example As String = \"Stack Overflow\"`\nDateTime Date 8 Bytes `Dim example As Date = Date.Now`\nByte N/A 1 byte `Dim example As Byte = 10`\nUInt16 UShort 2 bytes `Dim example As UShort = 10`\nUInt32 UInteger 4 bytes `Dim example As UInteger = 10`\nUInt64 ULong 8 bytes `Dim example As ULong = 10`\nObject N/A 4 bytes 32 bit architecture, 8 bytes 64 bit architecture `Dim example As Object = Nothing`\n\nThere also exist data identifier and literal type characters usable in replacement for the textual type and or to force literal type:\n\nType (or Alias) Identifier type character Literal type character\nShort N/A `example = 10S`\nInteger `Dim example%` `example = 10%` or `example = 10I`\nLong `Dim example&` `example = 10&` or `example = 10L`\nSingle `Dim example!` `example = 10!` or `example = 10F`\nDouble `Dim example#` `example = 10#` or `example = 10R`\nDecimal `Dim example@` `example = 10@` or `example = 10D`\nChar N/A `example = \"A\"C`\nString `Dim example\\$` N/A\nUShort N/A `example = 10US`\nUInteger N/A `example = 10UI`\nULong N/A `example = 10UL`\n\nThe integral suffixes are also usable with hexadecimal (&H) or octal (&O) prefixes:\n`example = &H8000S` or `example = &O77&`\n\nDate(Time) objects can also be defined using literal syntax:\n`Dim example As Date = #7/26/2016 12:8 PM#`\n\nOnce a variable is declared it will exist within the Scope of the containing type, `Sub` or `Function` declared, as an example:\n\n``````Public Function IncrementCounter() As Integer\nDim counter As Integer = 0\ncounter += 1\n\nReturn counter\nEnd Function\n\n``````\n\nThe counter variable will only exist until the `End Function` and then will be out of scope. If this counter variable is needed outside of the function you will have to define it at class/structure or module level.\n\n``````Public Class ExampleClass\n\nPrivate _counter As Integer\n\nPublic Function IncrementCounter() As Integer\n_counter += 1\nReturn _counter\nEnd Function\n\nEnd Class\n\n``````\n\nAlternatively, you can use the `Static` (not to be confused with `Shared`) modifier to allow a local variable to retain it's value between calls of its enclosing method:\n\n``````Function IncrementCounter() As Integer\nStatic counter As Integer = 0\ncounter += 1\n\nReturn counter\nEnd Function\n\n``````\n\n## # Levels of declaration – Local and Member variables\n\nLocal variables - Those declared within a procedure (subroutine or function) of a class (or other structure). In this example, `exampleLocalVariable` is a local variable declared within `ExampleFunction()`:\n\n``````Public Class ExampleClass1\n\nPublic Function ExampleFunction() As Integer\nDim exampleLocalVariable As Integer = 3\nReturn exampleLocalVariable\nEnd Function\n\nEnd Class\n\n``````\n\nThe `Static` keyword allows a local variable to be retained and keep its value after termination (where usually, local variables cease to exist when the containing procedure terminates).\n\nIn this example, the console is `024`. On each call to `ExampleSub()` from `Main()` the static variable retains the value it had at the end of the previous call:\n\n``````Module Module1\n\nSub Main()\nExampleSub()\nExampleSub()\nExampleSub()\nEnd Sub\n\nPublic Sub ExampleSub()\nStatic exampleStaticLocalVariable As Integer = 0\nConsole.Write(exampleStaticLocalVariable.ToString)\nexampleStaticLocalVariable += 2\nEnd Sub\n\nEnd Module\n\n``````\n\nMember variables - Declared outside of any procedure, at the class (or other structure) level. They may be instance variables, in which each instance of the containing class has its own distinct copy of that variable, or `Shared` variables, which exist as a single variable associated with the class itself, independent of any instance.\n\nHere, `ExampleClass2` contains two member variables. Each instance of the `ExampleClass2` has an individual `ExampleInstanceVariable` which can be accessed via the class reference. The shared variable `ExampleSharedVariable` however is accessed using the class name:\n\n``````Module Module1\n\nSub Main()\n\nDim instance1 As ExampleClass4 = New ExampleClass4\ninstance1.ExampleInstanceVariable = \"Foo\"\n\nDim instance2 As ExampleClass4 = New ExampleClass4\ninstance2.ExampleInstanceVariable = \"Bar\"\n\nConsole.WriteLine(instance1.ExampleInstanceVariable)\nConsole.WriteLine(instance2.ExampleInstanceVariable)\nConsole.WriteLine(ExampleClass4.ExampleSharedVariable)\n\nEnd Sub\n\nPublic Class ExampleClass4\n\nPublic ExampleInstanceVariable As String\nPublic Shared ExampleSharedVariable As String = \"FizzBuzz\"\n\nEnd Class\n\nEnd Module\n\n``````\n\n## # Example of Access Modifiers\n\nIn the following example consider you have a solution hosting two projects: ConsoleApplication1 and SampleClassLibrary. The first project will have the classes SampleClass1 and SampleClass2. The second one will have SampleClass3 and SampleClass4. In other words we have two assemblies with two classes each. ConsoleApplication1 has a reference to SampleClassLibrary.\n\nSee how SampleClass1.MethodA interacts with other classes and methods.\n\nSampleClass1.vb:\n\nSampleClass2.vb:\n\nSampleClass3.vb:\n\nSampleClass4.vb:\n\n#### # Syntax\n\n• Public counter As Integer\n• Private _counter As Integer\n• Dim counter As Integer"
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http://math.chapman.edu/~jipsen/structures/doku.php/hilbert_algebras?s%5B%5D=variety | [
"## Hilbert algebras\n\nAbbreviation: HilA\n\n### Definition\n\nA Hilbert algebra is a structure $\\mathbf{A}=\\langle A,\\to,1\\rangle$ of type $\\langle 2, 1\\rangle$ such that\n\n$x\\to(y\\to x)=1$\n\n$(x\\to(y\\to z))\\to((x\\to y)\\to(x\\to z))=1$\n\n$x\\to y=1\\mbox{ and }y\\to x=1 \\Longrightarrow x=y$\n\n##### Morphisms\n\nLet $\\mathbf{A}$ and $\\mathbf{B}$ be Hilbert algebras. A morphism from $\\mathbf{A}$ to $\\mathbf{B}$ is a function $h:A\\rightarrow B$ that is a homomorphism: $h(x\\to y)=h(x)\\to h(y)$ and $h(1)=1$.\n\n### Definition\n\nA Hilbert algebra is a structure $\\mathbf{A}=\\langle A,\\to,1\\rangle$ of type $\\langle 2, 1\\rangle$ such that\n\n$x\\to x=1$\n\n$1\\to x=x$\n\n$x\\to(y\\to z)=(x\\to y)\\to(x\\to z)$\n\n$(x\\to y)\\to((y\\to x)\\to x)=(y\\to x)\\to((x\\to y)\\to y)$\n\n### Examples\n\nExample 1: Given any poset with top element 1, $\\langle A,\\le, 1\\rangle$, define $a\\to b=\\begin{cases}1&\\text{ if$a\\le b$}\\\\ b&\\text{ otherwise.}\\end{cases}$ Then $\\langle A,\\to,1\\rangle$ is a Hilbert algebra.\n\n### Basic results\n\nHilbert algebras are the algebraic models of the implicational fragment of intuitionistic logic, i.e., they are $(\\to,1)$-subreducts of Heyting algebras.\n\nThe variety of Hilbert algebras is not generated as a quasivariety by any of its finite members 1).\n\n### Properties\n\nClasstype variety 2)\n\n### Finite members\n\n$\\begin{array}{lr} f(1)= &1\\\\ f(2)= &\\\\ f(3)= &\\\\ f(4)= &\\\\ f(5)= &\\\\ \\end{array}$ $\\begin{array}{lr} f(6)= &\\\\ f(7)= &\\\\ f(8)= &\\\\ f(9)= &\\\\ f(10)= &\\\\ \\end{array}$\n\n... subvariety\n\n... expansion\n\n### Superclasses\n\n... supervariety\n\n... subreduct\n\n##### Toolbox",
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https://proofwiki.org/wiki/Inner_Automorphism_Maps_Subgroup_to_Itself_iff_Normal | [
"# Inner Automorphism Maps Subgroup to Itself iff Normal\n\n## Theorem\n\nLet $G$ be a group.\n\nFor $x \\in G$, let $\\kappa_x$ denote the inner automorphism of $x$ in $G$.\n\nLet $H$ be a subgroup of $G$.\n\nThen:\n\n$\\forall x \\in G: \\kappa_x \\sqbrk H = H$\n$H$ is a normal subgroup of $G$.\n\n## Proof\n\n### Sufficient Condition\n\nLet $H$ be a normal subgroup of $G$.\n\nLet $x \\in G$ be arbitrary.\n\nBy definition, $\\kappa_x: G \\to G$ is a mapping defined as:\n\n$\\forall g \\in G: \\map {\\kappa_x} g = x g x^{-1}$\n\nLet $n \\in N$.\n\nThen:\n\n $\\ds \\map {\\kappa_x} n$ $=$ $\\ds x n x^{-1}$ $\\ds$ $\\in$ $\\ds N$ Definition of Normal Subgroup\n\n$\\Box$\n\n### Necessary Condition\n\nSuppose that:\n\n$\\forall x \\in G: \\kappa_x \\sqbrk H = H$\n\nLet $x \\in G$ be arbitrary.\n\nBy definition of inner automorphism of $x$ in $G$:\n\n$\\forall h \\in H: x h x^{-1} \\in H$\n\nSo, by definition, $H$ is a normal subgroup of $G$\n\n$\\blacksquare$"
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https://www.calculatoratoz.com/en/volume-of-a-rectangular-prism-calculator/Calc-257 | [
"## < ⎙ 32 Other formulas that you can solve using the same Inputs\n\nBody Fat Of Female Body\nBody Fat Of Female Body=163.205*log10(Waist+Hip-Neck)-97.684*log10(Height)-78.387 GO\nLateral Surface Area of a Conical Frustum\nBody Fat Of Male Body\nBody Fat Of Male Body=86.01*log10(Abdomen-Neck)-70.041*log10(Height)+36.76 GO\nCentroid of a Trapezoid\nCentroid Of Trapezoid=((Side B+2*Side A)/(3*(Side A+Side B)))*Height GO\nDiagonal of a Rectangle when length and perimeter are given\nDiagonal=sqrt((2*(Length)^2)-(Perimeter*Length)+((Perimeter)^2/4)) GO\nVolume of a Conical Frustum\nTotal Surface Area of a Cone\nSurface Area of a Rectangular Prism\nSurface Area=2*(Length*Width+Length*Height+Width*Height) GO\nTotal Surface Area of a Pyramid\nTotal Surface Area=Side*(Side+sqrt(Side^2+4*(Height)^2)) GO\nPotential Energy\nPotential Energy=Mass*Acceleration Due To Gravity*Height GO\nLateral Surface Area of a Cone\nPressure when density and height are given\nPressure=Density*Acceleration Due To Gravity*Height GO\nLateral Surface Area of a Pyramid\nLateral Surface Area=Side*sqrt(Side^2+4*(Height)^2) GO\nPerimeter of a rectangle when diagonal and length are given\nPerimeter=2*(Length+sqrt((Diagonal)^2-(Length)^2)) GO\nMagnetic Flux\nPerimeter of rectangle when diagonal and width are given\nPerimeter=2*(sqrt((Diagonal)^2-(Width)^2)+Width) GO\nDiagonal of a Rectangle when length and area are given\nDiagonal=sqrt(((Area)^2/(Length)^2)+(Length)^2) GO\nTotal Surface Area of a Cylinder\nArea of a Rectangle when length and diagonal are given\nArea=Length*(sqrt((Diagonal)^2-(Length)^2)) GO\nLateral Surface Area of a Cylinder\nArea of a Rectangle when length and perimeter are given\nArea=(Perimeter*(Length/2))-(Length)^2 GO\nDiagonal of a Rectangle when length and breadth are given\nVolume of a Circular Cone\nArea of a Trapezoid\nArea=((Base A+Base B)/2)*Height GO\nStrain\nStrain=Change In Length/Length GO\nSurface Tension\nSurface Tension=Force/Length GO\nVolume of a Circular Cylinder\nPerimeter of a rectangle when length and width are given\nPerimeter=2*Length+2*Width GO\nVolume of a Pyramid\nVolume=(1/3)*Side^2*Height GO\nArea of a Triangle when base and height are given\nArea=1/2*Base*Height GO\nArea of a Rectangle when length and breadth are given\nArea of a Parallelogram when base and height are given\nArea=Base*Height GO\n\n## < ⎙ 8 Other formulas that calculate the same Output\n\nVolume of a Conical Frustum\nVolume of a Capsule\nVolume of a Circular Cone\nVolume of a Circular Cylinder\nVolume of a Hemisphere\nVolume of a Pyramid\nVolume=(1/3)*Side^2*Height GO\nVolume of a Sphere\nVolume of a Cube\nVolume=Side^3 GO\n\n### Volume of a Rectangular Prism Formula\n\nVolume=Width*Height*Length\nMore formulas\nVolume of a Capsule GO\nVolume of a Circular Cone GO\nVolume of a Circular Cylinder GO\nVolume of a Cube GO\nVolume of a Hemisphere GO\nVolume of a Sphere GO\nVolume of a Pyramid GO\nVolume of a Conical Frustum GO\nPerimeter of a Parallelogram GO\nPerimeter of a Rhombus GO\nPerimeter of a Cube GO\nPerimeter of a Kite GO\nChord Length when radius and angle are given GO\nChord length when radius and perpendicular distance are given GO\nPerimeter Of Sector GO\nDiagonal of a Cube GO\nPerimeter Of Parallelepiped GO\n\n## What is Volume of a Rectangular Prism?\n\nIn geometry, a rectangular prism is a polyhedron (the shape whose all sides are flat) with two congruent and parallel bases. It is called prism because it forms a cross-section along the length. The volume of a rectangular prism is the amount of space covered by a rectangular prism. In other words, the number of units used to fill a rectangular prism is called the volume of a rectangular prism. The volume of a rectangular prism is the product of length (l), width (w), and height (h).\n\n## How to Calculate Volume of a Rectangular Prism?\n\nVolume of a Rectangular Prism calculator uses Volume=Width*Height*Length to calculate the Volume, Volume is the amount of space that a substance or object occupies or that is enclosed within a container. Volume and is denoted by V symbol.\n\nHow to calculate Volume of a Rectangular Prism using this online calculator? To use this online calculator for Volume of a Rectangular Prism, enter Height (h), Length (l) and Width (w) and hit the calculate button. Here is how the Volume of a Rectangular Prism calculation can be explained with given input values -> 252 = 7*12*3.\n\n### FAQ\n\nWhat is Volume of a Rectangular Prism?\nVolume is the amount of space that a substance or object occupies or that is enclosed within a container and is represented as V=w*h*l or Volume=Width*Height*Length. Height is the distance between the lowest and highest points of a person standing upright, Length is the measurement or extent of something from end to end and Width is the measurement or extent of something from side to side.\nHow to calculate Volume of a Rectangular Prism?\nVolume is the amount of space that a substance or object occupies or that is enclosed within a container is calculated using Volume=Width*Height*Length. To calculate Volume of a Rectangular Prism, you need Height (h), Length (l) and Width (w). With our tool, you need to enter the respective value for Height, Length and Width and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.",
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"Let Others Know"
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"https://www.calculatoratoz.com/Images/share.png",
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https://fim-mdu.info/and-relationship/edges-and-vertices-relationship-tips.php | [
"# Edges and vertices relationship tips\n\n### Vertices, Edges and Faces",
null,
"Relation between the numbers of vertices, edges, faces and components I need to determine an equation relating vertices, edges, faces and components. Hints. If the separate components have v 1, v 2, , v k vertices. In the domain of mathematics and computer science, graph theory is the study of graphs that concerns with the relationship among edges and vertices. Different shapes have different numbers of edges and vertices. Some tips can help you tell the difference between them and to use them as.",
