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https://shenviapologetics.com/the-central-spin-echo-problem/ | [
"# The Central Spin Echo Problem\n\nMy publication record as a theoretical chemist is diverse, to put it mildly. I’ve written papers on everything from high-dimensional functional representation to quantum search algorithms to proton-coupled electron transfer to superadiabatic dynamics. However, my favorite projects involves a problem I’ve been mulling over for almost 18 years. It emerges naturally from spin physics, but is basically a mathematical problem that raises basic questions that could be applicable to many other problems.\n\nI’ll sketch the problem below in the hopes that brighter minds than mine can solve it. The outline of this article will be: 1) A Big Question 2) The Physical Observation 3) The Required Proof and 4) A Few Hints.\n\n## The Big Question",
null,
"$\\textrm{Suppose we want to know whether the two quantum mechanical operators} \\hat{A} and \\hat{B} share exactly the same set of eigenvectors.$ The brute for solution to this problem is to obtain a complete set of eigenvectors and eigenvalues for",
null,
"$\\hat{A}$ and",
null,
"$14 \\hat{B}$ such that",
null,
"$\\vert\\psi_n \\rangle$ and",
null,
"$\\vert\\phi_n \\rangle$ are eigenvectors of",
null,
"$\\hat{A}$ and",
null,
"$\\hat{B}$ corresponding to eigenvalues",
null,
"$a_n$ and",
null,
"$b_n$ respectively."
] | [
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"https://s0.wp.com/latex.php",
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"https://s0.wp.com/latex.php",
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"https://s0.wp.com/latex.php",
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"https://s0.wp.com/latex.php",
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"https://s0.wp.com/latex.php",
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"https://s0.wp.com/latex.php",
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"https://s0.wp.com/latex.php",
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"https://s0.wp.com/latex.php",
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"https://s0.wp.com/latex.php",
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.92911834,"math_prob":0.9870406,"size":922,"snap":"2021-43-2021-49","text_gpt3_token_len":186,"char_repetition_ratio":0.10348584,"word_repetition_ratio":0.0,"special_character_ratio":0.18546638,"punctuation_ratio":0.06790123,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9936925,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-11-29T18:48:12Z\",\"WARC-Record-ID\":\"<urn:uuid:2d9b4756-7e08-43ac-aca6-b93dd71af88b>\",\"Content-Length\":\"113236\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a3186832-0e3e-4326-8fc1-101a7bdc8bd8>\",\"WARC-Concurrent-To\":\"<urn:uuid:4bcf5fb2-5a0f-4f71-ad9b-84df7bedb2f2>\",\"WARC-IP-Address\":\"192.0.78.24\",\"WARC-Target-URI\":\"https://shenviapologetics.com/the-central-spin-echo-problem/\",\"WARC-Payload-Digest\":\"sha1:O72XWYTAGR3J6OHXUOVJMGOZN75IDUVS\",\"WARC-Block-Digest\":\"sha1:GPWVROZ44HDQEM6XN5VVGDEUJN53PQTF\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964358786.67_warc_CC-MAIN-20211129164711-20211129194711-00600.warc.gz\"}"} |
https://organicdesign.nz/Haskell | [
"# Haskell\n\nHaskell is a functional programming langauge used in Cardano.\n\n## Getting Started\n\nInstall the Haskell platform with:\n\n``sudo apt-get install haskell-platform``\n\nThen run the interpreter via:\n\n``ghci``\n\nQuitting the Haskell interpreter is the same as vim: :q or :quit.\n\nYou can write Haskell in .hs files then compile using ghc like so:\n\n``ghc -o hello hello.hs``\n\nAnd then you can run via the executable file ./hello.\n\n## Types\n\nHaskell allows you to define types but this is optional if no type is declared it will infer the type. Types in Haskell must start with a capital letter.\n\n``````5 -- Infers the type\n5 :: Double -- Define the type.\n\n-- Ask ghci what type '5' is.\n:t 5``````\n\nThe unit type () is a type that has only one value () which is similar to void in other languages.\n\nYou can combine types easily in one of two ways: Tuples and Lists. Lists hold many values of the same type whereas Tuples can hold values of different types.\n\n``````[1, 2, 3] -- Simple list with the values 1 to 3.\n[1 .. 5] -- List with the values 1 to 5\n[1, 3 .. 10] -- List of odd values between 1 and 10.\n['H', 'e', 'l', 'l', 'o'] -- A String!\n\n(1, true) -- Simple Tuple.\n(1, True, 2.0, 2) -- A longer Tuple\n\nzip [1 .. 5] ['a' .. 'e'] -- Combine the two lists into a list of tuples: [(1, 'a'), (2, 'b') ...]\nmap (+ 2) [1 .. 5] -- Map function on a list: [3,4,5,6,7]\nfilter (> 2) [1 .. 5] -- Filter function on a list: [3,4,5]\nfst (1, 2) -- Get the first element of the Tuple.\nsnd (1, 2) -- Get the second element of the Tuple.\nmap fst [(1, 2), (3, 4), (5, 6)] -- Apply the first function to each tuple in the list: [1,3,5].``````\n\n## Functions\n\n``````inc x = x+1 -- Define an increment function.\nadd x y = x + y -- Define an addition function that takes two parameters.\n(\\x -> \\y -> x+y) 1 2 -- Lambda version of add taking 1 & 2 as it's parameters.``````\n\nYou can also give types to your functions:\n\n``````inc :: Int -> Int -- inc is a function that takes an Int and outputs an Int.\ninc x = x+1\n\nadd :: Int -> Int -> Int -- inc is a function that takes two Ints as parameters and outputs an Int.\nadd x y = x + y\n\n-- Define the factorial function in parts using pattern matching.\nfact :: Int -> Int\nfact 0 = 1\nfact n = n * fact ( n - 1 )\n\n-- Define the factorial function using guards, guards are like piecewise functions in mathematics.\nfact :: Integer -> Integer\nfact n | n == 0 = 1\n| n /= 0 = n * fact (n-1)\n\n-- You can split a complicated function into parts using 'where'\nroots :: (Float, Float, Float) -> (Float, Float)\nroots (a,b,c) = (x1, x2) where\nx1 = e + sqrt d / (2 * a)\nx2 = e - sqrt d / (2 * a)\nd = b * b - 4 * a * c\ne = - b / (2 * a)\n\n-- Haskell allows you to do function composition with the '.' operator.\ncomposedFunc = outer.inner -- outer and inner are functions.\n-- composedFunc will compute the inner function then pass the return value to the outer function, compute that and return.\n-- Note: the return value from inner needs to match that of the parameter value of outer.``````\n\nIn Haskell you can have conceptually infinite functions!\n\n``````numsFrom n = n : numsFrom (n+1) -- A list of all numbers (n -> Infinity) from the argument.\nsquares = map (^2) (numsFrom 0) -- A list of all squares of the positive integers.\nfib = 1 : 1 : [ a+b | (a,b) <- zip fib (tail fib) ] -- The list of all Fibonacci numbers!``````\n\nInfinite functions are cool, but you will probably want to get a finite sample from them:\n\n``````take 10 fib -- The first 10 Fibonacci numbers.\nfilter (< 100) (take 30 fib) -- All Fib numbers less than 100.\nfilter odd (filter (<300) (take 30 fib)) -- All odd Fib numbers less than 300.``````\n\n## Parallel Programming\n\nYou can write multi-threaded or parallel programs using the parallel library, you can install a library like so:\n\n``cabal install --lib parallel``\n``````import Control.Parallel\n\nmain = a `par` b `par` c `pseq` print (a + b + c)\nwhere\na = ack 3 10\nb = fac 42\nc = fib 34\n\nfac 0 = 1\nfac n = n * fac (n-1)\n\nack 0 n = n+1\nack m 0 = ack (m-1) 1\nack m n = ack (m-1) (ack m (n-1))\n\nfib 0 = 0\nfib 1 = 1\nfib n = fib (n-1) + fib (n-2)``````\n``./parallel -N3 # Use 3 cores.``\n\n## Modules\n\nYou can split Haskell code with modules. Each module must be in a Haskell file with the same name:\n\nCustom.hs\n\n``````module Custom (\nshowEven,\nshowBoolean\n) where\n\nshowEven:: Int-> Bool\nshowEven x = do\nif x `rem` 2 == 0\nthen True\nelse False\n\nshowBoolean :: Bool->Int\nshowBoolean c = do\nif c == True\nthen 1\nelse 0``````\n\nmain.hs\n\n``````import Custom\n\nmain = do\nprint(showEven 4)\nprint(showBoolean True)``````\n\n## Custom Types\n\n### Data\n\n``````-- Create the custom data type Shape that extends Show (so that print will output something)\ndata Shape =\tCircle Float Float Float\n|\tRectangle Float Float Float Float\nderiving (Show)\n\n-- A function for calculating the surface area.\nsurface :: Shape -> Float\nsurface (Circle _ _ r) = pi * r ^ 2\nsurface (Rectangle x1 y1 x2 y2) = (abs \\$ x2 - x1) * (abs \\$ y2 - y1)\n\n-- Override properties such as the == operator\ninstance Eq Shape where\nCircle _ _ r1 == Circle _ _ r2 = r1 == r2\nRectangle x11 y11 x12 y12 == Rectangle x21 y21 x22 y22 = (abs \\$ x12 - x21) == (abs \\$ x22 - x21) && (abs \\$ y12 - y11) == (abs \\$ y22 - y21)\n_ == _ = False\n\n-- Another custom data type with a different format.\ndata Animal = Animal {\nname :: String,\nlegCount :: Int,\nheight :: Float\n} deriving (Show)\n\nmain = do\nprint (surface \\$ Circle 10 20 10)\nprint (Circle 10 20 10)\n\nlet cow = Animal \"Cow\" 4 1.6\n\n-- Here we can output a specific value of our type.\nprint (height cow)``````\n\n### Type\n\nTypes is a way to alias a name with another type.\n\n``````-- Define PhoneNumber as the type String\ntype PhoneNumber = String\ntype Name = String\n\n-- Define PhoneBook as the type of a list of tuples containing types Name and PhoneNumber\ntype PhoneBook = [(Name,PhoneNumber)]\n\n-- Create a variable with type PhoneBook\nphoneBook :: PhoneBook\nphoneBook =\n[\n(\"name 1\", \"number 1\"),\n(\"name 2\", \"number 2\")\n]``````\n\n## Packages\n\nCabal is a system for building and packaging Haskell libraries and programs.\n\nSearch for a package:\n\n``cabal list <PACKAGE NAME>``\n\nInstall a package with Cabal:\n\n``cabal install --lib <PACKAGE NAME>``"
] | [
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https://mathshistory.st-andrews.ac.uk/Chronology/25/ | [
"# Chronology\n\n### 1870 - 1880\n\nPrevious Chronology\n(1860 - 1870)\nNext Chronology\n(1880 - 1890)\n\n#### 1870\n\n• Benjamin Peirce publishes Linear Associative Algebras at his own expense.\n\n#### 1871\n\n• Betti publishes a memoir on topology which contains the \"Betti numbers\".\n\n#### 1872\n\n• Dedekind publishes his formal construction of real numbers and gives a rigorous definition of an integer.\n• Heine publishes a paper which contains the theorem now known as the \"Heine-Borel theorem\".\n• Société Mathématique de France is founded.\n• Méray publishes Nouveau précis d'analyse infinitésimale which aims to present the theory of functions of a complex variable using power series.\n• Sylow publishes Théorèmes sur les groupes de substitutions which contains the famous three \"Sylow theorems\" about finite groups. He proves them for permutation groups.\n• Klein gives his inaugural address at Erlanger. He defines geometry as the study of the properties of a space that are invariant under a given group of transformations. This became known as the \"Erlanger programm\" and profoundly influences mathematical development.\n\n#### 1873\n\n• Maxwell publishes Electricity and Magnetism. This work contains the four partial differential equations, now known as \"Maxwell's equations\".\n• Hermite publishes Sur la fonction exponentielle (On the Exponential Function) in which he proves that $e$ is a transcendental number.\n• Gibbs publishes two important papers on diagrams in thermodynamics.\n• Brocard produces his work on the triangle.\n\n#### 1874\n\n• Cantor publishes his first paper on set theory. He rigorously describes the notion of infinity. He shows that infinities come in different sizes. He proves the controversial result that almost all numbers are transcendental.\n\n#### 1876\n\n• Gibbs publishes On the Equilibrium of Heterogeneous Substances which represents a major application of mathematics to chemistry.\n\n#### 1877\n\n• Cantor is surprised at his own discovery that there is a one-one correspondence between points on the interval [0, 1] and points in a square.\n\n#### 1878\n\n• Sylvester founds the American Journal of Mathematics.\n\n#### 1879\n\n• Kempe published his false proof of the Four Colour Theorem. (See this History Topic.)\n• Lexis publishes On the theory of the stability of statistical series which begins the study of time series.\n• Kharkov Mathematical Society is founded."
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https://www.jbigdeal.in/viteee/mock-test/ | [
"Vellore Institute of Technology Engineering Entrance Examination: VITEEE Online Mock Test\n\nVIT Engineering Test MCQ Questions Answers for the admission in B.tech: This mock test having 25 question each, with four choices. On each click on answers system will tell you where the answers is correct or incorrect. You can view this VITEEE question are available for Physics and Chemistry details at the end of the quiz. You can also download",
null,
"VITEEE Previous Year Question Papers.\n\nThis Vellore Institute of Technology Engineering Entrance Examination VITEEE 2017 questions answers are applicable for any kind of engineering entrance exam examination. You can practice as much as you can to gather knowledge of how to answers VIT Engineering Test critical type papers in short time and this can be a big factor for cracking VITEEE level exam.\n\nQuick Contents\n\nVITEEE Online Mock Test = Physics\n\nCongratulations - you have completed VITEEE Online Mock Test = Physics.You scored %%SCORE%% out of %%TOTAL%%.Your performance has been rated as %%RATING%%\n Question 1\nThe half-life of a radioactive element is 3.8 days. The fraction left after 19 days will be:\n A 0.124 B 0.062 C 0.093 D 0.031\n Question 2\nThe temperature coefficient of a zener mechanism is:\n A negative B positive C infinity D zero\n Question 3\nRadar waves are sent towards a moving aeroplane and the reflected waves are received. When the aeroplane is moving towards the radar, the wavelength of the wave:\n A decreases B increases C remains the same D sometimes increases or decreases.\n Question 4\nThe output stage of a television transmitter is most likely 10 be a:\n A plate- modulated class C amplifier B grid- modulated class C amplifier C screen- modulated class C amplifier D grid- modulated class A amplifier\n Question 5\nThe antenna current of an AM transmitter is 8 A when only the carrier is sent, but it increases to 8.93 A when the carrier is modulated by a single sine wave. Find the percentage modulation.\n A 60.1% B 70.1% C 80.1% D 50.1%\n Question 6\nA parallel plate capacitor of capacitance 100 pF is to be constructed by using paper sheets of 1 mm thickness as dielectric. If the dielectric constant of paper is 4, the number of circular metal foils of diameter 2 cm each required for the purpose is:\n A 40 B 20 C 30 D 10\n Question 7\nThe electric field intensity E, due to an electric dipolc of momcnt P, at a point on thc cquatorial\n A parallel to the axis of the dipole and opposite to the direction of the dipole moment P B perpendicular to the axis of the dipole and is directed away from it C parallel to the dipole moment D perpendicular to the axis of the dipole and is directed towards it\n Question 8\nThe temperature coefficient of resistance of a wire is 0.00125 / K. At 300 K, its resistance is 1(2. The resistance of the wire will be 2 0 at:\n A 1154 K B 1100 K C 1400 K D 1127 K\n Question 9\nA voltage of peak value 283 V and varying frequency is applied to a series L-C-R combination in which R = 3, L = 25 mH and C = 400p F. The frequency (in Hz) of the source at which maximum power is dissipated in the above, is:\n A 51.5 B 50.7 C 51.1 D 50.3\n Question 10\nIn Young’s double slit experiment, the interference pattern is found to have an intensity ratio between bright and dark fringes is 9. This implies that:\n A the intensities at the screen due to two slits are 5 units and 4 units respectively B the intensities at the screen due to the two slits are 4 units and 1 units, respectively C the amplitude ratio is 7 D the amplitude ratio is 6\n Question 11\nRising and setting sun appears to be reddish because:\n A diffraction sends red rays to earth at these times B scattering due to dust panicles and air molecules are responsible C refraction is responsible D polarization is responsible\n Question 12\nIndicate which one of the following statements is not correct?\n A Intensities of reflections from different crystallographic planes are equal B According to Bragg’s law higher order of reflections have high 9 values for a given wavelength of radiation C For a given wavelength of radiation, there is a smallest distance between the crystallographic planes which can be determined D Bragg’s law may predict a reflection from a crystallographic plane to be present but it may be absent due to the crystal symmetry\n Question 13\nAssuming f to be frequency of first line in Burner series, the frequency of the immediate next (i.e., second) line is:\n A 0.50 f B 1.35 f C 2.05 f D 2.70 f\n Question 14\nTwo electrons re moving in opposite direction with speeds 0.8 c and 0.4 c, where c is the speed of light in vacuum. Then the relative speed is about:\n A 0.4 c B 0.8 c C 0.9c D 1.2c\n Question 15\nA photo-sensitive material would emit electrons, if excited by photons beyond a threshold. To overcome the threshold, one would increase the:\n A voltage applied to the light source B intensity of light C wavelength of light D frequency of light\n Question 16\n A proportional to Its mass number B inversely proportional to its mass number C proportional to the cube root of its mass number D not related to its mass number\n Question 17\nTwo beams of light will not give rise to an interference pattern, if\n A they are coherent B they have the same wavelength C they are linearly polarized perpendicular to each other D they are not monochromatic\n Question 18\nA slit of width is an illuminated with a monochromatic light of wavelength A from a distant source and the diffraction pattern is observed on a screen placed at a distance D from the slit. To increase the width of the central maximum one should\n A decrease D B decrease U C decrease A D The width cannot be changed\n Question 19\nA thin film of soap solution (n = 1.4) lIes on the top of a glass plate (n = 1.5). When visible light is incident almost normal to the plate, two adjacent reflection maxima are observed at two wavelengths 400 and 630 nm. The minimum thickness of the soap solution is\n A 420 nm B 450 nm C 630 nm D 1260 nm\n Question 20\nIf the speed of a wave doubles as it passes from shallow water into deeper water, its wavelength will be\n A unchanged B halved C doubled D quadrupled\nOnce you are finished, click the button below. Any items you have not completed will be marked incorrect.\nThere are 20 questions to complete.\n ← List →\n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 End\n\nVITEEE Online Mock Test = Chemistry\n\nCongratulations - you have completed VITEEE Online Mock Test = Chemistry.You scored %%SCORE%% out of %%TOTAL%%.Your performance has been rated as %%RATING%%\n Question 1\nAn ion leaves its regular site occupy a position in the space between the lattice sites is called\n A Frenkel defect B Schottky defect C impurity defect D vacancy defect\n Question 2\nThe 8: 8 type of packing is present in:\n A MgF2 B CsCI C KCI D NaCI\n Question 3\nWhen a solid melts reversibly:\n A H decreases B G increases C E decreases D S increases\n Question 4\nEquivalent amounts of H2 and 12 are heated in a closed vessel till equilibrium is obtained. If 80% of the hydrogen can be converted to HI, the K at this temperature is:\n A 64 B 16 C 0.25 D 4\n Question 5\nHow long (in hours) must a current of 5.0 A be maintained to electroplate 60 g of calcium from molten CaCI2?\n A 27 h B 8.3 h C 11 h D 16h\n Question 6\nThe epoxide ring consists of which of the following:\n A three membered ring with two carbon and one oxygen B four membered ring with three carbon and one oxygen C five membered ring with four carbon and one oxygen D six membered ring with five carbon and one oxygen\n Question 7\nIn the Grignard reaction, which metal forms an organometallic bond?\n A Sodium B Titanium C Magnesium D Palladium\n Question 8\nPhenol is more acidic than:\n A p-chlorophenol B p-nitrophenol C onirrophenol D ethanol\n Question 9\nAldol condensation is given by:\n A trimethylacetaldehyde B acetaldehyde C benzaldehyde D formaldehyde\n Question 10\nIn which of the below reaction do we find a, -unsaturated carbonyl compounds undergoing a ring closure reaction with conjugated die nes?\n A Perkin reaction B Diels-Alder reaction C Claisen rearrangement D Rofmann reaction\n Question 11\nIdentify, which of the below does not possess any Iement of symmetry?\n A (+ ) (—) tartaric acid B Carbon tetrachioride C Methane D Meso-tartaric acid\n Question 12\nTrans esteriuication is the process of:\n A conversion of an alipharic acid to ester B conversion of an aromatic acid to ester C conversion of one ester to another ester D conversion of an ester into its components namely acid and alcohol\n Question 13\nCarbylamine reaction is given by aliphatic:\n A primary amine B secondary amine C tertiary amine D quaternary ammonium salt\n Question 14\nWhich of the following is hexadentate ligand?\n A Ethylene diamine B Ethylene diamine tetra acetic acid C 1, 10-phenanthroline D Acetyl acetonato\n Question 15\nA coordiante bond is a dative covalent bond. Which of the below is true?\n A Three atom form bond by sharing their electrons B Two atom form bond by sharing their electrons C Two atoms form bond and one of them provides both electrons D Two atoms form bond by sharing electrons obtained from third atom\n Question 16\nOn an X-ray diffraction photograph the irnensity of the spots depends on:\n A neutron density of the atoms/ions B electron density of the atoms/ions C proton density of the atoms/ions D photon density of the atoms/ions\n Question 17\nAIkyl cyanides undergo Stephen reduction to produce\n A aldehyde B seondary a ine C primary amine D amide\n Question 18\nThe continuous phase contains the dispersed phase throughout, example is\n A water in milk B fatin milk C water droplets in mist D oil in water\n Question 19\nMilk changes after digestion into\n A cellulose B fructose C glucose D lactose\n Question 20\nWhich of the following set consists only of essential amino acids?\n A Alanine, tyrosine, cystine B Leucine, lysine, tryptophane C Alanine, glutamine, lycine D leucine, proline, glycine\nOnce you are finished, click the button below. Any items you have not completed will be marked incorrect.\nThere are 20 questions to complete.\n ← List →\n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 End\n\nCongratulations - you have completed VITEEE Question Answers = Physics .You scored %%SCORE%% out of %%TOTAL%%.Your performance has been rated as %%RATING%%\n Question 1\nAn electron microscope is used to probe the atomic arrangements to a resolution of 5 A. What should be the electric potential to which the electrons need to be accelerated?\n A 2.5V B 5V C 2.5 kV D 5kV\n Question 2\nWhich phenomenon best supports the theory that matter has a wave nature?\n A Electron momentum B Electron diffraction C Photon momentum D Photon diffraction\n Question 3\nWhen a solid with a band gap has a donor level just below its empty energy band, the solid is\n A an insulator B a conductor C p-type semiconductor D n-type semiconductor\n Question 4\nA Zener diode has a contact potential of 1 V in the absence of biasing. It undergoes Zener breakdown for an electric field of 10 V/rn at the depletion region of p-n junction. If the width of the depletion region is 2.5 11 rn, what should be the reverse biased potential for the Zener breakdown to occur?\n A 3.5 V B 2.5 V C 1.5 V D 0.5 V\n Question 5\nIn Colpitt oscillator the feedback network consists of\n A two inductors and a capacitor B two capacitors and an inductor C three pairs of RC circuit D three pairs of RL circuit\n Question 6\nThe reverse saturation of p-n diode\n A depends on doping concentrations B depends on diffusion lengths of carriers C depends on the doping concentrations and diffusion lengths D depends on the doping concentrations, diffusion length and device temperature\n Question 7\nA radio station has two channels. One is AM at 1020 kHz and the other FM at 89.5 MHz. For good results you will use\n A longer antenna for the AM channel and shorter for the FM B shorter antenna for the AM channel and longer for the FM C Same length antenna will work for both D Information given is not enough to say which one to use for which\n Question 8\nThe communication using optical fibres is based on the principle of\n A total internal reflection B Brewster angle C polarization D resonance\n Question 9\nIn nature, the electric charge of any system is always equal to\n A half integral multiple of the least amount of charge B zero C square of the least amount of charge D integral multiple of the least amount of charge.\n Question 10\nA cylindrical capacitor has charge Q and length 1. If both the charge and length of the capacitors are doubled, by keeping other parameters fixed, the energy stored in the capacitor\n A remains same B increases two times C decreases two times D increases four times\n Question 11\nThe resistance of a metal increases with increasing temperature because\n A the collisions of the conducting electrons with the electrons increase B the collisions of the conducting electrons with the lattice consisting of the ions of the metal increase C the number of conduction electrons decrease D the number of conduction electrons increase\n Question 12\nIn the absence of applied potential, the electric current flowing through a metallic wire is zero because\n A the electrons remain stationary B direction with a speed of the order of 1O2 cm/s C the electrons move in random direction with a speed of the order close to that of velocity of light D electrons and Ions move In opposite direction\n Question 13\nIdentify the incorrect statement regarding a superconducting wire\n A transport current flows through its surface B transport current flows through the entire area of cross-section of the wire C it exhibits zero electrical resistivity and expels applied magnetic field D it is used to produce large magnetic field\n Question 14\nWhen a metallic plate swings between the poles of a magnet\n A no effect on the plate B eddy currents are set up inside the plate and the direction of the current is alone the motion of the plate C eddy currents are set up inside the plate and the direction of the current oppose the motion of the plate D eddy currents are set up inside the plate\n Question 15\nWhen an electrical appliance is switched on, it responds almost immediately, because\n A the electrons in the connecting wires move with the speed of light B the electrical signal is carried by electromagnetic waves moving with the speed of light C the electrons move with the speed which is close to but less than speed of light D the electrons are stagnant\n Question 16\nA transformer rated at 10 kW is used to connect a 5 kV transmission line to a 240 V circuit. The ratio of turns in the windings of the transformer is\n A 5 B 20.8 C 104 D 40\n Question 17\nA parallel beam of fast moving electrons is incident normally on a narrow slit. A screen is placed at a large distance from the slit. If the speed of the electrons is increased, which of the following statement is correct?\n A Diffraction pattern is not observed on the screen in the case of electrons B The angular width of the central maximum of the diffraction pattern will increase C The angular width of the central maximum will decrease D The angular width of the central maximum will remains the same\n Question 18\nTwo cylinders A and B fitted with pistons contain equal number of moles of an ideal monoatomic gas at 400 K. The piston of A is free to move while that of B is held fixed. Same amount of heat energy is given to the gas in each cylinder, If the rise in temperature of the gas in A is 42 K, the rise in temperature of the gas in B is\n A 21K B 35K C 42K D 70K\n Question 19\nTwo identical piano wires have a fundamental frequency of 600 cycle per second when kept under the same tension. What fractional increase in the tension of one wires will lead to the occurrence of 6 beats per second when both wires vibrate simultaneously?\n A 0.01 B 0.02 C 0.03 D 0.04\n Question 20\nThe two lenses of an achromatic doublet should have\n A equal powers B equal dispersive powers C equal ratio of their power and dispersive power D sum of the product of their powers and dispersive power equal to zero\nOnce you are finished, click the button below. Any items you have not completed will be marked incorrect.\nThere are 20 questions to complete.\n ← List →\n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 End\n\nCongratulations - you have completed VITEEE Question Answers = Chemistry .You scored %%SCORE%% out of %%TOTAL%%.Your performance has been rated as %%RATING%%\n Question 1\nWhich of the following is a ketohexose?\n A Glucose B Sucrose C Fructose D Ribose\n Question 2\nReaction of PCI3 and PhMgBr would give\n A bromobenzene B chlorobenzene C triphenyiphosphine D dichlorobenzene\n Question 3\nHair dyes contain\n A copper nitrate B gold chloride C silver nitrate D copper sulphate\n Question 4\nSchottky defects occurs mainly in electrovalent compounds where\n A positive ions and negative ions are of different size B positive ions and negative ions are of same size C positive ions are small and negative ions are big D positive ions are big and negative ions are small\n Question 5\nIf a plot of log10 C versus t gives a straight line for a given reaction, then the reaction is\n A zero order B first order C second order D third order\n Question 6\nA spontaneous process is one in which the system suffers\n A no energy change B a lowering of free energy C a lowering of entropy D an increase in internal energy\n Question 7\nThe electrochemical cell stops working after sometime because\n A electrode potential of both the electrodes becomes zero B electrode potential of both the electrodes becomes equal C one of the electrodes is eaten away D the cell reaction gets reversed\n Question 8\nThe amount of electricity required to produce one mole of copper from copper sulphate solution will be\n A 1 F B 2.33 F C 2 F D 1.33 F\n Question 9\nHydroboration oxidation of 4-methyl octene would give\n A 4-methyl octanol B 2-methyl decane C 4-methyl heptanol D 4-methyl-2-octanone\n Question 10\nAnisole is the product obtained from phenol by the reaction known as\n A coupling B etherification C oxidation D esterification\n Question 11\nDiamond is hard because\n A all the four valence electrons are bonded to each carbon atoms by covalent bonds B it is a giant molecule C it is made up of carbon atoms D it cannot be burnt\n Question 12\nA Wittig reaction with an aldehyde gives\n A ketone compound B a long chain fatty acid C olefin compound D epoxide\n Question 13\nMaleic acid and fumaric acid are\n A position isomers B geomet ic isomers C enantior.ers D functional isomers\n Question 14\nThe gas evolved on heating alkali formate with soda-lime is\n A CO B CO2 C hydrogen D water vapour\n Question 15\nOne mole of alkene on ozonolysis gave one mole of acetaldehyde and one mole of acetone. The IUPAC name of X is\n A 2-methyl-2-butene B 2-methyl- I -butene C 2-butene D 1-butene\n Question 16\nThe wavelengths of electron waves in two orbits is 3: 5. The ratio of kinetic energy of electrons will he\n A 25:9 B 5:3 C 9:25 D 3:5\n Question 17\nThe type of bonds present in sulphuric anhydnde are\n A 3and three pr-dr B 3 one pit-pit and two pr-dr C 2 and three pr- dr D 2and two pr-dr\n Question 18\nDipole moment of HCI 1.03 D, HI = 0.38 D. Bond length of HCI =1.3A and HI =1.6 A. The ratio of fraction of electric charge, 8 existing on each atom in HCI and HI is\n A 1:2:1 B 2.7:1 C 3.3:1 D 1:3.3\n Question 19\n1.5 g ofCdCl2 was found to contain 0.9 g of Cd. Calculate the atomic weight of Cd.\n A 118 B 112 C 106.5 D 53.25\n Question 20\nHow many ‘mL’ of perhydrol is required to produce sufficient oxygen which can be used to completely convert 2 L of SO2 to SO3 gas?\n A 10mL B 5mL C 20mL D 30mL\nOnce you are finished, click the button below. Any items you have not completed will be marked incorrect.\nThere are 20 questions to complete.\n ← List →"
] | [
null,
"https://upload.jbigdeal.in/wp-content/uploads/2015/06/Download-PDF.gif",
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https://www.meccanismocomplesso.org/en/first-steps-with-r/ | [
"# First steps with R\n\nTo start working effectively with R it is important to know at least the types of basic data and at least some fundamental commands to be able to start working on them. A brief overview to get started with this wonderful platform.\n\n## Arrays\n\nTo define an array in a very simple way in R it is sufficient to define the values of the elements as parameters of the function c() and then assign them to a variable, with any name, such as a.\n\n```a <- c(1,3,5,7,9,11)\n```\n\nTo read the elements inside it will be sufficient to write the name of the array, which in this case is a.\n\n```a\n 1 3 5 7 9 11\n```\n\nTo access a single element of the array, specify the name of the array and its index in square brackets (position of the element in the array).\n\n```a\n 5\n```\n\nIn this way it is also possible to modify an element inside it, directly assigning a new value to it.\n\n```> a <- 33\n> a\n 1 3 33 7 9 11\n```\n\n## Sequences\n\nA very quick way to generate arrays is through the use of sequences. That is, an instruction or a series of instructions that allow you to generate an array in a simple and fast way even with many elements. The elements, however, must respond to certain characteristics, that is, they must have rules in order to define the sequences that generate them.\n\nTo define a sequence in R we use the seq() function\n\n```seq(2,40,4)\n 2 6 10 14 18 22 26 30 34 38\n```\n\nwhere the first parameter is the starting value, the second the final value and the last is the distance between the elements of the sequence.\n\nAnother way to create a sequence of integer values is to use the ‘:’ between initial value and final value.\n\n```2:40\n 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\n 27 28 29 30 31 32 33 34 35 36 37 38 39 40\n```\n\nAnother way to create sequences is with the paste() function. This mode is very useful when you want to have an alphanumeric sequence with a prefix or suffix in characters. A sequence generator is then inserted in the first parameter, and in the second the suffix to be added to each generated element. The value of sep parameter defines any separator character to be added between the suffix and the sequence value.\n\n```paste(1:6, \"cm\", sep=\"\")\n \"1cm\" \"2cm\" \"3cm\" \"4cm\" \"5cm\" \"6cm\"\n```\n\nBut also the reverse, that is, the alphanumeric characters will be specified in the first argument that will act as a prefix for the sequence of values that will be generated in the second parameter. If you want to add a separator character, just define it in the sep parameter.\n\n```paste(\"A\", 1:5, sep =\":\")\n \"A:1\" \"A:2\" \"A:3\" \"A:4\" \"A:5\"\n```\n\nAlso interesting is the possibility to insert both parameters as sequence generators. The results can be interesting.\n\n```> paste(1:3, 3:5, sep=\"\")\n \"13\" \"24\" \"35\"\n> paste(1:3, 3:8, sep=\"\")\n \"13\" \"24\" \"35\" \"16\" \"27\" \"38\"\n```\n\nAnother way to create a sequence is with the rep() function. This function creates a sequence of elements that are all the same. The first parameter is the value to be replicated, and the second is the number of times it must be replicated.\n\n```> rep(1, 5)\n 1 1 1 1 1\n```\n\nIf instead we want a sequence of random numbers, we use the sample() function. In the first argument we pass the range of samples to choose from, the second parameter the number of random numbers to generate, and the key of the third replace, if specified TRUE as in this case, allows the repetition of the same values in the sequence, if FALSE avoids it.\n\n```sample(1:10, 7, replace=T)\n 2 5 4 10 1 3 8\n```\n\nThe possibilities of using these commands can be many, such as, for example, there is the possibility to choose between a set of values, passed as an array, or choose from a category of values, such as LETTERS which are the characters of the alphabet.\n\n```sample(c(1,4,5,8,7,11,15),4, replace=F)\n 15 5 4 8\nsample(LETTERS, 5, replace=T)\n \"P\" \"Z\" \"Z\" \"X\" \"W\"\n```\n\nAt each execution of these commands we will get different values\n\n```sample(LETTERS, 7)\n \"W\" \"D\" \"S\" \"X\" \"R\" \"U\" \"C\"\nsample(LETTERS, 7)\n \"I\" \"T\" \"L\" \"G\" \"X\" \"H\" \"F\"\n```\n\nIf, on the other hand, the generation of random values is reproducible, it is necessary to specify the command set.seed() previously and each time.\n\n```set.seed(200)\n> sample(LETTERS,5)\n \"F\" \"R\" \"O\" \"H\" \"L\"\n> set.seed(200)\n> sample(LETTERS,5)\n \"F\" \"R\" \"O\" \"H\" \"L\"\n```\n\nA very useful example could be to simulate the roll of a dice, for example, 10 times.\n\n```sample(1:6, 10, replace=T)\n 5 2 2 6 3 3 4 5 4 6\n```\n\n## Select a subset of elements in an array\n\nNow that we know how to create an array, either by defining it element by element or by generating it through sequences. It will be very useful to know a series of rules to be able to access the elements within it. It is often useful to extract a set of elements which will itself be an array (sub-array).\n\nSelection by conditions\n\nIt is possible to make selections of values within the array, imposing conditions. If for example we define the following array\n\n```a <- c(1,3,5,7,9,11)\n```\n\nA sub array will be returned containing only the elements that meet the conditions imposed.\n\n```a[ a > 3 & a < 8]\n 5 7\n```\n\nwhile if we write in this other way, we will obtain a sub array containing the positions of the elements that meet the conditions imposed.\n\n```which( a > 3 & a < 8)\n 3 4\n```\n\nSelection via functions\n\nThere are also certain functions that make particular selections on arrays passed as parameters.\n\nLet’s define an example array through a sequence.\n\n```samples <- sample(1:100, 12, replace=T)\n> samples\n 91 72 100 31 70 38 94 87 6 3 43 99\n```\n\nAnd now we want to know the first and last 6 elements of the array. In this case we will use the head() and tail() functions.\n\n```head(samples)\n 91 72 100 31 70 38\n> tail(samples)\n 94 87 6 3 43 99\n```\n\n## Statistics on the values of an array\n\nOther functions that R provides allows us to statistically evaluate the values contained within an array.\n\nFor example to know the maximum and minimum value, and the number of elements contained in an array.\n\n```> length(samples)\n 12\n> max(samples)\n 100\n> min(samples)\n 3\n```\n\nAnother command, namely the summary() function, allows us to obtain some statistical information.\n\n```> summary(samples)\nMin. 1st Qu. Median Mean 3rd Qu. Max.\n3.00 36.25 71.00 61.17 91.75 100.00\n```\n\nand the plot() function to place elements on a graph\n\n```plot(samples)\n```\n\n## Matrices\n\nHaving defined the arrays, now the next step is that of the matrices. To define a matrix it is possible to start from an array like those seen above. Let’s take samples for example. Let’s assign it to a variable M that we will use for the matrix.\n\n```M <- samples\n> M\n 91 72 100 31 70 38 94 87 6 3 43 99\n```\n\nNow the next steps will be to convert an array to an array. The array is of 12 elements which can be converted for example into a 4×3 matrix. So to change the size of the array, you can directly define the dim() function.\n\n```dim(M) <- c(3,4)\n> M\n[,1] [,2] [,3] [,4]\n[1,] 91 31 94 3\n[2,] 72 70 87 43\n[3,] 100 38 6 99\n```\n\nAs we can see, to convert an array to an array it is enough to vary its size. Another way to create or modify a matrix is through the fix () function which opens an editor that allows us to view the matrix and change its values.\n\nA very common operation that is performed with matrices is transposition, this is possible through the simple t() function.\n\n```> t(M)\n[,1] [,2] [,3]\ncol1 91 72 100\ncol2 31 70 38\ncol3 94 87 6\ncol4 3 43 99\n```\n\n## Lists\n\nThe objects seen so far had the characteristic of being able to contain only elements with values of the same type. Lists, on the other hand, allow you to group content of different types. To create a list, use the list() function with the elements inside it passed as parameters.\n\n```> t <- \"word\"\n> a <- 5\n> M <- sample(1:100, 12, replace=T)\n> dim(M) <- c(3,4)\n> mylist <- list(M,a,t)\n> mylist\n[]\n[,1] [,2] [,3] [,4]\n[1,] 91 35 6 33\n[2,] 13 91 21 71\n[3,] 67 27 31 30\n\n[]\n 5\n\n[]\n \"word\"\n```\n\nTo access the elements of the list, simply indicate the name of the list with the index of the desired element. The indices start from the value 1.\n\n```> mylist\n[]\n[,1] [,2] [,3] [,4]\n[1,] 91 35 6 33\n[2,] 13 91 21 71\n[3,] 67 27 31 30\n```\n\n## Dataframes\n\nThe most interesting type of data for working with data and using R as a tool for statistical and data processing and analysis is the dataframe. The dataframe is basically a data table with column headers and row indexes.\n\n```> a <- c(1,4,3,3,5)\n> b <- c(\"BMW\",\"Ford\",\"Opel\",\"Fiat\",\"Alfa Romeo\")\n> c <- c(TRUE,TRUE,FALSE,FALSE,FALSE)\n> df <- data.frame(a,b,c)\n> df\na b c\n1 1 BMW TRUE\n2 4 Ford TRUE\n3 3 Opel FALSE\n4 3 Fiat FALSE\n5 5 Alfa Romeo FALSE\n```\n\nTo access the elements of a dataframe column\n\n```> df\\$a\n 1 4 3 3 5\n```\n\nTo access the elements of a row of the dataframe\n\n```> df[,2]\n \"BMW\" \"Ford\" \"Opel\" \"Fiat\" \"Alfa Romeo\"\n```\n\n## Functions\n\nThe commands and functions present inside R are many, but they certainly cannot always cover the necessary. Moreover, often a series of instructions, commands and functions can be enclosed in a single operation, which we will define as a specific function.\n\nFor example, let’s create a function that calculates the area of the circle given the radius that we will call CircleArea. To define this function:\n\n```> CircleArea <- function(radius){\n```> CircleArea(12)"
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https://mammothmemory.net/maths/geometry/circumference-area-and-volume/the-circumference-of-a-circle-experiment.html | [
"",
null,
"# The circumference of a circle experiment\n\nFinding the circumference of a circle has many classrooms all over the world comparing the diameter of circle to their circumference:",
null,
"Compare the circumference of the barrel to the diameter of the barrel.\n\nOr in the snow:",
null,
"Compare the circumference of the circle in the snow with its diameter or rolling a car tyre.",
null,
"What every kid in the world has found is that\n\nRoughly 3 diameters = The circumference\nNo matter what size of circle\n\nTo be more precise mathematicians found that the number of times the diameter goes around the perimeter is 3.141592…… and the number goes on forever.\n\nCircumference = 3.142....times diameter\n\nAnd to further confuse things mathematicians called this number 3.142…. Pi (pronounced Pie).\n\n3.142....= Pi\n\nAnd to confuse things even further they gave Pi the symbol π\n\nSummary\n\nPi = pi\n\nSo the formula for circumference is\n\nCircumference of a circle = 3.142….times diameter\n\nOr\n\nCircumference of a circle = pitimesD\n\nNOTE 1:\n\n\\piD is the same as 2\\pir\n\nNOTE 2:\n\nEventually, mathematicians also found the Area of the circle = \\pir^2\n\nExample 1\n\nA tin of diameter 8 cm and height 15 cm has a label around it. The label is glued together using a 1 cm overlap. There is a 1 cm gap between the label and the top and the bottom of the tin.",
null,
"What length and height must the label be?\n\nHeight of the label = Height of the can – gap at top and bottom.\n\nTherefore height of the label =15–(1\\times\\2)=15–2=13cm\n\nLength of the label = Circumference of the can + overlap\n\nTherefore length of the label =2\\pir+1\n\nr = 1/2\\ diameter=1/2\\times8=4\n\nLength of the label =2\\times\\pi\\times4+1\n\nLength of the label =25.13+1=26.13cm\n\nThe label must be 26.13cm long and 13 cm high\n\nExample 2\n\nA factory makes novelty giant paper clips. A diagram of one is placed alongside a centimetre ruler as shown below. The curved ends are semicircles.",
null,
"The paperclips are cut from rolls of coiled wire 1000m long. Calculate how many paper clips can be made from each roll of wire.\n\nWe must first work out the length of wire required to make each paper clip.\n\nThe length of wire needed for each paper clip is the total length of all the straight sections (coloured sections shown below) and the arc length of the three semi circles (coloured grey below).",
null,
"",
null,
"The length of the red straight section shown below is:",
null,
"5cm–0.9cm=4.1cm\n\nThe length of the yellow straight section shown below is:",
null,
"6.8cm–2.1cm=4.7cm\n\nThe length of the green straight section shown below is:",
null,
"5cm–2.1cm=2.9cm\n\nThe length of the purple straight section shown below is:",
null,
"6.8cm–0.9cm=5.9cm\n\nTherefore length of straight sections = red length + yellow length + green length + purple length\n\nLength of straight sections =4.1+4.7+2.9+5.9=17.6cm\n\nThe length of the arc around a semicircle is half the circumference of the whole circle so if\n\nA circles circumference =2\\pir\n\nThen a semi circles arc =\\pir\n\nThe radius of the left hand semicircle on the paper clip shown below is:",
null,
"0.9cm–0cm=0.9cm\n\nTherefore the arc length of this semicircle =\\pir=\\pi\\times0.9=2.8cm\n\nThe radius of the middle semicircle on the paper clip shown below is:",
null,
"2.1cm–1.5cm=0.6cm\n\nTherefore the arc length of this semicircle = pir=pitimes0.6=1.9cm\n\nThe radius of the right hand semicircle on the paper clip shown below is:",
null,
"7.5cm–6.8cm=0.7cm\n\nTherefore the arc length of this semicircle =\\pir=\\pi\\times\\0.7=2.2cm\n\nSo the total length of the arcs formed by the paper clips semi-circles =2.8+1.9+2.2=6.9cm\n\nTherefore the total length of each paper clip = The total length of all the straight sections (17.6cm) plus the total arc lengths of the three semi circles (6.9cm) = 17.6+6.9=24.5cm\n\nEach roll of coiled wire = 1000m and there are 100cm in 1m\n\nTherefore each roll of coiled wire = 1000times100=100,000cm\n\n(100,000)/(24.5)=4081.63"
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null,
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https://dbdmg.polito.it/wordpress/wp-content/uploads/2019/11/Lab4_Solution.html | [
"## 2D Gaussian clusters¶\n\n### Exercise 1.1¶\n\nTo load the dataset, the numpy.loadtxt method can be used. This time, the dataset file contains an header in the first line. We will skip it using the method iself.\n\nIn :\nimport numpy as np\nimport matplotlib.pyplot as plt\n%matplotlib inline\n\nIn :\nX_gauss = np.loadtxt(\"2D_gauss_clusters.txt\", delimiter=\",\", skiprows=1)\nX_gauss\n\nOut:\narray([[845753., 636607.],\n[812954., 643720.],\n[868217., 609046.],\n...,\n[706472., 171207.],\n[659128., 142611.],\n[665898., 98088.]])\n\n### Exercise 1.2¶\n\nLet's use now matplotlib to explore our 2D data. Since we are likely going to need a scatter plot multiple times, we can define a simple function to handle it.\n\nIn :\ndef plot_2d_scatter(X):\n\"\"\"Display a 2D scatter plot\n\n:param X: input data points, array\n:return: fig, ax, objects\n\"\"\"\nfig, ax = plt.subplots(figsize=(6, 6), dpi=90)\nax.scatter(X[:,0], X[:,1])\nreturn fig, ax # use them for further modifications\n\nIn :\n_, _ = plot_2d_scatter(X_gauss) # the two underscores let you discard the returned values",
null,
"Gaussian, globular clusters are easily visible in the euclidean space. At first sight, you can count up to 15 clusters. Most of them have a regular shape, while some others are more elongated. Given this distribution, we known from theory that the K-means algorithm can achieve positive clustering performance (provided that the right number of cluster is chosen).\n\n### Exercises 1.3 and 1.4¶\n\nLet's implement now our version of the K-means algorithm. We will use a custom Python class. The basic blocks will be:\n\n• a fit_predict method exposed to the users of the class\n• a stateful structure: we do want to save the final clusters labels and centroids\n• some internal plotting functions\n• a dump_to_file method to save cluster labels to CSV file (see Exercise 1.4)\nIn :\nclass KMeans:\n\ndef __init__(self, n_clusters, max_iter=100):\nself.n_clusters = n_clusters\nself.max_iter = max_iter\nself.centroids = None\nself.labels = None\n\ndef __plot_clusters(self, X, labels, c=None):\nfig, ax = plt.subplots(figsize=(6,6), dpi=90)\nax.scatter(X[:,0], X[:,1], c=labels, cmap='Set3')\nif c is not None:\nax.scatter(c[:,0], c[:,1], marker=\"*\", color=\"red\")\n\nreturn fig, ax\n\ndef __init_random_centroids(self, X):\nc_idx = np.random.randint(0, X.shape, self.n_clusters)\nc = X[c_idx] # fancy-indexing\nreturn c\n\ndef fit_predict(self, X, plot_clusters=False, plot_steps=5):\n\"\"\"Run the K-means clustering on X.\n\n:param X: input data points, array, shape = (N,C).\n:return: labels : array, shape = N.\n\"\"\"\n# For each point, store the positional index of the closest centroid\nnearest = np.empty(X.shape)\n\nc_out = self.__init_random_centroids(X)\nfor j in range(self.max_iter):\nnearest_prev = nearest\n\n# For each point in X, compute the squared distance from each centroid\n# dist will have shape: (n_clusters, X.shape)\ndist = np.array([np.sum((X-c_out[i])**2, axis=1) for i in range(self.n_clusters)])\n\n# Find the nearest centroid for each point using argmin\n# nearest will have shape: (X.shape,)\nnearest = dist.argmin(axis=0)\n\nif plot_clusters and (j % plot_steps == 0):\nfig, ax = self.__plot_clusters(X, nearest, c_out)\nax.set_title(f\"Iteration {j}\")\n\n# Early stopping if centroids have not changed\nif np.array_equal(nearest, nearest_prev):\nprint(f\"Early stopping at iteration {j}!\")\nbreak\n\n# For each cluster, compute the average coordinates considering only points currently\n# assigned to it. Then, use them as the new centroid coordinates.\nfor i in range(self.n_clusters):\nc_temp = X[nearest == i].mean(axis=0) # indexing with a mask\nif not np.isnan(c_temp).any(): # handle the case of an empty cluster\nc_out[i] = c_temp\n\nself.centroids = c_out\nself.labels = nearest\nreturn self.labels\n\ndef dump_to_file(self, filename):\n\"\"\"Dump the evaluated labels to a CSV file.\"\"\"\nwith open(filename, 'w') as fp:\nfp.write('Id,ClusterId\\n')\nfor i, label in enumerate(self.labels):\nfp.write(f'{i},{label:d}\\n')\n\n\nThere are several things worth noting in the code above:\n\n1. since data are not shuffled during the execution, the class makes use of positional indices. The nearest array is a good example of that. For each point, it keeps track of the index of the centroid of the cluster that point is assigned to. In other words, if the ith item of nearest has value j, we know that the ith point of the dataset is assigned to the jth cluster. Using this convention, the choice of the cluster Ids is straightforward: the ith cluster will have ID = i\n2. this is a typical case in which NumPy can significantly speed up the execution. NumPy's broadcasting feature is used to compute the squared distances from each cluster centroid. Then, argmin is used to soft-sort them and find the closest centroid Id. Finally, array_equal lets you efficiently compare the current and previous centroid positions (if we wanted to compare them with a tolerance, we could have used the numpy.allclose method)\n3. some internal methods have a double underscore as name prefix. As you should know, Python does not provide the concept of private attributes or methods by choice. However, programmers that define members intended to be private can make use of name mangling (it remains a design choice, it does not prevent other to access to those members). Name mangling is commonplace in many languages. In Python, it is enabled by adding two leading underscore to your member name (actually, you are also restricted to have at most one trailing underscore). You can read more on name mangling here.\n\nWe strongly suggest you to stop and try to fully understand the first two points. For your convenience, we commented the shape of the numpy arrays involved at their respective lines.\n\nLet's try now to use our class and save our labels to file.\n\nIn :\nnp.random.seed(0)\nkmeans_model = KMeans(10)\nl_gauss = kmeans_model.fit_predict(X_gauss)\nl_gauss\n\nEarly stopping at iteration 11!\n\n/Users/giuseppe/miniconda3/envs/atsa-py37/lib/python3.7/site-packages/numpy/core/numeric.py:2591: RuntimeWarning: invalid value encountered in equal\nreturn bool(asarray(a1 == a2).all())\n\nOut:\narray([1, 1, 1, ..., 5, 5, 5])\n\nThe algorithm has stopped after 11 iterations since every centroid has not moved between iteration 10 and 11. In other words, at the 11th iteration, no point has changed its closest centroid (i.e. its membership cluster).\n\nNote also line 1 of the previous cell: it initializes the NumPy's random generator with a specific seed. With a fixed random generator, the same points will be chosen as initial centroids among different runs. This is commonplace whenever you want your results to be reproducible. Many scikit-learn classes offer you this functionality via the random_state parameter.\n\nIn :\nkmeans_model.dump_to_file('gauss_labels.csv')\n\n\n### Exercise 1.5¶\n\nLet's analyze now the Chameleon dataset just as before.\n\nIn :\nX_cham = np.loadtxt(\"chameleon_clusters.txt\", delimiter=\",\", skiprows=1)\nX_cham\n\nOut:\narray([[ 68.601997, 102.491997],\n[454.665985, 264.80899 ],\n[101.283997, 169.285995],\n...,\n[267.605011, 141.725006],\n[238.358002, 252.729996],\n[159.242004, 177.431 ]])\nIn :\n_, _ = plot_2d_scatter(X_cham)",
null,
"As you can notice, there are six interleaved areas with an high density of points and irregular shape. Also, the dataset looks much more noisier (note the sine wave superimposed). Given this distribution, we known from theory that the K-Means algorithm might suffer even choosing the right number of clusters.\n\n### Exercise 1.6¶\n\nIt is time to enhance our plotting toolkit. We hence define a new function that highlights the final centroids. Specifically, we can use a different marker style and color for them.\n\nIn :\ndef plot_centroids(X, c, title=None):\nfig, ax = plot_2d_scatter(X)\nax.scatter(c[:,0], c[:,1], marker=\"*\", color=\"red\")\n\nif title:\nax.set_title(title)\nreturn fig, ax\n\n\nLet's now try to inspect the final centroids obtained in both our datasets.\n\nIn :\nnp.random.seed(0)\nk_gauss = KMeans(10)\nk_cham = KMeans(10)\n\nk_gauss.fit_predict(X_gauss)\nk_cham.fit_predict(X_cham)\n\nplot_centroids(X_gauss, k_gauss.centroids, title=\"Gaussian, K=10\")\nplot_centroids(X_cham, k_cham.centroids, title=\"Chameleon, K=10\")\n\nEarly stopping at iteration 11!\nEarly stopping at iteration 29!\n\nOut:\n(<Figure size 540x540 with 1 Axes>,\n<matplotlib.axes._subplots.AxesSubplot at 0x109b78358>)",
null,
"",
null,
"We can visually see that the cluster identification might be improved choosing a different K. Our initial choice is too low for Gaussian data while too high for Chameleon.\n\nIn :\nnp.random.seed(0)\nk_gauss = KMeans(15)\nk_cham = KMeans(6)\n\nk_gauss.fit_predict(X_gauss)\nk_cham.fit_predict(X_cham)\n\nplot_centroids(X_gauss, k_gauss.centroids, title=\"Gaussian, K=15\")\nplot_centroids(X_cham, k_cham.centroids, title=\"Chameleon, K=6\")\n\nEarly stopping at iteration 40!\nEarly stopping at iteration 24!\n\nOut:\n(<Figure size 540x540 with 1 Axes>,\n<matplotlib.axes._subplots.AxesSubplot at 0x109a24f98>)",
null,
"",
null,
"Here some interesting happened. On one hand, the Gaussian dataset was clustered in a better way (again, visually speaking). Yet, there are two pairs of centroids in which the two points are close enough to stay in the same globular cluster. This is likely due to the random initialization of centroids (in literature, there exist other approaches rather than randomly picking them). On the other hand, centroids identified in the Chameleon dataset did not match the real data distribution. This is exactly what we expected: the initial distribution has shape and sizes the K-means algorithm can hardly fit.\n\nFor the sake of completeness, you can run multiple executions with different seed generators. Results are likely to remain the same for Chameleon clusters. Instead, a different random initialization, for the first dataset, could lead to a better result, as shown below.\n\nIn :\nnp.random.seed(6)\nk_gauss = KMeans(15)\nk_cham = KMeans(6)\n\nk_gauss.fit_predict(X_gauss)\nk_cham.fit_predict(X_cham)\n\nplot_centroids(X_gauss, k_gauss.centroids, title=\"Gaussian, K=15\")\nplot_centroids(X_cham, k_cham.centroids, title=\"Chameleon, K=6\")\n\nEarly stopping at iteration 14!\nEarly stopping at iteration 15!\n\nOut:\n(<Figure size 540x540 with 1 Axes>,\n<matplotlib.axes._subplots.AxesSubplot at 0x109a0bdd8>)",
null,
"",
null,
"### Exercise 1.7¶\n\nWe might be interested to the intermediate position of centroids, other than the final ones. We included this plotting functionality in the KMeans class defined above via the plot_clusters and plot_steps parameters of fit_predict. The plot is created in __plot_clusters. Take a close look at the c and cmap parameters. c accepts a list used to specify which points must have the same color. Points at indices with equal values in that list will have the same color. cmap instead lets you choose a color map among the ones predefined.\n\nLet's test it with Gaussian clusters.\n\nIn :\nnp.random.seed(6)\nk_gauss = KMeans(15)\n_ = k_gauss.fit_predict(X_gauss, True, 3)\n\nEarly stopping at iteration 14!",
null,
""
] | [
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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 ",
null,
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 ",
null,
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 ",
null,
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 ",
null,
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 ",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.7761992,"math_prob":0.93909293,"size":8302,"snap":"2020-34-2020-40","text_gpt3_token_len":2063,"char_repetition_ratio":0.12713908,"word_repetition_ratio":0.031329382,"special_character_ratio":0.24969886,"punctuation_ratio":0.17907692,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9956943,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-08-15T02:47:56Z\",\"WARC-Record-ID\":\"<urn:uuid:3f5dfe9f-b6da-403a-bc9d-1a884c07215f>\",\"Content-Length\":\"1049018\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:51afb3be-3673-4cd6-a61c-93328f61c3d2>\",\"WARC-Concurrent-To\":\"<urn:uuid:2b577c71-9e03-4bce-8549-15cb1395e276>\",\"WARC-IP-Address\":\"130.192.163.163\",\"WARC-Target-URI\":\"https://dbdmg.polito.it/wordpress/wp-content/uploads/2019/11/Lab4_Solution.html\",\"WARC-Payload-Digest\":\"sha1:ZPZBJTX4YGO5T5NMEB5FNP4ARFXUBKMZ\",\"WARC-Block-Digest\":\"sha1:WHS7U5B4KSCHKMOJ6KVETFMS5NJOE74Q\",\"WARC-Truncated\":\"length\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-34/CC-MAIN-2020-34_segments_1596439740423.36_warc_CC-MAIN-20200815005453-20200815035453-00148.warc.gz\"}"} |
https://kr.mathworks.com/matlabcentral/cody/solutions/1703087 | [
"Cody\n\nProblem 43114. Add the odd numbers\n\nSolution 1703087\n\nSubmitted on 5 Jan 2019 by Martin C.\nThis solution is locked. To view this solution, you need to provide a solution of the same size or smaller.\n\nTest Suite\n\nTest Status Code Input and Output\n1 Pass\nx = [1 2 3 4 5]; y_correct = 9; assert(isequal(addOdd(x),y_correct))\n\ny = 9\n\n2 Pass\nx = [1 2 3 4 5 7]; y_correct = 16; assert(isequal(addOdd(x),y_correct))\n\ny = 16\n\n3 Pass\nx = [1 2 4 5 7]; y_correct = 13; assert(isequal(addOdd(x),y_correct))\n\ny = 13"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.5034227,"math_prob":0.9975203,"size":524,"snap":"2019-43-2019-47","text_gpt3_token_len":185,"char_repetition_ratio":0.15,"word_repetition_ratio":0.094736844,"special_character_ratio":0.39694658,"punctuation_ratio":0.10909091,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99398685,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-15T17:03:11Z\",\"WARC-Record-ID\":\"<urn:uuid:3ece0102-5706-48af-ae54-ed5c072b3f21>\",\"Content-Length\":\"71286\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:53e793a4-2af9-41f4-8cf4-5861874aa580>\",\"WARC-Concurrent-To\":\"<urn:uuid:ac9dafca-166a-42ef-920a-da798dbcbca7>\",\"WARC-IP-Address\":\"23.13.150.165\",\"WARC-Target-URI\":\"https://kr.mathworks.com/matlabcentral/cody/solutions/1703087\",\"WARC-Payload-Digest\":\"sha1:GI7J6KU2BGHAFFRJ64JYOWCU2TUW2SS6\",\"WARC-Block-Digest\":\"sha1:GRYQO6W7P6D4X4CXUPJ7KVOFJLPYHIGG\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570986660067.26_warc_CC-MAIN-20191015155056-20191015182556-00435.warc.gz\"}"} |
https://caddellprep.com/common-core-algebra-assignments/adding-and-subtracting-radical-expressions/ | [
"In this video, we are going to be adding and subtracting radical expressions.\n\n• [nonmember]\n[/nonmember]\n\nWe can add",
null,
"$3x+5x=8x$\nand we can do the same to",
null,
"$3\\sqrt{2}+5\\sqrt{2}=8\\sqrt{2}$\n\nSince we can only combine like terms, we know that we cannot add",
null,
"$5x$ and",
null,
"$7y$ together\nso we cannot add",
null,
"$5\\sqrt{2}$ and",
null,
"$7\\sqrt{3}$ together either\n\nFor",
null,
"$9\\sqrt{6}+3\\sqrt{5}-4\\sqrt{6}+2\\sqrt{5}$,\nit would be",
null,
"$5\\sqrt{6}+5\\sqrt{5}$",
null,
"Let’s look at other examples:",
null,
"$3\\sqrt{2}+6\\sqrt{18}$",
null,
"$3\\sqrt{2}$ would stay like itself, while",
null,
"$6\\sqrt{18}$ can be broken into",
null,
"$18\\sqrt{2}$\nNow that both expressions are like terms, they can be combined into",
null,
"$21\\sqrt{2}$",
null,
"$6\\sqrt{12}-4\\sqrt{45}+2\\sqrt{3}-\\sqrt{80}$\nAfter simplifying each radical expression, it will be",
null,
"$12\\sqrt{3}-12\\sqrt{5}+2\\sqrt{3}-4\\sqrt{5}$\nAfter combining like terms, it will be",
null,
"$14\\sqrt{3}-16\\sqrt{5}$\n\n## Video-Lesson Transcript",
null,
"$3x + 5x = 8x$",
null,
"$3 \\sqrt{2} + 5 \\sqrt{2} = 8 \\sqrt{2}$\n\nOnly like terms can be added.\n\nJust like if we have",
null,
"$5x + 7y$",
null,
"$5 \\sqrt{2} + 7 \\sqrt{3}$\n\nit will just stay like this.\n\nThey won’t combine since they are different radicals.\n\nSo if we have",
null,
"$9 \\sqrt{6} + 3 \\sqrt{5} - 4 \\sqrt{6} + 2 \\sqrt{5}$\n\nwe can combine like terms, so the answer is",
null,
"$5 \\sqrt{6} + 5 \\sqrt{5}$\n\nLet’s look at this one",
null,
"$3 \\sqrt{2} + 6 \\sqrt{18}$\n\nThis may look unlike terms so we can’t combine them.\n\nBut we can simplify this first.\n\nThe first expression can’t be simplified so we simplify the second expression.\n\nLet’s simplify first.",
null,
"$6 \\sqrt{18}$",
null,
"$6 \\sqrt{9} \\sqrt{2}$\n\nI chose these because",
null,
"$9$ is a complete square.",
null,
"$6 \\times 3 \\sqrt{2}$",
null,
"$18 \\sqrt{2}$\n\nNow, let’s our new expressions are",
null,
"$3 \\sqrt{2} + 18 \\sqrt{2}$\n\nSince they are already like terms, we can combine them now.",
null,
"$21 \\sqrt{2}$\n\nSo always make sure that they are in their simplest terms before we add them.\n\nBecause maybe they can be combined, they are not just in the correct format.\n\nLet’s try this one now.",
null,
"$6 \\sqrt{12} - 4 \\sqrt{45} + 2 \\sqrt{3} - \\sqrt{80}$\n\nLet’s simplify all these first.",
null,
"$6 \\sqrt{4} \\sqrt{3} - 4 \\sqrt{9} \\sqrt{5} + 2 \\sqrt{3} - \\sqrt{4} \\sqrt{20}$",
null,
"$6 \\times 2 \\sqrt{3} - 4 \\times 3 \\sqrt{5} + 2 \\sqrt{3} - 2 \\sqrt{4} \\sqrt{5}$",
null,
"$12 \\sqrt{3} - 12 \\sqrt{5} + 2 \\sqrt{3} - 2 \\times 2 \\sqrt{5}$",
null,
"$12 \\sqrt{3} - 12 \\sqrt{5} + 2 \\sqrt{3} - 4 \\sqrt{5}$\n\nNow, let’s combine the like terms.",
null,
"$14 \\sqrt{3} - 16 \\sqrt{5}$"
] | [
null,
"https://s0.wp.com/latex.php",
null,
"https://s0.wp.com/latex.php",
null,
"https://s0.wp.com/latex.php",
null,
"https://s0.wp.com/latex.php",
null,
"https://s0.wp.com/latex.php",
null,
"https://s0.wp.com/latex.php",
null,
"https://s0.wp.com/latex.php",
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https://www.fmaths.com/tips/quick-answer-what-is-mark-on-in-business-mathematics.html | [
"## What is mark up in business math?\n\nMarkup refers to the difference between the selling price of a good or service and its cost. It is expressed as a percentage above the cost.\n\n## What is the formula of mark on?\n\nTo calculate the markup amount, use the formula: markup = gross profit /wholesale cost.\n\n## What is markup and markdown?\n\nMarkup is how much to increase prices and markdown is how much to decrease prices. If we are given a markdown percentage, we multiply the percentage with the original price to find how much of a decrease we are getting, then we subtract this difference from the original price to find the marked down price.\n\n## What is the difference between markon and markup?\n\nThe difference between margin and markup is that margin is sales minus the cost of goods sold, while markup is the the amount by which the cost of a product is increased in order to derive the selling price.\n\nYou might be interested: Question: What Is Fundamental Of Mathematics?\n\n## How do you calculate the selling price?\n\nHow to Calculate Selling Price Per Unit\n\n1. Determine the total cost of all units purchased.\n2. Divide the total cost by the number of units purchased to get the cost price.\n3. Use the selling price formula to calculate the final price: Selling Price = Cost Price + Profit Margin.\n\n## How do you calculate a 30% margin?\n\nHow do I calculate a 30 % margin?\n\n1. Turn 30 % into a decimal by dividing 30 by 100, which is 0.3.\n2. Minus 0.3 from 1 to get 0.7.\n3. Divide the price the good cost you by 0.7.\n4. The number that you receive is how much you need to sell the item for to get a 30 % profit margin.\n\n## What is the importance of mark on?\n\nA mark – on of 10% indicates that if the Cost price of the item is 100Rs, then the Selling price would be 110Rs. Additional mark – on is the additional increase in the price of the commodity, done to achieve higher profits, due to the increase in demand of the commodity during various seasons or holiday period.\n\n## How do you find markup and selling price?\n\nIf you have a product that costs \\$15 to buy or make, you can calculate the dollar markup on selling price this way: Cost + Markup = Selling price. If it cost you \\$15 to manufacture or stock the item and you want to include a \\$5 markup, you must sell the item for \\$20.\n\n## How do you calculate profit?\n\nWhen calculating profit for one item, the profit formula is simple enough: profit = price – cost. total profit = unit price * quantity – unit cost * quantity. Depending on the quantity of units sold, our profit calculator can also determine the total cost, profit per unit and total profit.\n\nYou might be interested: Readers ask: What Is The Meaning Of Subset In Mathematics?\n\n## How is markdown value calculated?\n\n1. Markdown = 50 x 20% = 10.\n2. Revenue = List Price – Markdown = 50 – 10 = 40.\n3. Gross Profit = Revenue – Cost = 40 – 10 = 30.\n4. Gross Margin = Gross Profit / Revenue = 30 / 40 = 75%\n\n## What is the markup rule?\n\nFrom Wikipedia, the free encyclopedia. A markup rule is the pricing practice of a producer with market power, where a firm charges a fixed mark-up over its marginal cost.\n\n## What is an example of a markdown?\n\nMarkdown Example In other words, if a broker sells a security to a client at a lower price than the highest bid (selling) price in the securities market among brokers, the price is a markdown price. To illustrate, suppose a broker sells shares of XYZ stock to his clients at \\$20 per share.\n\n## Why is margin better than markup?\n\nThe margin shows the relationship between gross profit and revenue, while markup shows the relationship between profit and the cost of goods sold. Markup is a great tool in the initial stages of a business since it helps you to better understand how cash flows into and out of your business.\n\n## What is margin vs markup?\n\nThe profit margin, stated as a percentage, is 30% (calculated as the margin divided by sales). Profit margin is sales minus the cost of goods sold. Markup is the percentage amount by which the cost of a product is increased to arrive at the selling price.\n\n## What is the difference between markup and gross profit?\n\nMarkup and gross profit percentage are not the same! Terminology speaking, markup percentage is the percentage difference between the actual cost and the selling price, while gross proft percentage is the percentage difference between the selling price and the profit.",
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] | [
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https://www.mycareerwise.com/programming/category/basic-programs/left-rotate-of-an-array | [
"## Left Rotate of an Array\n\nBack to Programming\n\n### Description\n\nThe elements are taken as the input. The array is rotated left. That means, the element of index 1 is stored in index 0, the element of index 2 is stored in index 1 and so on. And the element of index 0 is stored in index n-1..\n\nLet the array be:\n\n0 1 2 3 4\n\nFirst the element of index 0 (here, 14) will be stored in a temporary variable.\n\n0 1 2 3 4\n\nNow the second element will be copied to the first index making the array as:\n\n0 1 2 3 4\n\nBy the same process, the third element will be copied to the 2nd position and so on till the last element of the array will be stored at the 2nd last position of the array.\n\nThe array will be:\n\n0 1 2 3 4\n\nAt last the value of the temporary element will be stored at the last index so the array will be:\n\n0 1 2 3 4\n\n### Algorithm\n\nINPUT: Array elements\n\nOUTPUT: the array after left rotation\n\nPROCESS:\n\nStep 1: [taking the input]\n\nFor i=0 to n-1 repeat\n\n[end of ‘for’ loop]\n\nStep 2: [Rotating the array]\n\nSet t<-a\n\nFor i=1 to n-1 repeat\n\nSet a[i-1]<-a[i]\n\n[End of ‘for’ loop]\n\nSet a[n-1]<-t\n\nPrint “The array after rotation is: “\n\nFor i=0 to n-1 repeat\n\nPrint a[i]\n\n[End of ‘for’ loop]\n\nStep 3: Stop.\n\n### Code\n\nThe time complexity to take the number of elements is O(n) and the time complexity to left rotate is also O(n).\n\nTherefore, the time complexity of this program is O(n).\n\nt=a;--------------------------------------------------------O(1)\n\nfor(i=1;i<n;i++)---------------------------------------------O(n-1)\n\na[i-1]=a[i];----------------------------------------O(1)\n\na[n-1]=t;-----------------------------------------------------O(1)\n\ntherefore, the complexity is: O(n)"
] | [
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https://jasonlhy.com/Minimum-spanning-tree/ | [
"",
null,
"# Definition\n\nMinimum spanning tree is defined as given graph(G) which a set of vertexes and edges with weights. Find a path which connects all vertexes with minimum total weight of edges. There are two classic algorithms which are designed with greedy algorithm: Prim Algorithm and Kruskal Algorithm.\n\n## Generice MST\n\n``````A = {} // subset of some minimum spanning tree (V, E)\nwhile A is not a minimum spanning tree\nfind edge(u, v) to that is safe to A\nA = A union (u, v)``````\n\n## Safe Edge\n\nSafe edge is a edge that is safe to added into A which out destorying the invarient property that A is subet of some minimum spanning tree. In other words, when you add a edge into A which causes A cannot form MST in the future, the edge is not safe.\n\n### Light Edge is safe\n\nLet G=(V,E) be a connected, undirected graph with a real-valued weight function w defined on E. Let A be a subset of E that is included in some minimum spanning tree for G. Let (S,V-S) be any cut of G such that for any edge (u, v) in A, {u, v} S or {u, v} (V-S). Let (u,v) be a light edge crossing (S,V-S). Then, edge (u,v) is safe for A. (.... It just means finding a minimum weight edge which connects two parts of the graph, when it is cut then no vertexes are shared in two parts)\n\n# Prim Algorithm\n\nThis algorithm is based on shortest path algorithm. It builds a set of A in the process and select the light edge connecting A to others.\n\nSimple version\n\n`````` A = {}\nS = {r} // r is the random node you want to start with\nQ = V - {r}\nwhile Q is not empty\nFind the minimum edge(u, v) so that u in A and v in Q\nAdd (u, v) in A, add v in S, and delete v from Q``````\n\nPriortiy queue version The min-priority queue is implemented with binary heap. Use the key of the priority queue to keep track of the minimum distance from A to others. Note: Heap-Order: for every node v other than the root, key(v) >= key(parent(v))\n\n`````` Store all V in priority queue Q\nfor each u in Q\nkey[u] = infinity\nparent[u] = NUL\nkey[r] = 0\nwhile (Q is not empty)\nu = EXTRACT_MIN(Q)\n// v belongs to others but not the buidling tree\n// update its minimum distance if edge is smaller than its expected value before\nif (v belongs to Q && key[v] > w(u,v) )\nkey[v] = w(u, v)\nparent[v] = u``````\n\n## Running time analysis\n\nWhile loop executes V times EXTRACT_MIN(Q) : log V => V log V\n\nThe for loop (each v in adj[u]): total executes 2E times decrease key operation : log V => E log V\n\nOverall running time: (V log V + E log V) = E log V // E always > V\n\n# Kruskal Algorithm\n\nAdd the edges according to the increasing weight, as long as the operation will not violate the minimum tree property. It uses a disjoint set to keep track the grouping of vertexes, as long as the edge(u, v) where u and v are not in the same group, the edge is safe to be added.\n\n`````` A = {} // tree under construction\nSort the edges of E by weights by increasing order\nfor each v in G\nMAKE_SET(v) // every one belongs to its own group initially\nfor each edge(u, v) in E\nif (FIND_SET(u) != FIND_SET(v))\nA union (u, v)\nUNION(u, v) // they are the same group now\nreturn A``````\n\n## Running time analysis\n\n1. sort edges: E log E\n2. for loop V times: MAKE_SET: log V\n3. for loop execcutes E times FIND_SET and UNION: log V\n\nCombine 2 & 3 we ge V+E log V => E log V => combine with (1) E log E Overall Running time: E log E\n\n## Disjoint Set Implemented by array\n\nEvery child remember its parent index The parent remeber its size (-ve)\n\n``````int Find(int element){\nif (nodes[element] < 0)\nreturn element;\nelse\nreturn nodes[element] = Find(nodes[element]);\n}\n\nvoid UnionSet(int set1, int set2){\nnodes[set1] += nodes[set2];\nnodes[set2] = set1;\n}\n\nint Union(int element1, int element2){\nint root1 = Find(element1);\nint root2 = Find(element2);\n\nif (root1 == root2) // reject if form a cycle\nreturn 0;\n\nif (nodes[root1] < nodes[root2]) // root1 has more elements than root2\nUnionSet(root1, root2);\nelse\nUnionSet(root2, root1);\n\nreturn 1;\n}``````\n\n## Differene between Prim algorihtm and Kruskal algorithm\n\nPrim requires a connected graph, Kruskal can work on unconnected group in which many MST can be formed. Every step in prim is a partial solution.\n\n## Application of MST\n\nMST algorihtm can be also used to build spanning tree based on each side\n\n``````for (int i=0; i<m; i++){\n// based on each side, try to build a spanning tree with bigger side\n// compare their slimness\nfor (int j=1; j<=n; j++){\nnodes[j] = -1;\n}\n\nEdge b = edges[i];\nUnion(b.u, b.v);\n\nint largest = b.c;\nint smallest = b.c;\nfor (int j=i+1; j<m; j++){\nEdge c = edges[j];\nUnion(c.u, c.v);\n}\n}``````\n\nk - cluster with mini distance between point = MST - k most expensive edges.",
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https://www.arxiv-vanity.com/papers/1605.07372/ | [
"# Exponential Communication Complexity Advantage from Quantum Superposition of the Direction of Communication\n\nPhilippe Allard Guérin Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria Adrien Feix Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria Mateus Araújo Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria Časlav Brukner Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria\nJune 4, 2023\n###### Abstract\n\nIn communication complexity, a number of distant parties have the task of calculating a distributed function of their inputs, while minimizing the amount of communication between them. It is known that with quantum resources, such as entanglement and quantum channels, one can obtain significant reductions in the communication complexity of some tasks. In this work, we study the role of the quantum superposition of the direction of communication as a resource for communication complexity. We present a tripartite communication task for which such a superposition allows for an exponential saving in communication, compared to one-way quantum (or classical) communication; the advantage also holds when we allow for protocols with bounded error probability.\n\nQuantum resources make it possible to solve certain communication and computation problems more efficiently than what is classically possible. In communication complexity problems, a number of parties have to calculate a distributed function of their inputs while reducing the amount of communication between them Yao1979 ; Kushilevitz1996 . The minimal amount of communication is called the complexity of the problem. For some communication complexity tasks, the use of shared entanglement and quantum communication significantly reduces the complexity as compared to protocols exploiting shared classical randomness and classical communication Yao1993 ; Buhrman2010 . Important early examples for which quantum communication yields an exponential reduction in communication complexity over classical communication are the distributed Deutsch-Jozsa problem Buhrman1998 and Raz’s problem Raz1999 .\n\nQuantum computation and communication are typically assumed to happen on a definite causal structure, where the order of the operations carried on a quantum system is fixed in advance. However, the interplay between general relativity and quantum mechanics might force us to consider more general situations in which the metric, and hence the causal structure, is indefinite. Recently, a quantum framework has been developed with no assumption of a global causal order Oreshkov2012 ; Araujo2015 ; Oreshkov2015 . This framework can also be used to study quantum computation beyond the circuit model, for instance using the “quantum switch” as a resource — a qubit coherently controlling the order of the gates in a quantum circuit Chiribella2013 . It has recently been realized experimentally Procopio2015 .\n\nIt was shown that this new resource provides a reduction in complexity to black-box queries in a problem for which the optimal quantum algorithm with fixed order between the gates requires a number of queries that scales as Araujo2014_PRL . The quantum switch is also useful in communication complexity; a task has been found for which the quantum switch yields an increase in the success probability, yet no advantage in the asymptotic scaling of the communication complexity was found Feix2015 . Most generally, no information processing task is known for which the quantum switch (or any other causally indefinite resource) would provide an exponential advantage over causal quantum (or classical) algorithms.\n\nHere we find a tripartite communication complexity task for which there is an exponential separation in communication complexity between the protocol using the quantum switch and any causally ordered quantum communication scheme. The task requires no promise on inputs and is inspired by the problem of deciding whether a pair of unitary gates commute or anticommute, which can be solved by the quantum switch with only one query of each unitary Chiribella2012 . If the parties are causally ordered, the number of qubits that needs to be communicated to accomplish the task scales linearly with the number of input bits, whereas the protocol based on the quantum switch only requires logarithmically many communicated qubits. This shows that causally indefinite quantum resources can provide an exponential advantage over causally ordered quantum resources (i.e., entanglement and one-way quantum channels).\n\nThe tripartite causally ordered communication scenario we consider in this paper is illustrated in Fig. 1. Alice and Bob are respectively given inputs and , taken from finite sets , . There is a third party, Charlie, whose goal is to calculate a binary function of Alice’s and Bob’s inputs, while minimizing the amount of communication between all three parties. We shall first assume that communication is one-way only: from Alice to Bob and from Bob to Charlie. Furthermore, we grant the parties access to unrestricted local computational power and unrestricted shared entanglement. We will also consider bounded error communication, in which the protocol must succeed on all inputs with an error probability smaller than .\n\nIn quantum communication, the parties communicate with each other by sending quantum systems. Conditionally on their inputs, the parties may apply general quantum operations to the received system, and then send this system out. We require that the parties’ local laboratories receive a system only once from the outside environment. We impose this requirement to exclude sequential communication, in which the parties communicate back and forth by sending quantum systems to each other at different time steps. Alice’s laboratory has an input and output quantum state, consisting of and qubits, respectively; similar notation is used for Bob’s and Charlie’s systems. We seek to succeed at the communication task on all inputs with error probability lower than , while minimizing the number of communicated qubits . The optimal causally ordered strategy is for Bob to calculate and then communicate the result to Charlie using one bit of communication; in this case is a good lower bound for .",
null,
"Figure 1: Causally ordered quantum communication complexity scenario. Conditionally on their inputs x and y, Alice sends a state ρx to Bob, who then applies a CP map By and sends the system to Charlie. The unlimited entanglement shared between the parties is represented by |Ψ⟩. The optimal causally ordered protocol is the one that minimizes the number of qubits in ρx (which is a lower bound for the communication complexity of the task)\n\nThe communication complexity of any causally ordered tripartite communication complexity task can be bounded by considering the bipartite task obtained by identifying Bob and Charlie as a single party. Bearing this in mind, we prove a tight lower bound on the quantum communication complexity of an important family of one-way bipartite deterministic (error probability ) communication tasks, which in turn implies a lower bound on the communication complexity of causally ordered tripartite tasks. This result appears in Theorem 5 of Ref. Klauck2000 , but we present a different proof here.\n\n###### Lemma 1\n\nFor deterministic one-way evaluation of any binary distributed function such that , with , for which , the minimum Hilbert space dimension of the system sent between two parties sharing an arbitrary amount of entanglement is . Equivalently, the minimum number of communicated qubits is .\n\n• We recall a well-known result of quantum information Hausladen1996 , establishing that if Alice and Bob share unlimited entanglement, the largest number of orthogonal (perfectly distinguishable) states that Alice can transmit to Bob by sending a -dimensional system is . Therefore, they can deterministically compute if Alice sends a system of Hilbert space dimension .\n\nSuppose by way of contradiction that the Hilbert space dimension of the communicated system is only . The maximal number of orthogonal states that can be transmitted by Alice to Bob is . Therefore, there exist inputs such that the corresponding states , transmitted to Bob are not orthogonal, and thus not perfectly distinguishable NielsenChuang . By our assumption about the function , there exists an input such that . Therefore, if Bob receives the input , he will need to distinguish between and in order to output the function correctly, but this cannot be done with zero error probability.\n\nThe previous lemma establishes that for a very large class of deterministic communication complexity tasks, it is necessary for Alice to communicate all of her input to Bob. In these cases, the only advantage achieved by causal one-way quantum communication is a reduction by a constant factor of two due to dense coding Bennett1992 . An important example of this form is the Inner Product game Cleve1998 ; Nayak2002 . Note that Lemma 1 does not apply to relational tasks such as the hidden matching problem Bar-Yossef2004 , for which there is an exponential separation between quantum and classical communication complexity.",
null,
"Figure 2: Communication complexity setup using the quantum switch. A qubit in the state 1√2(|0⟩c+|1⟩c) coherently controls the path taken by a system of N qubits in initial state |ψ⟩t. One path goes first through Alice’s lab and then Bob’s, while the other path goes first through Bob’s lab and then Alice’s. Alice and Bob are given classical inputs x∈X, y∈Y, and Charlie (using the control qubit) computes a binary function of their inputs f(x,y)\n\nWe now seek to establish a communication complexity task for which indefinite causal order can be used as a resource. In the following we assume that the parties have local laboratories, and that they receive a quantum system from the environment only once. They then perform a general quantum operation on their system, and send it out. An example of a noncausally ordered process is the quantum switch Chiribella2013 , whose use in the context of communication complexity is shown in Fig. 2. Charlie is in the causal future of both Alice and Bob, and an ancilla qubit coherently controls the causal ordering of Alice and Bob; both the target state and the control qubit are prepared externally. Assume that Alice and Bob apply unitary gates and to their respective input systems of qubits. The global unitary describing the evolution of the system from Charlie’s point of view is\n\n V(UA,UB)=|0⟩⟨0|c⊗(UBUA)t+|1⟩⟨1|c⊗(UAUB)t, (1)\n\nwhere the index denotes the control qubit, and the unitaries and act on the target Hilbert space of qubits.\n\nUsing the quantum switch, one can determine whether two unitaries , commute or anticommute with a single query of each unitary, while at least one unitary must be queried twice in the causally ordered case Chiribella2012 . Explicitly, consider the quantum switch with the control qubit initially in state and with initial target state . If and apply local unitaries and , the resulting state after applying is\n\n 1√2(|0⟩c⊗UBUA|ψ⟩t+|1⟩c⊗UAUB|ψ⟩t). (2)\n\nIf Charlie subsequently applies a Hadamard gate to the control qubit, the resulting state is\n\n 12(|0⟩c⊗{UA,UB}|ψ⟩t−|1⟩c⊗[UA,UB]|ψ⟩t). (3)\n\nSuppose that Alice and Bob randomly choose unitaries from a set and that there exists a state such that , either or . Then Eq. (3) shows that the quantum switch with initial target state and control qubit as inputs allows Charlie to discriminate between these two possibilities with certainty by measuring the control qubit in the computational basis.\n\nWe now define a communication complexity task, the Exchange Evaluation game , for any integer . In this game, Alice and Bob are respectively given inputs , where is the set of functions over that evaluate to zero on the zero vector\n\n Fn={f:Zn2→Z2|f(0)=0}. (4)\n\nCharlie must output\n\n EEn(x,f,y,g)=f(y)⊕g(x), (5)\n\nwhere the symbol denotes addition modulo 2. This game can be interpreted as the sum modulo 2 of two parallel random access codes Ambainis1999 .\n\nWe first construct an encoding of the inputs in terms of local -qubit unitaries that all commute or anticommute; we then use the previous observation to conclude that the switch succeeds deterministically at this task with qubits of communication. We start with some definitions. The group of Pauli operators on qubits is defined as\n\n X(x)=Xx11⊗Xx22⊗⋯⊗Xxnn, (6)\n\nwhere is the th component of the binary vector . Here, is the single qubit Pauli -operator acting on the th qubit, and is the single qubit identity matrix.\n\nWe associate to every a diagonal matrix\n\n D(f)=∑z∈Zn2(−1)f(z)|z⟩⟨z|, (7)\n\nwhere is the state such that , with the single qubit Pauli operator acting on qubit . The set consists of all diagonal matrices with entries in the computational basis, such that the first entry is .\n\nWe define the set of unitaries\n\n Un={X(x)D(f)|(x,f)∈Zn2×Fn}, (8)\n\nwhich has dimension\n\n |Un|=22n+n−1. (9)\n\nThis superexponential scaling of is essential to establish a communication advantage with the quantum switch. Also note that\n\n X(x)D(f)X(y)D(g)|0⟩=(−1)f(y)|x⊕y⟩. (10)\n\nTherefore, when acting on the -qubit input state , the elements of all commute or anticommute with each other, and\n\n [X(x)D(f),X(y)D(g)]|0⟩ =0,if(−1)f(y)=(−1)g(x) {X(x)D(f),X(y)D(g)}|0⟩ =0,if(−1)f(y)=(−1)g(x)+1.\n\nTherefore, the game is equivalent to determining whether the corresponding unitaries and commute or anticommute when applied to the state . By the discussion following Eq. (3), this problem can be solved deterministically by Charlie using the quantum switch with qubits of communication from Alice to Bob, with a strategy consisting of applying the unitary corresponding to their input according to Eq. 8.\n\nWe now show that the Exchange Evaluation game satisfies the conditions of Lemma 1; this will allow us to conclude that for deterministic () evaluation in the one-way causally ordered case, requires an amount of communicated qubits that grows exponentially with .\n\n###### Proposition 2\n\nFor every , such that , there exists such that .\n\n• First note that if and only if\n\n f1(y)⊕f2(y)⊕g(x1)⊕g(x2)=1. (11)\n\nThen, since , either or holds. We check that the conditions of the lemma are satisfied in both cases.\n\n### (i) Case where x1≠x2:\n\nSuppose without loss of generality that and define as the function such that and . Also, because , . Therefore, the function we just defined and satisfy Eq. (11).\n\n### (ii) Case where f1≠f2:\n\nLet be a vector for which and differ, so that . Then this and the zero function satisfies Eq. (11).\n\nAccording to Eq. (9), the dimension of the set of inputs to is . Direct application of Proposition 2 with Lemma 1 establishes that the number of qubits of communication required for deterministic success in the causally ordered case is\n\nNote that with two-way (classical) communication, it is possible to solve the Exchange Evaluation game with bits of communication, simply by having Alice and Bob send their vectors , to the other party, followed by local evaluation of and by the parties and communication of the result to Charlie. We emphasize that once we allow two-way communication, the quantum advantage can also disappear in traditional quantum communication complexity (comparing causally ordered quantum communication with classical communication): this is the case for the distributed Deutsch-Jozsa problem Buhrman1998 , but not for Raz’s problem Klartag2011 .\n\nFor causally ordered communication complexity tasks, the exponential quantum-classical separation does not always continue to hold when allowing for protocols to have a small but nonzero error probability . Indeed, looking at early examples of tasks, the advantage disappears for the distributed Deutsch-Jozsa problem Buhrman1998 , while it remains for Raz’s problem Raz1999 . We prove in the Appendix that the one-way quantum communication complexity with bounded error for scales as , and thus that the exponential separation in communication complexity due to superposition of causal ordering persists when allowing for a nonzero error probability.\n\nTo show that it is possible to operationally distinguish quantum control of causal order from two-way communication one could introduce counters at the output ports of Alice’s and Bob’s laboratories, whose role is to count the number of uses of the channels. Such an argument has already been made in Ref. Araujo2014_PRL to justify a computational advantage. We can model a counter as a qutrit initially in the state , whose evolution when a system exits the laboratory is , where . Then, for both one-way communication and the quantum switch, the counters of Alice and Bob will be in the state at the end of the protocol; for genuine two-way communication, at least one of these counters will be in the final state . Therefore, the expectation value of the observables for the counters allows us to distinguish realizations of the quantum switch, such as Procopio2015 , from two-way quantum communication.\n\nIn conclusion, we have found a communication complexity task, the Exchange Evaluation game, for which a quantum superposition of the direction of communication — the quantum switch — results in an exponential saving in communication when compared to causally ordered quantum communication. An interesting feature of this game is that it is not a promise game, as are most known tasks for which quantum resources have an exponential advantage Buhrman2010 .\n\nIn future work, it would be interesting to explore other information processing tasks for which the quantum switch – or other causally indefinite processes – may yield interesting advantages. For example, one could look at the uses of the quantum switch for secure distributed computation Yao1982 ; Lo1997 ; Buhrman2012 ; Liu2013 . Indeed, imagine that Alice and Bob both want to learn about the value of , in such a way that the other party does not learn about their inputs. They could achieve this goal by enlisting a third party and using the quantum switch with the protocol.\n\nWe thank Ashley Montanaro for pointing out Ref. Klauck2000 to us, used to establish the bounded-error advantage. We acknowledge support from the European Commission project RAQUEL (No. 323970); the Austrian Science Fund (FWF) through the Special Research Programme FoQuS, the Doctoral Programme CoQuS and Individual Project (No. 2462), and the John Templeton Foundation. P. A. G. is also supported by FQRNT (Quebec).\n\n## Appendix A VC-dimension bounds on the bounded error one-way quantum communication complexity\n\nIn this section we show that if the protocol allows for some error probability, bounded by for all inputs, the one-way communication complexity of still scales as . As in Fig. 1, we assume that Alice and Bob share unlimited prior entanglement, and that Alice sends a quantum state to Bob. We note that under the promise that Bob’s input function is the zero function , the Exchange Evaluation game reduces to a random access code , for which optimal bounds on the bounded error communication complexity are known . However, it is more straightforward to apply a bound that uses the concept of VC-dimension .\n\n• VC-dimension. Let . A subset is shattered, if such that\n\n f(x,y)={1,if y∈R.0,if y∈S∖R. (12)\n\nThe VC-dimension is the size of the largest shattered subset of .\n\nGiven a function , we denote by the one-way (from Alice to Bob) bounded error quantum communication, where is the allowed worst-case error, and arbitrary prior shared entanglement is available. We make use of a theorem by Klauck (Theorem 3 of ) that relates the bounded error quantum communication complexity of a function to its VC-dimension.\n\n###### Theorem 3\n\nFor all functions , , where is the binary entropy\n\nLet us bound the VC-dimension of , where , by showing that is shattered. This is clear, since for any , there exists the indicator function\n\n fR(y)={1,if (y,0)∈R.0,otherwise, (13)\n\nso that is shattered.\n\nTherefore , and Theorem 3 implies that the one-way quantum communication complexity . This establishes that the number of communicated qubits scales exponentially with even in the bounded error case, so that the exponential separation between the quantum switch and one-way quantum communication continues to hold."