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"Then you have this face right over here, also in the back. The only way we can see this is because they've drawn it so that it is transparent. So that is the second face. Now you have this triangular face on top. So let me color that in. So you have this triangular face on top. So that's going to be our third face, third face. And then you have this triangular face on the bottom.\n\nThat's gonna be our fourth face. That's going to be our fourth face.\n\n## Graph Theory - Quick Guide\n\nAnd then the key question is are we done? Looks like I've colored all the ones that I can see, but there's one a little bit tricky here. There's the one that we are actually seeing through.\n\nEuler's Formula - 3 Dimensional Shapes\n\nThere is the face, there's, let me pick a color, there's the face out front that we can see through so that we can see faces one, two, and four. So that's actually going to be our fifth face.\n\nThe way they've drawn it, it's like it's made out of glass, so we can see faces one, two, and four. But that is our fifth face.\n\nAnd so this thing has five faces. It is because if any two edges are adjacent, then the degree of the vertex which is joining those two edges will have a degree of 2 which violates the matching rule.\n\nExample M1, M2, M3 from the above graph are the maximal matching of G. Maximum Matching It is also known as largest maximal matching. Maximum matching is defined as the maximal matching with maximum number of edges.",
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"Hence by using the graph G, we can form only the subgraphs with only 2 edges maximum. Hence we have the matching number as two. Perfect Matching A matching M of graph G is said to be a perfect match, if every vertex of graph g G is incident to exactly one edge of the matching Mi. Example In the following graphs, M1 and M2 are examples of perfect matching of G.\n\n### Graph Theory Quick Guide\n\nA maximum matching of graph need not be perfect. If it is odd, then the last vertex pairs with the other vertex, and finally there remains a single vertex which cannot be paired with any other vertex for which the degree is zero.",
null,
"It clearly violates the perfect matching principle. If G has even number of vertices, then M1 need not be perfect. Hamilton actually created this idea as a sort of puzzle, find the path to connect every vertex on a dodecahedron, visiting every vertex only once, and sold his dodecahedron puzzle to an Irish merchant who began to sell it.\n\nIt turns out that it is quite a difficult task to identify whether or not a solid has a Hamiltonian circuit or not, and it may require a proof by exhaustion to determine whether or not a path is possible. However, it has been proven that all Platonic solids, Archimedean solids, and planarconnected graphs have Hamiltonian circuits.",
null,
"Therefore, by counting the number of edges that we shade red we can determine the number of vertices. To prove this, assume this is not the case. Then there would be a vertex that is not coloured, which means we were not done colouring our edges red. Next we will begin by examining faces."
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"http://teknosrc.com/wp-content/uploads/2016/04/Gremlin-Query-Language-Create-VertexNode-and-EdgeRelationship.png",
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"http://slideplayer.com/5128968/16/images/10/Solid (pretruncating) Truncated Vertices. Edges. Faces. Tetrahedron. 12. 18. 8. Cube. 14. 36..jpg",
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"http://slideplayer.com/5165284/16/images/7/Model: Social Graph Social networks model social relationships by graph structures using vertices and edges..jpg",
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"http://slideplayer.com/4598702/15/images/23/What is the relationship between the number.jpg",
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"https://image.slidesharecdn.com/solshapes-120326132805-phpapp01/95/solid-shapes-6-728.jpg",
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https://www.rdocumentation.org/packages/spatstat/versions/1.59-0/topics/nearest.raster.point | [
"# nearest.raster.point\n\n0th\n\nPercentile\n\n##### Find Pixel Nearest to a Given Point\n\nGiven cartesian coordinates, find the nearest pixel.\n\nKeywords\nmanip, spatial\n##### Usage\nnearest.raster.point(x,y,w, indices=TRUE)\n##### Arguments\nx\n\nNumeric vector of $x$ coordinates of any points\n\ny\n\nNumeric vector of $y$ coordinates of any points\n\nw\n\nAn image (object of class \"im\") or a binary mask window (an object of class \"owin\" of type \"mask\").\n\nindices\n\nLogical flag indicating whether to return the row and column indices, or the actual $x,y$ coordinates.\n\n##### Details\n\nThe argument w should be either a pixel image (object of class \"im\") or a window (an object of class \"owin\", see owin.object for details) of type \"mask\".\n\nThe arguments x and y should be numeric vectors of equal length. They are interpreted as the coordinates of points in space. For each point (x[i], y[i]), the function finds the nearest pixel in the grid of pixels for w.\n\nIf indices=TRUE, this function returns a list containing two vectors rr and cc giving row and column positions (in the image matrix). For the location (x[i],y[i]) the nearest pixel is at row rr[i] and column cc[i] of the image.\n\nIf indices=FALSE, the function returns a list containing two vectors x and y giving the actual coordinates of the pixels.\n\n##### Value\n\nIf indices=TRUE, a list containing two vectors rr and cc giving row and column positions (in the image matrix). If indices=FALSE, a list containing vectors x and y giving actual coordinates of the pixels.\n\nowin.object, as.mask\n\n##### Aliases\n• nearest.raster.point\n##### Examples\n# NOT RUN {\nw <- owin(c(0,1), c(0,1), mask=matrix(TRUE, 100,100)) # 100 x 100 grid\nnearest.raster.point(0.5, 0.3, w)\nnearest.raster.point(0.5, 0.3, w, indices=FALSE)\n# }\n\nDocumentation reproduced from package spatstat, version 1.59-0, License: GPL (>= 2)\n\n### Community examples\n\nLooks like there are no examples yet."
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https://ecomodder.com/forum/showthread.php/aerodynamics-seminar-6-phil-knox-861-3.html | [
"",
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"EcoModder Forum",
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"Aerodynamics Seminar # 6 - by Phil Knox",
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"Register Now\n Remember",
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"02-17-2010, 10:13 PM #21 (permalink)\nRecreation Engineer\n\nJoin Date: Dec 2009\nLocation: Somewhere USA\nPosts: 521\n\nBlack Stallion - '02 Toyota Tundra 4WD xCab\n\nHalf Pint - '06 Yamaha XT225\nThanks: 311\nThanked 136 Times in 101 Posts\nMagic number\n\nQuote:\n Originally Posted by MetroMPG",
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"Frontal area can be approximated by multiplying your vehicles width times its height,times 0.84.\nI missed the basis for 16% reduction. Is height corrected for ground clearance, sides corrected for tapers, or what?\n\nCheers\nKB",
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"",
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"Today\nPopular topics",
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"Other popular topics in this forum...",
null,
">> See all the most popular projects & topics in our Aerodynamics subforum.",
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"02-18-2010, 12:26 AM #22 (permalink) (: Join Date: Jan 2008 Location: up north Posts: 12,636 Blue - '93 Ford Tempo Last 3: 27.29 mpg (US) F150 - '94 Ford F150 XLT 4x4 90 day: 18.5 mpg (US) Sport Coupe - '92 Ford Tempo GL Last 3: 69.62 mpg (US) ShWing! - '82 honda gold wing Interstate 90 day: 33.65 mpg (US) Moon Unit - '98 Mercury Sable LX Wagon 90 day: 21.24 mpg (US) Thanks: 1,550 Thanked 3,426 Times in 2,151 Posts I think it was statistically derived from comparing w x h and known frontal area values. __________________",
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"",
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"The Following User Says Thank You to Frank Lee For This Useful Post:",
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"08-08-2012, 07:12 PM #23 (permalink)\nMaster EcoModder\n\nJoin Date: Jan 2008\nLocation: Sanger,Texas,U.S.A.\nPosts: 10,631\nThanks: 16,651\nThanked 5,674 Times in 3,402 Posts\n375\n\nQuote:\n Originally Posted by kennybobby",
null,
"The 375 in the denominator should be 349. (348.66) That term comes from 0.5 times the conversion factor for mph^3 to (ft/sec)^3 divided by the definition factor for horsepower = 550 lbs-ft/sec. conversion factor: mph * 5280 ft/mile / 3600 seconds/hr = ft/sec. The 375 value assumes a mile is only 5153 ft.\nThree of my reference texts use the 375 value.I made a leap of faith that the Ph.Ds had checked their own work.Apologize for the trouble.",
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"",
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"08-09-2012, 06:41 PM #24 (permalink)\nMaster EcoModder\n\nJoin Date: Jan 2008\nLocation: Sanger,Texas,U.S.A.\nPosts: 10,631\nThanks: 16,651\nThanked 5,674 Times in 3,402 Posts\n375 seems okay\n\nQuote:\n Originally Posted by kennybobby",
null,
"The 375 in the denominator should be 349. (348.66) That term comes from 0.5 times the conversion factor for mph^3 to (ft/sec)^3 divided by the definition factor for horsepower = 550 lbs-ft/sec. conversion factor: mph * 5280 ft/mile / 3600 seconds/hr = ft/sec. The 375 value assumes a mile is only 5153 ft.\nI re-visited my books.And it looks like the 375 value is valid.\nWorking with the 550 lb'ft/sec value for horsepower calculation requires mph to be multiplied by 5,280 to get feet,then division by 3,600 sec/hr to get it into feet/sec..\nIf you already have a drag force at a given mph value,to get power,you can use this shortcut,multiplying the force by mph,then dividing by 375.\n550/375 yields a constant percentage = to( feet/sec)/(mph) at any given velocity.It's always 1.466X.\nHope that helps!",
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"",
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"09-09-2012, 12:18 AM #25 (permalink)\nSouthern Squidbillie\n\nJoin Date: Aug 2012\nLocation: Heart of Dixie\nPosts: 97\nThanks: 50\nThanked 25 Times in 21 Posts\nYes, your clever formula is quite correct...\n\nQuote:\n Originally Posted by aerohead",
null,
"I re-visited my books.And it looks like the 375 value is valid. Working with the 550 lb'ft/sec value for horsepower calculation requires mph to be multiplied by 5,280 to get feet,then division by 3,600 sec/hr to get it into feet/sec.. If you already have a drag force at a given mph value,to get power,you can use this shortcut,multiplying the force by mph,then dividing by 375. 550/375 yields a constant percentage = to( feet/sec)/(mph) at any given velocity.It's always 1.466X. Hope that helps!\nOkay yes that helps and now i see where my confusion arose, and i agree that if you already have the Aero drag Force in unit of lbs, then you can get the Power in Horsepower by multiplying by speed in mph and dividing by 375:\n\n1 mph x 5280 / 3600 = 1.466 ft/sec [the conversion from mph to ft/sec is 1.466].\n\npower (in units of lb-ft/sec) / 550 = power (in units of Horsepower, HP).\n\nSo 1.466 / 550 = 1 / 375 does indeed convert mph to ft/sec and power to HP when multiplying Force in lbs times Speed in mph.\n\nMy confusion with your HP formula was three-fold: there was a factor of 1/2 missing inside the square brackets in your equation for the Aero drag \"Force\", and there was no conversion factor inside the brackets to convert speed in mph to ft/sec, and the constant term inside the brackets was so close to the value for the density of air.\n\nQuote:\n Originally Posted by aerohead",
null,
"...The formulas,once posted,will allow everyone to calculate aerodynamic loads ... The horsepower it takes at the drivewheel of your vehicle to overcome aerodynamic drag can be estimated by the formula HP =V/375 [ 0.00256 X Cd X A X (V squared)] where V= speed in miles per hour, Cd is your drag coefficient,A= frontal area of your vehicle,and (V squared) is your speed times itself.\nSo now i see how your formula is correct, and please allow me to expand on the derivation of this formula:\n\nAero drag Force = 1/2 x (air density) x V^2 x Cd x A ; air density = 0.00237 lbm/ft^3\n\nPower = Force x Speed , so the fully expanded version of the formula for the Aero drag in Horsepower would be\n\nHP = (V x 1.466/550) x [ 0.5 x 0.00237 x Cd x A x (V squared) x (1.466 squared)]\n\nSo the constant term inside the square brackets of your formula is really NOT the air density, but is the product of 0.5 x 0.00237 x (1.466^2) = 0.00256 , and this all simplifies down to the clever formula that you provided:\n\nHP = (V/375) x [ 0.00256 x Cd x A x (V squared)]",
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"Similar Threads Thread Thread Starter Forum Replies Last Post MetroMPG Aerodynamics 2 05-10-2013 06:34 PM MetroMPG Aerodynamics 7 08-08-2012 07:00 PM MetroMPG Aerodynamics 4 02-16-2009 08:15 PM MetroMPG Aerodynamics 4 01-29-2008 02:41 PM MetroMPG Aerodynamics 0 01-28-2008 09:36 PM\n\n -- EcoModder Skin -- Mobile / Lightweight skin Contact Us - EcoModder.com - Archive - Recent Posts - Top",
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https://www.havefunteaching.com/resource/math/two-digit-addition-regrouping-worksheet | [
"",
null,
"# Two Digit Addition Regrouping Worksheet\n\n\\$0.99\n\nUsing Two Digit Addition Regrouping Worksheet, students solve double digit addition problems with regrouping using addition steps.\n\nYour students need a lot of practice solving addition problems. This worksheet will give your students the opportunity to practice.\n\nStudents solve each of the two digit addition problems by following the steps for adding two digit numbers. Then, check over your answers with a partner. Fix any incorrect answers.\n\n### Other resources to use with this Two Digit Addition Regrouping Worksheet\n\nUse this Double Digit with Regrouping Worksheet Pack as an additional resource for your students.\n\nIntroduce this worksheet by reviewing addition facts using the Addition Flash Cards.Next, create an anchor chart that shows the steps for adding. Then, have students complete the worksheet independently or with a partner. Finally, studentscheck over your answers with a partner and fix any incorrect answers. Once finished, have students write their own word problem based on the equations from the worksheet.\n\nBe sure to check out more Addition Activities."