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https://thekidsworksheet.com/molarity-worksheet-with-answers-pdf/ | [
"",
null,
"# Molarity Worksheet With Answers Pdf\n\nDetermine the mole fractions of each substance. Calculate the molarity of 0 289 moles of fecl 3 dissolved in 120 ml of solution.",
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"Molarity Worksheet Customizable And Printable With Images Teaching Chemistry Chemistry Worksheets Chemistry Classroom\n\n### Calculate molarity by dissolving 25 0g naoh in 325 ml of solution.",
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"Molarity worksheet with answers pdf. Work in groups on these problems. The molality of an aqueous solution of sugar c12h22o11 is 1 62m. To make a 4 00 m solution how many moles of solute will be needed if 12 0 liters of solution are required.\n\nMolarity problems. What is the molarity of a 0 30 liter solution containing 0 50 moles of nacl. Molarity problems worksheet m n n moles v v must be in liters change if necessary use m or mol l as unit for molarity 1.\n\nThe answers on the key are presented with the correct number of significant figures based on the significant figures in the volume and solute measurements. Show all work and circle your final answer. How many grams of potassium nitrate are required to prepare 0 250 l of a 0 700 m solution.\n\nMolarity worksheet w 331 everett community college student support services program what is the molarity of the following solutions given that. Calculate molarity if 25 0 ml of 1 75 m hcl diluted to 65 0 ml. 3 47 l 3 what is the concentration of an aqueous solution with a volume of 450 ml.\n\nYou should try to answer the questions without referring to your textbook. Molarity practice problems answer key 1 how many grams of potassium carbonate are needed to make 200 ml of a 2 5 m solution. Calculate the mole fractions of sugar and water.\n\n1 1 0 moles of potassium fluoride is dissolved to make 0 10 l of solution. Experiencing listening to the new experience adventuring studying training and. Molarity worksheet 2 identifiera what does molarity mean.\n\n4 53 mol lino 3 1 59 m lin0 3. Mol hno 3 12 6 g hno 3 1 mol hno 3 63 0 g hno 3 0 200 mol hno 3 m 0 200 mol hno 3 1 0 l 0 200 m 4. File type pdf molarity ph worksheet with answers molarity ph worksheet with answers page 1 3.\n\nWhat is the molarity of a solution of hno. 69 1 grams 2 how many liters of 4 m solution can be made using 100 grams of lithium bromide. Calculate grams of solute needed to prepare 225 ml of.\n\nWhat is the molarity of a solution of hno 3 that contains 12 6 grams hno 3 in 1 0 l of solution. After the worksheet is customized you can print or download it as a pdf in us letter or a4 format. 0 700 m moles of solute 0 250 l moles of.\n\nWhat is the molarity of a solution that contains 4 53 moles of lithium nitrate in 2 85 liters of solution. Mole fraction molality worksheet name. Each worksheet includes a matching answer key with the pdf.\n\nFile type pdf molarity ph worksheet with answers inspiring the brain to think better and faster can be undergone by some ways. Number of moles of solute. 2 1 0 grams of potassium fluoride is dissolved to make 0 10 l of solution.\n\nIf you get stuck try asking another group for help. A solution is prepared by mixing 100 0 g of water h2o and 100 0 g of ethanol c2h5oh. How many moles of sucrose are dissolved in 250 ml of solution if the solution concentration is 0 150 m.",
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.7820588,"math_prob":0.7377858,"size":5004,"snap":"2022-40-2023-06","text_gpt3_token_len":1119,"char_repetition_ratio":0.202,"word_repetition_ratio":0.050724637,"special_character_ratio":0.2116307,"punctuation_ratio":0.04587156,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9870126,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44],"im_url_duplicate_count":[null,2,null,2,null,null,null,2,null,2,null,2,null,null,null,null,null,null,null,2,null,null,null,2,null,null,null,2,null,2,null,null,null,4,null,4,null,null,null,null,null,1,null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-09-26T19:53:57Z\",\"WARC-Record-ID\":\"<urn:uuid:6b100a64-cd40-4739-afd1-acf3a83979e8>\",\"Content-Length\":\"113716\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:eef75d4c-ab00-4285-855a-808f27e33a19>\",\"WARC-Concurrent-To\":\"<urn:uuid:ad3952ff-69dc-4ff8-9e72-20c8605e3cd9>\",\"WARC-IP-Address\":\"172.67.144.98\",\"WARC-Target-URI\":\"https://thekidsworksheet.com/molarity-worksheet-with-answers-pdf/\",\"WARC-Payload-Digest\":\"sha1:YVWDBO7BN7D2BH7GP777GNQZZHEBF6N2\",\"WARC-Block-Digest\":\"sha1:73S2JJDL73HZPCOFMGZFWW3I34KX4M43\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030334915.59_warc_CC-MAIN-20220926175816-20220926205816-00063.warc.gz\"}"} |
https://myprogrammingschool.com/c-operators-learn-the-basics-of-programming-step-by-step-mps/ | [
"# C Operators Learn the Basics of Programming Step by Step – MPS\n\nContents\n\n## c operators with examples\n\nIn this tutorial, we will learn basic C operators step by step. In this C programming class, we’ll cowl all supported C operators, clarify their objectives with examples.\n\nThe operators assist in mathematical and statistical computing. Hence, please learn this tutorial with full focus.\n\nIn C programming, we might carry out many operations on variables like addition, subtraction, division, increment, decrement, and many others. And C language has many built-in operators to hold out such duties. Please see beneath.\n\n### What are Operators in C?\n\nThe operators are particular symbols that instruct the compiler to carry out a particular operation on the given variable(s).\nThere are primarily six sorts of operators. C Operators are given below:\nArithmetic Operators\nRelational Operators\nLogical Operators\nBitwise Operators\nAssignment Operators\nMiscellaneous Operators\n\nLet’s examine them out one by one.\n\n## Types of Operators Explanation\n\n### Arithmetic Operators in C\n\nThese operators are used to carry out easy arithmetic operations like addition, subtraction, product, quotient, the rest, and many others.\n\n### Relational Operators in C\n\nRelational operators are used to examine a relationship between two or more variables like ‘greater than,’ ‘less than,’ and many others. If the end result is optimistic, then the situation will succeed.\n\nThe following desk reveals some relational operators supported in C.\n\n### Logical Operators in C Programming\n\nLogical operators are used to carry out logical operations.\n\nHere are some logical operators supported in C\n\n### Bitwise Operators in C Programming\n\nBitwise operators are used to carry out operations on binary values.\n\nThis desk would enable you.\n\nNow you need to know the binary conversion of a decimal quantity. If not, this instance will enable you.\n\nLet us assume two numbers 3 and 4. Now, in binary format, they’re represented as\n\n``` 8421 //Here each ‘1’ beneath these numbers will add that worth to the quantity\n\nA = 0011 //It is for 3 it is 0+0+2+1 i.e. 3.\n\nB = 0100 //It is for 4 it is 0+1+0+0.\n\n-------\n\nA&B = 0000 //AND operation\n\nA|B = 0111 //OR operation\n\nComplement Operations :\n\n~A = ~3 = 1100 ~B = ~4 = 1011 (Just change 1 by 0 and 0 by 1)\n\nLeft Shift and Right Shift operations\n\nA<<1 = 0110 A>>1 = 0001\n\n(Just shift every binary factor to the left or proper by 1)```\n\n### Assignment Operators in C\n\nIn C programming, variables get values by utilizing the project operators.\n\nTake an instance, say, if you’ll want to assign the value “7” to a variable recognized as the “count,” then you’ll be able to do so with the following assertion.\n\n`var = 7;`\n\nThere are two subtypes of project operators in C programming.\n\n• The easy operator ( = )\n• The compound operators (+=, -=, *=, /=, %=, &=, ^=)\n\n### Miscellaneous Operators\n\nThese are some miscellaneous operators.\n\nYou might not see any applications or pattern code in this chapter as a result of we’ve got been utilizing these C operators in many of our different tutorials.\n\n## Related Posts",
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"Pramod Kumar Yadav is from Janakpur Dham, Nepal. He was born on December 23, 1994, and has one elder brother and two elder sisters. He completed his education at various schools and colleges in Nepal and completed a degree in Computer Science Engineering from MITS in Andhra Pradesh, India. Pramod has worked as the owner of RC Educational Foundation Pvt Ltd, a teacher, and an Educational Consultant, and is currently working as an Engineer and Digital Marketer.\n\n## Best PYthon Course",
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"",
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"",
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"Get More trending Courses"
] | [
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"https://d3njjcbhbojbot.cloudfront.net/api/utilities/v1/imageproxy/https://d15cw65ipctsrr.cloudfront.net/78/0b8c921b6346f69278f39ba6ca8128/Professional-Certificate---IBM-Machine-Language.png",
null,
"https://d3njjcbhbojbot.cloudfront.net/api/utilities/v1/imageproxy/https://d15cw65ipctsrr.cloudfront.net/a4/079d5e7c7b45ac9107f22bfcfeab91/Specialization-logo.png",
null,
"https://d3njjcbhbojbot.cloudfront.net/api/utilities/v1/imageproxy/https://coursera-course-photos.s3.amazonaws.com/07/887efbc26a42a9bec74f45ddb083c0/kosera_gweonyeongseon_sseomneil1.jpg",
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.8591556,"math_prob":0.91865766,"size":5888,"snap":"2023-14-2023-23","text_gpt3_token_len":1475,"char_repetition_ratio":0.16808294,"word_repetition_ratio":0.09686347,"special_character_ratio":0.26341712,"punctuation_ratio":0.098143235,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9857762,"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\":\"2023-05-30T17:50:59Z\",\"WARC-Record-ID\":\"<urn:uuid:db73ca6f-a770-4386-9e8c-245c60235d29>\",\"Content-Length\":\"170630\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:27398d2f-98b9-4c65-8838-fd09e45459d0>\",\"WARC-Concurrent-To\":\"<urn:uuid:c7a49be8-d561-43df-b91f-5688422c1e73>\",\"WARC-IP-Address\":\"34.230.232.255\",\"WARC-Target-URI\":\"https://myprogrammingschool.com/c-operators-learn-the-basics-of-programming-step-by-step-mps/\",\"WARC-Payload-Digest\":\"sha1:ZHQNTWLKSGPTPQZIGJFYEWPIC5V4XSCS\",\"WARC-Block-Digest\":\"sha1:RSR6MTHZ6PACO7TDINRFFXJYHRH4MU3C\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224646076.50_warc_CC-MAIN-20230530163210-20230530193210-00561.warc.gz\"}"} |
https://pattern-making-calculator.software.informer.com/ | [
"",
null,
"# Pattern-Making Calculator1.0\n\nFree\nConvert decimal fractions to simple fractions and more\n\nPattern-Making Calculator is a program designed to allow you to make simple calculations such as additions, subtractions, divisions or percentage; to more complex operations such as to convert decimals into fractions or from cm to inches and vice-versa. If you want to make a simple operation, e.g., an addition, you type the first number, then click the + button, then enter the new number and press =. So far, this can be done by any calculator, but when it comes to more complicated operations, this calculator comes handy, e.g., for those using the Imperial measurement system, since it is easier to represent a fraction than a decimal, e.g., you want to represent a decimal fraction 8.5 in a simple fraction, all you have to do is enter the decimal fraction and then the calculator will show you the simple fraction, 8½. Moreover you can convert from cm. to inches in a simple and fast way. Apart from this, the Radius of a circumference can be calculated. Either you want to calculate the full, 3/4, half, or quarter of a circle, all you have to do is type in the full length of the perimeter and click on the buttons which are located on the right of the calculator and which are represented by a full circle, 3/4 of a circle, half a circle, or quarter of a circle. This tool is very helpful for many people who make patterns using the Imperial measurement system.\n\n### Review summary\n\nPros\n\n• Big buttons help a lot\n\nCons\n\n• Its usage is very specific, and the help file could be difficult to understand for newcomers\nInfo updated on:\n\n•",
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"Surface Area Calculator\n•",
null,
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null,
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null,
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null,
"Gabe's TypOmeter\n•",
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] | [
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.92812306,"math_prob":0.9618347,"size":1605,"snap":"2021-21-2021-25","text_gpt3_token_len":353,"char_repetition_ratio":0.12866957,"word_repetition_ratio":0.014285714,"special_character_ratio":0.21619938,"punctuation_ratio":0.13213213,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9863845,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-05-18T07:11:10Z\",\"WARC-Record-ID\":\"<urn:uuid:512f658c-a9fc-4c7a-a592-0a31bcda5588>\",\"Content-Length\":\"81075\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c08b988f-69aa-4541-aa41-d1bbc550c042>\",\"WARC-Concurrent-To\":\"<urn:uuid:4ce67648-d524-49d4-b15c-b29a1150599b>\",\"WARC-IP-Address\":\"100.25.93.238\",\"WARC-Target-URI\":\"https://pattern-making-calculator.software.informer.com/\",\"WARC-Payload-Digest\":\"sha1:NBMQNB2MN3QZQLM3YI5B4G2QGSR7O66J\",\"WARC-Block-Digest\":\"sha1:NZ3AZQW77BMUHYJEPMKE4O2GBIWY6X5O\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-21/CC-MAIN-2021-21_segments_1620243989756.81_warc_CC-MAIN-20210518063944-20210518093944-00022.warc.gz\"}"} |
https://www.arxiv-vanity.com/papers/1104.3051/ | [
"arXiv Vanity renders academic papers from arXiv as responsive web pages so you don’t have to squint at a PDF. Read this paper on arXiv.org.\n\n# Time Reversal Invariance Violation in Neutron Deuteron Scattering\n\nYoung-Ho Song Department of Physics and Astronomy, University of South Carolina, Columbia, SC, 29208 Rimantas Lazauskas IPHC, IN2P3-CNRS/Université Louis Pasteur BP 28, F-67037 Strasbourg Cedex 2, France Vladimir Gudkov Department of Physics and Astronomy, University of South Carolina, Columbia, SC, 29208\nJune 19, 2020\n###### Abstract\n\nTime reversal invariance violating (TRIV) effects for low energy elastic neutron deuteron scattering are calculated for meson exchange and EFT-type of TRIV potentials in a Distorted Wave Born Approximation, using realistic hadronic strong interaction wave functions, obtained by solving three-body Faddeev equations in configuration space. The relation between TRIV and parity violating observables are discussed.\n\n###### pacs:\n24.80.+y, 25.10.+s, 11.30.Er, 13.75.Cs\n\n## I Introduction\n\nA search for Time Reversal Invariance Violation (TRIV) in nuclear physics has been a subject of experimental and theoretical investigation for several decades. It has covered a large variety of nuclear reactions and nuclear decays with T-violating parameters which are sensitive to either CP-odd and P-odd (or T- and P-violating) interactions or T-violating P-conserving (C-odd and P-even) interactions. There are a number of advantages of the search for TRIV in nuclear processes. The main advantage is the possibility of enhancement of T-violating observables by many orders of a magnitude due to complex nuclear structure (see, i.e. paper Gudkov (1992) and references therein). Another advantage to be mentioned is the availability of many systems with T-violating parameters which provides assurance to have enough observations against possible ‘‘accidental’’ cancellation of T-violating effects due to unknown structural factors related to strong interactions. Taking into account that different models of CP-violation may contribute differently to a particular T/CP-observable 111For example, QCD -term can contribute to neutron EDM, but cannot be observed in -meson decays. On the other hand, the CP-odd phase of Cabibbo-Kobayashi-Maskawa matrix was measured in -meson decays, but its contribution to neutron EDM is extremely small and beyond the reach with the current experimental accuracy., which may have unknown theoretical uncertainties, TRIV nuclear processes shall provide complementary information to electric dipole moments (EDM) measurements.\n\nOne promising approach for a search for TRIV in nuclear reactions is a measurement of TRIV effects in transmission of polarized neutron through polarized target. These effects could be measured at new spallation neutron facilities, such as the SNS at the Oak Ridge National Laboratory or the J-SNS at J-PARC, Japan. It was shown that these TRIV effects can be enhanced Bunakov and Gudkov (1983) by a factor of . Similar enhancement factors have been observed for parity violating effects in neutron scattering. In contrast to the parity violating (PV) case, the enhancement of TRIV effects lead not only to the opportunity to observe T violation, but also to select models of CP-violation based on the values of observed parameters. However, existing estimates of CP-violating effects in nuclear reactions have at least one order of magnitude of accuracy, or even worse. In this relation, it is interesting to compare the calculation of TRIV effects in complex nuclei with the calculations of these effects in simplest few body systems, which could be useful for clarification of influence of nuclear structure on values of TRIV effects. Therefore, as a first step to many body nuclear effects, we study TRIV and parity violating effects in one of the simplest available nuclear process, namely elastic neutron-deuteron scattering.\n\nWe treat TRIV nucleon-nucleon interactions as a perturbation, while non-perturbed three-body wave functions are obtained by solving Faddeev equations for realistic strong interaction Hamiltonian, based on AV18+UIX interaction model. For description of TRIV potentials, we use both meson exchange model and effective field theory (EFT) approach.\n\n## Ii Observables\n\nWe consider TRIV and PV effects related to correlation, where is the neutron spin, is the target spin, and is the neutron momentum, which can be observed in the transmission of polarized neutrons through a target with polarized nuclei. This correlation leads to the difference Stodolsky (1982) between the total neutron cross sections for parallel and anti-parallel to , which is\n\n Δσ⧸T⧸P=4πpIm(f+−f−), (1)\n\nand neutron spin rotation angle Kabir (1982) around the axis\n\n dϕ⧸T⧸Pdz=−2πNpRe(f+−f−). (2)\n\nHere, are the zero angle scattering amplitudes for neutrons polarized parallel and anti-parallel to the axis, respectively, is the target length, and is a number of target nuclei per unit volume. It should be noted that these two parameters cannot be simulated by final state interactions (see, for example Gudkov (1992) and references therein), therefore, their measurements are an unambiguous test of violation of time reversal invariance similar to the case of neutron electric dipole moment.\n\nThe scattering amplitudes can be represented in terms of matrix which is related to scattering matrix as . We define matrix element , where unprimed and primed parameters correspond to initial and final states, is an orbital angular momentum between neutron and deuteron, is a sum of neutron spin and deuteron total angular momentum, and is the total angular momentum of the neutron-deuteron system. For low energy neutron scattering, one can consider only - and -wave contributions, which leads to the following expressions for the TRIV parameters\n\n 1Ndϕ⧸T⧸Pdz = −π2p2Re[√2R12012,132−√2R12132,012+2R32032,112−2R32112,032], (3)\n Δσ⧸T⧸P = πp2Im[√2R12012,132−√2R12132,012+2R32032,112−2R32112,032]. (4)\n\nThe symmetry violating -matrix elements can be calculated with a high level of accuracy in Distorted Wave Born Approximation (DWBA) as\n\n RJl′S′,lS≃4i−l′+l+1μp(−)⟨Ψ,(l′S′)JJz|V⧸T⧸P|Ψ,(lS)JJz⟩(+), (5)\n\nwhere is a neutron-deuteron reduced mass, is TRIV nucleon-nucleon potential, and are solutions of 3-body Faddeev equations in configuration space for strong interaction Hamiltonian satisfying outgoing (incoming) boundary condition. The factor in this expression is introduced to match the -matrix definition in the modified spherical harmonics convention Varshalovich et al. (1988) with the wave functions in spherical harmonics convention used for wave-functions calculations. The matrix elements of TRIV potential in spherical harmonics convention are symmetric and -matrix in modified spherical harmonics convention is antisymmetric under the exchange between initial and final states.\n\nFor calculations of wave-functions, we used jj-coupling scheme instead of coupling scheme. We can relate -matrix elements in coupling scheme to jj-coupling scheme using unitary transformation (see, for example Song et al. (2011))\n\n |[ly⊗(sk⊗jx)S]JJz⟩ = ∑jy|[jx⊗(ly⊗sk)jy]JJz⟩ (6)\n\nThen,\n\n R12132,012=2√23R12112,012−13R12132,012,R32112,032=−23R32112,012−√53R32132,012 (7)\n\nwhere, is a R-matrix in -basis.\n\n## Iii Time reversal violating potentials\n\nThe most general form of time reversal violating and parity violating part of nucleon-nucleon Hamiltonian in first order of relative nucleon momentum can be written as the sum of momentum independent and momentum dependent parts, Herczeg (1966),\n\n H⧸T⧸Pstat = g1(r)σ−⋅^r+g2(r)τ1⋅τ2σ−⋅^r+g3(r)Tz12σ−⋅^r (8) +g4(r)τ+σ−⋅^r+g5(r)τ−σ+⋅^r\n H⧸T⧸Pnon−static = (g6(r)+g7(r)τ1⋅τ2+g8(r)Tz12+g9(r)τ+)σ×⋅¯pmN (9) +(g10(r)+g11(r)τ1⋅τ2+g12(r)Tz12+g13(r)τ+) ×(^r⋅σ×^r⋅¯pmN−13σ×⋅¯pmN) +g14(r)τ−(^r⋅σ1^r⋅(σ2ׯpmN)+^r⋅σ2^r⋅(σ1ׯpmN)) +g15(r)(τ1×τ2)zσ+⋅¯pmN +g16(r)(τ1×τ2)z(^r⋅σ+^r⋅¯pmN−13σ+⋅¯pmN),\n\nwhere exact form of depends on the details of particular theory. Here, we consider three different approaches for description of TRIV interactions: meson exchange model, pionless EFT, and pionful EFT.\n\nTRIV meson exchange potential in general involves exchanges of pions (, MeV), -mesons(, MeV), and - and -mesons (, MeV). To derive this potential, we use strong and TRIV Lagrangians, which can be written as Herczeg ; Liu and Timmermans (2004)\n\n Lst = gπ¯Niγ5τaπaN+gη¯Niγ5ηN (10) −gρ¯N(γμ−iχV2mNσμνqν)τaρaμN −gω¯N(γμ−iχS2mNσμνqν)ωμN,\n L⧸T⧸P = ¯N[¯g(0)πτaπa+¯g(1)ππ0+¯g(2)π(3τzπ0−τaπa)]N (11) +¯N[¯g(0)ηη+¯g(1)ητzη]N +¯N12mN[¯g(0)ρτaρaμ+¯g(1)ρρ0μ+¯g(2)(3τzρ0μ−τaρaμ)]σμνqνγ5N +¯N12mN[¯g(0)ωωμ+¯g(1)ωτzωμ]σμνqνγ5N,\n\nwhere , and are iso-vector and scalar magnetic moments of a nucleon ( and ), and are TRIV meson-nucleon coupling constants. Further, we use the following values for strong couplings constants: , , , .\n\nMeson exchange models from these Lagrangians lead to TRIV potential\n\n V⧸T⧸P = ⎡⎣−¯g(0)ηgη2mNm2η4πY1(xη)+¯g(0)ωgω2mNm2ω4πY1(xω)⎤⎦σ−⋅^r +⎡⎣−¯g(0)πgπ2mNm2π4πY1(xπ)+¯g(0)ρgρ2mNm2ρ4πY1(xρ)⎤⎦τ1⋅τ2σ−⋅^r +⎡⎣−¯g(2)πgπ2mNm2π4πY1(xπ)+¯g(2)ρgρ2mNm2ρ4πY1(xρ)⎤⎦Tz12σ−⋅^r +⎡⎣−¯g(1)πgπ4mNm2π4πY1(xπ)+¯g(1)ηgη4mNm2η4πY1(xη)+¯g(1)ρgρ4mNm2ρ4πY1(xρ)+¯g(1)ωgω2mNm2ω4πY1(xω)⎤⎦τ+σ−⋅^r +⎡⎣−¯g(1)πgπ4mNm2π4πY1(xπ)−¯g(1)ηgη4mNm2η4πY1(xη)−¯g(1)ρgρ4mNm2ρ4πY1(xρ)+¯g(1)ωgω2mNm2ω4πY1(xω)⎤⎦τ−σ+⋅^r,\n\nwhere , , .\n\nComparing eq. (8) with this potential, one can see that functions in meson exchange model are defined as\n\n gME1(r) = −¯g(0)ηgη2mNm2η4πY1(xη)+¯g(0)ωgω2mNm2ω4πY1(xω) gME2(r) = −¯g(0)πgπ2mNm2π4πY1(xπ)+¯g(0)ρgρ2mNm2ρ4πY1(xρ) gME3(r) = −¯g(2)πgπ2mNm2π4πY1(xπ)+¯g(2)ρgρ2mNm2ρ4πY1(xρ) gME4(r) = −¯g(1)πgπ4mNm2π4πY1(xπ)+¯g(1)ηgη4mNm2η4πY1(xη)+¯g(1)ρgρ4mNm2ρ4πY1(xρ)+¯g(1)ωgω2mNm2ω4πY1(xω) gME5(r) = −¯g(1)πgπ4mNm2π4πY1(xπ)−¯g(1)ηgη4mNm2η4πY1(xη)−¯g(1)ρgρ4mNm2ρ4πY1(xρ)+¯g(1)ωgω2mNm2ω4πY1(xω),\n\nFor TRIV potentials in pionless EFT potential, these functions are\n\n gπ/1(r) = cπ/12mNddrδ(3)(r)→−cπ/1μ22mNμ24πY1(μr) gπ/2(r) = cπ/22mNddrδ(3)(r)→−cπ/2μ22mNμ24πY1(μr) gπ/3(r) = cπ/32mNddrδ(3)(r)→−cπ/3μ22mNμ24πY1(μr) gπ/4(r) = cπ/42mNddrδ(3)(r)→−cπ/4μ22mNμ24πY1(μr) gπ/5(r) = cπ/52mNddrδ(3)(r)→−cπ/5μ22mNμ24πY1(μr), (14)\n\nwhere low energy constants (LECs) of pionless EFT have the dimension . In our calculations with this potential, we use Yukawa function (, where ) with regularization scale , instead of singular in paper Liu and Timmermans (2004).\n\nThe pionful EFT acquire long range terms due to the one pion exchange in addition to the short range term expressions equivalent to ones provided by the pionless EFT. Then, ignoring two pion exchange contributions at the middle range and higher order corrections, one can write functions for the pionful EFT as\n\n gπ1(r) = −cπ1μ22mNμ24πY1(μr) gπ2(r) = −cπ2μ22mNμ24πY1(μr)−¯g(0)πgπ2mNm2π4πY1(xπ) gπ3(r) = −cπ3μ22mNμ24πY1(μr)−¯g(2)πgπ2mNm2π4πY1(xπ) gπ4(r) = −cπ4μ22mNμ24πY1(μr)−¯g(1)πgπ4mNm2π4πY1(xπ) gπ5(r) = −cπ5μ22mNμ24πY1(μr)−¯g(1)πgπ4mNm2π4πY1(xπ). (15)\n\nFor this potential, the cutoff scale is larger than pion mass, because pion is a degree of freedom of the theory. Therefore, in general magnitudes of LECs and their scaling behavior, as a function of a cutoff parameter , are different from ones.\n\nOne can see that all these three potentials which come from different approaches have exactly the same operator structure. The only difference between them is related in different scalar function multiplied by each operator, which, in turn, defer only by different scales of characteristic masses: , , , and . Therefore, to unify notations, it is convenient to define new constants (of dimension of ) and scalar function (of dimension of ) as\n\n gn(r)≡∑aCanfan(r), (16)\n\nwhere the form of and can be read from eq. (III), (III) and (III).\n\nSince non-static TRIV potentials, with , do not appear either in meson exchange model or in the lowest order EFTs, they can be considered as a higher order correction to the lowest order EFT or related to heavy meson contributions in the meson exchange model. Nevertheless, for a completeness of consideration, we estimate the contributions of these operators using functions with proper mass scales.\n\n## Iv Calculation of TRIV amplitudes\n\nThe non-perturbed (parity conserving) 3-body wave functions for neutron-deuteron scattering are obtained by solving Faddeev equations (also often called Kowalski-Noyes equations) in configuration space Faddeev (1961); Lazauskas and Carbonell (2004). The wave function in Faddeev formalism is a sum of three Faddeev components,\n\n Ψ(x,y)=ψ1(x1,y1)+ψ2(x2,y2)+ψ3(x3,y3). (17)\n\nIn a particular case of three identical particles (this becomes formally true for three-nucleon system in the isospin formalism), three Faddeev equations (components) become formally identical. By accommodating the three-nucleon force, which under nucleon permutation might be expressed as a symmetric sum of three terms: Faddeev equations read:\n\n (E−H0−Vij)ψk=Vij(ψi+ψj)+12(Vijk+Vjki)Ψ (18)\n\nwhere are particle indices, is kinetic energy operator, is two body force between particles , and , and is Faddeev component.\n\nUsing relative Jacobi coordinates and , one can expand these Faddeev components in bipolar harmonic basis:\n\n ψk=∑αFα(xk,yk)xkyk∣∣∣(lx(sisj)sx)jx(lysk)jy⟩JM⊗∣∣(titj)txtk⟩TTz, (19)\n\nwhere index represents all allowed combinations of the quantum numbers presented in the brackets: and are the partial angular momenta associated with respective Jacobi coordinates, and are the spins and isospins of the individual particles. Functions are called partial Faddeev amplitudes. It should be noted that the total angular momentum as well as its projection are conserved, but the total isospin of the system is not conserved due to the presence of charge dependent terms in nuclear interactions.\n\nBoundary conditions for Eq. (18) can be written in the Dirichlet form. Thus, Faddeev amplitudes satisfy the regularity conditions:\n\n Fα(0,yk)=Fα(xk,0)=0. (20)\n\nFor neutron-deuteron scattering with energies below the break-up threshold, Faddeev components vanish for . If , then interactions between the particle and the cluster are negligible, and Faddeev components and vanish. Then, for the component , which describes the plane wave of the particle with respect to the bound particle pair ,\n\n limyk→∞ψk(xk,yk)lnjn = (21) ×i2[δl′nj′n,lnjnh−l′n(prnd)−Sl′nj′n,lnjnh+l′n(prnd)],\n\nwhere deuteron, being formed from nucleons and , has quantum numbers , , and , and its wave function is normalized to unity. Here, is the relative distance between neutron and deuteron target, and are the spherical Hankel functions. The expression (21) is normalized to satisfy a condition of unit flux for scattering wave function.\n\nFor the cases where Urbana type three-nucleon interaction (TNI) is included, we modify the Faddeev equation (18) into\n\n (E−H0−Vij)ψk=Vij(ψi+ψj)+12(Vijk+Vjki)Ψ (22)\n\nby noting that the TNI among particles can be written as the sum of three terms: .\n\nUsing decomposition of momentum which acts only on the nuclear wave function,\n\n ¯p=i←∇x−i→∇x2=i^x2⎛⎝←−−∂∂x−−−→∂∂x⎞⎠+i21x(←∇Ω−i→∇Ω), (23)\n\nwe can represent general matrix elements of local two-body parity violating potential operators as\n\n (−)⟨Ψf|O|Ψi⟩(+)=(√32)3∑αβ⎡⎢⎣∫dxx2dyy2⎛⎜⎝˜F(+)f,α(x,y)xy⎞⎟⎠^X(x)⎛⎜⎝˜F(+)i,β(x,y)xy⎞⎟⎠⎤⎥⎦⟨α|^O(^x)|β⟩,\n\nwhere means outgoing and incoming boundary conditions and is a scalar function or derivative acting on wave function with respect to . (Note that we have used the fact that .) The partial amplitudes represent the total systems wave function in one selected basis set among three possible angular momentum coupling sequences for three particle angular momenta:\n\n Ψi(f)(x,y)=∑α˜Fi(f),α(x,y)xy∣∣∣(lx(sisj)sx)jx(lysk)jy⟩JM⊗∣∣(titj)txtk⟩TTz. (25)\n\nThe “angular” part of the matrix element is\n\n ⟨α|^O(^x)|β⟩≡∫d^x∫d^yY†α(^x,^y)^O(^x)Yβ(^x,^y), (26)\n\nwhere is a tensor bipolar spherical harmonic with a quantum number . One can see that operators for “angular” matrix elements have the following structure:\n\n (27)\n\nwhere . We calculated the “angular” matrix elements by representing all operators as a tensor product of isospin, spin, spatial operators. For details of the calculations of matrix elements, see paper Song et al. (2011). Similar approaches have been successfully applied for calculations of weak and electromagnetic processes involving three-body and four-body hadronic systems Song et al. (2007, 2009); Lazauskas et al. (2009); Park et al. (2003); Pastore et al. (2009); Girlanda et al. (2010) and for calculation of parity violating effects in neutron deuteron scattering Schiavilla et al. (2008); Song et al. (2011).\n\n## V Results and discussions\n\nTypical results for contributions of different operators of a TRIV potential to matrix elements are shown in table 1, where a mass scale was chosen to be equal to . As it was discussed, both pionless and pionfull EFTs in the leading order, as well as the meson exchange model, have only first five operators which have non-zero values. Taking into account that the characteristic mass scale for operator with should be at least larger than two-pion mass (since two pion exchange corresponds to higher order corrections), the actual contributions of these operators are at least one order of magnitude smaller than the value shown in Table 1. Thus, one can neglect contributions from the suppressed operators provided coupling constants satisfy the naturalness assumption."
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https://www.reference.com/web?q=calculate+weight+kg+to+lbs&qo=relatedSearchBing&o=600605&l=dir | [
"https://www.rapidtables.com/convert/weight/kg-to-pound.html\n\nKilograms (kg) to Pounds (lbs) weight conversion calculator and how to convert.\n\nhttps://www.metric-conversions.org/weight/kilograms-to-pounds.htm\n\nClick here to convert Kilograms to Pounds (kg to lbs). Online conversion calculator for weight conversions with additional tables, formulas and sub units.\n\nhttps://www.metric-conversions.org/weight/pounds-to-kilograms.htm\n\nPounds to Kilograms (lbs to kg) conversion calculator. Click here for online weight conversions with additional tables, formulas and information.\n\nhttps://www.thecalculatorsite.com/conversions/common/kg-to-pounds-ounces.php\n\nblue icon of weight scales. The calculator tool featured below can be used to convert kilograms to pounds and ounces (kg, lb and oz) or vice-versa. A reference ...\n\nhttps://www.unitconverters.net/weight-and-mass/kg-to-lbs.htm\n\nThe kilogram [kg] to pound [lbs] conversion table and conversion steps are also listed. Also, explore tools to convert kilogram or pound to other weight and mass ...\n\nhttps://www.convertunits.com/from/kg/to/lbs\n\nYou can view more details on each measurement unit: kg or lbs The SI base unit for mass is the kilogram. 1 kilogram is equal to 2.2046226218488 lbs. Note that ...\n\nhttp://www.calculconversion.com/weight-converter-lbs-to-kg.html\n\nConversion of kilograms (kg) to pound (lbs) and reverse converter of lbs to kg.\n\nhttps://www.digikey.com/en/resources/conversion-calculators/conversion-calculator-weight\n\nConvert kilograms to grams, kilograms to pounds, and other units including tons, ... tons, and ounces using DigiKey's weight measurement conversion calculator. ... US Ton (Short Ton):. ST. Imperial Ton (Long Ton):. LT. Pounds: lb. Ounces: oz ...\n\nhttps://www.manuelsweb.com/kg_lbs.htm\n\nconvert kilograms & pounds. nursing calculators ... Enter weight to be converted at top of calculator. Select the radio button to ... 70 kg x 2.2 = 154 lbs. A woman ...\n\nhttps://www.inchcalculator.com/convert/kilogram-to-pound/\n\nConvert kilograms to pounds (kg to lb) with the weight conversion calculator, and learn the kilogram to pound calculation formula."
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https://ja.scribd.com/document/351265979/appendix-tensorflow-pdf | [
"You are on page 1of 14\n\n# Introduction to Artificial Neural Networks\n\n## and Deep Learning\n\nA Practical Guide with Applications in Python\n\nSebastian Raschka\n2016 - 2017 Sebastian Raschka\nCONTENTS\n\nContents\n\nWebsite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i\n\n## Appendix G - TensorFlow Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1\n\nTensorFlow in a Nutshell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1\nInstallation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3\nComputation Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3\nVariables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5\nPlaceholder Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8\nCPU and GPU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9\n\nDRAFT\nWebsite\nIf you like the content, please consider supporting the work by buying a copy of the book on\nLeanpub.\nI would appreciate hearing your opinion and feedback about the book! Also, if you have\nany questions about the contents, please dont hesitate to get in touch with me via mail@\nsebastianraschka.com or join the mailing list.\nHappy learning!\nSebastian Raschka\n\nhttps://github.com/rasbt/deep-learning-book\nhttps://leanpub.com/ann-and-deeplearning\nAppendix G - TensorFlow Basics\nThis appendix offers a brief overview of TensorFlow, an open-source library for numerical\ncomputation and deep learning. This section is intended for readers who want to gain a basic\noverview of this library before progressing through the hands-on sections that are concluding\nthe main chapters.\nThe majority of hands-on sections in this book focus on TensorFlow and its Python API,\nassuming that you have TensorFlow >=0.12 installed if you are planning to execute the code\nsections shown in this book.\nIn addition to glancing over this appendix, I recommend the following resources from\nTensorFlows official documentation for a more in-depth coverage on using TensorFlow:\n\nPython API documentation\nTutorials\nTensorBoard, an optional tool for visualizing learning\n\nTensorFlow in a Nutshell\n\nAt its core, TensorFlow is a library for efficient multidimensional array operations with a\nfocus on deep learning. Developed by the Google Brain Team, TensorFlow was open-sourced\non November 9th, 2015. And augmented by its convenient Python API layer, TensorFlow has\nTensorFlow shares some similarities with NumPy, such as providing data structures and com-\nputations based on multidimensional arrays. What makes TensorFlow particularly suitable\nfor deep learning, though, are its primitives for defining functions on tensors, the ability of\nparallelizing tensor operations, and convenience tools such as automatic differentiation.\nhttps://www.tensorflow.org/get_started/os_setup\nhttps://www.tensorflow.org/api_docs/python/\nhttps://www.tensorflow.org/tutorials/\nhttps://www.tensorflow.org/how_tos/summaries_and_tensorboard/\nAppendix G - TensorFlow Basics 2\n\nWhile TensorFlow can be run entirely on a CPU or multiple CPUs, one of the core strength\nof this library is its support of GPUs (Graphical Processing Units) that are very efficient\nat performing highly parallelized numerical computations. In addition, TensorFlow also\nsupports distributed systems as well as mobile computing platforms, including Android and\nApples iOS.\nBut what is a tensor? In simplifying terms, we can think of tensors as multidimensional\narrays of numbers, as a generalization of scalars, vectors, and matrices.\n\n1. Scalar: R\n2. Vector: Rn\n3. Matrix: Rn Rm\n4. 3-Tensor: Rn Rm Rp\n5.\n\nWhen we describe tensors, we refer to its dimensions as the rank (or order) of a tensor,\nwhich is not to be confused with the dimensions of a matrix. For instance, an m n matrix,\nwhere m is the number of rows and n is the number of columns, would be a special case of\na rank-2 tensor. A visual explanation of tensors and their ranks is given is the figure below.\n\nTensors\n\nDRAFT\nAppendix G - TensorFlow Basics 3\n\nInstallation\n\nCode conventions in this book follow the Python 3.x syntax, and while the code examples\nshould be backward compatible to Python 2.7, I highly recommend the use of Python >=3.5.\nOnce you have your Python Environment set up (Appendix - Python Setup), the most\nconvenient ways for installing TensorFlow are via pip or conda the latter only applies if you\nhave the Anaconda/Miniconda Python distribution installed, which I prefer and recommend.\nSince TensorFlow is under active development, I recommend you to consult the official\nsorFlow on you operating system, macOS, Linux, or Windows.\n\nComputation Graphs\n\nIn contrast to other tools such as NumPy, the numerical computations in TensorFlow can\nbe categorized into two steps: a construction step and an execution step. Consequently, the\ntypical workflow in TensorFlow can be summarized as follows:\n\n## Build a computational graph\n\nStart a new session to evaluate the graph\nInitialize variables\nExecute the operations in the compiled graph\n\nNote that the computation graph has no numerical values before we initialize and evaluate it.\nTo see how this looks like in practice, let us set up a new graph for computing the column sums\nof a matrix, which we define as a constant tensor (reduce_sum is the TensorFlow equivalent\nof NumPys sum function).\nIn :\n\nhttps://www.tensorflow.org/get_started/os_setup\n\nDRAFT\nAppendix G - TensorFlow Basics 4\n\n1 import tensorflow as tf\n2\n3 g = tf.Graph()\n4\n5 with g.as_default() as g:\n6 tf_x = tf.constant([[1., 2.],\n7 [3., 4.],\n8 [5., 6.]], dtype=tf.float32)\n9 col_sum = tf.reduce_sum(tf_x, axis=0)\n10\n11 print('tf_x:\\n', tf_x)\n12 print('\\ncol_sum:\\n', col_sum)\n\nOut :\n\n1 tf_x:\n2 Tensor(\"Const:0\", shape=(3, 2), dtype=float32)\n3\n4 col_sum:\n5 Tensor(\"Sum:0\", shape=(2,), dtype=float32)\n\nAs we can see from the output above, the operations in the graph are represented as Tensor\nobjects that require an explicit evaluation before the tf_x matrix is populated with numerical\nvalues and its column sum gets computed.\nNow, we pass the graph that we created earlier to a new, active session, where the graph gets\ncompiled and evaluated:\nIn :\n\n## 1 with tf.Session(graph=g) as sess:\n\n2 mat, csum = sess.run([tf_x, col_sum])\n3\n4 print('mat:\\n', mat)\n5 print('\\ncsum:\\n', csum)\n\nOut :\n\nDRAFT\nAppendix G - TensorFlow Basics 5\n\n1 mat:\n2 [[ 1. 2.]\n3 [ 3. 4.]\n4 [ 5. 6.]]\n5\n6 csum:\n7 [ 9. 12.]\n\nNote that if we are only interested in the result of a particular operation, we dont need\nto run its dependencies TensorFlow will automatically take care of that. For instance, we\ncan directly fetch the numerical values of col_sum_times_2 in the active session without\nexplicitly passing col_sum to sess.run(...) as the following example illustrates:\nIn :\n\n1 g = tf.Graph()\n2\n3 with g.as_default() as g:\n4 tf_x = tf.constant([[1., 2.],\n5 [3., 4.],\n6 [5., 6.]], dtype=tf.float32)\n7 col_sum = tf.reduce_sum(tf_x, axis=0)\n8 col_sum_times_2 = col_sum * 2\n9\n10\n11 with tf.Session(graph=g) as sess:\n12 csum_2 = sess.run(col_sum_times_2)\n13\n14 print('csum_2:\\n', csum_2)\n\nOut :\n\n1 csum_2:\n2 [array([ 18., 24.], dtype=float32)]\n\nVariables\n\nVariables are constructs in TensorFlow that allows us to store and update parameters of\nour models during training. To define a variable tensor, we use TensorFlows Variable()\n\nDRAFT\nAppendix G - TensorFlow Basics 6\n\nconstructor, which looks similar to the use of constant that we used to create a matrix\npreviously. However, to execute a computational graph that contains variables, we must ini-\ntialize all variables in the active session first (using tf.global_variables_initializer()),\nas illustrated in the example below.\nIn :\n\n1 g = tf.Graph()\n2\n3 with g.as_default() as g:\n4 tf_x = tf.Variable([[1., 2.],\n5 [3., 4.],\n6 [5., 6.]], dtype=tf.float32)\n7 x = tf.constant(1., dtype=tf.float32)\n8\n9 # add a constant to the matrix:\n10 tf_x = tf_x + x\n11\n12 with tf.Session(graph=g) as sess:\n13 sess.run(tf.global_variables_initializer())\n14 result = sess.run(tf_x)\n\nprint(result)\n\n1 print(result)\n\nOut :\n\n1 [[ 2. 3.]\n2 [ 4. 5.]\n3 [ 6. 7.]]\n\n## Now, let us do an experiment and evaluate the same graph twice:\n\nIn :\n\nDRAFT\nAppendix G - TensorFlow Basics 7\n\n## 1 with tf.Session(graph=g) as sess:\n\n2 sess.run(tf.global_variables_initializer())\n3 result = sess.run(tf_x)\n4 result = sess.run(tf_x)\n\nOut :\n\n1 [[ 2. 3.]\n2 [ 4. 5.]\n3 [ 6. 7.]]\n\nAs we can see, the result of running the computation twice did not affect the numerical values\nfetched from the graph. To update or to assign new values to a variable, we use TensorFlows\nassign operation. The function syntax of assign is assign(ref, val, ...), where ref is\nupdated by assigning value to it:\nIn :\n\n1 g = tf.Graph()\n2\n3 with g.as_default() as g:\n4 tf_x = tf.Variable([[1., 2.],\n5 [3., 4.],\n6 [5., 6.]], dtype=tf.float32)\n7 x = tf.constant(1., dtype=tf.float32)\n8\n9 update_tf_x = tf.assign(tf_x, tf_x + x)\n10\n11\n12 with tf.Session(graph=g) as sess:\n13 sess.run(tf.global_variables_initializer())\n14 result = sess.run(update_tf_x)\n15 result = sess.run(update_tf_x)\n16\n17 print(result)\n\nOut :\n\nDRAFT\nAppendix G - TensorFlow Basics 8\n\n1 [[ 3. 4.]\n2 [ 5. 6.]\n3 [ 7. 8.]]\n\nAs we can see, the contents of the variable tf_x were successfully updated twice now; in the\nactive session we\n\n## initialized the variable tf_x\n\nadded a constant scalar 1. to tf_x matrix via assign\nadded a constant scalar 1. to the previously updated tf_x matrix via assign\n\nAlthough the example above is kept simple for illustrative purposes, variables are an\nimportant concept in TensorFlow, and we will see throughout the chapters, they are not only\nuseful for updating model parameters but also for saving and loading variables for reuse.\n\nPlaceholder Variables\n\nAnother important concept in TensorFlow is the use of placeholder variables, which allow\nus to feed the computational graph with numerical values in an active session at runtime.\nIn the following example, we will define a computational graph that performs a simple\nmatrix multiplication operation. First, we define a placeholder variable that can hold 3x2-\ndimensional matrices. And after initializing the placeholder variable in the active session, we\nwill use a dictionary, feed_dict we feed a NumPy array to the graph, which then evaluates\nthe matrix multiplication operation.\nIn :\n\n1 import numpy as np\n2\n3 g = tf.Graph()\n4\n5 with g.as_default() as g:\n6 tf_x = tf.placeholder(dtype=tf.float32,\n7 shape=(3, 2))\n8\n9 output = tf.matmul(tf_x, tf.transpose(tf_x))\n10\n11\n\nDRAFT\nAppendix G - TensorFlow Basics 9\n\n## 12 with tf.Session(graph=g) as sess:\n\n13 sess.run(tf.global_variables_initializer())\n14 np_ary = np.array([[3., 4.],\n15 [5., 6.],\n16 [7., 8.]])\n17 feed_dict = {tf_x: np_ary}\n18 print(sess.run(output,\n19 feed_dict=feed_dict))\n\nOut :\n\n## 1 [[ 25. 39. 53.]\n\n2 [ 39. 61. 83.]\n3 [ 53. 83. 113.]]\n\nThroughout the main chapters, we will make heavy use of placeholder variables, which allow\nus to pass our datasets to various learning algorithms in the computational graphs.\n\n## CPU and GPU\n\nPlease note that all code examples in this book, and all TensorFlow operations in general,\ncan be executed on a CPU. If you have a GPU version of TensorFlow installed, TensorFlow\nwill automatically execute those operations that have GPU support on GPUs and use your\nmachines CPU, otherwise. However, if you wish to define your computing device manually,\nfor instance, if you have the GPU version installed but want to use the main CPU for\nprototyping, we can run an active section on a specific device using the with context as\nfollows\n\n## 1 with tf.Session() as sess:\n\n2 with tf.device(\"/gpu:1\"):\n\nwhere\n\n## /cpu:0: The CPU of your machine.\n\n/gpu:0: The GPU of your machine, if you have one.\n/gpu:1: The second GPU of your machine, etc.\netc.\n\nYou can get a list of all available devices on your machine via\n\nDRAFT\nAppendix G - TensorFlow Basics 10\n\n## 1 from tensorflow.python.client import device_lib\n\n2\n3 device_lib.list_local_devices()"
] | [
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.77903986,"math_prob":0.98312354,"size":10344,"snap":"2019-26-2019-30","text_gpt3_token_len":2585,"char_repetition_ratio":0.12562862,"word_repetition_ratio":0.10936556,"special_character_ratio":0.2623743,"punctuation_ratio":0.18263757,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99154466,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-07-18T13:25:10Z\",\"WARC-Record-ID\":\"<urn:uuid:06dfb703-af75-4ee0-b314-bbf707c0c7fd>\",\"Content-Length\":\"288962\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1072f5d3-e530-45c9-a936-fe35a355a0e9>\",\"WARC-Concurrent-To\":\"<urn:uuid:3dda485a-e2d9-4c00-9682-8de1a8653a8a>\",\"WARC-IP-Address\":\"151.101.202.152\",\"WARC-Target-URI\":\"https://ja.scribd.com/document/351265979/appendix-tensorflow-pdf\",\"WARC-Payload-Digest\":\"sha1:MAEFXJ4MUPNS6XJE5VX4MFG4FMBNRJB4\",\"WARC-Block-Digest\":\"sha1:OJ4GA7BAOYEKDSM436QYLVHEG5ZC2IUW\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-30/CC-MAIN-2019-30_segments_1563195525634.13_warc_CC-MAIN-20190718125048-20190718151048-00194.warc.gz\"}"} |
https://pktqq99.me/java-vector3d-37/ | [
"How do we handle problem users? Stack Overflow works best with JavaScript enabled. Unicorn Meta Zoo 9: Email Required, but never shown. Post as a guest Name. Since a vector does not have a location, we can arbitrarily choose one of the points to be the origin. Now, Vector3d only takes in 3 arguments x,y,z in its constructor.",
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"Uploader: Moshura Date Added: 14 May 2016 File Size: 8.76 Mb Operating Systems: Windows NT/2000/XP/2003/2003/7/8/10 MacOS 10/X Downloads: 6175 Price: Free* [*Free Regsitration Required]",
null,
"## Java example source code file (Vector3D.java)\n\nSo for this problem we do not need the location since all we need the vectors for is to find the angle. Is it safe then to definitively say vectors should not be used to calculate points of intersection in 3d space? Post as a guest Name.",
null,
"How do we handle problem users? I researched how to obtain a vector connecting two points: Asked 7 years, 6 months vcetor3d. Email Required, but never shown.\n\nNow, Vector3d only takes in 3 arguments x,y,z in vedtor3d constructor. You have a small error there: Sign up using Facebook. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. Sign up using Email and Password.\n\n# Java Vector3d And Vector Logic – Stack Overflow\n\nHow can we ever have a vector which does not intersect the origin if the only attributes contained in Vector3d are x,y,z? Since a vector does not have a location, we can arbitrarily choose one of the points to be the origin. First of all I am having trouble with the concept of a mathematical Vector when being applied to a Vector3d.\n\nYou can’t add two points in the same way.\n\n# Java example – – matharithmeticexception, override, string, vector, vector3d, zero\n\nI assumed this to be because the vector initially is assumed to start at the origin and go through the designated point. Can someone clear up the logic behind Vector3d for me please and how it can represent an arbitrary vector in 3D space yet it only contains x,y,z? For example, I am trying to program a function which calculates the distance between two points on a sphere: Stack Overflow works best with JavaScript enabled.",
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null,
"http://resources.esri.com/help/9.3/arcgisengine/java/api/arcobjects/com/esri/arcgis/geometry/bitmaps/GeomVectorDimension.gif",
null,
"https://pktqq99.me/download.png",
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"https://i.ytimg.com/vi/-TMXnB67T2I/maxresdefault.jpg",
null,
"http://resources.esri.com/help/9.3/arcgisengine/java/api/arcobjects/com/esri/arcgis/geometry/bitmaps/GeomVector3D.gif",
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"http://www.java2s.com/Code/JavaImages/BillboardTest.PNG",
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.91283363,"math_prob":0.7585987,"size":3236,"snap":"2021-04-2021-17","text_gpt3_token_len":748,"char_repetition_ratio":0.11819307,"word_repetition_ratio":0.16785714,"special_character_ratio":0.22589616,"punctuation_ratio":0.119335346,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96438056,"pos_list":[0,1,2,3,4,5,6,7,8,9,10],"im_url_duplicate_count":[null,1,null,1,null,1,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-01-18T10:48:00Z\",\"WARC-Record-ID\":\"<urn:uuid:a090b1c5-5791-4524-ab55-096da2bd956a>\",\"Content-Length\":\"38479\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:71c85eac-2559-4eb6-a6b7-9b10a57949a4>\",\"WARC-Concurrent-To\":\"<urn:uuid:069d7811-d7e0-42f6-924e-a50dab132c31>\",\"WARC-IP-Address\":\"104.21.45.245\",\"WARC-Target-URI\":\"https://pktqq99.me/java-vector3d-37/\",\"WARC-Payload-Digest\":\"sha1:VS2YIWNVEQEIC4WQG42WVWS7SXULM34G\",\"WARC-Block-Digest\":\"sha1:RO5KHVGLZWURLC4OOVEBQOBKTLPNBEJY\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-04/CC-MAIN-2021-04_segments_1610703514495.52_warc_CC-MAIN-20210118092350-20210118122350-00587.warc.gz\"}"} |
http://westclintech.com/SQL-Server-Financial-Functions/SQL-Server-PMTGA-function | [
"",
null,
"# SQL Server PMT function for a growing annuity\n\nPMTGA\n\nUpdated: 07 February 2011\n\nUse PMTGA to calculate the initial payment for a growing annuity, given the future value. The formula for the calculation of the initial payment of a growing annuity is:",
null,
"Syntax\nSELECT [wctFinancial].[wct].[PMTGA](\n<@FV, float,>\n,<@Pgr, float,>\n,<@Nper, int,>\n,<@Rate, float,>\n,<@Pay_type, int,>)\nArguments\n@FV\nthe future value of the annuity. @FV is an expression of type float or of a type that can be implicitly converted to float.\n@Pgr\nthe periodic growth rate of the annuity. This is the percentage amount, expressed as a decimal, by which the annuity will increase in each period. @Pgr is an expression of type float or of a type that can be implicitly converted to float.\n@Nper\nthe number of annuity payments. @Nper is an expression of type float or of a type that can be implicitly converted to float.\n@Rate\nthe percentage rate of return, expressed as a decimal, that you expect the annuity to earn over the number of periods. The annuity payments are compounded using this value. @Rate is an expression of type float or of a type that can be implicitly converted to float.\n@Pay_type\nthe number 0 or 1 and indicates when payments are due. @Pay_type is an expression of type int or of a type that can be implicitly converted to int. If @Pay_type is not 0 it is assumed to be 1.\n\n Set @Pay_type equal to If payments are due 0 At the end of a period 1 At the beginning of a period\n\nReturn Type\nfloat\nRemarks\n· The PMTGA value will have the same sign as @FV.\n· If the @Pay_type is not equal to zero, it is assumed to be 1.\n· To calculate the Future value of a growing annuity, use the FVGA function.\nExamples\nLet’s say you are going to work for 40 more years, and you would like to have a million dollars in your tax-deferred account after 40 years. Assuming that you can increase your contributions by 3% per year and that your tax-deferred account will earn 7% per year, what is the initial (annual) payment to be made into the annuity?\nSELECT\nwct.PMTGA(1000000 --@FV\n,.03 --@Pgr\n,40 --@Nper\n,.07 --@Rate\n,1 --@Pay_type\n) as PMT\nThis produces the following result.\nPMT\n----------------------\n3191.75519827819\n\n(1 row(s) affected)\n\nWe can verify this calculation by using the FVGA function.\nSELECT wct.FVGA(3191.75519827819,.03,40,.07,1) as FVGA\n\nThis produces the following result.\nFVGA\n----------------------\n1000000\n\n(1 row(s) affected)\n\n### Support",
null,
"",
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"Copyright 2008-2021 Westclintech LLC Privacy Policy Terms of Service"
] | [
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"http://westclintech.com/portals/0/download-free-trial.png",
null,
"http://westclintech.com/Portals/0/images/formula_PMTGA.jpg",
null,
"http://westclintech.com/Portals/0/WCT-MSPartner.png",
null,
"http://westclintech.com/Portals/0/GSAadvantage_90x32.jpg",
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.84621984,"math_prob":0.9548395,"size":2380,"snap":"2021-31-2021-39","text_gpt3_token_len":657,"char_repetition_ratio":0.13930976,"word_repetition_ratio":0.1589242,"special_character_ratio":0.28865546,"punctuation_ratio":0.13457558,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98244065,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,null,null,2,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-08-01T20:47:54Z\",\"WARC-Record-ID\":\"<urn:uuid:12ea387c-88d8-4222-85da-3730f1887fde>\",\"Content-Length\":\"714714\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:447c08a4-baa2-4e1d-911c-fb5969aead18>\",\"WARC-Concurrent-To\":\"<urn:uuid:50c13ee6-9003-49dd-afff-a4e62e38a15b>\",\"WARC-IP-Address\":\"54.225.104.172\",\"WARC-Target-URI\":\"http://westclintech.com/SQL-Server-Financial-Functions/SQL-Server-PMTGA-function\",\"WARC-Payload-Digest\":\"sha1:NAWY7ILZCR762TD7KBYFYHADKHHKYISI\",\"WARC-Block-Digest\":\"sha1:PPDIZVZS74PMCTNEQY2CEJ3NL66BM2HE\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-31/CC-MAIN-2021-31_segments_1627046154219.62_warc_CC-MAIN-20210801190212-20210801220212-00100.warc.gz\"}"} |
http://www.pism.io/docs/manual/modeling-choices/subglacier/bed-deformation.html | [
"# Earth deformation models¶\n\nThe option -bed_def [iso, lc, given] (flag bed_deformation.model) turns one of the three available bed deformation models.\n\n## Point-wise isostasy¶\n\nThe first model -bed_def iso, is instantaneous pointwise isostasy. This model assumes that the bed at the starting time is in equilibrium with the load. Then, as the ice geometry evolves, the bed elevation is equal to the starting bed elevation minus a multiple of the increase in ice thickness from the starting time:\n\n$b(t,x,y) = b(0,x,y) - f \\left[H(t,x,y) - H(0,x,y)\\right].$\n\nHere $$f$$ is the density of ice divided by the density of the mantle, so its value is determined by the values of bed_deformation.mantle_density and constants.ice.density in the configuration file. For an example and verification, see Test H in Verification.\n\n## Lingle-Clark¶\n\nThe second model -bed_def lc is much more physical. It is based on papers by Lingle and Clark and Bueler and others . It generalizes and improves the most widely-used earth deformation model in ice sheet modeling, the flat earth Elastic Lithosphere Relaxing Asthenosphere (ELRA) model . It imposes essentially no computational burden because the Fast Fourier Transform is used to solve the linear differential equation . When using this model in PISM, the rate of bed movement (uplift) and the viscous plate displacement are stored in the PISM output file and then used to initialize the next part of the run. In fact, if gridded “observed” uplift data is available, for instance from a combination of actual point observations and/or paleo ice load modeling, and if that uplift field is put in a NetCDF variable with standard name tendency_of_bedrock_altitude in the input file, then this model will initialize so that it starts with the given uplift rate.\n\nAll parameters (except for constants.ice.density) controlling the Lingle-Clark model are listed below (they all have the prefix bed_deformation.).\n\nParameters\n\nPrefix: bed_deformation.\n\n1. lc.elastic_model (yes) Use the elastic part of the Lingle-Clark bed deformation model.\n\n2. lc.grid_size_factor (4) The spectral grid size is (Z*(grid.Mx - 1) + 1, Z*(grid.My - 1) + 1) where Z is given by this parameter. See , .\n\n3. lc.update_interval (10 365days) Interval between updates of the Lingle-Clark model\n\n4. lithosphere_flexural_rigidity (5e+24 Newton meter) lithosphere flexural rigidity used by the bed deformation model. See , \n\n5. mantle_density (3300 kg meter-3) half-space (mantle) density used by the bed deformation model. See , \n\n6. mantle_viscosity (1e+21 Pascal second) half-space (mantle) viscosity used by the bed deformation model. See , \n\nHere are minimal example runs to compare these models:\n\nmpiexec -n 4 pismr -eisII A -y 8000 -o eisIIA_nobd.nc\nmpiexec -n 4 pismr -eisII A -bed_def iso -y 8000 -o eisIIA_bdiso.nc\nmpiexec -n 4 pismr -eisII A -bed_def lc -y 8000 -o eisIIA_bdlc.nc\n\n\nCompare the topg, usurf, and dbdt variables in the resulting output files. See also the comparison done in .\n\nTo include “measured” uplift rates during initialization, use the option -uplift_file (parameter bed_deformation.bed_uplift_file) to specify the name of the file containing the field dbdt (CF standard name: tendency_of_bedrock_altitude).\n\nUse the option -topg_delta_file (parameter bed_deformation.bed_topography_delta_file) to apply a correction to the bed topography field read in from an input file. This sets the bed topography $$b$$ at the beginning of a run as follows:\n\n(31)$b = b_{0} + \\Delta b.$\n\nHere $$b_{0}$$ is the bed topography (topg) read in from an input file and $$\\Delta b$$ is the topg_delta field read in from the file specified using this option.\n\nA correction like this can be used to get a bed topography field at the end of a paleo-climate run that is closer to observed present day topography. The correction is computed by performing a “preliminary” run and subtracting modeled bed topography from present day observations. A subsequent run with this correction should produce bed elevations that are closer to observed values.\n\nWarning\n\nThe variable viscous_bed_displacement does not correspond to any measured physical quantity. Do not even attempt to analyze it without a careful reading of .\n\nTrying to provide a “hand-crafted” viscous_bed_displacement field to PISM is not a good idea.\n\nKeep in mind that zero viscous_bed_displacement does not mean that the bed deformation model is in equilibrium.\n\n## Given bed deformation history¶\n\nThe last option -bed_def given can be used if a bed deformation history (i.e. bed elevation changes relative to a reference topography) is known from an external solid-Earth model1. This can be useful when running simulations using offline coupling to such a model.\n\nThe bed topography $$b$$ is set to\n\n$b(t,x,y) = b_{\\text{ref}}(x,y) + \\Delta b(t,x,y),$\n\nwhich is a time-dependent version of (31).\n\nThis class uses two input files:\n\n1. Reference topography $$b_{\\text{ref}}(x,y)$$ (variable topg, in meters).\n\n2. Time-dependent history of bed elevation changes $$\\Delta b(t,x,y)$$ relative to the reference topography (variable topg_delta, in meters).\n\nUse the following configuration parameters (prefix: bed_deformation.given.) to set them.\n\n1. file Name of the file containing time-dependent topg_delta.\n\n2. reference_file Name of the file containing the reference bed topography topg.\n\nNote\n\nIt is possible to combine high-resolution reference bed topography with low-spatial-frequency bed elevation changes: both files have to use the same grid projection and cover the modeling domain but they do not have to use the same grid.\n\nFootnotes\n\n1\n\nE.g. a relative sea level model.\n\n Previous Up Next"
] | [
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.7778084,"math_prob":0.9015665,"size":5516,"snap":"2023-14-2023-23","text_gpt3_token_len":1385,"char_repetition_ratio":0.12844703,"word_repetition_ratio":0.03473054,"special_character_ratio":0.22516316,"punctuation_ratio":0.10030706,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98122877,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-04-01T13:31:57Z\",\"WARC-Record-ID\":\"<urn:uuid:56c14287-408e-41f1-a6e2-e03e6e81dfcb>\",\"Content-Length\":\"24374\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9a2fad11-87e9-46fc-b81d-983737576a19>\",\"WARC-Concurrent-To\":\"<urn:uuid:e954dbf1-e94a-4983-8d6d-a14f4c7fd04b>\",\"WARC-IP-Address\":\"185.199.109.153\",\"WARC-Target-URI\":\"http://www.pism.io/docs/manual/modeling-choices/subglacier/bed-deformation.html\",\"WARC-Payload-Digest\":\"sha1:JULZIZR4QY53MQS45FCUQVUUWODLJPPV\",\"WARC-Block-Digest\":\"sha1:PXAQQE6YJYPCZQYEIFNN6OZBFREEH5OD\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-14/CC-MAIN-2023-14_segments_1679296950030.57_warc_CC-MAIN-20230401125552-20230401155552-00207.warc.gz\"}"} |
https://topanswers.xyz/databases?q=186 | [
"I am trying to understand how SQL Server try to estimate for 'greater than' and 'greater than equal to' where clauses in SQL Server 2014.\n\nI think I do understand the cardinality estimation when it hits the step for example if I do\n\nselect * from charge where charge_dt >= '1999-10-13 10:47:38.550'\n\nThe cardinality estimation is 6672 which can be easily calculated as\n32(EQ_ROWS) + 6624(RANGE_ROWS) + 16 (EQ_ROWS) = 6672 (histogram in below screenshot)\n\n[![enter image description here]]\n\nBut when I do\n\nselect * from charge where charge_dt >= '1999-10-13 10:48:38.550'\n(increased the time to 10:48 so its not a step)\n\nthe estimate is 4844.13.\n\nHow is that calculated?\n\n: http://i.stack.imgur.com/1p14c.png\nThe only difficulty is in deciding how to handle the histogram step(s) **partially covered** by the query predicate interval. Whole histogram steps covered by the predicate range are trivial as noted in the question.\n\n## Legacy Cardinality Estimator\n\nF = fraction (between 0 and 1) of the step range covered by the query predicate.\n\nThe basic idea is to use F (linear interpolation) to determine how many of the intra-step distinct values are covered by the predicate. Multiplying this result by the average number of rows per distinct value (assuming uniformity), and adding the step equal rows gives the cardinality estimate:\n\n none\nCardinality = EQ_ROWS + (AVG_RANGE_ROWS * F * DISTINCT_RANGE_ROWS)\n\n\nThe same formula is used for > and >= in the legacy CE.\n\n## New Cardinality Estimator\n\nThe new CE modifies the previous algorithm slightly to differentiate between > and >=.\n\nTaking > first, the formula is:\n\n none\nCardinality = EQ_ROWS + (AVG_RANGE_ROWS * (F * (DISTINCT_RANGE_ROWS - 1)))\n\n\nFor >= it is:\n\n none\nCardinality = EQ_ROWS + (AVG_RANGE_ROWS * ((F * (DISTINCT_RANGE_ROWS - 1)) + 1))\n\n\nThe + 1 reflects that when the comparison involves equality, a match is assumed (the inclusion assumption).\n\nIn the question example, F can be calculated as:\n\nDECLARE\n@Q datetime = '1999-10-13T10:48:38.550',\n@K1 datetime = '1999-10-13T10:47:38.550',\n@K2 datetime = '1999-10-13T10:51:19.317';\n\nDECLARE\n@QR float = DATEDIFF(MILLISECOND, @Q, @K2), -- predicate range\n@SR float = DATEDIFF(MILLISECOND, @K1, @K2) -- whole step range\n\nSELECT\nF = @QR / @SR;\n\nThe result is **0.728219019233034**. Plugging that into the formula for >= with the other known values:\n\n none\nCardinality = EQ_ROWS + (AVG_RANGE_ROWS * ((F * (DISTINCT_RANGE_ROWS - 1)) + 1))\n= 16 + (16.1956 * ((0.728219019233034 * (409 - 1)) + 1))\n= 16 + (16.1956 * ((0.728219019233034 * 408) + 1))\n= 16 + (16.1956 * (297.113359847077872 + 1))\n= 16 + (16.1956 * 298.113359847077872)\n= 16 + 4828.1247307393343837632\n= 4844.1247307393343837632\n= <b>4844.12473073933</b> (to float precision)\n\n\nThis result agrees with the estimate of 4844.13 shown in the question.\n\nThe same query using the legacy CE (e.g. using trace flag 9481) should produce an estimate of:\n\n none\nCardinality = EQ_ROWS + (AVG_RANGE_ROWS * F * DISTINCT_RANGE_ROWS)\n= 16 + (16.1956 * 0.728219019233034 * 409)\n= 16 + 4823.72307468722\n= <b>4839.72307468722</b>\n\n\nNote the estimate would be the same for > and >= using the legacy CE."