]
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null,
"https://www.facebook.com/tr",
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https://cs.stackexchange.com/questions/152744/calculate-shortest-cycle-that-contains-node-s | [
"# Calculate shortest cycle that contains node $s$\n\nLet $$G(V,E,w)$$ be a graph with no negative weights.\n\nDescribe an algorithm that returns the shortest cycle containing a node $$v$$.\n\nI came across this algorithm https://courses.engr.illinois.edu/cs374/sp2017/labs/solutions/lab10-sol.pdf\n\nI can't convince myself it is true, because $$d(s,v)+w(s,v)$$ might not be independant.\n\nBy that I mean that perhaps $$w(s,v)$$ is contained in $$d(s,v)$$.\n\nAn algorithm I came up with is as follows:\n\nResult arr=[]\nFor x in N(v): // N is neighbours of v\nremove(v,x) // remove the edge (v,x)\nT=Dijkstra_tree(x,G)\nif(v is in T):\nAdd d(v,x)+w(v,x) to Result Arr// add the weight of the tree+ the removed edge to arr\nreturn Min(Result arr)\n\n\nThis algorithm has a running time of $$O(|V|)(|E|+|V|\\log(|V|)$$.\n\nBecause $$v$$ might have $$|V|-1$$ neighbours, and then we run Dijkstra every time on them.\n\nThe algorithm they presented has a much better complexity but I just can't convince myself it indeed works, while my algorithm fixed that issue, but costs a lot of runtime.\n\n• What's the question? Jun 30 at 17:56\n• Why does the algorithm presented in the link work? And if it doesn't, does the fix I provided make it work? Jun 30 at 17:57\n• Is your graph directed or undirected? The algorithm in the link works for directed graphs (and is correct) Jun 30 at 17:58\n• I assumed the solution to both would be the same, but in this instance I was working on an undirected graph. Jun 30 at 18:05\n\nTo answer the question \"why is the linked algorithm correct?\", first of all notice that it works for directed graphs.\n\nWe want to show that the shortest cycle containing $$s$$ consists of a shortest path from $$s$$ to some vertex $$v$$ plus the edge $$(v,s)$$ such that $$d(s,v) + w(v,s)$$ is minimized.\n\nLet $$C = \\langle s=v_0, v_1, \\dots, v_\\ell, s\\rangle$$ be a cycle. Clearly, the length of $$C$$ is at least $$d(s, v_\\ell) + w(v_\\ell, s)$$. On the other hand, all shortest paths $$\\pi$$ from $$s$$ to a vertex $$v$$ such that $$(v,s)$$ exist imply the existence of a cycle of length $$d(s,v) + w(v,s)$$ (notice, in particular, that any simple path from $$s$$ contains no edges entering $$s$$, hence $$\\pi$$ does not already contain $$(v,s)$$).\n\nThe linked algorithm almost works when the graph is undirected. The only problem is that the shortest path $$\\pi$$ from $$s$$ to $$v$$ might be a single edge $$(s,v)$$, and hence the concatenation of $$\\pi$$ with $$(v,s)$$ would not yield a cycle.\n\nTo avoid this problem you can consider only the vertices $$v$$ that have depth at least $$2$$ in the shortest-path tree rooted in $$s$$. This only misses some cycles of length $$3$$, namely those of the form $$\\langle s, u, v, s \\rangle$$ where both $$u$$ and $$v$$ are neighbors of $$s$$. Fortunately, we can discover all such cycles in $$O(|E|)$$ time by checking all edges $$(u,v) \\in E$$.\n\nIn an undirected graph $$G$$, remove vertex $$v$$ and find the shortest path between all pairs of vertices in $$N(v)$$; i.e. Find $$d(a,b):=$$shortest path between $$a,b\\in N(v)$$ in graph $$G'=G-\\{v\\}$$.\n\nResult is $$min\\{d(a,b)+w(a,v)+w(b,v)|a,b\\in N(v)\\}$$.\n\n• This doesn't seem to work if $G$ itself is a cycle of length $> 3$. Jun 30 at 19:50\n• If $G$ is a cycle $v,a,v_1,...,v_n,b,v$ then by removing the vertex $v$ we find the shortest path $a,v_1,...,v_n,b$ between vertices of $N(v)$ and addition of $w(a,v)$ and $w(b,v)$ produces the cycle. Jun 30 at 20:58\n• Oh, you meant $N(v)$ as the neighborhood of $v$! I think you should add that to your answer. Jun 30 at 21:20"
]
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https://openstax.org/books/prealgebra/pages/5-review-exercises | [
"Prealgebra\n\n# Review Exercises\n\nPrealgebraReview Exercises\n\n### Review Exercises\n\n##### Decimals\n\nName Decimals\n\nIn the following exercises, name each decimal.\n\n534.\n\n$0.8 0.8$\n\n535.\n\n$0.375 0.375$\n\n536.\n\n$0.007 0.007$\n\n537.\n\n$5.24 5.24$\n\n538.\n\n$−12.5632 −12.5632$\n\n539.\n\n$−4.09 −4.09$\n\nWrite Decimals\n\nIn the following exercises, write as a decimal.\n\n540.\n\nthree tenths\n\n541.\n\nnine hundredths\n\n542.\n\ntwenty-seven hundredths\n\n543.\n\nten and thirty-five thousandths\n\n544.\n\nnegative twenty and three tenths\n\n545.\n\nnegative five hundredths\n\nConvert Decimals to Fractions or Mixed Numbers\n\nIn the following exercises, convert each decimal to a fraction. Simplify the answer if possible.\n\n546.\n\n$0.43 0.43$\n\n547.\n\n$0.825 0.825$\n\n548.\n\n$9.7 9.7$\n\n549.\n\n$3.64 3.64$\n\nLocate Decimals on the Number Line\n\n550.\n\n$0.6 0.6$\n\n$−0.9 −0.9$\n\n$2.2 2.2$\n\n$−1.3 −1.3$\n\nOrder Decimals\n\nIn the following exercises, order each of the following pairs of numbers, using $<<$ or $>.>.$\n\n551.\n\n$0.6 ___ 0.8 0.6 ___ 0.8$\n\n552.\n\n$0.2 ___ 0.15 0.2 ___ 0.15$\n\n553.\n\n$0.803 ____ 0.83 0.803 ____ 0.83$\n\n554.\n\n$−0.56 ____ −0.562 −0.56 ____ −0.562$\n\nRound Decimals\n\nIn the following exercises, round each number to the nearest: hundredth tenth whole number.\n\n555.\n\n$12.529 12.529$\n\n556.\n\n$4.8447 4.8447$\n\n557.\n\n$5.897 5.897$\n\n##### Decimal Operations\n\nIn the following exercises, add or subtract.\n\n558.\n\n$5.75 + 8.46 5.75 + 8.46$\n\n559.\n\n$32.89 − 8.22 32.89 − 8.22$\n\n560.\n\n$24 − 19.31 24 − 19.31$\n\n561.\n\n$10.2 + 14.631 10.2 + 14.631$\n\n562.\n\n$−6.4 + ( −2.9 ) −6.4 + ( −2.9 )$\n\n563.\n\n$1.83 − 4.2 1.83 − 4.2$\n\nMultiply Decimals\n\nIn the following exercises, multiply.\n\n564.\n\n$( 0.3 ) ( 0.7 ) ( 0.3 ) ( 0.7 )$\n\n565.\n\n$( −6.4 ) ( 0.25 ) ( −6.4 ) ( 0.25 )$\n\n566.\n\n$( −3.35 ) ( −12.7 ) ( −3.35 ) ( −12.7 )$\n\n567.\n\n$( 15.4 ) ( 1000 ) ( 15.4 ) ( 1000 )$\n\nDivide Decimals\n\nIn the following exercises, divide.\n\n568.\n\n$0.48 ÷ 6 0.48 ÷ 6$\n\n569.\n\n$4.32 ÷ 24 4.32 ÷ 24$\n\n570.\n\n$6.29 ÷ 12 6.29 ÷ 12$\n\n571.\n\n$( −0.8 ) ÷ ( −0.2 ) ( −0.8 ) ÷ ( −0.2 )$\n\n572.\n\n$1.65 ÷ 0.15 1.65 ÷ 0.15$\n\n573.\n\n$9 ÷ 0.045 9 ÷ 0.045$\n\nUse Decimals in Money Applications\n\nIn the following exercises, use the strategy for applications to solve.\n\n574.\n\nMiranda got $4040$ from her ATM. She spent $9.329.32$ on lunch and $16.9916.99$ on a book. How much money did she have left? Round to the nearest cent if necessary.\n\n575.\n\nJessie put $88$ gallons of gas in her car. One gallon of gas costs $3.528.3.528.$ How much did Jessie owe for all the gas?\n\n576.\n\nA pack of $1616$ water bottles cost $6.72.6.72.$ How much did each bottle cost?\n\n577.\n\nAlice bought a roll of paper towels that cost $2.49.2.49.$ She had a coupon for $0.350.35$ off, and the store doubled the coupon. How much did Alice pay for the paper towels?\n\n##### Decimals and Fractions\n\nConvert Fractions to Decimals\n\nIn the following exercises, convert each fraction to a decimal.\n\n578.\n\n$3 5 3 5$\n\n579.\n\n$7 8 7 8$\n\n580.\n\n$− 19 20 − 19 20$\n\n581.\n\n$− 21 4 − 21 4$\n\n582.\n\n$1 3 1 3$\n\n583.\n\n$6 11 6 11$\n\nOrder Decimals and Fractions\n\nIn the following exercises, order each pair of numbers, using $<<$ or $>.>.$\n\n584.\n\n$1 2 ___ 0.2 1 2 ___ 0.2$\n\n585.\n\n$3 5 ___ 0 . 3 5 ___ 0 .$\n\n586.\n\n$− 7 8 ___ −0.84 − 7 8 ___ −0.84$\n\n587.\n\n$− 5 12 ___ −0.42 − 5 12 ___ −0.42$\n\n588.\n\n$0.625 ___ 13 20 0.625 ___ 13 20$\n\n589.\n\n$0.33 ___ 5 16 0.33 ___ 5 16$\n\nIn the following exercises, write each set of numbers in order from least to greatest.\n\n590.\n\n$2 3 , 17 20 , 0.65 2 3 , 17 20 , 0.65$\n\n591.\n\n$7 9 , 0.75 , 11 15 7 9 , 0.75 , 11 15$\n\nSimplify Expressions Using the Order of Operations\n\nIn the following exercises, simplify\n\n592.\n\n$4 ( 10.3 − 5.8 ) 4 ( 10.3 − 5.8 )$\n\n593.\n\n$3 4 ( 15.44 − 7.4 ) 3 4 ( 15.44 − 7.4 )$\n\n594.\n\n$30 ÷ ( 0.45 + 0.15 ) 30 ÷ ( 0.45 + 0.15 )$\n\n595.\n\n$1.6 + 3 8 1.6 + 3 8$\n\n596.\n\n$52 ( 0.5 ) + ( 0.4 ) 2 52 ( 0.5 ) + ( 0.4 ) 2$\n\n597.\n\n$− 2 5 · 9 10 + 0.14 − 2 5 · 9 10 + 0.14$\n\nFind the Circumference and Area of Circles\n\nIn the following exercises, approximate the circumference and area of each circle.\n\n598.\n\n$radius = 6 in. radius = 6 in.$\n\n599.\n\n$radius = 3.5 ft. radius = 3.5 ft.$\n\n600.\n\n$radius = 7 33 m radius = 7 33 m$\n\n601.\n\n$diameter = 11 cm diameter = 11 cm$\n\n##### Solve Equations with Decimals\n\nDetermine Whether a Decimal is a Solution of an Equation\n\nIn the following exercises, determine whether the each number is a solution of the given equation.\n\n602.\n\n$x−0.4=2.1x−0.4=2.1$\n$x=1.7x=1.7$ $x=2.5x=2.5$\n\n603.\n\n$y + 3.2 = −1.5 y + 3.2 = −1.5$\n$y = 1.7 y = 1.7$ $y = −4.7 y = −4.7$\n\n604.\n\n$u 2.5 = −12.5 u 2.5 = −12.5$\n$u = −5 u = −5$ $u = −31.25 u = −31.25$\n\n605.\n\n$0.45 v = −40.5 0.45 v = −40.5$\n$v = −18.225 v = −18.225$ $v = −90 v = −90$\n\nSolve Equations with Decimals\n\nIn the following exercises, solve.\n\n606.\n\n$m + 3.8 = 7.5 m + 3.8 = 7.5$\n\n607.\n\n$h + 5.91 = 2.4 h + 5.91 = 2.4$\n\n608.\n\n$a + 2.26 = −1.1 a + 2.26 = −1.1$\n\n609.\n\n$p − 4.3 = −1.65 p − 4.3 = −1.65$\n\n610.\n\n$x − 0.24 = −8.6 x − 0.24 = −8.6$\n\n611.\n\n$j − 7.42 = −3.7 j − 7.42 = −3.7$\n\n612.\n\n$0.6 p = 13.2 0.6 p = 13.2$\n\n613.\n\n$−8.6 x = 34.4 −8.6 x = 34.4$\n\n614.\n\n$−22.32 = −2.4 z −22.32 = −2.4 z$\n\n615.\n\n$a 0.3 = −24 a 0.3 = −24$\n\n616.\n\n$p −7 = −4.2 p −7 = −4.2$\n\n617.\n\n$s −2.5 = −10 s −2.5 = −10$\n\nTranslate to an Equation and Solve\n\nIn the following exercises, translate and solve.\n\n618.\n\nThe difference of $nn$ and $15.215.2$ is $4.4.4.4.$\n\n619.\n\nThe product of $−5.9−5.9$ and $xx$ is $−3.54.−3.54.$\n\n620.\n\nThe quotient of $yy$ and $−1.8−1.8$ is $−9.−9.$\n\n621.\n\nThe sum of $mm$ and $−4.03−4.03$ is $6.8.6.8.$\n\n##### Averages and Probability\n\nFind the Mean of a Set of Numbers\n\nIn the following exercises, find the mean of the numbers.\n\n622.\n\n$2 , 4 , 1 , 0 , 1 , and 1 2 , 4 , 1 , 0 , 1 , and 1$\n\n623.\n\n$270270$, $310.50310.50$, $243.75243.75$, and$252.15252.15$\n\n624.\n\nEach workday last week, Yoshie kept track of the number of minutes she had to wait for the bus. She waited $3,0,8,1,and83,0,8,1,and8$ minutes. Find the mean\n\n625.\n\nIn the last three months, Raul’s water bills were $31.45,48.76,and42.60.31.45,48.76,and42.60.$ Find the mean.\n\nFind the Median of a Set of Numbers\n\nIn the following exercises, find the median.\n\n626.\n\n$4141$, $4545$, $3232$, $6060$, $5858$\n\n627.\n\n$2525$, $2323$, $2424$, $2626$, $2929$, $1919$, $1818$, $3232$\n\n628.\n\nThe ages of the eight men in Jerry’s model train club are $52,63,45,51,55,75,60,and59.52,63,45,51,55,75,60,and59.$ Find the median age.\n\n629.\n\nThe number of clients at Miranda’s beauty salon each weekday last week were $18,7,12,16,and20.18,7,12,16,and20.$ Find the median number of clients.\n\nFind the Mode of a Set of Numbers\n\nIn the following exercises, identify the mode of the numbers.\n\n630.\n\n$66$, $44$, $4,54,5$, $6,66,6$, $44$, $44$, $44$, $33$, $55$\n\n631.\n\nThe number of siblings of a group of students: $22$, $00$, $33$, $22$, $44$, $11$, $66$, $55$, $44$, $11$, $22$, $33$\n\nUse the Basic Definition of Probability\n\nIn the following exercises, solve. (Round decimals to three places.)\n\n632.\n\nThe Sustainability Club sells $200200$ tickets to a raffle, and Albert buys one ticket. One ticket will be selected at random to win the grand prize. Find the probability Albert will win the grand prize. Express your answer as a fraction and as a decimal.\n\n633.