] | [
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https://www.jiskha.com/questions/148605/1-given-ab-cd-cd-ef-prove-ab-ef-in-5-steps-that-show-why-it-is-corect-i-e-two-column | [
"# geometry\n\n1)given-AB=CD,CD=EF\nprove-AB-EF (in 5 steps that show why it is corect; i.e two-column proof)\n\n2)Given-<2=<3, <4=<5\nprove-<1 is supplementay to <6\n(in 3 steps, with the two column proof)\n\nTWO-COLUMN PROOF LOOKS LIKE THIS....\nSTATEMENT: REASON:\n1.AB=CD,CD=EF 1.Given\n2.?? 2.??\n3.?? 3.??\n4.?? 4.??\n5.AB=EF 5.??\n\n1. 👍 0\n2. 👎 0\n3. 👁 672\n1. Transitive Axiom If a = b and b = c then a = c\n\nSo it seems to me to be two steps, not five.\n\nYou second makes no sense, it does not indicate any relationship with <1 and any other angle.\n\n1. 👍 0\n2. 👎 0\n👨🏫\nbobpursley\n2. Purple because aliens dont wear hats\n\n1. 👍 0\n2. 👎 0\n3. wth does that mean\n\n1. 👍 0\n2. 👎 0\n\n## Similar Questions\n\n1. ### Geometry\n\nWrite a two-column proof. Given: 7y=8x-14; y=6 Prove: x=7 I need help making a two-column proof with the statements and the reasons, please! Thank you! ( This is what I have so far) Statements | Reasons 1. 7y=8x-14;y=6 | Given 2.\n\n2. ### Ed. Tech\n\nAfter creating a column heading and/or typing text within a column, what must you do to move text to the next column? A. Add a column break B. Select the next column and start typing C. Highlight the next column D. Change the page\n\n3. ### Tech\n\n4. after creating a column heading and or typing text within a column what must you do to move text to the next column? Add a column break select the next column and start typing** highlight the next column change the page\n\n4. ### Geometry\n\nGiven: ∠ABC and ∠CBD are supplementary angles. m∠ABC = 4x + 7, m∠CBD = 2x − 1. Prove: m∠ABC = 123 How do I write this in a two column proof?\n\n1. ### Geometry\n\nComplete the two column proof Given:angle 2 is about equal to angle 4, angle 2 = 110 Prove: angle 3 = 70 statement - proof angle 2 is about equal to angle 4, angle 2 =110 - given angle 2 = angle 4 - definition of congruent angles\n\n2. ### math\n\nwrite a two column proof. Given: RS=~ TS, V is the midpoint of RT Prove: /\\RSV=~ /\\TSV /\\ is the triangle sign =~ is the congruent sign\n\n3. ### Geometry\n\nUse the given plan to write a two-column proof of the Symmetric Property of Congruence. Given: segment AB ≅ segment EF Prove: segment EF ≅ segment AB Plan: Use the definition of congruent segments to write segment AB ≅\n\n4. ### Math\n\nWrite a two column proof. Given: 7y = 8x - 14; y = 6 Prove: x = 7\n\n1. ### Math\n\nWrite a two column proof. -If XZ=ZY,XZ=4x+1,and ZY=6x-13, then x=7. Statements: Reason: 1.XZ=ZY,XZ=4x+1 and ZY=6x-13 1.Given That as far as I got to ^. Thanks\n\n2. ### discrete math\n\nprove that if n is an integer and 3n+2 is even, then n is even using a)a proof by contraposition b)a proof by contradiction I'll try part b, you'll have to refresh me on what contraposition means here. Here is the claim we start\n\n3. ### math\n\nSegments MN, LT, PQ, and OR all intersect at point S. If m∠LSO = m∠PSN , prove m∠LSP = m∠OSN . write a two column proof\n\n4. ### math\n\n1)Find the third iterate x3 of f(x)=x2-4 for an initial value of x0=2 A)-4 B)4 C)12 D)-12 I chose C 2)Use Pascal's triangle to expand:(w-x)5 This ones long so I chose w5-5w4x+10w3x3-10w2x4+5wx4-x5 3)Use the binomial Theorem to"
] | [
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https://cstheory.stackexchange.com/questions/10753/sparse-graphs-versus-dense-graphs | [
"# Sparse graphs versus dense graphs\n\nI am curious if there are graphs problems for which either -\n\n1. we know that time and/or space complexity is independent of graph sparsity\n2. we do not know whether or not graph sparsity can be exploited to reduce time and/or space complexity\n\nAmong many possible notions of the sparsity, I am particularly interested in the one that relies on edge density (or alternatively, average degree).\n\n• Suppose the problem takes time O(m+n) to solve ? is that considered \"independent of the sparsity\" ? – Suresh Venkat Mar 18 '12 at 1:44\n• Here is one example - storing all pairs shortest distances is believed to, I think, require $\\Omega(n^2)$ space. If this is right, that would be one example. – Rachit Mar 18 '12 at 2:33\n• I see so one thing you might be looking for is a problem where lower bounds depend only on $n$ ? – Suresh Venkat Mar 18 '12 at 2:46\n• for example Johnson's algorithm for all pairs shortest path is $O(V^2 \\log V + VE)$ and for sparse graphs e.g when $|E| = O(V)$ it will be $O(V^2 \\log V)$, It's not independent from $E$ in general but it's extremely faster than normal ford-falkerson in sparse graphs. – Saeed Mar 18 '12 at 12:00\n• I don't understand. If we know that the time complexity is independent of sparsity, then by definition we know that sparsity cannot be exploited to reduce the time complexity. What am I missing? – Jeffε Mar 18 '12 at 20:36"
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.9104781,"math_prob":0.983124,"size":389,"snap":"2020-24-2020-29","text_gpt3_token_len":78,"char_repetition_ratio":0.11168831,"word_repetition_ratio":0.0,"special_character_ratio":0.19537275,"punctuation_ratio":0.04347826,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99628764,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-07-12T13:27:10Z\",\"WARC-Record-ID\":\"<urn:uuid:d9dd950f-47b7-4edc-bab3-18fe16ebd15a>\",\"Content-Length\":\"141590\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:ae7b00ab-dbe6-4e24-b9f6-ebae000930e4>\",\"WARC-Concurrent-To\":\"<urn:uuid:a8480552-89b6-47cc-8d3f-7a4ee4f40014>\",\"WARC-IP-Address\":\"151.101.193.69\",\"WARC-Target-URI\":\"https://cstheory.stackexchange.com/questions/10753/sparse-graphs-versus-dense-graphs\",\"WARC-Payload-Digest\":\"sha1:SD6OJRMUTXMA4NXMHN527KNXGP7AUOIA\",\"WARC-Block-Digest\":\"sha1:VQZ6Z73KOM2KBKYKCSWTCVRJOISF5YIJ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-29/CC-MAIN-2020-29_segments_1593657138718.61_warc_CC-MAIN-20200712113546-20200712143546-00018.warc.gz\"}"} |
https://openkim.org/id/Sim_LAMMPS_ReaxFF_StrachanVanDuinChakraborty_2003_CHNO__SM_107643900657_001 | [
"#### Sim_LAMMPS_ReaxFF_StrachanVanDuinChakraborty_2003_CHNO__SM_107643900657_001\n\nInteratomic potential for Carbon (C), Hydrogen (H), Nitrogen (N), Oxygen (O).\n\n### Verification Check Dashboard\n\nGrade Name Category Brief Description Full Results Aux File(s)\nP vc-species-supported-as-stated mandatory\nThe model supports all species it claims to support; see full description.\nResults Files\nF vc-periodicity-support mandatory\nPeriodic boundary conditions are handled correctly; see full description.\nResults Files\nF vc-permutation-symmetry mandatory\nTotal energy and forces are unchanged when swapping atoms of the same species; see full description.\nResults Files\nD vc-forces-numerical-derivative consistency\nForces computed by the model agree with numerical derivatives of the energy; see full description.\nResults Files\nN/A vc-dimer-continuity-c1 informational\nThe energy versus separation relation of a pair of atoms is C1 continuous (i.e. the function and its first derivative are continuous); see full description.\nResults Files\nF vc-objectivity informational\nTotal energy is unchanged and forces transform correctly under rigid-body translation and rotation; see full description.\nResults Files\nF vc-inversion-symmetry informational\nTotal energy is unchanged and forces change sign when inverting a configuration through the origin; see full description.\nResults Files\nP vc-memory-leak informational\nThe model code does not have memory leaks (i.e. it releases all allocated memory at the end); see full description.\nResults Files\nThe model returns the same energy and forces when computed in serial and when using parallel threads for a set of configurations. Note that this is not a guarantee of thread safety; see full description.\nResults Files\n\n### Visualizers (in-page)\n\n#### BCC Lattice Constant\n\nThis bar chart plot shows the mono-atomic body-centered cubic (bcc) lattice constant predicted by the current model (shown in the unique color) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.\n\n#### Cohesive Energy Graph\n\nThis graph shows the cohesive energy versus volume-per-atom for the current mode for four mono-atomic cubic phases (body-centered cubic (bcc), face-centered cubic (fcc), simple cubic (sc), and diamond). The curve with the lowest minimum is the ground state of the crystal if stable. (The crystal structure is enforced in these calculations, so the phase may not be stable.) Graphs are generated for each species supported by the model.\n\n#### Diamond Lattice Constant\n\nThis bar chart plot shows the mono-atomic face-centered diamond lattice constant predicted by the current model (shown in the unique color) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.\n\n#### FCC Elastic Constants\n\nThis bar chart plot shows the mono-atomic face-centered cubic (fcc) elastic constants predicted by the current model (shown in blue) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.\n\n#### FCC Lattice Constant\n\nThis bar chart plot shows the mono-atomic face-centered cubic (fcc) lattice constant predicted by the current model (shown in red) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.\n\n#### FCC Stacking Fault Energies\n\nThis bar chart plot shows the intrinsic and extrinsic stacking fault energies as well as the unstable stacking and unstable twinning energies for face-centered cubic (fcc) predicted by the current model (shown in blue) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.\n\n(No matching species)\n\n#### FCC Surface Energies\n\nThis bar chart plot shows the mono-atomic face-centered cubic (fcc) relaxed surface energies predicted by the current model (shown in blue) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.\n\n(No matching species)\n\n#### SC Lattice Constant\n\nThis bar chart plot shows the mono-atomic simple cubic (sc) lattice constant predicted by the current model (shown in the unique color) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.\n\nSpecies: C\n\nSpecies: H\n\nSpecies: N\n\nSpecies: O\n\n### Tests\n\nCohesive energy versus lattice constant curve for monoatomic cubic lattices v003\n\nCreators: Daniel S. Karls\nContributor: karls\nPublication Year: 2019\nDOI: https://doi.org/10.25950/64cb38c5\n\nThis Test Driver uses LAMMPS to compute the cohesive energy of a given monoatomic cubic lattice (fcc, bcc, sc, or diamond) at a variety of lattice spacings. The lattice spacings range from a_min (=a_min_frac*a_0) to a_max (=a_max_frac*a_0) where a_0, a_min_frac, and a_max_frac are read from stdin (a_0 is typically approximately equal to the equilibrium lattice constant). The precise scaling and number of lattice spacings sampled between a_min and a_0 (a_0 and a_max) is specified by two additional parameters passed from stdin: N_lower and samplespacing_lower (N_upper and samplespacing_upper). Please see README.txt for further details.\nTest Test Results Link to Test Results page Benchmark time\nUsertime muliplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.\n\nMeasured in Millions of Whetstone Instructions (MWI)\nCohesive energy versus lattice constant curve for bcc C v003 view 16431\nCohesive energy versus lattice constant curve for bcc N v003 view 7065\nCohesive energy versus lattice constant curve for bcc O v003 view 18413\nCohesive energy versus lattice constant curve for diamond C v003 view 20715\nCohesive energy versus lattice constant curve for diamond N v003 view 12755\nCohesive energy versus lattice constant curve for diamond O v003 view 11188\nCohesive energy versus lattice constant curve for fcc C v003 view 12755\nCohesive energy versus lattice constant curve for fcc N v003 view 16079\nCohesive energy versus lattice constant curve for fcc O v003 view 16335\nCohesive energy versus lattice constant curve for sc C v003 view 2110\nCohesive energy versus lattice constant curve for sc N v003 view 4411\nCohesive energy versus lattice constant curve for sc O v003 view 1918\n\nElastic constants for cubic crystals at zero temperature and pressure v006\n\nPublication Year: 2019\nDOI: https://doi.org/10.25950/5853fb8f\n\nComputes the cubic elastic constants for some common crystal types (fcc, bcc, sc, diamond) by calculating the hessian of the energy density with respect to strain. An estimate of the error associated with the numerical differentiation performed is reported.\nTest Test Results Link to Test Results page Benchmark time\nUsertime muliplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.\n\nMeasured in Millions of Whetstone Instructions (MWI)\nElastic constants for bcc C at zero temperature v006 view 42612\nElastic constants for bcc H at zero temperature v006 view 16751\nElastic constants for bcc N at zero temperature v006 view 26213\nElastic constants for bcc O at zero temperature v006 view 64605\nElastic constants for diamond C at zero temperature v001 view 1647867\nElastic constants for diamond H at zero temperature v001 view 59810\nElastic constants for diamond N at zero temperature v001 view 1036019\nElastic constants for diamond O at zero temperature v001 view 602354\nElastic constants for fcc C at zero temperature v006 view 40918\nElastic constants for fcc H at zero temperature v006 view 108592\nElastic constants for fcc N at zero temperature v006 view 46736\nElastic constants for fcc O at zero temperature v006 view 72437\nElastic constants for sc C at zero temperature v006 view 4731\nElastic constants for sc H at zero temperature v006 view 8759\nElastic constants for sc N at zero temperature v006 view 13011\nElastic constants for sc O at zero temperature v006 view 5179\n\nCohesive energy and equilibrium lattice constant of hexagonal 2D crystalline layers v002\n\nCreators: Ilia Nikiforov\nContributor: ilia\nPublication Year: 2019\nDOI: https://doi.org/10.25950/dd36239b\n\nGiven atomic species and structure type (graphene-like, 2H, or 1T) of a 2D hexagonal monolayer crystal, as well as an initial guess at the lattice spacing, this Test Driver calculates the equilibrium lattice spacing and cohesive energy using Polak-Ribiere conjugate gradient minimization in LAMMPS\nTest Test Results Link to Test Results page Benchmark time\nUsertime muliplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.\n\nMeasured in Millions of Whetstone Instructions (MWI)\nCohesive energy and equilibrium lattice constant of graphene v002 view 639\n\nEquilibrium lattice constant and cohesive energy of a cubic lattice at zero temperature and pressure v007\n\nCreators: Daniel S. Karls and Junhao Li\nContributor: karls\nPublication Year: 2019\nDOI: https://doi.org/10.25950/2765e3bf\n\nEquilibrium lattice constant and cohesive energy of a cubic lattice at zero temperature and pressure.\nTest Test Results Link to Test Results page Benchmark time\nUsertime muliplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.\n\nMeasured in Millions of Whetstone Instructions (MWI)\nEquilibrium zero-temperature lattice constant for bcc C v007 view 17614\nEquilibrium zero-temperature lattice constant for bcc H v007 view 7736\nEquilibrium zero-temperature lattice constant for bcc N v007 view 10741\nEquilibrium zero-temperature lattice constant for bcc O v007 view 19340\nEquilibrium zero-temperature lattice constant for diamond C v007 view 42037\nEquilibrium zero-temperature lattice constant for diamond H v007 view 31967\nEquilibrium zero-temperature lattice constant for diamond N v007 view 41781\nEquilibrium zero-temperature lattice constant for diamond O v007 view 31136\nEquilibrium zero-temperature lattice constant for fcc C v007 view 20139\nEquilibrium zero-temperature lattice constant for fcc H v007 view 38137\nEquilibrium zero-temperature lattice constant for fcc N v007 view 23656\nEquilibrium zero-temperature lattice constant for fcc O v007 view 24615\nEquilibrium zero-temperature lattice constant for sc C v007 view 3708\nEquilibrium zero-temperature lattice constant for sc H v007 view 4955\nEquilibrium zero-temperature lattice constant for sc N v007 view 4667\nEquilibrium zero-temperature lattice constant for sc O v007 view 3069\n\n### Errors\n\nTest Error Categories Link to Error page\nMonovacancy formation energy and relaxation volume for sc O mismatch view\n\nTest Error Categories Link to Error page\nVacancy formation and migration energy for sc O mismatch view\n\nVerification Check Error Categories Link to Error page\nUnitConversion__VC_128739598203_000 mismatch view"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.7800496,"math_prob":0.8057431,"size":13689,"snap":"2020-45-2020-50","text_gpt3_token_len":3275,"char_repetition_ratio":0.16097918,"word_repetition_ratio":0.39037976,"special_character_ratio":0.2422383,"punctuation_ratio":0.065559044,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95862186,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-10-24T15:31:48Z\",\"WARC-Record-ID\":\"<urn:uuid:0ab940ff-d9cc-4617-b6fd-07f3bc96f324>\",\"Content-Length\":\"183876\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d343f6cc-64da-4b04-93b3-8500d91fa527>\",\"WARC-Concurrent-To\":\"<urn:uuid:4a19d7c3-c746-4822-bc4a-80409b560845>\",\"WARC-IP-Address\":\"96.126.117.69\",\"WARC-Target-URI\":\"https://openkim.org/id/Sim_LAMMPS_ReaxFF_StrachanVanDuinChakraborty_2003_CHNO__SM_107643900657_001\",\"WARC-Payload-Digest\":\"sha1:VNF2UGV26SXGBDWMUDHRZINOPTGFYUYW\",\"WARC-Block-Digest\":\"sha1:4JTPCYLVC2ZSPXMXP6HJHXDCRNRYQ6VP\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-45/CC-MAIN-2020-45_segments_1603107883636.39_warc_CC-MAIN-20201024135444-20201024165444-00659.warc.gz\"}"} |
https://taweihuang.hpd.io/2017/03/21/mlbayes/ | [
"# 機器學習中的貝氏定理：生成模型 (Generative Model) 與判別模型 (Discriminative Model)\n\nGAN (Generative Adversarial Networks) 是這幾年來很紅的議題，在 GAN 的兩階段訓練架構下，我們可以很好的逼近生成資料的機率分配，也就是訓練出一個很好的生成模型 (generative model)。這種手法特殊的地方在於，他透過兩層的神經網路(明確一點，是multi-layer perceptron)，一層訓練生成模型 (generative model)，一層訓練判別模型 (discriminative model)，讓這兩層在訓練的過程中進行對抗，使得訓練過程中能夠同時更新生成模型與判別模型中的參數。\n\n### 貝氏精神決定建模邏輯\n\n• 先驗分配 (prior distribution)：目標變數的機率分配",
null,
"$p(Y):\\mathcal{Y}\\rightarrow [0,1]$\n• 聯合分配 (joint distribution)：特徵向量與目標變數的機率分配",
null,
"$p(\\mathbf{X},Y):\\mathcal{D}\\rightarrow [0,1]$\n• 後驗分配 (posterior distribution)：目標變數在給定特徵向量時的條件機率",
null,
"$p(Y|\\mathbf{X}):\\mathcal{Y}\\rightarrow [0,1]$\n\n(註：在這裡我懶的解釋 likelihood 跟 joint distribution的不同，所以暫時都用聯合分配來解釋。)",
null,
"$p(Y|\\mathbf{X}) = \\frac{p(\\mathbf{X},Y)}{p(\\mathbf{X})}=\\frac{p(Y)p(\\mathbf{X}|Y)}{p(\\mathbf{X})}\\propto p(Y)p(\\mathbf{X}|Y)$\n\n### 生成模型：單純貝氏分類器 (Naive Bayes Classifier)",
null,
"$l_{gen}(\\mathbf{X}) = \\log\\frac{p(Y=T|\\mathbf{X})}{p(Y=F|\\mathbf{X})}=\\frac{p(Y=T) \\times \\prod_{i=1}^d p(X_i|Y=T)}{p(Y=F) \\times \\prod_{i=1}^d p(X_i|Y=F)}$\n\n### 判別模型：邏輯式迴歸 (Logistic Regression)",
null,
"$p(Y=T|\\mathbf{X}) = \\frac{\\exp(\\mathbf{X}^T\\boldsymbol\\beta)}{1+\\exp(\\mathbf{X}^T\\boldsymbol\\beta)}$\n\n### 生成模型與判別模型的比較",
null,
"1.",
null,
"Katy 說：\n\nNice essay! 看到小錯字提醒一下，\"從上面的推倒可以看到\" -> 導\n\n1.",
null,
"David Huang 說：\n\n已經修正~ 非常感謝你！:D\n\n2.",
null,
"Melison 說：\n\nThanks for your sharing.✧(≖ ◡ ≖✿)嘿嘿\n\n3.",
null,
"kst 說：\n\n很清楚的解釋，謝謝！\n\n在生成模型的 「計算對數概度比(log likelihood ratio)」那邊，第二個等號的後面是不是少了 log？"
] | [
null,
"https://s0.wp.com/latex.php",
null,
"https://s0.wp.com/latex.php",
null,
"https://s0.wp.com/latex.php",
null,
"https://s0.wp.com/latex.php",
null,
"https://s0.wp.com/latex.php",
null,
"https://s0.wp.com/latex.php",
null,
"https://secure.gravatar.com/avatar/59959899375290ea0bdcd2857d9f7858",
null,
"https://secure.gravatar.com/avatar/84601ab2fad608d9ee0b91467db6c8a2",
null,
"https://secure.gravatar.com/avatar/59959899375290ea0bdcd2857d9f7858",
null,
"https://secure.gravatar.com/avatar/529c80a591c561752da110dd9ea08924",
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"https://secure.gravatar.com/avatar/d71372104a1d1ca157a35a066a0117dc",
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] | {"ft_lang_label":"__label__zh","ft_lang_prob":0.97350425,"math_prob":0.999501,"size":2761,"snap":"2020-45-2020-50","text_gpt3_token_len":2816,"char_repetition_ratio":0.07798331,"word_repetition_ratio":0.0,"special_character_ratio":0.14704818,"punctuation_ratio":0.010909091,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99982053,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-10-31T10:16:05Z\",\"WARC-Record-ID\":\"<urn:uuid:dd752dba-6145-47a7-837e-5bb6bb8f0a54>\",\"Content-Length\":\"48202\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:3f822a16-f64c-4ae2-a30a-39733158bcc2>\",\"WARC-Concurrent-To\":\"<urn:uuid:3d0b75c6-bf32-4468-a026-4c6347ef576f>\",\"WARC-IP-Address\":\"207.38.86.13\",\"WARC-Target-URI\":\"https://taweihuang.hpd.io/2017/03/21/mlbayes/\",\"WARC-Payload-Digest\":\"sha1:3EHONEHISPT5NSQTIUA2M62FCMZ3QAF5\",\"WARC-Block-Digest\":\"sha1:4GJTZBJM6LCOQFZJIGLVF6NROWHCQHHN\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-45/CC-MAIN-2020-45_segments_1603107917390.91_warc_CC-MAIN-20201031092246-20201031122246-00429.warc.gz\"}"} |
https://gitlab.flux.utah.edu/xcap/xcap-capability-linux/-/commit/114bdef0be28aa9aa71e291d133e79edd514f8dc | [
"nfp: preallocate RX buffers early in .ndo_open\n\nWe want the .ndo_open() to have following structure:\n- allocate resources;\n- configure HW/FW;\n- enable the device from stack perspective.\nTherefore filling RX rings needs to be moved to the beginning\nof .ndo_open().\nSigned-off-by:\nSigned-off-by:\nparent 1934680f\n ... ... @@ -1666,28 +1666,19 @@ static void nfp_net_clear_config_and_disable(struct nfp_net *nn) * @nn: NFP Net device structure * @r_vec: Ring vector to be started */ static int nfp_net_start_vec(struct nfp_net *nn, struct nfp_net_r_vector *r_vec) static void nfp_net_start_vec(struct nfp_net *nn, struct nfp_net_r_vector *r_vec) { unsigned int irq_vec; int err = 0; irq_vec = nn->irq_entries[r_vec->irq_idx].vector; disable_irq(irq_vec); err = nfp_net_rx_ring_bufs_alloc(r_vec->nfp_net, r_vec->rx_ring); if (err) { nn_err(nn, \"RV%02d: couldn't allocate enough buffers\\n\", r_vec->irq_idx); goto out; } nfp_net_rx_ring_fill_freelist(r_vec->rx_ring); napi_enable(&r_vec->napi); out: enable_irq(irq_vec); return err; enable_irq(irq_vec); } static int nfp_net_netdev_open(struct net_device *netdev) ... ... @@ -1742,6 +1733,10 @@ static int nfp_net_netdev_open(struct net_device *netdev) err = nfp_net_rx_ring_alloc(nn->r_vecs[r].rx_ring); if (err) goto err_free_tx_ring_p; err = nfp_net_rx_ring_bufs_alloc(nn, nn->r_vecs[r].rx_ring); if (err) goto err_flush_rx_ring_p; } err = netif_set_real_num_tx_queues(netdev, nn->num_tx_rings); ... ... @@ -1814,11 +1809,8 @@ static int nfp_net_netdev_open(struct net_device *netdev) * - enable all TX queues * - set link state */ for (r = 0; r < nn->num_r_vecs; r++) { err = nfp_net_start_vec(nn, &nn->r_vecs[r]); if (err) goto err_disable_napi; } for (r = 0; r < nn->num_r_vecs; r++) nfp_net_start_vec(nn, &nn->r_vecs[r]); netif_tx_wake_all_queues(netdev); ... ... @@ -1827,18 +1819,14 @@ static int nfp_net_netdev_open(struct net_device *netdev) return 0; err_disable_napi: while (r--) { napi_disable(&nn->r_vecs[r].napi); nfp_net_rx_ring_reset(nn->r_vecs[r].rx_ring); nfp_net_rx_ring_bufs_free(nn, nn->r_vecs[r].rx_ring); } err_clear_config: nfp_net_clear_config_and_disable(nn); err_free_rings: r = nn->num_r_vecs; err_free_prev_vecs: while (r--) { nfp_net_rx_ring_bufs_free(nn, nn->r_vecs[r].rx_ring); err_flush_rx_ring_p: nfp_net_rx_ring_free(nn->r_vecs[r].rx_ring); err_free_tx_ring_p: nfp_net_tx_ring_free(nn->r_vecs[r].tx_ring); ... ...\nMarkdown is supported\n0% or .\nYou are about to add 0 people to the discussion. Proceed with caution.\nFinish editing this message first!"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.7273499,"math_prob":0.8043957,"size":500,"snap":"2022-05-2022-21","text_gpt3_token_len":137,"char_repetition_ratio":0.098790325,"word_repetition_ratio":0.0,"special_character_ratio":0.234,"punctuation_ratio":0.17204301,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98463744,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-26T19:44:20Z\",\"WARC-Record-ID\":\"<urn:uuid:7ec45f2d-9b4e-40dd-b142-3130227c9d08>\",\"Content-Length\":\"220959\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c31ae3df-616b-4fed-80bb-18ecd4a2b5b1>\",\"WARC-Concurrent-To\":\"<urn:uuid:cede16fa-27c8-4636-9513-79a69af34f92>\",\"WARC-IP-Address\":\"155.98.60.16\",\"WARC-Target-URI\":\"https://gitlab.flux.utah.edu/xcap/xcap-capability-linux/-/commit/114bdef0be28aa9aa71e291d133e79edd514f8dc\",\"WARC-Payload-Digest\":\"sha1:G5M2L6IRIDCDUJHC3DSQGXQVEREOGPXO\",\"WARC-Block-Digest\":\"sha1:JKQE4UH66MF54D6G3C6MHL6A56R4W7XA\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320304961.89_warc_CC-MAIN-20220126192506-20220126222506-00427.warc.gz\"}"} |
http://narimanfarsad.blogspot.com/2012/11/uniformly-distributed-points-inside.html | [
"Friday, 9 November 2012\n\nUniformly Distributed Random Points Inside a Circle (2)\n\nSo much for posting the answer in a few days! Sorry, I have been Very Very busy.\n\nSo here is the answer. Lets assume we have the Cartesian coordinate system with ($$x,y$$) representing the points. Then joint probability distribution function (PDF) of our random points inside the circle (i.e. the joint distribution of random variable $$X$$ and random variable $$Y$$ representing the $$x$$ and $$y$$ coordinate of the random point) is given by:\n\n$$f_{X,Y}(x,y)= \\begin{cases} \\frac{1}{A}=\\frac{1}{\\pi R_c^2} & x^2+y^2 \\leq R_c^2 \\\\ 0 & \\text{otherwise} \\end{cases},$$\nwhere $$R_c$$ is the radius of the circle.\n\nNow lets consider the polar coordinate system where $$r=g_1(x,y)= \\sqrt{x^2+y^2}$$ and $$\\theta=g_2(x,y)=\\arctan (y/x)$$. Also, from inverting the functions $$g_1$$ and $$g_2$$ we have $$x=h_1(r,\\theta)=r\\cos \\theta$$ and $$y=h_2(r,\\theta)=r\\sin\\theta$$. Now calculating the Jacobian of the transformation we have:\n\n$$J(x,y)= \\det \\begin{bmatrix} \\frac{\\partial r}{\\partial x}=\\frac{x}{\\sqrt{x^2+y^2}} & \\frac{\\partial r}{\\partial y}=\\frac{y}{\\sqrt{x^2+y^2}} \\\\ \\frac{\\partial \\theta}{\\partial x}=\\frac{-y}{x^2+y^2} & \\frac{\\partial \\theta}{\\partial y}=\\frac{x}{x^2+y^2} \\end{bmatrix}= \\frac{1}{\\sqrt{x^2+y^2}}=\\frac{1}{r}.$$\nAlso we have\n$$|J(r,\\theta)|=\\frac{1}{|J(x,y)|}$$\n\nThe joint PDF of random variables $$R$$ and $$\\Theta$$ can then be calculated using the joint PDF of $$X$$ and $$Y$$ as:\n\n$$f_{R,\\Theta}(r,\\theta)= f_{X,Y}\\left( h_1(r,\\theta),h_2(r,\\theta) \\right) = \\begin{cases} \\frac{r}{\\pi R_c^2} & 0 \\leq \\theta \\leq 2\\pi, 0 \\leq r \\leq R_c \\\\ 0 & \\text{otherwise} \\end{cases}.$$\n\nWe can rewrite the non zero part as:\n$$f_{R,\\Theta}(r,\\theta) = \\frac{1}{2\\pi} \\times \\frac{2r}{R_c^2} = f_\\Theta(\\theta)f_R(r)$$\nwhere\n$$f_\\Theta(\\theta) = \\frac{1}{2\\pi}$$\nand\n$$f_R(r)=\\frac{2r}{R_c^2}.$$\nTherefore, $$\\Theta$$ is uniformly distributed between $$0$$ and $$2\\pi$$. The random variable $$R$$ can be generated by first calculating its cumulative distribution function as\n$$F_R(r) = \\int_0^r \\frac{2\\alpha}{R_c^2}d\\alpha = \\frac{r^2}{R_c^2},$$\nand then using a uniformly distributed random variable $$U$$ over the interval $$[0,1]$$ to get\n$$U = \\frac{R^2}{R_c^2} \\implies R=R_c \\sqrt{U}.$$\n\nThe following MATLAB code generates 1000 random numbers inside a circle with radius $$20$$ centered at $$-30$$, $$-40$$.\n\n%**********************************************\nn = 10000;\nRc = 20;\nXc = -30;\nYc = -40;\n\ntheta = rand(1,n)*(2*pi);\nr = Rc*sqrt(rand(1,n));\nx = Xc + r.*cos(theta);\ny = Yc + r.*sin(theta);\n\nplot(x,y,'.'); axis square;\n\n%**********************************************\n\n\nIf you don't understand how I did the PDF transformation see\nChapter 6 (6.2.3 to be exact) or\nChapter 8 (8.3 to be exact).\n\nI hope this helps someone out there.\n\n1.",
null,
"Thank you for the informative post. It really helps me out of what I am currently stuck with. One typo I found if I am right is that R_{c} on the right hand side of last expression should not be squared.\n\n1.",
null,
"Thank you. I fixed the typo.\n\n2.",
null,
"Maybe you did not expect your post to help someone after almost one year .. it did for me : )\n\nBTW another typo -- one of the \"theta\"'s should have been \"\\theta\" ..\n\nThanks a lot for this helpful post!\n\n1.",
null,
"I am glad it helped. I fixed the typo.\n\n3.",
null,
"4.",
null,
"5.",
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""
] | [
null,
"http://lh3.googleusercontent.com/zFdxGE77vvD2w5xHy6jkVuElKv-U9_9qLkRYK8OnbDeJPtjSZ82UPq5w6hJ-SA=s35",
null,
"http://lh3.googleusercontent.com/zFdxGE77vvD2w5xHy6jkVuElKv-U9_9qLkRYK8OnbDeJPtjSZ82UPq5w6hJ-SA=s35",
null,
"http://lh3.googleusercontent.com/zFdxGE77vvD2w5xHy6jkVuElKv-U9_9qLkRYK8OnbDeJPtjSZ82UPq5w6hJ-SA=s35",
null,
"http://lh3.googleusercontent.com/zFdxGE77vvD2w5xHy6jkVuElKv-U9_9qLkRYK8OnbDeJPtjSZ82UPq5w6hJ-SA=s35",
null,
"http://lh3.googleusercontent.com/zFdxGE77vvD2w5xHy6jkVuElKv-U9_9qLkRYK8OnbDeJPtjSZ82UPq5w6hJ-SA=s35",
null,
"http://resources.blogblog.com/img/blank.gif",
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"http://resources.blogblog.com/img/blank.gif",
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.7266753,"math_prob":0.9999918,"size":3360,"snap":"2019-26-2019-30","text_gpt3_token_len":1093,"char_repetition_ratio":0.14243147,"word_repetition_ratio":0.0,"special_character_ratio":0.38065475,"punctuation_ratio":0.11884058,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.0000097,"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\":\"2019-06-18T17:11:08Z\",\"WARC-Record-ID\":\"<urn:uuid:232dbc0a-4da8-437c-a228-565e3cab867e>\",\"Content-Length\":\"67417\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:81080a51-16dd-40fd-9b69-34e0daa6c14d>\",\"WARC-Concurrent-To\":\"<urn:uuid:46950e8f-b81b-4bca-9ef4-9f4590047bb6>\",\"WARC-IP-Address\":\"172.217.164.161\",\"WARC-Target-URI\":\"http://narimanfarsad.blogspot.com/2012/11/uniformly-distributed-points-inside.html\",\"WARC-Payload-Digest\":\"sha1:WB3KYSFGZRA33PM35GIWHKPAKY5FJ3AZ\",\"WARC-Block-Digest\":\"sha1:S6M6MDPTT2JQICAY7PI44AKNODHVBCZZ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-26/CC-MAIN-2019-26_segments_1560627998808.17_warc_CC-MAIN-20190618163443-20190618185443-00384.warc.gz\"}"} |
https://mathoverflow.net/questions/156265/a-question-about-consistent-fragments-of-formalized-mathematical-theories-with-n | [
"A question about consistent fragments of formalized mathematical theories with Natural Deduction\n\nRef to : Sara Negri & Jan von Plato, Structural Proof Theory (2001).\n\nIn Ch.6 : Structural Proof Analysis of Axiomatic Theories [page 126-on], they\n\ngive a method of adding axioms to sequent calculus, in the form of nonlogical rules of inference.\n\nTheorem 6.4.1 [page 136] : If $\\Gamma \\implies \\Delta$ is derivable in $G3im^*$ or $G3c^*$, [where the first is an extesion of $G3im$, the intuitionistic multisuccedent sequent calculus] the derivation are either subformulas of the endsequent or atomic formulas.\n\nConsider a theory having as axioms a finite set $D$ of regular formulas. Define $D$ to be inconsistent if $\\implies \\bot$ is derivable in the corresponding extension and consistent if it is not inconsistent. For a theory $D$, inconsistency surfaces with the axioms through regular decomposition, with no consideration of the logical rules:\n\nTheorem 6.4.2: [...]\n\nIt follows that if an axiom system is inconsistent, its formula traces contain negations and atoms or disjunctions. Therefore, if there are neither atoms nor disjunctions, the axiom system is consistent, and similarly if there are no negations. [page 137]\n\nFinally, they consider [page 147-148] Lattice theory, and conclude with :\n\nAll structural rules are admissible in the proof-theoretical formulation of lattice theory. The underivability of $\\implies \\bot$ follows, by Theorem 6.4.2, from the fact that no axiom of lattice theory is a negation.\n\nConsider now, for simplicity, one of the following systems [see Peter Smith, An Introduction to Gödel's Theorems (1st ed - 2007), page 51-on] :\n\nBA, Baby Arithmetic\n\nQ, Robinson Arithmetic\n\nBoth have the axiom : $\\lnot 0 = S(x)$, that is (using standard \"unabbreviation\" for $\\lnot$) : $0 = S(x) \\rightarrow \\bot$.\n\nUsing the fact established above, may we say that if we have systems whose axioms does not include the $\\bot$ sign, they are ipso facto consistent ?\n\nAre there “interesting fragments” of arithmetic, based on intuitionistic sequent calculus, that are “negation-free” ?\n\nIn negation-free arithmetic, replace the axiom $\\neg 0=S(x)$ with $0=S(x) \\rightarrow 0=1$. This has the same negation-free theorems as ordinary arithmetic.\nThe amusing reason for this is that any arithmetical statement follows from $0=1$, even without negation: $0=1$, so $0=a$ and $0=b$ and therefore $a=b$, and so on.\n• Thanks for your hints, but I'm not sure that it works. My idea (perhaps a stupid one) was : I'm asking if we can try to exploit the nature of sequent calculus rules with the above result of Negri & von Plato [i.e.if the axioms do not contain $\\lnot$ nor $\\bot$ we may have a consistentcy proof \"by inspection] to a theory like Robinson arithmetic, omitting the axioms with the $\\lnot$ symbol (eventually, replacing them). I think that $0=1$ is only $\\bot$ \"in disguise\", so that using $0=S(x) \\rightarrow 0=1$ in place of $\\lnot 0=S(x)$ will inhibit the application of the above result. – Mauro ALLEGRANZA Feb 1 '14 at 16:02"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.84461325,"math_prob":0.9979802,"size":1995,"snap":"2019-43-2019-47","text_gpt3_token_len":502,"char_repetition_ratio":0.10748368,"word_repetition_ratio":0.0,"special_character_ratio":0.24761905,"punctuation_ratio":0.15322581,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99973994,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-24T06:00:40Z\",\"WARC-Record-ID\":\"<urn:uuid:7064ae0d-09ea-4bed-94da-01c4643f7e45>\",\"Content-Length\":\"119088\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:88be5ab6-c907-4982-b630-9701e9a8c753>\",\"WARC-Concurrent-To\":\"<urn:uuid:2c189e5c-fb81-4f82-b501-eadc6ee6ba3a>\",\"WARC-IP-Address\":\"151.101.129.69\",\"WARC-Target-URI\":\"https://mathoverflow.net/questions/156265/a-question-about-consistent-fragments-of-formalized-mathematical-theories-with-n\",\"WARC-Payload-Digest\":\"sha1:EJGSWDNZJ2BVNWCLEQK3GRNTCJUCIS3E\",\"WARC-Block-Digest\":\"sha1:QKP6IKQIMTDFWSENE5S3Z5FGOMRXFUU2\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570987841291.79_warc_CC-MAIN-20191024040131-20191024063631-00246.warc.gz\"}"} |
https://socratic.org/questions/in-how-many-years-will-the-population-of-the-city-be-120-000-if-the-population-p | [
"In how many years will the population of the city be 120,000 if the population P in thousands of a city can be modeled by the equation P=80e^0.015t , where t is the time in years?\n\nMar 29, 2015\n\n$P = 80 {e}^{0.015} t$ can be re-written as\n$t = \\frac{P}{80 {e}^{0.015}}$\n\nWe are given that $P = 120$ (thousand).\nSo\n$t = \\frac{120}{80 {e}^{0.015}}$\n\nwith a little help from Excel:\n$t = 2.216502$ years",
null,
"Mar 29, 2015\n\nApproximately 27 years.\nI misread this question.\n\nIf the the model is: $P = 80 {e}^{0.015 t}$ with P measured in thousands, then:\n\nWhen the population is $120 , 000$, the variable $P$ will have a value of $120$\n\nWe've been asked to solve:\n\n$120 = 80 {e}^{0.015 t}$\n\n$80 {e}^{0.015 t} = 120$\n\n${e}^{0.015 t} = \\frac{120}{80} = \\frac{3}{2} = 1.5$\n\n${e}^{0.015 t} = 1.5$\n\n$0.015 t = \\ln \\left(1.5\\right)$\n\n$t = \\ln \\frac{1.5}{0.015}$\n\nUsing a table of values or electronics gives an approximation of $t \\approx 27.03$.\n\nNotes:\n\n1. Here I used $\\ln$ to mean the natural logarithm function. If your teacher or textbook uses $\\log$ to mean the natural logarithm, then you should too.\n2. When solving an exponential function, it is most convenient to start by making the form of the equation: $\\text{base\"^\"variable expression\" = \"constant expression}$. In this equation, that is the reason we divided by $80$ before taking the natural logs of both sides of the equation.\n(A constant expression is a number, like $1.5$ or $\\frac{3}{2}$ or (5+sqrt7)/8)"
] | [
null,
"https://d2jmvrsizmvf4x.cloudfront.net/zi14nR8RKP2JPQU8cGqg_CityPopSS.GIF",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.84853727,"math_prob":0.9999646,"size":1097,"snap":"2019-43-2019-47","text_gpt3_token_len":284,"char_repetition_ratio":0.10704483,"word_repetition_ratio":0.0,"special_character_ratio":0.26709208,"punctuation_ratio":0.1,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.0000054,"pos_list":[0,1,2],"im_url_duplicate_count":[null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-24T02:28:37Z\",\"WARC-Record-ID\":\"<urn:uuid:4e1ebb9e-c5b1-47c4-a407-d88860a6a37a>\",\"Content-Length\":\"36079\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:af0d7ccf-405f-4cf4-a096-5ba67bb54b90>\",\"WARC-Concurrent-To\":\"<urn:uuid:bc9e6346-a34e-43eb-81d6-660c12a92f82>\",\"WARC-IP-Address\":\"54.221.217.175\",\"WARC-Target-URI\":\"https://socratic.org/questions/in-how-many-years-will-the-population-of-the-city-be-120-000-if-the-population-p\",\"WARC-Payload-Digest\":\"sha1:BRSCZDLKAY6GVXN5UXXKV4WINFZDRJL6\",\"WARC-Block-Digest\":\"sha1:ZXTWW42LH7KJUBCTX6YAIQX743SYZK5M\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570987838289.72_warc_CC-MAIN-20191024012613-20191024040113-00483.warc.gz\"}"} |
https://www.icserankers.com/2021/08/frank-icse-solutions-for-heat-class9-physics.html | [
"# Frank Solutions for Chapter 5 Heat Class 9 Physics ICSE\n\n### Exercise 5.1\n\n1. What do you mean by heat?\n\nHeat is defined as a form of energy which flows from one point to another on account of temperature difference.\n\n2. Is heat a form of energy?\n\nYes, heat is a form of energy.\n\n3. Name the SI unit of heat.\n\nJoule is the SI unit of heat.\n\n4. Define one joule of heat.\n\nOne calorie is defined as the quantity of heat required to raise the temperature of 1 gram of water through 1°C.\n\n5. What is the relation between joule and calorie?\n\n1 calorie = 4.2 joules.\n\n6. Define temperature and write its SI unit.\n\nTemperature is the degree of hotness or coldness of a body compared to other bodies around it.\n\nSI unit of temperature is Kelvin (K).\n\n7. Why does a piece of ice when touched with hands appear cold?\n\nWe feel cold on touching ice because heat flows from our warm hands to cold ice. Due to this flow of heat from hand to ice, the temperature of our hand falls. This is why we feel cold.\n\n8. Distinguish between heat and temperature.\n\n9. Two bodies at different temperatures are placed in contact with each other. State the direction in which heat flows.\n\nHeat flows from a body at a higher temperature to a body of lower temperature.\n\n10. Is it correct to say that heat is the cause of temperature?\n\nYes, heat is the cause of temperature because temperature of a body rises when the heat flows into the body.\n\n11. What causes a change in the temperature of a body?\n\nHeat changes the temperature of a body due to flow of heat in or out of the given body.\n\n12. Which is more, a calorie or a joule?\n\nCalorie. Because 1 calorie = 4.2 joules.\n\n13. 1 joule = 4.2 calorie\n\nIs this relation correct?\n\nNo, the exact relation is as given\n\n1 calorie = 4.2 joules.\n\n14. Two bodies are at same temperature. Do they necessarily contain same amount of heat?\n\nYes, because the heat flow is only due to temperature difference between the temperature of two bodies.\n\n### Exercise 5.2\n\n1. What do you mean by temperature?\n\nTemperature is the degree of hotness or coldness of a body compared to other bodies around it.\n\nSI unit of temperature is Kelvin (K)\n\n2. What is the normal temperature of human body?\n\nNormal temperature of human body is 37°C.\n\n3. Convert 20°C into Fahrenheit scale.\n\nTo convert 20° into°F\n\nt°c /100 = (t°f - 32)/180\n\n⇒ 20/100 = (t°f – 32)/180\n\n⇒ 20 × 180/100 = t°f – 32\n\n⇒ t°f = 36 + 32\n\n⇒ t°f = 68°f\n\n4. What is the upper fixed point on the Celsius scale?\n\nUpper fixed point on the Celsius scale is 100°C.\n\n5. Convert 80 K temperatures on the Celsius scale.\n\nTk = 80K\n\n⇒ Tc = Tk - 273\n\n⇒ Tc = 80 - 273\n\n⇒ Tc = -153° C\n\n6. Write down the SI unit of latent heat.\n\nSI unit of latent heat is Joule per kg (J/kg).\n\n7. What do you mean by relative humidity?\n\nRelative humidity is defined as the amount of water vapour in the air compared to the amount needed for saturation.\n\n8. Define coefficient of linear expansion. Write its SI unit.\n\nCoefficient of Linear expansion is equal to the change in length of a rod of length 1m when its temperature rises by 1°C. Its SI unit is °c-1.\n\n9. Name the scientist who designed the first thermometer.\n\nCelsius was the scientist who discovered the first thermometer in 1710.\n\n10. What is the principle of calorimetry?\n\nAccording to principle of calorimetry of mixtures,\n\nHeat gained = Heat lost\n\n11. Write the SI unit of coefficient of cubical expansion.\n\nSI unit of coefficient of cubical expansion is °c\".\n\n12. State two uses of a bimetallic strip.\n\nTwo uses of bimetallic strip are\n\n1. As thermostat in electric iron\n2. As balance wheel in watches\n\n13. Why do telephone wires sag during summer?\n\nTelephone wires sag in summer because due to heat of the sun, the wire expands and increases in length, thus they sag in summer.\n\n14. State the types of thermal expansion. What is the relation between α and γ?\n\nThere are three types of thermal expansion\n\n1. Linear expansion\n2. Superficial expansion\n3. Cubical expansion\n\nCoefficient of linear expansion be α\n\nCoefficient of cubical expansion be γ\n\nγ = 3α\n\n15. Do all substances expand on heating? Give examples.\n\nNot all substances expand on heating. Some examples of substances which do not expand on heating are plastics, polythene and rubber.\n\n16. What is evaporation? Why does it cause cooling?\n\nEvaporation is the phenomenon of a change of a liquid into vapour without raising the temperature. Evaporation needs energy for phase change from liquid to gases. As water evaporates off your skin, it absorbs energy(heat) from the body to make the phase change to gas thus cooling the body.\n\n17. State three factors affecting evaporation.\n\nFactors affecting evaporation are\n\n1. Humidity- more the humidity less is the evaporation\n2. Surface area- more the surface area more is the evaporation\n3. wind- more the wind more is the evaporation\n4. temperature- more the temperature more is the evaporation\n\n18. What are land and sea breezes? Explain with the help of a labelled diagram.\n\nThe cold air that blows from land towards sea during night, is called land breeze\n\nThe cold air that blows from the sea towards the land during the day is known as the sea breeze. These breezes are the examples of natural convection current.\n\n19. Is conduction possible in gases?\n\nNo, the conduction is not possible in gases. Gases are bad conductors.\n\n20. Is conduction possible in vacuum?\n\nNo, conduction is not possible in vacuum.\n\n21. What is the velocity of thermal radiations?\n\nThe velocity of thermal radiations is equal to the speed of light i.e,.3 x 108 m/s.\n\n22. Why do we wear woolen clothes in winter?\n\nWe wear woolen clothes in winter because woolen clothes have tiny pores and air is trapped in these pores and being a bad conductor, the trapped air obstructs the flow of body heat to the surroundings.\n\n23. Why is a newly made quit warmer than an old one?\n\nA newly made quilt is warmer than an old one because the cotton in the old quilt gets compressed and very little air will remain trapped in it, hence heat insulation is quite poor.\n\n24. In cold countries, the water pipes are covered with poor conductors. Why?\n\nIn cold countries, water pipes are covered with poor conductors because poor conductor prevents water from freezing and thus prevent these pipes from bursting.\n\n25. Name three devices which are used to detect heat radiations.\n\nThree devices used to detect heat radiations are\n\n1. Blackened bulb thermometer\n2. Differential air thermo scope\n3. Thermopile\n\n26. What is meant by thermal expansion?\n\nThe increase in size of a body on heating is called thermal expansion.\n\n27. What do you mean by linear expansion?\n\nLinear expansion is the increase in length of a solid on heating.\n\n28. Define coefficient of linear expansion.\n\nCoefficient of Linear expansion is equal to the change in length of a rod of length 1m when its temperature rises by 1°c.\n\n29. What is a bimetallic strip?\n\nA bimetallic strip consists of two metal strips- one with high coefficient of expansion and the other with low coefficient of expansion.\n\n30. What is the unit of coefficient of linear expansion?\n\nSI unit of coefficient of linear expansion is °c’.\n\n31. Name the substance which contracts when heated from 0°C to 4°C.\n\nWater is the substance which contracts, when heated from 0°C to 4°C.\n\n32. Define coefficient of volume expansion.\n\nCoefficient of volume expansion is equal to the change in volume of a rod of volume 1m3 when its temperature rises by 1°C.\n\n33. What is the unit of coefficient of volume expansion?\n\nSI unit of coefficient of volume expansion is °C-1.\n\n34. State two uses of bimetallic strip.\n\nTwo uses of bimetallic strip are\n\n1. As thermostat in electric iron\n2. As balance wheel in watches\n\n35. How can a glass stopper jammed in the neck of a bottle be removed?\n\nWe should heat the neck of the bottle because due to heating the neck will expand and loosen the stopper stuck in the neck. In this way, we can easily remove the stopper from the bottle.\n\n36. Why does a thick glass tumbler crack when very hot water is poured in it?\n\nWhen hot water is poured into a thick glass tumbler, it generally cracks because on pouring hot water in the tumbler the inner surface heats up and expands more as compared to its outer surface. This unequal expansion between the two surfaces causes a strain and the tumbler cracks.\n\n37. Why does a substance expand on heating?\n\nA substance is made up of molecules arranged in a lattice. On heating, the molecules vibrate faster in the lattice and bump into each other harder. So the distance between the molecules increases thus expanding lattice. Thus, the substances expand on heating.\n\n38. What are the different types of thermal expansions?\n\nThere are three types of thermal expansion\n\n1. Linear expansion\n2. Superficial expansion\n3. Cubical expansion\n\n39. A small gap is left between two iron rails of the railway track. Why?\n\nGaps are left in the railway tracks because the tracks gets heated during the day and as a result they increase in length. If the gaps are not provided, the railway line would buckle outward and may cause derailment.\n\n40. Why are bridges made of steel girders put on rollers?\n\nThe beams of the bridges expand maximum during the summer days and contract maximum during the winter nights. If the beams are fixed at both ends on the pillars, they may develop crack due to expansion and contraction. To avoid this, beams are made to rest on rollers on the pillars to provide space for expansion.\n\n41. What is the relation between α and γ?\n\nLet Coefficient of linear expansion be α\n\nCoefficient of cubical expansion be y\n\nThe relation between them is\n\nγ = 3 α\n\n42. A copper wire 10 cm long is heated from 20°C to 30°C. Find the increase in length of the wire, if coefficient of linear expansion of copper is 1.7 × 10-5°C-1?\n\nOriginal length, | = 10 cm = 0.1 m\n\nRise in temperature, t = 30 - 20 = 10°C\n\nCoefficient of linear expansion, a = 1.7 ×10-5 °C-1\n\nIncrease in length = I ×t × a\n\n= 0.1 × 10 × 1.7 × 10-5\n\n= 1.7 × 10-5 m\n\n43. One liter of mercury at 10°C is heated to 30°C. Find the increase in the volume of mercury. The coefficient of cubical expansion of mercury is 1.8 × 10-4 0c-1\n\nVolume of mercury, V = 1 liter\n\nRise in temperature, t = 30 - 20 = 20°C\n\nCoefficient of volume expansion, y = 1.8 ×10-4°C-1?\n\nIncrease in volume = V ×t ×y\n\n= 1 ×20 ×1.8 ×10-4\n\n= 3.6×10-3 liter\n\n44. Why is a ventilator provided in a room?\n\nA ventilator is provided in a room because it helps in removing the hot air from the room and allows the fresh and cold air to come in.\n\n45. Is it possible to heat a liquid or gas from above? Explain your answer.\n\nNo, it is not possible to heat a liquid or gas from above because the transfer of heat through convection takes place vertically upwards in liquids and gases.\n\nSo if they are heated from above, the liquid or gas at the top will only be heated because most liquids and gases are themselves bad conductor of heat so they cannot conduct heat from top layer to the bottom layer.\n\n46. Explain the following:\n\n(i) Water is heated generally from below.\n\n(ii) Land becomes warmer than water during the day.\n\n(i) Water is heated generally from below because water itself is a bad conductor of heat and the transfer of heat through convection take place vertically upwards.\n\n(ii) Land becomes warmer than water during the day because water has more specific heat capacity so it absorbs the heat and heats up slowly but on the other hand land has less specific heat and it heats up faster than water.\n\n47. State three main characteristics of a thermometric substance.\n\nMain characteristics of thermometric substance are\n\n1. The substance should have high coefficient of expansion so that it is sensitive to the smallest change in temperature\n2. The substance should have uniform expansion all over its entire volume\n3. The substance should have minimum specific heat so that it absorbs minimum heat from the body under measurement.\n\n48. Name a substance which is an insulator of heat.\n\nWood is an insulator of heat.\n\n49. (i) Why in cold countries windows have two glass panes with a thin layer of air between them?\n\n(ii) What is the relation between joule and calorie?\n\n(iii) Is it possible to boil water in a thin paper container? Explain with a reason.\n\n(a) In cold countries, windows are provided with two glass panes because in between these two glass panes, a thin layer of air is present: air being a bad conductor obstructs the conduction of heat from the room to outside.\n\n(b) 1 calorie = 4.2 joules\n\n(c) Yes, it is possible to boil water in a thin paper cup because when heated the heat in the paper cup is transferred to the water through convection and paper cup doesn't get sufficient heat to get burnt\n\n50. What is the principle of the thermometer?\n\nThermometer works on the principle that substances expand on heating and contract on cooling. So we use a thermometric substance which expands and contracts uniformly.\n\n51. State the advantages and disadvantages of mercury and alcohol as thermometric liquids.\n\nAdvantages of mercury and alcohol as thermometric liquid:\n\n1. They both are good conductors of heat.\n2. They have high coefficient of expansion thus are sensitive to the smallest change in temperature\n3. Their freezing points are very low and boiling point is high in case of mercury\n\nDisadvantages f mercury and alcohol as thermometric liquid:\n\n1. Alcohol is transparent and this makes hard to read the thermometer.\n2. It does not have uniform expansion.\n3. Mercury is less sensitive than alcohol as its coefficient of expansion is less than alcohol.\n4. Alcohol is a volatile liquid.\n\n52. What is meant by the lower and upper fixed points of a thermometer?\n\nLower point of a thermometer is the temperature at which ice starts melting at normal atmospheric pressure i.e. 0°C\n\nUpper point of a thermometer is the temperature at which water just starts boiling at normal atmospheric pressure i.e. 100°C.\n\n53. Draw a neat and labelled diagram of a clinical thermometer.\n\nA clinical thermometer is used to measure the body temperature. The capillary tube has a constriction above the bulb preventing mercury to fall back once it has risen.\n\n54. State one use of each of the following types of thermometers: (i) Laboratory thermometer, (ii) Clinical thermometer, (iii) Six's maximum and minimum thermometer.\n\n(i) Laboratory thermometer is used to measure and observe the temperature of various chemical reactions\n\n(ii) Clinical thermometer is used to measure human body temperature\n\n(iii) Six's maximum and minimum thermometer is used in meteorology and horticulture.\n\n55. Distinguish between a clinical and a laboratory thermometer.\n\nDifference between laboratory and clinical thermometer.\n\n56. Which is the temperature that is common in the Celsius and the Fahrenheit scale?\n\nThe temperature that is common in both clinical and Fahrenheit scale is 40°C\n\nDerivation is as follows\n\nLet the temperature be x\n\nC/100 = (F - 32)/180\n\n⇒ x/100 = (x - 32)/180\n\n⇒ x × 180/100 = x - 32\n\n⇒ 9/5x = x - 32\n\n⇒ -4/5x = 32\n\n⇒ x = - 40\n\n57. Convert the following temperatures into Fahrenheit scale:\n\n60°C, 100°, -40°C, 85°C\n\n(a) 60°C\n\n60/100 = (F - 32) /180\n\n⇒ F = 6×18 + 32\n\n= 110° F\n\n(b) 100 ° C\n\n100/100 = (F – 32)/180\n\nF = 180×1 + 32\n\n= 212°F\n\n(c) - 40° C\n\n-40/100 = (F – 32)/180\n\nF = - 4×18 + 32\n\n= 40° F\n\n(d) 85°c\n\n85/100 = (F – 32)/180\n\nF = 85× 18/10 + 32\n\n= 185°F\n\n58. Convert the following temperatures into Celsius scale.\n\n(a) 104 °F\n\nC = (F – 32)× 100/180\n\nC = 72 x 100/180\n\n= 40 °C\n\n(b) 95°F\n\nC = (F – 32)× 100/180\n\n= 63 x 10/18\n\n= 35° C\n\n(c) 113° F\n\nC = (F – 32)× 100/180\n\n= 81 x 10/18\n\n= 45°C\n\n(d) 32°F\n\nC = (F – 32)× 100/180\n\n= 0 x 10/18\n\n= 0°C\n\n59. Draw a neat and labelled diagram of a Six's maximum and minimum thermometer. Explain briefly, the working of this thermometer. Give a use of this thermometer.\n\nDiagram of six’s maximum and minimum thermometer\n\nSix's thermometer is a thermometer which can measure the maximum and minimum temperatures reached over a period of time, usually during a day. It is commonly used wherever a simple way is needed to measure the extremes of temperature at a location, for instance in meteorology and horticulture.\n\n60. Explain the three modes of transfer of heat.\n\nThree modes of heat transfer are\n\n1. Conduction involves the transfer of heat from the hot end to the cold end from particle to particle of the medium.\n2. Convection is the transfer of heat from one body to another by actual movement of the particles of the medium\n3. Radiation is the transfer of heat from one body to another without the need of an intervening material medium\n\n61. With the help of a diagram, show that water is a bad conductor of heat.\n\nAn ice cube is wrapped into a wire mesh and is put at the bottom of the glass test tube. The test tube is then heated near the top of the water. It will be Noticed that though the water at the top starts boiling, the ice at the bottom does not melt. This clearly shows that water is poor conductor of heat.\n\n62. Write a short note on Land Breeze and Sea Breeze.\n\nThe cold air that blows from land towards sea during night, is called land breeze\n\nThe cold air that blows from the sea towards the land during the day is known as the sea breeze. These breezes are the examples of natural convection current.\n\n63. A wooden knob and a metal latch on a door are both at room temperatures. Explain, why the latch is colder to touch.\n\nA wooden knob and a metal latch are both being at same temperature but it feels colder to touch the latch because metal is a good conductor and as soon as we touch it heat from our hand flows to the latch and we feel cold while on the other hand wood is a bad conductor of heat, heat of our hand does not flow into it therefore it does not feel cold.\n\n64. Draw a neat and labeled diagram of a vacuum flask (thermos flask). Explain, how it minimizes loss of heat by preventing conduction, convection and radiation.\n\nThe flask consists of double walled glass container with vacuum between the walls A and B to prevent heat loss due to conduction and convection as vacuum is the excellent insulator .to prevent heat loss by radiation, the inner side of the wall A and outer side of wall B is silvered. It has a narrow mouth which is closed by a non-conducting rubber stopper.\n\n65. A spiral cut from a thick chart paper is pivoted at O and is held slightly above a burning candle (Fig. 1). You will notice that the spiral starts moving. Explain.\n\nThe spiral starts moving because due to the flame of the candle the spiral heats up and expands. While expanding, the spiral tries to create space for the extension in length and an outward pull is created which causes the spiral to move.\n\n66. Give scientific reasons for the following:\n\n(i) In winter the human body covered with a blanket keeps warm.\n\n(ii) It is better to use thin blankets to keep the body warm rather than using a single blanket of thickness equal to their combined thickness.\n\n(iii) In winter the birds fluff up their feathers.\n\n(iv) Old quits are less warm than the new ones.\n\n(v) On a hot sunny day, it is advisable to wear light coloured clothes.\n\n(i) In winters, the human body covered with a blanket keeps warm because the blanket has air trapped in it which provide heat insulation to the body from the surroundings and keep us warm.\n\n(ii) It is better to use two thin blankets to keep the body warm rather than using a single blanket of equal thickness because in between the two thin blankets there is more air trapped than in the single blanket of equal thickness so using two thin blankets better heat insulation is provided to the body from the surroundings and keep us warm\n\n(iii) In winter the birds fluff their feathers in order to trap air in their feathers so that the air provides heat insulation to their body from the surroundings and keep them warm and save them from winter.\n\n(iv) Old quilts are less warmer than new ones because the cotton in the old quilt gets compressed and very little air will remain trapped in it, hence heat insulation is quite poor\n\n(v) People wear light coloured clothes in winter because these clothes reflect most of the sun's radiations and absorb only a little of them. Therefore, they keep themselves cool.\n\n67. What is meant by energy flow?\n\nTransformation of Sun's energy in sun-eco system through a food chain is called energy flow.\n\n68. Draw a flow chart to establish that the transfer of sun's energy in a sun-eco system combination in not cyclic.\n\nHeat produced in various conversion processes like production, consumption, etc is not returned to the sun. Thus energy flow of the sun-eco system is not cyclic.\n\n69. State reason why any energy transfer cannot be 100%.\n\nAny energy transfer is not 100% because energy is lost to the surroundings in the form of heat, friction losses during the transfer of energy. Therefore complete energy is not transferred.\n\n70. State briefly the functioning of a biogas power-source.\n\nBio gas is produced by the action of bacteria on decaying organic matter. The primary source of bio gas in villages is dung of cow, or buffalo. The bio gas is mostly methane which can be used as chief source of light and heat energy.\n\n71. The diagram (Fig. 2) shows two air filled bulbs connected by a U-tube containing mercury kept equidistant from a glassing bulb.\n\n(i) Explain, how will the level X and Y change?\n\nThe level Y will rise and the level X will drop because the air in blackened bulb is heated more than clear bulb; hence the air expands and pushes the mercury to the other limb.\n\n72. The following diagrams illustrate three situations involving thermometers which are labeled A, B and C (Fig. 3). In each situation the thermometers indicate different readings.\n\n(i) What do you expect the approximate reading of the thermometer B and C would be? Give a reason for your answer.\n\n(i) Temperature of steam and boiling water is equal so reading of thermometer is same. But due to addition of salt boiling point of water elevates so reading of thermometer would be slightly higher than the boiling point of water i.e. 100°C.\n\n(ii) Due to addition of salt boiling point of water increases so thermometer has to measure temperature for a wider range and thus it helps in calibration of thermometer.\n\n73. A hot metal ball is suspended from a string in a metal box as shown in fig. 4.\n\n(i) What are the ways in which the ball loses heat?\n\n(ii) Which side of the box will be the hottest and which the least hot after sometime? Explain.\n\n(ii) Speed of heat radiation is equal to the speed of light and intensity of heat radiation does net depend upon direction so all side of the box would be equally het as the box is cubical.\n\n74. Fig. 5 shows a metal cylinder, containing boiling water. One half side A, is polished and another half, B is painted black. Two thin metal sheets X and Y are painted black and have one rubber stopper fixed with wax on each sheet. These sheets are equidistant from the boiling water (container A, B) as shown in the diagram. What would you expect to happen after a few minutes? Give reason for your answer.\n\nAfter a few minutes the rubber stopper fixed to plate y will drop down because since the plate y is on the black side of the cylinder. The black side of the cylinder radiates more heat than the polished side so it heats up the plate Y faster than heating up of plate X by polished surface of the cylinder which melts down the wax holding the stopper and the stopper will drop down.\n\n75. Distinguish between Mercury and Alcohol as a thermometric liquid.\n\nDifference between mercury and alcohol as thermometric substance\n\n76. Water is not used as a thermometric liquid. Why?\n\nWater is not used as a thermometric liquid because It has low coefficient of expansion so it is less sensitive to temperature changes. Moreover, It is transparent thus making it difficult to read the thermometer and water evaporates with time thus producing error and also the freezing and boiling points are also low.\n\n77. How can you increase the sensitivity of a thermometer?\n\nThe sensitivity of a thermometer can be increased by using a substance having high coefficient of expansion and uniform expansion so that its expands with the slightest change in temperature.\n\n78. Explain the following:\n\n(i) Why a thick glass tumbler is likely to crack when hot water is poured in it?\n\n(ii) Why does not a Pyrex tumbler crack when hot water is poured in it?\n\n(i) When hot water is poured into a thick glass tumbler, it generally cracks because on pouring hot water in the tumbler the inner surface heats up and expands more as compared to its outer surface. This unequal expansion between the two surfaces causes a strain and the tumbler cracks.\n\n(ii) Pyrex glass tumbler does not crack on adding hot water because Pyrex glass has low coefficient of expansion. It does not expand less when hot water is added to the tumbler.\n\n79. Water at 0°C is heated to 10°C. Sketch a temperature-volume graph to show the behavior on heating.\n\nIt can be seen from the graph that the volume of the water decrease from 0°C to 4°C and the volume is minimum at 4°C. After 4°C the volume increases with the increase in temperature.\n\n80. Differentiate between clinical thermometer and laboratory thermometer.\n\nDifference between laboratory and clinical thermometer\n\n81. Study the following diagrams (Fig. 6) and write down your observations.\n\nIn the diagram it is dear that the ice will melt faster in the flask than in the test tube because water is bad conductor of heat and the transfer of heat in liquid through convection is from bottom to top\n\n82. The temperature of two bodies A and B differ by 1°C. By how much will it differ on a Fahrenheit scale?\n\nTemperature in °C = 1°C\n\nC/100 = (F - 32)/180\n\nF = 1× 18/10 + 32\n\n= 33.8° F\n\n83. On a faulty thermometer lower fixed point is marked at 10°C and upper fixed point is marked as 130°C. What will be the reading on this thermometer when it is placed in a liquid which is actually at 40°C?\n\nLower fixed point = 10°C\n\nUpper fixed point =130°C\n\nRange of thermometer = 130°C - 10°C\n\n= 120°C\n\nNo of divisions = 100\n\nSo least count = 120/100 = 1.2°C\n\nOn actual thermometer 40°C would have 40 divisions\n\nSo, on this thermometer it would show\n\n= 40× LC = 48°C\n\n84. What is greenhouse effect?\n\nThe green house is referred to a glass house. The heat enters the house but cannot escape out, because the glass reflects the heat back to the inside of the house. This makes glass house warmer than the outside environment. This phenomenon is called green house effect.\n\n85. How global warming occurs?\n\nGlobal warming occurs due to the presence of carbon di oxide, CFCs, methane in the atmosphere. Carbon dioxide acts as a transparent gas to incoming shortwave radiations which the earth re-radiates into space. It, therefore traps the outgoing radiations thus warming lower atmosphere of the earth thereby causing global warming.\n\n86. What are the harmful effects of global warming?\n\nHarmful effects of global warming are\n\n1. The atmospheric temperature of earth would increase thereby making it difficult for a living being to survive\n2. It would melt down the polar caps thus increasing the size of the ocean and leading to floods, tsunami, etc.\n3. The increase in temperature would affect climate and rainfall thus affecting flora and fauna.\n4. Human beings would be vulnerable to diseases as microbes would get warmth to grow.\n\n87. What is the reason behind rising of temperature inside a greenhouse?"
] | [
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https://www.kopykitab.com/blog/rgpv-previous-year-question-papers-b-e-firstsecond-semester-communication-skill-dec-2011/ | [
"# RGPV Previous Year Question Papers BE\n\n## Communication Skill 2nd Sem Dec 2011\n\nNote : Attempt any five questions. Use of Steam table is permitted. Support your answer with figures, charts, etc.\n\nAll questions carry equal marks.\n\n1- (a) Sketch stress-strain diagram for M. S. and cast iron. Discuss various points for M. S.\n\n(b) Discuss the effect Of alloying elements on the properties of cast iron.\n\nOr\n\n1. (a) Describe the various mechanical properties of materials in short.\n\n(b) Define Steel. Discuss its various types, uses and their applications.\n\n1. (a) Discuss any three operations that can be performed on a radial drilling machine. Also draw a tabelled diagram of a radial drilling machine.\n\n(b) Explain the following properties of any measuring instrument :\n\n(i) Hysteresis\n\n(ii) Sensitivity\n\n(iii) Accuracy and precision\n\n(iv) Errors\n\n(v) Response time\n\nOr\n\n1. (a) . What is the use of sine bar ? State the process to\n\nmeasure any angle using sine bar with neat sketch.\n\n(b) Draw a neat labelled diagram of shaper machine. Also state the operations performed on it.\n\n1. (a) Describe the construction and working of any one\n\nhydraulic turbine.\n\n(b) What do you understand by fluid coupling ? Explain its working. State its uses.\n\nOr\n\n1. (a) State the function of a compressor. State its various\n\ntypes. Discuss the working of any one type.\n\n(b) Discuss in short any three of the following properties related to fluids.:\n\n(i) Viscous flow\n\n(ii) Laminar flow\n\n(iii) Turbulent flow ‘\n\n(iv) Pressure, viscosity, density\n\n(a) Differentiate between vapour absorption system and vapour compression system.\n\n(b) Calculate the equivalent evaporation from and at 100°C for a boiler, which receives water at 60°C and produces steam at 15 MPa and 300°C. The steam generation rate is 16000 kg/hr. Coal is burnt at the rate of 1800 kg/hr. The calojific value of coal is 34750 kJ/kg. Also calculate the thermal efficiency of boiler.\n\nOr\n\n1. (a) Discuss Eco-Friendly refrigerants. State their\n\nproperties. Why are they more important in present time ?\n\n(b) A chimney of 30 m high is discharging hot gases at 320°C, when outside temperature is 30°C. The air-fuel ratio is 20. Calculate :\n\n(i) The draught produced in mm of water column.\n\n(ii) The temperature of gases for maximum discharge in a given time and what would be the draught produced corresponding ?\n\n1. (a) Discuss the working principle and functions of each part of steam engine.\n\n(b) Discuss the working of two-stroke petrol engine.\n\nOr\n\n1. (a) Explain Otto cycle and derive an expression for efficiency of Otto cycle.\n\n(b) In an engine working on ideal Otto cycle, the temperature at the beginning and at the end of compression 27°C and 327°C.\n\nFind the compression ratio and air standard efficiency of the engine."
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.86423093,"math_prob":0.9209283,"size":2737,"snap":"2021-21-2021-25","text_gpt3_token_len":637,"char_repetition_ratio":0.1075741,"word_repetition_ratio":0.0,"special_character_ratio":0.23821703,"punctuation_ratio":0.11153846,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9675276,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-05-19T00:00:33Z\",\"WARC-Record-ID\":\"<urn:uuid:3171c4f0-1cd3-43da-9ab8-2c736afc9f66>\",\"Content-Length\":\"89866\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:19a83b47-30a7-4363-b68b-a8fbc64f7a1f>\",\"WARC-Concurrent-To\":\"<urn:uuid:772a345d-0118-476b-993c-c51f3d18e1dd>\",\"WARC-IP-Address\":\"54.186.64.191\",\"WARC-Target-URI\":\"https://www.kopykitab.com/blog/rgpv-previous-year-question-papers-b-e-firstsecond-semester-communication-skill-dec-2011/\",\"WARC-Payload-Digest\":\"sha1:QPWPTOMFWZ2CQPMIB6YQU56PDEQSAII4\",\"WARC-Block-Digest\":\"sha1:IFCFFFX2CVAF4GYUHTEHDQ2GPFSQTSTS\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-21/CC-MAIN-2021-21_segments_1620243989874.84_warc_CC-MAIN-20210518222121-20210519012121-00497.warc.gz\"}"} |
https://www.provue.com/panoramax/help/function_min.html | [
"min(\nVALUE1\n,\nVALUE2\n,\nVALUE3\n,\nVALUE4\n,\nVALUE999\n)\n\nThe min( function compares a series of values and returns the smallest value.\n\nParameters\n\nThis function has five parameters:\n\nvalue1 – The first text or numeric value (required).\n\nvalue2 – The second text or numeric value (required).\n\nvalue3 – The third text or numeric value (optional).\n\nvalue4 – The fourth text or numeric value (optional).\n\nvalue999 – This function allows an unlimited number of additional values.\n\nDescription\n\nThe min( function compares a series of values and determines the smallest value. Although it states above that the function has five parameters, it actually has no limit - you can enter as many numerical values as you like.\n\nThis example calculates the coldest city, LA or NY.\n\n`````` min(LosAngelesTemp,NewYorkTemp)\n``````\n\nIf you need to calculate the minimum of three or more values you can supply additional parameters like this.\n\n``````min(LosAngelesTemp,NewYorkTemp,ChicagoTemp,SeattleTemp,DenverTemp)\n``````\n\nYou can use an unlimited number of parameters with this function.\n\nIn addition to numbers, the min( function can also be used with text values. However, you cannot mix text and numeric parameters – they must either be all numeric, or all text. (Of course you can convert numeric values to text with the str( or pattern( functions, or convert text to numbers with the val( function.\n\nHere are some example of the min( function in action:\n\n``````min(5,3,7,9) ☞ 3\nmin(4,-7,23) ☞ -7\nmin(\"x\",\"b\",\"g\") ☞ b\nmin(254,\"zero\") ☞ Error!\n``````\n\nError Messages\n\nmin( function must have at least two parameters – You’ll see this error message if you supply only one parameter, or no parameters at all.\n\nmin( function parameters must be either all text or all numbers. – You’ll see this error message if you mix text and numbers in the parameter list (for example min(3,“hello”)."