\n\nLuc has to read $33$ novels and $1212$ short stories for his literature class. The professor will choose one reading at random for the final exam. Find the probability that the professor will choose a novel for the final exam. Express your answer as a fraction and as a decimal.\n\n##### Ratios and Rate\n\nWrite a Ratio as a Fraction\n\nIn the following exercises, write each ratio as a fraction. Simplify the answer if possible.\n\n634.\n\n$2828$ to $4040$\n\n635.\n\n$5656$ to $3232$\n\n636.\n\n$3.53.5$ to $0.50.5$\n\n637.\n\n$1.21.2$ to $1.81.8$\n\n638.\n\n$1 3 4 to 1 5 8 1 3 4 to 1 5 8$\n\n639.\n\n$2 1 3 to 5 1 4 2 1 3 to 5 1 4$\n\n640.\n\n$6464$ ounces to $3030$ ounces\n\n641.\n\n$2828$ inches to $33$ feet\n\nWrite a Rate as a Fraction\n\nIn the following exercises, write each rate as a fraction. Simplify the answer if possible.\n\n642.\n\n$180180$ calories per $88$ ounces\n\n643.\n\n$9090$ pounds per $7.57.5$ square inches\n\n644.\n\n$126126$ miles in $44$ hours\n\n645.\n\n$612.50612.50$ for $3535$ hours\n\nFind Unit Rates\n\nIn the following exercises, find the unit rate.\n\n646.\n\n$180180$ calories per $88$ ounces\n\n647.\n\n$9090$ pounds per $7.57.5$ square inches\n\n648.\n\n$126126$ miles in $44$ hours\n\n649.\n\n$612.50612.50$ for $3535$ hours\n\nFind Unit Price\n\nIn the following exercises, find the unit price.\n\n650.\n\nt-shirts: $33$ for $8.978.97$\n\n651.\n\nHighlighters: $66$ for $2.522.52$\n\n652.\n\nAn office supply store sells a box of pens for $11.11.$ The box contains $1212$ pens. How much does each pen cost?\n\n653.\n\nAnna bought a pack of $88$ kitchen towels for $13.20.13.20.$ How much did each towel cost? Round to the nearest cent if necessary.\n\nIn the following exercises, find each unit price and then determine the better buy.\n\n654.\n\nShampoo: $1212$ ounces for $4.294.29$ or $2222$ ounces for $7.29?7.29?$\n\n655.\n\nVitamins: $6060$ tablets for $6.496.49$ or $100100$ for $11.99?11.99?$\n\nTranslate Phrases to Expressions with Fractions\n\nIn the following exercises, translate the English phrase into an algebraic expression.\n\n656.\n\n$535535$ miles per $hhourshhours$\n\n657.\n\n$aa$ adults to $4545$ children\n\n658.\n\nthe ratio of $4y4y$ and the difference of $xx$ and $1010$\n\n659.\n\nthe ratio of $1919$ and the sum of $33$ and $nn$\n\n##### Simplify and Use Square Roots\n\nSimplify Expressions with Square Roots\n\nIn the following exercises, simplify.\n\n660.\n\n$64 64$\n\n661.\n\n$144 144$\n\n662.\n\n$− 25 − 25$\n\n663.\n\n$− 81 − 81$\n\n664.\n\n$−9 −9$\n\n665.\n\n$−36 −36$\n\n666.\n\n$64 + 225 64 + 225$\n\n667.\n\n$64 + 225 64 + 225$\n\nEstimate Square Roots\n\nIn the following exercises, estimate each square root between two consecutive whole numbers.\n\n668.\n\n$28 28$\n\n669.\n\n$155 155$\n\nApproximate Square Roots\n\nIn the following exercises, approximate each square root and round to two decimal places.\n\n670.\n\n$15 15$\n\n671.\n\n$57 57$\n\nSimplify Variable Expressions with Square Roots\n\nIn the following exercises, simplify. (Assume all variables are greater than or equal to zero.)\n\n672.\n\n$q 2 q 2$\n\n673.\n\n$64 b 2 64 b 2$\n\n674.\n\n$− 121 a 2 − 121 a 2$\n\n675.\n\n$225 m 2 n 2 225 m 2 n 2$\n\n676.\n\n$− 100 q 2 − 100 q 2$\n\n677.\n\n$49 y 2 49 y 2$\n\n678.\n\n$4 a 2 b 2 4 a 2 b 2$\n\n679.\n\n$121 c 2 d 2 121 c 2 d 2$\n\nUse Square Roots in Applications\n\nIn the following exercises, solve. Round to one decimal place.\n\n680.\n\nArt Diego has $225225$ square inch tiles. He wants to use them to make a square mosaic. How long can each side of the mosaic be?\n\n681.\n\nLandscaping Janet wants to plant a square flower garden in her yard. She has enough topsoil to cover an area of $3030$ square feet. How long can a side of the flower garden be?\n\n682.\n\nGravity A hiker dropped a granola bar from a lookout spot $576576$ feet above a valley. How long did it take the granola bar to reach the valley floor?\n\n683.\n\nAccident investigation The skid marks of a car involved in an accident were $216216$ feet. How fast had the car been going before applying the brakes?\n\nOrder a print copy\n\nAs an Amazon Associate we earn from qualifying purchases."
]
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.909528,"math_prob":0.99991035,"size":6162,"snap":"2023-40-2023-50","text_gpt3_token_len":1409,"char_repetition_ratio":0.2211757,"word_repetition_ratio":0.14921223,"special_character_ratio":0.20123337,"punctuation_ratio":0.12468408,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99997795,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-23T18:36:40Z\",\"WARC-Record-ID\":\"<urn:uuid:8b2fc391-ebef-4882-9596-1f05c5a0f4bc>\",\"Content-Length\":\"443049\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:502c7753-8660-44bb-ae64-f586ff5e97fe>\",\"WARC-Concurrent-To\":\"<urn:uuid:f100e74c-72ab-4ae5-9052-b6faefce1308>\",\"WARC-IP-Address\":\"99.84.191.115\",\"WARC-Target-URI\":\"https://openstax.org/books/prealgebra/pages/5-review-exercises\",\"WARC-Payload-Digest\":\"sha1:42CQTBLNRV56VZS4JSRW277Z2SSNU2CI\",\"WARC-Block-Digest\":\"sha1:AJSVBSXEBCITRDOAIC3OKVMNWOHIWXOL\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233506528.19_warc_CC-MAIN-20230923162848-20230923192848-00315.warc.gz\"}"} |
https://uk.mathworks.com/help/images/color-based-segmentation-using-the-l-a-b-color-space.html | [
"# Color-Based Segmentation Using the L*a*b* Color Space\n\nThis example shows how to identify different colors in fabric by analyzing the L*a*b* colorspace. The fabric image was acquired using the Image Acquisition Toolbox™.\n\n### Step 1: Acquire Image\n\nRead in the `fabric.png` image, which is an image of colorful fabric. Instead of using `fabric.png`, you can acquire an image using the following functions in the Image Acquisition Toolbox.\n\n```% Access a Matrox(R) frame grabber attached to a Pulnix TMC-9700 camera, and % acquire data using an NTSC format. % vidobj = videoinput('matrox',1,'M_NTSC_RGB'); % Open a live preview window. Point camera onto a piece of colorful fabric. % preview(vidobj); % Capture one frame of data. % fabric = getsnapshot(vidobj); % imwrite(fabric,'fabric.png','png'); % Delete and clear associated variables. % delete(vidobj) % clear vidobj; fabric = imread('fabric.png'); imshow(fabric) title('Fabric')```",
null,
"### Step 2: Calculate Sample Colors in L*a*b* Color Space for Each Region\n\nYou can see six major colors in the image: the background color, red, green, purple, yellow, and magenta. Notice how easily you can visually distinguish these colors from one another. The L*a*b* colorspace (also known as CIELAB or CIE L*a*b*) enables you to quantify these visual differences.\n\nThe L*a*b* color space is derived from the CIE XYZ tristimulus values. The L*a*b* space consists of a luminosity 'L*' or brightness layer, chromaticity layer 'a*' indicating where color falls along the red-green axis, and chromaticity layer 'b*' indicating where the color falls along the blue-yellow axis.\n\nYour approach is to choose a small sample region for each color and to calculate each sample region's average color in 'a*b*' space. You will use these color markers to classify each pixel.\n\nTo simplify this example, load the region coordinates that are stored in a MAT-file.\n\n```load regioncoordinates; nColors = 6; sample_regions = false([size(fabric,1) size(fabric,2) nColors]); for count = 1:nColors sample_regions(:,:,count) = roipoly(fabric,region_coordinates(:,1,count), ... region_coordinates(:,2,count)); end imshow(sample_regions(:,:,2)) title('Sample Region for Red')```",
null,
"Convert your fabric RGB image into an L*a*b* image using `rgb2lab` .\n\n`lab_fabric = rgb2lab(fabric);`\n\nCalculate the mean 'a*' and 'b*' value for each area that you extracted with `roipoly`. These values serve as your color markers in 'a*b*' space.\n\n```a = lab_fabric(:,:,2); b = lab_fabric(:,:,3); color_markers = zeros([nColors, 2]); for count = 1:nColors color_markers(count,1) = mean2(a(sample_regions(:,:,count))); color_markers(count,2) = mean2(b(sample_regions(:,:,count))); end```\n\nFor example, the average color of the red sample region in 'a*b*' space is\n\n`fprintf('[%0.3f,%0.3f] \\n',color_markers(2,1),color_markers(2,2));`\n```[69.828,20.106] ```\n\n### Step 3: Classify Each Pixel Using the Nearest Neighbor Rule\n\nEach color marker now has an 'a*' and a 'b*' value. You can classify each pixel in the `lab_fabric` image by calculating the Euclidean distance between that pixel and each color marker. The smallest distance will tell you that the pixel most closely matches that color marker. For example, if the distance between a pixel and the red color marker is the smallest, then the pixel would be labeled as a red pixel.\n\nCreate an array that contains your color labels, i.e., 0 = background, 1 = red, 2 = green, 3 = purple, 4 = magenta, and 5 = yellow.\n\n`color_labels = 0:nColors-1;`\n\nInitialize matrices to be used in the nearest neighbor classification.\n\n```a = double(a); b = double(b); distance = zeros([size(a), nColors]);```\n\nPerform classification\n\n```for count = 1:nColors distance(:,:,count) = ( (a - color_markers(count,1)).^2 + ... (b - color_markers(count,2)).^2 ).^0.5; end [~,label] = min(distance,[],3); label = color_labels(label); clear distance;```\n\n### Step 4: Display Results of Nearest Neighbor Classification\n\nThe label matrix contains a color label for each pixel in the fabric image. Use the label matrix to separate objects in the original fabric image by color.\n\n```rgb_label = repmat(label,[1 1 3]); segmented_images = zeros([size(fabric), nColors],'uint8'); for count = 1:nColors color = fabric; color(rgb_label ~= color_labels(count)) = 0; segmented_images(:,:,:,count) = color; end ```\n\nDisplay the five segmented colors as a montage. Also display the background pixels in the image that are not classified as a color.\n\n```montage({segmented_images(:,:,:,2),segmented_images(:,:,:,3) ... segmented_images(:,:,:,4),segmented_images(:,:,:,5) ... segmented_images(:,:,:,6),segmented_images(:,:,:,1)}); title(\"Montage of Red, Green, Purple, Magenta, and Yellow Objects, and Background\")```",
null,
"### Step 5: Display 'a*' and 'b*' Values of the Labeled Colors\n\nYou can see how well the nearest neighbor classification separated the different color populations by plotting the 'a*' and 'b*' values of pixels that were classified into separate colors. For display purposes, label each point with its color label.\n\n```purple = [119/255 73/255 152/255]; plot_labels = {'k', 'r', 'g', purple, 'm', 'y'}; figure for count = 1:nColors plot(a(label==count-1),b(label==count-1),'.','MarkerEdgeColor', ... plot_labels{count}, 'MarkerFaceColor', plot_labels{count}); hold on; end title('Scatterplot of the segmented pixels in ''a*b*'' space'); xlabel('''a*'' values'); ylabel('''b*'' values');```",
null,
""
]
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null,
"https://uk.mathworks.com/help/examples/images/win64/LabColorSegmentationExample_01.png",
null,
"https://uk.mathworks.com/help/examples/images/win64/LabColorSegmentationExample_02.png",
null,
"https://uk.mathworks.com/help/examples/images/win64/LabColorSegmentationExample_03.png",
null,
"https://uk.mathworks.com/help/examples/images/win64/LabColorSegmentationExample_04.png",