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.61529213,"math_prob":0.9580776,"size":2003,"snap":"2023-14-2023-23","text_gpt3_token_len":477,"char_repetition_ratio":0.17508754,"word_repetition_ratio":0.08176101,"special_character_ratio":0.22965552,"punctuation_ratio":0.11873351,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9682237,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-03-25T11:42:37Z\",\"WARC-Record-ID\":\"<urn:uuid:b7440dfe-a0be-4e91-a9f4-bbb48ade944a>\",\"Content-Length\":\"5460\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b54a3e0f-c646-4dc4-bef2-fa9428c816e9>\",\"WARC-Concurrent-To\":\"<urn:uuid:b10a4aa5-e8bb-436f-9f64-dcdbdbfccfc3>\",\"WARC-IP-Address\":\"162.253.133.14\",\"WARC-Target-URI\":\"https://www.provue.com/panoramax/help/function_min.html\",\"WARC-Payload-Digest\":\"sha1:AI7O6NBLAKCTV3T5FFUEJFT7YTSRM6GP\",\"WARC-Block-Digest\":\"sha1:3EJ5ELR6OZUUXJBSWSZ27ATTN6TLC7LD\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-14/CC-MAIN-2023-14_segments_1679296945323.37_warc_CC-MAIN-20230325095252-20230325125252-00744.warc.gz\"}"} |
https://javascriptio.com/view/173365/i-have-no-idea-object-this-means | [
"# I have no idea Object(this) means\n\nthere is a line like\n\n``````// Steps 1-2.\nif (this == null) {\nthrow new TypeError('this is null or not defined');\n}\n\nvar O = Object(this); // <- WHAT IS THIS???????????\n\n// Steps 3-5.\nvar len = O.length >>> 0;\n\n// Steps 6-7.\nvar start = arguments;\nvar relativeStart = start >> 0;\n\n// Step 8.\nvar k = relativeStart < 0 ?\nMath.max(len + relativeStart, 0) :\nMath.min(relativeStart, len);\n\n// Steps 9-10.\nvar end = arguments;\nvar relativeEnd = end === undefined ?\nlen : end >> 0;\n\n// Step 11.\nvar final = relativeEnd < 0 ?\nMath.max(len + relativeEnd, 0) :\nMath.min(relativeEnd, len);\n\n// Step 12.\nwhile (k < final) {\nO[k] = value;\nk++;\n}\n\n// Step 13.\nreturn O;\n``````\n\nand I can't find any necessity to assign O as Object(this).\n\nIs it written just for readability or is there any specific reason for assigning?",
null,
"As suggested in the comments on the code, this section is to accurately pollyfill the first steps documented in the spec.\n\n1. Let O be ToObject(this value).\n2. ReturnIfAbrupt(O).\n\nThough a bit out-of-order, this is performing the fucntion of `ToObject(this value)`:\n\n``````var O = Object(this);\n``````\n\nBasically, if it is called on a non-object, the non-object should be cast to an `Object`.\n\nFor example, if we were to run this bit of mostly-nonsensical code in a JavaScript engine which natively supports this method, we would see a `Number` object instance gets returned.\n\n``````Array.prototype.fill.call(123);\n``````\n\nThat line would ensure the same result from the polyfill.",
null,
"The Object constructor returns its argument when the argument is already an object. If it's not an object, it returns the \"objectified\" version of the argument: a String instance if it's a string, a Number instance if it's a number, etc.\n\nThe function in question is a little weird, and in particular the value of `this` will usually be an object anyway. It doesn't have to be, but you kind-of have to go out of your way to get to the innards of the polyfill with a `this` value that isn't an object."
] | [
null,
"https://javascriptio.com/static/a.png",
null,
"https://javascriptio.com/static/a.png",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.7936176,"math_prob":0.8721542,"size":2046,"snap":"2020-45-2020-50","text_gpt3_token_len":531,"char_repetition_ratio":0.12389814,"word_repetition_ratio":0.0057471264,"special_character_ratio":0.285435,"punctuation_ratio":0.18518518,"nsfw_num_words":1,"has_unicode_error":false,"math_prob_llama3":0.9720228,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-11-23T21:32:19Z\",\"WARC-Record-ID\":\"<urn:uuid:f2199472-9c19-43b4-a89f-ef33b7f6ef0e>\",\"Content-Length\":\"14204\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c07cea89-353d-4732-8638-ace02754f5ed>\",\"WARC-Concurrent-To\":\"<urn:uuid:a64c849e-cc24-4670-8a7c-2d1b6e936741>\",\"WARC-IP-Address\":\"104.27.146.115\",\"WARC-Target-URI\":\"https://javascriptio.com/view/173365/i-have-no-idea-object-this-means\",\"WARC-Payload-Digest\":\"sha1:6GQ3IEUWAYJDDHXGG5NRUL4K67QGZQ2Q\",\"WARC-Block-Digest\":\"sha1:Z5CZHPCKWZPKYO7I3EYAZAQUHVPJ2BLT\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141168074.3_warc_CC-MAIN-20201123211528-20201124001528-00123.warc.gz\"}"} |
http://safecurves.cr.yp.to/proof/2384153.html | [
"Primality proof for n = 2384153:\n\nTake b = 2.\n\nb^(n-1) mod n = 1.\n\n5623 is prime.\nb^((n-1)/5623)-1 mod n = 1249200, which is a unit, inverse 711091.\n\n(5623) divides n-1.\n\n(5623)^2 > n.\n\nn is prime by Pocklington's theorem."
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https://www.docslides.com/lois-ondreau/on-the-development-and-use-of | [
"",
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"127K - views\n\n# On the Development and Use of Dierential Analyzers Dominik Schultes\n\nApril 2004 Abstract In this essay we present the development of an important analogue calculating device the di64256erential analyzer Section 1 introduces the main purpose that this type of machine was built for namely the solution of di64256erenti\n\n## On the Development and Use of Dierential Analyzers Dominik Schultes\n\nDownload Pdf - The PPT/PDF document \"On the Development and Use of Dierential...\" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.\n\n## Presentation on theme: \"On the Development and Use of Dierential Analyzers Dominik Schultes\"— Presentation transcript:\n\nPage 1\nOn the Development and Use of Differential Analyzers Dominik Schultes 28. April 2004 Abstract In this essay, we present the development of an important analogue calculating device, the differential analyzer . Section 1 introduces the main purpose that this type of machine was built for, namely the solution of differential equations and, in this context, the integration of a function. Section 2 summarizes the most important milestones regarding the development of mechanical differential analyzers. Section 3 deals with some typical applications. Section 4\n\nconcludes with some improvements of the differential analyzer that were achieved by replacing mechanical parts with electrical ones. Furthermore, a short comparison of the differential analyzer with the present-day technology is done. 1 Introduction An ordinary differential equation of -th order can be written in explicit form as ) = x,y ,y ,y 00 ,...,y 2) ,y 1) )) [Hei00, p. 153]. The function is given, while the function has to be determined. To get started, let us deal with a very simple example, namely = 2 and x,y ,y )) = ). Thus, we have the following second-order\n\ndifferential equation: 00 ) = ). An equivalent notation of this equation is ) = RR dxdx . At this point, the principle difficulty can be observed that arises when a differential equation has to be solved: appears on both sides of the equation, i.e., the value of the function at the point depends on the integral of . Furthermore, we can realize that integrals can play a distinct role with respect to the solution of a differential equation. We will pick up on these points soon, but first we want to introduce one physical example in order to demonstrate that\n\ndifferential equations are not just a “toy” of mathematicians, but have direct reference to real world applications. If a capacitor and a resistor appear in a series connection, the total voltage sums up to ) = /C ). Furthermore, the charge of the capacitor can be expressed by ) = dt . Hence, we obtain ) = 1 /C dt ) = 1 /R /C dt Thus, we have exactly the same situation as in the simple theoretical example. The current at the point of time depends on the current because contributes to the integrand. A similar example with an inductance and a resistor is presented in [Har49, p. 4]. The\n\nfollowing basic strategy, which forms the foundation of a differential analyzer, can be used to solve such differential equations. 1. Take an initial value (0) = 2. Evaluate the right side of the equation, i.e., the integral, for a “small and obtain a value 3. Use the obtained as input and re-evaluate the right side. 4. Iterate. The correct result is obtained for 0, i.e., has to become an infinitesimal small dx Obviously, the main component of this strategy is the integrator (also often called planimeter [Hor14, p. 190]), and the next section will present how such an\n\nintegrator has been implemented and what other parts are required for a differential analyzer, a machine that can solve differential equations.\nPage 2\n2 Development of the Differential Analyzer 2.1 Basics The first integrators and differential analyzers consisted only of mechanical components. In these machines, a variable is represented by a shaft and the value of the variable by the rotation of the shaft. In order to build an integrator that computes dx , we need some kind of gear between a driving shaft and a driven shaft , where the ratio of the gear\n\nis specified by ). When the shaft is rotated by an infinitesimal small amount dx , the shaft is rotated by dx and when we continue the rotation of , the rotation of sums up to dx . The prerequisite for this method is the possibility of selecting continuously the appropriate gear ratio. [Har49, p. 5] According to [Hor14, p. 190], the first attempts of implementing such a device took probably place in 1814 and in the following years many other attempts followed, but the results were either not adequately published or the machines were too inaccurate to be reliable. The\n\nbreakthrough was achieved by James Thomson, the brother of Lord Kelvin [Wil97, p. 201], published in 1876 [Hor14, p. 192]. His design (see Figure 1(a)) consists of a disk that is rotated by a driving shaft, a cylinder that is connected with the driven shaft that represents the value of the integral, and a sphere that is the “mediator” between the disk and the sphere. The sphere has always contact with both the disk and the cylinder, but it can be placed to different positions on a line between the center of the disk and the border. The farer the sphere is away from the center, the\n\ngreater is the gear ratio. A simpler integrator can be built using two disks that are arranged perpendicular (see Figure 1(b)), one is connected with the driving shaft , the other with the driven shaft . Again, the point of contact can be arbitrarily selected on a line between the center of the driving disk and its border [Har49, p. 5]. (a) The disk-sphere-cylinder integrator (b) The disk-wheel integrator Figure 1: Two types of integrators [Wil97, p. 202], [Har49, p. 5] 2.2 Bush’s Differential Analyzer at the MIT While Lord Kelvin in 1876 already thought about the combination of several\n\nof his brother’s integrators in order to solve differential equations [Har49, p. 7], it took 55 years until a first differential analyzer could be realized. In 1931, Vannevar Bush constructed a working machine at the MIT [Wil97, p. 203]. One major problem that Bush was able to master was the slip of the mechanical parts that interacted only by friction. When several components of this kind are combined, it is likely that the tension gets so big that the friction between two wheels is not sufficient so that they slip; this, of course, leads to a falsification of the\n\nresults. The way out that\nPage 3\nwas successfully implemented by Bush is the installation of torque amplifiers for shafts that are used simultaneously as output and input, i.e., a driven shaft that is also a driving shaft (for the next component) is broken and a torque amplifier is installed inbetween. The amplifier takes the driven shaft as input and rotates the outgoing driving shaft exactly the same way, but by more power. Figure 2: Principle of Bush’s torque amplifier (from the 1931 article by Bush, taken from [Wil00]) To achieve this aim, Bush took\n\nadvantage of the principle of the ship’s capstan in a quite in- ventive way. Figure 2 demonstrates his design. Both the input and the output shaft are connected with an arm each. Around the shafts is a friction drum each. The frictions drums are continuously rotated by a powerful motor. The input and output arms are connected by two threads that are winded round one of the friction drums each. The rolling direction of the threads and of the friction drums is important: looking at the amplifier on Figure 2 from the left, on the output side, the friction drum rotates counter-clockwise and\n\nthe cord from the input to the output arm is winded clockwise, while on the input side, the friction drum rotates clockwise and the thread is rolled counter-clockwise. The invariant of this system is that the input and the output arms are always opposite to each other. The threads are so long that they are just loosely rolled round the drums when the arms are exactly opposite to each other. When the input shaft is rotated in either direction, exactly one of both threads is tensed. In order to tense a thread, only a minor amount of power is required. Now, a friction between that thread and the\n\ncorresponding friction drum arises. Hence, the cord is pulled in the rolling direction of the drum – that is driven by the powerful motor. Therefore, the output arm is pulled with much power. Due to the above mentioned choice of the rolling directions of the friction drums and of the cords, it is ensured that the output arm is always dragged in the correct direction, namely in the same as the input arm. As soon as the output shaft – and consequently the output arm – approaches the correct position, the thread is loosed and the friction decreases so that the output shaft does not overshoot the\n\nmark. [Wil00] Beside the integrators and amplifiers, Bush’s differential analyzer consisted of gears for constant multiplications and gears for doing addition and subtraction [Wil97, p. 204]. Figure 3(b) demonstrates how a differential analyzer could be used to solve the introductory example 00 ) = ). The used schematic notation for an integrator is given in Figure 3(a). For the sake of simplicity, the amplifiers are omitted. The right integrator integrates (resp. 00 once and outputs ydx (resp. ). The left integrator integrates the output of the right one and outputs RR\n\nydxdx (resp. the “new ). 2.3 The Developments in the United Kingdom Since Bush’s differential analyzer was able to solve a wide range of differential equations and since such equations appeared in many applications – while it was usually difficult to solve them without a machine –, there were many people that copied Bush’s machine. A common problem\nPage 4\n(a) Schematic notation for an integrator (b) Schematic notation for the differential analyzer Figure 3: Setup for solving the equation 00 ) = ) [Wil00] for some of these imitators was to convince their\n\nfinancial backers of the usefulness of a differential analyzer. An inventive solution for this problem was found by Douglas Hartree who built a model of a differential analyzer together with A. Porter at the University of Manchester in 1934 [Har49, p. 13]. The costs could be kept very low because almost every part of the machine was built using Meccano, a kind of construction set that was a popular toy for boys at this time. Only for the integrator disks, ground glass instead of a Meccano part was used, and some other parts, particularly for the amplifiers, had to be\n\nbuilt using other materials [Irw02]. The Meccano model was surprisingly successful and its accuracy was in the order of 2% so that it could be used for serious applications [Har49, p. 14]. Due to this success, one year later a full scale machine was built by Metropolitan Vickers. A similar way was chosen at the University of Cambridge at the instance of J. E. Lennard- Jones. In 1935, J. B. Bratt built a model of a differential analyzer. Similar to Hartree’s machine, Meccano was used for most parts apart from those that were crucial to the precision of the machine [Wil85, p. 25]. In 1939,\n\na full scaled machine replaced the Meccano model. Of course, the development and the use of differential analyzers – inspired both by Bush’s original work and by the British Meccano models – was not limited to the USA and the UK, but spread out throughout Europe (e.g., Germany and Norway) and North America. For instance, one Meccano machine was installed by Beatrice “Trixie” Worsley at the University of Toronto in the early 1950s [Wil97, p. 205]. 3 Applications The development of the differential analyzer was advanced mainly by people who were interested in the applications of the\n\nmachine rather than in the machine itself from the engineering point of view. Of course, the people who built those machines had to deal with mechanical problems that arose and it can be observed that these problems were often dominant in comparison with the theoretical problems that usually had been solved much earlier. For example, as already mentioned, it took 55 years from Lord Kelvin’s theoretical deliberations regarding a differential analyzer to Bush’s first realization. However, the applications were always the mainspring. Lord Kelvin applied the planimeter developed by his\n\nbrother to his tide calculating machine (which is no actual differential analyzer, but shares one of its main components) [Hor14, p. 193]. Such a machine was quite important since it was able to predict the tide for a given time in the future with sufficient accuracy. This information was essential for ships that called at a harbour in order to judge if the tide was high enough to reach the harbour safely without touching some rocks on the ground [Wil97, p. 198].\nPage 5\nVannevar Bush dealt with differential equations related to the electric power network. He started\n\nto solve the equations analytically, but he soon realized that this took far too much time so that he decided to concentrate his efforts on the construction of a machine that would take this time-consuming task over [Wil97, p. 204]. Similarly, Douglas Hartree was no engineer but a physicist and, particularly, an expert in numerical methods of computation [Wil85, p. 107]. At the University of Cambridge, Maurice V. Wilkes used the differential analyzer for different applications. He investigated the propagation of long-wave radio waves, supported E. Monroe in solving a\n\ndifferential equation emerging in the two-centre problem in wave machines, and analysed a model of graphite with respect to the interrelationship between the potential energy and the situation of the carbon atoms [Wil85, pp. 25–27]. In [Har49, p. 25] some other applications are listed that demonstrate the wide range of use. The examples belong to the fields of physics (e.g. “motion of electrified particles in the magnetic field of the earth”), electronics (e.g. “problems in non-linear electrical circuits”), chemistry (e.g. “chemical kinetics”), and scheduling (e.g.\n\n“running times of railroad trains”). However, the most frequent field of application, at least during the Second World War, was probably a military one – in fact across all borders, i.e., in the USA, in the UK and in Germany. One common task was the computation of ballistic firing tables. For instance, with the help of the MIT, the British tried to calculate the ballistic trajectory of the German V2 rockets [Wil97, p. 206]. 4 Further Developments and the State of the Art 4.1 Further Developments While the first differential analyzers consisted exclusively of mechanical\n\nparts, during the further development, more and more parts were replaced by electrical ones so that as intermediate step electromechanical machines and finally purely electrical differential analyzers were built. The basic concepts have never changed, i.e., on principle, the electrical parts that replaced the mechanical ones fulfilled the same functionality as their predecessors. Again, Vannevar Bush counts to the precursors. In 1945, he built together with S. H. Caldwell a new differential analyzer at the MIT. While he still used mechanical integrators, he replaced the\n\nmechanical connections between the shafts by electrical ones. The azimuth of the output shaft about its axis is encoded by a pair of variable condensers into an electrical value. Similarly, the azimuth of the input shaft that should be driven by the above mentioned output shaft is represented by an electrical value. Both values are compared in order to calculate the difference, which should be minimized. This comparison is done by a unit that controls a motor that drives the input shaft so that both shafts are synchronized [Har49, p. 14]. Later on, differential analyzers were\n\nconstructed where the remaining mechanical parts were replaced by electrical ones. For instance, an electrical integrator can be built using a condenser (see Figure 4). The advantages of the electrical differential analyzer over the mechanical one are manifold. First of all, the computation can be done much faster due to the high speed that electrical compo- nents operate at. Furthermore, it is more convenient to setup the machine to an initial condition as a control desk can be used for this purpose. In contrast, “setting up a mechanical differential analyzer was not a job for\n\nanyone who liked to keep his hands clean” [Wil85, p. 30], because of the fact that you had to deal directly with the oily shafts and gears.\nPage 6\nis short for d [KK56, p. 9]. Figure 4: An electrical integrator [KK56, p. 13] 4.2 State of the Art Although the mechanical differential analyzers had already been very useful and electrical ones were even much more sophisticated, this type of machine practically died out – because it was an analogue one. In [Wil85, p. 123], the computer pioneer M. V. Wilkes describes his reaction when he was asked in 1946 if there was a future for\n\nthe differential analyzer: “This was not a question that I had consciously considered, but I found myself saying no, and from that moment on I had no doubt in my mind that the days of analogue devices for scientific computation were numbered.” But why ? The advantages of digital machines had become visible. Nowadays, differential equations are solved by numerical algorithms on a digital computer. On principle, these algorithms often base on the same strategy as the differential analyzers, which is described in Section 1. However, there is one essential difference.\n\nThe numerical algorithms on digital computers always deal with discrete steps [Hei00, p. 160], never with infinitesimal small ones as a differential analyzer does this. Hence, at first sight, the analogue differential analyzer is better than a modern digital computer because in theory it computes the exact result, while a digital computer only approximates the solution. But, in practice , an analogue machine can never operate with 100% accuracy, i.e., it deviates from the exact solution and the crucial disadvantage is the fact that it is barely possible to set a bound\n\nfor the deviation. Worse is the fact that it is generally not even possible to get bound for the deviation, i.e., you do not know how good the results are that you have obtained. Of course, you can realize that usually the deviation is less than 1%, but if you get the results of just one computation, you cannot exclude that this time the deviation is bigger because of some missing oil, for example. The numerical algorithms on digital computers have both properties. Firstly, for a given algorithm and the selected parameters (particularly, the selected step size), you can compute an error bound\n\nthat is never exceeded. Secondly, you can choose the parameters of the algorithm in order to set the error bound. In order to get better results, you have to reduce the step size – in general, you do not have to build a new machine in order to improve the accuracy of the results. List of Figures 1 Two types of integrators [Wil97, p. 202], [Har49, p. 5] . . . . . . . . . . . . . . . . 2 2 Principle of Bush’s torque amplifier (from the 1931 article by Bush, taken from [Wil00]) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 Setup for solving the\n\nequation 00 ) = ) [Wil00] . . . . . . . . . . . . . . . . . . 4 4 An electrical integrator [KK56, p. 13] . . . . . . . . . . . . . . . . . . . . . . . . . . 6 References [Har49] D. R. Hartree. Calculating instruments and machines . Univ. of Illinois Press, 1949.\nPage 7\n[Hei00] S. Heinrich. Numerische algorithmen. lecture notes, University of Kaiserslautern, Ger- many, 2000. [Hor14] E. M. Horsburgh, editor. Modern instruments and methods of calculation : a handbook of the Napier tercentenary exhibition . Bell, 1914. [Irw02] W. Irwin. The differential analyser explained. The New\n\nZealand Federation Of Meccano Modellers Magazine , 26(3):3–5, June 2002. http://www.dalefield.com/nzfmm/magazine/ Differential Analyser.html. [KK56] G. A. Korn and T. M. Korn. Electronic analog computers (d-c analog computers) McGraw-Hill, 2nd edition, 1956. [Wil85] M. V. Wilkes. Memoirs of a computer pioneer . MIT Press, 1985. [Wil97] M. R. Williams. A history of computing technology . IEEE Computer Society Press, 2nd edition, 1997. [Wil00] M. V. Wilkes. Encyclopedia of computer science , chapter Differential Analyzer. Nature Pub. Group, 4th edition, 2000."
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http://catalog.mansfield.edu/preview_course_nopop.php?catoid=1&coid=1052 | [
"Jul 17, 2019\n HELP Mansfield University 2007-2008 Undergraduate Catalog [Archived Catalog]",
null,
"Print-Friendly Page [Add to Portfolio]\n\n# MA 3314 - APPLIED PROBABILITY AND STATISTICS\n\nAn introduction to applications of descriptive, inferential statistics, and probability. Descriptive statistics including frequency distributions, measures of location and variation; axioms of probability, probability (both theoretical and simulated), permutations, combinations, random variables, expected value, and decision making; probability distributions (both discrete and continuous), distribution functions, sampling and sampling distributions; statistical inferences concerning means, standard deviations, and proportions; analysis of variance, non-parametric methods, regression, correlation, planning surveys and experiments. (Addresses NCTM Standards 1 .5.6, 1 .5.7, and 1 .5.11 for Mathematics Education majors.)\n\nPrerequisites & Notes: Prerequisite: MA 11 70 or 2232.\n\nCredits: 3 cr."
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https://riecoin.dev/Constellations/Block/1640521 | [
"Constellation Explorer\n\n# Block 1640521\n\n Height 1640521 Timestamp (UTC) 1640610851 -> 2021-12-27 13:14:11 Difficulty D = 969.14453125 = 969 + 37/256 Finder Anonymous Target (T) ⌊D⌋ = 969L = 27H = 3730830682997846793099633891349826106178128482661594158489300546190089317205T = 2⌊D⌋ + L × 2⌊D⌋ - 8 + H × 2⌊D⌋ - 264 Offset (X) P = 88f = 13263479o = 145844141558231o' = 0X = pP# - (T mod pP#) + f × pP# + o Base Prime n = T + X + o' = 5516475720097783006293730877306014745390311585064130309858931847658063368738189720525251751822368797232520892605606927896902871931978826255583507694841023318155883430184982551330806292545345804534308639663048846031980560911312431718215470344065634644917610927721011825715231559101616556626811 = 251727441254713493073689830369931517858240213181317376033987793889813901659139411734453238385578230329274 × p88# + 145844141558231log2(n) = ~969.14482248703, 292 digits Pattern n + (0, 2, 6, 8, 12, 18, 20), length 7"
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https://www.gradesaver.com/textbooks/math/calculus/university-calculus-early-transcendentals-3rd-edition/chapter-3-section-3-1-tangents-and-the-derivative-at-a-point-exercises-page-118/11 | [
"## University Calculus: Early Transcendentals (3rd Edition)\n\nThe equation of the tangent line is $y=4x-3$.\nThe slope $m$ of the tangent line of the curve $f(x)$ at $A(a,b)$ is also the slope of the curve at that point, which is calculated by $$m=\\lim_{h\\to0}\\frac{f(a+h)-f(a)}{h}$$ $$y=f(x)=x^2+1\\hspace{1cm}A(2,5)$$ 1) Find the slope $m$ of the tangent: $$m=\\lim_{h\\to0}\\frac{f(a+h)-f(a)}{h}$$ Here $a=2$ and $f(a)=b=5$ $$m=\\lim_{h\\to0}\\frac{f(2+h)-5}{h}=\\lim_{h\\to0}\\frac{(2+h)^2+1-5}{h}$$ $$m=\\lim_{h\\to0}\\frac{4+4h+h^2+1-5}{h}=\\lim_{h\\to0}\\frac{4h+h^2}{h}$$ $$m=\\lim_{h\\to0}(4+h)$$ $$m=4+0=4$$ 2) Find the equation of the tangent line at $A(2,5)$: The tangent line would have this form: $$y=4x+m$$ Substitute $A(2,5)$ here to find $m$: $$4\\times2+m=5$$ $$8+m=5$$ $$m=-3$$ So the equation of the tangent line is $y=4x-3$."
] | [
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https://www.arxiv-vanity.com/papers/hep-th/9907019/ | [
"###### Abstract\n\nSolutions in multidimensional gravity with -branes related to Toda-like systems (of general type) are obtained. These solutions are defined on a product of Ricci-flat spaces and are governed by one harmonic function on . The solutions are defined up to the solutions of Laplace and Toda-type equations and correspond to null-geodesics of the (sigma-model) target-space metric. Special solutions relating to Toda chains (e.g. with ) are considered.\n\nSOLUTIONS WITH INTERSECTING P-BRANES RELATED TO TODA CHAINS\n\n[15pt] V.D. Ivashchuk111, and S.-W. Kim 222\n\n[10pt]\n\nCenter for Gravitation and Fundamental Metrology, VNIIMS, 3/1 M. Ulyanovoy Str., Moscow 117313, Russia\n\nDepartment of Science Education and Basic Science Research Institute, Ewha Womans University, Seoul 120-750, Korea\n\n## I Introduction\n\nAt present there exists a special interest to the so-called theory (see, for example, -). This theory is “supermembrane” analogue of superstring models in . The low-energy limit of -theory after a dimensional reduction leads to models governed by a Lagrangian containing metric, fields of forms and scalar fields. These models contain a large variety of so-called -brane solutions (see - and references therein).\n\nIn it was shown that after dimensional reduction on the manifold and when the composite -brane ansatz for fields of forms is considered the problem is reduced to the gravitating self-interacting -model with certain constraints imposed. (For electric -branes see also [16, 17, 26].) This representation may be considered as a powerful tool for obtaining different solutions with intersecting -branes (analogues of membranes). In [25, 26, 36, 37, 38] the Majumdar-Papapetrou type solutions (see ) were obtained (for non-composite case see [16, 17]). These solutions correspond to Ricci-flat , ( is metric on ) , and were also generalized to the case of Einstein internal spaces . Earlier some special classes of these solutions were considered in [8, 9, 11, 19, 20, 21]. The obtained solutions take place, when certain (block-)orthogonality relations (on couplings parameters, dimensions of ”branes”, total dimension) are imposed. In this situation a class of cosmological and spherically-symmetric solutions was obtained [31, 40]. Special cases were also considered in [12, 27, 29, 30]. The solutions with the horizon were considered in details in [7, 22, 23, 31, 33].\n\nIn models under consideration there exists a large variety of Toda-chain solutions, when certain intersection rules are satisfied . Cosmological and spherically symmetric solutions with -branes and internal spaces related to Toda chains were previously considered in [12, 13] and [39, 42].\n\nIt is well known that geodesics of the target space equipped with some harmonic function on a three-dimensional space generate a solution to the -model equations [46, 47]. (It was observed in that null geodesics of the target space of stationary five-dimensional Kaluza-Klein theory may be used to generate multisoliton solutions similar to the Israel-Wilson-Perjès solutions of Einstein-Maxwell theory.) Here we apply this null-geodesic method to our sigma-model and obtain a new class of solutions in multidimensional gravity with -branes governed by one harmonic function . The solutions ¿from this class correspond to null-geodesics of the target-space metric and are defined by some functions with being solutions to Toda-type equations.\n\n## Ii The model\n\nWe consider a model governed by the action \n\n S=∫dDz√|g|{R[g]−hαβgMN∂Mφα∂Nφβ−∑a∈△θana!exp[2λa(φ)](Fa)2} (2.1)\n\nwhere is a metric, is a vector of scalar fields, is a constant symmetric non-degenerate matrix , , is a -form (), is a 1-form on : , , . Here is some finite set.\n\nWe consider a manifold\n\n M=M0×M1×⋯×Mn, (2.2)\n\nwith a metric\n\n g=e2γ(x)g0+n∑i=1e2ϕi(x)gi (2.3)\n\nwhere is a metric on the manifold , and is an Einstein metric on satisfying the equation\n\n Rmini[gi]=ξigimini, (2.4)\n\n; , . (Here we identify notations for and , where is the pullback of the metric to the manifold by the canonical projection: , . An analogous agreement will be also kept for volume forms etc.)\n\nAny manifold is supposed to be oriented and connected and , . Let\n\n τi≡√|gi(yi)|dy1i∧⋯∧dydii,ε(i)≡sign(det(gimini))=±1 (2.5)\n\ndenote the volume -form and signature parameter respectively, . Let be a set of all subsets of , . For any , , we denote\n\n τ(I)≡τi1∧⋯∧τik,d(I)≡∑i∈Idi,ε(I)≡∏i∈Iε(i). (2.6)\n\nWe also put and .\n\nFor fields of forms we consider the following composite electromagnetic ansatz\n\n Fa=∑I∈Ωa,eF(a,e,I)+∑J∈Ωa,mF(a,m,J) (2.7)\n\nwhere\n\n F(a,e,I)=dΦ(a,e,I)∧τ(I), (2.8) F(a,m,J)=e−2λa(φ)∗(dΦ(a,m,J)∧τ(J)) (2.9)\n\nare elementary forms of electric and magnetic types respectively, , , and , are non-empty subsets of . In (2.9) is the Hodge operator on . For scalar functions we put\n\n φα=φα(x),Φs=Φs(x), (2.10)\n\n, .\n\nHere and below\n\n S=Se∪Sm,Sv=⋃a∈△{a}×{v}×Ωa,v, (2.11)\n\n. The set consists of elements , where , and .\n\nDue to (2.8) and (2.9)\n\n d(I)=na−1,d(J)=D−na−1, (2.12)\n\nfor , .\n\n### ii.1 The sigma model\n\nLet and\n\n γ=γ0(ϕ)≡12−d0n∑j=1djϕj, (2.13)\n\ni.e. the generalized harmonic gauge is used.\n\nWe impose the restriction on sets . These restrictions guarantee the block-diagonal structure of a stress-energy tensor (like for the metric) and the existence of -model representation .\n\nWe denote , and (i.e. is the number of 1-dimensional spaces among , ).\n\nRestriction 1. Let 1a) or 1b) and for any , , , , there are no such that , and .\n\nRestriction 2 (only for ). Let 2a) or 2b) and for any , there are no , such that for and for . Here and in what follows\n\n ¯I≡{1,…,n}∖I. (2.14)\n\nThese restrictions are satisfied in the non-composite case [16, 17]: , (i.e when there are no two -branes with the same color index , .) Restriction 1 and 2 forbid certain intersections of two -branes with the same color index for and respectively.\n\nIt was proved in that equations of motion for the model (2.1) and the Bianchi identities: , , for fields from (2.3)–(2.13), when Restrictions 1 and 2 are imposed, are equivalent to equations of motion for the -model governed by the action\n\n Sσ=∫dd0x√|g0|{R[g0]−^GABg0μν∂μzA∂νzB −∑s∈Sεse−2UsAzAg0μν∂μΦs∂νΦs−2V}, (2.15)\n\nwhere , the index set is defined in (2.11),\n\n V=V(ϕ)=−12n∑i=1ξidie−2ϕi+2γ0(ϕ) (2.16)\n\nis the potential,\n\n (^GAB)=(Gij00hαβ), (2.17)\n\nis the target space metric with\n\n Gij=diδij+didjd0−2, (2.18)\n (UsA)=(diδiIs,−χsλαas), (2.19)\n\nare vectors, , , ;\n\n δiI=∑j∈Iδij (2.20)\n\nis the indicator of belonging to : for and otherwise; and\n\n εs=(−ε[g])(1−χs)/2ε(Is)θas, (2.21)\n\n, . More explicitly (2.21) reads for and , for .\n\n## Iii Exact solutions with one harmonic function\n\n### iii.1 Toda-like Lagrangian\n\nAction (II.1) may be also written in the form\n\n Sσ=∫dd0x√|g0|{R[g0]−G^A^B(X)g0μν∂μX^A∂νX^B−2V} (3.1)\n\nwhere , and minisupermetric\n\n G=G^A^B(X)dX^A⊗dX^B (3.2)\n\non minisuperspace\n\n M=RN,N=n+l+|S| (3.3)\n\n( is the number of elements in ) is defined by the relation\n\n (G^A^B(X))=⎛⎜⎝Gij000hαβ000εsexp(−2Us(X))δss′⎞⎟⎠. (3.4)\n\nHere we consider exact solutions to field equations corresponding to the action (3.1)\n\n Rμν[g0]=G^A^B(X)∂μX^A∂νX^B+2Vd0−2g0μν, (3.5) 1√|g0|∂μ[√|g0|G^C^B(X)g0μν∂νX^B]−12G^A^B,^C(X)g0,μν∂μX^A∂νX^B=V,^C, (3.6)\n\n. Here is the Laplace-Beltrami operator corresponding to and .\n\nWe put\n\n X^A(x)=F^A(H(x)), (3.7)\n\nwhere is a smooth function, is a harmonic function on , i.e.\n\n △[g0]H=0, (3.8)\n\nsatisfying for all .\n\nThe substitution of (3.7) into eqs. (3.5) and (3.6) leads us to the relations\n\n Rμν[g0]=G^A^B(F(u))˙F^A˙F^B∂μH∂νH+2Vd0−2g0μν, (3.9) [ddu(G^C^B(F(u))˙F^B)−12G^A^B,^C(F(u))˙F^A˙F^B]g0,μν∂μH∂νH=V,^C, (3.10)\n\nwhere and .\n\nLet all spaces be Ricci-flat, i.e.\n\n Rmini[gi]=0, (3.11)\n\n. In this case the potential is zero : and the field equations (3.9) and (3.10) are satisfied identically if obey the Lagrange equations for the Lagrangian\n\n L=12G^A^B(F)˙F^A˙F^B (3.12)\n\nwith the zero-energy constraint\n\n E=12G^A^B(F)˙F^A˙F^B=0. (3.13)\n\nThis means that is a null-geodesic map for the minisupermetric (3.2). Thus, we are led to the Lagrange system (3.12) with the minisupermetric defined in (3.4).\n\nThe problem of integrability may be simplified if we integrate the Lagrange equations corresponding to (i.e. the Maxwell equations for and Bianchi identities for ):\n\n ddu(exp(−2Us(z))˙Φs)=0⟺˙Φs=Qsexp(2Us(z)), (3.14)\n\nwhere are constants, . Here . We put\n\n Qs≠0, (3.15)\n\nfor all .\n\nFor fixed the Lagrange equations for the Lagrangian (3.12) corresponding to , when equations (3.14) are substituted, are equivalent to the Lagrange equations for the Lagrangian\n\n LQ=12^GAB˙zA˙zB−VQ, (3.16)\n\nwhere\n\n VQ=12∑s∈SεsQ2sexp[2Us(z)], (3.17)\n\nare defined in (2.17) respectively. The zero-energy constraint (3.13) reads\n\n EQ=12^GAB˙zA˙zB+VQ=0. (3.18)\n\n### iii.2 Toda-type solutions\n\nLet us define the scalar product as follows\n\n (U,U′)=^GABUAU′B, (3.19)\n\nfor , where . The scalar products (3.19) for vectors were calculated in \n\n (Us,Us′)=d(Is∩Is′)+d(Is)d(Is′)2−D+χsχs′λαasλβas′hαβ, (3.20)\n\nwhere ; and belong to .\n\nHere we are interested in exact solutions for a special case when the vectors satisfy the following conditions\n\n Ks=(Us,Us)≠0, (3.21)\n\nfor all , and a (“quasi-Cartan”) matrix\n\n (Ass′)=(2(Us,Us′)(Us′,Us′)) (3.22)\n\nis a non-degenerate one. Here some ordering in is assumed. It follows from (3.21) and the non-degeneracy of the matrix (3.22) that the vectors are linearly independent. Hence, the number of the vectors should not exceed the dimension of , i.e.\n\n |S|≤n+l. (3.23)\n\n¿From (3.20)-(3.22) we get the following intersection rules \n\n d(Is∩Is′)=d(Is)d(Is′)D−2−χsχs′λas⋅λas′+12Ks′Ass′, (3.24)\n\n.\n\nThe exact solutions to Lagrange equations corresponding to (3.16) with the potential (3.17) could be readily obtained using the relations from Appendix. The solutions read\n\n zA=∑s∈SUsA(Us,Us)qs+cAu+¯cA, (3.25)\n\nwhere are solutions to Toda-type equations\n\n ¨qs=−Bsexp(∑s′∈SAss′qs′), (3.26)\n\nwith\n\n Bs=2KsAs,As=12εsQ2s, (3.27)\n\n. These equations correspond to the Lagrangian\n\n LTL=14∑s,s′∈SK−1sAss′˙qs˙qs′−∑s∈SAsexp(∑s′∈SAss′qs′). (3.28)\n\nVectors and satisfy the linear constraint relations (see (6.11) in Appendix)\n\n Us(c)=UsAcA=∑i∈Isdici−χsλasαcα=0, (3.29) Us(¯c)=UsA¯cA=∑i∈Isdi¯ci−χsλasα¯cα=0, (3.30)\n\n.\n\nThe contravariant components are [25, 31]\n\n Usi=GijUsj=δiIs−d(Is)D−2,Usα=−χsλαas, (3.31)\n\nHere (as in )\n\n Gij=δijdi+12−D, (3.32)\n\n, are the components of the matrix inverse to from (2.18).\n\nUsing (3.25) and (3.31) we obtain\n\n ϕi=∑s∈Shs(δiIs−d(Is)D−2)qs+ciu+¯ci, (3.33)\n\nand\n\n φα=−∑s∈Shsχsλαasqs+cαu+¯cα, (3.34)\n\n, and . For from (2.13) we get\n\n γ0(ϕ)=−∑s∈Sd(Is)D−2hsqs+c0u+¯c0, (3.35)\n\nwhere we denote\n\n hs=K−1s (3.36)\n\nand\n\n c0=12−d0n∑j=1djcj,¯c0=12−d0n∑j=1dj¯cj. (3.37)\n\nThe zero-energy constraint reads (see Appendix)\n\n 2E=2ETL+^GABcAcB= (3.38) 2ETL+hαβcαcβ+n∑i=1di(ci)2+1d0−2(n∑i=1dici)2=0.\n\nwhere\n\n ETL=14∑s,s′∈SK−1sAss′˙qs˙qs′+∑s∈SAsexp(∑s′∈SAss′qs′), (3.39)\n\nis an integration constant (energy) for the solutions from (3.26).\n\n¿From the relation\n\n exp(2Us(z))=∏s′∈Sf−Ass′s′, (3.40)\n\nfollowing from (3.22), (3.25), (3.29) and (3.30) we get for electric-type forms (2.8)\n\n Fs=Qs(∏s′∈Sf−Ass′s′)dH∧τ(Is), (3.41)\n\n, and for magnetic-type forms (2.9)\n\n Fs=exp[−2λa(φ)]∗[Qs(∏s′∈Sf−Ass′s′)dH∧τ(Is)]=¯Qs(∗0dH)∧τ(¯Is), (3.42)\n\n, where and is defined by the relation , (see eq. (2.26) in ). Here is the Hodge operator on .\n\nRelations for the metric and scalar fields follows from (3.33)-(3.35)\n\n g=(∏s∈Sf2d(Is)hs/(D−2)s){exp(2c0H+2¯c0)g0 (3.43) +n∑i=1(∏s∈Sf−2hsδiIss)exp(2ciH+2¯ci)gi}, (3.44) exp(φα)=(∏s∈Sfhsχsλαass)exp(cαH+¯cα), (3.45)\n\n. Here\n\n fs=fs(H)=exp(−qs(H)), (3.46)\n\nwhere is a solution to Toda-like equations (3.26) and () is a harmonic function on (see (3.8)).\n\nThe solution is presented by relations (3.41)-(3.46) with the functions defined in (3.26) and the relations on the parameters of solutions , , , imposed in (3.29),(3.30), (3.37) and (3.36), respectively.\n\nThis solution describes a set of charged (by forms) overlapping -branes (, ) “living” on submanifolds of . The solution is valid if the dimensions of -branes and dilatonic coupling vector satisfy the relations (2.12).\n\n## Iv Solutions corresponding to Am Toda chain\n\nHere we consider exact solutions to equations of motion of a Toda-chain corresponding to the Lie algebra [50, 51] ,\n\n ¨qs=−Bsexp(m∑s′=1Ass′qs′), (4.1)\n\nwhere\n\n (Ass′)=⎛⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜⎝2−10…00−12−1…000−12…00\\omit\\span\\omit\\span\\omit\\span\\omit\\span\\omit\\span\\omit000…2−1000…−12⎞⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟⎠ (4.2)\n\nis the Cartan matrix of the Lie algebra and , . Here we put .\n\nThe equations of motion (4.1) correspond to the Lagrangian\n\n LT=12m∑s,s′=1Ass′˙qs˙qs′−m∑s=1Bsexp(m∑s′=1Ass′qs′). (4.3)\n\nThis Lagrangian may be obtained from the standard one by separating a coordinate describing the motion of the center of mass.\n\nUsing the result of A. Anderson we present the solution to eqs. (4.1) in the following form\n\n Csexp(−qs(u))=m+1∑r1<⋯\n\n, where\n\n Δ(wr1,…,wrs)=s∏i\n\ndenotes the Vandermonde determinant. The real constants and , , obey the relations\n\n m+1∏r=1vr=Δ−2(w1,…,wm+1),m+1∑r=1wr=0. (4.6)\n\nIn (4.4)\n\n Cs=m∏s′=1B−Ass′s′, (4.7)\n\nwhere\n\n Ass′=1m+1min(s,s′)[m+1−max(s,s′)], (4.8)\n\n, are components of a matrix inverse to the Cartan one, i.e. (see Ch.7 in ). Here\n\n vr≠0,wr≠wr′,r≠r′, (4.9)\n\n. We note that the solution with may be obtained ¿from the solution with (see ) by a certain shift .\n\n ET=12m∑s,s′=1Ass′˙qs˙qs′+m∑s=1Bsexp(m∑s′=1Ass′qs′)=12m+1∑r=1w2r. (4.10)\n\nIf , , then all are real and, moreover, all , . In a general case , , relations (4.4)-(4.7) also describe real solutions to eqs. (4.1) for suitably chosen complex parameters and . These parameters are either real or belong to pairs of complex conjugate (non-equal) numbers, i.e., for example, , . When some of are negative, there are also some special (degenerate) solutions to eqs. (4.1) that are not described by relations (4.4)-(4.7), but may be obtained from the latter by certain limits of parameters (see example in the next section).\n\nFor the energy (3.39) we get\n\n ETL=12KET=h4m+1∑r=1w2r. (4.11)\n\nHere\n\n Ks=K,hs=h=K−1, (4.12)\n\n.\n\nThus, in the Toda chain case (4.1) eqs. (4.4)-(4.12) should be substituted into relations (3.38) and (3.41)-(3.46) for the general solution.\n\n### iv.1 Examples for d0>2\n\nHere we consider the case . Let matrix be positively defined and . Then from the energy constraint (3.38) we get\n\n ETL≤0⟹ET≤0. (4.13)\n\nIn this case\n\n cα=ci=0⟺ETL=ET=0, (4.14)\n\n, and . When is negatively defined (as it takes place in -dimensional theory from ) there exist solutions with .\n\n#### iv.1.1 A1-case.\n\nHere we consider the case of one “brane”, i.e. . Solving the Liouville equation\n\n ¨qs=−Bsexp(2q"
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.8629384,"math_prob":0.9956016,"size":11478,"snap":"2023-14-2023-23","text_gpt3_token_len":3127,"char_repetition_ratio":0.14275753,"word_repetition_ratio":0.016780283,"special_character_ratio":0.301272,"punctuation_ratio":0.17484537,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9988605,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-03-30T04:11:39Z\",\"WARC-Record-ID\":\"<urn:uuid:ce25d98e-fe9b-4fc7-828d-c140543f221c>\",\"Content-Length\":\"1049410\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:3b6a4ea4-f03c-4284-a69c-2fa59d947c8c>\",\"WARC-Concurrent-To\":\"<urn:uuid:476c5050-8df5-4557-8e73-8876ffe89ba7>\",\"WARC-IP-Address\":\"104.21.14.110\",\"WARC-Target-URI\":\"https://www.arxiv-vanity.com/papers/hep-th/9907019/\",\"WARC-Payload-Digest\":\"sha1:ATQVYWFQ4TZWD2XEITYJHWW5O627PEY2\",\"WARC-Block-Digest\":\"sha1:PZU2V5E2EJ76DZLUT5R2WBISEOZ6VTTP\",\"WARC-Truncated\":\"length\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-14/CC-MAIN-2023-14_segments_1679296949097.61_warc_CC-MAIN-20230330035241-20230330065241-00744.warc.gz\"}"} |
http://www.mrelativity.net/VBForum/showthread.php?494-Did-Einstein-make-a-manipulation-in-the-theory-SR&s=7a18b7f45321dca192ddd456b05e63f3 | [
"# Thread: Did Einstein make a manipulation in the theory SR?\n\n1.",
null,
"Join Date\nJan 2018\nPosts\n45\n\n##",
null,
"Did Einstein make a manipulation in the theory SR?\n\nDid Einstein get a manipulation or a simple trick in the theory SR?\n\nEinstein had used Lorentz transformations in his book (Relativity, The Special and The General theory 1916).\n\nIn this book, The coordinates of a photon for the reference systems inertial K (x,y,z,t) and moving K' (x', y', z',t') are summarized: x = c.t\n\nx' = (x - vt) [1 - (v/c)2]-1/2 = c.t'\n\ny' = y\n\nz' = z\n\nt' = [t - vx/c2 ]-1/2\n\nNow, the same book says: https://www.emu.dk/sites/default/files/relativity.pdf page 35\n\n\"Let us now consider a seconds-clock which is permanently situated at the origin (x' =0) of K' . t' =0 and t' = 1 are two successive ticks of this clock. The first and fourth equations of the Lorentz transformation give for these two ticks :\n\nt = 0 and\n\nt = 1 / [1- (v/c)2]-1/2\n\njudged from K, the clock is moving with the velocity v; as judged from this referencebody, the time which elapses between two strokes of the clock is not one second, but\n\n1 / [1- (v/c)2]-1/2 seconds.\n\na somewhat larger time. As a consequence of its motion the clock goes more slowly than when at rest. Here also the velocity c plays the part of an unattainable limiting velocity.\"\n\nI cannot understand that when we put the clock at the centre of K', \"is it possible x' = 0 for t' = 1 ?\" Because, for t' = 1, x' > 0 (x' never be zero) ??????\n\nPlease help me.\nLast edited by Ersanozgen; 04-23-2018 at 02:16 AM.",
null,
"",
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"Reply With Quote\n\n2.",
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"Join Date\nJan 2018\nPosts\n45\n\n##",
null,
"x'= (x - vt) [1 - (v/c) 2] -1/2\n\nt' = (1 - vx/c2) [1 - (v/c)2] -1/2",
null,
"",
null,
"Reply With Quote\n\n3.",
null,
"Join Date\nJan 2018\nPosts\n45\n\n##",
null,
"In SR and Lorentz mentality, the units of parameters (length and time) is changed to keep the fixity of light's velocity. So, rail.km, rail.second and train.km, train.second are mentioned. And the standarts of these units are different.\n\nWhen we use SR and Lorentz transfomations we always find the value of velocity of Light as:\n\nc = 300 000 rail.km / rail.second (original velocity of Light)\n\nand\n\nc = 300 000 train.km / train.second (relative velocity of light)\n\nNow, please actice your cognitive performance; are these values or \"traveling amount on unit time\" equal? Is numerical equality sufficient?\n\nWhereas the theory SR accepts as primary / apriori postulate that the fixity of light's velocity.\n\nIntrinsically / fundamentally / authentically, this requirement has not been realized.\n\nWhen the units are different, the numeric values must be different for equality of the action.\n\nIf the fixity of light's velocity (travelling ability of the light) is the primary target, it must be that: for v = 60 % c\n\n300 000 rail.km/rail.second = 468 750 train.km /train.second\nLast edited by Ersanozgen; 04-25-2018 at 06:41 AM.",
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"",
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"Reply With Quote\n\n####",
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"Posting Permissions\n\n• You may not post new threads\n• You may not post replies\n• You may not post attachments\n• You may not edit your posts\n•"
] | [
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https://goprep.co/a-battery-of-emf-100-v-and-a-resistor-of-resistance-10-k-are-i-1nm2vl | [
"Q. 22\n\n# A battery of emf\n\n10mA\n\nGiven,\n\nEmf of the battery, E= 100V\n\nResistance of series resistor, r= 10kΩ=10000kΩ\n\nResistance of external resistor, R=0-100Ω\n\nFormula used:\n\nA constant-current source is a power source that supply constant current to an external load, even if there is a change in load resistance.\n\nWhen the battery is connected to the external resistance that vary from 0 to 100 Ω, the effective resistance will change across the potential difference provided by the battery.",
null,
"Solution:\n\nLet’s find out the current when R=0Ω or when there is no external resistance is connected,\n\nWe know that, current i for a series resistor connection is",
null,
"By substituting the known values, we get i as,",
null,
"Now let’s take R as 2 Ω (or a low value like 1 Ω or so)\n\nThe value of current, i is",
null,
"Where Rtot is the effective resistance across the battery. From the figure, Rtot can be calculated as,",
null,
"Hence by putting R=2 Ω, we get i as,",
null,
"Similarly, by putting R=100Ω , the highest possible, we get the current i as,",
null,
"So, as the principle predicted, the value of the current, 1mA, does not change much, or it stays consistent till two significant digits.\n\nRate this question :\n\nHow useful is this solution?\nWe strive to provide quality solutions. Please rate us to serve you better.\nTry our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts\nDedicated counsellor for each student\n24X7 Doubt Resolution\nDaily Report Card\nDetailed Performance Evaluation",
null,
"view all courses",
null,
"RELATED QUESTIONS :\n\n<span lang=\"EN-USPhysics - Exemplar\n\n<span lang=\"EN-USPhysics - Exemplar\n\nLet there be n rePhysics - Exemplar\n\n<span lang=\"EN-USPhysics - Exemplar\n\n<span lang=\"EN-USPhysics - Exemplar\n\nTwo cells of emf Physics - Exemplar\n\n<span lang=\"EN-USPhysics - Exemplar\n\n<span lang=\"EN-USPhysics - Exemplar\n\nKirchhoff ’s juncPhysics - Exemplar"
] | [
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https://webstore.vsni.co.uk/resources/documentation/multivariate-analysis/ | [
"Multivariate Analysis\n\nMultivariate analysis is useful when you have several different measurements on a set of n objects. In Genstat the measurements would usually be stored in separate variates, and these would have a unit for each object. The objects are often regarded as being a set of n points in p dimensions (p being the number of variates). Many techniques, for example principal components analysis (Chapter 2) and canonical variates analysis (Chapter 3) are aimed at reducing the dimensionality. That is, they aim to find a smaller number of dimensions (usually 2 or 3) that exhibit most of the variation present in the data. This can help you determine patterns or structure in the data, as well as identify the relative importance of individual variables.\n\nGenstat has several menus for producing graphical representations, for example principal coordinates analysis (Chapter 4) and multidimensional scaling (Chapter 5). It also has facilities for modelling multivariate data, including multivariate analysis of variance (Chapter 8) and partial least squares. Another important requirement is to take a set of units and classify them into groups based on their observed characteristics. Hierarchical cluster analysis (Chapter 6) starts with a set of groups each of which contains one of the units. These initial groups are successively merged into larger groups, according to their similarity, until there is just one group containing all the observations.\n\nGenstat also provide menus for nonhierarchical classification (Chapter 7), where the aim is to form a single grouping of the observations that optimizes some criterion such as the within-class dispersion, or the Mahalanobis squared distance between the groups, or the between-group sum of squares. Chapter 9 describes the facilities for constructing classification trees, which allow you to predict the classification of unknown objects using multivariate observations. Regression trees, which predict the value of a response variate from multivariate observations are described in Chapter 10.\n\nFinally, Chapter 11 describes how generalized Procrustes analysis can be used to obtain a consensus from assessors in activities such as wine tasting. The book works through a series of straightforward examples, with frequent practicals to allow you to try the methods for yourself. The examples work mainly through the menus of Genstat for Windows, so there is no need for prior knowledge of the Genstat command language."
] | [
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.94072366,"math_prob":0.867806,"size":2462,"snap":"2019-43-2019-47","text_gpt3_token_len":468,"char_repetition_ratio":0.1179821,"word_repetition_ratio":0.0,"special_character_ratio":0.17993501,"punctuation_ratio":0.08009709,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9631413,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-17T02:33:25Z\",\"WARC-Record-ID\":\"<urn:uuid:16749a74-eca9-4521-8e50-35bf814fc7e6>\",\"Content-Length\":\"24577\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2a490b8f-4f09-4ccd-bdf1-5b2132b90703>\",\"WARC-Concurrent-To\":\"<urn:uuid:c2ed16fe-d38e-4c77-a7ad-5cdcd0269ace>\",\"WARC-IP-Address\":\"77.104.172.141\",\"WARC-Target-URI\":\"https://webstore.vsni.co.uk/resources/documentation/multivariate-analysis/\",\"WARC-Payload-Digest\":\"sha1:AOOO362AHDLT5O6DWRZ6E55DLLQEFAH7\",\"WARC-Block-Digest\":\"sha1:37BRF5XQSQOBINWBIMRUAUHWRAYXA75I\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570986672548.33_warc_CC-MAIN-20191017022259-20191017045759-00520.warc.gz\"}"} |
https://vedantu.xyz/preview/how_do_you_teach_adding_mixed_fractions_/165231385670256d5db2776/ | [
"## How Do You Teach Adding Mixed Fractions?\n\nAdding mixed numbers with like denominators\n\n1. To add mixed numbers with the same denominator, follow these steps:\n2. First, add the whole numbers.\n3. Then, add the fractions. Add the numerators and keep the denominator the same.\n4. Now, simplify.\n\n### What is a fraction explain about it using real life examples?\n\nIn Mathematics, a fraction defined as the part of the whole thing. For example, a pizza is divided into four equal pieces, then each piece is represented by ¼. Fractions help to distribute and judge the numbers easily and make the calculation faster.\n\n### Are fractions hard to learn?\n\nWhy are fractions so difficult to understand? A major reason is that learning fractions requires overcoming two types of difficulty: inherent and culturally contingent. Inherent sources of difficulty are those that derive from the nature of fractions, ones that confront all learners in all places.\n\n### How do you introduce a fraction?\n\nAnswer: Fractions are numbers representing a part of the whole. When we divide an object or group of them into equal parts, then each individual part is referred to as a fraction. We usually write down fractions as ½ or 6/12 and more. Moreover, it divides into a numerator and denominator.\n\n### How do you explain fractions ks2?\n\nA fraction is a number that is used to represent a whole number that has been divided into equal parts. For example, if we divide a cake into 8 equal parts and we take one piece, this would mean that 1/8 of the cake is gone and 7/8 is left. There are two parts of a fraction, the top and the bottom number.\n\n### How do you teach adding mixed fractions?\n\nAdding mixed numbers with like denominators\n\n1. To add mixed numbers with the same denominator, follow these steps:\n2. First, add the whole numbers.\n3. Then, add the fractions. Add the numerators and keep the denominator the same.\n4. Now, simplify.\n\n### How do you add fractions in elementary school?\n\nTo add fractions there are Three Simple Steps:\n\n1. Step 1: Make sure the bottom numbers (the denominators) are the same.\n2. Step 2: Add the top numbers (the numerators), put that answer over the denominator.\n3. Step 3: Simplify the fraction (if possible)\n\n### Is determinant linear?\n\nFor example, viewing an n × n matrix as being composed of n rows, the determinant is an n-linear function.\n\n### What is the sum property of determinants?\n\nIn a determinant the sum of the product of the elements of any row (or column) with the cofactors of the corresponding elements of any other row (or column) is zero. For example, d = ai1*Aj1 + ai2*Aj2 + ai3*Aj3 +……\n\n### What is a radian measure in physics?\n\nThe radian is the Standard International (SI) unit of plane angular measure. There are 2 pi, or approximately 6.28318, radians in a complete circle. Thus, one radian is about 57.296 angular degrees.\n\n### Can you multiply two determinants?\n\nTwo determinants can be multiplied together only if they are of same order. The rule of multiplication is as under: Take the first row of determinant and multiply it successively with 1st, 2nd & 3rd rows of other determinant. The three expressions thus obtained will be elements of 1st row of resultant determinant.\n\n### How do you find radians?\n\nSo one radian = 180/ PI degrees and one degree = PI /180 radians. Therefore to convert a certain number of degrees in to radians, multiply the number of degrees by PI /180 (for example, 90º = 90 × PI /180 radians = PI /2). To convert a certain number of radians into degrees, multiply the number of radians by 180/ PI .\n\n### Can a matrix have more than one determinant?\n\nA matrix cannot have multiple determinants since the determinant is a scalar that can be calculated from the elements of a square matrix. Swapping of rows or columns will change the sign of a determinant.\n\n### What is 2 radian in terms of pi?\n\nWe know that 2π radian = 360°. To find the angle 2 radians in terms of π, just divide the equation both sides by π, then we get 2 radians = 360°/π.\n\n### Why is circumference 2pir?\n\nBasically this is a definition thing. π is defined to be the ratio of the circumference of a circle over its diameter (or 2 times its radius). This ratio is a constant since all circles are geometrically similar and linear proportions between any similar geometric figures are constant.\n\n### How many properties are there in determinants?\n\nThere are 10 important properties of Determinants that are widely used. These properties make calculations easier and also are helping in solving various kinds of problems. The description of each of the 10 important properties of Determinants is given below.\n\n### Why are radians expressed as pi?\n\nRadians are not measured in Pi, they are just a number. A radian is defined as the ratio between the length of a circular arc and the radius of the circle. For example if the arc goes around 360 degrees (a full circle), the radians are 2PiR divided by R. So 360 degrees is 2 Pi radians.\n\n### Can determinant be plural?\n\nThe plural form of determinant is determinants.\n\n### Does addition affect determinant?\n\nTherefore, when we add a multiple of a row to another row, the determinant of the matrix is unchanged. Note that if a matrix A contains a row which is a multiple of another row, det(A) will equal 0.\n\n### Does Ref change determinant?\n\nThe row operation Ri ↔ Rj changes the sign of the determinant. Every elementary product of the original determinant contains exactly one entry from row i. Multiplying all those entries by c just multiplies the whole determinant by c. The row operation Ri ← cRi, c ≠ 0 multiplies the determinant by c.\n\nDated : 11-Jul-2022\n\nCategory : Education"
] | [
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https://www.vedantu.com/physics/relation-between-torque-and-moment-of-inertia | [
"Relation Between Torque and Moment of Inertia",
null,
"",
null,
"",
null,
"",
null,
"",
null,
"Relation Between Torque and Moment of Inertia in Detail\n\nWe know that the turning effect of the fan is called the torque and there is a direct relationship between the torque and the moment of inertia.\n\nSo, here on switching the button of the fan, when the fan begins to rotate, its moment of force or torque varies inversely with the acceleration. Here, this relationship can be considered as the sister of Newton’s second law of motion. The moment of inertia is the rotational mass of the fan and the torque is its rotational force or its turning force.\n\nRelation Between Inertia and Torque\n\nAccording to Newton’s first law of motion, the body remains at rest or in the state of motion unless it is driven by an external force. So, here when the condenser of the AC, washing machine remains at rest unless we switch on the power button, and allows it to rotate with the help of electricity.\n\nSo, we can see that all the rotating electrical appliances remain at rest, and when the turning effect or the torque is offered, where each particle in the system having their individual rotational masses start rotating about their axis of rotation. So, this is how we can understand the relationship between the torque and inertia by applying Newton’s first law of motion.\n\nSo far we understood the relationship of torque with inertia and moment of inertia. Now, we will derive the relation between torque and moment of inertia.\n\nConcept Used in Rotational Motion\n\nAccording to the mechanics of rotational motion, every rigid body executing rotational motion about the fixed axis bears a uniform angular acceleration motion, i.e., under the action of torque or the moment of force.\n\nDerive Relation Between Torque and Moment of Inertia\n\nLet’s suppose that a particle ‘Q’ of mass ‘m’ is rotating around the axis of rotation where it is making an arc along the circle of radius ‘r’. Now, according to Newton’s second law of motion, we have:\n\nF = ma\n\nWhere a is the acceleration by which the body is rotating.\n\nNow, a = F/m….(a)\n\nIf we say that the particle is moving along the circle with displacement ‘s’, then we can rewrite the equation for linear acceleration as the double derivative of angular displacement in the following manner:\n\n$a = \\frac{d}{dt} \\frac{d(s)}{dt}$ ….(1)\n\nSince a system has ‘n’ number of particles, so the acceleration of each particle will be a1, a2, a3,...., an.\n\nFor a body executing the rotational motion, the relation is: ‘s = r’, let’s apply this is in the equation (1):\n\n$a = \\frac{d}{dt} \\frac{d(r \\theta)}{dt}$\n\nSince ‘r’ is the radius of the circle along which the particle is rotating and it is a constant value, so taking it out of the derivative form and rewriting the equation in the following manner:\n\n$a = \\frac{d}{dt} \\frac{rd(\\theta)}{dt}$ ….(2)\n\nAlso, we know that the relation between the linear and the angular acceleration, for which let’s write the same:\n\n$a = r \\alpha$……(3)\n\nFrom, equation (2), we are getting equation (3), as we can see that the rate of change of angular displacement is the angular velocity, let’s see how it happens:\n\n$\\frac{rd(\\theta)}{dt} = \\omega$\n\nAnd,\n\n$\\frac{d \\omega}{dt} = \\alpha$\n\nHere, is the angular acceleration of particle ‘Q’. So, we derived equation (3) as well. Now, proceeding to the next step:\n\nForce and Moment of Force\n\nWe know one more relationship and that is between the force applied to the body and the torque, and that is as follows:\n\n$\\tau = rF$\n\n$F = \\frac{\\tau}{r}$ …..(4)\n\nSubstituting the value of equation (3) and (4) in equation (a) we get:\n\n$r \\alpha = \\frac{(\\frac{\\tau}{r})}{m}$\n\nAdjusting the above equation, we get:\n\n$\\alpha m r^{2} = \\tau$ …..(5)\n\nWe also know that $I = mr^{2}$ ….(6)\n\nWhere,\n\nm = mass of the particle ‘Q’ and r is the square of the distance of the particle from the axis of rotation or simply the radius of gyration, so substituting the value of eq (6) in (5), we get:\n\n$\\tau = I \\alpha$ …..(7)\n\nSo, equation (7) is the desired equation for which we have done all this mathematical derivation. Equation (7) describes the ultimate relationship between moment of inertia and torque.\n\nWe can rewrite the equation (7) in the vector form as:\n\n$\\overrightarrow{\\tau} = I \\overrightarrow{\\alpha}$\n\nWe call this equation the fundamental law of rotational motion or the law of rotational motion. Now, let’s define the above equation:\n\nDefinition of Fundamental Law of Rotational Motion\n\nIf α = 1, then τ = I * 1. From this statement, we can say that the moment of inertia and the torque applied to the body are equal to each other in the absence of angular acceleration.\n\nSince the system has ‘n’ number of particles, and each particle follows equation (7), so the law of rotational motion applies to each and every particle of the system.\n\nQuestion 1: What are the Significance of Torque and the Moment of Inertia?\n\nAnswer: The torque is similar to the applied force in the linear motion. It is a fundamental criterion that keeps the body in rotational motion. So when the torque is offered to the body, it starts making rotations with uniform angular acceleration.\n\nQuestion 2: Name Two Theorems on the Moment of Inertia.\n\nAnswer: When we are known with the moment of inertia of an object or a system about a given axis, then we can calculate the moment of inertia about any other axis easily. This can be done by the following two theorems:\n\n• Parallel axes theorem.\n\n• Perpendicular axes theorem.\n\nQuestion 3: Is Torque a Vector Quantity?\n\nAnswer: Yes, the torque is a vector quantity. It is equivalent to the vector product of the vector pointing from the axis to the point of application of force applied and the vector of force. The torque points upward from a counterclockwise rotation, and vice-versa.\n\nQuestion 4: Is the Moment of Inertia an Extensive Property?\n\nAnswer: Yes, the moment of inertia is an extension (additive) attribute for a point mass object.\n\nWe define the moment of inertia as the product of the mass and the square of the perpendicular distance to the axis of rotation.\n\nFor a rigid system, it is the sum of the moments of inertia of its component subsystems when taken about the same axis of rotation.\n\nComment"
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https://numbermaniacs.com/what-number-is-a-of-b/24/what-number-is-24-of-80.html | [
"What number is 24 of 80?\n\nWhat number is 24 of 80, you ask? Here we will explain what 24 of 80 means and show you how to answer the question.\n\nAs the question spells out, you are asking for a number. Thus, the answer should be a number. However, 24 and 80 are not specified and can mean different things, so we have to make assumption to answer the question.\n\nTherefore, to answer the question \"What number is 24 of 80?\", we will assume that 24 is a percent and that 80 is also a number.\n\nTo get the answer, we multiply 24 by 80 and then divide that product by 100. Here is the math and answer to your question:\n\n24 x 80 = 1920\n1920 / 100 = 19.2\n\nIn summary, to answer \"What number is 24 of 80?\", we assumed you meant 24% of 80 and the answer is 19.2 as illustrated and calculated above.\n\nWhat Number is A of B Calculator\nWant the answer to a similar problem? Enter another \"What number is A of B?\" problem here.\n\nof\n\nWhat number is 24 of 81?\nWant to see the next problem we solved? No problem! Go here to learn more."
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https://www.physicsforums.com/threads/throws-a-stone-horizontally-with-a-velocity-of-20ms-1.635287/ | [
"# Throws a stone horizontally with a velocity of 20ms-1\n\n## Homework Statement\n\n1. Don Joriel stands on a vertical cliff edge throwing stones into the sea below. He throws a stone horizontally with a velocity of 20ms-1, 560 m above sea level.\na. How long does it take for the stone to hit the water from leaving Don Joriel’s hand?\nUse g = 9.81 ms-2 and ignore air resistance?\nb. Find the distance of the stone from the base of the cliff when it hits the water.\n\n2. When Maggie applies the brakes of her car, the car slows uniformly from 15.00 m/s to 0.00 m/s in 2.50 s. How many meters before a stop sign must she apply her brakes?\n\n## The Attempt at a Solution\n\nb. 20.39 m\n2. 18.75 m\n\nHope you can help me, if got the wrong answer please show me the solution... Thanks a lot...\n\nRelated Introductory Physics Homework Help News on Phys.org\nrl.bhat\nHomework Helper\n\nSimon Bridge\nHomework Helper\n\nWhat rl.bhat said: if you don't show us what you tried or your reasoning, then we cannot know how to help you best.\n\nwait i'll show you when i got home.. thanks...\n\nfor 1a. i use v = u + at,\nb. s = ut +1/2 at squared\n\nfor 2. s = 1/2 (u +v)t\n\nare those correct?\n\nCAF123\nGold Member\n\nfor 1a. i use v = u + at,\nb. s = ut +1/2 at squared\n\nfor 2. s = 1/2 (u +v)t\n\nare those correct?\nI don't see how you can use the equation in 1a without first knowing the final velocity of the ball (I.e the velocity of the ball prior to impact with the ground). From your answer, it seems you have assumed this to be 0, but this is not the final vertical component of velocity.\n\nCAF123\nGold Member\n\nFor 1b, we are considering a horizontal distance. There is no acceleration of the ball in x direction so the eqn you were using simplifies to simply $s = v_{ox}t$.\nFor 2, if I understand the wording of the question correctly, you are correct.\n\nI don't see how you can use the equation in 1a without first knowing the final velocity of the ball (I.e the velocity of the ball prior to impact with the ground). From your answer, it seems you have assumed this to be 0, but this is not the final vertical component of velocity.\nFor 1b, we are considering a horizontal distance. There is no acceleration of the ball in x direction so the eqn you were using simplifies to simply $s = v_{ox}t$.\nFor 2, if I understand the wording of the question correctly, you are correct.\n\nrl.bhat\nHomework Helper\n\nfor 1a. i use v = u + at,\nb. s = ut +1/2 at squared\n\nfor 2. s = 1/2 (u +v)t\n\nare those correct?\nBefore you attempt this problem, please go through the projectile motion.\n\nCAF123\nGold Member\n\nWe are not allowed to simply hand over solutions. For 1a, you can use the equation $s_y = v_{oy}t - \\frac{1}{2}gt^2$ right away to find the time of descent. Alternatively, the final vertical component of velocity can be found first so you can then use $v_{fy} = v_{oy} -gt$.\nYet another way is to do all three problems via sketching v-t diagrams for each of the x and y components of velocity.\n\nWe are not allowed to simply hand over solutions. For 1a, you can use the equation $s_y = v_{oy}t - \\frac{1}{2}gt^2$ right away to find the time of descent. Alternatively, the final vertical component of velocity can be found first so you can then use $v_{fy} = v_{oy} -gt$.\nYet another way is to do all three problems via sketching v-t diagrams for each of the x and y components of velocity.\ni didnt get your equation because of so much symbols, sorry...\n\nrl.bhat\nHomework Helper\n\nCan you find the time taken by a stone dropped from a height 560 m?\n\nCAF123\nGold Member\n\nOk, for 1a, initial vertical component of velocity is 0, right? This is because the ball is projected horizontally. So in our equation, $v_{oy} =0.$ The eqn therefore reduces to $s_y = \\frac{1}{2}at^2.$ If you define downwards as negative, then the ball will fall downwards 500m so $s_y = -500m.$ Think of the ball moving 500 units down the y axis (I.e starts at y =0 and finishes at y = -500). Now, if downwards is negative, a =-g and so our final equation is $-s_y = -\\frac{1}{2}gt^2$ Rearrange for t and you are done with 1a.\n\nso t = 10.68... by the way where did you get 500? is it 560?\n\nCAF123\nGold Member\n\nYes, sorry 560m not 500m. For 1b, again use the relation $s_x = v_{ox}t + \\frac{1}{2}at^2,$ but this time considering the x direction. No forces act on the body in the horizontal direction so ax = 0. The horizontal distance covered will be proportional to the time of flight because of a constant (non zero) horizontal component of velocity.\n\nSimon Bridge\nHomework Helper\n\nPlease tell us what you got... be specific: it makes sure we have not accidentally sent you up the wrong tree. When you show working, also be specific: we need to see your reasoning, like how you used an equation, in order to help you properly.\n\nCAF is doing the detail work. Can you see how CAF is choosing which equation to use?\n\nis this correct for 1a.\n-560 = -1/2 (9.81) t^2\nt = 10.68\n\nim not sure if that s correct\n\nCAF123\nGold Member\n\nis this correct for 1a.\n-560 = -1/2 (9.81) t^2\nt = 10.68\n\nim not sure if that s correct\nYes, that is correct. But do you understand why? What makes you unsure?\nHow did you get on with 1b?\n\ntell me if i got 1b correct.\ns = 20 m/s (10.68 s)\ns = 213.6 m...\n\nis it right?\nthanks a lot....\n\nhow about the number 2? this is my solution:\ns = 1/2(u+v)t\n= 18.75 m\n\nCAF123\nGold Member\n\nYes, all questions are correct now. I would now suggest a few more problems to make sure you are on top of things."
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https://mymathangels.com/problem-1109/ | [
"# Problem 1109\n\nFind the length s of the arc of a circle of radius 85 centimeters subtended by the central angle 36°.\n\nSolution:-\n\nA central angle is an angle whose vertex is at the center of a circle. The rays of a central angle subtend (intersect) an arc on the circle. We have the following theorem.\n\nArc Length\n\nFor a circle of radius r, a central angle θ radians subtends an arc whose length s is\n\ns = r θ\n\nConvert angle in degrees to radians.\n\n1° =",
null,
"radian\n\n36° = 36 *",
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"radian",
null,
"",
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"radian\n\ns(arc length) = rθ\n\n= 85 centimeters*",
null,
"=17π centimeters",
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"53.407 centimeters"
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"https://mymathangels.com/wp-content/ql-cache/quicklatex.com-7cb9b1ae5cb445f3c73f8da715740dfe_l3.png",
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.76964146,"math_prob":0.99530536,"size":536,"snap":"2023-40-2023-50","text_gpt3_token_len":149,"char_repetition_ratio":0.17481203,"word_repetition_ratio":0.0,"special_character_ratio":0.27238807,"punctuation_ratio":0.074074075,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9988755,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12],"im_url_duplicate_count":[null,null,null,null,null,null,null,5,null,5,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-29T04:13:45Z\",\"WARC-Record-ID\":\"<urn:uuid:9bb73e93-a385-4fb1-8eff-b7f4582bccf5>\",\"Content-Length\":\"61334\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:79ab047a-65dd-4f0e-a3fb-b08828dc93fb>\",\"WARC-Concurrent-To\":\"<urn:uuid:5fceadaa-7d56-4b0f-bffe-7dd90e9b6f3f>\",\"WARC-IP-Address\":\"185.212.70.183\",\"WARC-Target-URI\":\"https://mymathangels.com/problem-1109/\",\"WARC-Payload-Digest\":\"sha1:UO2HZAZ4YT37WBG2XR426QVKWOLYH26U\",\"WARC-Block-Digest\":\"sha1:2HKOVNBXDGPXUCAFT7W3R6SJRDG4AUCU\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510481.79_warc_CC-MAIN-20230929022639-20230929052639-00202.warc.gz\"}"} |
https://www.imsbio.co.jp/RGM/R_rdfile?f=Luminescence/man/calc_IEU.Rd&d=R_CC | [
"Last data update: 2014.03.03\n\nR: Apply the internal-external-uncertainty (IEU) model after...\n calc_IEU R Documentation\n\n## Apply the internal-external-uncertainty (IEU) model after Thomsen et al. (2007) to a given De distribution\n\n### Description\n\nFunction to calculate the IEU De for a De data set.\n\n### Usage\n\n```calc_IEU(data, a, b, interval, decimal.point = 2, plot = TRUE, ...)\n```\n\n### Arguments\n\n `data` `RLum.Results` or data.frame (required): for `data.frame`: two columns with De `(data[,1])` and De error `(values[,2])` `a` `numeric`: slope `b` `numeric`: intercept `interval` `numeric`: fixed interval (e.g. 5 Gy) used for iteration of Dbar, from the mean to Lowest.De used to create Graph.IEU [Dbar.Fixed vs Z] `decimal.point` `numeric` (with default): number of decimal points for rounding calculations (e.g. 2) `plot` `logical` (with default): plot output `...` further arguments (`trace, verbose`).\n\n### Details\n\nThis function uses the equations of Thomsen et al. (2007). The parameters a and b are estimated from dose-recovery experiments.\n\n### Value\n\nReturns a plot (optional) and terminal output. In addition an `RLum.Results` object is returned containing the following element:\n\n `summary` data.frame summary of all relevant model results. `data` data.frame original input data `args` list used arguments `call` call the function call `tables` list a list of data frames containing all calculation tables\n\nThe output should be accessed using the function `get_RLum`.\n\n### Function version\n\n0.1.0 (2016-05-02 09:36:06)\n\n### Author(s)\n\nRachel Smedley, Geography & Earth Sciences, Aberystwyth University (United Kingdom)\nBased on an excel spreadsheet and accompanying macro written by Kristina Thomsen.\nR Luminescence Package Team\n\n### References\n\nSmedley, R.K., 2015. A new R function for the Internal External Uncertainty (IEU) model. Ancient TL 33, 16-21.\n\nThomsen, K.J., Murray, A.S., Boetter-Jensen, L. & Kinahan, J., 2007. Determination of burial dose in incompletely bleached fluvial samples using single grains of quartz. Radiation Measurements 42, 370-379.\n\n`plot`, `calc_CommonDose`, `calc_CentralDose`, `calc_FiniteMixture`, `calc_FuchsLang2001`, `calc_MinDose`\n\n### Examples\n\n```\ndata(ExampleData.DeValues, envir = environment())\n\n## apply the IEU model\nieu <- calc_IEU(ExampleData.DeValues\\$CA1, a = 0.2, b = 1.9, interval = 1)\n\n```\n\n### Results\n\n```\nR version 3.3.1 (2016-06-21) -- \"Bug in Your Hair\"\nCopyright (C) 2016 The R Foundation for Statistical Computing\nPlatform: x86_64-pc-linux-gnu (64-bit)\n\nR is free software and comes with ABSOLUTELY NO WARRANTY.\nYou are welcome to redistribute it under certain conditions.\nType 'license()' or 'licence()' for distribution details.\n\nR is a collaborative project with many contributors.\n'citation()' on how to cite R or R packages in publications.\n\nType 'demo()' for some demos, 'help()' for on-line help, or\n'help.start()' for an HTML browser interface to help.\nType 'q()' to quit R.\n\n> library(Luminescence)\nWelcome to the R package Luminescence version 0.6.0 [Built: 2016-05-30 16:47:30 UTC]\nA motivated R-Team member: 'We are doing this not just for statistical reasons, there is real science behind it!'\n> png(filename=\"/home/ddbj/snapshot/RGM3/R_CC/result/Luminescence/calc_IEU.Rd_%03d_medium.png\", width=480, height=480)\n> ### Name: calc_IEU\n> ### Title: Apply the internal-external-uncertainty (IEU) model after\n> ### Thomsen et al. (2007) to a given De distribution\n> ### Aliases: calc_IEU\n>\n> ### ** Examples\n>\n>\n> data(ExampleData.DeValues, envir = environment())\n>\n> ## apply the IEU model\n> ieu <- calc_IEU(ExampleData.DeValues\\$CA1, a = 0.2, b = 1.9, interval = 1)\n\n[calc_IEU]\n\nDbar: 46.67\nIEU.De (Gy): 46.67\nIEU.Error (Gy): 2.55 Number of De: 24\na: 0.2000\nb: 1.9000\n>\n>\n>\n>\n>\n>\n> dev.off()\nnull device\n1\n>\n\n```"
] | [
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.5104112,"math_prob":0.7768623,"size":3305,"snap":"2022-27-2022-33","text_gpt3_token_len":955,"char_repetition_ratio":0.08209633,"word_repetition_ratio":0.04338843,"special_character_ratio":0.29319212,"punctuation_ratio":0.19398496,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9753048,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-08-15T13:53:57Z\",\"WARC-Record-ID\":\"<urn:uuid:4cd21788-5ba1-456f-873e-9bb3a225ab47>\",\"Content-Length\":\"11690\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b16374ff-7882-4035-993b-5e69caefa094>\",\"WARC-Concurrent-To\":\"<urn:uuid:5818b6b2-4c76-4392-bcd0-a0338ca8c309>\",\"WARC-IP-Address\":\"219.117.242.224\",\"WARC-Target-URI\":\"https://www.imsbio.co.jp/RGM/R_rdfile?f=Luminescence/man/calc_IEU.Rd&d=R_CC\",\"WARC-Payload-Digest\":\"sha1:TPK5CP3HP7TOBO6WJBFDPWWMYUTKMQ2D\",\"WARC-Block-Digest\":\"sha1:TYVKB3VJ4CPDMD5MZVDXBNDSLC5A5XPD\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-33/CC-MAIN-2022-33_segments_1659882572174.8_warc_CC-MAIN-20220815115129-20220815145129-00345.warc.gz\"}"} |
https://abdul-quader.com/research/ | [
"# Research\n\nI study the model theory of Peano Arithmetic (PA). Currently, I am focused on the connection between the “Lattice Problem for models of PA” and the question of which sets can be coded in elementary end extensions.\n\nGiven a model of PA, the collection of its elementary submodels forms a lattice under inclusion, called the “substructure lattice”. Given an elementary extension",
null,
"$\\mathcal{M} \\prec \\mathcal{N}$ of models of PA, the collection of all models",
null,
"$\\mathcal{K}$ such that",
null,
"$\\mathcal{M} \\preceq \\mathcal{K} \\preceq \\mathcal{N}$ also forms a lattice, called the “interstructure lattice”, and is denoted Lt(",
null,
"$\\mathcal{N} / \\mathcal{M}$).\n\nAnother invariant of an elementary (end) extension is the collection of subsets of the ground model “coded” in the extensions. To make this more precise, given",
null,
"$\\mathcal{M} \\prec_\\text{end} \\mathcal{N}$ the set",
null,
"$\\{ X \\cap M : X \\in \\textrm{Def}(\\mathcal{N}) \\}$ is denoted Cod(",
null,
"$\\mathcal{N} / \\mathcal{M}$). It’s not clear, in general, if there is a connection between these two invariants. A recent paper by Jim Schmerl studies this connection for minimal end extensions (that is, end extensions realizing the interstructure lattice 2)."
] | [
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"https://s0.wp.com/latex.php",
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"https://s0.wp.com/latex.php",
null,
"https://s0.wp.com/latex.php",
null,
"https://s0.wp.com/latex.php",
null,
"https://s0.wp.com/latex.php",
null,
"https://s0.wp.com/latex.php",
null,
"https://s0.wp.com/latex.php",
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.9257038,"math_prob":0.9977758,"size":927,"snap":"2020-45-2020-50","text_gpt3_token_len":192,"char_repetition_ratio":0.15492958,"word_repetition_ratio":0.013605442,"special_character_ratio":0.20280474,"punctuation_ratio":0.105882354,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9997738,"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\":\"2020-10-21T02:04:47Z\",\"WARC-Record-ID\":\"<urn:uuid:3d171411-e6c9-47cb-bbb2-0280e1fdedf6>\",\"Content-Length\":\"32559\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:5fd6e5b2-9364-48b0-8080-97b619a4c636>\",\"WARC-Concurrent-To\":\"<urn:uuid:3794c10c-d7b4-4d9c-9240-e2ef212c2ce2>\",\"WARC-IP-Address\":\"192.0.78.24\",\"WARC-Target-URI\":\"https://abdul-quader.com/research/\",\"WARC-Payload-Digest\":\"sha1:FN4DICCM453SF6LPPZQJRMYGGENMAEIW\",\"WARC-Block-Digest\":\"sha1:CACFNUE52AWF23XXYAABXJYZAXGFZCIZ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-45/CC-MAIN-2020-45_segments_1603107874637.23_warc_CC-MAIN-20201021010156-20201021040156-00271.warc.gz\"}"} |
https://id.scribd.com/document/374406264/Pda | [
"Anda di halaman 1dari 87\n\nvulcanhammer.info\nVulcan Iron Works\nInc. and the pile\ndriving equipment it\nmanufactured\n\nhttp://www.vulcanhammer.org\nTerms and Conditions of Use:\nAll of the information, data and computer software (“information”)\npresented on this web site is for general information only. While every\neffort will be made to insure its accuracy, this information should not\nbe used or relied on for any specific application without independent,\ncompetent professional examination and verification of its accuracy, suit-\nability and applicability by a licensed professional. Anyone making use\nof this information does so at his or her own risk and assumes any and all\nliability resulting from such use. The entire risk as to quality or usability of\nthe information contained within is with the reader. In no event will this web\npage or webmaster be held liable, nor does this web page or its webmaster\nprovide insurance against liability, for any damages including lost profits, lost\nsavings or any other incidental or consequential damages arising from the use\nor inability to use the information contained within.\n\nThis site is not an official site of Prentice-Hall, Pile Buck, or Vulcan Foundation\nEquipment. All references to sources of software, equipment, parts, service or\nrepairs do not constitute an endorsement.\nTEXAS\nTRANSPORTATION\nINSTITUTE\n\nTEXAS\nHIGHWAY\nDEPARTMENT\n\n- COOPERATIVE\nRESEARCH\n\n## PILE DRIVING ANALYSIS-.\n\n_ j. 1 C . . C 7~ = - - . -, , . ,\nI I\n\n-. -\nSTATE OF THE ART\nL\n\nk t\n\n## in cooperation with the\n\nDepartment of Transportation .\n\n## RESEARCH REPORT 33-13 (FINAL)\n\nSTUDY 2-5-62-33\nPILING BEHAVIOR\nPILE DRIVING ANALYSIS\nSTATE OF THE ART\n\n## Lee Leon Lowery, Jr.\n\nAssociate Research ~ n g i n e e r\nT. J. Hirsch\nResearch Engineer\nThomas C. Edwards\nAssistant Research Engineer\nHarry M. Coyle\nAssociate Research Engineer\nCharles H. Samson, Jr.\nResearch Engineer\n\n## Research Study No. 2-5-62-33\n\nPiling Behavior\n\nThe Texas Highway Department\nin cooperation with the\nU. S. Department of Transportation, Federal Highway Administration\n\nJanuary 1969\n\n## TEXAS TRANSPORTATION INSTITUTE\n\nTexas A&M University\nCollege Station, Texas\nForeword\nThe information contained herein was developed on the Research Study 2-5-62-33\nentitled \"Piling Behavior\" which is a cooperative research endeavor sponsored jointly\nby the Texas Highway Department and the U. S. Department of Transportation,\nFederal Highway Administration, Bureau of Public Roads, and also by the authors\nas evidenced by the number of publications during the past seven years of intense\nstudy and research. The broad objective of the project was to fully develop the\ncomputer solution of the wave equation and its use for pile driving analysis, to\ndetermine values for the significant parameters involved to enable engineers to\npredict driving stresses in piling during driving, and to estimate the static soil resist-\nance to penetration on piling at the time of driving from driving resistance records.\nThe opinions, findings, and conclusions expressed in this report are those of the\nauthors and not necessarily those of the Bureau of Public Roads.\nAcknowledgments\nSince this report is intended to summarize the research efforts and experience\ngained by the authors over a seven-year period, it is impossible to mention all of the\npersons, companies, and agencies without whose cooperation and support no \"state\nof the art\" in the analysis of piling by the wave equation would exist.\nThe greatest debt of gratitude is due Mr. E. A. L. Smith, Chief Mechmical Engi-\nneer of Raymond International (now retired), who not only first proposed the method\nof analysis but also maintained a continuing interest throughout the work and con-\ntributed significantly to the accomplishments of the research. His advice and guid-\nance, based on his extensive field experience, and his intimate knowledge of the wave\nequation have proven invaluable throughout all phases of the research.\nThe authors gratefully acknowledge the assistance and support of Farland C.\nBundy and Wayne Henneberger of the Bridge Division of the Texas Highway De-\npartment, who worked closely with the authors in accomplishing several of the proj-\nects. A debt of gratitude is due the Bass Bros. Concrete Company of Victoria, Ross\nAnglin and Son, General Contractors, and the California Company of New Orleans\nfor their unselfish cooperation with all phases of the field work. It was indeed\nfortunate to have these foresighted and progressive businessmen as contractors on\nthe various jobs. They willingly invested considerable amounts of their own time\nand effort to the accomplishment of the research projects.\nSincere thanks and our personal appreciation are extended to the Texas Highway\nDepartment and the U. S. Department of Transportation, Federal Highway Adminis-\nleading to this report a reality.\nSeveral graduate students and research assistants contributed significantly to\nthe accomplishment of this work. They were Tom P. Airhart, Gary N. Reeves, Paul\nC. Chan, Carl F. Raba, Gary Gibson, I. H. Sulaiman, James R. Finley, M. T. Al-Layla,\nand John Miller.\n\niii\nPage\nLIST OF FIGURES --------------------------------- ........................................ v\n\n## LIST OF TABLES _----- ri\n\nCHAPTER\nI INTRODUCTION -----, 1\nI1 PILE DRIVING ANALYSIS 1\n2.1 General 1\n2.2 Smiths Numerical Solution of the Wave Equation\n9\n2\n..\n2.3 Critical Time Interval 4\n2.4 Effect of Gravity - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 5\nI11 PILE DRIVING HAMMERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6\n3.1 Energy Output of Impact Hammers 6\n. .\n3.2 Dekermination of Hammer Energy Output. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6\n. . . ..\n3.3 Significance of Driving Accessories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8\n. .\n3.4 Explosive Pressure in Diesel Hammers 10\n..\n3.5 Effect of Ram Elasticity ------------------------------------ 1.......................... 11\nIV CAPBLOCKS AND CUSHION BLOCKS 12\n4.1 Method Used to Determine Capblock and Cushion Properties ----------------------------- 12\n4.2 Idealized Load-Deformation Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - 14\n.. . .\n41.3 Coefficient of Rest1:ution- . 14\nV STRESS WAVES IN PILING 15\n5.1 Comparison with Laboratory Experiments 15\n. .. . .\n5.2 Significance of Material Damping in the Pile -,\n----------------- 16\nVI SOIL PROPERTIES ------------------------------------------------------------------------ 17\n6.1 General 17\n6.2 Equations to Describe Soil Behavior 17\n6.3 Soil Parameters to Describe Dynamic Soil Resistance During Pile Driving .................... 18\n6.4 Laboratory Tests on Sands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19\n..\n6.5 Static Soil Resistance After Pile Driving (Time Effect) --------..--.T----------------------- 20\n6.6 Field Test in Clay. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20\nVI I USE OF THE WAVE EQUATION TO PREDICT PILE LOAD\nBEARING CAPACITY AT TIME OF DRIVING ----------------------------------------------- 21\n7.1 Introduction ......................... 21\n7.2 Wave Equation Method ----------------------------------------------------------------- 21\n. .\n7.3 Comparison of Prehctions with Field Tests ---------------------- ........................ 24\nVIII PREDICTION OF DRIVING STRE,SSES------------------------------------------------------ 25\n8.1 Introduction -------------------------.---------------------------------- 25\n8.2 Comparison of Smith's Numerical Solution with the Classical Solution -- ---------------------- 25\n. 3 Sdution with Field Measurements\n8.3 Correlation of Smiths 26\n8.4 Effect of Hammer Type and Simulation Method ------------------------------------------ 26\n8.5 Effect of Soil Resistance ----------------------- .................... 27\n8.6 Effects of Cushion Stiffness, Coefficient of Restitution, and Pile Material Damping-------------27\n..\n8.7 Fundamental Driving Stress Considerations ------------------------ 27\n..\n8.8 Summary of Fundamental Driving Stress Considerations 31\nUSE OF THE WAVE EQUATION FOR PARAMETER STUDIES 32\n9.1 Introduction ......................... 32\n. ..\n9.2 Significant Parameters -----------------.------------------------------------ 32\n9.3 Examples of Parameter Studies--------------------- 2 ------------------------------------ 32\nSUMMARY AND CONCLUSIONS. . . . . . . . . . . . . . . . . . . . . . . . . . . . 36\nAPPENDIX A ...................... --------------- 38\nDEVELOPMENT OF ,EQUATIONS FOR IMPACT STRESSES '\nIN A LO,NG, SLENDER, ELASTIC PILE 38\nA1 Introduction ....................... - 38\nI A2 One Dimensional. .Wave Equation 38\nA3 Boundary Conditions 39\n. .\nI A4 Solving the Basic Differential Equation 39\n\n## I A5 Maximum Compressive Stress at the Head of the Pile\n\nA6 Length of the Stress Wave .........................................................\n41\n---- 42\nI\nI APPENDIX B-------------------------------------- ......................................... 43\nWAVE EQUATION COMPUTER PROGRAM UTILIZATION MANUAL 43\nB1 Introduction 43\n. .\nB2 Idealization of Hammers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43\n. .\nB3 Ram Kinetic Energies 44\nB4 Method of Including Coefficient of Restitution in Capblock and Cushion Springs .----------- 45\n. .\nB5 . Idealization of Piles 47\nB6 Explanation of Data Input Sheets 47\nB7 Comments on Data Input - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 50\nAPPENDIX C _------------------------------------- 56\nOS/360 FORTRAN IV PROGRAM STATEMENTS 5.6\nLIST OF REFERENCES ------- ...................... ---- ..................................... 78\n\nLIST OF FIGURES\nFigure Page\n2.1 Method of Representing Pile for Purpose of Calculation (After Smith) ---------------------------- 2\n2.2 Load Deformation Relationships for Internal Springs------------------------ 3\n2.3\n..\nLoad Deformation Charactenstics Assumed for Soil Spring M ---------------- ---------------------- 3\n3.1 Typical\n.-\nForce vs Time Curve for a Diesel Hammer 6\nSteam Hammer-------------------------------\nDiesel Hammer------------------------------- 11\nStress Strain Curve for a Cushion Block .-------- . . 13\n1 .\nDynamic and Static Stress Strain Curves for a Fir Cushion _ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -1 3\nCushion Test Stand ------------------------- 14\nDynamic Stress Strain Curve for an Oak Cushion 14\nDynamic Stress Strain Curve for a Micarta Cushion 15\nStress vs Strain for Garlock Asbestos Cushion - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 15\nTheoretical vs Experimental Solution _----------------------------------------------------------- 16\nTheoretical vs Experimental Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16\nTheoretical vs Experimental Solution 16\nTheoretical vs Experimental Solution ------------ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16\nComparison of Experimental and Theoretical Solutions for Stresses --------- ------------------------ 17\nModel Used by Smith to Describe Soil Resistance on Pile ----------------- ........................ 17\n..\nLoad Deformation Charactenstics of Soil-------- ................................................ 18\nLoad Deformation Properties . . of Ottawa\n. Sand Determined by Triaxial Tests\n(Specimens Nominally 3 in. in Diameter by 6.5 in. High) 18\nc'Jyyvs \"V\" for Ottawa\ncc\nSet up\" or Recovery of Strength After Driving in Cohesive Soil (After Reference 6.7) ---- ------------ 20\nPore Pressure Measurements in Clay Stratum-50 ft Depth --------------------------- ------------ 20\nUltimate Driving Resistance vs Blows per Inch for a n Example Problem ............................ 22\nComparison of Wave Equation Predicted Soil Resistance to Soil Resistance Determined\nby Load Test for Piles Driven in Sands (Data from Table 7.1) .................................... 22\nComparison of Wave Equation Predicted Soil Resistance to Soil Resistance Determined\nby Load Tests for Piles Driven in Clay (Data from Table 7.2) ----------------7-------------------- 23\nComparison of Wave Equation Predicted Soil Resistance to Soil Resistance Determined\n. .\nby Load Tests for Piles Driven in Both Sand and Clay 24\nSummary of Piles Tested to Failure in Sands (From Reference 7.2) 24\nWave Equation Ultimate Resistance vs Test Load Failure (From Reference 7.2) ..................... 25\nMaximum Tensile Stress Along a Pile 25\nMaximum Compressive Stress Along a Pile 26\n. .\nStress in Pile Head vs Time for Test Pile 26\nStress at Mid-length of Pile vs Time for Test Pile - - - - - - - - - - - - - - - - - - - - - - - - - - - -27 -------\n\nIdealized Stress Wave Produced When Ram Strikes Cushion at Head of Concrete Pile. 29\nReflection of Stress Wave at Point of a Long Pile 1-1-------------- 30\nReflection of Stress Wave at Point of a Short Pile -----------------------2- l---- 30\nEffect of Ratio of Stress Wave Length on Maximum Tensile Stress for Pile with Point Free\nEffect of Cushion Stiffness, Ram Weight, and Driving Energy on Sti-esses---------------- 33\nEffect of Cushion Stiffness, Ram Weight, and Driving Energy on Permanent Set 34\nComputer Analysis\n. . of Pile Hammer Effectiveness. . in Overcoming Soil Resistance,\nRu, When Driving a Pile Under Varying Conditions 35\nEvaluation of Vulcan 020 Hammer (60,000 ft-lb) for Driving a Pile to Develop Ultimate\nCapacity of 2000 Tons ---- 35\nBlows/In. vs RU (Total) for Arkansas Load Test Pile 4 35\n. .\nLong Slender Elastic Pile ---------------------------7------------------------------------------ 38\nRam, Cushion, Pile --- 39\nCase I.-Ram, Capblock, and Pile Cap 43\n.\nCase 11.-Ram, Capblock, Pile Cap, and Cushion 44\nCase 111.-Ram, Anvil, Capblock, and Pile Cap 44\n. .. .. . .\nDefinition of Coefficient of Restitution 46\n. .\nPile Idealization .............................. 47\nExample Problem_---------------------------- ------------------------------------------------5l\nNormal Output (Option 15=1) for Prob. 1 53\nEffect of Varying Cushion Stiffness 54\nSummary Output for RU (Total) vs Blows/In. (Option 11=1) for Prob. 1 and 2 54\nNormal Output for Single RU (Total) (Option 11=2) for Prob. 3 _---------------------------------55\nDetailed Output for Single RU (Total) (Option 15=2) for Prob. .4_------------_------------------ 5 5\n\nLIST OF TABLES\nTable Page\n3.1\n. . ..\nSummary of Hammer Properties in Operating Characteristics _--------------------------------------- 8\n3.2 Effect of Cushion Stiffness on ENTHRU 9\n3.3 Effect of Cushion Stiffness on FMAX 9\n3.4 Effect of Cushion Stiffness on LIMSET 9\n3.5 Effect of Removing Load Cell on ENTHRU, LIMSET, and Permanent Set of Pile ---------------------- 10\n3.6 Effect of Coefficient of Restitution on ENTHRU (Maximum Point Displacement) ----_--------------- 10\n.. . .\nEffect of Coefficient of Restitution on ENTHRU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10\n3.7\n3.8 Effect of Breaking Ram Into Segments When Ram Strikes a Cushion or Capblock .------------------- 11\n3.9 Effect of Breaking Ram Into Segments When Ram Strikes a Steel Anvil ............................ 12\n4.1 Typical Secant Moduli . of. Elasticity ( E ) and Coefficients of Restitution (e)\nof Various Pile Cushioning Materials ---- ............................................. 14\nJ (point)\nErrors Caused by Assuming J(point) = 0.1 and J1(side) =\n3\nfor Sand-Supported Piles Only------------------ ............................................. 22\nErrors Caused by Assuming J(point) = 0.3 and J1(side) = -\nJ (point)\n7.2 3\nfor Clay (for Clay-Supported Piles Only) 23\n7.3 Errors Caused by Assuming a Combined J(point) = 0.1 for Sand and J(point) = 0.3\nfor Clay Using Equation 7.1 (for Piles Supported by Both Sand and Clay) 24\n8.1\n..\nVariation of Driving Stress With Ram Weight and Velocity 28\n8.2 Variation of Driving Stress With Ram Weight and Ram Energy 29\nB.1 Drop Hammers and Steam Hammers ------------ -................................................ 45\nB.2 Diesel Hammers-------------------------------------------------------------------------- 46\nPile Driving Analysis -State of the Art\nCHAPTER I\nIntroduction\nThe tremendous increase in the use of piles in both gation of the influence of various parameters on the\nlandbased and offshore foundation structures and the ap- behavior of piles during driving and to present the re-\npearance of new pile driving methods have created great sults in the form of charts, diagrams or tables for direct\nengineering interest in finding more reliable methods application by office design engineers.\nfor the analysis and design of piles. Ever since\nIsaac published his paper, \"Reinforced Concrete Pile 4. T o present recommendations concerning good\nFormula,\" in 1931,l.l):' it has been recognized that the driving practices which would prevent cracking and\nbehavior of piling during driving does not follow the spalling of prestressed concrete piles during driving.\nsimple Newtonian impact as assumed by many simplified 5. To determine the dynamic load-deformation\npile driving formulas, but rather is governed by the one properties of various pile cushion materials which had\ndimensional wave equation. Unfortunately, an exact tacitly been assumed linear.\nmathematical solution to the wave equation was not\npossible for most practical pile driving problems. 6. To determine the dynamic load-deformation\nproperties of soils required by the wave equation\nIn 1950, E. A. L. Smith12 developed a tractable analysis.\nsolution to the wave equation which could be used to\nsolve extremely complex pile driving problems. The 7. To generalize Smith's original method of analy-\nsolution was based on a discrete element idealization of sis and to develop the full potential of the solution by\nthe actual hammer-pile-soil system coupled with the use using the most recent and accurate parameter values\nof a high speed digital computer. In a paper published determined experimentally.\nin 1960, he dealt exclusively with the application of 8. To illustrate the significance of the parameters\nwave theory to the investigation of the dynamic behavior involved, such as the stiffness and coefficient of retitu-\nof Piling during driving. From that time to the present tion of the cushion, ram velocity, material damping in\nthe authors have engaged in research dealing with wave the pile, etc., and to determine the quantitative effect\nequation analysis. The major objectives of these studies of these parameters where possible.\nwere as follows:\n9. To study and if possible evaluate the actual\n1. To develop a computer program based upon a energy output for various pile driving hammers, the\nprocedure developed by Smith to provide the en,'Wineer magnitudes of which were subject to much 'disagree-\nwith a mathematical tool with which to investigate the ment.\nbehavior of a pile during driving.\n10. To develop the computer solution for the wave\n2. To conduct field tests to obtain experimental equation so that it may be used to estimate the resistance\ndata with which to correlate the theoretical solution. to penetration of piling at the time of driving from the\n3. T o make an orderly theoretical computer investi- driving records.\n\n*Numerical superscripts refer t o corresponding items in 11. To develop a comprehensive users manual for\nthe References. the final computer program to enable its use by others.\n\nCHAPTER I1\nPile Driving Analysis\n2.1 General In 1851, Sanders (Army Corps of Engineers) pro-\nposed the first dynamic pile driving formula by equating\nThe rapidly increasing use of pile foundations and the total energy of the ram at the instant of impact to the\nthe appearance of new pile driving techniques have work done in forcing down the pile, that is, the product\ncaused great interest among engineers in finding more of the weight of the ram and the stroke was assumed\nreliable methods of pile analysis and design. As noted equal to the product of the ultimate soil resistance by\nby D ~ n h a m , \"\"A\n~ pile driving formula is an attempt to the distance through which the pile moved. Sanders\nevaluate the resistance of a pile to the dynamic forces applied a safety factor of 8 to this ultimate soil resist-\napplied upon it during the driving and to estimate from ance to determine an assumed safe load capacity for the\nthis the statical longitudinal load that the pile can sup- pile. Since that time, a multitude of formulas have been\nport safely as a part of the permanent substructure.\" proposed, some of which are semirational, others being\nPAGE ONE\nstricdy empirical. Many of the formulas proposed at-\ntempt to account for various impact losses through the\ncushion, capblock, pile, and soil.\nWhen restricted to a particular soil, pile, and driv-\ning condition for which correlation factors were derived,\ndynamic formulas are often able to predict ultimate\nbearing capacities which agree with observed test loads.\nHowever, since several hundred pile driving formulas\nhave been proposed there is usually the problem of\nchoosing an appropriate or suitable ~ n e . ~Also . ~ dis-\n-\ntressing is the fact that in manv cases no dvnamic for-\nmula yields acceptable results; for example, long heavy\npiles generally show much greater ultimate loads than\npredicted by pile driving equation^.^.^ This has become\nincreasingly significant since prestressed concrete piles\n172 ft long and 54 in. in diameter have been successfully\nand more and more large diameter steel piles SIDE\nseveral hundred feet long are being used in offshore FRICTIONAL\ndatforms. Numerous field tests have shown that the\nI~\n~ -\nRESISTANCE\nuse of pile driving formulas may well lead to a foun-\ndation design ranging from wasteful to d a n g e r ~ u s . ~ . ~\nDriving stresses are also of major importance in\nthe design of piles, yet compressive stresses are com-\nmonly determined simply by dividing the ultimate driv- POINT\nRESISTANCE\ning resistance by the cross-sectional area of the pile.2.7v2.8\nFurthermore, conventional pile driving analyses are un-\nable to calculate tensile stresses, which are of the utmost ACTUAL AS REPRESENTED\nimportance in the driving of precast or prestressed con- (a 1 (b 1\ncrete piles. This method of stress analysis complete'y\noverlooks the true nature of the problem and computed\nstresses almost never agree with experimeltal val- Figure 2.1. Method of represenring pile for purpose o f\nu e ~ . ~ . ~ ~ ~ . V efailures\nn s i l e of piles have becn noted analysis (after Smith).\non numerous '.ll and the absence of a\nreliable method of stress analysis has proven to be a\nserious problem.\nbased on dividing the distributed mass of the pile into\nAlthough most engineers today realize that pile a number of concentrated weights W ( l ) through\ndriving formulas have serious limitations and cannot be W ( p ) , which are connected by weightless springs K ( 1 )\ndepended upon to give accurate results, they are still through K ( p - l ) , with the addition of soil resistance\nused for lack of an adequate substitute. For further acting on the masses, as illustrated in Figure 2 . l ( b ) .\ndiscussion of pile formulas in general, the reader is Time is also divided into small increments.\nreferred to the work of C h e l l i ~ . ~ . ~\nSmith's proposed solution involved the idealization\nIsaacs2.l is thonght to have first pointed out the of the actual continuous pile shown in Figure 2 . l ( a ) ,\noccurrence of wave action in piling during driving. He as a zeries of weights and springs as shown in Figure\nproposed a solution to the wave equation assuming that 2 . l ( b ) . For the idealized system he set up a series of\nthe point of the pile was fixed and that side resistance equations of motion in the form of finite difference equa-\nwas absent. These assumptions were so restrictive that tions which were easily solved using high-speed digital\nthe solution was probably never used in practice. Cum- computers. Smith extended his original method of analy-\nmings\"1° in an earlier writing noted that although the sis to include various nonlineal parameters such as elasto-\npile driving formulas were based on numerous erroneous plastic soil resistance including velocity damping and\nassumptions and that only the wave equation could be others.\nexpected to yield accurate results for all driving con-\nditions, he also pointed out that such solutions involved Figure 2.1 illustrates the idealization of the pile\n(6\nlong and complicated mathematical expressions so system suggested by Smith. In general, the system is\nthat their use for practical probjems would involve considered to be composed of (see Figure 2.1 ( a ) ) :\nlaborous, numerical calculations.\" In fact, with the\nadvent of a multitude of different type driving hammers 1. A ram, to which an initial velocity is imparted\nand driving conditions, an exact solution to the wave by the pile driver;\nequation was not known. 2. A capblock (cushioning material) ;\n3. A pile cap ;\n2.2 Smith's Numerical Solution of the\n4. A cushion block (cushioning material) ;\nWave Equation\n5. A pile; and\nIn 1950, Smith2.2proposed a more realistic solution\nto the problem of longitudinal impact. This solution is 6. The supporting medium, or soil.\nPAGE TWO\nIn Figure 2.1 (b) are shown the idealizations for the\nvarious components of the actual pile. The ram, cap- RCm3\nblock, ~ i l ecap, cushion block, and pile are pictured as LOAD\n1 appropriate discrete weights and springs. The frictional\n!\nI\nsoil resistance on the side of the pile is represented by\na series of side springs; the point resistance is accounted\nl for by a single spring at the point of the pile. The char.\nacteristics of these various components will be discussed\nin greater detail later in this report.\n0\nActual situations may deviate from that illustrated\nin Figure 2.1. For example, a cushion block may not\nbe used or an anvil may be placed be~weenthe ram and\ncapblock. However, such cases are readily accommo-\ndated.\nInternal Springs. The ram, capblock, pile cap, and E - 0\ncushion block may in general be considered to consist\nof \"internal\" springs, although in the representation of\nFigure 2.l(b) the ram and the pile cap are assumed\nrigid ( a reasonable assumption for many practical\ncases). Figure 2.3. Load-deformation characterisrics assumed\nfor soil spring m.\nFigures 2.2(a) and 2.2 ( b ) suggest different possi-\nbilities for representing the load-deformation character-\nistics of the internal springs. In Figure 2.2 ( a ) , ,the\nmaterial is considered to experience no internal damping. tion characteristics assumed for the soil in Smith's pro-\ncedure, exclusive of damping effecis. The path OABC-\nIn Figure 2.2(b) the material is assumed to have inter-\nE x t e r d Springs. The resistance to dynamic load- and the lozding and unloading path would be along\ning afforded by the soil in shear along the outer surface OABCF.\nof the pile and in bearing at the point of the pile is\nextremely complex. Figure 2.3 shows the load-deforma- It is seen that the characteristics of Figure 2.3 are\ndefined essentially by the quantities \"Q\" and \"Ru.\"\n\"Q\" is termed the soil quake and represents the maxi-\nmum deformation which may occur elastically. \"Ru\" is\nthe ultimate ground resisiance, or the load at which the\nsoil spring behave; purely plastically.\nA load-deformation diagram of the type in Figure\n2.3 may be established separately for each spring. Thus,\nK'(m) equals Ru(m) divided by Q ( m ) , where K'(m)\nis the spring constant (during elastic deformation) for\nexternal spring m.\nBmic Equations. Equations (2.3) through (2.7)\nwere developed by Smith.2.2\n\n## (0) NO INTERNAL DAMPING\n\nqk yoRMATloN\n\nwhere\n( ) = functional designation;\n( b ) INTERNAL DAMPING PRESENT m = element number;\nt = number of time interval;\nAt = size of time interval (sec) ;\nFigure 2.2. Load-deformation relationships for internal C(m,t) = compression of internal spring m in\nsprings. time interval t (in.) ;\nPAGE T H R E E\nD(m,t) = displacement of element m in time The computations proceed as foliows:\ninterval t (in.) ;\n1. The initial velocity of the ram is determined\nD1(m,t) = plastic displacement of external soil spring from the properties of the pile driver.: Other time-\nm in time interval t (in.) ; dependent quantities are initialized at zero or to satisfy\nstatic equilibrium conditions.\nF(m,t) = force in internal spring m in time\ninterval t(1b) ; 2. Displacements D ( m , l ) are calculated by Equa-\ntion (2.3). It is to be noted that V(1,O) is the initial\ng = acceleration due to gravity (ft/sec2) ; velocity of the ram.\nJ ( m ) = damping constant of soil at element m 3. Compressions C(m,l) are calculated by Equa-\n(sec/ft) ; tion (2.4).\nK ( m ) = spring constant associated with internal 4. Internal spring forces F ( m , l ) are calculated by\nspring m (lb/in.) ; Equation (2.5) or Equation (2.8) as appropriate.\nK'(m) = spring constant associated with external 5. External spring forces R ( m , l ) are calculated\nsoil spring m (lb/in.) ; by Equation (2.6).\nR(m,t) = force exerted by external spring m on 6. Velocities V(m,l) are calculated by Equation\nelement m in time interval t (lb) ; (2.7).\n7. The cycle is repeated for successive time inter-\nV(m,t) = velocity of element m in time -interval t vals.\n(ft/sec) ; and\nIn Equation (2.6), the plastic deformation Dr(m,t):\nW ( m ) = weight of element m (lb). for a given external spring follows Figure (2.3) and\nThis notation differs slightly from that used by may be determined by special routines. For example,\nSmith. Also, Smith restricts the soil damping constant when D(m,t) is less than Q(m) , D' (m,t) is zero; when\nJ to two values, one for the point of the pile in bearing D (m,t) is greater than Q(m) along line AB (see Figure\nand one for the side of the pile in friction. While the 2.3), D' (m,t) is equal to D (m,t) - Q (m) .\npresent knowledge of damping behavior of soils perhaps\ndoes not justify greater refinement, it is reasonable to Smith notes that Equation (2.6) produces no damp-\nuse this notation as a function of m for the sake of ing when D(m,t) - D1(m,t) becomes zero. He sug-\ngenerality. gests an alternate equation to be used after D(m,t) first\nbecomes equal to Q(m) :\nThe use of a spring constant K ( m ) implies a load-\ndeformation behavior of the sort shown in Figure 2.2 ( a ) .\nFor this situation, K ( m ) is the slope of the straight line.\nSmith develops special relationships to account for in-\nternal damping in the capblock and the cushion block. Care must be used to satisfy conditions at the head\nHe obtains instead of Equation 2.5 the following equa- and point of the pile. Consider Equation (2.5). When\nm = p, where p is number of the last element of the\ntion :\npile, K ( p ) must be set equal to zero since there is no\nE- F(p,t) force (see Figure 1.1). Beneath the point of the\npile, the soil spring must be prevented from exerting\ntension on the pile point. In applying Equation (2.7)\nto the ram (m = l ) , one should set F(0,t) equal to zero.\nFor the idealization of Figure 2.1, it is apparent\nthat the spring associated with K ( 2 ) represents both the\ncushion block and the top element of the pile. Its spring\n2 rate may be obtained by the following equation:\nwhere\ne ( m ) = coefficient of restitution of internal spring\nm; and\nA more complete discussion of digital computer\n,, = temporary maximum value of C (m,t) .\nC (m,t) , programming details and recommended values for vari-\nWith reference to Figure 2.1, Equation (2.8) would be ous physical quantities are given. in the Appendices.\napplicable in the calculation of the forces in internal From the point of view of basic mechanics, the wave\nsprings m = 1 and m = 2. The load-deformation equation solution is a method of analysis well founded\nrelationship characterized by Equation (2.8) is illustrated physically and mathematically.\nby the path OABCDEO in Figure 2.2(b). For a pile\ncap or a cushion block, no tensile forces can exist; con- 2.3 Critical Time Interval\nsequently, only this part of the diagram applies. Inter-\nestablished by control of the quantity C(m,t),,, in related to the size of the time increment At. H e i ~ i n g , ~ . ~ ~\nEquation (2.8). The slopes of lines AB, BC, and DE in his discussion of the equation of motion for free\ndepend upon the coefficient of restitution e(m). longitudinal vibrations in a continuous elastic bar, points\nPAGE FOUR\nout that the discrete-element solution is an exact solution thehsystem. Strictly speaking, these initial values should\nof the partial differential equation when be those in effect as a result of the previous blow. How-\never, not only would it be awkward to \"keep books\" on\nthe pile throughout the driving so as to identify the\ninitial conditions for successive blows, but it is highly\nquestionable that this refinement is justified in light of\nwhere AL is the se,gment length. Smith 3.\"raws a simi- other uncertainties which exist.\nlar conclusion and has expressed the critical time inter-\nval as follows: A relatively simple scheme has been developed as\na means of getting the gravity effect into the compu-\ntations.\nSmith suggests that the external (soil) springs be\nassumed to resist the static weight of the system accord-\ning to the relationship\n\n## If a time increment larger than that given by Equa- where\n\ntion 2.11 is used, the discrete-element solution will di- W(tota1) = total. static weight resisted by soil\nverge and no valid results can be obtained. As pointed (lb) ; and -\nout by Smith, in this case the numerical calculation of\nthe discrete-element stress wave, does not progress as Ru(tota1) = total ultimate ground resistance (lb) .\nrapidly as the actual stress -wave. Consequently, the\nvalue of At given by Equation (2.11) is called the \"criti- The quantity W(tota1) is found by\ncal\" value.\nHeising2.13 has also pointed out that when W(tota1) = W ( b ) + F(c) + I: W(m) (2.13)\nm=2\nwhere\nW(b) = weight of body of hammer, excluding\nram (Ib) ; and\nis used in a discrete-element solution, a less accurate = force exerted by compressed gases, as\nF(c)\nsolution is obtained for the continuous bar. As At be- under the ram of a diesel hammer (lb).\ncomes progressively smaller, the solution approaches the\nactual behavior of the discrete-element system (se,gnent The internal forces which initially exist in the pile\nlengths equal to AL) used to simulate the pile. may now be obtained:\nThis in general leads to a less accurate solution for\nthe longitudinal vibrations of a slender continuous bar.\nIf, however, tlie 'discrete-element system were divided and in general,\ninto a large number of segments, the behavior of this\nsimulated pile would be essentially the same as that of * .>\n\nthe slender continuous bar irrespective of how small At In the absence of compressed gases and hammer weight\nbecomes, provided resting on the pile system, the right-hand side of Equa-\ntion (2.14) is zero.\nAL\n- The amount that each internal spring m is com-\n\nELAt > O\nThis means that if the pile is divided into only a few\npressed may now be expressed\n\n## By working upward from the point, one finds displace-\n\nsegments, the accuracy of the solution will be more sensi- ments from ;,. ' ,-\ntive to the choice of At than if it is divided into many\nsegments. For practical problems, a choice of At equal\nto about one-half the \"critical\" value appears suitable\nsince inelastic springs and materials of different densi-\nties and elastic moduli are usually involved. For the inclusion of gravity, Equation (2.7) should be\nmodified as follows:\n2.4 Effect of Gravity\nThe procedure as originally presented by Smith\ndid not account for the static weight of the pile. In\nother words, at t = 0 all springs, both internal and\nexternal, exert zero force. Stated symbolically, In order that the initial conditions of the external\nsprings be compatible with the assumed initial forces\nR(m,O) and initial displacements D(m,O), plastic dis-\nIf the Gffect of gravity is to be included, these forces placements D1(m,O) should be set equal to D (m,O) -\nmust be given initial values to produce equilibrium of R(m,O) /K'(m).\nCHAPTER 111\n\n## Pile Driving Hammers\n\n3.1 Energy Output of Impact Hammer explosive pressure also does some useful work on the\npile given by:\nOne of the most significant parameters involved in\npile driving is the energy output of the hammer. This E, = 1F ds (3.1)\nenergy output must be known or assumed before the where F = the explosive force, and\nwave equation or dynamic formula can be applied. Al-\nthough most manufacturers of pile driving equipment ds = the infinitesimal distance through which the\nfurnish maximum energy ratings for their hammers, force acts.\nthese are usually downgraded by foundation experts for Since the total energy output is the sum of the\nvarious reasons. A number of conditions such as Door kinetic energy at impact plus the work done by the\nhammer condition, lack of lubrication, and wear are explosive force.\nknown to seriously reduce ehergy output of a hammer.\nIn addition, the energy output of many hammers can\nbe controlled by regulating the steam pressure or quan-\ntity of diesel fuel supplied to the hammer. Therefore, where Et,t,l = the total energy output per blow,\na method was needed to determine a simple and uniform El, = the kinetic energy of the ram at the\nmethod which would accurately predict the energy output instant of impact,\nof a variety of hammers in general use. Towards this\npurpose, the information generated by the Michigan and E, = the diesel explosive energy which does\nState Highway Commission in 1965 and presented in usejd work on the pile.\ntheir paper entitled \"A Performance Investigation of It has been noted that after the ram passes the\nPile Driving Hammers and Piles\" by the Office of Test- exhaust ports, the energy required to compress the air-\ning and Research, was used. These data were analyzed fuel mixture is nearly identical to that gained by the\nby the wave equation to determine the pile driver energy remaining fall (d) of the Therefore, the velocity\nwhich would have been required to produce the reported of the ram at the exhaust ports is essentially the same\nbeha~ior.~.~ as at impact, and the kinetic energy at impact can be\nclogely approximated by:\n3.2'~eterminationof Hammer Energy Output\nDiesel Hammers. At present the manufacturers of where WR = the ram weight,\ndiesel hammers arrive at the energy delivered per blow h = the total observed stroke of the ram, and\nby two different methods. One manufacturer feels that\n\"Since the amount of (diesel) fuel injected per blow is d = the distance the ram moves after closing\nconstant, the compression pressure is constant, and the the exhaust ports and impacts with the\ntemperature constant, the energy delivered to the piling anvil.\nis also ~ o n s t a n t . \" ~ .The\n~ energy output per blow is thus\ncomputed as the kinetic energy of the falling ram plus\nthe explosive energy found by thermodynamics. Other\nmanufacturers simply give the energy output per blow\nas the product of the weight of the ram-piston W, and\nthe length of the stroke h, or the equivalent stroke in the\ncase of closed-end diesel hammers.\nThe energy ratings given by these two methods\ndiffer considerably since the ram stroke h varies greatly\nthereby causing much controversy as to which, if either,\nmethod is correct and what energy output should be used\nin dynamic pile analysis.\nIn conventional single acting steam hammers the\nsteam pressure or energy is used to raise the ram for\nW\neach blow. The magnitude of the steam force is too\nsmall to force the pile downward and consequently it\nworks only on the ram to restore its potential energy,\nWE x h, for the next blow. In a diesel hammer, on.the\nother hand, the diesel explosive pressure used to raise\n\"I)\nLL\njf IDEALIZED DIESEL EXPLOSIVE FORCE\nON THE ANVIL AND RAM\n\nthe ram is, for, a short time at least, relatively large (see\nFigure 3.1).\nWhile this explosive force works on the ram to Figure 3.1. Typical jorce us time curve for a diesel\nrestore its potential energy- WR x h, the initially large hummer.\nPAGE SIX\nThe total amount of explosive energy Eectotnl)is This can be reduced in terms of Equation (3.7) by\ndependent upon the amount of diesel fuel injected, com- using an equivalent stroke, he which will give the same\npression pressure, and temperature; and therefore, may energy output as Equation (3.10).\nvary somewhat.\nThus :\nUnfortunately, the wave equation must be used in Eta,, = WR he (3.11)\neach case to determine the exact magnitude of Ee since\ni t not only depends on the hammer characteristics, but Setting Equations (3.10) and (3.11) equal yields\nalso on the characteristics of the anvil, helmet, cushion,\npile, and soil resistance. However, values of E, deter-\nmined by the wave equation for several typical pile prob-\nlems indicates that it is usually small in proportion to the\ntotal explosive energy output per blow, and furthermore,\nthat it is on the same order of magnitude as WR X d.\nThus, Equation (3.1) can be simplified by assuming:\n\n## or solving for the equivalent stroke:\n\nSubstituting Equations (3.3) and (3.4) into Equation\n(3.1) gives:\nEtotal = E, +Ee = WR ( h - d ) +\nWR d (3.5)\nhe=h l + -P\nPrated\nX\nWR\n( (3.12)\n\nso that :\nEtob1 = WR h (3.6) Conclusions. The preceding discussion has shown\nthat it is possible to determine reasonable values of ham-\nThe results given by this equation were compared with mer energy output simply by taking the product of the\nexperimental values and the average efficiency was found ram weight and its observed or equivalent stroke, and\nt o be 100%. applying an efficiency factor. This method of energy\nS t e m Hammers. Using the same equation for com- rating can be applied to all types of impact pile drivers\nparison with experimental values indicated an efficiency with reasonable accuracy.\nrating of 60% for the single-acting steam hammers, and\n87% for the double-acting hammer, based on an energy A brief summary of this simple procedure for ar-\noutput given by: riving at hammer energies and initial ram velocities is\nas follows:\nEta,, = WR h (3.7)\nOpen End Diesel Hammers\nIn order to determine an equivalent ram stroke for\nthe double-acting hammers, the internal steam pressure E WR h (e)\nabove the ram which is forcing it down must be taken VR = V 2g (h-d) (e)\ninto consideration. The manufacturers of such hammers where WR = ram weight\nstate that'the maximum steam pressure or force should\nnot exceed the weight of the housing or casing, or the VR = initial ram velocity\nhousing may be lifted off the pile. Thus the maximum h = observed total stroke of ram\ndownward force on the ram is limited to the total weight = Distance from anvil to exhaust ports\nd\nof the ram and housing.\ne = efficiency of open end diesel hammers,\nSince these forces both act on the ram as it falls approximately 100% when energy is\nthrough the actual ram stroke h, they add kinetic energy computed by this method.\nto the ram, which is given by:\nClosed End Diesel Ha,mmers\nE\" = WR he (e)\nwhere WR = the ram weight,\nVR = V 2g (he-d) (el\nFR a steam force not exceeding the weight\nof the hammer housing, and where WR = ram weight\nh = the observed or actual ram stroke. VR = initial ram velocity\nSince the actual steam pressure is not always applied at he = equivalent stroke derived from bounce\nthe rated maximum, the actual steam force can be chamber pressure gage\nexpressed as : d = distance from anvil to exhaust ports\ne = efficiency of closed end diesel hammers,\napproximately 100% when energy is\ncomputed by this method.\nwhere WE = the hammer housing weight,\np = the operating pressure, and Double-Acting Steam Hammers\nPrated= the maximum rated steam pressure. E = WR he (e)\n\n## I The total energy output is then given by v = V 2g he (el\n\n*Note: For the Link Belt Hammers, this energy can be\nread directly from the manufacturer's chart using bounce\nchamber pressure gage.\nPAGE SEVEN\nwhere WR = ram weight 3.3 Significance of Driving Accessories\nhe = equivalent ram stroke In 1965 the Michigan State Highway Commission\ncompleted an extensive research program designed to\nobtain a better understanding of the complex problem\nof pile driving. Though a number of specific objectives\nwere given, one was of primary importance. As noted\nh = actual or physical ram stroke by H o u ~ e l , ~\n\"Hammer\n.~ energy actually delivered to the\n- pile, as compared with the manufacturer's rated energy,\np - operating steam pressure was the focal point of a major portion of this investi-\nPrated = maximum steam pressure recommended gation of pile-driving hammers.\" In other words, they\nby manufacturer. hoped to determine the energy delivered to the pile and\nto compare these values with the manufacturer's ratings.\nWH = weight of hammer housing\ne = efficiency of double-acting steam ham- The energy transmitted to the pile was termed\nmers, approximately 85 % by this \"ENTHRU\" by the investigators and was determined _\nmethod. by the summation\nENTHRU = XFAS\nSingle-Achg Steam Hammers\nE = WR h (e) Where F, the average force on the top of the pile during\na short interval of time, was measured by a specially\nVR = d 2g h (e) designed load cell, and AS, the incremental movement\nwhere WR = ram weight of the head of the pile during this time interval, was\nfound using displacement transducers and/or reduced\nh = ram stroke from accelerometer data. It should be pointed out that\ne = efficiencv of single-acting\nu u\nsteam ham- ENTHRU is not the total energy output of the hammer\nmers, normally recommended around blow, but only a measure of that portion of the energy\n75 % to 85 %. In a study of the Michi- delivered below the load-cell assemblv.\ngan data, a figure of 60% was found.\nThe writers feel the 60% figure is un- Many variables ,influence the value of ENTHRU.\nusually low and would not recommend As was noted in the Michigan report: \"Hammer type and\nit as a typical value. operating conditions; pile typf, mass, rigidity, and\nlength: and the t v ~ eand condit~onof cav blocks were\nA summary of the properties and operating character- allvfa&ors that &ect ENTHRU, but w&n, how, and\nistics of various hammers is given in Table 3.1. how much could not be ascertained with any degree of\n\n## TABLE 3.1. SUMMARY OF HAMMER PROPERTIES AND OPERATING CHARACTERISTICS\n\nHammer Hammer Maximum Ram Hammer Anvil Maxi- d Rated Maximum Cap\nManu- Type Rated Weight Housing Weight mum or (ft) Steam Explosive Block\nfacturer Energy (lb) Weight (lb) Equiva- Pres- Pressure Normally\n(ft lb) (lb) lent sure (lb) Specified\nStroke (psi)\n(ft)\nVulcan #1 15,000 5,000 4,700\n014 42,000 14,000 13,500\n50C 15,100 5,000 6,800\n80C 24.450 8.000 9.885\n\nLink Belt 312 18,000 3,857 1188 4.66 0.50 98,000 5 Micarta\ndisks\n1\" x 10%\"\ndia.\n520 30,000 5,070 1179 5.93 0.83 98,000\nMKT Corp DE20 16,000 2,000 640 8.00 0.92 46,300 nylon disk\n2\" x 9\"\ndia.\nDE30 22,400 2,800 775 8.00 1.04 98,000 nylon disk\n2\" x 19\"\ndia.\nDE40 32,000 4,000 ' 1350 8.00 1.17 138,000 nylon disk -.\n2\" x 24\"\ndia.\nDelmag D-12 22,500 2,750 754 8.19 1.25 93,700 15\" x 15\"\nX 5\"\nGerman\nOak\n158,700 15\" x 15\"\nx 5\"\nGerman\nOak\n\nPAGE EIGHT\n\nh\ncertainty.\" However, the wave equation' can account TABLE 3.3. EFFECT OF CUSHION STIFFNESS ON\nfor each of these factors so that their effects can be THE FORCE MEASURED AT THE LOAD\ndetermined. CELL (FMAX) .\nThe maximum displacement of the head of the pile FMAX (kip)\nwas also reported and was designated LIMSET. Oscillo- Ram Cushion Stiffness (kip/in.)\ngraphic records of force vs time measured in the load Velocity RUT\n(ft/sec) (kip) 540 1080 2700 27,000\ncell were also reported. Since force was measured only\nat the load cell, the single maximum observed values for\neach case was called FMAX.\nThe wave equation can be used to determine (among\nother quantities) the displacement D(m,t) of mass \"m\"\nat time \"t\", as well as the force F(m,t) acting on any\nmass \"m\" at time \"t.\" Thus the equation for ENTHRU\nat any point in the system can be determined by simply\nletting the computer calculate the equation previously\nmentioned :\nENTHRU = ZFAS From Table 3.2, it can be seen that ENTHRU does\nor in terms of the wave equation: not always increase with increasing cushion stiffness,\nand furthermore, the maximum increase in ENTHRU\nnoted h e r e is relatively small-only about 10%.\nWhen different cushions are used, the coefficient of\nrestitution will probably change. Since the coefficient\nof restitution of the cushion may affect ENTHRU, a\nnumber of cases were solved with \"e\" ranging from\nwhere ENTHRU (m) = the work done on any mass 0.2 to 0.6. As shown in Tables 3.6 and 3.7, an increase\n(m + 11, in \"e\" from 0.2 to 0.6 normally increases ENTHRU from\n18 to 20%, while increasing the permanent set from 6\nm = the mass number, . and to 11%. Thus, for the case shown; the coefficient of\nt = the time interval number. restitution of the cushion has a greater influence on rate\nof penetration and ENTHRU than does its stiffness.\nENTHRU is greatly influenced by several parame- This same effect was noted in the other solutions, and\nters, especially the type, condition, and coefficient of the cases shown in Tables 3.6 and 3.7 are typical of the\nrestitution of the cushion, and the weight of extra driv- results found in other cases.\ning caps. As can be seen from Table 3.3, any increase in\nIt has been shown,\".\" that the coefficient of restitu- cushion stiffness also increases the driving stress. Thus,\ntion alone can change ENTHRU by 20%, simply by according to the wave equation, increasing the cushion\nchanging e from 0.2 to 0.6. Nor is this variation in e stiffness to increase the rate of penetration (for example\nunlikely since cushion condition varied from new to by not replacing the cushion until it has been beaten to\n\"badly burnt\" and \"chips added.\" a fraction of its original height or by omitting the cush-\nion entirely) is both inefficient and poor practice be-\nThe wave equation was therefore used to analyze cause of the high stresses induced in the pile. It would\ncertain Michigan problems to determine the influence be better to use a cushion having a high coefficient of\nof cushion stiffness, e, additional driving cap weights, restitution and a low cushion stiffness in order to in-\ndriving resistance encountered, etc. crease ENTHRU and to limit the driving stress.\nTable 3.5 shows how ENTHRU and SET increases Unfortunately, the tremendous variety of driving\nwhen the load cell assembly is removed from Michigan accessories precludes general conclusions to be drawn\npiles.\n\n## TABLE 3.4. EFFECT OF CUSHION STIFFNESS ON\n\nTABLE 3.2. EFFECT OF CUSHION STIFFNESS ON THE MAXIMUM DISPLACEMENT OF THE HEAD OF\nENERGY TRANSMITTED TO THE PILE (ENTHRU) THE PILE (LIMSET)\nENTHRU ( k i ~ft) LIMSET (in.)\nRam Cushion Stiffness (kip/in.) Ram Cushion Stiffness (kip/in.)\nVelocity Velocity RUT\n(ft/sec) \\$?: 540 1080 2700 27,000 (ft/sec) (kip) 540 1080 2700 27,000\n\n## 30 1.09 1.08 1.08 1.13\n\n8 90 0.44 0.44 0.45 0.45\n\nPAGE N I N E\nTABLE 3.5 EFFECT OF REMOVING LOAD CELL ON ENTHRU, LIMSET, AND PERMANENT SET OF PILE\nENTHRU LIMSET PERMANENT SET\n(kip f t ) (in.) (in.)\nRam With Without With Without With Without\nC a ~ e ~ , ~ (ft/sec) Cell Cell Cell Cell Cell Cell\n\nfrom wave equation analyses in all but the most general which the force tapers to zero. As shown in Figure 3.1,\nof terms. the force between the ram and anvil reaches some maxi-\nmum due to the steel on steel impact, afterwards the\nAlthough the effect of driving accessories is quite force decreases to the minimum diesel explosive force\nvariable, it was generally noted that the inclusion of\non the anvil. This force is maintained for 10 rnillisec-\nadditional elements between the driving hammer and the onds, thereafter decreasing to zero at 12.5 milliseconds.\npile and/or the inclusion of heavier driving accessories' The properties of this curve, including values of the\nconsistently decreased both the energy transmitted to the minimum explosive force and time over which this force\nhead of the pile and the permanent set per blow of the acts, were determined from the manufacturer's published\nhammer. Increasing cushion stiffness will increase com-\nliterature for the diesel hammers.\npressive and tensile stresses induced in a pile during\ndriving. The effect of explosive pressure was found to be\nextremely variable, possibly more so than the effect of\n3.4 Explosive Pressure in Diesel Hammers the driving accessories, and few conclusions could be\ndrawn. The only consistent effect that could be ob-\nIn order to account for the effect of explosive force served was that if the maximum impact force induced\nin diesel hammers, the force between the ram and the by the falling ram was insufficient to produce perma-\nanvil is assumed to reach some maximum due to the nent set, the addition of explosive force had little or no\nimpact between the ram and anvil, and then decrease. effect on the solution. In other words, unless the par-\nHowever, should this impact force tend t o decrease below ticular hammer, driving accessories, pile, and soil con-\nsome specified minimum, it is assumed that the diesel ditions were such that it was possible to get the pile\nexplosive pressure maintains this specified minimum moving, the explosive force, being so much smaller than\nforce between the ram and anvil for a given time, after the maximum impact force, had no effect.\n\n## TABLE 3.6. EFFECT OF COEFFICIENT OF RESTITUTION ON MAXIMUM POINT DISPLACEMENT\n\nRam Maximum Point Displacement (in.) Maximum\nPile RUT Velocity Change\nI.D. (kip) (ft/sec) e = 0.2 e = 0.4 e = 0.6 (%)\n\n## TABLE 3.7. EFFECT OF COEFFICIENT OF RESTITUTION ON ENTHRU\n\nRam ENTHRU (kip f t ) Maximum\nPile RUT Velocity Change\nI.D. (kip) (ft/sec) e = 0.2 e = 0.4 e = 0.6 (%\n\nPAGE TEN\nHowever, the addition of explosive pressure in-\ncreased the permanent set of the pile in some cases\nwhere the maximum impact force is sufficient to start\nthe pile moving; on the other hand, its addition was\nfound ineffective in an equal number of circumstances.\nThe explosive forces assumed to be acting within\nI various diesel hammers are listed in Table 3.1. These\n1 forces were determined by experiment, personal corre- ANVIL\nspondence with the hammer manufacturers, and from\ntheir published literature. CAPBLOCK\nPlLE CAP\nCUSHION\n3.5 Effect of Ram Elasticity\nIn 1960, when Smith first proposed his numerical\nsolution to the wave equation for application to pile\ndriving problems, he suggested that since the ram is\nusually short in length, it can in many cases'be repre-\nsented by a single weight having infinite stiffness. The\nexample illustrated in Figure 2.1 makes this assumption,\nsince K ( l ) represents the spring constant of only the\ncapblock, the elasticity of the ram having been neglected.\nSmith also noted that if greater accuracy was desired,\nthe ram could also be divided into a series of weights\nand springs, as is the pile.\nAs noted in Figures 3.2 and 3.3, there is a signifi-\ncant difference between the steam or drop hammers and\ndiesel hammers, i.e., the steam hammer normally strikes\na relatively soft capblock, whereas the diesel hammer in-\nvolves steel on steel impact between the ram and anvil.\n\nGUIDES\n\n## To determine the influence of dividing the ram into\n\nRAM\na number of segments, several ram lengths ranging from\n2 to 10 ft were assumed, driving a 100-ft pile having\npoint resistance only. The total weight of the pile being\nHAMMERBASE driven varied from 1500 to 10,000 lb, while the ultimate\nCAPBLOCK soil resistance ranged from 0 to 10,000 Ib. The cushion\nwas assumed to have a stiffness of 2,000 kips per in.\nPlLE CAP\nTable 3.8 lists the results found for a typical prob-\nCUSHION lem solved in this study, the problem consisting of a\nADAPTER 10-ft long ram traveling at 20 fps striking a cushion\nwith a stiffness of 2000 kips per in. The pile used was\na 100-ft 12H53 steel pile, driven by a 5,000-lb ram.\n\n## TABLE 3.8. EFFECT OF BREAKING THE RAM INTO\n\nSEGMENTS WHEN RAM STRIKES A CUSHION OR\nCAPBLOCK\nMaxi-\nmum Maxi- Maxi-\nCompres- mum mum\nLength sive Tensile Point\nNumber of Pile Force Force in Displace- .\nSol L of Ram Segments in Pile, Pile ment\nDivisions (ft) (kip) (kip) (in.)\n\nPlPE PlLE\nPlPE PlLE CLOSED AT TIP\n\n## Figure 3.2. Steam hammer.\n\nPAGE ELEVEN\nTABLE 3.9. EFFECT O F BREAKING RAM INTO SEGMENTS WHEN RAM STRIKES A STEEL ANVIL\n\n## Length Maximum Com~ressive Maximum\n\nNumber of Each Force on PiIe Point\nAnvil Ram of Ram Ram At At At Displace-\nWeight Length Divisions Segment Head Center Tip ment\nIb ft fb kip kip kip in.\n\nNo pile cap was included in the soluiion, the cushion held constant and the ram was divided equally into seg-\nbeing placed directly between the hammer and the head ment lengths as noted in Table 3.9. These variables were\nof the pile. Since the ram was divided into very .short picked because of their possible influence on the solution.\nlengths, the pile was also divided into short segments.\nThe pile used was again a 12H53 point bearing pile\nAs shown in Table 3.8, the solution is not changed having a cushion of 2,000 kip per in. spring rate placed\nto any significant extent whether the ram is divided into between the anvil and the head of the pile. The soil\n1, 2, or 10 segments. The time interval was held con- parameters used were RU = 500 kips, Q = 0.1 in.,\nstant in each case. and J = 0.15 sec. per ft. These factors were held con-\nstact for all problems listed in Tables 3.8 and 3.9.\nIn the case of a diesel hammer, the ram strikes\ndirectly on a steel anvil rather than on a cushion.' This The most obvious result shown in Table 3.9 is that\nmakes the choice of a spring rate between the ram and when the steel ram impacts directly on a steel anvil,\nanvil difficult because the impact occurs between two dividing the ram into se,ments has a marked effect on\nsteel elements. The most obvious solution is to place a the solution.\nspring having a rate dictated by the elasticity of the\nram and/or anvil. A second possible solution is to break An unexpected result of the study was that even\nthe ram into a series of weights and springs as is the pile. when the ram was short, breaking it into segments still\neffected the solution. As seen in Table 3.9, the solutions\nT o determine when the ram should be divided, a for forces and displacements for both 6 through 1 0 ft\nparameter study was run in which the ram length varied ram lengths continue to change until a ram segment\nbetween 6 and 10 ft, and the anvil weight varied from, length of 2 ft was reached for the 2,000-lb anvil and a\n1,000 to 2,000 lb. In each case the ram parameter was seapent length of 1 ft for the 1,000-lb anvil was reached.\n\nCHAPTER IV\nCapblock and Cushions\n4.1 Methods Used to Determine Capblock and terial placed between the steel helmet and ~ i l e(usually\nCushion Properties used only when driving concrete piles).\nAs used here, the word \"capblock\" refers to the Although a capblock and cushion serve several\nmaterial placed between the pile driving hammer and purposes, their primary function is to limit impact\nthe steel helmet. The term \"cushion\" refers to the ma- siresses in both the pile and hammer. In general, it has\nP A G E TWELVE\nbtxn found that a wood capblock is quite effective in\nreducing driving stresses, more so than a relatively stiff\ncapblock material such as Micarta. However, the stiffer\nMicarta is usually more durable and transmits a greater\npercentage of the hammer's energy to the pile because\nof its higher coefficient of restitution. DYNAMIC S-S CURVE\n\n## For example, when fourteen different cases of the A STATIC S - s CURVE\n\nMichigan study were solved by the wave equation, the\nMicarta assemblies averaged 14% more efficient than\ncapblock assemblies of wood. However, the increased\ncushion stiffness in some of these cases increased the\nimpact stresses to a point where damage to the pile or\nhammer might result during driving. The increase in\nstress was particularly important when concrete or\nprestressed concrete piles were driven. When driving\nconcrete piles, it is also frequently necessary to include\ncushioning material between the helmet and the head of P\nthe pile to distribute the impact load uniformly over the\nsurface of the pile head and prevent spalling. w\nn\nI-\nTo apply the wave equation to pile driving, Smith\nassumed that the cushion's stress-strain curve was a\nseries of straight lines as shown in Figure 4.1. Although\nthis curve was found to be sufficiently accurate to pre-\ndict maximum compressive stresses in the pile, the shape\nof the stress wave often disagreed with that of the actual\nstress wave. T o eliminate the effects of soil resistance\nseveral test piles were suspended horizontally above the\nground. These test piles were instrumented with strain\ngages at several points along the length of the pile, and\nespecially at the head of the pile. A cushion was placed\nat the head of the pile which was then hit by a hori-\nzontally swinging ram, and displacements, forces, and\naccelerations of both the ram and head of the pile were\nmeasured. Thus, by knowing the force at the head of\nthe pile and the relative displacement between the ram o 002 004 008 012 o 16 0.20\nand the head of the pile, the force exerted in the cushion STRAIN (IN./IN.)\n\na fir cushfo~. .\n\n## and the compression in the cushion at all times could\n\nbe calculated. Thus the cushion's stress-strain diagram\ncould be plotted to determine whether or not it was\nactually a straight line.\nUsing this method, the dynamic stress-strain prop-\nerties were measured for several types 04 cushions.\nIt was further determined that the stress-strain\ncurves were not linear as was assumed by Smith, but\nrather appeared as shown in Figure 4.2. Because it was\nextremely difficult to determine the dynamic stress-strain\ncurve by this method, a cushion test stand was con-\nstructed as shown in Figure 4.3 in an attempt to simplify\nthe procedure.\nSince it was not known how much the rigidity of\nthe pedestal affected the cushion's behavior, several\ncushions whose stress-strain curve had been previously\ndetermined by the first method were checked. These\nA D studies indicated that the curves determined by either\nSTRAIN method were similar and that the cushion test stand\ncould be used to accurately study the dynamic load-\nFigure 4.1. Stress-strain curve for a cush,ion block. deformation properties of cushioning material.\nPAGE THIRTEEN\nTABLE 4.1. TYPICAL SECANT MODULI OF ELAS-\n.-\"\"LLLI TICITY (E) AND COEFFICIENTS OF RESTITUTION\n(e) OF VARIOUS PILE CUSHIONING MATERIAL\n\nE e\npsi\nGUIDES\nMicarta Plastic\nOak (Green)\nAsbestos Discs\nFir Plywood\nPine Plywood\nGum\nGUIDE RAIL\n*Properties of wood with load applied perpendicular to\nwood grain.\n\n## 4.3 Coefficient of Restitution\n\nAlthough the cushion is needed to limit the driving\nstresses in both hammer and pile, its internal damping\nCUSHION BLOCK reduces the available driving energy transmitted to the\nhead of the pile. Figure 4.1 illustrates4this energy loss,\nwith the input energy being given by the area ABC while\nthe energy output is given by area BCD. This energy\nFLOOR SLAB loss is commonly termed coefficient of restitution of the\nI L cushion \"e\", in which\n/ FIXED BASE\nCONCRETE PILE\ne = d Area\nArea ABD\nBCD\n/\nFigure 4.3. Cushion test stand.\n\n## Throughout this investigation, a static stress-strain\n\ncurve was also determined for each of the cushions.\nSurprisingly, the static and dynamic stress-strain curves\nfor wood cushions agreed remarkably well. A typical\nexample of this agreement is shown in Figure 4.2. The\nstress-strain curves for a number of other materials\ncommonly used as pile cushions and capblocks, namely\noak, Micarta, and asbestos are shown by Figures 4.4-4.6.\n\nThe major difficulty encountered in trying to use\nthe dynamic curves determined for the various cushion\nmaterials was that it was extremely difficult to input the\ninformation required by the wave equation. Although\nthe initial portion of the curve was nearly parabolic, the\nplex. This prevented the curve from being input in\nequation form, and required numerous points on the\ncurve to be specified.\nFortunately, it was found that the wave equation\naccurately predicted both the shape and magnitude of\nthe stress wave induced in the pile even if a linear force-\ndeformation curve was assumed for the cushion, so long\nof elasticity for the material (as opposed to the initial,\nfinal, or average modulus of elasticity), and the unload-\ning portion of the curve was based on the actual dynamic STRAIN (IN./lN.) !\ncoefficient of restitution. Typical secant moduli of\nelasticity and coefficient of restitution values for various Figure 4.4. Dynamic stress-strain curve for an oak I\nmaterials are presented in Table 4.1. cushion. 1\n\nPAGE FOURTEEN\nSTRAIN IN IN. PER IN.\nSTRAIN (IN./IN.)\nFigure 4.6. Stress us strain for garlock asbestos cushion.\n'\n\n## Figure 4.5. Dynamic stress-strain curve for a micarta\n\ncushion.\nof elasticity values for well consolidated cushions should\nbe used. Table 4.1 shows typical secant moduli of well\nOnce the coefficient of restitution for the material consolidated wood cushions. Table 4.1 also lists the\nis known, the slope of the unloading curve can be deter- coefficient of restitution for the materials which should\nmined as noted in Figure 4.1. be used when analyzing the problem by the wave equa-\nFor practical pile driving problems, secant moduli tion.\n\nI CHAPTER V\nI\n1\n\n## i 5.1 Comparison with Laboratory Experiments\n\nAs noted in the preceding section, several test piles\nequation, the following information is normally\nrequired :\n1. The initial velocity and weight of the ram,\nwere instrumented and suspended horizontally above the\nground. This example pile was a steel pile, 85 ft in 2. The actual dynamic stress-strain curve for the\nlength with a cross-sectional area of 21.46 sq. in. The cushion,\ncushion was oak, 7 in. thick. The ram had a weight of 3. The area and length of the pile, and\n2128 lb and a velocity of 13.98 fps. The cushion was\nclamped to the head of the pile and then struck by a 4. The density and modulus of elasticity of the pile.\nhorizontally swinging ram. The pile was instrumented Since the stress-strain curve for the cushion was un-\nwith strain gages at six points along the pile, and dis- known, the numerical solution was rewritten such that\nplacements and accelerations of both the ram and head it was not needed. This was possible since the pile was\nof the pile were also measured. instrumented with a strain gage approximately 1 ft from\n\nI In order to utilize Smith's solution to the wave the head of the pile which recorded the actual stress\n\nI P A G E FIFTEEN\nI-ExPERIMEmAL SOLUTION?\nO n O D THEORETICAL SOLUTION USING\nI\nKNOWN FORCES AT THE PlLE\nCAUSED B Y T H E R I M AND\n- SOLUTION WrrH KNOWN FORCES PLACED ON HEAD OF PlLE\n*DsD SOLUTION USING A LlNEaR CUSHION SPRING RATE\nCUSHION\nSOLUTION USING A PARABOLIC WSHION SPRING RATE\nI1\n- DODO\n\n160 I I 8 J ' I l I I I I I I I I I I I I\nl ' l l l f I ~ ' m ~ I I I I J I I I\n0 I 2 3 4 5 6 7 8 9 0 11 12 13 14 15 16 17 18 19 20\n0 1 2 3 4 5 6 7 8 9 ID 11 12 13 14 15 16 17 16 19 20\nT l M E ( S E C X 10.3) T l M E I S E C X 10-31\n\nFigure 5.1. Theoretical vs experimental solution, S ~ r a i n Figure 5.3. Theoretical us experimental solution for\n25 ft from pile head. strains 25 ft from the pile head.\n\ninduced in pile by the ram and cushion. The force tensile and compressive stresses. Furthermore, ft pre-\nmeasured at the held of the pile was then placed directly dicts the shape of the stress wave reasonably well.\nat the head of the pile and the wave equation was used\nto compute stresses and displacements at all of the gage 5.2 Significance of Material Damping .\npoints along the pile. Figures 5.1 and 5.2 present typi- in the Pile\ncal comparisons between the experimental results and Other parameters were often varied in an attempt to\nwave equation solutions at two points on the pile, and obtain more accurate results, one of which was the\nillustrate the degree of accuracy obtained by use of material damping capacity of the pile material. How-\nthe wave equation. ever, most suspended pile cases studied strongly indicated\nI t must be emphasized that this excellent correlation that damping would be negligible because of the extreme-\nbetween experimental and theoretical results was in ef- ly low rate of decay of the stress wave in the pile. The\nfect obtained by using ,the actual dynamic load-deforma- only pile in which damping was thought to be sipnili-\ntion curve for that particular case. However, as men- cant was a lightweight concrete pile with a static modulus\ntioned earlier, the stress-strain curve for the cushion is of elasticity of 3.96 x 10\"nd a \"sonic\" modulus of\nnormally assumed to be linear as shown in Figure 4.1. elasticity of \\$.63 x lo6 psi. This problem was chosen\nsince E, was relatively larger than E, indicating the pos-\nTo determine how much the use of the linear stress- sibility of rather high damping. It can be seen in Figure\nstrain curve will affect the solution, the previous case 5.5 that the magnitude of the experimental results di-\nwas rerun using the straight line stress-strain curves. As minishes slightly after four cycles. The magnitud-: of\nnoted in Figures 5.3 and 5.4, the solutions for the linear the theoretical solution with damping neglected would\nand nonlinear cushion assumptions agreed favorably. not. Figure 5.5 compares the experimental and theo-\nThe use of the straight line assumption is reasonable retical solutions for stresses when Smith's proposed\nsince it gives fairly accurate results for both maximum method of damping is included. In this case, the ex-\n\nI - EXPERIMENTAL SOLUTION I I\n\nII\nOmsD THEORETICAL SOLUTION USING\nKNOWN FORCES AT THE PILE\n- SOLUTION WITH KNOWN FORCES PLACE0 ON HEAD OF PlLE\nCAUSED BY THE RAM 1 N D 00.- SOLUTION USING A LINEAR CUSHION SPRING R A T E\nCUSHION \"00 SOLUTION USING A PARABOLIC CUSHION SPRING RATE\nI I\nI60\n0\n\"\nI\n\"\n2\n'\n3\n\"\n4\n'\n5\n'\n6\n'\n7\n'\n6\n\"\n9\n'\n10\n'\n11\n~\n12\n~\n13\nI\n14\n'\n15 16 17 16 19 20\n1 6 1 \" \" \" \" ' \" \" \" \" \" I\n0 1 2 3 4 5 6 7 B 9 10 11 I2 13 14 15 16 17 I8 19 20\nT l M E (SEC X lo1) T I M E (SECXIO-~I\n\nFigure 5.2. Theoretical vs experimental solution. Strain Figure 5.4. Theoretical vs experimental solution for\n52 ft from pile head. strains 52 ft from the pile head.\nPAGE SIXTEEN\nperimental and theoretical solutions are in excellent\nagreement, both in wave shape and rate of decay.