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.71402514,"math_prob":0.97726166,"size":4974,"snap":"2020-34-2020-40","text_gpt3_token_len":1254,"char_repetition_ratio":0.13903421,"word_repetition_ratio":0.0,"special_character_ratio":0.2844793,"punctuation_ratio":0.24177949,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9735794,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,3,null,3,null,3,null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-08-05T13:37:33Z\",\"WARC-Record-ID\":\"<urn:uuid:49169e84-05cf-4e5b-8acc-099012f9c0e4>\",\"Content-Length\":\"76050\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1437a4e4-b020-4407-8ea4-93e435670bd7>\",\"WARC-Concurrent-To\":\"<urn:uuid:d79b1bc4-1aee-4649-b556-3185550dcadb>\",\"WARC-IP-Address\":\"23.212.144.59\",\"WARC-Target-URI\":\"https://uk.mathworks.com/help/images/color-based-segmentation-using-the-l-a-b-color-space.html\",\"WARC-Payload-Digest\":\"sha1:NMDLIFQABQU33JVHXXPQMQSCX6KK2A3G\",\"WARC-Block-Digest\":\"sha1:3E6HTNR7AGOLTXVZORH6N6XR5U24YYAE\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-34/CC-MAIN-2020-34_segments_1596439735958.84_warc_CC-MAIN-20200805124104-20200805154104-00478.warc.gz\"}"} |
https://socratic.org/questions/a-right-triangle-has-sides-a-b-and-c-side-a-is-the-hypotenuse-and-side-b-is-also-111 | [
"# A right triangle has sides A, B, and C. Side A is the hypotenuse and side B is also a side of a rectangle. Sides A, C, and the side of the rectangle adjacent to side B have lengths of 3 , 1 , and 9 , respectively. What is the rectangle's area?\n\nJun 1, 2016\n\n$18 \\sqrt{2}$\n\n#### Explanation:\n\nGiven $A = 3$ and $C = 1$\nby the Pythagorean Theorem\n$\\textcolor{w h i t e}{\\text{XXX}} B = \\sqrt{{3}^{2} - {1}^{1}} = 2 \\sqrt{2}$\n\nSince the rectangle has sides of length $B$ and $9$\nthe rectangle's area is\n$\\textcolor{w h i t e}{\\text{XXX}} 2 \\sqrt{2} \\times 9 = 18 \\sqrt{2}$"
]
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.8489463,"math_prob":0.9997732,"size":507,"snap":"2022-05-2022-21","text_gpt3_token_len":132,"char_repetition_ratio":0.15705766,"word_repetition_ratio":0.0,"special_character_ratio":0.2504931,"punctuation_ratio":0.123809524,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9998863,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-28T01:48:26Z\",\"WARC-Record-ID\":\"<urn:uuid:106dd09c-6f9a-4ac5-a94b-49882ab5563b>\",\"Content-Length\":\"33815\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:19ccae8b-b5a9-4418-aa73-1eae51e5fee7>\",\"WARC-Concurrent-To\":\"<urn:uuid:127a061f-53be-41de-8814-9169ca431e72>\",\"WARC-IP-Address\":\"216.239.38.21\",\"WARC-Target-URI\":\"https://socratic.org/questions/a-right-triangle-has-sides-a-b-and-c-side-a-is-the-hypotenuse-and-side-b-is-also-111\",\"WARC-Payload-Digest\":\"sha1:G4CDT243GUW2Q6BB772G5ZPEM4HGEBQP\",\"WARC-Block-Digest\":\"sha1:Q3B6ECM2QAMO7HI4Y4VEBEYCQI5R6MSK\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652663011588.83_warc_CC-MAIN-20220528000300-20220528030300-00553.warc.gz\"}"} |
http://georgemaciunas.com/bayesian-statistical-reasoning-an-inferential-predictive-and-decision-making-paradigm-for-the-21st-century-by-professor-david-draper-phd/ | [
"# Bayesian Statistical Reasoning: an inferential, predictive and decision-making paradigm for the 21st century by Professor David Draper, PhD\n\n### Bayesian Statistical Reasoning\n\n#### an inferential, predictive and decision-making paradigm for the 21st century\n\nProfessor David Draper, PhD\n\nProfessor Draper gives examples of Bayesian inference, prediction and decision-making in the context of several case studies from medicine and health policy. There will be points of potential technical interest for applied mathematicians, statisticians, and computer scientists. Broadly speaking, statistics is the study of uncertainty: how to measure it well, and how to make good choices in the face of it. Statistical activities are of four main types: description of a data set, inference about the underlying process generating the data, prediction of future data, and decision-making under uncertainty. The last three of these activities are probability based.\n\nTwo main probability paradigms are in current use: the frequentist (or relative-frequency) approach, in which you restrict attention to phenomena that are inherently repeatable under “identical” conditions and define P(A) to be the limiting relative frequency with which A would occur in hypothetical repetitions, as n goes to infinity; and the Bayesian approach, in which the arguments A and B of the probability operator P(A|B) are true-false propositions (with the truth status of A unknown to you and B assumed by you to be true), and P(A|B) represents the weight of evidence in favor of the truth of A, given the information in B.\n\nThe Bayesian approach includes the frequentest paradigm as a special case,so you might think it would be the only version of probability used in statistical work today, but (a) in quantifying your uncertainty about something unknown to you, the Bayesian paradigm requires you to bring all relevant information to bear on the calculation; this involves combining information both internal and external to the data you’ve gathered, and (somewhat strangely) the external-information part of this approach was controversial in the 20th century, and (b) Bayesian calculations require approximating high-dimensional integrals (whereas the frequentist approach mainly relies on maximization rather than integration), and this was a severe limitation to the Bayesian paradigm for a long time (from the 1750s to the 1980s).\n\nThe external-information problem has been solved by developing methods that separately handle the two main cases: (1) substantial external information, which is addressed by elicitation techniques, and (2) relatively little external information, which is covered by any of several methods for (in the jargon) specifying diffuse prior distributions.\nGood Bayesian work also involves sensitivity analysis: varying the manner in which you quantify the internal and external information across reasonable alternatives, and examining the stability of your conclusions.\n\nAround 1990 two things happened roughly simultaneously that completely changed the Bayesian computational picture: * Bayesian statisticians belatedly discovered that applied mathematicians (led by Metropolis), working at the intersection between chemistry and physics in the 1940s, had used Markov chains to develop a clever algorithm for approximating integrals arising in thermodynamics that are similar to the kinds of integrals that come up in Bayesian statistics, and * desk-top computers finally became fast enough to implement the Metropolis algorithm in a feasibly short amount of time.\n\nAs a result of these developments, the Bayesian computational problem has been solved in a wide range of interesting application areas with small-to-moderate amounts of data; with large data sets, variational methods are available that offer a different approach to useful approximate solutions.\n\nThe Bayesian paradigm for uncertainty quantification does appear to have one remaining weakness, which coincides with a strength of the frequentest paradigm: nothing in the Bayesian approach to inference and prediction requires you to pay attention to how often you get the right answer (thisis a form of calibration of your uncertainty assessments), which is an activity that’s (i) central to good science and decision-making and (ii) natural to emphasize from the frequentist point of view.\n\nHowever, it has recently been shown that calibration can readily be brought into the Bayesian story by means of decision theory, turning the Bayesian paradigm into an approach that is (in principle) both logically internally consistent and well-calibrated.\n\nIn this talk I’ll (a) offer some historical notes about how we have arrived at the present situation and (b) give examples of Bayesian inference, prediction and decision-making in the context of several case studies from medicine and health policy.\n\nThere will be points of potential technical interest for applied mathematicians, statisticians and computer scientists."
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.9446277,"math_prob":0.8351743,"size":4827,"snap":"2023-14-2023-23","text_gpt3_token_len":898,"char_repetition_ratio":0.12150114,"word_repetition_ratio":0.07334273,"special_character_ratio":0.17775016,"punctuation_ratio":0.07672956,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9529904,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-05-31T20:02:51Z\",\"WARC-Record-ID\":\"<urn:uuid:b5349428-2398-4c13-851f-db0c5899eca8>\",\"Content-Length\":\"208419\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:dc570952-c20b-438a-a84f-596cf9a43dd8>\",\"WARC-Concurrent-To\":\"<urn:uuid:2b60489f-1b78-4fdf-a48f-e9cba7d9de34>\",\"WARC-IP-Address\":\"208.109.26.224\",\"WARC-Target-URI\":\"http://georgemaciunas.com/bayesian-statistical-reasoning-an-inferential-predictive-and-decision-making-paradigm-for-the-21st-century-by-professor-david-draper-phd/\",\"WARC-Payload-Digest\":\"sha1:7KSM5OJLBSLZMNT47DTJCIIB2KUWNJL5\",\"WARC-Block-Digest\":\"sha1:KA4TQFKJIGMBN6AURBX4Z2FFWHLMQPOV\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224647409.17_warc_CC-MAIN-20230531182033-20230531212033-00725.warc.gz\"}"} |
https://getacho.com/how-to-divide-30000-by-4/ | [
"# How to Divide 30,000 by 4\n\nDividing numbers can be difficult for those who are unfamiliar with mathematics, but it doesn’t have to be. Knowing how to divide numbers can help you in many areas of life, from balancing a budget to solving everyday problems. One of the most basic divisions you can perform is 30,000 divided by 4. In this article, we’ll take a look at how to divide 30,000 by 4 and why it’s important to understand this basic mathematical concept.\n\n## How Does Division Work?",
null,
"Division is a mathematical operation that is used to find the number of times one number can be divided into another. It is a subset of multiplication and can be represented by fractions or decimals. When dividing two numbers, the larger number (the dividend) is divided by the smaller number (the divisor). The result is the quotient. In the case of 30,000 divided by 4, the dividend is 30,000, the divisor is 4, and the quotient is 7,500.\n\n## Why Is Division Important?",
null,
"Division is an important mathematical concept to understand as it is used in everyday life in various ways, from calculating the cost per unit when buying groceries to measuring ingredients for a recipe. It’s also important for more complex tasks such as budgeting, determining mortgage payments, and calculating profits and losses. Knowing how to divide numbers is an essential part of understanding the world around us.\n\n## How to Divide 30,000 by 4",
null,
"Now that we understand why division is important, let’s take a look at how to divide 30,000 by 4. The process is simple and can be broken down into a few easy steps:\n\n• Step 1: Write down the dividend and divisor.\n• Step 2: Divide the dividend by the divisor.\n• Step 3: The result is the quotient.\n\nIn this case, the dividend is 30,000 and the divisor is 4. When you divide 30,000 by 4, the result is 7,500. This means that 4 can be divided into 30,000 7,500 times.\n\n## Using Division to Solve Real-World Problems",
null,
"Once you understand the basics of division, you can use it to solve real-world problems. For example, if you have 30,000 dollars and you want to split it evenly among 4 people, you can use division to calculate how much each person will receive. To do this, you would divide 30,000 by 4, which would give you a result of 7,500. This means that each person will receive 7,500 dollars.\n\n## \u0001\n\nDividing numbers can be a difficult concept, but it’s an important one to understand. Knowing how to divide numbers can help you in a variety of ways, from solving everyday problems to budgeting and determining profits. This article has discussed how to divide 30,000 by 4 and why it’s important to understand this basic mathematical concept. With the proper knowledge and understanding of division, you can use it to solve a variety of real-world problems."