\nlorn\nAlthough it is extremely interesting to be able to\npredict the dynamic behavior of piling with such accu-\n800\nracy, most practically the primary interest is in the\n600\nmaximum stresses induced in the pile which occur\n-\n400\nduring the first or second pass of the stress wave along\n- zoo the pile. During this time, the effects of damping are\no extremely small even for the lightweight aggregate pile,\n=\nu,\nW\n\nU)\nZoo and are apparently of no practical importance. Whether\n400 this conclusion will be accurate for timber or other piles\n600 having much higher damping capccities than either steel\n800 or concrete piles is unknown. A higher damping ca-\n1oC\nl.\npacity could affect the results earlier in the solution and\nthus be of significance.\n0 1 2 3 4 5 6 7 8 9 10 11 P 13 14 I5 16 17 18 I9 20\nTIME (SEC x 10 31 It should be emphasized that the above conclusions\nare valid only for normal pile driving conditions. If the\nwave must be studied for an extended period of time,\nFigure 5.5. Comparison of experimentaJ and theoreticd damping in the ~ i l emay be significant and should be\nsolutions for stresses 25 ft from the ~ i l ehead. accounted for.\n\nCHAPTER VI\nSoil Properties\n6.1 General It is also assumed to be constant for a given soil under\ngiven conditions as is the static shear strength of the\nA limited amount of work has been done on soil soil from which Ru on a pile segment is determined.\nproperties and their effects on the wave equation solution Ru is defined as the maximum soil resistance on a pile\nof the piling behavior problem. A total of three re- segment.\nsearch reports concerning soil properties have been pub-\nlished by the Texas Transportation Institute during the Smith notes that Equation (6.1) produces no damp-\n\"Piling Behavior\" study. Research Reports 33-7 and ing when D(m,t) -- D1(m,t) becomes zero. He sug-\n33-7A6.I,6 2 give the results of a series of laboratory gests an alternate equation to be used after D(m,t) first\ndynamic (impact) and static tests conducted on satu- becomes equal to Q (m) :\nrated sands. Research Report [email protected] the results R(m,t) = [D(m,t) - D1(m,t)] K1(m)\nof a field test on a full scale instrumented pile in clay.\nA brief summary of the results of these tests are given\n+\nJ ( m ) Ru(m) V(m,t-1) (6.2)\nin this chapter. Care must be used to satisfy conditions at the point\nof the pile. Consider Equation (6.1) when m p,\n6.2 Equations to Describe Soil Behavior where p is the number of the last element of the pile.\nK ( p ) is used as the point soil spring and J ( p ) as the\nExamination of Equation (6.1) shows that Smith's point soil damping constant. Also at the point of the\nequation describes a type of Kelvin rheological model\nas shown in Figure 6.1.\nSOIL RESISTANCE\nR\n\n## The soil spring behaves elastically until the deformation\n\nD(m,t) equals Q and then it yields plastically with a\n1 DISPLACEMENT\n\nThe dashpot J develops a resisting force proportional to\nKelvin model slightly as shown by Equation (6.2). This\nequation will produce a dynamic load-deformation be-\n\n~\nI\nhavior shown by path OABCDEF in Figure 6.2(b). If\nterms in Equation (6.1) are examined, it can be seen\nthat Smith's dashpot force is given by\n\nThe dimensions of J are sec/ft and it is assumed to be Figure 6.1. Model used by Smith to describe soil re-\nindependent of the total soil resistance or size of the pile. sistance on pile.\nPAGE SEVENTEEN\npile, the soil spring must be prevented from exerting\ntension on the pile point. The point soil resistance will V = 10 f t per sec\nfollow the path OABCFG in Figure 6.2(b). It should be\nkept in mind that at the pile point the soil is loaded in\ncompression or bearing. The damping constant J ( p )\nin bearing is believed to be larger than the damping\nconstant J ( m ) in friction along the side of the pile.\n/ V = 6.7 f t per sec\n\n## 6.3 Soil Parameters to Describe Dynamic\n\nSoil Resistance During Pile Driving V: 3.3 ft p e r sec\nThe soil parameters used to describe the soil resist-\nance in the wave equation are Ru, Q, and J.\nV = 0 (static test)\n\n## DATA FOR SATURATED OTTAWA SAND\n\nVOID RATIO e = 0 . 5 0\nCONFINING PRESSURE u3 = 4 5 Ib per in\n'ION\n\n.I .2 .3 .4 .5 .6\nDEFORMATION 0 (in.)\n\n## Figure 6.3. Load-deformaion properties of Ottawa sand\n\ndetermined b y triaxial tests (specimens n o m i d l y 3 in.\nI D i n diam. b y 6.5 in. high).\n\n( a ) STATIC\nSoil Resistance \"Ru.\" For the side or friction soil\nresistance, Ru is determined by the maximum static soil\nadhesion or friction against the side of a given pile\nsegment by:\nLOAD Ru(m) = fs 2, AL (6.3)\nwhere\nfs = maximum soil adhesion or friction (lb/ft2),\nZ, = perimeter of ~ i l esegment (ft), and\nAL = length of pile segment (ft).\nIn cohesionless materials (sands and gravels)\nfs = a tan 4' (6.4)\nwhere\n-\ncr = effective normal stress against the side of the\npile (lb per ft2), and\n4' = angle of friction between soil and pile (de-\ngrees).\nIn cohesive soils (clays) fs during driving is the re-\nmolded adhesion strength between the soil and pile.\nAt the point of the pile Ru is determined by the\nmaximum static bearing strength of the soil and is\nfound by\nRu = (Qu) (AP) (6.5)\nwhere\nQu = ultimate bearing strength of soil (lb/ft\",\n(b) DYNAMIC and\nFigure 6.2. Load-deformation characteristics of soil. Ap = area of pile point (ft\".\nP A G E EIGHTEEN\nIn cohesive soils (clays) it is believed that the undis-\nturbed strength of the soil may be used conservatively e = VOID RATIO\n\nto determine Qu, since the material at the pile point is 5=EFFECTIVE CONFINING\nPRESSURE\nin the process of being compacted and may even have\na higher bearing value.\nQuake \"Q\". The value of Q, the elastic deformation\nof the soil is difficult to determine for various types of\nsoils conditions. Various sources of data indicate that\nvalues of Q in both friction and point bearing probably\nrange from 0.05 in. to 0.15 in.\nChellisG.l indicates that the most typical value\nfor average pile driving conditions is Q = 0.10 in. If\nthe soil strata immediately underlying the pile tip is very\nsoft, it is possible for Q to go as high as 0.2 in. or more.\nAt the present state of the art of pile driving technology\nit is recommended that a value of Q = 0.10 in. be used Figure 6.5. \"J\" versus \"V\" for Ottawa sand.\nfor computer simulation of friction and point soil re-\nsistance. However, in particular situations where more\nprecise values of Q are known, they should be used. sand are in reasonable agreement with those recom-\nDampimg Constant \"J\". The Texas Transportation mended by Smithe.j and Forehand and R e e ~ e ~ (0.1\n. ~ to\nInstitute has conducted static and dynamic tests 0.4).\non cohesionless soil samples to determine if Smith's The value of J ( p ) for cohesive soils (clays) is not\nrheological model adequately describes the load-defor- presently known. The very limited data available indi-\nmation properties of these soils. Triaxial soil tests were cate it is at least equal to that for sand. Forehand and\nconducted on Ottawa sand at different loading velocities. Reese believe it ranges from 0.5 to 1.0.\nFigure 6.3 shows typical results from a series of such\ntests. There are no data now available to indicate the\nvalue of J ( m ) in friction along the side of the pile.\nFigure 6.4 shows additional data concerning the Smith believes it is smaller than J (p) and recommends\nincrease in soil strength as the rate of loading is in- J ( m ) values in friction of about 1/3 those at the point.\ncreased. Since these tests were confined compression Research is under way at Texas A&M University which\ntests it is believed that they simulate to some extent the should indicate the value of J in friction. At the present\nsoil behavior at the pile point. The J value increases as time J (m) in friction or adhesion is assumed to be 1/3 of\nthe sand density increases (void ratio e decreases) and\nit increases as the effective\n- confining stress(T3 increases. J(P).\n6.4 Laboratory Tests on Sands\nwhere\ncr3 = total confining pressure, and During the laboratory tests in saturated sands, at-\ngiven to the determination of the soil darn^-\ntention was \"\nu = pore water pressure. ing constant. The peak dynamic resistance of the soil\nFor saturated Ottawa sand specimens, J ( p ) varied at the pile point can be represented in equation form\nfrom about 0.01 to 0.12. When the sand was dry J ( p ) for Smith's mathematical model as follows:\nwas nominally equal to zero. These values of J ( p ) for\n\n## where: = peak load developed in dynamically\n\nPdynnmic\nloaded sample at a constant veloci-\nty, v ;\nPstntic = peak load developed in statically\nJ = a damping constant; and\nAII specimens w e r e s a t u r a t e d .\nAt beginning of tests .me pore\nV = impact velocity of the dynamic\nw ~ t e rpressure u was nominally load.\n80% of the confining pressure q\n\n## The laboratory tests on sands were conducted in\n\nsuch a manner that PdyunIllio Pstatic,and V were meas-\nured, and consequently it was possible to evaluate J for\na given set of test conditions.\nThe laboratory tests conducted on saturated sands\nwere conducted with the sand sample subjected to triaxial\n' \" \" ' ' ' ' ~ ' 'I 2 0 ' ~ confinement. Particular attention was given to the ef-\n20 40 60 80\nties, and effective initial confining pressures. The\nFigure 6.4. Increase in strength vs rate of loading- machine used for testing was developed for this particu-\nOttawa sand. lar research and a complete description of the machine\nPAGE NINETEEN\nand the instrumentation used is given in Research Report\n33-7A.6.2\nThe results of the study of Ottawa sand are sum-\nmarized in Figure 6.5. Application of Smith's mathe-\nmatical model with the experimental data yields a damp-\ning factor, J, which varies from 0.01 to 0.07. For two\nother sands tested, Arkansas sand and Victoria sand,\nthe value of J varied from 0.04 to 0.15. These values of\nJ are not constant, and therefore Smith's equation did\nnot accurately predict peak dynamic loads for the ranges\nof loading velocities ( 3 to 12 fps) used in these tests.\nAdditional tests have been conducted on these sands\nat loading velocities from 0 to 3 fps. Also, a series of\nof from 0 to 12 fps. This work has been accomplished ELAPSED TIME (HRS)\nunder a new research study entitled \"Bearing Capacity\nof Axially Loaded Piles.\" The tests on clays have shown Figure 6.7. Pore pressure measurements in clay stratum\nthat the use of Smith's original equation (Equation 6.2) -50' depth.\nyields a variable J value as was the case in sands. How-\never, if Smith's equation is modified by raising the ve-\nlocity, V, to some power, n, less than 1.0, a reasonably Ru(p) = bearing or compressive strength of\nconstant value of J can be obtained for the full range soil at the pile point m = p (lb).\nof loading velocities of from 0 to 12 fps. The proposed - Note this is taken as the strength of\nmodified equation is as follows: the soil in an undisturbed condition\nwhich should be conservative.\nAs time elapses after driving, Ru(m) for m 1 to p\n6.5 Static Soil Resistance After - 1 may increase as the disturbed or remolded soil\nPile Driving (Time Effect) along the side of the pile reconsolidates and the excess\npore water pressure dissipates back to an equilibrium\nImmediately after driving, the total static soil re- condition. In cohesive soils (clays) the increase in\nsistance or bearing capacity of the pile equals the sum strength upon reconsolidation (sometimes referred to as\nof the Ru values discussed previously. Thus, Ru(tota1) \"setup\") is often considerable.\nis the bearing capacity immediately after driving.\nm=p The bearing capacity of the pile will increase as\nRu(tota1) = 2 Ru (m) the remolded or disturbed clay along the side of the pile\nreconsolidates and gains strength, since the adhesion or\nm = l friction strength of clay is generally restored with the\nRu(m) = soil adhesion or friction on seg- of time show that ultimate adhesion is approximately\nments m = 1 to m = p - 1 (lb), equal to the undisturbed cohesion. Therefore, the\n(note that this is the strength of the amount of increase in bearing capacity with time is\ndisturbed or remolded soil along related to the sensitivity and reconsolidation of the clay\".\nthe side of the pile), and\nFigure 6.6 illustrates the time effect or \"setup\" of\na pile driven in a cohesive soil. In cohesionless soils\n(sands and gravels) the friction strength of the soil will\nusually change very little. Normally, the value of Ru(p)\nat the pile point changes very little.\n\n## 6.6 Field Test in Clay\n\nThe purpose of the field test s t ~ d ywas\n~ , to\n~ investi-\ngate the failure mechanisms of clay soils subjected to\nwith pressure transducers, strain gages, and accelerome-\nters was driven into a saturated clay at a site in Beau-\nmont, TexasG.j\nMeasurements of strains and accelerations of the\npile were taken during driving. Pore pressure measure-\nments were made at the pile-soil interface for a continu-\nous period of 30 days after driving. Figure 6.7 shows\na typical plot of pore pressure versus elapsed time in the\nT l M E AFTER DRIVING (HOURS)\nclay stratum at a 50 ft depth. Strain measurements were\nFigure 6.6. \"Setup\" or recovery of strength after driv- undisturbed strength\ning in cohesive soil (after reference 6.7). *Sensitivity of clay = remolded strengith\n\nPAGE TWENTY\nmade during static load tests at 13 days and 30 days where: r = radial distance from pile center; and\nafter driving. Soil borings were made for the in-situ, rl = radius of pile.\nremolded, and reconsolidated conditions, and at specific\nradial distances from the pile. Conventional tests were Results of this study also suggest that the time after\nconducted on the soil samples to measure the changes driving required for piles of different radii to attain\nin engineering properties for the different conditions. comparable percentages of their ultimate bearing capaci-\nty can be expressed as follows:\nA mode of failure was established in this study for\na cohesive soil involved in the load response of a pile-\nsoil system. The behavior of the soil in this study indi-\ncates that soil disturbances which involve new soil parti- where: rl = radius of pile 1 ;\ncle arrangement and altered engineering properties are\nlimited to a distance from the center of the pile of ap- r2 = radius of pile 2;\nproximately 4.5 radii.\"j This relationship can be ex- T1 = time for pile 1 to attain a stated percent-\npressed as follows: age of ultimate bearing capacity; and\nTz = time for pile 2 to attain the same per-\ncentage of ultimate bearing capacity.\n\nCHAPTER VII\nUse of the Wave Equation to Predict Pile\nLoad Bearing Capacity At Time of Driving\n7.1 Introduction J ( m ) side = 0.05 sec/ft Q(m) side = 0.10 is.\nIn general, engineers are interested in the static load Soil is a soft marine deposit of fine sand, silt, and muck,\ncarrying capacity of the driven pile. In the past the with the pile point founded on a dense layer of sand and\nengineer has often had to rely on judgement based on gravel.\nsimplified dynamic pile equations such as the Hiley or ASSUMED SOIL DISTRIBUTION:\nEngineering News formulas. By the wave equation\nmethod of analysis a much more realistic engineering Curve I : 25% side friction (triangular distri-\nestimate can be made using information generated by bution) 75% point bearing.\nthe program. Curve 11: 10% side friction (triangular distri-\nThe previous chapters have shown how the hammer bution) 90% point bearing.\npile-soil system can be simulated and analyzed by the This information is used to simulate the system to\nwave equation to determine the dynamic behavior of be analyzed by the wave equation. A total soil resist-\npiling during driving. W i t h this simulation the driving ance Ru(tota1) is assumed by the computer for analysis\nstresses and penetration of the pile can be computed. in the work. It then computes the pile penetration or\n\"permanent set\" when driven against this Ru (total).\n7.2 Waue Equation Method The reciprocal of \"permanent set\" is usually computed\nto convert this to blows per in.\nIn the field the pile penetration or permanent set\nper blow (in. per blow) is observed and this can be The computer program then selects a larger\ntranslated -into the static soil resistance through the use Ru(tota1) and computes the corresponding blows per\nof the wave equation. in. This is done several times until enough points are\ngenerated to develop a curve relating blows per in. to\nConsider the following example: Ru(tota1) as shown in Figure 7.1 (two curves for the\ntwo different assumed distributions of soil resistance\nPILE: 72 ft steel step taper pile are shown).\nHAMMER: No. 00 Raymond In the field if driving had ceased when the resist-\nEfficiency = 80% ance to penetration was 1 0 blows per in. ( a permanent\nRam Weight = 10,000 lb set equal to 0.1 in. per blow), then the ultimate pile\nload bearing capacity immediately after driving should\nEnergy = 32,500 ft lb have been approximately 370 to 380 tons as shown on\nCAPBLOCK: Micarta Figure 7.1. It is again emphasized that this Ru(tota1)\nis the total static soil resistance encountered during driv-\nK = 6,600,000 lb/in. ing, since the increased dynamic resistance was consid-\ne = 0.8 ered in the analysis by use of J. If the soil resistance\nis predominantly due to cohesionless materials such as\nASSUMED SOIL PARAMETERS: sands and gravels, the time effect or soil \"setup\" which\nJ ( p ) point = 0.15 sec/ft Q ( p ) point = 0.10 in. tends to increase the pile bearing capacity will be small\nPAGE TWENTY-ONE\nPILE: 72 ft. Step Taper. 12 ft. steps. No. 1 to No. 6\nHAHHER: No. 00 Ramond\nSHELL: Step Taper Corrugated\nCAPBLOCK: Hicarta; Coeff. of Rest. = .BO; K = 6,600,000 ? ~ i\nDISTRIBUTION OF RESISTANCE:\nCurve 1: 25% Side (Triangular Distribution); 75% Point\nCurve 11: 10% Side (Triangular Distribution); 90% Point\nCONSTANTS\n.-- -.:\nJ (Point) = 0.15: J (Side) = 0.05\nQ (Point) = 0.10; Q (Side) = 0.10\n\n.- -\n\nW TONS\n>\na\n3 SOIL RESISTANCE A T TIME OF DRIVING - Rd,\nFigure 7.2. Cwnparison of m e equcntioln predicted sod\nresistance to soil resistawe d & r m i d by bod tests for\n5 10 15 20\npiles driven in sands. (Data from table 7.1.)\n25\nBLOWS PER IN.\n\n## Figure 7.1. Ultimate driving resistance us blows per\n\nIn developing the curves of Figure 7.1, it was\ninch for cn example problem. necessary to assume the following soil parameters:\n1. Distribution of soil resistance\nor negligible. If the soil is a cohesive clay, the time\neffect o r soil \"setup\" might increase the bearing capacity 2. Soil Quake \"Q\"\nas discussed in Chapter VI. The magnitude of this 3. Soil damping constant \"J\"\n\"setup7' can be estimated if the \"sensitivity\" and recon-\nsolidation of the clay is known. I t can also be con- As illustrated by Curves I and I1 on Figure 7.1,\nservatively disregarded since the \"setup\" bearing ca- small variations in the distribution of soil resistance\npacity is usually greater than that predicted by a curve between side friction and point bearing will not affect\nsimilar to Figure 7.1. the wave equation results- significantly. All that is re-\n\n## TABLE 7.1.- ERRORS CAUSED BY ASSUMING J(point) = 0.1 AND &\n\n.(e)j'J = J(point) FOR SAND (For Sand-\nSupported Piles Only)\nRar* RWE\n(Resistance (Indicated % Error\nLoad a t Time of Soil in Ra.\nTest Driving) Resistance)\nLocation Pile (kips) . (kips) (R m ~\nRdr ) (100)\nArkansas\n\nCopano Bay\nMuskegon\n\n## Mean or Average % Error\n\n*Rd, for piles driven in sands was assumed equal to the actual load test measurements since no \"setup\" was considered.\nP A G E TWENTY-TWO\nW\n250 -\n0\nZ\na\nI-\n??\nV)\n200 -\nW\n(r\n\n-1\n0\nV)\n150 -\n\n## 50 100 150 200 250\n\nTONS\nSOlL RESISTANCE AT TlME OF DRIVING (Rd,) SOlL RESISTANCE AT TlME OF DRIVING\n' CRdrI- TONS\nFigure 7.3. Comparison of wave equation predicted soil\nresistance to soil resistance determined by load tests for Figure 7.4. Comparison of wave eqllation predicted soil\npiles driven in clay. (Data from table 7.2.) resistance t o soil resistance determined b y lo& tests for\npiles driven i n both sand and clay. (Data from table\n7.3.)\n\n## quired is a reasonable estimate of the situation. For\n\nmost conditions an assumption of soil quake Q = 0.1 in.\nis satisfactory (see Chapter VI). The value of J ( m ) is confidence in the previously described method of pre-\nassumed to be 1/3 of J ( p ) . dicting static bearing capacity.\nFor the sand-supported piles (Table 7.1) damping\n7.3 Comparison of Predictions with Field Tests constants of J (point) = 0.1 and J' (side) = J (point) /3\nwere found to give the best correlation. Figure 7.2\nCorrelations of wave equation solutions with full- shows the accuracy of the correlation to be approxi-\nscale load tests to failure have provided a degree of mately +250/0. In Table 7.2, for clay-supported piles\n\n## TABLE 7.2. ERROR CAUSED BY ASSUMING J(point) = 0.3 AND Jf(dde) = 7\n\nJ(point) FOR CLAY (For Clay-\nSupported Piles Only)\n\nTest (~es-istance (~ndicited\nLoad Resist- a t time of soil % Error in Kr\n( R\"Ecr\nTest ance) driving) resistance)\nLocation Pile (kips) (kips) (kips) ) (100) Rdr\n\nBelleville I**\n4*\n5*\nDetroit 70 +156\n155 6\n205\n240\n++- 33\n29\n250 + L\nTotal = 436\n436\nAverage % Error = - = 54.5%\n\n## *90% clay-supported piles.\n\n**The test values for these piles were questionable.\n***Rd, for piles driven in clay were actual load test measurements corrected to account for soil \"set-up.\"\nPAGE TWENTY-THREE\nDEPTH TYPICAL PILE PILE PILE PILE PILE PILE PILE PILE PILE PILE PILE PILE I\nFT.\nBORING B C E I R2 R4 R5 R6 R9 R 12 R20 R23\n\n8 LOOSE SANDY\nCLAYEY SILT\n\nMEDIUM\nDENSE\nF I N E TO\nMEDIUM\nSAND\n\n10\n\nMEDIUM\n2\nTO DENSE\nI:\nFINE Rt\nTO\nCOARSE\nSAND\nWITH\nTRACE\nGRAVEL NOTE.'- ALL P/LESDR/VEN WITH A I - S HAfdMER,\n6 5 0 0 LB. RAM. 19,500 F % LBS. -\n\nI00 -\nF I N A L DRIVING\n2 3 4 6 3 4 '12 4 5 5 7\n\nTEST LOAD 60 104 80 170 185 125 140 140 140 140 240\n\nWAVE EQUATION\n70 86 95 140 190 105 150 135 164 152 200\n( R U -TONS\nQ = 0.1 in. and J(point) = 0.15, J(side) = 0.05. Soil resistance was assumed to be 59% at the point and 50%\nfriction distributed uniformly over the embedded length below a depth of 10 ft. Hammer efficiency assumed to be\n80%.\nFigare 7.5. Summary of piles tested to failure in sands.\nTABLE 7.3. ERRORS CAUSED BY ASSUMING A COMBINED J(point) = 0.1 FOR SAND AND J(point) = 0.3 F O E\nCLAY USING EQ. 7.1 (For Piles Supported by Both Sand and Clay)\nRJTD\nRIr Rdr** (Indi-\nTest ance a t Soil % Error\nLocation\nTest\nPile\nA R ~ I ~\nx 0.3\nARsana\nx 0.1\nJ(point)\n(sec/ft)\nance)\n(kips)\nDriving)\n(kips)\nance)\n(kips)\n( Rwn\nVictoria 35 0.090 0.070 0.16 208 176 170 3%\n40\n45\n0.087\n0.093\n0.071\n0.069\n0.16\n0.16\n160\n352\n136\n300\n148\n380\n+\\$2776\n-\n9%\n\n## Chocolate 40 0.126 0.058 0.18 210 166 150 -10%\n\nBayou 60 0.120 0.060 0.18 * * 740 b -\n\nCopano\nBay 58 0.252\nBelleville 3 0.102\n\nMuskegon 7 * 320\n8 * 295\nTotal = 131'\nAverage % Error = = 14.5%\n\n*Indicates piles which exceeded the testing equipment's capacity, and could not be load-tested to failure.\n**Rd. for these piles were actual load test measurements corrected to account for soil \"setup.\"\nPAGE TWENTY-FOUR\nthe damping constants J(point) = 0.3 and J' (side) =\nJ ( ~ o i n t/3) gave the best correlation. The accuracy of\n-a\nI the correlation is shown in Figure 7.3 to be approxi-\nmately -+SO %.\n-\n3\n\nW\nNOTE: TEST\nTHOSE\nFAILURE\nEVALUATED\nBY If more than one soil was involved the damping\n0\nz EBASCO ' S ENGINEERS constant used was a weighted average calculated from\n\n~ ( ~ o i i=\nt) C. [ Ri X J (point) i 1 (7.1)\n\n## where Ri = the ratio of the amount of resistance of\n\neach type of soil \"i\", to the-total soil\nresistance, both determined after setup\nhas ceased, and\n\nJ' (si-de) =\nJ (point)\n3\nTable 7.3 shows the damping constant that was\ncalculated from Equation 7.1 using J ( ~ o i n t 1= 0.3 for\nclay and J (point) = 0.1 for sand. The accuracy of the\ncorrelation, as shown in Figure 7.4 was approximately\nk25%.\nM o ~ l e has\n~ ~ found\n. ~ a similar co.rrelation with 12\npiles driven in sand. Figure 7.5 is a summary of the\nTEST LOAD FAILURE - TONS piles tested. Figure 7.6 shows that all resistances on\nFigure 7.6. Wave equation ultimate r e s i s t a m us test these piles fall within -t20% of that predicted by the\nload failure (after Ref. 7.2, data from Fig. 7.5) (sands). wave equation.\n\nCHAPTER VIII\nPrediction of Driving Stresses\n8.1 Introduction numerical solution by comparing its results with the\ntheoretical solution of Appendix A and with field data.\nIn Appendix A the exact solution for the stress\nwave introduced into a long slender elastic pile is de-\nrived using the classical one-dimensional wave equation. 8.2 Comparison of Smith's Numerical\nThe solution of this equation depends upon certain Solution with the Classical Solution\nassumptions. It is assumed that the pile is prismatic For the purpose of correlation, consider a concrete\nwith lateral dimensions small in comparison to its length pile, square in cross-section, with an area of 489 in.2\n(Poisson's effects can be neglected), that the' pile and and 90 ft long. The modulus of elasticity of the pile\ncushion material are linearly elastic, and the ram has material is assumed to be 5 x lo6 psi. The pile is con-\ninfinite rigidity (assumed to be a rigid body). The sidered to be free at the top with the bottom end fixed\nequation which governs the stress amplitude in most rigidly against movement. No side resistance is present.\npractical cases, shows that the magnitude of the stress\ninduced at the head of the pile, by the falling ram, is\ndirectly proportional to the velocity of the ram at im-\npact. The equation further shows that the stiffnesses of\nthe cushion and pile also have a significant effect on the 0---A1 :1 1 1 4 0 SECOND : ( ~ l l c r\nmagnitude of the stress generated. The soil resistance 0---A1 :I / W 0 0 SECOND\nA - - - A t : 1 / 5 W SECDND\non the side and at the point of the pile will also affect IOENTICL RESULTS WERE LEAtNED\nFOR THE FOLLOWING VALUES OF A I\nthe magnitude of the stresses in the pile. I/Y)OO. 1/1QD00, AND 1/20.000\nSECOND\nA L :PILE LENGTHAO\n\n## Chapter I1 discusses Smith's numerical solution of\n\nthe one-dimensional wave equation. This particular\ntechnique for solving the wave equation is much simpler\nfor application to problems which can have inelastic\ncushions and material properties as well as soil on the\nside and point of the pile. Chapter V discusses the\ngeneration of stress waves in piling, the significance of\nmaterial damping in the pile and the effects of pile\n3\n\nX\n9\n1000\n\n0\n\n10 20 30 40 50\nPOINT OF PlLE (FIXED)\n\n60 70 80\n-90\ndimensions on driveability. DISTANCE FROM HEAD OF PlLE IN FEET\n\nThis chapter demonstrates the validity of Smith's Figure 8.1. Maximum tensile stress along the pile.\nPAGE TWENTY-FIVE\n8.3 Correlations of Smith's Solution\nZ with Field Measurements\n500f --EXACT\nW\nLT\nO-'AI: 1/1410 SECOND\n=...At' 1 1 2 5 0 0 SECOND\n:l A l l c r\nIn previous report^^.^, the writers have shown\nIDENTICAL RESULTS WERE OBTAINED several correlations of the wave equation with stresses\nFOR THE FOLLOWWG VALUES OF A1\nVZ500. 1/5000. 1/10.000, AND measured in piles during the time of driving in the field.\n1/20,000 SECOND\na A L : PILE Lm(iTH/Io Typical examples of these correlations are shown in Fig.\n8 3000 ures 8.3 and 8.4. The significant conclusions drawn\na from these tests are as follows:\n1. The maximum compressive stresses occurred\nat the head of the pile.\nPOINT OF PlLE (FIXED)\n\\ 2. Maximum tensile stresses were found to occur\nnear the midpoint of the piles.\n0\n0\nI\n10\nI\n20\nI\n30\nI\n40\nI\n50\nI\n60\nI\n70\nPlLE IN FEET\nI\n80\n1\n90\n3. The computed compressive stresses and dis-\nplacements agree very well with the measured data.\n-\nFigure 8.2. Maximum compressive stress along the pile. 4. The computed tensile stresses appeared high\nbut in view of the unknown dynamic properties of the\nsoil, concrete, and cushioning materials involved in the\nThe f ~ l l o w i ninformation\n'~ is also applicable to the cor- problem, the quantitative comparisons shown were con-\nrelation : sidered good.\nWeight of the ram = 11,500 lb,\n8.4 Effect of Hammer Type and\nVelocity of the ram = 14.45 fps Simulation Method\nCushion block stiffness = 3,930,000 lb/in.,\nIt has been s h o ~ n (see\n~ . ~Chapter 111) that the ram\nCoefficient of restitution of a pile hammer can be idealized as a rigid body pro-\nof the cushion block = 1.00 vided it strikes on a capblock or cushion. If the ram\nstrikes directly on steel, as in the case of the diesel ham-\nSolutions have been obtained for the exact solution of mers, the accuracy of the solution for stresses is im-\nthe one-dimensional wave equation and for Smith's proved by breaking the ram into segments.\nnumerical method using 10 segments. Previous studies8.l\nhad shown that segment lengths of L/10 would yield\naccurate results. Figures 8.1 and 8.2 show comparisons\nof the maximum tensile stress and maximum compres-\nsive stress, respectively, versus position along the length\nof the pile. Note the time interval used (time differenc-\ning interval used in the numerical solution) for solutions\nshown is varied from 1/1410 seconds (this is the critical\ntime differencing interval) to 1/20,000 seconds. Note\nthat when the differencing interval became very small,\ni.e., 1/5000 seconds, the accuracy of the solution was\nnot improved. Note also that the numerical solution\nis very close to the exact solution. Other comparisons\nhave been made for the stresses at other points in the\npile and for other combinations of the end boundary\nconditi~ns.~.' H e i ~ i n and\n~~.~ have shown that\nthe discrete-element numerical solution is an exact solu-\ntion of the one-dimensional wave equation when\n\nwhere,\nAt = critical. time differencing interval,\nAL = segment length,\nE ,= modulus of elasticity, and\np = mass density of the pile material. I M e a s u r e d Stress\nI\nThis time interval is the \"critical\" time interval.\nFor practical problems, a choice of At = one-half the\n\"critical value,\" appears suitable since inelastic springs, TIME IN SECONDS !\nmaterials of different densities, and elastic moduli are\nusually involved. Figure 8.3. Stress i n pile head us time for test pile.\nPAGE TWENTY-SIX\n8.6 Effects of Cushion Stiffness, Coefficient\nof Restitution, and Pile Material Damping\nIt has been s h o ~ n (see\n~ . ~ Chapter IV) that the\nactual load deformation curve for a cushion is not a\nstraight line, but is parabolic. However, a straight line\nwhich has a slope given by the secant modulus will give\nreasonably accurate results. The cushion's dynamic\ncoefficient of restitution was found to agree with com-\nmonly recommended values. It has also been shown\nthat the effect of internal damping in the concrete and\nsteel piles will usually have a negligible effect on the\ndriving stresses.\n\n## 8.7 Fundamental Driving Stress Considerations\n\nThe purpose of this discussion is to briefly describe\nand discuss the phenomena of impact stresses during\ndriving.\nCompressive Stresses. High compressive stress at\nthe head of the pile can be caused by the following:\n\nLEGEND\n1. Insufficient cushioning material between the pile\n---- Computed Stress driving ram and the pile will result in a very high com-\n- Measured Stress pressive stress on impact.\n2. When a pile is struck 'by a ram at a very high\nvelocity, or from a very high drop, a stress wave of high\nmagnitude is produced. This stress is directly propor-\nFigure 8.4. Stress a;t mid-length of pile vs time for test tional. to the ram velocity.\npile. If the pile is idealized as a long elastic rod, with\nan elastic cushion on top an equation for the compres-\nsive stress can be developed (see Appendix A). The\nFor diesel hammers, the explosive force used to approximate equations for the maximum compressive\nraise the hammer for the next blow does work on the stress at the pile head are as follows:\npile and should be included. Notations used are:\nI n all hammer simulations, all parts which are in c0max = maximum compressive stress at pile\nthe force transmission chain should be included. The head (psi),\nhousing and other parts which do not serve to transmit\nthe driving energy may be neglected. W = ram weight (lb),\nRefer to Appendix B, Tables B.l and B.2, for V = ram irnpact velocity (in./sec) ,\n-\nrecommended values for use in the simulation.\n= V2gh,\nh = ram free fall (in.),\n8.5 Effect of Soil Resistance\ng = acceleration due to gavity,\nIf soil borings are available, the distribution of the 386 in./sec2,\nsoil resistance on the pile should be estimated from soil\nshear strength data. In general, piles in uniform co- K = cushion stiffness (Ib/in.) ,\nhesive soils will have the soil resistance distributed - Ac Ec\nuniformly in side friction with about 10 to 20% point --\ntc\nresistance. Cohesionless soils can generally be simu-\nlated with a triangular friction distribution with about A, cross-sectional area of cushion (in.2),\n40% in side friction and 60% of the total resistance\nat the point. The actual dis:ributions used will, of EC = modulus of elasticity of cushion (psi),\ncourse, depend on the properties of the soils, pile length, t, = initial uncompressed thickness of\ntype, etc., and should be studied for each case. It is cushion (in.),\nimportant to note, however, that the soil distribution\nwill affect the magnitude of the driving stresses. This t = time (sec),\nis particularly true for the reflected tensile stresses. In -\nA - cross-sectional area of pile (in.2),\nmost investigations for driving stresses, it is best to vary\nthe distribution over the expected range and choose the E = modulus of elasticity of pile (psi),\nmost conservative result. Reflected tensile stresses are = length of pile (in.),\nhighest when the soil resistance acting at the pile point L,\nis small. Y = unit weight of pile (lb/in.3),\nPAGE TWENTY-SEVEN\nCalculations :\n\nCase I. n<p\n-KV e-nt Since n < p Equation 8.1 of Case I applies.\na, max = sin ( t V p 2 - n2)\nA .\n= VP\" n2\nL\n\n## (8-1) tan (t Vp\" n2)\n\nwhere t is found from the expression\n\n## tan (t d p\" nn\") =\n\nV p2 - n2\nn so t dp2- n2 = 62.2\" or 1.085 radians\nt = .00255 sec\nUsing Equation 8.1\n-KV e-llt\na, max = sin ( t Vp' - n2)\nL 2 A VpLn2\nCase III. n>p 3 X 106 X 167 e-244 x ,00255\n- (sin 62.2\")\nKV e-nt 200 X 425\nuomax = - y s i n h (t V n\" p2 )\nA Vn2 -p- a, max = 2920 psi\n(8.3)\nwhere t is found from the expression Using these equations, Tables 8.1 and 8.2 were\ndeveloped to illustrate the effect of ram weight and\nV n 2 - p2 velocity on driving stresses. Table 8.1 shows the varia-\ntanh ( t V n 2 - p2) =\nn tion of the driving stress (compressive) with the ram\nweight and ram velocity. It can be seen that the stress\nEquations (8.1), (8.2), or (8.3) can be used to magnitude also increases with ram weight, however,\ndetermine the maximum compressive stress at the pile this is usually not of serious consequence. Table 8.2\nhead. For most practical pile problems n will be less shows the variation of driving stress (compression)\nthan p and Equation (8.1) will be used. However, this with ram weight and ram driving energy. At a constant\nis not always the case. For a given pile these equations driving energy the driving stress decreases as the ram\ncan be used twdetermine a desirable combination of ram weight increases. Therefore, it is better to obtain driving\nweight W, ram velocity V, and cushion stiffness K so energy with a heavy ram and short stroke than use a\nas not to exceed a given allowable compressive stress light ram and large stroke.\n3. When the top of the pile is not perpendicular\nT o illustrate the use of the equations consider the to the longitudinal axis of the pile, the ram impacting\nfollowing situation. force will be eccentric and may cause very high stress\nconcentrations.\nGiven :\nConcrete Pile 4. If the reinforcing steel in a concrete pile is not\ncut flush with the end of the pile, high stress concen-\nI&, = 65 ft trations may result in the concrete adjacent to the rein-\nA = 200 in.2 forcing. The ram impact force may be transmitted to\ny = 0.0868 lb/in.3 (150 lb/ft3) the concrete through the projecting reinforcing steel.\nE = 5.00 x lo6 psi 5. Lack of adequate spiral reinforcing at the head\nof a concrete pile and also at the pile point may lead\nGreen oak cushion, grain horizontal\nA, = 200 in.2\nE, = 45,000 psi (for properties of wood see Chap- TABLE 8.1. VARIATION OF DRIVING STRESS WITH\nter IV) RAM WEIGHT AND VELOCITY\nt, = 3.0 in. Result from Equation 8.1 for 65 f t long concrete\npile, 200 in.' area, and 3 in. wood cushion. Stress-\nes shown are maximum compression a t pile head.\nE, = 45,000 psi.\n- - - - -\n\n## Steel ram Ram Weight Ram Velocitv. ft/sec-Stroke. ft\n\nW = 5000 lb\nh = 3 6 in. 2,000 1,790 psi 2,200 ~ s i2,540 psi 2,840 psi\n5,000 2,380 psi 2,920 psi 3,380 psi 3,780 psi\nV = ~ 2 g h= 167 in./sec 10,000 2,830 psi 3,470 psi 4,000 psi 4,480 psi\ng = 386 in./sec2 20,000 3,250 psi 3,980 psi 4,600 psi 5,150 psi\n\nPAGE TWENTY-EIGHT\nTABLE 8.2. VARIATION OF DRIVING STRESS WITH ion, it will also stay in contact for a longer period of\nRAM WEIGHT AND RAM ENERGY time than when it strikes a thin hard cushion. For Case\nResults from Equation 8.1 for 65 f t long concrete\npile, 200 in.' area, and 3 in. wood cushion. Stress- I (when n < p which is typical for most practical con-\nes shown are maximum compression a t pile head. crete pile conditions) the length of the stress wave can\nE, = 45,000 psi. be calculated by the equation which follows.\nRam Weight Driving Energy L, = ct,\nlb f t - lb or\n20,000 40,000\n2,000 4,010 psi 5,680' psi\n5,000 3,380 psi 4,780 psi where L, = length of stress wave (in.) and\n10,000 2,830 psi 4,000 psi\n20,000 2,290 psi 3,250 psi t, = time of contact of ram (sec).\nFigure 8.5(b) shows the compressive stress wave\nto spalling or splitting. In prestressed concrete piles building up while the ram is in contact with the cushion.\nanchorage of the strands is being developed in these After the ram rebounds clear of the cushion, the com-\nareas, and transverse tensile stresses are present. If no pressive stress wave is completely formed and travels\nspiral reinforcing is used, the pile head may zpall or down the length of the pile as shown by Figure 8.5 (c) .\nsplit on impact of the ram. When the compressive stress wave reaches the point of\nthe pile, it will be reflected back up the pile in some\n6. Fatigue of the pile material can be caused by a manner depending on the soil resistance. If the point of\nlarge number of blo,ws at a very high stress level. the pile is experiencing 1it:le or no resistance from the\n7. If the top edges and corners of a concrete pile soil, it will be reflected back up the pile as a tensile\nare not chamfered the edges or corners are likely to spa11 stress wave as shown in Figure 8.6(a). If the point of\non impact of the ram. the pile is completely free, the reflected tensile wave will\nbe of the same magnitude and length as the initial com-\nYielding of steel or spalling of concrete at the poin; pressive wave. As shown in Figure 8.6(a) these two\nof the pile can be caused by extremely hard driving\nwaves may overlap each other. The net stress at a par-\nresistance at the point. This type resistance may be ticular point on the pile at a par:icular time will be the\nencountered when founding the pile point on bed rock. algebraic sum of the initial compressive ( - ) stress\nCompressive stress under such driving conditions can\nbe twice the magnitude of that produced at the head of\n+\nwave and reflected tensile ( ) stress wave. Whether\nthe pile by the hammer impact (see Figure 8.2).\nTension. Transverse cracking of a concrete pile\ndue to a reflected tensile stress wave is a complex phe-\nnomenon usually occurring in long piles (50 ft or over).\nI t may occur in the upper end, midlength, or lower end\nof the pile. It can occur when driving in a very soft\nsoil or when the driving resistance is extremely hard or\nrigid at the point such as in bearing on solid rock.\nWhen a pile driver ram strikes the head of a pile\nor the cushion on top, a compressive stress is produced\nat the head of the pile. This compressive stress travels\ndown the pile at a velocity\n\nwhere\nc = velocity of the stress wave through the pile\nmaterial in in./sec,\nE = modulus of elasticity of the pile material in\npsi, and\np = mass density of the pile material in lb-\nse~~/in.~\nThe intensity of the stress wave (a,, max.) can be deter-\nmined by Equations 8.1, 8.2, or 8.3 and depends on the\nweight of the ram, velocity of the ram, stiffness of the\ncushion, and stiffness of the pile. Since in a given\nconcrete pile the stress wave tradels at a constant veiocity\n(about 13,000 to 15,000 ft/sec) the length of the stress\nwave (L,) will depend on the length of time (t,) the\nram is in contact with the cushion or pile head. A\nCOMPRESSION COMPRESSIW\nheavy ram will stay in contact with the cushion or pile\nhead for a longer time than a light ram, thus producing figure 8.5. Idealized stress wave produced when r a n\na longer stress wave. If a ram strikes a thick soft cush- strikes cushion at head of concrete pile.\nPAGE T W E N N - N I N E\npendix A ) and piles with a free point. These values are\nconservative since material damping of the pile and soil\nresistance will tend to reduce them.\nIf the point soil resistance is hard or very firm, the\ninitial compressive stress wave traveling down the pile\nwill be reflected back up the pile also as a compressive\nstress wave, as shown in Figure 8.6(b). If the point of\nthe pile is fixed from movement, the reflected compres-\nsive stress wave will be on the same magnitude and\nlength as the initial compressive stress wave. As shown\nin Figure 8.6(b) these two stress waves may overlap\neach other at certain points. The net compressive stress\nat a particular point at a particular time will be the\nalgebraic sum of the initial compressive ( - ) stress wave\nand the reflected compressive (- ) stress wave. (Note\nthat under these conditions the maximum compressive\nstress at the pile point can be twice that at\nthe pile head by ram impact.) Tensile stress will not\noccur here until the compressive stress wave is reflected\nfrom the free head of the pile back down the pile as a\ntensile stress wave (similar to the reflection shown at\nthe free point in Figure 8.6(a) ). It is possible for\ncritical tensile stress to occur near the pile head in this\ncase; however, damping characteristics of the surround-\ning soil may reduce the magnitude of this reflected\ntensile stress wave by this time. Such failures have\noccurred, however.\nFigure 8.7 shows the reflection of the initial com-\npressive ( - ) stress wave from the point of a relatively\ntu -u -0 - u short pile. If the pile is short compared to the length\nTENSION COMPRESSION COMPRESSION of the stress wave (L,) critical tensile stresses are not\nPOINT FREE POINT FIXED likely to occur. In Figure 8.7(a) the reflected tensile\n(A) (B)\n+\n( ) stress wave overlaps the initial compressive (- )\nstress wave coming down the pile. Since the net stress\nFigure 8.6. Reflection of stress wave on a long pile. at any point is the algebraic sum of the two, they tend\nto cancel each other and critical tension is not likely\nto occur. A similar phenomenon will occur when the\nreflected compressive ( -) stress wave from the point\nor not the pile will ever experience critical tensile stresses is likely to find the ram still in contact with the pile head\nwill depend on the pile length ( L ) relative to the length when it arrives there. In such a case, little or no re-\nof the stress wave (L,) and on material damping. If flected tensile stress wave will occur. In Figure 8.7(b)\nt h e pile is long compared to the length of the stress wave, the initial compressive ( - ) stress wave is being reflected\ncritical tensile stresses may occur at certain points.\nWhen a heavy ram strikes a thick soft cushion, the stress\nwave may be around 150 ft in length. When a light\nram strikes a thin hard cushion it may be only 50 or\n60 ft in length.\nThe results of a theoretical study on ideal piles\nwith the point free of soil resistance has shown that the\nmaximum reflected tensile stress ( a t rnax.) can be com-\n.puted approximately by Equations 8.5 and 8.6 given\nbelow.\ncrt max. = a. max. (8.5)\nwhen L/& 5 2\n8 a, max.\nand crt max. =\n(I-rg/LD)\nwhen L,/L, 12 to -u -u -u\nTENSION COMPRESSION COMPRESSION\nFigure 8.8 shows in dimensionless parameters how POINT FREE POINT FIXED\nat max. is affected by cr, rnax., the length of the stress (A (B\nwave L,, and the length of the pile b. The data points\nshown were computed using stress wave theory (Ap- Figure 8.7. Reflection of stress wave along a short pile.\nP A G E THIRTY\nfrom the fixed point also as a compressive (-) stress\nwave. In this case also, little or no reflected tensile 10 ---------->--\nstress will occur.\n' 0 40'PILE\nP:\nThe cases illustrated by Figures 8.6 and 8.7 are high- A,\nX A 65'PILE \\a\nly idealized and simplified, but they skould indicate some fl 90mPILE\n(TT MAX\nof the basic factors which can cause tensile stress failures b\"\nA, ,D I L ~ I L ~ ) ~\n\n## in concrete piles. In summary, tensile cracking of con- 5 ';r O5 A\\\\ o\n\nCrete piles can be caused by the following:\nb+\nI\nA\\ .\nA ' A\n0\n\n0\n1. When insufficient cushioning material is used * a\n' .,\n---\nbetween the pile driver's steel helmet or cap and the ._\n\n## concrete pile, a stress wave of high magnitude and of o\n\n0 2 3 4\nshort length is produced, both characteristics being L s / L ~\nundesirable.\n2. When a pile is struck by a ram at a very high Figure 8.8. E f f e c t o f ratio o f stress wame length o n\nvelocity, or from a very high drop, a stress wave of tensile stress for Pile with point free.\nhigh magnitude is produced. The stress is proportional\nto the ram velocity.\n3. When the tensile sbren@h of the concrete pile every pile. If driving is extremely hard, the cushion\nis too low to resist a reflected tensile stress, severe crack- may have to be replaced several times during driving of\ning can occur. a single pile. Use of an adequate cushion is usually a\nvery economical means of controlling driving stresses.\n4. When little or no soil resistance at the point of\nlong piles is present during driving, critical tensile stress- 2. Driving stresses can be reduced by using a\nes may occur in the lower half or near rnid-length of heavy ram with a low impact velocity (short stroke) to\nthe pile. obtain the desired driving energy rather than a light\nram with a high impact velocity (large stroke). Driving\n5. When hard driving resistance is encountered at stresses are proportional to he ram impact velocity.\nthe point of long piles, critical tensile stresses may occur maximum compressive stress can be determined\nin the 'PPer -of 'he pile when the tensile stress is approximately by Equations (8.1), (8.2), or (8.3).\n3. Reduce the ram velocity or stroke during early\nTorsion. Or transverse cracking of concrete\ndriving when light soil resistance is encountered. Antici-\npiles can be caused by a combination of torsion and pate soft driving or at the first sign of easy driving\nreflected tensile stress. Diagonal tensile stress resulting reduce the ram velocity or stroke to avoid critical tensile\nfrom a twisting moment applied to the pile can by itself stresses. This is very effective when driving long con-\ncause pile failure. However, if reflected tensile stresses crete piles through very soft soil layers. when the point\noccur during driving and they combine with diagonal of the pile is free of resistance, the maximum tensile\ntensile stress due to torsion the situation can become stress can be determined approximately by using E ~ ~ ~ -\neven more critical. Torsion on the pile may be caused- tions (8.5) or (8.6).\nby the following:\n1. The helmet or pile cap fitting too tightly on the 4. If pre-drilling or jetting is permitted in placing\npile, preventing it from rotating slightly due to soil ac- concrete piles, ensure that the pile point is well seated\ntion on the embedded portion of the pile. with reasonable soil resistance at the point before full\ndriving energy is used. Driving and jetting of concrete\n2. Excessive restraint of the pile in the leads and piles should not be done simultaneously.\n5. Ensure that the pile driving helmet or cap fits\n8.8 Summary of Fundamental Driving loosely around ~ i l top\ne so that the pile may rotate slightly\nStress Considerations without binding within the driving head to prevent\ntorsional stress.\nFrom the preceding discussion some very basic\nand fundamental considerations have been revealed. 6. Ensure that the pile is straight and not cambered.\nHigh flexural stresses may result during driving of a\nThese fundamentals for good design and driving crooked pile.\npractices for piles and particularly for concrete piles\ncan be summarized as follows: 7. Ensure that the top of the pile is square or\nperpendicular to the longitudinal axis of the pile.\n1. Use adequate cushioning material between the\npile driver's ram and the pile head. For concrete piles 8. Cut ends of prestressing or reinforcing steel in\nthree or four inches of wood cushioning material concrete piles flush with the end of the pile head to\n(qreen oak, gum, pine or fir plywood, etc.) may be prevent their direct loading by the ram sthke.\nadequate for short (50 ft or less) piles with reasonably 9. Use adequate spiral reinforcing at the head and\ngood point soil resistances. Six to eight inches or more tip concrete piles to reduce tendency of pile to split\nof wood cushioning material may be required when or spall.\ndriving longer concrete piles in very soft soil. The\n10. Use adequate amount of prestress in re stressed\nwood cushioning material should be placed on top of\nthe pile with the grain horizontal and inspected to see\nconcrete piles or reinforcement in ordinary precast con-\n+hat it is in good condition. When it begins to become crete piles to resist reflected tensile stresses.\nhighly compressed, charred or burned, it should be re- 11. Chamfer top and bottom edges and comers of\nplaced. Some specifications require a new cushion on concrete ~ i l e sto reduce tendency of concrete to spaU.\nP A G E THIRTY-ONE\nCHAPTER IX\nUse of the Wave Equation for Parameter Studies\n9.1 Introduction (3) The soil\nThe wave equation can be used effectively to evalu- a. soil quake at the point.\nate the effects of the numerous parameters which affect\nb. soil quake in side friction.\nthe behavior of a pile during driving. For exam-\nple: the determination of the optimum pile driver to c. damping constant of the soil at the point.\ndrive a given pile to a specified soil resistance, the\ndetermination of the pile stiffness which will yield the d. damping constant of the soil in friction.\nmost efficient use of a specified pile hammer and cushion e. distribution of point and side frictional\nassembly, the determination of the optimum cushion resistance.\nstiffness to make the most efficient utilization of a speci-\nfied pile hammer and driving assembly to drive a spe-\ncific pile, and to determine the effects of various distri- 9.3 Examples of Parameter Studies\nbutions of soil side and point resistance on the pile bear-\ning capacity, driving stresses, and penetration per blow. The most notable parameter study which has been\nreported to date is that presented by H i r ~ c h . ~ . lIn that\nreport, the results of 2,106 problems are presented\n9.2 Significant Parameters graphically. This study was oriented toward provid-\ning information on the effects of ram weight and energy,\nThe parameters which are known to significantly stiffness of cushion blocks, length of pile, soil resistance,\naffect the behavior of a pile during driving are as and distribution of soil resistance on the driving be-\nfollows : havior of representative square concrete piles. Figures\n(1) The pile driving hammer 9.1 and 9.2 show representative curves from this study.\nThe results of this study have played a very significant\na. stiffness and weight of the pile driver's part in formulating recommended driving practices for\nram. prestressed concrete\nb. the energy of the falling ram which is Parameter studies of this type have been used by\ndependent upon the ram weight, the effec- others. McClelland, Focht, and E m r i ~ h ~have . ~ used\ntive drop and the mechanical efficiency of the wave equation to investigate the characteristics of\nthe hammer. available pile hammers for obtaining pile penetrations\nc. in the case of a diesel hammer, the weight sufficient to support the heavy loads required in off-\nof the anvil and the impulse of the explo- shore construction. The parameters varied in this study\nsive force. were the pile length above the mud line, pile penetration,\nand the ratio of the soil resistance at the pile point to the\nd. the stiffness of the capblock, which is de- total soil resistance, (see Figure 9.3 ( a ) ) . The results of\npendent upon its mechanical properties, this study enabled the authors to determine the pile\nthickness, cross sectional area, and me- driving limit versus the design load capacity as shown in\nchanical conditioning effects caused by Figure 9.4 ( a ) and ( b ) . Figure 9.3 (b) shows the re-\nrepeated blows of the hammer. sults of one study to determine the effects of varying\nthe unembedded portion of a pile whose total length was\ne. the weight of the pile helmet and the stiff-\nheld constant. Fisure 9.3 (c) is for the same pile, but\nness of the cushion between the helmet and with the unembedded length held constant and the em-\nthe pile. In the case of steel piles the bedded length varied. Figure 9.3 (d) gives the results\ncushion is usually omitted. when the ratio of point soil resistance to total resistance\nf. the coefficient of restitution of the cap- is varied.\nblock and cushion influence the shape of\nthe wave induced in the pile and hence In Research Report 33-109.4 the writers used the\naffects the magnitude of the stresses which wave equation to determine the soil damping values for\nare generated. various soils encountered in field tests. In this particu-\nlar parameter study the pile, hammer-soil system was\n(2) The pile held constant and the soil damping values were varied.\nBy generating an ultimate soil resistance, Ru (total)\na. the length of the pile. versus blows/in. curve the appropriate soil damping\nb. the stiffness of the pile which is a function properties could be determined by comparing the com-\nof its cross sectional area and the modulus puter generated solution with the measured data taken\nof elasticity of the pile material. from a full-scale field test pile (see Figure 9.5). This\nstudy yielded representative values of the soil damping\nc. the weight of the pile, specifically the dis- constants for the soil at the point of the pile and the\ntribution of the weight. soil in side friction.\nd. the existence of physical joints in the pile It is not necessary that all parameters for a particu-\nwhich cannot transmit tension. lar pile installation be known. For example, several\nPAGE THIRTY-TWO\n'PAGE THIRTY-THREE\nP A G E THIRTY-FOUR\nASSUMED CON~I~IONS 6 0.d k,.. i o M 5\nHAMMER EFFICIENCY :8 0 %\nALUMINUM -MICARTA CUSHION\nBLOCK, e :0 . 6 0\nVISCOUS DAMPING s a c / f t :\nSIDE, J' = o . o ~ REQUIRED :\nEND, J =0.15 DESIGN\nCAPACITY '\nL2 = 290'\nW\n0 I\" (QUAKE) REQUIRED\n4 8 \" DIAM.\n0 20 40 60 80\nR p = END RESISTANCE BLOWS PER INCH\nIRu = TOTAL RESISTANCE) '0 20 40 60 BO\nBLWS PER INCH (A (6)\n(A)\n(8)\nFigure 9.4. Evaluation of 0-20 hcmmer (60,000 ft-16)\nRp /R\" = 5% 20% 75% for driving to develop uLtima;te capacity of 2000\ntons: ( A ) summary of wave equation analysis (Fig.\nV)\nZ 9.3) estcllblishing approximate p& driving limit, R,\nLl = 320' LI :3 2 0 , ( m a x ) ; ( B ) comparison of R,, (max) with required\nRp /R\" = 5% L2 :z oo design capacity (from Ref. 9.3).\n48\"DIAM 4 8 \" DIAM\n\n0\n0\n0 - 2 0 HAMMER\n\n20 40 60\n1\n80\n0\n0 - 2 0 HAMMER\n\n0 20 40 €0 80\nBLOWS PER INCH BLOWS PER INCH\n(C (D)\n\nFigure 9.3. Computer analysis of pik hammer effective- problems can be solved in which the unknown parameter\nness i n overcoming soil resistance, R,,, when driving pile is varied between the upper and lower limits. These\nunder varying conditions : ( A ) computer inpa? repre- limits can usually be established with a reasonable\nsenting conditions of problem; ( B ) variations i n pile amount of engineering judgement. Parameter studies\nlength above ground; ( C ) vcriu.tions i n pile penetra- of this type were conducted by the in studies\ntion; ( D ) variations in distribution of soil resistance, of the effect of ram elasticity and in the correlation and\nR,, (from Ref. 9.3). analysis of the Michigan pile data.\n\n1000 -\n\n\"\ncn\n800 - J(p)=o\nd\n0\nP\n\na\nY m-\nn\nJ ( ~ ) =0.1\nz J(p)=0.2 &\nA\n\nJ(P)= 0.3\n\n-\n0\nI-\n\nI\nI\nI\nI\n0 I\nA 1~2 1'6 d0 4 2's 3!2 J6\n\nBLOWS / I N C H\nFigure 9.5. Blom/inch us. R, (to&) fo~r Arkansas load test pile 4.\nPAGE THIRTY-FIVE\nCHAPTER X\nSummary and Conclusions\nThe numerical computer solution of the one dimen- equation has been compared with the results of thousands\nsional wave equation can be used with reasonable confi- of actual field tests performed throughout the country.\ndence for the analysis of pile driving problems. The Among the more significant were the comparisons with\nwave equation can be used to predict impact stresses in the Michigan pile study which dealt almost exclusively\na pile during driving and can also be used to estimate with extremely long, slender steel piles, a wide variety\nthe static soil resistance on a pile at the time of driving of prestressed concrete piles driven in the Gulf Coast\nfrom driving records. area for the Texas Highway Depar~ment. Extensive\ncorrelation and research has and is being conducted by\nBy using this method of analysis, the effects of sig- many contractors, petroleum companies, and others in-\nnificant parameters such as type and size of pile driving terested in the economical design of pile foundations.\nhammer, driving assemblies (capblock, helmet, cushion\nblock, etc.), type and size of pile, and soil condition can 4. The driving accessories significantly affect the\nbe evaluated during the foundation design stage. From piling behavior. For this reason, their selection should\nsuch an analysis appropriate piles and driving equipment be carefully considered and analyzed whenever possible.\ncan be selected to correct or avoid expensive and time\nconsuming construction problems such as excessive driv- 5. The effect of explosive pressure in diesel ham-\ning stresses or pile breakage and inadequate equipment mers varies greatly depending on the condition and\nto achieve desired penetration or bearing capacity. characteristics of the hammer, anvil, helmet, cushion,\nA thorough discussion of the significant parameters pile, and soil resistance, especially regarding the in-\ncreased permanent set per blow claimed by the manu-\ninvolved in pile driving has been presented in this report. facturer. In general, when the driving resistance is large\nSome of the significant conclusions are as follows: (which is usually the case near the end of driving) the\n1. The elasticity of the ram was found to have a explosive pressure does not have a large effect on the\nnegligible effect on the solution in the case of steam, pile penetration per blow.\ndrop, and other hammers in which steel on steel impact\nbetween the ram and anvil is not present. However, in 6. Three methods were used to determine cushion\nthe case of diesel hammers, steel on steel impact does properties in this report. These included actual full-\noccur, and in this case, if the elasticity of the ram is scale cushion tests dynamically loaded between a ram\ndisregarded, a conservative solution for driving stresses and pile, tests performed using a cushion test stand in\nand permanent set results. When the elasticity of the which a ram was dropped on the cushion specimen which\nram is accounted for, maximum driving stresses and had been placed on a concrete pedestal atop a large\npoint displacements may be reduced as much as 20%. concrete base embedded in the floor, and finally static\ntests. It was found that the two dynamic testing methods\n2. Comparisons with the Michigan pile study indi- used yielded almost identical results. It was also found\ncated that a relatively simple yet accurate method of that for a given material, the dynamic curves during the\ndetermining the energy output for pile driving hammers loading of the specimens were almost identical to the\ncan be used. It was determined that for the cases in- corresponding static curves. Static tests can be used to\nvestigated, a simple equation relating energy output for determine cushion stiffness, but not for the coefficient\nboth diesel and steam hammers gave accurate results. of restitution. Typical properties are presented in\nThis equation is Chapter IV.\nE = (WR) ( h ) (e) 7. It was shown in Chapter IV that the stress-strain\nwhere diagrams for the material used as cushions are not\nWR = ram weight, linearly related to compression. Instead, the curve is\nh = actual observed total ram stroke (or the use of the exact load-deformation curve for the cushion\nequivalent stroke for double acting steam is both time consuming and cumbersome, and its use\nhammers and closed end diesel hammers), is relatively impractical.\nand\n8. It was found that the load-deformation diagram\ne = efficiency of the hammer in question. of the cushion could be idealized by a straight line hav-\nThe efficiencies determined during the course of this ing a slope based on the secant modulus of elasticity of\ninvestigation were 100% for diesel hammers, 87% for the material.\ndouble acting steam hammers, and 60% for single acting 9. The dynamic coefficient of restitution for the\nsteam hammers. The writers feel that 60% was un- cushion materials studied herein were found to agree\nusually low for the single acting hammer and would generally with commonly recommended values.\nnot recommend it as a typical value. An efficiency of\n80% is believed to be more typical for the single acting 10. When the wave equation was compared with\nsteam hammer. the results of laboratory experiments, the numerical solu-\ntion to the wave equation proposed by Smith was found\n3. Comparisons between field test results and the to be extremely accurate.\nnumerical solution of the wave equation proposed by\nSmith were indeed encouraging. To date, the wave 11. The effect of internal damping in concrete and\nP A G E THIRTY-SIX\nsteel piles was found to be negligible for the cases stud- 13. The wave equation can be used to estimate soil\nied, although, if necessary, it can be accurately ac- resistance on a pile at the time of driving. Before long-\ncounted for by the wave equation. term bearing capacity can be extrapolated from this\nsoil resistance at the time of driving, however, engineers\n12. The effect of pile dimensions on ability to must consider the effect of soil \"setup\" or possible soil\ndrive the pile varied greatly. In general, it was found \"relaxation\" which is a function of time, soil type and\nthat the stiffer the pile, the greater soil resistance to condition, and size or type of pile, and other time ef-\npenetration it can overcome. fects which might be of importance.\n\nPAGE THIRTY-SEVEN\nAPPENDIX A\nDevelopment of Equations for Impact Stresses\nin a Long, Slender, Elastic Pile\nA1 Introduction u = the longitudinal displacement of a point on\nthe pile in the X-direction, and\nThe study of the behavior of piling has received\nconsiderable attention in the past, but only since 1960 t = time.\n, when Smith1 h d a p t e d the general theory of stress wave Figure A1 demonstrates the variables mentioned above.\npropagation to pile driving problems, was it possible to\naccurately determine the magnitudes of stress induced It has been shown that any function f ( x +ct),\nin the pile during driving. Smith's method utilized a or f ( x - ct) is a solution to the above differential\nhigh-speed electronic digital computer to generate the equation. Further, the general solution is given by\nsolution, and while the calculations involved are sim-\nple, it can often prove to be an expensive method of\nu = f(x + ct) + f1(x - ct)\nsdution. Therefore, it is the purpose of this Appendix From this solution, it can be shown that\nto develop a series of equations from which a solution\nto a limited number of piles can be obtained without\nthe use or expense of a computer.\nwhere\nA2 One Dimensional Wave Equation\nu = the stress in the pile.\nUnlike a number of other approaches to the prob-\nlem, wave theory does not involve a formula in the The negative sign is used to denote compressive stress.\nusual sense, but rather is based on the classical, one- Usually an elastic cushion is placed between the pile\ndimensional wave equation. driving ram and the head of the pile in order to reduce\nthe impact stresses in the pile (Figure A2). The falling\nram first strikes the cushion which in turn applies a\nforce to the head of the pile. The sum of the forces on\nthe hammer are given by\nwhere -\nc = the stress wave velocity = E/p ,\nE = the modulus of elasticity of the pile material, where\np = the mass density of the pile, M = the ram mass,\nW the ram weight,\nP = force exerted between the head of the pile\nand the cushion,\ni\nt = time, and\nz = displacement of the ram.\n\nT-\nThis equation can now be written in the form\n\nwhere\nU -\ng - acceleration due to gravity, and\nW = Mg\nConsidering the ram as being infinitely stiff, the\ndisplacement of the ram, z, and the displacement of the\nLong slender head of the pile u, defines the total compression in the\nelastic pile cushion at any time. Therefore,\nCushion compression = z - u,\nAssuming the cushion to be linearly elastic, with a spring\nconstant of K lb per in., then the cushion compression\nis given by:\nCushion compression = P/K.\nTherefore,\nX\nFigure A.I.\nP A G E THIRTY-EIGHT\nV = velocity of Ram at impact du\nSince V, is equal to -2, where V, is the velocity of\nI dt\nthe head of the pile, it is found that\nR a m (mass M, weight W )\n7\n\nz\nCushion (stiffness K ) Equation A.9 may be rewritten in the following form:\nMd2Vo\ndt2\n+ -McK\n-\nAE\ndV,\ndt\n+ KV, =\ncKMg\n-\nAE\n(A.lO)\n\n## which is the basic differential equation to be solved.\n\nA3 Boundary Conditions\nIn order to satisfy the boundary conditions, it is\nnecessary to set V, = O at time t = 0. Further, at\nt = 0 we find that\nz = v\nand\nU, =0\nFigure A.2.\nwhere V is the initial ram velocity and the dotted quanti-\nties denote differentiation with respect to time. From\nDifferentiating Equation A.3 with respect to time Equation A.3, we see that at t = 0,\nwe find\nDifferentiating this equation with respect to time, we find\n\nP =K (z - u,)\nCombining Equation A.2 and A.4 gives and\nP = K V a t t = O\nAE\nFrom Equation A.7, we note that P = -- V,, so that\nC\nL\n\n## Noting Equation A.1 ( b ) it follows that\n\nTherefore, at time t = 0,\nKVc\nwhere v, = -\nAE\nuo = the stress at the pile head, and\nIn summary, the boundary conditions at time t = 0\nu, = the displacement of the pile head. are given by Equations A . l l and A.12.\nP\nSince uoequals - - , where A is the cross-sectional\nA KVc\narea of the pile, it is seen that v, = -\nAE\n\n## A4 Solving the Basic Differential Equation\n\nDifferentiating Equation A.7 twice with respect to time The general solution of the differential Equation\ngives A.10 is obtained by combining the homogeneous solution\nVh, and the articular solution Vp.\nThe particd~arsolution to Equation A.10 is given by\n- cMg\nSubstituting Equations A.7 and A.8 into Equation Vp - -AE (A. 13)\nA.5 yields\nThe homogeneous solution to Equation A.10 is de-\n- --\nAE -duo AE d3u0 termined as follows:\nc dt ..\nVh -t 2nVh + p2V1, = 0 (A.14)\nPAGE THIRTY-NINE\nRewriting Equation A.17 using the values of Al,\nas noted above, yields\ncKV e-nt sin t v p 2 - n2\nvo =\nAE v p 2 - n2\n\n## We shall now investigate solutions for this case\n\nhaving the form\nSubstituting Equation A.18 into Equation A.6 gives the\nfinal solution for the stress at the head of the pile when\nBy substituting Equation A.15 into Equation A.lO, we the value of n is less than p.\nobtain\nm2 +\n2 n m + p 2 = 0 q =\n-KVe-nt\nsin t v\np2 - n2\nA v p 2 - n2\n\n1\nand therefore\nm = -n +_ vn2-p2 (A.16)\n+ 1- e-nt (COSt v p 2 - n2\nThree possible variations to this solution will now be\nconsidered.\n\nCASE I ( n < p)\nThe first case is where n is less than p. When n is\n+ n\n- sin t v p-\nV p 2 - n2\n2 - n2) 1 (1.19)\n\n## The homogeneous solution to Equation A.ll then\n\nbecomes\nVh = e-nt (A1 sin t v p 2 - n2 + A2 cos t v p 2 - n2)\nAnd the general solution is given by Equation A.19 gives the solution for the stress at\nthe head of the pile at all times after impact.\n\nCASE II ( n = p)\nApplying the boundary conditions noted by Equations The second case is when n is equal to p in which\nA.14 to A.17 we find case the solution of the homogeneous differential equa-\ntion (Equation A.14) assumes the form\n\n## The complete solution for this case is given by\n\nApplying the boundary conditions of Equation A.12 to\nEquation A.17 results in vo = v, + v,\nVo = -ne-nt(Al sin t v p 2 - n2 +A2 cos t v p 2 - n2) Vo = e-nt (A1 + A2 t ) + cMa\n-\nAE\n(A.21)\n+ e-nt (A1 v p 2 - n2 cos t v p 2 - n2\nSubstituting the required boundary conditions given by\n- A 2 v p 2 - n2 sin t v p 2 - n2) Equation A . l l and A.12, we find ,that\n\n## Using the boundary condition given by Equation A.12,\n\nwe determine\nC\nA1 = [KV - nMg]\nAE v p 2 - n2\n\nPAGE F O R N\nWhen t is equal to 0, we find that Substituting the required boundary conclition given by\nEquation A.12 then gives\n+ -ncMg\nAE\nA2=-+ KVc\nAE\nV, = -ne-nt (A1 sinh t v n 2 - p2 +\nA2 cosh\nA , = - KVc\nAE\nncMg\n- -\nAE\nt V n 2 - p2) +eWnt(Al v n L p2 cosh\nt v n 2 - p2 + A2 V n 2 - p2 sinh t V n 2 - p2)\nC then :\nA2 = - (KV - nMg)\nAE\nRewriting Equation A.21, using the values of A1 and\nKVc\n- - - -nA2\nAE\n+ Al v n 2 - p2\n\nvo = e-bt LI\nA2, as given above, yields\n\n+ ct\n- (KV - nMg)\nAE\nJ\nand :\n7\n\n## Rewriting Equation A.24 gives\n\nKVc e-nt\nSubstituting Equation A.22 into Equation A.6 gives v, =\nAE V=2\nsinh t \\/n2 - p2\n-t\nuo = - (KV - nMg) e-nt - -\nMg ( 1 -\nA A\n\nu,,=\n-t\n-\nA\n(KV - nW) e-nt f n sinh t VnLI p2)\n\n## where Substituting Equation A.25 into Equation A.6 gives\n\n-KV\nU, = e-nt sinh t v n 2 - p2 (A.26)\nA \\/n2 - p2\n\n## y = unit weight of pile material\n\nEquation (A.23) gives the compressive stress at the\nhead of the pile, as a function of time for the case when\nn is equal to p.\nCASE III (n > p) 'where\nThe third and final case is where n is greater than\np. For this condition, the solution of the homogeneous\ndifferential equation, given by Equation (A.14), assumes\nthe form\nn = - \" d&,\n2A\n-\nand\n\n## v,, = e-nt t V n 2 - p2 + e t V n 2 - p21\n\nor\nVh = e-nt [A1 sinh t \\/n2 - p2 Equation A.26 gives the stress at the head of the\n+ A2 cosh t v n 2 - p 2 ) ] pile as a function of time in the case where n is greater\nthan p.\nThe general solution then becomes\nv, = v, + v, A5 Maximum Compressive Stress at the\nV, = e-nt (A1 sinh t V n 2 - p2 Head of the Pile\n+ A2 cosh t V n 2 - p2) +- cMa\nAE\nTo compute the maximum compressive stress at the\npile head, Equations A.19, A.23, and A.26 are required.\nApplying the boundary conditions required by Equation Numerical studies of these equations have shown\nA . l l yields that if the last term in each equation is omitted, little\naccuracy is lost, and the expression becomes relatively\nsimple. Since it is necessary to know the time, t, at\nwhich the maximum stress occurs, Equations A.19, A.23,\nand A.26 will be differentiated with respect to time and\nset equal to 0. This in turn will allow the maximum\nPAGE FORTY-ONE\nstress to be found. The following notations are again ram velocity, V, and the required cushion stiffness, K,\nused : in order to prevent excessive stresses at the head of the\nW = the ram weight (lb) pile. In most cases, there is some minimum amount of\n-\nV = the ram impact velocity (in./sec) = v 2 g h , driving energy which must be available to drive the\nA E pile. For example, the maximum energy output avail-\nK = cushion stiffness (lb per in.) = able to a drop hammer is given by its kinetic energy\nt\" at the instant of impact. Therefore,\nt = time (seconds)\nA = the cross-sectional area of the pile (inO2) K.E. = W -\nV\"\nE = modulus of elasticity of the pile (psi) 2,a\ny = unit weight of the pile (lb per in.3) should be equal to or greater than the energy required.