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"https://tse1.mm.bing.net/th",
null,
"https://tse1.mm.bing.net/th",
null,
"https://tse1.mm.bing.net/th",
null,
"https://tse1.mm.bing.net/th",
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]
| {"ft_lang_label":"__label__en","ft_lang_prob":0.94939595,"math_prob":0.965698,"size":5938,"snap":"2023-14-2023-23","text_gpt3_token_len":1360,"char_repetition_ratio":0.14863499,"word_repetition_ratio":0.06641721,"special_character_ratio":0.24587403,"punctuation_ratio":0.09758132,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9991923,"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\":\"2023-05-28T09:04:41Z\",\"WARC-Record-ID\":\"<urn:uuid:201d8461-69bd-4159-a74a-c7a3ce9a288d>\",\"Content-Length\":\"53064\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4e072f32-b943-4441-986f-b365da232c08>\",\"WARC-Concurrent-To\":\"<urn:uuid:20c738e3-870d-40c2-9343-40f702f46e8d>\",\"WARC-IP-Address\":\"172.67.200.201\",\"WARC-Target-URI\":\"https://getacho.com/how-to-divide-30000-by-4/\",\"WARC-Payload-Digest\":\"sha1:HMHFZZRPUEK4IY6HKYBFU2HNG4VZ4BUC\",\"WARC-Block-Digest\":\"sha1:SZALRYTMOIHXTJJK4Z7RE4UT7SY5ANKK\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224643663.27_warc_CC-MAIN-20230528083025-20230528113025-00203.warc.gz\"}"} |
https://tutorial.eyehunts.com/python/what-is-a-tuple-in-python-basics/ | [
"# What is a tuple in Python | Basics\n\nTuples are store multiple items in a single variable in Python. A tuple is an immutable object meaning that we cannot change, add or remove items after the tuple has been created.\n\n``empty_tuple = ()``\n``mytuple = (\"apple\", \"banana\", \"cherry\")``\n\nPython Tuples are used to store collections of data, and their other data type is List, Set, and Dictionary, all with different qualities and usage.\n\nIn Python, a tuple is an ordered, immutable collection of elements enclosed in parentheses `()`. It is a data structure similar to a list, but unlike lists, tuples cannot be modified once created. Tuples can contain elements of different types, such as numbers, strings, or even other tuples.\n\n## How to create and use tuples in Python\n\nSimple example code creating non-empty tuples. Tuples that are ordered will not change, are unchangeable, and Allow Duplicates.\n\n``````# One way of creation\ntup = 'A', 'B'\nprint(tup)\n\n# Another for doing the same\ntup = ('X', 'Y')\nprint(tup)\n``````\n\nOutput:\n\nAccessing tuple elements: You can access individual elements of a tuple using indexing. Python uses zero-based indexing, so the first element is at index 0. Here’s an example:\n\n``````print(my_tuple) # Output: 1\n``````\n\nHow Tuple assignment: You can assign the elements of a tuple to multiple variables in a single statement. Here’s an example:\n\n``````my_tuple = (1, 2, 3)\na, b, c = my_tuple\nprint(a) # Output: 1\nprint(b) # Output: 2\nprint(c) # Output: 3\n``````\n\nTuple concatenation: You can concatenate tuples using the `+` operator. It creates a new tuple that combines the elements of the original tuples.\n\n``````tuple1 = (1, 2)\ntuple2 = (3, 4)\ncombined_tuple = tuple1 + tuple2\nprint(combined_tuple) # Output: (1, 2, 3, 4)\n``````\n\nIterating over a tuple: You can use a `for` loop to iterate over the elements of a tuple. Here’s an example:\n\n``````my_tuple = (1, 2, 3)\nfor element in my_tuple:\nprint(element)\n``````\n\nUse Tuple methods: Tuples have a few built-in methods, such as `count()` and `index()`. The `count()` method returns the number of occurrences of a specific element in the tuple, while the `index()` method returns the index of the first occurrence of a specific element. Here’s an example:\n\n``````my_tuple = (1, 2, 2, 3, 3, 3)\nprint(my_tuple.count(2)) # Output: 2\nprint(my_tuple.index(3)) # Output: 3\n``````\n\nIn this case, the `count()` method returns 2 since the value 2 appears twice in the tuple, and the `index()` method returns 3, which is the index of the first occurrence of 3.\n\nComment if you have any doubts or suggestions on this Python tuple basics tutorial.\n\nNote: IDE: PyCharm 2021.3.3 (Community Edition)\n\nWindows 10\n\nPython 3.10.1\n\nAll Python Examples are in Python 3, so Maybe its different from python 2 or upgraded versions."
]
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null
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.8099806,"math_prob":0.84412694,"size":2624,"snap":"2023-40-2023-50","text_gpt3_token_len":686,"char_repetition_ratio":0.14618321,"word_repetition_ratio":0.03837472,"special_character_ratio":0.2660061,"punctuation_ratio":0.16074766,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97650003,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-25T07:38:09Z\",\"WARC-Record-ID\":\"<urn:uuid:a367f4dd-1961-4c6e-afac-1e6cd30b66de>\",\"Content-Length\":\"199194\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:ad0c45e4-7b80-4b3c-9e5e-ea90df3a33da>\",\"WARC-Concurrent-To\":\"<urn:uuid:04be4146-3b2b-4efe-b8f8-c84cf8e3e5db>\",\"WARC-IP-Address\":\"104.21.30.79\",\"WARC-Target-URI\":\"https://tutorial.eyehunts.com/python/what-is-a-tuple-in-python-basics/\",\"WARC-Payload-Digest\":\"sha1:VMGWNMQAVBOJAILAB7FKK2OCZDUCGRKB\",\"WARC-Block-Digest\":\"sha1:YQV2G4UOV7VVRROHLYIHJZ6A5A2QX6ZN\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233506686.80_warc_CC-MAIN-20230925051501-20230925081501-00828.warc.gz\"}"} |
https://studybullet.com/udemy/zero-to-hero-intro-to-algebra-variables-fractions-more/ | [
"• Post category:Udemy (Sept 2021)",
null,
"## Learn algebra basics; how to work with variables, perform fraction operations, perfect squares, cubes and roots.\n\nWhat you will learn\n\nAlgebra Basics: What are variables, rules of fractions, perfect squares, cubes, roots\n\nAddition, subtraction, multiplication & division of fractions with variables.\n\nDitchYour Calculator! Speed up your own ability to calculate squares, cubes & roots\n\nHow roots work and occur in other parts of algebra….A\n\nVariables Can Have A “Definite Answer”, More Than One Solution Or Infinite Answers\n\nLearn how to understand and use “x” plus how it is just a “placeholder” for variables\n\nLearn how to understand and use other variable placeholders like p, q, r, s and t (commonly time)\n\nApply different operations with fractions; multiplication, division, addition and subtraction\n\nDescription\n\nIn this course you will get professional maths tutoring to help you be successful at Algebra. We cover the basics of algebra such as variables, fractions, operations, cubes, roots and squares. You will get practical, step by step explanations, practice examples and demonstration lessons. A solid introduction to algebra is so important for the rest of your maths journey so join us in this course as we help you achieve your goals.\n\nThis course is engaging, practical and takes you on a powerful journey that supports your journey as a student…………………….\n\nGet the following when you enrol:\n\n• Engaging lessons that teach you key concepts and build up your confidence so you can apply what you’ve learnt\n• A wipeboard lesson that teaches you an overview of the course and your journey of transformation to achieve your goals\n• Practice questions for each concept so you can take action and apply what you have learnt and make sufficient progress\n• Downloadable worksheets that you can refer to and get the answers and explanations you need for future reference\n• Access to Kyle De Vos at any time through the messaging and assignments feature of the platform\n• Encouragement from other students who are focused on the same goal, just like you\n• Articles, resources and additional material to maximise your learning experience and ensure you achieve your goal\n\nEnrol today and we look forward to seeing your success as a maths student!\n\n## English\n\nLanguage\n\nContent\n\nIntroduction\n\nIntroduction\n\nHello My Name Is Kyle, Welcome To This Course, I Am A Professional Maths Tutor\n\nHow This Course Works: Overview On A Whiteboard & Your Learning Journey\n\nGo Ahead And Please Introduce Yourself To Everyone Else In This Course\n\nIntroduction To Algebra Basics: Variables, Fractions, Squares, Cubes & Roots\n\nAlgebra Basics: What Are Variables, Rules Of Fractions, Perfect Squares, Cubes,\n\nLet’s Get Started On Algebra Basics With Professional Maths Tutor Kyle De Vos\n\nSubscribe to latest coupons on our Telegram channel.\n\nLearn The Basics Of Variables: How To Work With Them & What To Expect\n\nLearn The Basic Rules Of Fractions And Related Concepts In Algebra\n\nExamples Of Division Of Fractions; Learn By Practising\n\nHow Are You Doing? This Is Kyle Checking On Your Journey To Algebra Hero\n\nLearn Squares, Cubes And Roots\n\nLearn How To Quickly Recognise & Calculate Squares & Intro To Exponents\n\nLearn Perfect Cubes; See Examples And Get An Intro To Exponent Notation\n\nLearn About Roots; A Very Important Concept In Algebra\n\nLearn Basic Algebra Operations: Addition, Subtraction, Multiplication Division\n\nExamples Of Addition & Subtraction Of Fractions; Learn Multiplication & Division\n\nExamples Of Combination Operations Of Fractions; Eg Multiplication & Subtraction\n\nPractice, Practice, Practice: Worksheets And Sample Worked Solutions\n\nOverview Of The Worksheet Containing The Algebra Basics Practice Questions\n\nAlgebra Basics Questions 1-3 Solutions Shown\n\nAlgebra Basics Question 4 Solutions Shown\n\nQuiz And Assignment\n\nAssignment: Tell Us How You Did In The Practice Questions So We Can Help You\n\nAlgebra Basics\n\nConclusion\n\nBonus Lecture"
]
| [
null,
"https://studybullet.com/wp-content/uploads/2021/09/Zero-To-Hero-Intro-To-Algebra-Variables-Fractions-amp-More.jpg",
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https://www.aimspress.com/article/doi/10.3934/era.2021087 | [
"### Electronic Research Archive\n\n2021, Issue 6: 4315-4325. doi: 10.3934/era.2021087\nSpecial Issues\n\n# Canonical maps of general hypersurfaces in Abelian varieties\n\n• Received: 01 December 2020 Revised: 01 September 2021 Published: 26 October 2021\n• 14E05, 14E25, 14M99, 14K25, 14K99, 14H40, 32J25, 32Q55, 32H04\n\n• The main theorem of this paper is that, for a general pair $(A,X)$ of an (ample) hypersurface $X$ in an Abelian Variety $A$, the canonical map $\\Phi_X$ of $X$ is birational onto its image if the polarization given by $X$ is not principal (i.e., its Pfaffian $d$ is not equal to $1$).\n\nWe also easily show that, setting $g = dim (A)$, and letting $d$ be the Pfaffian of the polarization given by $X$, then if $X$ is smooth and\n\n$\\Phi_X : X {\\rightarrow } {\\mathbb{P}}^{N: = g+d-2}$\n\nis an embedding, then necessarily we have the inequality $d \\geq g + 1$, equivalent to $N : = g+d-2 \\geq 2 \\ dim(X) + 1.$\n\nHence we formulate the following interesting conjecture, motivated by work of the second author: if $d \\geq g + 1,$ then, for a general pair $(A,X)$, $\\Phi_X$ is an embedding.\n\nCitation: Fabrizio Catanese, Luca Cesarano. Canonical maps of general hypersurfaces in Abelian varieties[J]. Electronic Research Archive, 2021, 29(6): 4315-4325. doi: 10.3934/era.2021087\n\n### Related Papers:\n\n• The main theorem of this paper is that, for a general pair $(A,X)$ of an (ample) hypersurface $X$ in an Abelian Variety $A$, the canonical map $\\Phi_X$ of $X$ is birational onto its image if the polarization given by $X$ is not principal (i.e., its Pfaffian $d$ is not equal to $1$).\n\nWe also easily show that, setting $g = dim (A)$, and letting $d$ be the Pfaffian of the polarization given by $X$, then if $X$ is smooth and\n\n$\\Phi_X : X {\\rightarrow } {\\mathbb{P}}^{N: = g+d-2}$\n\nis an embedding, then necessarily we have the inequality $d \\geq g + 1$, equivalent to $N : = g+d-2 \\geq 2 \\ dim(X) + 1.$\n\nHence we formulate the following interesting conjecture, motivated by work of the second author: if $d \\geq g + 1,$ then, for a general pair $(A,X)$, $\\Phi_X$ is an embedding.",
null,
"###### 通讯作者: 陈斌, [email protected]\n• 1.\n\n沈阳化工大学材料科学与工程学院 沈阳 110142",
null,
"1.604 0.8\n\nArticle outline\n\n## Other Articles By Authors\n\n• On This Site",
null,
"",
null,
"DownLoad: Full-Size Img PowerPoint"
]
| [
null,
"https://www.aimspress.com/style/web/images/article/1.gif",
null,
"https://www.aimspress.com/aimspress-upload/journal/era/cover_202172162552724.png",
null,
"https://www.aimspress.com/article/doi/10.3934/era.2021087",
null,
"https://www.aimspress.com/style/web/images/article/download.png",
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]
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https://en.wikipedia.org/wiki/Communicating_Sequential_Processes | [