\ng = acceleration due to gravity (386 in. per It would appear that the most efficient way to increase\nsec2) hammer energy would be by increasing the ram velocity\nh = the free fall of the ram (in.) V. However, Equations A.27, A.28, and A.29 show that\nthe maximum compressive stress at the head of the pile\nA, = the cross-sectional area of the cushion (in.') will increase ~ r o ~ o r t i o n a l with\nl v velocitv. On the other\nI I\nE, = the modulus of elasticity of the cushion hand, to increase driving energy the maximum compres-\n(psi) sive stress at the head of the pile increases slightly\nt, = cushion thickness (in.) as W increases. It is therefore desirable (considering\ndriving stresses) to increase the ram weight, W, if the\npile driving situation requires that the driving energy be\nincreased. Once the ram weight and its velocity at im-\npact have been selected, the spring rate of the cushion\n( K ) can be varied to hold tke maximum compressive\nstress within allowable limits.\nIn order to further simplify the solutions, the fol-\nlowing approximate equations for the maximum com- A6 Length of the Stress Waue\npressive stress are presented: It is known that the magnitude of the reflected\nstresses in a pile will be a function of the length of the\nCase I (where n is less than p ) stress wave and the length of the pile. The length of\n-KV this stress wave is easily found from Equations A.19,\ne-nt sin ( t q p2 - n2)\nuo (max) = -- A.23, and A.26.\nA vp2-n (A.27)\nIf the last term is again omitted in each of these\nwhere t is given by the equation equations, little accuracy is lost and relatively simple\nexpressions are obtained for the stress at the head of the\nv p 2 - n2 pile. Omitting the last term in Equation A.19 yields\ntan ( t v p 2 - n2 =\nn\n-KV e-nt sin t v p 2 - n2\nCase 2 (where n is equal to p ) uo =\nA vp\" n2 (A.30)\nEquation A.30 is seen to equal 0 at time t equals 0 and\nu, (max) = - again at\n\n## where the value of t was given by\n\nThus, the second of these equations gives the duration\nof the impulse stress.\nNoting Equation A.l a, the stress wave velocity, c,\nCase 3 (where n is greater than p ) is found to be\n-\nuo (max) =\n-KV e-nt sinh ( t v n 2 - p2) c = 11-\nE\nA v n 2 - p2 (A.29) vP\nwhere t is found from the expression The length of the stress wave, L,, is then obtained from\n-\n. -\nv n 2 - p2\ntanh t v n L p2 =\nn\nEquations A.27, A.28, and A.29 can be used to\ndetermine the maximum compressive stress at the head\nof the pile. In most practical pile problems, n will be for n < p (A.31)\nless than p, and Equation A.27 will most often be used, y (p2 - n2)\nalthough this is not always the case. Similarly use Equations A.23 and A.26 to establish that\nFor a given pile these equations can be used to\nwhen n = p and n >\np the stress wave is infinitely long\ndetermine the proper combination of ram weight, W, L, = co\nPAGE FORTY-TWO\nAPPENDIX B\n\n## Wave Equation Computer Program Utilization Manual\n\nBl Introduction the hammer at the specified soil embedment arid soil\nresistance.\n- This appendix describes the utilization of the com-\nputer program for the application of the one-dimensional The techniques for idealization can be categorized\nwave equation to the investigation of a pile during in three groups:\ndriving. 1. the hammer and driving accessories,\nThe program can be used to obtain the following 2. the pile, and\ninformation for one blow of the pile driver's ram for\nany specified soil resistance: 3. the soil.\n1. Stresses in the pile.\nBZ Idealization of Hammers\n2. Displacement of the pile (penetration per\nblow). The program is formulated to handle drop ham-\nmers, single, double, and differential acting steam ham-\n3. Static load capacity of the pile for specified mers and diesel hammers that operate on the head of\nsoil resistance and distribution. This ca- the pile. The techniques presented in this section are\npacity is the static resistance at the time of general in scope and are presented for illustration.\ndriving and does not reflect soil set-up due Appendix B gives the idealizations and pertinent infor-\nto consolidation. mation for the most common hammers.\nThe program is valuable in that system parameters ig- Figures B1 through B3 describe the idealization for\nnored before (in pile driving formulas) can be included, the following cases:\nand their effects investigated. It makes possible an engi-\nneering evaluation of driving equipment and pile type, 1. Case I -Ram, capblock, pile cap, and pile\nrather than relying only upon experience and judgement. (Figure B1) .\nIn order t o simulate a given system, the following 2. Case I1 -Ram, capblock, pile cap, cushion, and\ninformation is essential: pile (Figure B2).\n1. Pile driver. 3. Case III-Ram, anvil, capblock, pile cap, and\npile (Figure B3).\na ) energy and efficiency of hammer,\nb ) weight and dimensions of ram,\nc ) weight and dimensions of anvil (if\nincluded),\nd ) dimensions and mechanical properties\nof capblocks, ,\ne ) weight and dimensions of pile cap 5- CAPBLOCK, K(1)\n\nhelmet,\nf ) and dimensions and mechanical prop-\nerties of cushion. 9- PILE CAP, W(2)\n\n## 2. Dimensions, weight, and mechanical prop-\n\nerties of the pile.\n3. Soil medium.\na ) embedment of pile,\n9- PILE SEGMENT, W(3)\n\n## b) distribution of frictional soil resistance Calculations for idealization\n\nover the embedded length of the pile W(1) = weight of ram, (lb)\nexpressed as a percentage of the total\nstatic soil resistance, K(1) = , stiffness of the capblock, (lblin)\n\n## c) Point soil resistance expressed as a per-\n\ncentage of the total static soil resistance, Where\n\n## d ) ultimate elastic displacement for the soil\n\non the side and point of pile,\n~(1) - cross sectional area of the capblock, (in2\n\n## E(1) = modulus of elasticity of the capblock, (psi)\n\ne) and the damping constant for the soil L(1) = thickness of the capblock,(in)\non the side and point of the pile.\nNote: See Table 4.1 for capblock properties.\nIt should be recognized that the solution obtained\nwith the program represents the results for one blow of Figure B.1. Case I-ram, capblock, and pile cap.\nPAGE FORTY-THREE\n3. Diesel hammers:\nEH = W ( 1 ) (he -C) (Q) (B.3)\nwhere\nCAPBLOCK. K ( 1 )\nhe = actual ram stroke for open-end hammers,\nPILE CAP. W(2) and the effective stroke (includes effect of\n\ne-\n>- CUSHION, K(2IC\nK(2)\nbounce chamber pressure) for closed-end\nhammers, (ft). The energy EH for the\ndirectly from the manufacturer's chart using\n1ST PILE SEGMENT, W(3)\nbounce chamber pressure),\nef = efficiency of diesel hammers is approximate-\nly 100%\nCalculations for idealization\n\n## W(1) - Weight of cam, (Ib)\n\nC = distance from bottom-dead-center ef anvil to\nexhaust ports, (ft) .\nK(1) = Stiffness of the Capblock, (lblin.)\n\nK(2)C - Stiffness of cushion. (lblin.) Work done on the pile by the diesel explosive force is\nK(2)p = Stiffness of pile spring, (lblin.) automatically accounted for by using an-explosive pres-\nsure (see Sample Problem and Table 2 ) .\nK(2) - K(2)C\nK(2)C\nK(2)\n+ K(2j)p , combined stiffness of K(2)C\nCalculations for idealization\nand K(2) in series.\nW(1) = weight of ram, (lb)\nNote: See Table 4.1 for eapblock and cushion properties.\nAE\nKc = - K ( l ) = A(1) E ( l ) , stiffness of the capblock,\nwhere\nL(1)\nA = cross-section area of cushion, in.'\n@/in.)\nWhere\nE - secant modulus of elasticity of cushion material, psi\nA ( l ) = cross sectional area of the capblock, (in2)\nL = thichess of cushion, in.\nE ( l ) = modulus of elasticity of the capblock (psi)\nFigure B.2. Case II - ram, capblock, pile cap, ond\ncushion. L(l) = thickness of the capblock, (in)\nNote: See Table 4.1 for capblock properties.\nCalculations for idealization\nB3 Ram Kinetic Energies\nW ( l ) = Weight of ram, lb)\nThe kinetic energy of the ram for specific hammer\ntypes can be calculated as follows:\n\nwhere\n1. Drop hammers and single acting steam hammers:\n\nEH\nEH = W ( 1 ) (h) ( 4\n\n(B.1) n=\nu RAM, W(1)\n\n## h = ram stroke, (ft) 2\n\n- = CAPBLOCK, K(2)\n\n## ef = hammer mechanical efficiency (usually\n\nbetween 0.75 and 0.85 for most single &a4 PILE CAP;W(3)\n\nacting hammers).\nn\n5 -\nPILE SPRING, K(3)\n\n## I v-- FIRST PILE SEGMENT. W(4)\n\nE H = h\n\nwhere\nI l+&e!!L\nPrated\n. -\nW(h)\nW(1)\nW ( 1 ) ef (B.2) Calculations f o r i d e a l i z a t i o n\n\nW(1)\n\nK(1)\n=\n\n=\nWeight of ram, ( l b . )\n\n## h = actual ram stroke., (ft)\n\n. ,\nwhere A(1) = ram c r o s s s e c t i o n a l area, ( i n . )\nPactual = actual steam pressure, (psi)\nE(1) = modulus of e l a s t i c i t y o f ram material. (psi)\nprated = manufacturers rated steam pressure, (psi)\nL(1) = l e n g t h of ram, ( i n . )\nW ( h ) = hammer housing weight, (lb)\nThis c a l c u l a t i o n assumes t h a t t h e p i l e cap and a n v i l a r e r i g i d .\nW ( l ) = ram weight, (lb)\n9 = efficiency is approximately 85% for these Figure B.3. Case Ill-ram, anvil, capblock, and pile\nhammers. cap.\nP A G E FORTY-FOUR\nK ( l ) = Stiffness of the Capblock, (lb/in.) E ( l ) = modulus of elasticity of ram material,\nK ( 2 ) c = Stiffness of cushion, (lb/in.) (psi)\nK ( 2 ) , = Stiffness of pile spring, (lb/in.) L ( 1 ) = length of ram, (in.)\nThis calculation assumes that the pile cap is rigid.\nK(2) = K ( 2 ) c K ( 2 ) p , combined stiffness of\nK ( 2 ) c + K(21, In the hammer idealization, note that the parts com-\nK ( 2 ) c and K ( 2 ) , in series. posing the pile driver are physically separated, i.e., the\nram is capable of transmitting compressive force\nNote: See Table 4.1 for capblock and cushion properties. to the anvil but not tension. The same is true of the\ninterface between the anvil and pile cap, and the pile\ncap and the head of the pile. The program contains\nwhere provisions for eliminating the capability of transmitting\ntensile forces between adjacent segments. The me-\nA = cross-sectional area of cushion, in.2 chanics of this provision are more fully explained in\nE = secant modulus of elasticity of cushion ma- the following section.\nterial, psi Tables B1 and B2 list the information needed for\nL = thickness of cushion, in. the simulation of the most common types of pile driving\nhammers.\nCalculations for idealization\nW ( l ) = Weight of ram, (lb) B4 Methods of Including Coefficient of\nRestitution in Capblock and Cushion Springs\nK ( l ) = A(1) E(l) , the stiffness of the ram,\nL(1) In the case where K ( l ) is a capblock (Cases I, 11,\n(lb/in.) and 111), and K ( 2 ) is a cushion (Case 11), it is desirable\nwhere to include the energy loss due the coefficient of restitu-\nA(1) = ram cross sectional area, (in.) tion of the particular material.\n\nHOUSING W,,\n\nRAM W ( I )\nRAM W ( I )\nCAPBLOCK K ( I CAPBLOCK K ( I )\n\nw (2) u P l L E CAP W ( 2 )\nI\n\n-CUSHION K(2)-\n\n## DROP HAMMERS DOUBLE AND DIFFERENTIAL ACTING\n\nSINGLE ACTING STEAM HAMMERS STEAM HAMMERS\n(A) (0)\n\n## TABLE 81 DROP HAMMERS AND STEAM HAMMERS\n\nTYPE\n\n8z ! !m!\nW\nW\na &\nW\n0 a\n0\na\na\n+ REPRESENTATIVE VALUES FOR PlLE NORMALLY USED IN .HIGt YAY CONS\n\nPAGE FORTY-FIVE\nI n Figure B4 the coefficient of restitution is defined\nas\n\ne = q Area BCD -\nArea ABC - d\nEnergy output\nEnergy input\n(B.5)\nI n Case I1 it is necessary to combine springs K ( 2 ) c\nand K (2), to determine the equivalent spring K (2). In w\nthis instance it is also necessary to determine the coeffi- o\nK\nI\ncient of restitution of the combined springs. The stiff- 0\nness of the spring in the restitution phase is the slope of I\n\n## the line DB in Figure B4.\n\nFB\nKDB = Ac - AD (B.6)\n\nSince,\nEnergy output = Area BCD = FB (AC - AD) /2\nA - DEFORMATION\n\nEnergy input = Area ABC = FB (AC)/2 Figure B.4. Definition of coefficient of restitution.\nFB\nez = Fn (Ac - An) -\n-\nAc - KAB\n- -\nFB (Ac) FB KDB\nThe combined restitution stiffness of K ( 2 ) c and\n(Ac - AD) K ( 2 ) , can be determined from,\nor\n(for restitution\n1\nK(2)\n- 1\nK(2)c\n+ -phase DB in\nK ( 2 ) p Figure B4)\n\n## + for actual stroke use f i e l d observotions\n\nA(l) E l l ) (may vary from 4 . 0 to 8 . 0 f t . )\n\n## r + determine f r o m bounce chamber\n\nANVIL W (2) pressure ( h e = E / W ( I ) where E = Indicated\nEnergy\n\n## PlLE CAP W (3)\n\nCUSHION K ( 3)c\n\nPlLE K( 3 ) ~\n\nW\n2\n0\n- PlLE W (4)\n\n-\nTABLE 8 . 2 DIESEL HAMMERS\n\nPAGE FORTY-SIX\nfrom Equation (A-7), where\nK(m-1) = spring stiffness for segment m,\n(lb/in. )\nA(m) = cross sectional area of segment m,\n(in.2)\nE ( m ) = modulus of elasticity of the material\nof segment m, (psi)\nL ( m ) = length of segment m, (in.)\nsince\nThe weight of each pile segment is calculated by\nW(m) = A(m) L(m) a\nwhere\na = unit weight of pile material, (lb/in.)\nIf the pile is tapered, the average value of A(m)\n235 Idealization of Piles should be used.\nThe idealization of the pile is handled by breaking The program has provisions for handling cases\nthe continuous pile into discrete segments. Each seg- where the physical construction of the pile prohibits the\nment is represented by its weight and spring repre- transmission of tensile stresses or is capable of trans-\nsenting the total segment stiffness. In Figure B5, the mitting tensile stresses only after a specified movement\nweight representing the segment is assumed to be con- of a mechanical joint (joint slack or looseness) . These\ncentrated at the end of the seapent away from the point conditions occur with certain types of pile splices. The\nof impact. This places the spring on top of the weight program provides for this eventuality by entering the\nwhose stiffnejs it represents, i.e., IC(2) is associated following :\nwith W ( 3 ) .\n1 ) If a joint ( a joint is defined as the interface\nPiles should be broken into segments not to exceed between two segments) can transmit tension,\napproximately 10 feet in lengths, but into not less than the slack or looseness is entered as SLACK (m)\nfive se,grnents. The stiffness of each pile segment spring = 0. (Refer to Figure B5)\nis calculated from\n2 ) If a joint is completely loose, no tension can be\ntransmitted and SLACK (m) should be made\na very large number, i.e., SLACK (m) =\n1000.0.\n3) If a joint is capable of moving 1.25 in. before\nRAM\ntransmitting tension, SLACK (m) = 1.25, i.e.,\nCAP BLOCK\nPILE CAP the physical value of the slack or looseness in\nCUSHION a joint is entered in inches.\nThe SLACK (m) values are always associated with\nspring K ( m ) . In Figure B5, if tension can be trans-\nSLACK ( 3 ) = 0 - mitted across the interface between segments 3 and 4,\nthe slack value would be associated with spring K ( 3 ) ,\ni.e., SLACK (3) = 0.\nThe interfaces between the various parts composing\nthe pile driver (ram, capblock, pile cap, its.) which can-\nnot transmit tension are also handled by setting the\nSLACK values equal to 1000.\n\n## B6 Explanation of Data Input Sheets\n\nData for the Pile Driving Analysis program is en-\ntered on two sheets. Page 1 contains data pertaining\nSLACK to the physical parameters of a particular pile. Page 2\nis used to vary the soil, pile driver, or cushion charac-\nteristics for the pile described on page 1. Examples of\nthe data sheets follow the explanation.\nSLACK\nPage 1\nCase No. = Any combination of up to six alpha-\nbetic or numerical characters used for\nidentifying information. These char-\nSLACK acters will identify all problems as-\n\nREAL\n*\nIDEALIZED\nsociated with the pile data entered on\nsheets 1 and 2.\nNo. of Probs. = Total number of problems listed on\nFigure B.5. Pile idealization. page 2.\nPAGE FORTY-SEVEN\n= This space may be left blank in most Option 4 = 2. Option 4 may be left\ncases as the program calculates the blank in which case i t is automatically\ncritical time interval from the param- set equal to 2.\neters of the system. The value cal- IPRINT = This is an option on the amount of\nculated is data printed out when the long form\nl/DELTA T = 2(19.698 d m ) output is used (Option 15 = 2). If\nIf, however, one desires to use a spe- Option 15 = 2, IPRINT is the print\ncific l/DELTA T, it may be entered. interval expressed as the number of\nThe problem will then compare the time intervals. As an example, if a\nentered value with the critical value print out is required every 10th time\ncalculated by the above formula and interval, 10 would be entered for\nuse the larger of the two. This is IPRINT. If Option 15 is \"1\" or \"3\",\ndone so that the user cannot inadver- leave IPRINT blank.\ntently enter a value too small and\nhence introduce instability into the NSEG 1 = NSEG 1 is the mass number of the\nnumerical process. first pile segment. If NSEG 1 is left\nP = Total number of weights including blank, NSEG 1 = 2 will be used by\nthe program.\nram of hammer, follower, and helmet,\netc. The total weight of each segment, in pounds, is\nSLACK (1) = This indicates a specified looseness\nbetween W ( l ) and W(2) in inches.\n. .\nentered in the rows marked W ( 2 ) , W ( 3 ) , . . W (24).\nThe weights, W's, are entered for 2 to P inclusive. Note\nThis is the amount of movement re-\nquired before K ( l ) will take tension. that W ( 1 ) is not entered as it will be included on page 2.\nIf there is complete tensile freedom\nof K ( l ) , then enter SLACK (1) = The spring stiffness of each seapent, in lb/in., is\n1000. Leave blank if option 3 is \"2\". entered in the rows marked K ( l ) , K ( 2 ) , . . . . K ( 2 4 ) .\nSLACK (2), The stiffnesses, K's, are entered from 1 to P - 1 inclu-\nSLACK (3) = see notes on Slack (1). sive. Spring K ( P ) is the soil spring at the pile tip and\nOption 1 = This is an option for the manual en- is calculated by the program from the soil data entered\ntry of the cross sectional area of each on Page 2.\nsegment.\n( a ) Enter \"1\" and all AREAS will If Option 1 = 2, the average area of each segment\nautomatically be set equal to 1.00. must be entered in the rows marked A ( 1 ) , A ( 2 ) , . . . .\nIn this case, draw a horizontal line A ( 2 4 ) . The units of A should be consistent with the\nthrough all AREA rows on the mid- stress units desired in the output. The basic force unit\ndle portion of page 1. If \"1\" is used,\ndo not enter areas in AREA rows. of the output is the pound. The areas, A's, are entered\n(b) Enter \"2\" if the cross sectional from 1 to P inclusive. A ( P - 1 ) and A ( P ) in most\narea of each segment is to be entered instances will be the same. Areas of segments of the\nmanually in the AREA rows. In this hammer are usually entered as A ( l ) = 1.00, etc., since\ncase enter AREAS (1) to ( P ) inclu- stress values obtained for these segments are not usually\nsive.\nof concern. If Option 1 = 1, the area row should be\nOption 2 = This is an option for the manual marked through with a solid horizontal line indicating\nentry of soil resistances.\nn o data cards are to be included.\n(a) Enter \"2\" if the soil resistances\n(expressed as a percentage of the If Option 2 = 2, the side soil resistance on each\ntotal soil resistance) are to be entered\nmanually in the RU rows. The RU seapent, expressed as a percentage of the total soil resist-\n\n## 1) inclusive. Note that (P + +\n\nvalues are entered from (1) to ( P\n1) is\nance, is entered in the rows marked R U ( 1 ) , R U ( 2 ) ,\n... R U ( 2 4 ) . The soil resistances, RU's, are entered\nthe point resistance and all others are\nside resistances. The total of all RU from 1 to P + 1 inclusive. The value of RU ( P 1)+\npercentages entered must total 1 0 0 ~ o . is the pile tip resistance. Mark out all rows when Option\n(b) Enter \"1\" if the soil resistances 2 = 1.\nare not listed in the RU rows but are\nindicated under Option 12 on page 2. If Option 3 = 2, the physical slack or looseness,\nOption 3 = This i s a n option for manual entry of expressed in inches, is _entered in each row marked\nthe SLACK values. SLACK ( l ) , SLACK ( 2 ) , .\n. . . SLACK (24).\n(a) Enter \"1\" if SLACK values from SLACK'S are entered from 1 to P - 1 inclusive. If\nSLACK (4) to SLACK (P - 1) are there is n o slack, enter 0.0; if ihere is complete loose-\nall 0.00 (indicating K(4) to K ( P - 1 ) ness, enter 1000.0. SLACK ( P ) is automatically set\ncan take tension). In this case only\nSLACK (1) to SLACK (3) are en- equal to 1000.0 since the point soil spring cannot take\ntered in row 1. Draw a horizontal tension. If Option 3 = 1, mark out all rows.\nline through all SLACK rows in the\nlower portion of page 1. In this case Note that the forms have 24 spaces for W's, K's,\ndo not enter any values in the Slack A's, RU's, and SLACK'S. The program is capable of\nrows. handling a pile with a maximum of 149 segments. Ad-\n(b) Enter \"2\" if SLACK values are\nto be entered manually. In this case, ditional cards may be added to each parameter as needed.\nSLACK (1) to SLACK (3) in row 1\nmay be left blank. Page 2\nOption 4 = This is an option on the routine used w(l) = The weight of the pile driver's ram\nto simulate the material behavior of in pounds.\nsprings K(1), K(2), and K(3). NC = The number of the spring for which\n(a) Enter \"1\" for use of Smith's K(NC) is being varied.\nroutine 3 and 4. K(NC) = The spring constant of the spring be-\n(b) Enter \"2\" for use of Texas ing varied in lbs/in. Only one spriny\nA&M's routine.4 I t is suggested that can take on variable values per case.\nA G E FORTY-EIGHT\nEFF = The efficiency of the pile hammer. J SIDE = Damping constant for the soii on the\nside of the pile.\nENERGY = Kinetic energy of the falling ram\ncalculated by Equation B-1, B-2, or FEXP = The diesel explosive force (in pounds)\nB-3. which acts on the ram and anvil of\nERES (1) = The coefficient of restitution of a diesel hammer. In the case where\nspring K ( l ) no explosive force exists, a s with drpp\nhammers or steam hammers, leave\nERES (2) = The coefficient of restitution of FEXP blank.\nspring K(2) Option 11 = This option provides for single or\nERES ( 3 ) = The\ncoefficient of restitution of multiple calculations.\nspring K(3) (a) Enter \"I\" if multiple calcula-\nRU (TOTAL) = This space should be used only when tions for RU(T0TAL) VS BLOW/\nOption 11 = 2. In this case RU IN., data are desired. The computer\n(TOTAL) is the desired ultimate pile will assign suitable values of RU\nresistance in pounds. When Option (TOTAL). Leave RU(T0TAL) space\n11 = 1, leave this entry blank. on page 2 blank.\n% RU (TOTAL (b) Enter \"2\" if single calculation is\nAT POINT = The percentage of the total pile soil to be made with RU(T0TAL) value\nresistance, RU(T0TAL) , under the entered on page 2.\npoint of the pile. This value is en- Option 12 = This option is used for designation\ntered a s a percentage.\nof the distribution of side friction on\nMO = If Option 12 is \"1\" or \"2\", enter the the pile.\nnumber of the first pile segment act- ( a ) Enter \"1\" for a uniform distri-\ned upon by soil resistance. This space bution of side friction from segment\nmay be left blank if Option 12 = 3, MO to P.\ni.e., RU's are read in on page 1.\n(b) Enter \"2\" for a triangular dis-\nQ POINT = Quake of the soil a t the point. Nor- tribution of side friction from seg-\nmally \"0.10\" is used. ment MO to P.\nQ SIDE = Quake of the soil on the side of the (c) Enter \"3\" if Option 2 = 2, i.3.,\npile. Normally \"0.10\" i s used. RU values are entered on page 1.\nJ POINT = Damping constant for the soil a t the Option 13 = This option provides for computer\npoint. plotted curves using the data gen-\n\n. .. .. . . .. .. . . .\n\n## NOTES : ONE OR MORE PROBLEMS MUST BE LISTED ON PAGE 2\n\nK's A N D SLACK'S I TO P-l INCL;\nW'S AND A R E A S I TO P INCL.; RU'S I TO P+I INCL. (P+I IS % RU UNDER POINT OF PILE.)\n\nPAGE FORTY-N IN E\nerated for RU(T0TAL) VS BLOW/ B7 Comments on Data Input\nIN. (Option 11 = 1).\n(a) Enter \"1\" for computer plot of On page 2 of the input forms, provisions are made\ndata. If no plot is desired, leave for varying the stiffness of any spring, K ( l ) through\nblank. K ( P - l ) , in the hammer or pile idealization. This is\nOption 14 = This is used to include or exclude accomplished by entering the number of the spring to\ngravity in the calculations.\n(a) Enter \"1\" if the forces of gravity be changed in the NC column and then the stiffness of\nare to be included in the calculations. spring K(NC) in the K(NC) column. As soon as this\n(b) Enter \"2\" if the forces of gravity problem is completed, the spring stiffnesses, K(NC) will\nare to be excluded from the calcula-\ntion. This alternate in effect excludes be reset automatically to the value on page 1 of the\nthe weight of the pile from the calcu- input forms.\nlations. It is used when the pile driv-\ner is in a horizontal position or for The program is capable of handling pile idealiza-\nan extreme batter. tions with a maximum of 149 segments. There is no\nOption 15 = This option provides for versatility limit on the number of problems that can be run for\nin the outpnt format. each case.\n(a) Enter \"1\" for a normal data\nprintout.\n(b) Enter \"2\" for extra detail in Sample Problem\nprintout. This alternate gives perti- Consider the pile shown in Figure B-6.\nnent stresses, deformations, velocities,\netc., at the print interval, specified Pile: 16 in. square prestressed concrete pile, 26 ft\nas IPRINT on page 1. in length. The modulus of the concrete is 7.82 X lo6\n(c) Enter '13\" for short output. This psi and its unit weight is 154 lb/ft3. The pile is as-\nalternate gives only a tabular sum-\nmary of BLOW/IN. VS RU(T0TAL). sumed to be embedded for its full length.\nOption 15 = 3 should be used only Pile hammer: Hypothetical diesel hammer with\nwhen Option 11 = 2. 4850 lb ram with an input ram kinetic energy of 39,800\nSPECIAL NOTE Where anything listed for Prob- ft lb. The explosive force by the diesel fuel\nlem 1 is to be repeated for Problem 2, 3, etc., draw an is 158,700 lb. The stiffness of the ram is given as 42.25\narrow down through the last problem to indicate repeti- X lo6 lb/in. The anvil is assumed rigid and weighs\ntion. 1150 Ib. The capblock stiffness is 24.5 X lo6 lb/in.\n\n3 J , ,, 0,\n\n4 d 2, 4, .\nI 8, an .\n\n5 - -\n\n6 J.\n7\n\n10 I\nI I\n\n1 2 3 . 4 ,I\n\n1 3\n\n1 4 3 .\nI \" tl I 1\n1 5 J 4, I\n. I\n. A A 1\n\n1 6\n\n17 1. 1 II n <%\n\n1 8 J.. ,, dm 1 , 0,\n\n19 A II 4. 1 1 ,,\n2 0 I . 1 1 .\nNOTE . IF OPTION ell = I, R U (TOTAL) NOT REQUIRED 07\n\n0 Y\n5\ni: > o\na\\$,5+ z\n0704\nO Y A C C\nZ ( L L U L\n\nPAGE FIFTY\nwhere\nA(3), = 254 in.\"\nE ( 3 ) , = 7.32 X lo6 psi\nL(3), = 39 in.\ntherefore\n\n## ( b ) Cushion: Spring K ( 3 ) in Figure B6 (b)\n\nrepresents the combined stiffness of\nthe cushion and first pile segment.\nFRICTIONAL In Problem 1 and 3\nRESISTANCE\n\nwhere\nA ( 3 ) c = 254 in.\"\nE ( 3 ) c = 1.00 X lo6 psi\nL ( 3 ) c = 6.25 in.\nPOINT RESISTA\nthen\n(a) ACTUAL P I L E ~ (b) IDEALIZED P I L E\n\n## Figure B.6. Sample problem.\n\nThe combined stiffness of K (3) 0 and K ( 3 ) , is\nIn order to illustrate the utilization of the input\ndata sheets and explain the output data sheets, four prob-\nlems are considered.\nK ( 3 ) = 22.6 X lo6 lb/in.\nProblem 1 and Problem 2 are concerned with the\ndriving effects produced by two different cushions. The The coefficient of restitution for the combined\nobject of these two cases is to determine the dynamic- springs is assumed to be 0.50.\nstatic resistance curves (RU(T0TAL) VS BLOWS/IN.) For Problem 2 and 4 similar calculation yields\nfor one blow of the hammer. In Problem 1, the cushion\nis assumed to have a cross sectional area equal to that K(3) 31.3 X lo6 Ib/in.\nof the pile, is 634 in. thick and has a modulus of elas- The output data sheets are completed as follows:\nticity of 1.0 X lo6 psi. In Problem 2 the cushion area\nand properties are the same as in Problem 1, but the Page 1 (Same for all 4 problems)\nthickness is 3% in. In Problem 1 and 2 the soil side No. of Problems = 4, there are 4 problems to be solved\nfriction is assumed to have a triangular distribution with on page 2.\n10% point resistance. The soil constants are: l/DELTA T = 0.0, since the program will calculate the\ncorrect value.\n(a) Q Q' = 0.10 in. P = 11, there are 11 weights ( 3 for the\n( b ) J = 0.15 sec./ft. hammer and 8 for the pile).\nSLACK'S = all set equal to 1000 since there is com-\n(c) J' = 0.05 sec./ft. plete looseness between the ram, anvil,\ncapblock, pile cap, cushion, and pile\nProblems 3 and 4 illustrate the use of program to head.\ninvestigate the penetration of a pile to 200 tons of static OPTION 1 = 2, all areas are entered manually in\nsoil resistance produced by one blow of the hammer. In AREA rows.\nProblem 3 the soil resistance is distributed uniformly OPTION 2 = 1, since OPTION 12 is used to describe\nalong the side with 10% at the point. The cushion is the soil distribution.\nthe same as in Case 1. In Problem 4 the soil has a tri- OPTION 3 = 1, all pile segments are connected,\nangular distribution along the side with 10% soil resist- hence SLACK (4) to SLACK (10) =\n0.0.\nance (same as Problem 2 ) . The cushion is the same OPTION 4 = left blank since it is desired to use the\nas in Problem 2. Problem 4 will also illustrate the use A&M routine.\nof the output option (OPTION 15). IPRINT = 10, in Problem 4, OPTION 15 = 2, i t is\ndesired to print output every 10 itera-\nThe following calculations illustrate the computa- tions.\ntions for the hammer and pile idealization. NSEGl = 4, the first pile segment, see Figure\nB6 (b).\n( a ) Pile: The ~ i l eis broken into eight equal W'S = enter the weight of each element in lb.\nlength segments of 39 in. The spring Note that W ( l ) is blank since it will\nstiffness for each segment is, be entered on page 2.\nPAGE FIFTY-ONE\nK'S = enter all spring stiffnesses f o r the pile FEXP = 158,700, lb. the diesel explosive force.\nsystem considered t o b e basic, i.e., the OPTION 11 = 1, for program generated RU(T0TAL)\nprogram will automatically reset the VS BLOWS/IN. curve.\nstiffnesses to these values after each\nproblem on page 2. OPTION 12 = 2, for triangular side soil resistance\ndistribution.\nA'S = enter all cross sectional areas of pile OPTION 13 = leave blank since computer plotted\nsegments only. curve is not desired.\nPage 2-Problem 1 OPTION 14 = 1, to indicate gravity.\nw(1) = 4850 lb., the r a m weight. OPTION 15 = 1, for normal data output.\nNC = 3, the cushion spring number, see Fig- Page 2, Problem 2\nure B6 (b).\nK(NC) = Only the value of K(3), is changed.\nK(3) = 22,500,000, the stiffness of the com- NC = 3\nbined springs. K(NC) = 31,300,000.\nEFF = 1.00, diesel hammers a r e considered to K(3) = 3.\nbe 100% efficient. P a g e 2, Problem 3\nENERGY = 39,800, the input energy f o r this par- The value of K(3) and the OPTIONS a r e changed.\nticular hammer blow.\nERES(1) = 0.60, coefficient of restitution of steel\non steel impact. ~ ( 3 ') = 22,500,000.\nERES(2) = 0.80, coefficient of restitution of cap- RU(T0TAL) = 400,000 lb f o r a 200 ton total static soil\nblock material. resistance.\nERES(3) = 0.50, coefficient of restitution of com- OPTION 11 = 2, for single calculation using RU\nbined cushion and first pile spring. (TOTAL) = 400,000.\nRU(T0TAL) = leave blank, since OPTION 11 = 1, OPTION 12 = 1, for uniform side soil resistance dis-\ni.e., t h e program will generate suitable tribution.\nvalues f o r curve generation. Page 2, Problem 4\n% AT I n t h i s problem the cushion and the options a r e changed.\n~OINT = 10%. NC = 3\nMO = 4, t-he first pile sezment\n.* with side soil K(NC) =\nresistance. K(3) = 31,300,000\n@POINT = 0.10, Q. OPTION 12 = 2, for triangular side soil resistance\n(\\$SIDE = 0.10, Q'. distribution.\nJPOINT = 0.15, J. OPTION 15 = 2, for output a t interval expressed by\nJSIDE := 0.05, J'. IPRINT on page 1.\n\nW'S AND AREAS I TO P INCL.; K'S AND SLACK'S I TO P-l INCL; RU'S I TO P + I INCL. (P+I I S % RU UNDER POINT OF PILE.)\n\nPAGE FIFTY-TWO\nNOTE : IF OPTION ell = I, RU (TOTAL) NOT REQUIRED\n\nlilI I I I\n\nThe output for the four sample problems are shown data. The RU(T0TAL) value of 1,0g0,962.1 is the\nin Figures B7 through B-11. Figure B7 is the output total static soil resistance for which this problem was\nfor one point on the RU(T0TAL) VS BLOWS/IN. run. This value was generated by the program and is -\ncurve generated for Problem 1. The block of data on only one point of 10 used to develop the data for the\nthe upper part of the figure is a printout of the input total RU(T0TAL) VS BLOWS/INCH curve shown in\n\n## T E X ~ SA • M U N I V E R S I T Y P I L E D R I V I N G ANALYSIS CASE NO.HSP 1 0 PROBLEM NO. 1 OF 4\n\nIlOELTAT P OPTIONS 1 2 3 4 11 12 13 14 15 EXP. FORCE\n9443.9 11 2 1 1 2 1 2 0 1 1 1 5 8 7 0 0.\nENERGY HAMMER EFFIENCY RUITOTALI PERCENT UNDER POINT MU R I P O I N T I ~ P I S I D E 1 JIPOINT) JISIDE) N2\n39800.00 1.00 1040962.1 10.0 4 0.10 0.10 0.15 0.05 125\nM WIM) KIM) AREAIM) RUIM) SLACKIMI ERESlMl VSTARTlMl KPRIMEIMI\n\nSEGMENT AREA TIME N MAX C STRESS TIME N MAX T STRESS OMAXIM) DIM1 VIM)\n1 1.000 4 2RR3699. 0 -0.0 0.487338 0.406179 -0.50\n2 1.000 7 2245092. 0 -0.0 0.430214 0.430214 4.07\n3 254.000 11 7432. 42 -0.0 0.359616 0.359616 -1.17\n4 254.000 13 7324. 0 -0.0 0.238627 0.223646 -3.80\n5 254.000 15 7107. 0 -0.C 0.231331 0.211913\n\n0.39\n10 254.000 35 4195. 30 2491. 0.172878 0.168807 -0.03\n1I 254.000 27 1320. 0 -0.0 0.167608 0.166761 -1.43\nPERMANENT SET OF P I L E = 0.06760806 INCHES NUMBER OF BLOWS PER INCH = 14.79113579 TOTAL INTERVALS =\n\n## Figure B.7. Normal output ( o p ~ i o n15=1) for Prob. I .\n\nPAGE FIFTY-THREE\ndata is printed for each point on the RU(T0TAL) VS\nBLOWS/IN. shown in Figure B8.\nFigure B9 shows the summary of the data for the\nRU(T0TAL) VS BLOWS/IN. for Problems 1 and 2.\nData of this type can be used to construct curves like\nthat shown in Figure B8. These curves can be used to\ncompare the effects of cushion stiffness (the cushion\nstiffness, K ( 3 ) c, in Problem 2 was twice that in Problem\n1 ) . Note the stiffer cushion (Problem 2) produces the\nmost efficient driving since for a specified resistance the\npenetration per blow is larger (BLOWS/IN. is smaller).\nA CASE I\nFigure B-10 is a typical output when RU(T0TAL)\nCASE 2 is specified. The maximum penetration of the point of\nthe pile under one blow of the hammer is 0.473011 in.,\nlisted under DMAX(M), and the permanent set is\n0.473011-0.100000 (the ground quake Q) or 0.373011\nin. Note that the input data is listed as well as the\nmaximum stresses and the displacement of each segment.\nFigure B-11 is a sampling of the output when data\nis desired at some specified interval (OPTION 15 = 2,\nIPRINT = 1). The input information is listed in the\nBLOWS PER INCH first block of data. The next two blocks show the stress-\nes at time interval N = O and N = 1. The data is\nFigure B.8. Effect of varying cushion stiffness. defined as follows:\nD(M) = displacement of each mass point,\n(in.),\nC(M) = the compression in each spring, (in.),\nFigure B8. The second block of data shows the maxi- STRESS(M) = stress in each segment, (psi),\nmum compressive and tensile stresses and the maximum\ndisplacement of each segment. The column labeled F(M) = force in each spring, (lb),\nTIMEN is the time interval at which the maximum R(M) = force in each soil spring, (lb),\ncompressive stress (MAX C STRESS) occurred, i.e., the W(M) = weight of each segment, (lb),\nmaximum compressive stress of 7432 psi occurred in V(M) = velocity of each segment, (fps),\nae,ment 5 at time interval 11 (11/9443.9 sec.) . Similar DPRIME(M) = elastic displacement of soil, (in.),\n\n## P I L E D R I V I N G ANALYSIS CASE NUMBER HSP 1 0 PROBLEM NUVBER 1\n\nOPOINT = 0 . 1 0 JPOINT = 0.15\nBLCWS PER I N . RUTOTAL P O I N T FORCE MAX C STRESS SEG MAX T STRESS SEG\n\n## P I L E D R I V I N G ANALYSIS CASE NUMBER HSP 1 0 PROBLEM NUMBER 2\n\nQPOINT = 0 . 1 0 JPOINT = 0.15\nB L ~ H SPER IN. RUTOTAL POINT FORCE MAX c STRESS SEG M A X r STRESS SEG\n\nFigure B.9. Summary output for RU (total) us blows/in. (option I 1 = I ) for Prob. 1 and 2.\n\nPAGE FIFTY-FOUR\nAPPENDIX C\n0s-360 Fortran IV Program Statements\nThe listing that follows is known as an XREF list- variable in the program and makes the logic much easier\ning. Each statement is numbered, for reference, consecu- to follow.\ntively from the first to the last statement. The variables\nand program statement numbers are indexed by their A flow diagram of the program logic is included\nreference number. This listing facilitates finding each for reference.\nC TEXAS A * M U N I V C R S I T Y\nC P l L E D R I V I N G A N A L Y S I S BY THE WAVE E O U A T I U N\nC TEXAS A AN0 M PROGRAM R t V I S E D 1 2 / 1 / 6 5 BY E A S\nC PERMANENT SET.BLUWS PER I N C H\nC LCCSEITIGHT.OK L I M I T E D MOTION AT J O I N T S\nC CAXIMUM S T R t S S E S OR FORCES\nC I O P T USCD FOR OPTION.\nC I . J T ~ J T H . L A M P , L A Y I L T ~ L A C K ~ I R E U S E 0 FOR CONTROL\nC X AT END OF NAME = L A S T PRECEDING VALUE EXCkPT I N MAX = MAXIMUM\nC N ALWAYS MEANS NUMBER OF T l M E I N T E R V A L .\nC N O T A T I O N FOLLOWS S M I T H S ASCE PAPER CLOSELY. TO DECOCE NOTE THAT\nC NFMAXT = NO. OF T I M E I N T E R V A L WHERE FORCE = MAXIMUM I N T E N S I O N\nISY 0002 5 0 0 0 REAL J P O l N T l J S l U E t K t K P R l M E ~ N P A S S t N P 1 v K H U L D D C A S E ~ 8\nI 5 N 0003 5 0 0 1 IKTEbER P.PPLUSlrPLESS1~PKOC,PROBS\nISY 0004 5 0 0 2 UICCNSION A R E A ( 1 5 0 1 ~ C 1 1 5 0 1 ~ C X I 1 5 0 1 ~ C M A X ( 1 5 0 I ~ 0 1 1 5 0 1 ~ 0 X I 1 5 0 1\n\n## C 2 4 CF EACH OF ADOVE S U F F I C I k N T FOR USUAL PRUBLEMS\n\nC---- INPUT -- GEYERAL\n5 0 1 0 K E A U ( 5 ~ 5 1 1 3 IC 4 S E I P R O B S ~ T T D E L T I P ~ S L n C K ( l I ~ S L A C K ( 2 I ~ S L A C K 1 3 I ~ I U P T L ~\nI LCPT211UPT3~IOPT411PRINT~NSEGl\nkKITE16.50031\nISY 0007 5003 FOHMATILHII\nISN 0008 IFITTOELT.LE.0.) TTCELT=l.O\nISN 0010 I F 1 IllPT4.LE.01 IOPT4=2\nISN 0012 1FIIPdINT.LE.OI IPRlNTrl\n1 Siv 0014 IFINbEGL.LE.01 NSEGl=2\n1SN 0016 TCELTA=TTDtLr\nIS& 0017 5 0 7 0 UELTAT = l . I T U E L T A\nISN 0018\nISN 0019\nISN 0020\nISH 0021\nC-----CALCULATL P I L E WCIGHT\nISN 0022 L\"PILE=O.\n1 SH 0023 0 0 6 JT=NSEGI.P\nISN 0024 6 WPILE=WPILE+W(JTI\nISN 0025\n\n1SN 0026\nISN 0027\n1SN 0028\nISN 0029\nISN 0030\nISN 0031\nISN 0032 5 0 8 8 READ I5.5114IlAREAlMI.R=L.P)\nISN 0033\n1SN 0035\n1SN 0037\nISN 0038 5 0 9 2 READ ( 5 . 5 1 1 6 1 ( K U L I S T ( M I ~ M = I I P P L U S I I\n1SN 0039 5 1 0 0 IF(lOPT3-215101~5104.5104\nISN 0040 5 1 0 1 0 0 5 1 0 2 M=4.PLESSI\nISN 0041 5 1 0 2 S L A C K I M I = 0.0\nISN 0042 5 1 0 3 GO TO- 5\n~. - 1- 0 ~\n5 -\nISN 0043 5 1 0 4 READ (5,5lL4IISLACKIMI.K=I.PLESSII\nISN 0044 5 1 0 5 S L A C K I P I = 1000.0\nISN 0045 5 1 0 6 S L A C K I P P L U S L I = -0.0\nISN 0046\nISN 0047\nISN 0048\nISN 0049\nISN 0050 5114 FCRMATIRFl0.3I\nISN 0051 5115 FCRMAT18F10.01\nISN 0052 5116 FOHMATI8F10.71\n5117 FOYMAT l l 2 ~ F 8 ~ 2 ~ 1 1 1 F 9 . 0 ~ F 3 . 2 ~ F 6 . O ~ 3 F 3 . 2 ~ F 9 . l r F 4 . l ~ I 3 ~ 4 F 3 . 2 ~ F 9 . O\n.....\n1.511 1\nISN 0054 5 1 1 8 F G R M A T I 1 H O 9 5 H C A S E 1 A 7 . 4 X v 5 H P R O U l A b r 7 4 H RU PERCENTACES ON OATA SHC\nLET PAGE 1 SHOULD TOTAL 1 0 0 . 0 BUT ACTUALLY TUTAL.FL5.71\nC---- DO 5 5 7 0 SflLVES PROBLEMS ONE AFTER ANOTHER\nISN 0055 NC= I\nLSN 0056\nISN 0057\nISN 0058\n\nISN 0059\nISN 0061 VSTAHT= S Q R T 1 6 4 . 4 * E F F * I E N E R G Y / W ( L I l I\n1 SN 0062 0 0 9 0 0 9 M=1,50\nISN 0063 FTVAXIMI=O.\nISN 00.64 9009 FCCAXIMI=O.\nNKCNT=O\nISN 0066 5140 KUTTLX = 0.0\nISN 0067 5141 ULCHSX = 0.0\nISN 0068 5150 V I I I = VSTART\nISN 0009 5152 LT = 0\nC---- F I R S T DETERMINE VALUE OF HUTOTL\n5 1 5 4 IFIIUPTll-215151v5160~5151\n\nPAGE FIFTY-SIX\nC FUR CURVE P L O T T I N G\n5 1 5 1 KUTOTL = Y l l l * V l l ) * * 2 / 1 2 . 0\n\nC FOR S I N G L E PROBLEM\nISN 0073 5 1 6 0 RUTOTL=RUSUM\n1SN 0 0 1 4 GO TO 5 1 7 0\nC COPPUTEI< C Y C L E S FROP 7 0 7 NEAR E N 0 OF PROGRAM\nISN 0075\nISN 0076\nlSN 0077\nISN 0078\n1SN 0079\nISN 0080\nISN 0081\nISN 0082\nISN 00b3\nISN 0084\nISN 0085\n~ ~\n\nGO TO 7 0 6\n706 RUTTLX = RUTOTL\nKUTOTL = R U T T L X + I OB+SLOPE)\nISN 0090 DLCWSX = BLOWS\nC---- SECOND D E T E R M I N E A L L V A L U E S OF R U I M )\nISN 0091 5170 DO I 3 M=l.MU\nISN 0092 13 R U I M ) = 0.0\n1SN 0093 5171 HUPINT = lPERCNT/100.0)*RUTOTL\nISN 0094 5172 1F110PT12-2)143~146~5176\nC FOR U N I F O R M U l S T R l R U T l O N\nISN 0095\nISN 0096\nISN 0097\nISN 0098\nC FCR T R I A N G U L A H O L S T H l f l U T l U N\n1SN 0 0 9 9 1 4 6 UO I 4 5 M=CO.P\n1SN 0 1 0 0 145 HUIM1 = I2.O*lRUTOTL-RUPINTIr(FLOATIM-M0~+0O5~)/1FL0AT1P-M0+1~1*42\nISN 0101 5 1 7 5 K U l P P L U S l ~= HUPINT\nGC T U 7 1 3\nC FCH U I S T K I B U T I O N PER R U L I S T ON GATA SHEET\nISN 0103 5 1 7 6 TOTAL = 0 . 0\nISN OIU4 IIC 5 1 7 7 M = l . P P L U S l\n1514 OlUZ 5 1 7 7 TCTAL = T O T A L + R U L I S l I M I\nISV 0106\n1SN 0107\nISN OLUR\nISN 0109\nISN 0110\nIsri 0111\nC---- T H l R U U E T E H M I N E S T A R T I N G VALUES OF V I M )\nISN 0112 713 VIl)=V~TART\nISN 0113 DO 1 8 0 M=2.P\nISN 0114 1 8 0 VIP) = 0.0\nISN 0115 5 1 8 3 V I P P L U S L I = -0.0\nC---- F O L R T H D E T E R M I N E V A L U E FOR K I P )\n5 1 8 4 K I P ) = RUIPPLUS1)IQPOINT\nC F I F T H CHANGE C Y C L E - COUNT .\n5186 LT = LT + 1\nC----CHECK ON O E L T A T\nCALL D E L T C K I N P A S S ~ T T O E L T ~ P ~ U U K K T O E L T A ~ O E L T A I ~ N ~ ~\nC----EN0 OELTAT-CHECK\n\n1SN 0119\nISN 0120\nISN 0121 C I P ) = 0.0\nISN 0122 F l P ) = 0.0\nISN 0123 C M A X I M ) = 0.0\nISN 0124 LAPlM)=L\nISN 0125 O l l r ) = 0.0\nISN 0126 NFMAXCIMI = 0\nISN 0127 NFMAXTIM) = 0\nU H A X I M I = 0.0\nNOPAXIMI = 0\nF M A X C I M ) = 0.0\nF M A X T I M ) = 0.0\nISN 0132 H I M ) = 0.0\nISN 0133 5218 D P R I M E I M ) = 0.0\n1SN 0134 KPRIMEIPPLUSLI=O.\nISN 0135 O P R I M P = 0.0\nISN 0136 LAPP = 1\nC---- S I X T H P R I N T I N P U T FOR ONE PROBLEM\nISN 0137 5190 WRITE 16.52001CASEIPROB~PROflS\nISN 0138 5191 WRITE 16.5201)\nISN 0139 5192 URITEl6.52021 T D E L T A ~ P ~ I U P T l ~ I O P T 2 ~ I O P T 3 ~ l O P T 4 I~O P T l I .\n1 IOPTl2rlOPTL3~1UPTl4~1OPTI5tFEXP\n1SN 0 1 4 0 5 1 9 3 WRITE 16~52031\nISN 0141 5194 WHITEl6.5204) ENERCYIEFF~RUTOTL~PCRCNT~MO~QPOINTtQSIDF,JPOINT,JSI\n10E.NL\nISN 0142 5 1 9 5 WRITE (6.5205)\nISN 0143 5 1 9 6 WRITE l 6 ~ 5 2 0 6 ) l M ~ U I M l r K I M ~ ~ A K E A l H ~ ~ R U l M ~ ~ S L A C K l M ~ ~ E H E S l M l ,\n1 VIM)lKPRIMEIM)lM=lrPPLUSll\nISN 0144 5 2 0 0 F O R M A T 1 / / / 2 7 H TEXAS A 4 M U N I V E R S I T Y 1 3 X . 2 2 H P I L E D R I V I N G ANALY\nl S I S 1 4 X . 9 H CASE N U . ~ A 7 . 3 X , I 2 l - PROBLEM N0..14,3H OF114)\nISN 0145 5 2 0 1 FORMATl2XIOH I l D E L T A T3XIHP4XbZHUPTIONS I 2 3 4\n1 I1 12 I 3 14 151OXLOHEXP. FORCE)\nISN 0146 5 2 0 2 FORMATIFII.L~15111X415~10X5155F18.0)\n1SN 0 1 4 7 5 2 0 3 F O R M A T l I I 3 H ENERGY HAMMER E F F I E N C Y HUITOTAL) PERCENT UN\n\nPAGE FIFTY-SEVEN\nLUEH P O I N T MD O ( P 0 1 ~ f QISIOEI J(PbINtl J(SID61 k21\n15.N 0 1 4 8 5204 FCRM&TI2F10~2r10XF12.1~F16.1~l11~F1O02~F9~2~F10.2~F9.2~171\nISN 0149 5 2 0 6 FCRMATIl3. F14.3rE15.7~F10.3~2F14433F9.22F1112tE15.71\n15N 0150 5 2 0 5 b C U Y A T ( 3 H M.7X.5H W(M1,7X15H K ( M I n 7 X v 8 H A R E A I M l r 6 X v 6 H R U ( M I r 7 X ~ 4 1\nI H SLACKlMl EKES(M1 VSTARTIMI KPRIME(M1)\nC---- E F F E C T OF G R A V I T Y BEFORE KAM S T R I K E S - - T E X A S A AN0 M SMITHS GRAVITY\nISN 0151 5 2 5 8 IFIIOPT14-2)5220~5221r5221\nISN 0152 5 2 2 0 WTCTAL = 0 . 0\nISN 0153 R T G T A L = 0.0\nlSN 0154 DO 5 J T = 2 , P P L U S L\nISN 0155 WTCTAL = WTUTAL + W l J T l\nISN 0156 5 KTCTAL = RTOTAL + R U I J T I\nISN 0157 0 0 8 J T = 2.PLESS1\n1SN 0158\nISN 0159\nISN 0160\nISN 0161 6 6 lF(KPRIME(P))67w63.67\nISN 0162 6 7 I ) ( P ) = (F(PLESS1I+W(PI)/IKPRIMEIPI+K(PII\nISN 0163 IFIPSIUE-DIPIl64r65.65\nISN 0164 6 4 K I P ) = RU(P1\nISN 0165 F ( P 1 = F ( P L E S S 1 I + W(P) -R(PI\nISN 0166 UlPl = FIP)/K(PI\nISN 0167 GC TO 6 3\nISN 0168 6 5 K I P 1 = U(P)*KPRIME(PI\nISN 0169 FIP) = O(PI* KIP1\nISN 0170 6 3 CONTINUE\nlSlv 0171 0 0 111 JT = lrPLESSl\nISN 0172 JTM = P-JT\nISN 0173 C(JTM1 = F(JTMIIKIJTM1\nISN 0174 UlJTMl = O(JTM+II+CIJTMI\nISN 0175 O P R I M E I J T M ) = DCJTMI-WTDTAL*QSIUE/RTOTAL\nISN 0176 I 1 1 CONTINUE\nISN 0177 DO 8 0 0 0 M=l.P\nISN 0178 0000 SIRESSIM)=F(M)/AKEA(Ml\nISN 0179 5 2 7 1 N=O\nISN 0160 LAY = 1\nISN 0161 5 2 3 0 IFIIOPT15-215240.5231.5240\nISN 0182 5 2 3 1 WRITE(6.5234)N,DPRIPPPN2\nISN 0183 5 2 3 2 WRITC (6,5235)\nISN 0184 5233 W K ~ T E ( 6 ~ 5 2 3 6 ) ~ M ~ D ~ M l r C ( M I ~ S T K E S S ( M ~ ~ F l M l ~ R l M ~ ~ H ( M l ~ V l M ~ ~ O P R l M E i M l ~\n~KPRIMEIYI~FMAXC(M)IFMAXTIM)~M=I~P~\nISN 0 1 8 5 NKCNT=O\nISN 0116 5 2 3 4 F O R Y A T I / / l 8 H TIME INTERVAL N = I 6 * 7 X 1 8 H N E T PENETRATION = f10.6.\nL7X5HY1 = 15.2XSHN2 = 1 5 )\nISN 0187 5 2 3 5 F O R X A T ( 1 2 O H SEGMENT M D(MI C(M) STRESSIMI F(M)\n1 K(MI W(M1 V(M1 DPKIMEIMI KPRIMEtM) FMAXCtM) FMAXTIM))\n:Sfi 0188 5236 ~ C R M A T ~ ~ ~ ~ F ~ ~ ~ ~ ~ F I O ~ ~ ~ F ~ I I O O ~ F ~ O ~ O ~ F ~ O ~ ~ ~ ~ F ~ O . ~ ~ ~ F ~ C ~ O ~\nC---- D Y N A M I C COMPUTATION B A S F D ON S M I T H S PAPER M O D I F I E D ( T E X A S R E P N I\nISN Old9 5 2 4 0 LACK = 1\nISN 0199 5 2 4 1 LJLI 6 8 M=l.P\nC 6 8 I S UETWECN 5 4 3 9 AND 5 4 4 0\nU I P ) = O(Ml+ViM)*l2.O*DELTA1\n\n~ . --.-\n3 4 C I C ) = U(Ml-U~M+l)-V~M+l)*l2.O*OELTAT\nC 5TATCMEUT 3 4 MUST USE A CDMPUrEO V A L U E FOR THE A C T U A L D ( M + L )\n5242 lFlC(M))5243.30.30\n\nISN 020U\n1SN 0 2 0 1\nISN 0262\nC NOTE T l l A T ONLY A N E G A T I V E V A L U E GF C ( M ) H E S U L T S FHOP 5 2 4 6\nISN 0203 3 0 FX(:+I = F l M l\nC 4 TCXAS K O U T I N E F D K B ( M I I S O M I T T E D HEKE\n15'4 0 2 0 4\nC---- 3 6 TO 3 5 I S A TEXAS R O U T I N E R C P L A C I N G S M I T H R O U T I N E 3 OR 4\n3 6 1F~AB~IEKES(Ml-1~0)-.00001138t38t14\n3 8 F i r ) = CIM)*KIM)\n20 TO 5 4 0 0\n1SN 0208 14 IF(C(M)-CXIM))12.35p15\nISN 0209 1 5 F 1 P ) = FXIM)+(ICIM)-CX(M)I*K(Mll\nISN 0210 GO TO 3 5\nlSN 0211 1 2 FIG) = FX(M)+((C(P)-CX(M)I*KIM)/ERESlM1**21\nISN 0212 3 5 r ( v ) = AMAXIIO.O.FICI)\nISN 0213 L O TO 5 4 0 0\nC A TCXAS K O U T I N E FOR GAMNA I S O M I T T E D HEKE\nC---- S P I T H H O U T I h E 3 OR 4\n\nISN 0218\nISN 0219\nISiu 02ZO\n\n1SN 0222\nISN 0223\n1SN 3224\nISN 0225\nISN 0226\nISN 0227\nISN 022'3\nISN 0231\n\nPAGE FIFTY-EIGHT\nI S- N 0 2\n- 34\n\n1SN 0 2 3 5\nISN 0236\nISN 0237\nISN 0238\n1SN 0239\nISN 0240\nISN 0241\n1SN 0 2 4 2 5 2 CONTINUE\nISN 0243 IFIOPRIME(M1-DlM)-QSlUEi53953,54\nI S N 0244 5 4 OPRIME(MI = U l M l + Q S I D E\nISN 0245 5 3 CONTINUE\nISN 0246 5 4 1 0 LAP = LAMIMI\nlSN 0247 GO T 0 ( 1 0 ~ 5 7 ) . L A P\n1SN 0 2 4 8 1 0 IF(U(M1-GPKIME(M)-QSIOE156b57.57\nISN 0249\nISN 0250\n1SN 0 2 5 1\nISN 0252\nISN 0253\nlSN 0254 73 IFIM-P)71~74,71\nISN 0255 74 IF(UPK1MP-O(Pl+OPOINT)75,76,76\nISN 0256 75 DPRIMP = U I P I - Q P O I N T\nISN 0257 76 CONTINUE\nIS4 0250 L n r P = LAMP\nISN 0259 GO TO 1 7 7 * 7 B ) . L A M P\nISN 0260 77 I F ~ D ~ P ) - U P R I M P - Q P O I N T ~ ~ ~ I ~ ~ ~ ~ ~\nISN 0261 7 9 F ( P ) = (UIPI-OPRIMPl*KlPl*ll.O+JPOIYT~VIP)I\nISN 0262 ;lC TU 1 7 1\nISN 0263 7 8 F ( P ) = Ib(PI-DPRIMP+JPOINT*CPOINT*V(Pl~*K(P)\nISN 0264 LAPP = 2\n1SN 0 2 6 5 1 7 1 F I P I = AMAXLIO.0,FIP)I\nISN 0266 7 1 CONTINUE\nC GRAVITY UPTIUN\nISN 0267\nISN 0268\nISN 0269\nISN 0270 LACK = 7\nGO TO 5 4 2 9\nISN 0272\n1SN 0273\nISN 0274\nISN\n~ 0 2- 7 5 5424 V I 1 ) = Vll~-lF(1l+R11))*32.17*DELTAT/Wl1)\nISN 0276 5 4 2 5 LACK = 2\nISN 0277 GO TO 5 4 2 9\n1SN 0278 5427 VIP) = V(MI+(FIM-II-FIM)-RIMIl*32Z17*OELTAT/WlMl\n5 4 2 9 CONTINUE\nISN 0280 IFIK.CT.11 GO TO 5 4 3 0\n151.1 0 2 8 2 lF(FllI.LE.O..ANU.VIl).LE.-0.1) Vll)=-VSTART\nISN 0 2 8 4\n\nISN 0286\n-\n5 4 3 0 FPAXC(M) = AMAXI(FMPXCIM).FIM)I\nFPAXT(M) AMINLIFMAXTIMI.FIM~)\n5439 IF~FMAXC(M)-FlMII166~1677166\n15N 0287 1 6 7 NFCAXC(M) = Y + l\n1SN 0268 I66 IFlr#AXTlMl-F(M~168~69968\nISN 028'2 6 9 NFPfiXT(F1I = Y + l\nISN 0290 6 8 STRESS(M)=FIM)/AKEA(Ml\nIS\\$; 0291 N=N+ 1\nC T H I S I S END OF 0 0 6 8 S T A R T I N G AT 5 2 4 1\nISN 0292 5 4 4 0 IF(I[lPT15-715444.5441.5444\nISN 0293 5441 l ~ I N - 1 ) 7 0 0 0 ~ 7 0 0 1 ~ 7 0 0 O\nISN 0294 7 0 0 0 kUCNT=NKONT+l\nISN 0295 IFIYKONT-IPIIINTI5444.7001.5444\n\nISM 0299\n. ISN 0300\nISN 0301\nISN 0303 Wv=Il.')\nISN 0304 0 0 1'13 JA=NSEGL.P\nISN 0305 193 hV=hV+WIJA)*VIJAl\nISh 0306 IFIVII).LT.O..AND.WV.LT.O..ANO.bMAXIPI.GT.UIP GI; TO 1 9 0\nISN\n~- 0 3- 0 8\n~ L C TI1 I 4 2\nISN 0309 1 9 0 LAY=2\n1SN 0310 (,ti TO ( 1 9 2 r L 9 4 . L 7 2 ~ t I O P T 1 5\nISN 0311 1'14 k l t I T E 1 6 . 5 2 3 4 1 N,UPKIMP,N2\nWllITt(L.5735)\n~ R I T ~ ~ ~ ~ ~ ~ ~ ~ ) ( M ~ D ( M ) ~ C I M ~ ~ S T K E S S ~ M ~ ~ F ( M ~ I R ~ N ~ ~ W ~ M ~ I V ~ M ~ ~ U P ~ I M E ~ M ~ ,\nlKPHIv~E(M1~FMAXCINl~FMAXTIH)~M=l~PI\nISN 0314 192 ~ F ( V ( ~ ) / V S T A K T - ~ . ~ ~ ~ ~ ~ ~ O O ~ O\n1SN 0 3 1 5 60 h R l T E (O, 1 0 5 )\nISN 0316 1 0 5 tOHElATI74H THE d 4 T I l l OF THC V E L O C I T Y OF W ( 2 ) TO THE VELCICITY O t T\nLHk RAN CXCLCUS 3 . 1 )\nISN 0317 GO TU 5 5 7 0\nISN 0316\nISN 0319\n1SN 0320\nlSN 0321 1 0 6 F C R W A T l 7 4 H THE R1.11O OF THE V t L U C l T Y [IF WII') TO THE V E L U C I T Y OF T\nI H C K 4 N FXCEEOS 3 . 1 )\nC --- CNC OF TEXAS REPN\n1 6 3 LCATlNUC\nIF(LAY.EC.2) GO TO 5 4 4 7\nIFIhl-N21524U15447r5447\nC---- 5 2 4 0 CYCLES FOR NEXT T I M E I N T t K V A L\n\nPAGE FIFTY-NINE\n0326 5 4 4 7 UO 5 4 4 9 M = l ,P\n0327 5 4 4 8 FPnXC(M1 = FMAXCIM)/AREA(M)\n0378 5449 FPbXTIM)=FMAXTIMI/I-AKEAIM))\n0329 GC T U ( 5 4 4 2 ~ 5 4 4 2 ~ 5 5 5 3 1 ~ I O P T 1 5\n0330 5 4 4 2 WHITE (6,2105)\n0331 5550 W R I T t ( 6 ~ 2 L 0 6 ) I M ~ A K E A l M ) ~ N F M A X C I M ) ~ F M A X C ( M ) ~ N F M A X T I M ) ~ F M A X T I M ~ ~ O M A X\nlIV).UIM),VIMI,M=LIPI\n0332 DLCWS=O.O\n0333 5 5 5 3 IFIOPRIMP.GT.O.0) BLOWS=l.O/OPKIHP\n0335 5 5 5 1 U D L O W S I L T ) = BLOWS\n0336 U H L T T L I L T ) = RUTOTL\n0337 UFPAXC(LT) = FMAXCIP)*AREAIPI\nC I N I T I A L U ABOVE I O E N T I F I € S F I G U R E S U S E 0 I N SUMMARY\n0338 GO T 0 1 5 5 5 2 e 5 5 5 2 . 150~~IOPT15\n0339 5552 WKlTt I6~2107)OPKIMP.RLOUS~k\n2 1 0 5 F C R M A T ( / / 1 0 3 H SEGPEhT AREA T I M E N MAX C STKESS TlMt N\n1 PAX T STRESS CMAXIMI DIM) V(M))\nI5N 0341 2106 FCRMATl13~F15.3~18rFI2.O~ll4~FL2ZO~F16.6~F1O.6rFl3~2)\nISN 0342 2 1 0 7 F C K M A T 1 2 4 H PERMANENT SET U F P I L E = F 1 5 . 8 .- . 3 8 H ~ I N C H E- S - NUMBER OF R\n1 L O h S PER I N C H = F l 6 . 8 . 2 2 H TOTAL I N T E R V A L 5 = 1 8 )\nISN 0343 1 5 0 CCNTINUE\nISN 0344 5 5 5 8 UO 5 5 6 3 M=NSEGL,P\nISN 0345 FTVAX(LTI=AMAXL(FTMAX(LT),FIrAXTIMI)\nISN 0346 FCPAXILTl=ACAXl(FCMAX(LT),FPAXC(M))\nISN 0347 IFIFCMAXILTI-FMAXCIM) l556O1556Lv5560\nlSN 0340 5 5 6 1 NCPAX(LTl=M\nISN 0349 5560 IF(FTMAX(LT)-FMAXT(rI)55631556215563\nISN 0350 5562 NTPAXILT)=M\nISN 0351 5 5 6 3 CCNTINUE\nISN 0352 5 5 5 5 IF(IOPTl1-215556.5570.5570\nISN 0353 5 5 5 6 I F (UPRIMP-0.001)59r707~707\nI5N 0354 707 I F (HLOWS-60.0)701170L~59\nISN 0335 5 9 CONTINUE\n1SN 0356 W ? I T E ( 6 . 8 0 3 ) CASE.PKO8\n\n## 8 0 3 FORM41 I l H U . I O X . 2 2 H P I L E U R l V l N G A N A-L Y S ~~.\n\nIS.\nI I O X I I Z H L A S E N U M H E K ~ 3 X ~ A 6 ~ 1 0 X ~FKOBLEM\nI5H NUMDER,~XII~)\n804 FOHl~lAT(l9X~9HOPOIN= T F5.2~11X19HJP111NT = F5.2)\n8 0 5 FORMAT(2XL3HULOWS PER I N . 2 X 7 H R U T O T A L 7 X l l H P O l N T FOKCEZXIZHMAX C STR\nltSS2X3HSCGZXL2HMAX T STRE5SZX3HSEG//)\nC-----PLCTTING HOUTINF\nIFIIOPTl3-115570~5574~5574\n5574 CALL uK~kIWTOTn,rvmr..L~UOLOWS,LT,C4SEIPKUD)\nC-----F hC P L O T T I N G K O U T I N E\n1 siu 5570 WHITt(6.5572)\nC IJU S ~ ~ O ' S T A ~ AT T S5 1 2 0\n5572 FOflElArI L H L I\n5571 G O TU 5 9 1 0\nLNC\n\nHhAL 51\nUL21\nC222\n0125\nC244\n0122\nC222\nC284\n\n0360\n0004\nC224\n0020\nOC43\nC114\n0144\nC184\n0196\nC201r\n\nPAGE S I X T Y\n* * * * * F O R T R A N C K C S S R E F E R E N C E L I S T I N G * * * * *\n\n## a'lMOOL I N T C R h A L STbTEMEkT NllMDFRC\n\n-~ .... ...-\nAOS 0106 0199 0205\nEFF 0058 C061 0141\nJTM 0172 0173 0173 0173 0174 0174 0174 0175 0175\nLAM 0004 0124 0246 0252\nLAP 0746 0747\nLAY\nNPI\nAREA\nCASE\nCMAX\nDMAX\nDRAW\nEltES\nFCXP\nL4CK\nLAMP\nPKOD\nSOH1\nAMAX 1\nAMlNl\nBL0I.S\nFCMAX\nFLUPT\nFHAXC\nFMAXT\nFTMAX\nIUPTL\n\nJSIDE\nKHVLD\nNCMAX\nNUMbX\nNKUNT\nNPASS\nNSEGI\nNTMAX\nPKOBS\nQSlDE\nRUHlL\nKUSUM\nHWENH\nSLACK\nSLOPE\n\n## SYMBOL I ~ T E K ~ ASLT A T E X E R T NUMHCRS\n\nTUTAL 0103 0105 0105 ill06 0107\nWPlLE ,Os72 0024 0024\nXPLOT 0004\nYPLUT 0004\nHLOWSX 0067 0075 0090\n0197\nUtLTLK\nDPR IME 0184\nOPKIMP 0256\n\n0357\n0094\n\n0267\n0292\n0295\n0261\n0134\n0331\n0331\n\n0040\nOO2h\n0255\nKTLITAL ill58\nHUL l ST OLIO\nKUPIVT OLOO~\nKUTllTL OOHH\nKUTTLX 0389\nUwEIICH\nSTHESS 0299\n\nPAGE S I X T Y - O N E\nLABEL DEFINED KEFEHENCES\n5 0156 0154\n0024\n0159\n0248\n0211\n0092\n0208\n0209\n0193\n\n## LABEL DEFINED HEFEHENCES\n\n78 0263 0259 0260 0260\n79 0261 0260\n\nP A G E SIXTY-TWO\nLABEL DEFINED\n5084 0029\n5086 0030\n5087\n5088\n5090\n5092\n5100\n\n* * * * * F O R T R A N C R O S S R E F E R E N C E L I S T I N G * * * * *\n\n## LABEL DEFINED REFERENCES\n\n5184 0116\n5186 0117\n\nPAGE SIXTY-THREE\n4****FORTAAN C R O S S R E F E R E N C E LISTING*****\nLAUEL REFERENCES\n5422\n5423\n5424\n5425\n5427\n5429\n5430\n5439\n5440\n5441\n5442\n5443\n5444\n5447\n5448\n5449\n\nCOPPILEU OPTICNS - N A M E = - M A I N ~ O P T = ~ ~ ~ L I N E C N T = ~ O O S O U R C E ~ E ~ C D I C I N U L ~ S T ~ N O D E C K ~ L U A U ~ N O M A P ~ N O E U I T ~ ~ D ~ X R E F\nIS,\" 0002 LCBHOUTINE U ~ A W ~ W T O T A L ~ U R U T T L , U D L ~ W S , L T . C ~ S E , P K O B I\nISN 0003 DIPENSINN U R U T T L 1 1 5 0 l ~ U R L O W S l 1 5 O l ~ Y P L O T l 5 1 l ~ X P L O I l 5 l l\n1Sk 0004 5574 YPLUTII I=WTOTAC\nlSN 0005 XPLrJTlll=O.\nlSN 0006 LTPI=LT+l\n1SN 0007 UO 5573 IP=l.LT\n1SN OOeB YPLUT(IP+ll-UKUTTLIIPl12000.\nISN 0009 5573 XPLOT(IP+ll=URLUWSIIPl\n1SN 0010 YCAX=YPLUTlLTPLl\n1SN 0011 NZ=N2\nI SY 0012 IF(YMAX.LE.400.1 GO TO 3\nISN 0014 IFIYMAX-LE.800.1 6 0 TO 4\nISN 0016 IFIYHAX.LE.l600.1 GO TO 5\n1SN 0018 IFlY~AX.LE.3200.1 GO TO 6\n1SN 0020 3 DY=50.\nISN 0021 G C TO 10\nISK 0022 4 bY=lOO.\nISN 0023 G C TO 10\nlSN 0024 5 I)Y=200.\nISN 0025 G O TO 10\nISN 0026 6 UY-400.\nISN 0027 10 DX=10.\nISN 0028 PPKUU=PKOfl\nIS!4 0029 HETU!<N\nISN 0030 t hU\n\n**+**FORrRAN C R O S S R E F E K E N C E LISTING*****\nSyrndL\nox\nUY\nIP\nLT\nN2\nCASE\nDRAW\nLTPl\nPKUC\nYMAX\nPPROU\nXPLOT\nYPLOT\nUHLUWS\nUHUTTL\nHTllTAL\n\nP A G E SIXTY-FOUR\nLABEL C t l lNE0 REFERENCES\n3 0020 0012\n4 0022 0014\n5 0024 0016\n\nOS/36O FORTRAN H\n\n## COCPILFK OPTICNS NAME= -\n\nMAIN,0PT=OO,LINECNT=50~SUUKCttEHCUIC~NOLIST~NOUECK~LUAO~NOMAP~NO~UIT~IU~XR~F\n1SN 0 0 0 2 SUEXOUTINE G E L T C K 1 N P A S S . T T D E L T t P t W w K r T O E L T A . O E L T A T ~ N 2 )\n\nISN 0006\nISN 0007\nISN 0008\n\nISN 0010\nISN 0011\nISN 0012\n\nISN 0014\nISN 0015\n1SN 0 0 1 6\n- -\n\nISN 0019 G C TU 3\nISN 0020 2 UEL1I1NI=SCRTl~~Pl/K1P~l/lY.648\nISN 002 1 3 UC 4 M = l . N\nISN 0022 4 TCIN=AMINIIT~IN~UELTlIMI)\nISN 0023 lFITHIN/2.-UELTATI5I616\nISN 0024. 5 UELTAT-TMINI2.\nI S-\n. N 0 0 -~\n75 lGELlA=l.O/UtLTAT\nISN 0026\nISN 0027\nISN 0028\nKETUXN\nEhC\n\nSOH T\nTMIY\nAMlivl\nUCLTl\nNPASS\nUELTAT\nUtLTCK\n\n## LABEL DEFIhtD REFCKENCES\n\n1 0015 0012\n\n**t*++ENO OF C O M P l L h T l C N ******\n\n## ILF2851 SYS68134.T1454C5.KPOOl.A49394.ROO00444 DELETED\n\nIFF2851 VOL SEH l i U S = 5 5 5 5 5 5 .\nICFZH,l SYS68134.T145405.~POOlLA49394.R0000445 OELETEO\nIEF2U51 VOL SEK NOS= STURAU.\nIEF2851 SYSCUT SYSOUT\nltF285l VOL SER NOS-\nICF2851 SYS68L34.TL454C5.RPOOl.A49394.LOAOSET PASSED\nILF285I VCL SEW NUS= 6 6 6 6 6 6 .\n\nPAGE S I X T Y - F I V E\nC START\n\nCHANGE TO FLDATING\nPOINT JPOINT, JSIDE,\n\nCHAN6E TO FIXED P O I N T\nP. PPLUSI. PLESSI, PROB,\n\nPROGRAM\nVARIABLES\nY\n1\nI\n\nPROGRAM\nVARIABLES\n\nTTDELT -\n\n, , ,\nIPRINT-I\n\n*TDELTA\nTTDELT\n\nDELTAT\n\nPLESSI-\n-\n-\n\nM ' I TOP\n\n~(PPLusI). 0 . 0\nWPlLE r 0.0\n\ni\"\n- l'l\"\nWPlLE WPILE tW(37)\n\nPAGE SIXTY-SIX\nI BLOWSX-0.0\nVI- V S T A I T\nLT-0 , I\n\nPAGE SIXTY-SEVEN\nI I J\nM- MO\nRU[M)=(Z OI~RUTOTL -\nM-I 7 RUPINT)(I FLOAT(M-~d.\nRU(M)- (RUTOTL-RUPINT)\n+. ~~/(FLOAT(P-MO*I))\n*a\nw /FLOAT(P-MOII)\n\nTOTAL- T O T A L +\n\nRU(PPLUS~)s R U P I N T\nRU(PPLUSI)=\nRUPINT\n\nI\nWRITE\nCASE, PROB,\nTOTAL\n\nM-l\n\n4\nRU(MI\n=(RULI ST(M)/IOO.)\nr RUTOTL\n\n--\nI1\n\nPAGE SIXTY-EIGHT\nI\n\nv\nI MAKE REAL 1\n\nMAKE INTERGER\n\nI\nDIMENSION\n\nI VARIABLES I\n\nTMIN = I.\nTDELTA-TTDELT\nDELTAT- ).ITDELTA\n\nCRSE, P I O I , PROBS\n\nPERCENT, OPOINT,QSIDE,\n\nP A G E SIXTY-NINE\n0\nRETURN\n\n0 CONTINUE\n\nI I\nI I JTM- P-JT I\n\nI LAY-I I\n\nu\nLACK-I\n\nPAGE S E V E N T Y\nPAGE SEVENTY-ONE\nFEXP <0\n\ne 51 NPI-N*I\n\nDELTAT\n\nI AND 0.0 I\n\n07 KPRIME (M)\n\n1 CONTINUE 1\n\nI CONTINUE I\n\nPAGE SEVENTY-TWO\n- El\nCONTWM\n\nDPRINP -DIP)-QPOINT\n\nCONTINUE\n\nI\nLAMP.\na -\nLAMP LAMP\n\n## v~M)=v~M)+F(M+)- F(MI vi~\\-vl~\\-(rcd+RII))\n\n-RIM))*32.17 *32.17* D E L T A T\n\nPAGE SEVENTY-THREE\nI1\nYES\n& CONTINUE\n\nNO\n\nNO\n\nFNAX(M-AMAXI PICK\nu\nV(I) =-V S T A R T\n\n## THE MAXIM POSITIVE\n\n1 FMAXT(M)-AMAII\n\nI\nPICK\nT H E M A X I M U M POSITIVE\nv n L u E FROM F M A X ~\n\nPAGE SEVENTY-FOUR\n0\n- LAY 2\n\nCONTINUE\nW R I T E THC RATIO OF\n\n':\\. y\n9\n.\nTHE VELOCITY W e ) TO\nrue VELOCITY OF THE\nRAM EXCEEDS 3.1 1\n\nPAGE SEVENTY-FIVE\nI I\n\nYES\nBLOWS = '.%PR~ME\nBLOWS I O . 0\nI\n\nURUTTL(LT)- RUTOTL\n\nUFMAXC(LT)- FMAXC(P)\n\nCONTINUE\n\nFTMAX(LT) - A M A X 1\nPICK A POSITIVE MAX.\nVALUE FROM FTMAX(LT)\n\nI CONTINUE 1\n\nP A G E SEVENTY-SIX\nr-l\nCONTINUE\n\nCASE, PRO8\n\nURUTON -URUTTL(J)/\nI\n2000.\nI RUTTLX =RUTOTL 1\n\nCALL SUBROUTINE\n\n- 9\nDIMENSION\nVARIABLES\n\nIP-LT\n\nRETURN\n\nP A G E SEVENTY-SEVEN\nI\nREFERENCES\n1.1 Isaacs, D. V., \"~einforcedConcrete Pile Formula,\" 3.3 Lowery, L. L., Hirsch, T. J. and Samson, C. H.,\nInst. Aust. Eng. J., Vol. 12, 1931. \"Pile Driving Analysis-Simulation of Hammers,\n1.2 Smith, E. A. L., \"Pile Driving Impact,\" Proceed- Cushions, Piles and Soils,\" Research Report 33-9,\nings, Industrial Computation Seminar, September, Texas Transportation Institute, August, 1967.\n1950, International Business Machines Corp., New 6.1 Chan, P. C., Hirsch, T. J. and Coyle, H. M., \"A\nYork, N.Y., 1951, p. 44. Laboratory Study of Dynamic Load-Deformation\n1.3 Smith, E. A. L., \"Pile Driving Analysis by the and Damping Properties of Sands Concerned with\nWave Equation,\" Proceedings, ASCE, August, a Pile-Soil System,\" Texas Transportation Institute,\n1960. Research Report No. 33-7, June, 1967.\n2.1 Isaacs, D. V., \"Reinforced Concrete Pile Formula,\" 6.2 Reeves, G. N., Coyle, H. M., and Hirsch, T. J.,\nInst. Aust. Eng. J., Vol. 12, 1931. \"Investigation of Sands Subjected to Dynamic\n2.2 Smith, E. A. L., \"Pile Driving Impact,\" Proceed- Report No. 33-7A, December, 1967.\nings, Industrial Computation Seminar, September,\n1950, International Business Machines Corp., New 6.3 Airhart, T. P., Hirsch, T. J. and Coyle, H. M.,\nYork, N. Y., 1951, p. 44. \"Pile-Soil System Response in Clay as a Function\n2.3 Smith, E. A. L., \"Pile Driving Analysis by the of -Excess Pore Water Pressure and Other Soil\nWave Equation,\" Proceedings, ASCE, August, Properties,\" Texas Transportation Institute, Re-\n1960. search Report No. 33-8, September, 1967.\n2.4 Dunham, C. W., Foundations o f Structures, Mc- 6.4 Chellis, R. D., \"Pile Foundations,\" McGraw-Hill\nGraw-Hill Book Company, New York, 1962. Book Co., New York, 1951.\n\n## 2.5 Chellis, R. D., Pile F o u n d ~ i o n sMcGraw-Hill\n\n, Book 6.5 Smith, E. A. L., \"Pile Driving Analysis by the\nCo., New York, 1951. Wave Equation,\" Transactions, ASCE, Paper No.\n3306, Vol. 127, Part I, 1962.\n2.6 Fowler, J. W., \"Chesapeake Bay Bridge-Tunnel\nProject,\" Civil Engineering, December, 1963. 6.6 Forehand, P. W. and Reese, J. L., \"Pile Driving\nAnalysis Using the Wave Equation,\" Master of\n2.7 Chellis, R. D., Pile Foundations, McGraw-Hill Science in Engineering Thesis, Princeton Univer-\nBook Co., New York, 1951. sity, 1963.\n2.8 Leonards, G. A., Foundation Engineering, Mc- 6.7 Mansur, C. I., \"Pile Driving and Loading Test,\"\nGraw-Hill Book Co., New York, 1962. Presented at ASCE Convention, New York, Octo-\nber 22, 1964.\n2.9 Janes, R. L., \"Driving Stresses in Steel Bearing\nPiles,\" Dissertation at Illinois Institute of Tech- 7.1 Lowery, L. L., Jr., Edwards, L. C., and Hirsch,\nnology, June, 1955. T. J., \"Use of the Wave Equation to Predict Soil\nResistance on a Pile During Driving,\" Texas\n2.10 Cumrnings, A. E., \"Dynamic Pile Driving For- Transportation Institute, Research Report 33-10,\nmulas,\" J o u r d o f the Boston Society of Civil Au,pst, 1968.\nEngineers, January, 1940.\n2.11 Gardner, S. V. and Holt, D., \"Some Experiences 7.2 Moseley, E. T., \"Test Piles in Sand at Helena,\nwith Prestressed Concrete Piles,\" Proceedings of Arkansas, Wave Equation Analysis,\" Foundation\nthe Institute of Civil Engineers, London, Vol. 18, Facts, Vol. 3, No. 2, Raymond International, Con-\nJanuary, 1961. crete Pile Division, New York, 1967.\n\n2.12 Glanville, W. H., Grime, G., Fox, E.-N., and Davies, 8.1 Samson, C. H., Hirsch, T. J. and Lowery, L. L.,\nW. W., \"An Investigation of the Stresses in Rein- \"Computer Study of The Dynamic Behavior of\nPilinq,\" Journal o f the Structural Division, Pro-\nforced Concrete Piles During Driving,\" British ceedings, ASCE, Paper No. 3608, ST4, August,\nBldg. Research Board Technical Paper No. 20, 1963, p. 413. 7 - I - . -\nD.S.I.R., 1938.\n2.13 Heising, W. P., Discussion of \"Impact and Longi- 8.2 Heisinq, W. P., Discussion of \"Impact and Longi-\ntudinal Wave Transmission\" by E. A. L. Smith, tudinal Wave Transmission\" by E. A. L. Smith,\nTransactions, ASME, August, 1955, p. 963. Transactions, ASME, August, 1955, p. 963.\n\n3.1 Rand, Mogens, \"Explosion Adds Driving Force to 8.3 Smith, E. A. L., \"Pile Driving Analysis by the\nDiesel Hammer,\" Engineering Contract Record, Wave Equation,\" Trans~ctions,ASCE, Vol. 127,\nDecember, 1960. 1962, Part I, p. 1145.\n3.2 Housel, W. S., \"Pile Load Capacity: Estimates and 8.4 Hirsch. T. J., \"A Report on Stresses in Long Pre-\nTest Results,\" Journal o f the Soil Mechanics and stressed Concrete Piles During Driving,\" Research\nFoundations Division, ASCE, Proc. Paper 4483, Report No. 27, Texas Transportation Institute,\nSeptember, 1965. September, 1962.\n?AGE SEVENTY-EIGHT\n8.5 Hirsch, T. J., \"A Report on Field Tests of Pre- Cushions, Piles and Soils,\" Research Report No.\nstressed Concrete Piles During Driving,\" Progress 33-9, Texas Transportation Institute, August, 1967.\nReport, Project No. 2-5-62-33, Texas Transporta-\ntion Institute, August, 1963. B1. Smith, E. A. L., \"Pile Driving Analysis by the\nWave Equation,\" Journal of the Soil Mechanics\n8.6 Lowery, L. L., Hirsch, T. J. and Samson, C. H., and Foundations Division, Proceedings of the\n\"Pile Driving Analysis-Simulation of Hammers, American Society of Civil Engineers, Proc. Paper\nCushions, Piles and Soils,\" Research Report No. 2574, SM4, August, 1960, pp. 35-61.\n33-9, Texas Transportation Institute, August, 1967.\nB2. Hirsch, T. J., and Edwards, T. C., \"Impact Load-\n9.1 Hirsch, T. J., \"A Report on Computer Study of Deformation Properties of Pile Cushioning Ma-\nVariables which Affect the Behavior of Concrete terials,\" Research Report 33-4, Project 2-5-62-33,\nPiles During Driving,\" Progress Report, Project\nPiling Behavior, Texas Transportation Institute,\nNo. 2-5-62-33, Texas Transportation Institute, Texas A&M University, College Station, Texas,\nAugust, 1963.\nMay, 1966, p. 12.\n9.2 Hirsch, T. J., and Samson, C. H., \"Driving Prac-\ntices for Prestressed Concrete Piles.\" Research Re- B3. Smith, E. A. L., \"Pile Driving Analysis by the\nport 33-3, Texas Transportation Institute, April, Wave Equation,\" J o u r d of the Soil Mechunics\n1965. and Foundations Division, Proceedings of the\nAmerican Society of Civil Engineers, Proc. Paper\n9.3 McClelland, B., Focht, J., and Emrich, W., \"Prob- 2574, SM4, August, 1960, p. 47.\nlems in Design and Installation of Heavily Load-\ned Pipe Piles,\" Presented to ASCE Specialty Con- 84,. Samson, C. H., Hirsch,, T. J., and Lowery, L. L.,\nference on Civil Engineering in the Oceans, San \"Computer Study of Dynamic Behavior of Piling,\"\nFrancisco, September, 1967. Journal of the Structural Division, Proceedings of\n9.4 Lowery, L. L., Hirsch, T. J. and Edwards, T. C., the American Society of Civil Engineers, Proceed-\n\"Use of the Wave Equation to Predict Soil Resist- ings Paper 3608, ST4, August, 1963, p. 419.\nance on a Pile During Driving,\" Research Report\nNo. 33-10, Texas Transportation Institu'e, April, B5. Smith, E. A. L., \"Pile Driving Analysis by the\n1967. Wave Equation,\" Journal of the Soil Mechanics\nand Foundations Division, Proceedings of the\n9.5 Lowery, L. L., Hirsch, T. J. and Samson, C. H., American Society of Civil Engineers, Proc. Paper\n\"Pile Driving Analysis-Simulation of Hammers, 2574, SM4, August, 1960, p. 44.\n\nPAGE SEVENTY-NINE"
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.84591997,"math_prob":0.94133055,"size":125034,"snap":"2019-26-2019-30","text_gpt3_token_len":38859,"char_repetition_ratio":0.15241942,"word_repetition_ratio":0.055983063,"special_character_ratio":0.31364268,"punctuation_ratio":0.12961173,"nsfw_num_words":1,"has_unicode_error":false,"math_prob_llama3":0.98073953,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-07-16T08:02:22Z\",\"WARC-Record-ID\":\"<urn:uuid:9674b7df-74f6-412b-a831-26c72566f1fe>\",\"Content-Length\":\"737883\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e842105b-b49c-4c49-b905-c6649e6832b5>\",\"WARC-Concurrent-To\":\"<urn:uuid:a74b30b7-0d84-4634-94ed-b718e90e1da5>\",\"WARC-IP-Address\":\"151.101.250.152\",\"WARC-Target-URI\":\"https://id.scribd.com/document/374406264/Pda\",\"WARC-Payload-Digest\":\"sha1:MNYJU7265P3RQLZD7AYN5RYTJ44ZDOR2\",\"WARC-Block-Digest\":\"sha1:DUGZ2BK3K6TPN6WQKZFOVMBNUSTLBQRV\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-30/CC-MAIN-2019-30_segments_1563195524517.31_warc_CC-MAIN-20190716075153-20190716101153-00432.warc.gz\"}"} |
https://www.analyzemath.com/calculus/multivariable/second_order_derivative.html | [
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"# Second Order Partial Derivatives in Calculus\n\nExamples with detailed solutions on how to calculate second order partial derivatives are presented.\n\n## Definitions and Notations of Second Order Partial Derivatives\n\nFor a two variable function f(x , y), we can define 4 second order partial derivatives along with their notations.",
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"## Examples with Detailed Solutions on Second Order Partial Derivatives\n\nExample 1\nFind f\nxx, fyy given that f(x , y) = sin (x y)\nSolution\n\nfxx may be calculated as follows\nf\nxx = ∂2f / ∂x2 = ∂(∂f / ∂x) / ∂x\n= ∂(∂[ sin (x y) ]/ ∂x) / ∂x\n= ∂(y cos (x y) ) / ∂x\n= - y\n2 sin (x y) )\nfyy can be calculated as follows\nf\nyy = ∂2f / ∂y2 = ∂(∂f / ∂y) / ∂y\n= ∂(∂[ sin (x y) ]/ ∂y) / ∂y\n= ∂(x cos (x y) ) / ∂y\n= - x\n2 sin (x y) )\n\nExample 2\nFind fxx, fyy, fxy, fyx given that f(x , y) = x3 + 2 x y.\nSolution\n\nfxx is calculated as follows\nfxx = ∂2f / ∂x2 = ∂(∂f / ∂x) / ∂x\n= ∂(∂[ x3 + 2 x y ]/ ∂x) / ∂x\n= ∂( 3 x2 + 2 y ) / ∂x\n= 6x\nfyy is calculated as follows\nfyy = ∂2f / ∂y2 = ∂(∂f / ∂y) / ∂y\n= ∂(∂[ x3 + 2 x y ]/ ∂y) / ∂y\n= ∂( 2x ) / ∂y\n= 0\nfxy is calculated as follows\nfxy = ∂2f / ∂y∂x = ∂(∂f / ∂x) / ∂y\n= ∂(∂[ x3 + 2 x y ]/ ∂x) / ∂y\n= ∂( 3 x2 + 2 y ) / ∂y\n= 2\nfyx is calculated as follows\nfyx = ∂2f / ∂x∂y = ∂(∂f / ∂y) / ∂x\n= ∂(∂[ x3 + 2 x y ]/ ∂y) / ∂x\n= ∂( 2x ) / ∂x\n= 2\n\nExample 3\nFind fxx, fyy, fxy, fyx given that f(x , y) = x3y4 + x2 y.\nSolution\n\nfxx is calculated as follows\nfxx = ∂2f / ∂x2 = ∂(∂f / ∂x) / ∂x\n= ∂(∂[ x3y4 + x2 y ]/ ∂x) / ∂x\n= ∂( 3 x2y4 + 2 x y) / ∂x\n= 6x y4 + 2y\nfyy is calculated as follows\nfyy = ∂2f / ∂y2 = ∂(∂f / ∂y) / ∂y\n= ∂(∂[ x3y4 + x2 y ]/ ∂y) / ∂y\n= ∂( 4 x3y3 + x2 ) / ∂y\n= 12 x3y2\nfxy is calculated as follows\nfxy = ∂2f / ∂y∂x = ∂(∂f / ∂x) / ∂y\n= ∂(∂[ x3y4 + x2 y ]/ ∂x) / ∂y\n= ∂( 3 x2y4 + 2 x y ) / ∂y\n= 12 x2y3 + 2 x\nfyx is calculated as follows\nfyx = ∂2f / ∂x∂y = ∂(∂f / ∂y) / ∂x\n= ∂(∂[ x3y4 + x2 y ]/ ∂y) / ∂x\n= ∂(4 x3y3 + x2) / ∂x\n= 12 x2y3 + 2x\n\n## More References and Links to Partial Derivatives and Multivariable Functions\n\nMultivariable Functions"
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https://www.onlinemathlearning.com/function-domain-range.html | [
"# Functions: Domain, Range, Mappings\n\nRelated Topics:\nMore lessons for A-Level Maths\n\nAre you looking for A-Level Maths help?\n\nHave a look at our collection of videos, activities and worksheets that are suitable for A Level Mathematics.\n\nFunctions : Domain - Range : tutorial 1\nWhat is the domain and range of a function.\nThis tutorial introduces you to this concept by looking at linear and quadratic functions.\nf(x) = 2x -1, -1 ≤ x ≤ 1\nf(x) = 2x -1\ng(x) = x2\n\nFunctions : Domain - Range : tutorial 2\nThis tutorial looks at square root and reciprocal functions.\n\nDefinition of a function. Domain and range of functions.\n\nA-Level Edexcel C3 June 2009 Q5(c)\nWorked solution to this question on range of a function.\n\nA-Level Edexcel C3 June 2009 Q5(e)\nWorked solution to this question on domains.\n\nTry the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.",
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.8306321,"math_prob":0.86943567,"size":1087,"snap":"2023-40-2023-50","text_gpt3_token_len":254,"char_repetition_ratio":0.12650046,"word_repetition_ratio":0.06521739,"special_character_ratio":0.23551057,"punctuation_ratio":0.104761906,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9919403,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-26T02:26:36Z\",\"WARC-Record-ID\":\"<urn:uuid:8b5a2ab0-14ba-43ca-bede-5d3a02839b05>\",\"Content-Length\":\"36164\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:729149ba-2049-4e65-b0c9-6e4cf59aefd0>\",\"WARC-Concurrent-To\":\"<urn:uuid:748e78b0-87cd-4dbd-a89f-f3c326d16311>\",\"WARC-IP-Address\":\"173.247.219.45\",\"WARC-Target-URI\":\"https://www.onlinemathlearning.com/function-domain-range.html\",\"WARC-Payload-Digest\":\"sha1:OGZ4DNRUQUDOOB4ZRHVMKWN44DZNH5S7\",\"WARC-Block-Digest\":\"sha1:CMZOBILSF6SALDKDNSKIZNHML7O255UO\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510130.53_warc_CC-MAIN-20230926011608-20230926041608-00376.warc.gz\"}"} |
https://mathematica.stackexchange.com/questions/208816/is-there-an-issue-with-the-correlation-function | [
"# Is there an issue with the correlation function?\n\nI am trying to find the correlation between Uniform R.V.s using the Correlation command in mathematica, but it seems that either I am implementing it wrong or the software cannot find the answer. My code is pretty straight forward:\n\nCorrelation[UniformDistribution[], Sqrt[1-(UniformDistribution[])^2]]\n\n\nI also tried\n\nCorrelation[x, Sqrt[1-(x)^2], x \\[Distributed] UniformDistribution[]]\n\n\nI am aware that I can implement directly the definition of correlation and compute it in terms of expectation, but I was wondering if it was possible directly through this function.\n\n• The documentation for Correlation says \"Correlation[v1,v2] gives the correlation between the vectors v1 and v2... The lists v1 and v2 must be the same length...\" and it doesn't look like you are testing this on two vectors of values. If you study the documentation and click on the orange \"Details\" and study do you come to the same conclusion? – Bill Oct 31 '19 at 3:08\n\nUpdate: A much more compact approach...\n\ndist = TransformedDistribution[{x, Sqrt[1 - x^2]}, x \\[Distributed] UniformDistribution[]];\n\nCorrelation[dist, 1, 2]\n(* (8 - 3 π)/Sqrt[32 - 3 π^2] *)\n\n\nEnd of update\n\nI think you want the correlation between $$X$$ and $$\\sqrt{1-X^2}$$ where $$X \\sim Uniform(0,1)$$.\n\nμX = Mean[UniformDistribution[]]\n(* 1/2 *)\n\nvarX = Variance[UniformDistribution[]]\n(* 1/12 *)\n\ndistY = TransformedDistribution[Sqrt[1 - x^2], x \\[Distributed] UniformDistribution[]];\nμY = Mean[distY]\n(* π/4 *)\n\nvarY = Variance[distY]\n(* 1/48 (32-3 π^2) *)\n\ncovXY = Integrate[x Sqrt[1 - x^2], {x, 0, 1}] - μX μY\n(* 1/48 (32-3 π^2) *)\n\nρ = covXY/Sqrt[varX varY] // FullSimplify\n(* (8-3 π)/Sqrt[32-3 π^2] *)\nρ // N\n\n\nAs a check consider random samples from a uniform distribution:\n\nSeedRandom;\nn = 100000;\nz = RandomVariate[UniformDistribution[], n];\nCorrelation[z, Sqrt[1 - z^2]]\n(* -0.9214182413747128$$$$ *)\n\n• As an aside: this is an example where there is a \"perfect\" one-to-one relationship with a correlation other than -1 or +1. – JimB Oct 31 '19 at 17:02\n\nIn general you can get correlation matrix for multivariate symbolic distribution like this:\n\ncorr = Correlation[ ProductDistribution[UniformDistribution[], TransformedDistribution[Sqrt[1 - x^2],\nx \\[Distributed] UniformDistribution[]]]]\n\n\n{{1, 0}, {0, 1}}\n\nI believe you are looking for corr[[2,1]]`."