"# Communicating sequential processes\n\nIn computer science, communicating sequential processes (CSP) is a formal language for describing patterns of interaction in concurrent systems. It is a member of the family of mathematical theories of concurrency known as process algebras, or process calculi, based on message passing via channels. CSP was highly influential in the design of the occam programming language and also influenced the design of programming languages such as Limbo, RaftLib, Erlang, Go, Crystal, and Clojure's core.async.\n\nCSP was first described in a 1978 article by Tony Hoare, but has since evolved substantially. CSP has been practically applied in industry as a tool for specifying and verifying the concurrent aspects of a variety of different systems, such as the T9000 Transputer, as well as a secure ecommerce system. The theory of CSP itself is also still the subject of active research, including work to increase its range of practical applicability (e.g., increasing the scale of the systems that can be tractably analyzed).\n\n## History\n\nThe version of CSP presented in Hoare's original 1978 article was essentially a concurrent programming language rather than a process calculus. It had a substantially different syntax than later versions of CSP, did not possess mathematically defined semantics, and was unable to represent unbounded nondeterminism. Programs in the original CSP were written as a parallel composition of a fixed number of sequential processes communicating with each other strictly through synchronous message-passing. In contrast to later versions of CSP, each process was assigned an explicit name, and the source or destination of a message was defined by specifying the name of the intended sending or receiving process. For example, the process\n\nCOPY = *[c:character; west?c → east!c]\n\n\nrepeatedly receives a character from the process named west and sends that character to process named east. The parallel composition\n\n[west::DISASSEMBLE || X::COPY || east::ASSEMBLE]\n\n\nassigns the names west to the DISASSEMBLE process, X to the COPY process, and east to the ASSEMBLE process, and executes these three processes concurrently.\n\nFollowing the publication of the original version of CSP, Hoare, Stephen Brookes, and A. W. Roscoe developed and refined the theory of CSP into its modern, process algebraic form. The approach taken in developing CSP into a process algebra was influenced by Robin Milner's work on the Calculus of Communicating Systems (CCS) and conversely. The theoretical version of CSP was initially presented in a 1984 article by Brookes, Hoare, and Roscoe, and later in Hoare's book Communicating Sequential Processes, which was published in 1985. In September 2006, that book was still the third-most cited computer science reference of all time according to Citeseer[citation needed] (albeit an unreliable source due to the nature of its sampling). The theory of CSP has undergone a few minor changes since the publication of Hoare's book. Most of these changes were motivated by the advent of automated tools for CSP process analysis and verification. Roscoe's The Theory and Practice of Concurrency describes this newer version of CSP.\n\n### Applications\n\nAn early and important application of CSP was its use for specification and verification of elements of the INMOS T9000 Transputer, a complex superscalar pipelined processor designed to support large-scale multiprocessing. CSP was employed in verifying the correctness of both the processor pipeline and the Virtual Channel Processor, which managed off-chip communications for the processor.\n\nIndustrial application of CSP to software design has usually focused on dependable and safety-critical systems. For example, the Bremen Institute for Safe Systems and Daimler-Benz Aerospace modeled a fault-management system and avionics interface (consisting of about 23,000 lines of code) intended for use on the International Space Station in CSP, and analyzed the model to confirm that their design was free of deadlock and livelock. The modeling and analysis process was able to uncover a number of errors that would have been difficult to detect using testing alone. Similarly, Praxis High Integrity Systems applied CSP modeling and analysis during the development of software (approximately 100,000 lines of code) for a secure smart-card certification authority to verify that their design was secure and free of deadlock. Praxis claims that the system has a much lower defect rate than comparable systems.\n\nSince CSP is well-suited to modeling and analyzing systems that incorporate complex message exchanges, it has also been applied to the verification of communications and security protocols. A prominent example of this sort of application is Lowe’s use of CSP and the FDR refinement-checker to discover a previously unknown attack on the Needham–Schroeder public-key authentication protocol, and then to develop a corrected protocol able to defeat the attack.\n\n## Informal description\n\nAs its name suggests, CSP allows the description of systems in terms of component processes that operate independently, and interact with each other solely through message-passing communication. However, the \"Sequential\" part of the CSP name is now something of a misnomer, since modern CSP allows component processes to be defined both as sequential processes, and as the parallel composition of more primitive processes. The relationships between different processes, and the way each process communicates with its environment, are described using various process algebraic operators. Using this algebraic approach, quite complex process descriptions can be easily constructed from a few primitive elements.\n\n### Primitives\n\nCSP provides two classes of primitives in its process algebra:\n\nEvents\nEvents represent communications or interactions. They are assumed to be indivisible and instantaneous. They may be atomic names (e.g. on, off), compound names (e.g. valve.open, valve.close), or input/output events (e.g. mouse?xy, screen!bitmap).\nPrimitive processes\nPrimitive processes represent fundamental behaviors: examples include STOP (the process that communicates nothing, also called deadlock), and SKIP (which represents successful termination).\n\n### Algebraic operators\n\nCSP has a wide range of algebraic operators. The principal ones are:\n\nPrefix\nThe prefix operator combines an event and a process to produce a new process. For example,\n$a\\to P$",
null,
"is the process that is willing to communicate a with its environment and, after a, behaves like the process P.\nDeterministic choice\nThe deterministic (or external) choice operator allows the future evolution of a process to be defined as a choice between two component processes and allows the environment to resolve the choice by communicating an initial event for one of the processes. For example,\n$(a\\to P)\\Box (b\\to Q)$",
null,
"is the process that is willing to communicate the initial events a and b and subsequently behaves as either P or Q, depending on which initial event the environment chooses to communicate. If both a and b were communicated simultaneously, the choice would be resolved nondeterministically.\nNondeterministic choice\nThe nondeterministic (or internal) choice operator allows the future evolution of a process to be defined as a choice between two component processes, but does not allow the environment any control over which one of the component processes will be selected. For example,\n$(a\\to P)\\sqcap (b\\to Q)$",
null,
"can behave like either $(a\\to P)$",
null,
"or $(b\\to Q)$",
null,
". It can refuse to accept a or b and is only obliged to communicate if the environment offers both a and b. Nondeterminism can be inadvertently introduced into a nominally deterministic choice if the initial events of both sides of the choice are identical. So, for example,\n$(a\\to a\\to {\\text{STOP}})\\Box (a\\to b\\to {\\text{STOP}})$",
null,
"is equivalent to\n$a\\to {\\big (}(a\\to {\\text{STOP}})\\sqcap (b\\to {\\text{STOP}}){\\big )}$",
null,
"Interleaving\nThe interleaving operator represents completely independent concurrent activity. The process\n$P\\;|||\\;Q$",
null,
"behaves as both P and Q simultaneously. The events from both processes are arbitrarily interleaved in time.\nInterface parallel\nThe interface parallel operator represents concurrent activity that requires synchronization between the component processes: any event in the interface set can only occur when all component processes are able to engage in that event. For example, the process\n$P\\;|[\\{a\\}]|\\;Q$",
null,
"requires that P and Q must both be able to perform event a before that event can occur. So, for example, the process\n$(a\\to P)\\;|[\\{a\\}]|\\;(a\\to Q)$",
null,
"can engage in event a and become the process\n$P\\;|[\\{a\\}]|\\;Q$",
null,
"while\n$(a\\to P)\\;|[\\{a,b\\}]|\\;(b\\to Q)$",
null,
"Hiding\nThe hiding operator provides a way to abstract processes by making some events unobservable. A trivial example of hiding is\n$(a\\to P)\\setminus \\{a\\}$",
null,
"which, assuming that the event a doesn't appear in P, simply reduces to\n$P$",
null,
"### Examples\n\nOne of the archetypal CSP examples is an abstract representation of a chocolate vending machine and its interactions with a person wishing to buy some chocolate. This vending machine might be able to carry out two different events, “coin” and “choc” which represent the insertion of payment and the delivery of a chocolate respectively. A machine which demands payment (only in cash) before offering a chocolate can be written as:\n\n$\\mathrm {VendingMachine} =\\mathrm {coin} \\rightarrow \\mathrm {choc} \\rightarrow \\mathrm {STOP}$",
null,
"A person who might choose to use a coin or card to make payments could be modelled as:\n\n$\\mathrm {Person} =(\\mathrm {coin} \\rightarrow \\mathrm {STOP} )\\Box (\\mathrm {card} \\rightarrow \\mathrm {STOP} )$",
null,
"These two processes can be put in parallel, so that they can interact with each other. The behaviour of the composite process depends on the events that the two component processes must synchronise on. Thus,\n\n$\\mathrm {VendingMachine} \\left\\vert \\left[\\left\\{\\mathrm {coin} ,\\mathrm {card} \\right\\}\\right]\\right\\vert \\mathrm {Person} \\equiv \\mathrm {coin} \\rightarrow \\mathrm {choc} \\rightarrow \\mathrm {STOP}$",
null,
"whereas if synchronization was only required on “coin”, we would obtain\n\n$\\mathrm {VendingMachine} \\left\\vert \\left[\\left\\{\\mathrm {coin} \\right\\}\\right]\\right\\vert \\mathrm {Person} \\equiv \\left(\\mathrm {coin} \\rightarrow \\mathrm {choc} \\rightarrow \\mathrm {STOP} \\right)\\Box \\left(\\mathrm {card} \\rightarrow \\mathrm {STOP} \\right)$",
null,
"If we abstract this latter composite process by hiding the “coin” and “card” events, i.e.\n\n$\\left(\\left(\\mathrm {coin} \\rightarrow \\mathrm {choc} \\rightarrow \\mathrm {STOP} \\right)\\Box \\left(\\mathrm {card} \\rightarrow \\mathrm {STOP} \\right)\\right)\\setminus \\left\\{\\mathrm {coin,card} \\right\\}$",
null,
"we get the nondeterministic process\n\n$\\left(\\mathrm {choc} \\rightarrow \\mathrm {STOP} \\right)\\sqcap \\mathrm {STOP}$",
null,
"This is a process which either offers a “choc” event and then stops, or just stops. In other words, if we treat the abstraction as an external view of the system (e.g., someone who does not see the decision reached by the person), nondeterminism has been introduced.\n\n## Formal definition\n\n### Syntax\n\nThe syntax of CSP defines the “legal” ways in which processes and events may be combined. Let e be an event, and X be a set of events. Then the basic syntax of CSP can be defined as:\n\n${\\begin{array}{lcll}{Proc}&::=&\\mathrm {STOP} &\\;\\\\&|&\\mathrm {SKIP} &\\;\\\\&|&e\\rightarrow {Proc}&({\\text{prefixing}})\\\\&|&{Proc}\\;\\Box \\;{Proc}&({\\text{external}}\\;{\\text{choice}})\\\\&|&{Proc}\\;\\sqcap \\;{Proc}&({\\text{nondeterministic}}\\;{\\text{choice}})\\\\&|&{Proc}\\;\\vert \\vert \\vert \\;{Proc}&({\\text{interleaving}})\\\\&|&{Proc}\\;|[\\{X\\}]|\\;{Proc}&({\\text{interface}}\\;{\\text{parallel}})\\\\&|&{Proc}\\setminus X&({\\text{hiding}})\\\\&|&{Proc};{Proc}&({\\text{sequential}}\\;{\\text{composition}})\\\\&|&\\mathrm {if} \\;b\\;\\mathrm {then} \\;{Proc}\\;\\mathrm {else} \\;Proc&({\\text{boolean}}\\;{\\text{conditional}})\\\\&|&{Proc}\\;\\triangleright \\;{Proc}&({\\text{timeout}})\\\\&|&{Proc}\\;\\triangle \\;{Proc}&({\\text{interrupt}})\\end{array}}$",
null,
"Note that, in the interests of brevity, the syntax presented above omits the $\\mathbf {div}$",
null,
"process, which represents divergence, as well as various operators such as alphabetized parallel, piping, and indexed choices.\n\n### Formal semantics\n\nCSP has been imbued with several different formal semantics, which define the meaning of syntactically correct CSP expressions. The theory of CSP includes mutually consistent denotational semantics, algebraic semantics, and operational semantics.\n\n#### Denotational semantics\n\nThe three major denotational models of CSP are the traces model, the stable failures model, and the failures/divergences model. Semantic mappings from process expressions to each of these three models provide the denotational semantics for CSP.\n\nThe traces model defines the meaning of a process expression as the set of sequences of events (traces) that the process can be observed to perform. For example,\n\n• $\\mathrm {traces} \\left(\\mathrm {STOP} \\right)=\\left\\{\\langle \\rangle \\right\\}$",
null,
"since $\\mathrm {STOP}$",
null,
"performs no events\n• $\\mathrm {traces} \\left(a\\rightarrow b\\rightarrow \\mathrm {STOP} \\right)=\\left\\{\\langle \\rangle ,\\langle a\\rangle ,\\langle a,b\\rangle \\right\\}$",
null,
"since the process $(a\\rightarrow b\\rightarrow \\mathrm {STOP} )$",
null,
"can be observed to have performed no events, the event a, or the sequence of events a followed by b\n\nMore formally, the meaning of a process P in the traces model is defined as $\\mathrm {traces} \\left(P\\right)\\subseteq \\Sigma ^{\\ast }$",
null,
"such that:\n\n1. $\\langle \\rangle \\in \\mathrm {traces} \\left(P\\right)$",
null,
"(i.e. $\\mathrm {traces} \\left(P\\right)$",
null,
"contains the empty sequence)\n2. $s_{1}\\smallfrown s_{2}\\in \\mathrm {traces} \\left(P\\right)\\implies s_{1}\\in \\mathrm {traces} \\left(P\\right)$",
null,
"(i.e. $\\mathrm {traces} \\left(P\\right)$",
null,
"is prefix-closed)\n\nwhere $\\Sigma ^{\\ast }$",
null,
"is the set of all possible finite sequences of events.\n\nThe stable failures model extends the traces model with refusal sets, which are sets of events $X\\subseteq \\Sigma$",
null,
"that a process can refuse to perform. A failure is a pair $\\left(s,X\\right)$",
null,
", consisting of a trace s, and a refusal set X which identifies the events that a process may refuse once it has executed the trace s. The observed behavior of a process in the stable failures model is described by the pair $\\left(\\mathrm {traces} \\left(P\\right),\\mathrm {failures} \\left(P\\right)\\right)$",
null,
". For example,\n\n• $\\mathrm {failures} \\left(\\left(a\\rightarrow \\mathrm {STOP} \\right)\\Box \\left(b\\rightarrow \\mathrm {STOP} \\right)\\right)=\\left\\{\\left(\\langle \\rangle ,\\emptyset \\right),\\left(\\langle a\\rangle ,\\left\\{a,b\\right\\}\\right),\\left(\\langle b\\rangle ,\\left\\{a,b\\right\\}\\right)\\right\\}$",
null,
"• $\\mathrm {failures} \\left(\\left(a\\rightarrow \\mathrm {STOP} \\right)\\sqcap \\left(b\\rightarrow \\mathrm {STOP} \\right)\\right)=\\left\\{\\left(\\langle \\rangle ,\\left\\{a\\right\\}\\right),\\left(\\langle \\rangle ,\\left\\{b\\right\\}\\right),\\left(\\langle a\\rangle ,\\left\\{a,b\\right\\}\\right),\\left(\\langle b\\rangle ,\\left\\{a,b\\right\\}\\right)\\right\\}$",
null,
"The failures/divergence model further extends the failures model to handle divergence. The semantics of a process in the failures/divergences model is a pair $\\left(\\mathrm {failures} _{\\perp }\\left(P\\right),\\mathrm {divergences} \\left(P\\right)\\right)$",
null,
"where $\\mathrm {divergences} \\left(P\\right)$",
null,
"is defined as the set of all traces that can lead to divergent behavior and $\\mathrm {failures} _{\\perp }\\left(P\\right)=\\mathrm {failures} \\left(P\\right)\\cup \\left\\{\\left(s,X\\right)\\mid s\\in \\mathrm {divergences} \\left(P\\right)\\right\\}$",
null,
".\n\n## Tools\n\nOver the years, a number of tools for analyzing and understanding systems described using CSP have been produced. Early tool implementations used a variety of machine-readable syntaxes for CSP, making input files written for different tools incompatible. However, most CSP tools have now standardized on the machine-readable dialect of CSP devised by Bryan Scattergood, sometimes referred to as CSPM. The CSPM dialect of CSP possesses a formally defined operational semantics, which includes an embedded functional programming language.\n\nThe most well-known CSP tool is probably Failures/Divergence Refinement 2 (FDR2), which is a commercial product developed by Formal Systems (Europe) Ltd. FDR2 is often described as a model checker, but is technically a refinement checker, in that it converts two CSP process expressions into Labelled Transition Systems (LTSs), and then determines whether one of the processes is a refinement of the other within some specified semantic model (traces, failures, or failures/divergence). FDR2 applies various state-space compression algorithms to the process LTSs in order to reduce the size of the state-space that must be explored during a refinement check. FDR2 has been succeeded by FDR3, a completely re-written version incorporating amongst other things parallel execution and an integrated type checker. It is released by the University of Oxford, which also released FDR2 in the period 2008-12.\n\nThe Adelaide Refinement Checker (ARC) is a CSP refinement checker developed by the Formal Modelling and Verification Group at The University of Adelaide. ARC differs from FDR2 in that it internally represents CSP processes as Ordered Binary Decision Diagrams (OBDDs), which alleviates the state explosion problem of explicit LTS representations without requiring the use of state-space compression algorithms such as those used in FDR2.\n\nThe ProB project, which is hosted by the Institut für Informatik, Heinrich-Heine-Universität Düsseldorf, was originally created to support analysis of specifications constructed in the B method. However, it also includes support for analysis of CSP processes both through refinement checking, and LTL model-checking. ProB can also be used to verify properties of combined CSP and B specifications. A ProBE CSP Animator is integrated in FDR3.\n\nThe Process Analysis Toolkit (PAT) is a CSP analysis tool developed in the School of Computing at the National University of Singapore. PAT is able to perform refinement checking, LTL model-checking, and simulation of CSP and Timed CSP processes. The PAT process language extends CSP with support for mutable shared variables, asynchronous message passing, and a variety of fairness and quantitative time related process constructs such as deadline and waituntil. The underlying design principle of the PAT process language is to combine a high-level specification language with procedural programs (e.g. an event in PAT may be a sequential program or even an external C# library call) for greater expressiveness. Mutable shared variables and asynchronous channels provide a convenient syntactic sugar for well-known process modelling patterns used in standard CSP. The PAT syntax is similar, but not identical, to CSPM. The principal differences between the PAT syntax and standard CSPM are the use of semicolons to terminate process expressions, the inclusion of syntactic sugar for variables and assignments, and the use of slightly different syntax for internal choice and parallel composition.\n\nVisualNets produces animated visualisations of CSP systems from specifications, and supports timed CSP.\n\nCSPsim is a lazy simulator. It does not model check CSP, but is useful for exploring very large (potentially infinite) systems.\n\nSyncStitch is a CSP refinement checker with interactive modeling and analyzing environment. It has a graphical state-transition diagram editor. The user can model the behavior of processes as not only CSP expressions but also state-transition diagrams. The result of checking are also reported graphically as computation-trees and can be analyzed interactively with peripheral inspecting tools. In addition to refinement checks, It can perform deadlock check and livelock check.\n\n## Related formalisms\n\nSeveral other specification languages and formalisms have been derived from, or inspired by, the classic untimed CSP, including:\n\n## Comparison with the actor model\n\nIn as much as it is concerned with concurrent processes that exchange messages, the actor model is broadly similar to CSP. However, the two models make some fundamentally different choices with regard to the primitives they provide:\n\n• CSP processes are anonymous, while actors have identities.\n• CSP uses explicit channels for message passing, whereas actor systems transmit messages to named destination actors. These approaches may be considered duals of each other, in the sense that processes receiving through a single channel effectively have an identity corresponding to that channel, while the name-based coupling between actors may be broken by constructing actors that behave as channels.\n• CSP message-passing fundamentally involves a rendezvous between the processes involved in sending and receiving the message, i.e. the sender cannot transmit a message until the receiver is ready to accept it. In contrast, message-passing in actor systems is fundamentally asynchronous, i.e. message transmission and reception do not have to happen at the same time, and senders may transmit messages before receivers are ready to accept them. These approaches may also be considered duals of each other, in the sense that rendezvous-based systems can be used to construct buffered communications that behave as asynchronous messaging systems, while asynchronous systems can be used to construct rendezvous-style communications by using a message/acknowledgement protocol to synchronize senders and receivers.\n\nNote that the aforementioned properties do not necessarily refer to the original CSP paper by Hoare, but rather the modern incarnation of the idea as seen in implementations such as Golang and Clojure's core.async. In the original paper, channels were not a central part of the specification, and the sender and receiver processes actually identify each other by name.\n\n## Award\n\nIn 1990, “A Queen’s Award for Technological Achievement has been conferred ... on [Oxford University] Computing Laboratory. The award recognises a successful collaboration between the laboratory and Inmos Ltd. … Inmos’ flagship product is the ‘transputer’, a microprocessor with many of the parts that would normally be needed in addition built into the same single component.” According to Tony Hoare, “The INMOS Transputer was as embodiment of the ideas … of building microprocessors that could communicate with each other along wires that would stretch between their terminals. The founder had the vision that the CSP ideas were ripe for industrial exploitation, and he made that the basis of the language for programming Transputers, which was called Occam. … The company estimated it enabled them to deliver the hardware one year earlier than would otherwise have happened. They applied for and won a Queen’s award for technological achievement, in conjunction with Oxford University Computing Laboratory.”"
]
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https://www.jiskha.com/questions/589526/what-is-the-weight-of-6-3-10-21-atoms-of-phosphorus-answer-in-units-of-g | [
"What is the weight of 6.3 × 10\n21\natoms of\nphosphorus?\n\n1. 👍 0\n2. 👎 0\n3. 👁 117\n1. 1mol of any substance = 6.022 * 10^23 elementary entities of that substance (be it atoms, molecules or whatever. Think of it as the chemist's \"dozen\" only it's 6.022 * 10^23 rather than 12.)\n\nFor finding the amount of grams in 1 mol of an element, find the element's atmoic mass and that number is the amount of grams.\n\n6.3 * 10^21 P atoms * 1mol of P/6.022 * 10^23 P atoms * 30.97g of P/mol = 0.324g of Phosphorus.\n\n1. 👍 0\n2. 👎 0\n2. Erm, *atomic mass, sorry.\n\n1. 👍 0\n2. 👎 0\n\n## Similar Questions\n\n1. ### Chemistry\n\nBoron Phosphide, BP, is a semiconductor, and a hard, abrasion resistant material. It is made by reacting Boron tribromide and phosphorus tribromide in a hydrogen atmosphere at high temperature (>750 degrees C) (a) Write a Balanced\n\nasked by Laffy Taffy on March 11, 2012\n2. ### Physics\n\nHow many atoms of hydrogen are in 220g of hydrogen peroxide (H2O2)? the molecular weight of H2O2 = 2*1 +2*16 =34 therefore, there are 220/34 moles of the molecule = 6.47 moles, so there are 6.47xAvogadro's number of molecules\n\nasked by ana on November 18, 2009\n3. ### chemistry\n\nUsing your answer from Part A, calculate the volume of a mole of Na atoms (in cm3/mol ). Assume that the entire volume is occupied by Na atoms leaving no gaps or holes between adjacent atoms. (Answer A is V= 2.70*10^7)\n\nasked by sara on November 10, 2008\n4. ### chemistry\n\nwhat is the mass in grams? a) 3.011 x 10^23 atoms F b)1.50 x 10^23 atoms Mg c)4.50 x 10^12 atoms Cl d)8.42 x 10^18 atoms Br e) 25 atoms w f) 1 atom Au can you please explain a and b to me then i'll come back later and see if i did\n\nasked by john on February 23, 2008\n5. ### chemistry help!!! please!!! DrBob222 I need you!!\n\nHow many atoms of carbon are needed to produce 0.45 mol Al? 3C + 2Al2O3 4Al + 3CO2 A. 2.6 × 1026 atoms B. 9.7 × 1024 atoms C. 3.0 × 1022 atoms D. 2.0 × 1023 atoms I'm really very stuck with this question. please help me!!!\n\nasked by emma on August 20, 2016\n1. ### chemistry\n\nA compound is found to contain 15.12 % phosphorus, 6.841 % nitrogen, and 78.03 % bromine by weight. what is the emperical formula\n\nasked by Jeremy on June 28, 2015\n2. ### Chemistry\n\nSuppose that a device is using a 5.00-mg sample of silicon that is doped with 1 × 10-5% (by mass) phosphorus. How many phosphorus atoms are in the sample?\n\nasked by Angel on March 6, 2018\n3. ### Chemistry\n\nWhich product is formed by beta emission from phosphorus -32? The atomic number of phosphorus is 15. A)28 Al 13 B)30 Al 13 C)32 S 16 D)32 P 15 E)33 P 15\n\nasked by jim on April 28, 2010\n4. ### chemistry\n\nCalculate the density of atoms along in molybdenum (Mo). Use only the information provided in your class Periodic Table, and express your answer in units of atoms/cm.\n\nasked by selly on November 22, 2012\n5. ### chemistry\n\nHow many atoms of carbon are needed to produce 0.45 mol Al? 3C + 2Al2O3 4Al + 3CO2 A. 2.6 × 1026 atoms B. 9.7 × 1024 atoms C. 3.0 × 1022 atoms D. 2.0 × 1023 atoms\n\nasked by emma on August 19, 2016\n6. ### Physics\n\nA rock weighs 140 N in air and has a volume of 0.00273 m3. What is its apparent weight when sub- merged in water? The acceleration of gravity is 9.8 m/s2 . Answer in units of N. If it is submerged in a liquid with a density\n\nasked by Laura on November 28, 2010"
]
| [
null
]
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https://kotlinlang.org/api/latest/jvm/stdlib/kotlin.collections/zip-with-next.html | [
"# zipWithNext\n\nCommon\nJVM\nJS\nNative\n1.2\n`fun <T> Iterable<T>.zipWithNext(): List<Pair<T, T>>`\n\nReturns a list of pairs of each two adjacent elements in this collection.\n\nThe returned list is empty if this collection contains less than two elements.\n\n``````import kotlin.test.*\n\nfun main(args: Array<String>) {\n//sampleStart\nval letters = ('a'..'f').toList()\nval pairs = letters.zipWithNext()\n\nprintln(letters) // [a, b, c, d, e, f]\nprintln(pairs) // [(a, b), (b, c), (c, d), (d, e), (e, f)]\n//sampleEnd\n}``````\nCommon\nJVM\nJS\nNative\n1.2\n`inline fun <T, R> Iterable<T>.zipWithNext( transform: (a: T, b: T) -> R): List<R>`\n\nReturns a list containing the results of applying the given transform function to an each pair of two adjacent elements in this collection.\n\nThe returned list is empty if this collection contains less than two elements.\n\n``````import kotlin.test.*\n\nfun main(args: Array<String>) {\n//sampleStart\nval values = listOf(1, 4, 9, 16, 25, 36)\nval deltas = values.zipWithNext { a, b -> b - a }\n\nprintln(deltas) // [3, 5, 7, 9, 11]\n//sampleEnd\n}``````"
]
| [
null
]
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