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.89944595,"math_prob":0.99359673,"size":927,"snap":"2020-10-2020-16","text_gpt3_token_len":215,"char_repetition_ratio":0.14842904,"word_repetition_ratio":0.0,"special_character_ratio":0.23408845,"punctuation_ratio":0.11363637,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99815285,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-04-05T14:39:12Z\",\"WARC-Record-ID\":\"<urn:uuid:60f905e0-5442-4f87-824e-20c34f3f78ea>\",\"Content-Length\":\"150701\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b86db70c-5f93-44d7-b37e-a170d85f52aa>\",\"WARC-Concurrent-To\":\"<urn:uuid:78f67791-2395-4add-a1e5-6a6989281d47>\",\"WARC-IP-Address\":\"151.101.65.69\",\"WARC-Target-URI\":\"https://mathematica.stackexchange.com/questions/208816/is-there-an-issue-with-the-correlation-function\",\"WARC-Payload-Digest\":\"sha1:E5WM27RCXJPMHGLMHBS2V4ND2ZTYVW7C\",\"WARC-Block-Digest\":\"sha1:GPLMUKFFLGLOQ73EBVBBFDFV735JJDKN\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-16/CC-MAIN-2020-16_segments_1585371604800.52_warc_CC-MAIN-20200405115129-20200405145629-00111.warc.gz\"}"} |
https://dynamics-and-control.readthedocs.io/en/latest/1_Dynamics/5_Complex_system_dynamics/Simulation%20of%20arbitrary%20transfer%20functions.html | [
"# 27. Simulation of arbitrary transfer functions¶\n\nIn some cases we can calculate the response of a system to an input completely analytically using Sympy as discussed in other notebooks. Sometimes these methods are not sufficient as they fail to calculate the inverse or because we have different inputs. This notebook covers several methods of simulating systems of arbitrary complexity.\n\n:\n\nimport numpy\nimport matplotlib.pyplot as plt\n%matplotlib inline\n\n\n## 27.1. Convert to ODE and integrate manually¶\n\nWe are very familiar with the Euler integration method by now. Let’s recap a quick simulation of a first-order system\n\n$G = \\frac{y(s)}{u(s)} = \\frac{K}{\\tau s + 1}$\n\nWe can rewrite this in the time domain as\n\n$y(s) (\\tau s + 1) = K u(s)$\n$\\tau \\frac{dy}{dt} + y(t) = K u(t)$\n$\\frac{dy}{dt} = -\\frac{1}{\\tau}y(t) + \\frac{K}{\\tau}u(t)$\n:\n\nK = 1\ntau = 5\n\n\nThis is our input function. Note that it could be anything (not just a step)\n\n:\n\ndef u(t):\nif t<1:\nreturn 0\nelse:\nreturn 1\n\n:\n\nts = numpy.linspace(0, 20, 1000)\ndt = ts\ny = 0\nys = []\nfor t in ts:\ndydt = -1/tau*y + 1/tau*u(t)\n\ny += dydt*dt\nys.append(y)\n\n:\n\nplt.plot(ts, ys)\n\n:\n\n[<matplotlib.lines.Line2D at 0x231e91d1eb0>]",
null,
"## 27.2. LTI support in scipy.signal¶\n\nNotice in the previous code that all the differential equations were linear and that that none of the coefficients of the variables change over time. Such a system is known as a Linear, Time Invariant (LTI) system. The scipy.signal module supplies many functions for dealing with LTI systems\n\n:\n\nimport scipy.signal\n\n\nWe define an LTI system by passing the coefficients of the numerator and denominator to the lti constructor\n\n:\n\nnumerator = K\ndenominator = [tau, 1]\nG = scipy.signal.lti(numerator, denominator)\n\n:\n\nG\n\n:\n\nTransferFunctionContinuous(\narray([0.2]),\narray([1. , 0.2]),\ndt: None\n)\n\n:\n\ntype(G)\n\n:\n\nscipy.signal.ltisys.TransferFunctionContinuous\n\n\n### 27.2.1. Step responses¶\n\nWe can obtain the step response of the system by using the step method of the object\n\n:\n\ndef plotstep(G):\n_, ys_step = G.step(T=ts)\nplt.plot(ts, ys_step);\n\n:\n\nplotstep(G)",
null,
"### 27.2.2. Responses to arbitrary inputs¶\n\nWe can also find the response of the system to an arbitrary input signal by using scipy.signal.lsim(). This is useful when simulating a complicated response or a response to an input read from a file.\n\n:\n\nus = [u(t) for t in ts] # evaluate the input function at all the times\n_, ys_lsim, xs = scipy.signal.lsim(G, U=us, T=ts)\nplt.plot(ts, ys)\nplt.plot(ts, ys_lsim, '--');\nplt.legend(['Euler', 'lsim'])\n\n:\n\n<matplotlib.legend.Legend at 0x231ea2517c0>",
null,
"### 27.2.3. Manual integration using state space form¶\n\nWe can also use our Euler loop to simulate arbitrary systems using the state space representation\n\n\\begin{align} \\dot{x} &= Ax + Bu \\\\ y &= Cx + Du \\end{align}\n\nThis is a useful technique when simulating Hybrid systems (where some parts are LTI and some are nonlinear systems).\n\nLuckily the lti object we created earlier can be converted to a state space representation.\n\n:\n\nGss = G.to_ss()\nGss\n\n:\n\nStateSpaceContinuous(\narray([[-0.2]]),\narray([[1.]]),\narray([[0.2]]),\narray([[0.]]),\ndt: None\n)\n\n:\n\nx = numpy.zeros((Gss.A.shape, 1))\nys_statespace = []\nfor t in ts:\nxdot = Gss.A.dot(x) + Gss.B.dot(u(t))\ny = Gss.C.dot(x) + Gss.D.dot(u(t))\n\nx += xdot*dt\nys_statespace.append(y[0,0])\n\n:\n\nplt.plot(ts, ys)\nplt.plot(ts, ys_statespace, '--')\nplt.legend(['Euler (manual)', 'Euler (state space)'])\n\n:\n\n<matplotlib.legend.Legend at 0x231ea2dfdf0>",
null,
"### 27.2.4. Demonstration for higher order functions¶\n\nAs mentioned before, Sympy cannot always be used to obtain inverse Laplace transforms. The scipy.signal functions continue to work for higher order functions, too. Let’s find the step response of the following transfer function:\n\n$G_2 = \\frac{1}{s^3 + 2s^2 + s + 1}$\n\nFeel free to uncomment and run the block below: I gave up waiting for the inverse to be calculated.\n\n:\n\n# import sympy\n\n# s, t = sympy.symbols('s, t')\n# G2 = 1/(s**3 + 2*s**2 + s + 1)\n# r = sympy.inverse_laplace_transform(G2/s, s, t)\n\n\nHowever, the step response is calculated quickly by the LTI object.\n\n:\n\nnumerator = 1\ndenominator = [1, 2, 1, 1]\nG2 = scipy.signal.lti(numerator, denominator)\n\n:\n\nplotstep(G2)",
null,
"### 27.2.5. State space for higher order functions¶\n\n:\n\nGss = G2.to_ss()\n\n:\n\nGss\n\n:\n\nStateSpaceContinuous(\narray([[-2., -1., -1.],\n[ 1., 0., 0.],\n[ 0., 1., 0.]]),\narray([[1.],\n[0.],\n[0.]]),\narray([[0., 0., 1.]]),\narray([[0.]]),\ndt: None\n)\n\n\nWe can use the same code as before. Now, I’m going to store all the states as well. Notice that we have three states for the third order system.\n\n:\n\nx = numpy.zeros((Gss.A.shape, 1))\nys_statespace = []\nxs = []\nfor t in ts:\nxdot = Gss.A.dot(x) + Gss.B.dot(u(t))\ny = Gss.C.dot(x) + Gss.D.dot(u(t))\n\nx += xdot*dt\nys_statespace.append(y[0, 0])\n# We need to copy otherwise the x update will overwrite all the values\nxs.append(x.copy())\n\n:\n\nplt.plot(ts, ys_statespace)\n\n:\n\n[<matplotlib.lines.Line2D at 0x231eb3bad90>]",
null,
":\n\nplt.plot(ts, numpy.concatenate(xs, axis=1).T)\n\n:\n\n[<matplotlib.lines.Line2D at 0x231ea3750a0>,\n<matplotlib.lines.Line2D at 0x231ea3750d0>,\n<matplotlib.lines.Line2D at 0x231ea375460>]",
null,
"### 27.2.6. Systems in series¶\n\nWhat if we wanted to see the response of $$G_3(s) = G(s) G_2(s)$$? You may expect that we would be able to find the product of two transfer functions, but the scipy.signal functions don’t allow this.\n\n:\n\nG\n\n:\n\nTransferFunctionContinuous(\narray([0.2]),\narray([1. , 0.2]),\ndt: None\n)\n\n:\n\n# G*G2\n\n# TypeError Traceback (most recent call last)\n# <ipython-input-25-2585f2f9cba1> in <module>()\n# ----> 1 G*G2\n\n# TypeError: unsupported operand type(s) for *: 'TransferFunctionContinuous' and 'TransferFunctionContinuous'\n\n\nInstead, we could use the convolution of the numerators and the denominators. This is equivalent to polynomial multiplication. For instance, let’s work out $$(s + 1)^3$$\n\n:\n\nnumpy.convolve(numpy.convolve([1, 1], [1, 1]), [1, 1])\n\n:\n\narray([1, 3, 3, 1])\n\n:\n\nG.num\n\n:\n\narray([0.2])\n\n:\n\nnumerator = numpy.convolve(G.num, G2.num)\nnumerator\n\n:\n\narray([0.2])\n\n:\n\ndenominator = numpy.convolve(G.den, G2.den)\ndenominator\n\n:\n\narray([1. , 2.2, 1.4, 1.2, 0.2])\n\n:\n\nG3 = scipy.signal.lti(numerator, denominator)\n\n:\n\nplotstep(G3)",
null,
"## 27.3. 3. Control module¶\n\nAnother option for handling LTI systems is to use the Python Control Systems Libaray. Unfortunately, this is not included in anaconda, so you will have to install it before use by uncommenting the line below and running it:\n\n:\n\n#!pip install control\n\n:\n\nimport control\n\n\nA big benefit of this module is that its transfer function objects support arithmetic operations:\n\n:\n\nG = control.tf(K, [tau, 1])\nG2 = control.tf(1, [1, 2, 1, 1])\nG3 = G*G2\n\n:\n\n_, y = control.step_response(G3, ts)\nplt.plot(ts, y)\n\n:\n\n[<matplotlib.lines.Line2D at 0x231eb5af490>]",
null,
"[ ]:"
] | [
null,
"https://dynamics-and-control.readthedocs.io/en/latest/_images/1_Dynamics_5_Complex_system_dynamics_Simulation_of_arbitrary_transfer_functions_9_1.png",
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"https://dynamics-and-control.readthedocs.io/en/latest/_images/1_Dynamics_5_Complex_system_dynamics_Simulation_of_arbitrary_transfer_functions_19_0.png",
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"https://dynamics-and-control.readthedocs.io/en/latest/_images/1_Dynamics_5_Complex_system_dynamics_Simulation_of_arbitrary_transfer_functions_22_1.png",
null,
"https://dynamics-and-control.readthedocs.io/en/latest/_images/1_Dynamics_5_Complex_system_dynamics_Simulation_of_arbitrary_transfer_functions_27_1.png",
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"https://dynamics-and-control.readthedocs.io/en/latest/_images/1_Dynamics_5_Complex_system_dynamics_Simulation_of_arbitrary_transfer_functions_56_1.png",
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.6484537,"math_prob":0.9963002,"size":6547,"snap":"2023-14-2023-23","text_gpt3_token_len":2012,"char_repetition_ratio":0.10622039,"word_repetition_ratio":0.049382716,"special_character_ratio":0.33694822,"punctuation_ratio":0.23217922,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9994221,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],"im_url_duplicate_count":[null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-06-10T11:04:02Z\",\"WARC-Record-ID\":\"<urn:uuid:b696d73d-4a4c-4958-93e4-17b2a44a15a9>\",\"Content-Length\":\"99833\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1785fd08-4591-46bc-83d0-16e272911116>\",\"WARC-Concurrent-To\":\"<urn:uuid:f6fc50ad-a314-4088-a22a-3c4a12302f26>\",\"WARC-IP-Address\":\"104.17.32.82\",\"WARC-Target-URI\":\"https://dynamics-and-control.readthedocs.io/en/latest/1_Dynamics/5_Complex_system_dynamics/Simulation%20of%20arbitrary%20transfer%20functions.html\",\"WARC-Payload-Digest\":\"sha1:LI5NO6ATXP2C3DP7GCXME72YEURSGGUL\",\"WARC-Block-Digest\":\"sha1:Q7FBUYTD2IMEDEN65PQC6Q7727Q7BBIQ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224657169.98_warc_CC-MAIN-20230610095459-20230610125459-00583.warc.gz\"}"} |
https://bmcbioinformatics.biomedcentral.com/articles/10.1186/1471-2105-14-368 | [
"# Meta-analysis methods for combining multiple expression profiles: comparisons, statistical characterization and an application guideline\n\n## Abstract\n\n### Background\n\nAs high-throughput genomic technologies become accurate and affordable, an increasing number of data sets have been accumulated in the public domain and genomic information integration and meta-analysis have become routine in biomedical research. In this paper, we focus on microarray meta-analysis, where multiple microarray studies with relevant biological hypotheses are combined in order to improve candidate marker detection. Many methods have been developed and applied in the literature, but their performance and properties have only been minimally investigated. There is currently no clear conclusion or guideline as to the proper choice of a meta-analysis method given an application; the decision essentially requires both statistical and biological considerations.\n\n### Results\n\nWe performed 12 microarray meta-analysis methods for combining multiple simulated expression profiles, and such methods can be categorized for different hypothesis setting purposes: (1) HS A : DE genes with non-zero effect sizes in all studies, (2) HS B : DE genes with non-zero effect sizes in one or more studies and (3) HS r : DE gene with non-zero effect in \"majority\" of studies. We then performed a comprehensive comparative analysis through six large-scale real applications using four quantitative statistical evaluation criteria: detection capability, biological association, stability and robustness. We elucidated hypothesis settings behind the methods and further apply multi-dimensional scaling (MDS) and an entropy measure to characterize the meta-analysis methods and data structure, respectively.\n\n### Conclusions\n\nThe aggregated results from the simulation study categorized the 12 methods into three hypothesis settings (HS A , HS B , and HS r ). Evaluation in real data and results from MDS and entropy analyses provided an insightful and practical guideline to the choice of the most suitable method in a given application. All source files for simulation and real data are available on the author’s publication website.\n\n## Background\n\nMicroarray technology has been widely used to identify differential expressed (DE) genes in biomedical research in the past decade. Many transcriptomic microarray studies have been generated and made available in public domains such as the Gene Expression Omnibus (GEO) from NCBI (http://www.ncbi.nlm.nih.gov/geo/) and ArrayExpress from EBI (http://www.ebi.ac.uk/arrayexpress/). From the databases, one can easily obtain multiple studies of a relevant biological or disease hypothesis. Since a single study often has small sample size and limited statistical power, combining information across multiple studies is an intuitive way to increase sensitivity. Ramasamy, et al. proposed a seven-step practical guidelines for conducting microarray meta-analysis : \"(i) identify suitable microarray studies; (ii) extract the data from studies; (iii) prepare the individual datasets; (iv) annotate the individual datasets; (v) resolve the many-to-many relationship between probes and genes; (vi) combine the study-specific estimates; (vii) analyze, present, and interpret results\". In the first step although theoretically meta-analysis increases the statistical power to detect DE genes, the performance can be deteriorated if problematic or heterogeneous studies are combined. In many applications, the data inclusion/exclusion criteria are based on ad-hoc expert opinions, a naïve sample size threshold or selection of platforms without an objective quality control procedure. Kang et al. proposed six quantitative quality control measures (MetaQC) for decision of study inclusion . Step (ii)-(v) are related to data preprocessing. Finally, Step (vi) and (vii) involve the selection of meta-analysis method and interpretation of the result and are the foci of this paper.\n\nMany microarray meta-analysis methods have been developed and applied in the literature. According to a recent review paper by Tseng et al. , popular methods mainly combine three different types of statistics: combine p-values, combine effect sizes and combine ranks. In this paper, we include 12 popular as well as state-of-the-art methods in the evaluation and comparison. Six methods (Fisher, Stouffer, adaptively weighted Fisher, minimum p-value, maximum p-value and rth ordered p-value) belonged to the p-value combination category, two methods (fixed effects model and random effects model) belonged to the effect size combination category and four methods (RankProd, RankSum, product of ranks and sum of ranks) belonged to the rank combination category. Details of these methods and citations will be provided in the Method section. Despite the availability of many methods, pros and cons of these methods and a comprehensive evaluation remain largely missing in the literature. To our knowledge, Hong and Breitling , Campain and Yang are the only two comparative studies that have systematically compared multiple meta-analysis methods. The number of methods compared (three and five methods, respectively) and the number of real examples examined (two and three examples respectively with each example covering 2-5 microarray studies) were, however, limited. The conclusions of the two papers were suggestive with limited insights to guide practitioners. In addition, as we will discuss in the Method section, different meta-analysis methods have different underlying hypothesis setting targets. As a result, the selection of an adequate (or optimal) meta-analysis method depends heavily on the data structure and the hypothesis setting to achieve the underlying biological goal.\n\nIn this paper, we compare 12 popular microarray meta-analysis methods using simulation and six real applications to benchmark their performance by four statistical criteria (detection capability, biological association, stability and robustness). Using simulation, we will characterize the strength of each method under three different hypothesis settings (i.e. detect DE genes in \"all studies\", \"majority of studies\" or \"one or more studies\"; see Method section for more details). We will compare the similarity and grouping of the meta-analysis methods based on their DE gene detection results (by using a similarity measure and multi-dimension scaling plot) and use an entropy measure to characterize the data structure to determine which hypothesis setting may be more adequate in a given application. Finally, we give a guideline to help practitioners select the best meta-analysis method under the choice of hypothesis setting in their applications.\n\n## Methods\n\n### Real data sets\n\nSix example data sets for microarray meta-analysis were collected for evaluations in this paper. Each example contained 4-8 microarray studies. Five of the six examples were of the commonly seen two-group comparison and the last breast cancer example contained relapse-free survival outcome. We applied the MetaQC package to assess quality of the studies for meta-analysis and determined the final inclusion/exclusion criteria. The principal component analysis (PCA) bi-plots and the six QC measures are summarized in Additional file 1: Figure S1, Tables S2 and S3. Details of the data sets are available in Additional file 1: Table S1.\n\n### Underlying hypothesis settings\n\nFollowing the classical convention of Brinbaum and Li and Tseng (see also Tseng et al. ), meta-analysis methods can be classified into two complementary hypothesis settings. In the first hypothesis setting (denoted as HS A ), the goal is to detect DE genes that have non-zero effect sizes in all studies:\n\n$H 0 : ∩ k = 1 K θ k = 0 versus H a : ∩ k = 1 K θ k ≠ 0 H S A$\n\nwhere θ k is the effect size of study k. The second hypothesis setting (denoted as HS B ), however, aims to detect a DE gene if it has non-zero effect size in \"one or more\" studies:\n\n$H 0 : ∩ k = 1 K θ k = 0 versus H a : ∩ k = 1 K θ k ≠ 0 H S B$\n\nIn most applications, HS A is more appropriate to detect conserved and consistent candidate markers across all studies. However, different degrees of heterogeneity can exist in the studies and HS B can be useful to detect study-specific markers (e.g. studies from different tissues are combined and tissue specific markers are expected and of interest). Since HS A is often too conservative when many studies are combined, Song and Tseng (2012) proposed a more practical and robust hypothesis setting (namely HS r ) that targets on DE genes with non-zero effect sizes in \"majority\" of studies, where majority of studies is defined as, for example, more than 50% of combined studies (i.e. r ≥ 0.5K). The robust hypothesis setting considered was:\n\n$H 0 : ∩ k = 1 K θ k = 0 versus H a : ∑ k = 1 K I θ k ≠ 0 ≥ r H S r$\n\nA major contribution of this paper is to characterize meta-analysis methods suitable for different hypothesis settings (HS A , HS B and HS r ) using simulation and real applications and to compare their performance with four benchmarks to provide a practical guideline.\n\n### Microarray meta-analysis data pre-processing\n\nAssume that we have K microarray studies to combine. For study k (1 ≤ k ≤ K), denote by x gsk the gene expression intensity of gene g (1 ≤ g ≤ G) and sample s (1 ≤ s ≤ S k ; S k the number of samples in study k), and y sk the disease/outcome variable of sample s. The disease/outcome variable can be of binary, multi-class, continuous or censored data, representing the disease state, severity or prognosis outcome (e.g. tumor versus normal or recurrence survival time). The goal of microarray meta-analysis is to combine information of K studies to detect differentially expressed (DE) genes associated with the disease/outcome variable. Such DE genes serve as candidate markers for disease classification, diagnosis or prognosis prediction and help understand the genetic mechanisms underlying a disease. In this paper, before meta-analysis we first applied penalized t-statistic to each individual study to generate p-values or DE ranks for a binary outcome. In contrast to traditional t-statistic, penalized t-statistic adds a fudge parameter s0 to stabilize the denominator $T = X ¯ - Y ¯ / ( s ^ + s 0$; $X ¯$ and $Y ¯$ are means of case and control groups) and to avoid a large t-statistic due to small estimated variance $s ^$. The p-values were calculated using the null distributions derived from conventional non-parametric permutation analysis by randomly permuting the case and control labels for 10,000 times . For censored outcome variables, Cox proportion hazard model and log-rank test were used . Meta-analysis methods (described in the next subsection) were then used to combine information across studies and generate meta-analyzed p-values. To account for multiple comparison, Benjamini and Hochberg procedure was used to control false discovery rate (FDR) . All methods were implemented using the \"MetaDE\" package in R . Data sets and all programming codes are available at http://www.biostat.pitt.edu/bioinfo/publication.htm.\n\n### Microarray meta-analysis methods\n\nAccording to a recent review paper , microarray meta-analysis methods can be categorized into three types: combine p-values, combine effect sizes and combine ranks. Below, we briefly describe 12 methods that were selected for comparison.\n\n#### Combine p-values\n\nFisher The Fisher’s method sums up the log-transformed p-values obtained from individual studies. The combined Fisher’s statistic $χ Fisher 2 = - 2 ∑ i = 1 k log P i$ follows a χ2 distribution with 2 k degrees of freedom under the null hypothesis (assuming null p-values are un;iformly distributed). Note that we perform permutation analysis instead of such parametric evaluation for Fisher and other methods in this paper. Smaller p-values contribute larger scores to the Fisher’s statistic.\n\nStouffer Stouffer’s method sums the inverse normal transformed p-values. Stouffer’s statistics $T Stouffer = ∑ i = 1 k z i / k ( z i Φ - 1 p i ,$ where Φ is standard normal c.c.f) follows a standard normal distribution under the null hypothesis. Similar to Fisher’s method, smaller p-values contribute more to the Stouffer’s score, but in a smaller magnitude.\n\nAdaptively weighted (AW) Fisher The AW Fisher’s method assigns different weights to each individual study $T AW = - ∑ k = 1 K w k ⋅ log P i , w k = 0 or 1$ and it searches through all possible weights to find the best adaptive weight with the smallest derived p-value. One significant advantage of this method is its ability to indicate which studies contribute to the evidence aggregation and elucidates heterogeneity in the meta-analysis. Details can be referred to the Additional file 1.\n\nMinimum p -value (minP) The minP method takes the minimum p-value among the K studies as the test statistic . It follows a beta distribution with degrees of freedom α = 1 and β = k under the null hypothesis. This method detects a DE gene whenever a small p-value exists in any one of the K studies.\n\nMaximum p -value (maxP) The maxP method takes maximum p-value as the test statistic . It follows a beta distribution with degrees of freedom α = K and β = 1 under the null hypothesis. This method targets on DE genes that have small p-values in \"all\" studies.\n\nr-th ordered p -value (rOP) The rOP method takes the r-th order statistic among sorted p-values of K combined studies. Under the null hypothesis, the statistic follows a beta distribution with degrees of freedom α = r and β = K - r + 1. The minP and maxP methods are special cases of rOP. In Song and Tseng , rOP is considered a robust form of maxP (where r is set as greater than 0.5∙K) to identify candidate markers differentially expressed in \"majority\" of studies.\n\n#### Combine effect size\n\nFixed effects model (FEM) FEM combines the effect size across K studies by assuming a simple linear model with an underlying true effect size plus a random error in each study.\n\nRandom effects model (REM) REM extends FEM by allowing random effects for the inter-study heterogeneity in the model. Detailed formulation and inference of FEM and REM are available in the Additional file 1.\n\n#### Combine rank statistics\n\nRankProd (RP) and RankSum (RS) RankProd and RankSum are based on the common biological belief that if a gene is repeatedly at the top of the lists ordered by up- or down-regulation fold change in replicate experiments, the gene is more likely a DE gene . Detailed formulation and algorithms are available in the Additional file 1.\n\nProduct of ranks (PR) and Sum of ranks (SR) These two methods apply a naïve product or sum of the DE evidence ranks across studies . Suppose R gk represents the rank of p-value of gene g among all genes in study k. The test statistics of PR and SR methods are calculated as $P R g = ∏ k = 1 K R gk$ and $S R g = ∑ k = 1 K R gk ,$ respectively. P-values of the test statistics can be calculated analytically or obtained from a permutation analysis. Note that the ranks taken from the smallest to largest (the choice in the method) are more sensitive than ranking from largest to smallest in the PR method, while it makes no difference to SR.\n\n### Characterization of meta-analysis methods\n\n#### MDS plots to characterize the methods\n\nThe multi-dimensional scaling (MDS) plot is a useful visualization tool for exploring high-dimensional data in a low-dimensional space . In the evaluation of 12 meta-analysis methods, we calculated the adjusted DE similarity measure for every pair of methods to quantify the similarity of their DE analysis results in a given example. A dissimilarity measure is then defined as one minus the adjusted DE similarity measure and the dissimilarity measure is used to generate an MDS plot of the 12 methods. In the MDS plot, methods that are clustered in a neighborhood indicate that they produce similar DE analysis results.\n\n#### Entropy measure to characterize data sets\n\nAs indicated in the Section of \"Underlying hypothesis settings\", selection of the most suitable meta-analysis method(s) largely depends on their underlying hypothesis setting (HS A , HS B and HS r ). The selection of a hypothesis setting for a given application should be based on the experimental design, biological knowledge and the associated analytical objectives. There are, however, occasions that little prior knowledge or preference is available and an objective characterization of the data structure is desired in a given application. For this purpose, we developed a data-driven entropy measure to characterize whether a given meta-analysis data set contains more HS A -type markers or HS B -type markers . The algorithm is described below:\n\n1. 1.\n\nApply Fisher’s meta-analysis method to combine p-values across studies to identify the top H candidate markers. Here we used H = 1,000, H represents the rough number of DE genes (in our belief) that are contained in the data.\n\n2. 2.\n\nFor each selected marker, the standardized minus p-value score for gene g in the k-th study is defined as $l gk = - log p gk / - ∑ k = 1 K log p gk .$ Note that 0 ≤ l gk ≤ 1, large l gk corresponds to more significant p-value p gk , and $∑ k = 1 K l gk = 1 .$\n\n3. 3.\n\nThe entropy of gene g is defined as $e g = - ∑ k = 1 K l gk log l gk$. Box-plots of entropies of the top H genes are generated for each meta-analysis application (Figure 1(b)).\n\nIntuitively, a high entropy value indicates that the gene has small p-values in all or most studies and is of HS A or HS r -type. Conversely, genes with small entropy have small p-values in one or only few studies where HS B -type methods are more adequate. When calculating l gk in step 2, we capped -log(p gk ) at 10 to avoid contributions of close-to-zero p-values that can generate near-infinite scores. The entropy box-plot helps determine an appropriate meta-analysis hypothesis setting if no pre-set biological objective exists.\n\n### Evaluation criteria\n\nFor objective quantitative evaluation, we developed the following four statistical criteria to benchmark performance of the methods.\n\n#### Detection capability\n\nThe first criterion considers the number of DE genes detected by each meta-analysis method under the same pre-set FDR threshold (e.g. FDR = 1%). Although detecting more DE genes does not guarantee better \"statistical power\", this criterion has served as a surrogate of statistical power in previous comparative studies . Since we do not know the underlying true DE genes, we refer to this evaluation as \"detection capability\" in this paper. An implicit assumption underlying this criterion is that the statistical procedure to detect DE genes in each study and the FDR control in the meta-analysis are accurate (or roughly accurate). To account for data variability in the evaluation, we bootstrapped (i.e. sampled with replacement to obtain the same number of samples in each bootstrapped dataset) the samples in each study for B = 50 times and show the plots of ean with standard error bars. In the bootstrapping, the entire sample is either selected or not so the gene dependence structure is maintained. Denote by r meb the rank of detection capability performance (the smaller the better) of method m (1 ≤ m ≤ 12) in example e (1 ≤ e ≤ 6) and in the bth (1 ≤ b ≤ 12) bootstrap simulation. The mean standardized rank (MSR) for method m and example e is calculated as $MSR me = ∑ b = 1 B r meb / # of methods compared / B$ and the aggregated standardized rank (ASR) is calculated as $ASR m = ∑ e = 1 6 MSR m e / 6 ,$ representing the overall performance of method m across all six examples. Additional file 1: Table S4 shows the MSR and ASR of all 12 methods and Figure 2 (in the Result section) shows plot of mean with standard error bars for each method ordered by ASR. We note that MSR and ASR are both standardized between 0 and 1. The standardization in MSR is necessary because in the breast cancer survival example we cannot apply FEM, REM, RankSum and RankProd as they are developed only for a two group comparison.\n\n#### Biological association\n\nThe second criterion requires that a good meta-analysis method should detect a DE gene list that has better association with pre-defined \"gold standard\" pathways related to the targeted disease. Such a \"gold standard\" pathway set should be obtained from biological knowledge for a given disease or biological mechanism under investigation. However, since most disease or biological mechanisms are not well-studied, obtaining such \"gold standard\" pathways is either difficult or questionable. To facilitate this evaluation without bias, we develop a computational and data-driven approach to determine a set of surrogate disease-related pathways out of a large collection of pathways by combining pathway enrichment analysis results from each single study. Specifically, we first collected 2,287 pathways (gene sets) from MSigDB (http://www.broadinstitute.org/gsea/msigdb/): 1,454 pathways from \"GO\", 186 pathways from \"KEGG\", 217 pathways from \"BIOCARTA\" and 430 pathways from \"REACTOME\", respectively. We filtered out pathways with less than 5 genes or more than 200 genes and 2,113 pathways were left for the analysis. DE analysis was performed in each single study separately and pathway enrichment analysis was performed for all the 2,113 pathways by the Kolmogorov-Smirnov (KS) association test. Denote by p uk the resulting pathway enrichment p-value from KS test for pathway u (1 ≤ u ≤ 2,113) and study k (1 ≤ k ≤ K). For a given study k, enrichment ranks over pathways were calculated as r uk = rank u (p uk ). A rank-sum score for a given pathway u was then derived as $S u = ∑ k = 1 K r uk .$ Intuitively, pathways with small rank-sum scores indicate that they are likely associated with the disease outcome by aggregated evidence of the K individual study analyses. We choose the top |D| pathways that had the smallest rank-sum scores as the surrogate disease-related pathways and used these to proceed with the biological association evaluation of meta-analysis methods in the following.\n\nGiven the selected surrogate pathways D, the following procedure was used to evaluate performance of the 12 meta-analysis methods for a given example e (1 ≤ e ≤ 6). For each meta-analysis method m (1 ≤ m ≤ M = 12), the DE analysis result was associated with pathway u and the resulting enrichment p-value by KS-test was denoted by $P ˜ med 1 ≤ d ≤ | D | .$ The rank of $P ˜ med$ for method m among 12 methods was denoted by $v med = rank m P ˜ med .$ Similar to the detection capability evaluation, we calculated the mean standardized rank (MSR) for method m and example e as $MSR me = ∑ d = 1 D v med / # of the methods compared / D$ and the aggregated standardized rank (ASR) as $ASR m = ∑ e = 1 6 MSR me / 6 ,$ representing the overall performance of method m. To select the parameter |D| for surrogate disease-related pathways, Additional file 1: Figure S4 shows the trend of MSR me (on the y-axis) versus |D| (on the x-axis) as |D| increases. The result indicated that the performance evaluation using different D only minimally impacted the conclusion when D > 30. We choose D = 100 throughout this paper.\n\nNote that we used KS test, instead of the popular Fisher’s exact test because each single study detected variable number of DE genes under a given FDR cutoff and the Fisher’s exact test is usually not powerful unless a few hundred DE genes are detected. On the other hand, the KS test does not require an arbitrary p-value cutoff to determine the DE gene list for enrichment analysis.\n\n#### Stability\n\nThe third criterion examines whether a meta-analysis method generates stable DE analysis result. To achieve this goal, we randomly split samples into half in each study (so that cases and controls are as equally split as possible). The first half of each study was taken to perform the first meta-analysis and generate a DE analysis result. Similarly, the second half of each study was taken to perform a second meta-analysis. The generated DE analysis results from two separate meta-analyses were compared by the adjusted DE similarity measure (to be described in the next section). The procedure is repeated for B = 50 times. Denote by S meb the adjusted DE similarity measure of method m of the bth simulation in example e. Similar to the first two criteria, MSR and ASR were calculated based on S meb to evaluate the methods.\n\n#### Robustness\n\nThe final criterion investigates the robustness of a meta-analysis method when an outlying irrelevant study is mistakenly added to the meta-analysis. For each of the six real examples, we randomly picked one irrelevant study from the other five examples, added it to the specific example for meta-analysis and evaluated the change from the original meta-analysis. The adjusted DE similarity measure was calculated between the original meta-analysis and the new meta-analysis with an added outlier. A high adjusted DE similarity measure shows better robustness against inclusion of the outlying study. This procedure was repeated until all irrelevant studies were used. The MSR and ASR are then calculated based on the adjusted DE similarity measures to evaluate the methods.\n\n### Similarity measure between two ordered DE gene lists\n\nTo compare results of two DE detection methods (from single study analysis or meta-analysis), a commonly used method in the literature is to take the DE genes under certain p-value or FDR threshold, plot the Venn diagram and compute the ratio of overlap. This method, however, greatly depends on the selection of FDR threshold and is unstable. Another approach is to take the generated DE ordered gene lists from two methods and compute the non-parametric Spearman rank correlation . This method avoids the arbitrary FDR cutoff but gives, say, the top 100 important DE genes and the bottom 100 non-DE genes equal contribution. To circumvent this pitfall, Li et al. proposed a parametric reproducibility measure for ChIP-seq data in the ENCODE project . Yang et al. introduced an OrderedList measure to quantify similarity of two ordered DE gene lists . For simplicity, we extended the OrderedList measure into a standardized similarity score for the evaluation purpose in this paper. Specifically, suppose G 1 and G 2 are two ordered DE gene lists (e.g. ordered by p-values) and small ranks represent more significant DE genes. We denote by O n (G1, G2) the number of overlapped genes in the top n genes of G 1 and G 2 . As a result, 0 ≤ O n (G1, G2) ≤ n and a large O n (G1, G2) value indicates high similarity of the two ordered lists in the top n genes. A weighted average similarity score is calculated as $S G 1 , G 2 = ∑ n = 1 G e - an · O n G 1 , G 2 ,$ where G is the total number of matched genes and the power α controls the magnitude of weights emphasized on the top ranked genes. When α is large, top ranked genes are weighted higher in the similarity measure. The expected value (under the null hypothesis that the two gene rankings are randomly generated) and maximum value of S can be easily calculated: $E null S G 1 , G 2 = ∑ n = 1 G e - α n · n 2 / G$ and $max S G 1 , G 2 = ∑ n = 1 G e - an · n .$ We apply an idea similar to adjusted Rand index used to measure similarity of two clustering results and define the adjusted DE similarity measure as\n\n$S * G 1 , G 2 = S G 1 , G 2 - E null S G 1 , G 2 Max S G 1 , G 2 - E null S G 1 , G 2$\n\nThis measure ranges between -1 to 1 and gives an expected value of 0 if two ordered gene lists are obtained by random chance. Yang et al. proposed a resampling-based and ROC methods to estimate the best selection of α. Since the number of DE genes in our examples are generally high, we choose a relatively small α = 0.001 throughout this paper. We have tested different α and found that the results were similar (Additional file 1: Figure S7).\n\n## Results\n\n### Simulation setting\n\nWe conducted simulation studies to evaluate and characterize the 12 meta-analysis methods for detecting biomarkers in the underlying hypothesis settings of HS A , HS B or HS r . The simulation algorithm is described below:\n\n1. 1.\n\nWe simulated 800 genes with 40 gene clusters (20 genes in each cluster) and other 1,200 genes do not belong to any cluster. The cluster indexes C g for gene g (1 ≤ g ≤ 2, 000) were randomly sampled, such that ∑ I{C g = 0} = 1, 200 and ∑ I{C g = c} = 20, 1 ≤ c ≤ 40.\n\n2. 2.\n\nFor genes in cluster c (1 ≤ c ≤ 40) and in study k (1 ≤ k ≤ 5), we sampled $∑ ck ' ~ W - 1 Ψ , 60 ,$ where Ψ = 0.5I 20 × 20 + 0.5J 20 × 20, W - 1 denotes the inverse Wishart distribution, I is the identity matrix and J is the matrix with all elements equal 1. We then standardized $Σ ck '$ into Σ ck where the diagonal elements are all 1’s.\n\n3. 3.\n\n20 genes in cluster c was denoted by the index of g c1, …, g c20, i.e. $C g cj = c , where 1 ≤ c ≤ 40 and 1 ≤ j ≤ 20 .$ We sampled gene expression levels of genes in cluster c for sample n as $X g c 1 nk ' , … , X g c 20 nk ' T ~ MVN 0 , ∑ ck$ where 1 ≤ n ≤ 100 and 1 ≤ k ≤ 5, and sample expression level for the gene $g ~ N 0 , σ k 2$ which is not in any cluster for sample n, where 1 ≤ n ≤ 100, 1 ≤ k ≤ 5 and $σ k 2$ was uniformly distributed from [0.8, 1.2], which indicates different variance for study k.\n\n4. 4.\n\nFor the first 1,000 genes (1 ≤ g ≤ 1, 000), k g (the number of studies that are differentially expressed for gene g) was generated by sampling k g = 1, 2, 3, 4 and 5, respectively. For the next 1,000 genes (1, 001 ≤ g ≤ 2, 000), k g = 0 represents non-DE genes in all five studies.\n\n5. 5.\n\nTo simulate expression intensities for cases, we randomly sampled δ gk {0, 1}, such that ∑ k δ gk = k g . If δ gk = 1, gene g in study k was a DE gene, otherwise it was a non-DE gene. When δ gk = 1, we sampled expression intensities μ gk from a uniform distribution in the range of [0.5, 3], which means we considered the concordance effect (up-regulated) among all simulated studies. Hence, the expression for control samples are $X gnk = X gnk ' ,$ and case samples are $Y gnk = X g n + 50 k ' + μ gk · δ gk ,$ for 1 ≤ g ≤ 2, 000, 1 ≤ n ≤ 50 and 1 ≤ k ≤ 5.\n\nIn the simulation study, we had 1,000 non-DE genes in all five studies (k g = 0), and 1,000 genes were differentially expressed in 1 ~ 5 studies (k g = 1, 2, 3, 4, 5). On average, we had roughly the same number (~200) of genes in each group of k g = 1, 2, 3, 4, 5. See Additional file 1: Figure S2 for the heatmap of a simulated example (red colour represents up-regulated genes). We applied the 12 meta-analysis method under FDR control at 5%. With the knowledge of true k g , we were able to derive the sensitivity and specificity for HS A and HS B , respectively. In HS A , genes with k g = 5 were the underlying true positives and genes with k g = 0 ~ 4 were the underlying true negatives; in HS B , gene with k g = 1 ~ 5 were the underlying true positives and genes with k g = 0 were the true negatives. By adjusting the decision cut-off, the receiver operating characteristic (ROC) curves and the resulting area under the curve (AUC) were used to evaluate the performance. We simulated 50 data sets and reported the means and standard errors of the AUC values. AUC values range between 0 and 1. AUC = 50% represents a random guess and AUC = 1 reaches the perfect prediction. The above simulation scheme only considered the concordance effect sizes (i.e. all with up-regulation when a gene is DE in a study) among five simulated studies. In many applications, some genes may have p-value statistical significance in the meta-analysis but the effect sizes are discordant (i.e. a gene is up-regulation in one study but down-regulation in another study). To investigate that effect, we performed a second simulation that considers random discordant cases. In step 5, the μ gk became a mixture of two uniform distributions: π gk Unif [-3, -0.5]+ (1 - π gk ) Unif[0.5, 3], where π gk is the probability of gene g (1 ≤ g ≤ 2, 000) in study k(1 ≤ k ≤ 5) to have a discordant effect size (down-regulated). We set π gk = 0.2 for the discordant simulation setting.\n\n### Simulation results to characterize the methods\n\nThe simulation study provided the underlying truth to characterize the meta-analysis methods according to their strengths and weaknesses for detecting DE genes of different hypothesis settings. The performances of 12 methods were evaluated by receiver operating characteristic (ROC) curves, which is a visualization tool that illustrates the sensitivity and specificity trade-off, and the resulting area under the ROC curve (AUC) under two different hypothesis settings of HS A and HS B . Table 1 shows the detected number of DE genes under nominal FDR at 5%, the true FDR and AUC values under HS A and HS B for all 12 methods. The values were averaged over 50 simulations and the standard errors are shown in the parentheses.\n\nFigure 3 shows the histogram of the true number of DE studies (i.e. k g ) among the detected DE genes under FDR = 5% for each method. It is clearly seen that minP, Fisher, AW, Stouffer and FEM detected HS B -type DE genes and had high AUC values under HS B criterion (0.98-0.99), compared to lower AUC values under HS A criterion (0.79-0.9). For these methods, the true FDR for HS A generally lost control (0.41- 0.44). On the other hand, maxP, rOP and REM had high AUC under HS A criterion (0.96-0.99) (true FDR = 0.068-0.117) compared to HS B (0.75-0.92). maxP detected mostly HS A -type of markers and rOP and REM detected mostly HS r -type DE genes. PR and SR detected mostly HS A -type DE genes but they surprisingly had very high AUC under both HS A and HS B criteria. The RankProd method detected DE genes between HS r and HS B types and had a good AUC value under HS B . The RankSum detected HS B -type DE genes but had poor AUC values (0.5) for both HS A and HS B . Table 1 includes our concluding characterization of the targeted hypothesis settings for each meta-analysis method (see also Additional file 1: Figure S5 of the ROC curve and AUC of HS A -type and HS B -type in 12 meta-analysis methods). Additional file 1: Figure S3 shows the result for the second discordant simulation setting. The numbers of studies with opposite effect size are represented by different colours in histogram plot (green: all studies with concordance effect size; blue: one study has opposite effect size with the remaining; red: two studies have opposite effect size with the remaining). In summary, almost all meta-analysis methods could not avoid inclusion of genes with opposite effect sizes. Particularly, methods utilizing p-values from two-sided tests (e.g. Fisher, AW, minP, maxP and rOP) could not distinguish direction of effect sizes. Stouffer was the only method that accommodated the effect size direction in its z-transformation formulation but its ability to avoid DE genes with discordant effect sizes seemed still limited. Owen (2009) proposed a one-sided correction procedure for Fisher’s method to avoid detection of discordant effect sizes in meta-analysis . The null distribution of the new statistic, however, became difficult to derive. The approach can potentially be extended to other methods and more future research will be needed for this issue.\n\n### Results of the four evaluation criteria\n\n#### Detection capability\n\nFigure 2 shows the number of DE genes identified by each of the 12 meta-analysis methods (FDR = 10% for MDD and breast cancer due to their weak signals and FDR = 1% for all the others). Each plot shows mean with standard error bars for 50 bootstrapped data sets. Additional file 1: Table S4 shows the MSR and ASR for each method in the six examples. The methods in Figure 2 are ordered according to their ASR values. The top six methods with the strongest detection capability were those that detected HS B -type DE genes from the conclusion of Table 1: Fisher, AW, Stouffer, minP, FEM and RankSum. The order of performance of these six methods was pretty consistent across all six examples. The next four methods were rOP, RankProd, maxP and REM and they targeted on either HS r or HS A . PR and SR had the weakest detection capability, which was consistent with the simulation result in Table 1.\n\n#### Biological association\n\nFigure 4 shows plots of mean with standard error bars from the pathway association p-values (minus log-transformed) of the top 100 surrogate disease-related pathways for the 12 methods. Additional file 1: Table S5 shows the corresponding MSR and ASR. We found that Stouffer, Fisher and AW had the best performance among the 12 methods. Surprisingly we found that although PR and SR had low detection capability in simulation and real data, they consistently had relatively high biological association results. This may be due to the better DE gene ordering results these two methods provide, as was also shown by the high AUC values under both hypothesis settings in the simulation.\n\n#### Stability\n\nFigure 5 shows the plots of mean with standard error bars of stability calculated by adjusted DE similarity measure. Additional file 1: Table S6 contains the corresponding MSR and ASR. In summary, RankProd and RankSum methods were the most stable meta-analysis methods probably because these two nonparametric approaches take into account all possible fold change calculations between cases and controls. They do not need any distributional assumptions, which provided stability even when sample sizes were small . The maximum p-value method consistently had the lowest stability in all data sets, which is somewhat expected. For a given candidate marker with a small maximum p-value, the chance that at least one study has significantly inflated p-values is high when sample size is reduced by half. The stability measures in the breast cancer example were generally lower than other examples. This is mainly due to the weak signals for survival outcome association, which might be improved if larger sample size is available.\n\n#### Robustness\n\nFigure 6 shows the plots of mean with standard error bars of robustness calculated by adjusted DE similarity measure between the original meta-analysis and the new meta-analysis with an added outlier. Additional file 1: Table S7 shows the corresponding MSR and ASR values. In general, methods suitable for HS B (minP, AW, Fisher and Stouffer) have better robustness than methods for HS A or HS r (e.g. maxP and rOP). The trend is consistent in the prostate cancer, brain cancer and IPF examples but is more variable in the weak-signal MDD and breast cancer examples. RankSum was surprisingly the most sensitive method to outliers, while RankProd performs not bad.\n\n### Characterization of methods by MDS plots\n\nWe applied the adjusted DE similarity measure to quantify the similarity of the DE gene orders from any two meta-analysis methods. The resulting dissimilarity measure (i.e. one minus adjusted similarity measure) was used to construct the multidimensional scaling (MDS) plot, showing the similarity/dissimilarity structure between the 12 methods in a two-dimensional space. When two methods were close to each other, they generated similar DE gene ordering. The patterns of MDS plots from six examples generated quite consistent results (Additional file 1: Figure S6). Figure 1(a) shows an aggregated MDS plot where the input dissimilarity matrix is averaged from the six examples. We clearly observed that Fisher, AW, Stouffer, minP, PR and SR were consistently clustered together in all six individual and the aggregated MDS plot (labeled in red). This is not surprising given that these methods all sum transformed p-value evidence across studies (except for minP). Two methods to combine effect sizes and two methods to combine ranks (FEM, REM, RankProd and RankSum labeled in blue) are consistently clustered together. Finally, the maxP and rOP methods seem to form a third loose cluster (labeled in green).\n\n### Characterization of data sets by entropy measure\n\nFrom the simulation study, selection of a most suitable meta-analysis method depends on the hypothesis setting behind the methods. The choice of a hypothesis setting mostly depends on the biological purpose of the analysis; that is, whether one aims to detect candidate markers differentially expressed in \"all\" (HS A ), \"most\" (HS r ) or \"one or more\" (HS B ) studies. However, when no biological prior information or preference exists, the entropy measure can be objectively used to determine the choice of hypothesis setting. The analysis identifies the top 1,000 genes from Fisher’s meta-analysis method and the gene-specific entropy of each gene is calculated. When the entropy is small, the p-values are small in only one or very few studies. Conversely, when the entropy is large, most or all of the studies have small p-values. Figure 1(b) shows the box-plots of entropy of the top 1,000 candidate genes identified by Fisher’s method in the six data sets. The result shows that prostate cancer comparing primary and metastatic tumor samples had the smallest entropy values, which indicated high heterogeneity across the three studies and that HS B should be considered in the meta-analysis. On the other hand, MDD had the highest entropy values. Although the signals of each MDD study were very weak, they were rather consistent across studies and application of HS A or HS r was adequate. For the other examples, we suggest using the robust HS r unless other prior biological purpose is indicated.\n\n## Conclusions and discussions\n\n### An application guideline for practitioners\n\nFrom the simulation study, the 12 meta-analysis methods were categorized into three hypothesis settings (HS A , HS B and HS r ), showing their strengths for detecting different types of DE genes in the meta-analysis (Figure 3 and the second column of Table 2). For example, maxP is categorized to HS A since it tends to detect only genes that are differentially expressed in all studies. From the results using four evaluation criteria, we summarized the rank of ASR values (i.e. the order used in Figures 2 and 6) and calculated the rank sum of each method in Table 2. The methods were then sorted first by the hypothesis setting categories and then by the rank sum. The clusters of methods from the MDS plot were also displayed. For methods in the HS A category, we surprisingly see that the maxP method performed among the worst in all four evaluation criteria and should be avoided. PR was a better choice in this hypothesis setting although it provides a rather weak detection capability. For HS B , Fisher, AW and Stouffer performed very well in general. Among these three methods, we note that AW has an additional advantage to provide an adaptive weight index that indicates the subset of studies contributing to the meta-analysis and characterizes the heterogeneity (e.g. adaptive weight (1,0,…) indicates that the marker is DE in study 1 but not in study 2, etc.). As a result, we recommend AW over Fisher and Stouffer in the HS B category. For HS r , the result was less conclusive. REM provided better stability and robustness but sacrificed detection capability and biological association. On the other hand, rOP obtained better detection capability and biological association but was neither stable nor robust. In general, since detection capability and biological association are of more importance in the meta-analysis and rOP has the advantage to link the choice of r in HS r with the rOP method (e.g. when r = 0.7∙K, we identify genes that are DE in more than 70% of studies), we recommend rOP over REM.\n\nBelow, we provide a general guideline for a practitioner when applying microarray meta-analysis. Data sets of a relevant biological or disease hypothesis are firstly identified, preprocessed and annotated according to Step (i) - (v) in Ramasamy et al. Proper quality assessment should be performed to exclude studies with problematic quality (e.g. with the aid of MetaQC as we did in the six examples). Based on the experimental design and biological objectives of collected data, one should determine whether the meta-analysis aims to identify biomarkers differentially expressed in all studies (HS A ), in one or more studies (HS B ) or in majority of studies (HS r ). In general, if higher heterogeneity is expected from, say, heterogeneous experimental protocol, cohort or tissues, HS B should be considered. For example, if the combined studies come from different tissues (e.g. the first study uses peripheral blood, the second study uses muscle tissue and so on), tissue-specific markers may be expected and HS B should be applied. On the contrary, if the collected studies are relatively homogeneous (e.g. use the same array platform or from the same lab), HS r is generally recommended, as it provides robustness and detects consistent signals across the majority of studies. In the situation that no prior knowledge is available to choose a desired hypothesis setting or if the researcher is interested in a data-driven decision, the entropy measure in Figure 1(b) can be applied and the resulting box-plot can be compared to the six examples in this paper to guide the decision. Once the hypothesis setting is determined, the choice of a meta-analysis method can be selected from the discussion above and Table 2.\n\n## Conclusions\n\nIn this paper, we performed a comprehensive comparative study to evaluate 12 microarray meta-analysis methods using simulation and six real examples with four evaluation criteria. We clarified three hypothesis settings that were implicitly assumed behind the methods. The evaluation results produced a practical guideline to inform biologists the best choice of method(s) in real applications.\n\nWith the reduced cost of high-throughput experiments, data from microarray, new sequencing techniques and mass spectrometry accumulate rapidly in the public domain. Integration of multiple data sets has become a routine approach to increase statistical power, reduce false positives and provide more robust and validated conclusions. The evaluation in this paper focuses on microarray meta-analysis but the principles and messages apply to other types of genomic meta-analysis (e.g. GWAS, methylation, miRNA and eQTL). When the next-generation sequencing technology becomes more affordable in the future, sequencing data will become more prevalent as well and similar meta-analysis techniques will apply. For these different types of genomic meta-analysis, similar comprehensive evaluation could be performed and application guidelines should be established as well.\n\n## References\n\n1. 1.\n\nRamasamy A, Mondry A, Holmes CC, Altman DG: Key issues in conducting a meta-analysis of gene expression microarray datasets. PLoS Med. 2008, 5 (9): e184-10.1371/journal.pmed.0050184.\n\n2. 2.\n\nKang DD, Sibille E, Kaminski N, Tseng GC: MetaQC: objective quality control and inclusion/exclusion criteria for genomic meta-analysis. Nucleic Acids Res. 2012, 40 (2): e15-10.1093/nar/gkr1071.\n\n3. 3.\n\nTseng GC, Ghosh D, Feingold E: Comprehensive literature review and statistical considerations for microarray meta-analysis. Nucleic Acids Res. 2012, 40 (9): 3785-3799. 10.1093/nar/gkr1265.\n\n4. 4.\n\nHong F, Breitling R: A comparison of meta-analysis methods for detecting differentially expressed genes in microarray experiments. Bioinformatics. 2008, 24 (3): 374-382. 10.1093/bioinformatics/btm620.\n\n5. 5.\n\nCampain A, Yang YH: Comparison study of microarray meta-analysis methods. BMC Bioinforma. 2010, 11: 408-10.1186/1471-2105-11-408.\n\n6. 6.\n\nBirnbaum A: Combining independent tests of significance. J Am Stat Assoc. 1954, 49: 559-574.\n\n7. 7.\n\nLi J, Tseng GC: An adaptively weighted statistic for detecting differential gene expression when combining multiple transcriptomic studies. Ann Appl Stat. 2011, 5: 994-1019. 10.1214/10-AOAS393.\n\n8. 8.\n\nTusher VG, Tibshirani R, Chu G: Significance analysis of microarrays applied to the ionizing radiation response. Proc Natl Acad Sci USA. 2001, 98 (9): 5116-5121. 10.1073/pnas.091062498.\n\n9. 9.\n\nPesarin F, Salmaso L: Permutation tests for complex data: theory, applications and software. 2010, Ames, IA 50010: Wiley.com\n\n10. 10.\n\nCox DR: Regression models and life-tables. J R Stat Soc Ser B. 1972, 34 (2): 187-220.\n\n11. 11.\n\nBenjamini Y, Hochberg Y: Controlling the false discovery rate: a practical and powerful approach to multiple testing. J R Stat Soc Ser B. 1995, 57 (1): 289-300.\n\n12. 12.\n\nWang X, Kang DD, Shen K, Song C, Lu S, Chang LC, Liao SG, Huo Z, Tang S, Ding Y, et al: An R package suite for microarray meta-analysis in quality control, differentially expressed gene analysis and pathway enrichment detection. Bioinformatics. 2012, 28 (19): 2534-2536. 10.1093/bioinformatics/bts485.\n\n13. 13.\n\nFisher RA: Statistical methods for research workers. 1925, Edinburgh: Genesis Publishing, Oliver and Boyd\n\n14. 14.\n\nStouffer SA: A study of attitudes. Sci Am. 1949, 180 (5): 11-15. 10.1038/scientificamerican0549-11.\n\n15. 15.\n\nTippett LHC: The Methods of Statistics. An introduction mainly for workers in the biological sciences. The Methods of Statistics An Introduction mainly for Workers in the Biological Sciences. 1931, London: Williams &Norgate Ltd\n\n16. 16.\n\nWilkinson B: A statistical consideration in psychological research. Psychol Bull. 1951, 48 (3): 156-158.\n\n17. 17.\n\nSong C, Tseng GC: Order statistics for robust genomic meta-analysis. Ann Appl Stat. 2012, Accepted\n\n18. 18.\n\nChoi JK, Yu U, Kim S, Yoo OJ: Combining multiple microarray studies and modeling interstudy variation. Bioinformatics. 2003, 19 (Suppl 1): i84-i90. 10.1093/bioinformatics/btg1010.\n\n19. 19.\n\nHong F, Breitling R, McEntee CW, Wittner BS, Nemhauser JL, Chory J: RankProd: a bioconductor package for detecting differentially expressed genes in meta-analysis. Bioinformatics. 2006, 22 (22): 2825-2827. 10.1093/bioinformatics/btl476.\n\n20. 20.\n\nDreyfuss JM, Johnson MD, Park PJ: Meta-analysis of glioblastoma multiforme versus anaplastic astrocytoma identifies robust gene markers. Mol Cancer. 2009, 8: 71-10.1186/1476-4598-8-71.\n\n21. 21.\n\nBorg I: Modern multidimensional scaling: theory and applications. 2005, New York, NY 10013: Springer\n\n22. 22.\n\nMartin NF, England JW: Mathematical theory of entropy, vol. 12. 2011, Cambridge CB2 8BS United Kingdom: Cambridge University Press\n\n23. 23.\n\nWu W, Dave N, Tseng GC, Richards T, Xing EP, Kaminski N: Comparison of normalization methods for CodeLink Bioarray data. BMC Bioinforma. 2005, 6: 309-10.1186/1471-2105-6-309.\n\n24. 24.\n\nSpearman C: The proof and measurement of association between two things. Amer J Psychol. 1904, 15: 72-101. 10.2307/1412159.\n\n25. 25.\n\nLi Q, Brown JB, Huang H, Bickel PJ: Measuring reproducibility of high-throughput experiments. Ann Appl Stat. 2011, 5 (3): 1752-1779. 10.1214/11-AOAS466.\n\n26. 26.\n\nYang X, Bentink S, Scheid S, Spang R: Similarities of ordered gene lists. J Bioinform Comput Biol. 2006, 4 (3): 693-708. 10.1142/S0219720006002120.\n\n27. 27.\n\nHubert L, Arabie P: Comparing partitions. J Classification. 1985, 2: 193-218. 10.1007/BF01908075.\n\n28. 28.\n\nOwen AB: Karl Pearson's meta-analysis revisited. Ann Statistics. 2009, 37 (6B): 3867-3892. 10.1214/09-AOS697.\n\n29. 29.\n\nBreitling R, Herzyk P: Rank-based methods as a non-parametric alternative of the T-statistic for the analysis of biological microarray data. J Bioinform Comput Biol. 2005, 3 (5): 1171-1189. 10.1142/S0219720005001442.\n\n## Acknowledgements\n\nThis work was supported by the National Institutes of Health [R21MH094862].\n\n## Author information\n\nAuthors\n\n### Corresponding author\n\nCorrespondence to George C Tseng.\n\n### Competing interests\n\nThe authors declare that they have no competing interests.\n\n### Authors’ contributions\n\nGCT supervised the whole project. LCC developed all statistical analysis and HML developed partial statistical analysis. GCT and LCC drafted the manuscript. All authors read and approved the final manuscript.\n\n## Electronic supplementary material\n\n### Supplementary methods of (1) Adaptive weighted (AW) Fisher, (2) Combined statistical estimates (effect size) methods of FEM and REM, (3) Combined rank statistics methods: Rank Product (RankProd) and Rank Sum (RankSum).\n\nAdditional file 1: Figure S1. MetaQC. Figure S2. Heatmap of simulated example (red color represents up-regulated genes). Figure S3. The histograms of the true number of DE studies among detected DE genes under FDR = 5% in each method for discordance case. Figure S4. Cumulative moving average to determine D = 100. Figure S5. The ROC curves and AUC for the hypothesis settings of HS A -type and (red line) HS B -type (black line) in each meta-analysis method. Figure S6. Multidimensional scaling (MDS) plots of individual data sets. Figure S7. Stability and Robustness plot for α = 0.0001, 0.005 and 0.01. Table S1. Detailed data sets description. Table S2. MetaQC results. Table S3. Data sets and number of matched genes. Table S4. Mean standardized rank (MSR) and aggregated standardized rank (ASR) for detection capability. Table S5. Mean standardized rank (MSR) and aggregated standardized rank (ASR) for biological association. Table S6. Mean standardized rank (MSR) and aggregated standardized rank (ASR) for stability. Table S7. Mean standardized rank (MSR) and aggregated standardized rank (ASR) for robustness. (PDF 1 MB)\n\n## Authors’ original submitted files for images\n\nBelow are the links to the authors’ original submitted files for images.\n\n## Rights and permissions\n\nReprints and Permissions\n\nChang, L., Lin, H., Sibille, E. et al. Meta-analysis methods for combining multiple expression profiles: comparisons, statistical characterization and an application guideline. BMC Bioinformatics 14, 368 (2013). https://doi.org/10.1186/1471-2105-14-368",
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"https://bmcbioinformatics.biomedcentral.com/track/article/10.1186/1471-2105-14-368",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.8967942,"math_prob":0.87784183,"size":52447,"snap":"2020-34-2020-40","text_gpt3_token_len":11649,"char_repetition_ratio":0.15243216,"word_repetition_ratio":0.046569794,"special_character_ratio":0.22538944,"punctuation_ratio":0.11352731,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97335744,"pos_list":[0,1,2],"im_url_duplicate_count":[null,4,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-23T04:24:10Z\",\"WARC-Record-ID\":\"<urn:uuid:c90e8c08-aaff-4a7f-af69-c9fb3141a7f1>\",\"Content-Length\":\"344170\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:be4c1e15-3276-445a-b208-8c0f99a54cca>\",\"WARC-Concurrent-To\":\"<urn:uuid:50cc9282-49a5-48e4-bd78-0b0457e608d2>\",\"WARC-IP-Address\":\"151.101.200.95\",\"WARC-Target-URI\":\"https://bmcbioinformatics.biomedcentral.com/articles/10.1186/1471-2105-14-368\",\"WARC-Payload-Digest\":\"sha1:ILARX5OAEZONUYI3KRVC66MEAZFJECGH\",\"WARC-Block-Digest\":\"sha1:ASODFSV63DSTPVLBKUWVG5QIDGNRBOHF\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600400209665.4_warc_CC-MAIN-20200923015227-20200923045227-00316.warc.gz\"}"} |
https://turcomat.org/index.php/turkbilmat/article/view/5422 | [
"# A Review Article On Mathematical Aspects Of Nonlinear Models\n\n## Abstract\n\nThe main objective of this review article is to propose some mathematical aspects of nonlinear models. In mathematics, nonlinear modelling is empirical or semi-empirical modelling which takes at least some nonlinearities into account. Nonlinear modelling in practice therefore means modelling of phenomena in which independent variables affecting the system can show complex and synergetic nonlinear effects. Contrary to traditional modelling methods, such as linear regression and basic statistical methods, nonlinear modelling can be utilized efficiently in a vast number of situations where traditional modelling is impractical or impossible. This review article mainly explores on mathematical preliminaries of nonlinear models, solution of algebraic and transcendental equations and solution of system of nonlinear equations. In addition to these Taylor polynomial and finite difference operators, least - squares polynomial approximation and the roots of the equations are also discussed here.\n\nSection\nArticles"
] | [
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https://www.r-bloggers.com/moving-the-earth-well-alaska-hawaii-with-r/ | [
"# Moving The Earth (well, Alaska & Hawaii) With R\n\nNovember 16, 2014\nBy\n\nWant to share your content on R-bloggers? click here if you have a blog, or here if you don't.\n\nIn a previous post we looked at how to use D3 TopoJSON files with R and make some very D3-esque maps. I mentioned that one thing missing was moving Alaska & Hawaii a bit closer to the continental United States and this post shows you how to do that.\n\nThe D3 folks have it easy. They just use the built in modified Albers composite projection. We R folk have to roll up our sleeves a bit (but not much) to do the same. Thankfully, we can do most of the work with the elide (“ih lied”) function from the `maptools` package.\n\n``` library(maptools) library(mapproj) library(rgeos) library(rgdal) library(RColorBrewer) library(ggplot2) # for theme_map devtools::source_gist(\"33baa3a79c5cfef0f6df\") ```\n\nI’m using a GeoJSON file that I made from the 2013 US Census shapefile. I prefer GeoJSON mostly due to it being single file and the easy conversion to TopoJSON if I ever need to use the same map in a D3 context (I work with information security data most of the time, so I rarely have to use maps at all for the day job). I simplified the polygons a bit (passing `-simplify 0.01` to `ogr2ogr`) to reduce processing time.\n\nWe read in that file and then transform the projection to Albers equal area and join the polygon ids to the shapefile data frame:\n\n``` # https://www.census.gov/geo/maps-data/data/cbf/cbf_counties.html # read U.S. counties moderately-simplified GeoJSON file us <- readOGR(dsn=\"data/us.geojson\", layer=\"OGRGeoJSON\") # convert it to Albers equal area us_aea <- spTransform(us, CRS(\"+proj=laea +lat_0=45 +lon_0=-100 +x_0=0 +y_0=0 +a=6370997 +b=6370997 +units=m +no_defs\")) [email protected]data\\$id <- rownames([email protected]data) ```\n\nNow, to move Alaska & Hawaii, we have to:\n\n• extract them from the main shapefile data frame\n• perform rotation, scaling and transposing on them\n• ensure they have the right projection set\n• merge them back into the original spatial data frame\n\nThe `elide` function has parameters for all the direct shape munging, so we’ll just do that for both states. I took a peek at the D3 source code for the Albers projection to get a feel for the parameters. You can tweak those if you want them in other positions or feel the urge to change the Alaska rotation angle.\n\n``` # extract, then rotate, shrink & move alaska (and reset projection) # need to use state IDs via # https://www.census.gov/geo/reference/ansi_statetables.html alaska <- us_aea[us_aea\\$STATEFP==\"02\",] alaska <- elide(alaska, rotate=-50) alaska <- elide(alaska, scale=max(apply(bbox(alaska), 1, diff)) / 2.3) alaska <- elide(alaska, shift=c(-2100000, -2500000)) proj4string(alaska) <- proj4string(us_aea) # extract, then rotate & shift hawaii hawaii <- us_aea[us_aea\\$STATEFP==\"15\",] hawaii <- elide(hawaii, rotate=-35) hawaii <- elide(hawaii, shift=c(5400000, -1400000)) proj4string(hawaii) <- proj4string(us_aea) # remove old states and put new ones back in; note the different order # we're also removing puerto rico in this example but you can move it # between texas and florida via similar methods to the ones we just used us_aea <- us_aea[!us_aea\\$STATEFP %in% c(\"02\", \"15\", \"72\"),] us_aea <- rbind(us_aea, alaska, hawaii) ```\n\nRather than just show the resultant plain county map, we’ll add some data to it. The first example uses US drought data (from November 11th, 2014). Drought conditions are pretty severe in some states, but we’ll just show areas that have any type of drought (levels D0-D4). The color ramp shows the % of drought coverage in each county (you’ll need a browser that can display SVGs to see the maps):\n\n``` # get some data to show...perhaps drought data via: # http://droughtmonitor.unl.edu/MapsAndData/GISData.aspx droughts <- read.csv(\"data/dm_export_county_20141111.csv\") droughts\\$id <- sprintf(\"%05d\", as.numeric(as.character(droughts\\$FIPS))) droughts\\$total <- with(droughts, (D0+D1+D2+D3+D4)/5) # get ready for ggplotting it... this takes a cpl seconds map <- fortify(us_aea, region=\"GEOID\") # plot it gg <- ggplot() gg <- gg + geom_map(data=map, map=map, aes(x=long, y=lat, map_id=id, group=group), fill=\"#ffffff\", color=\"#0e0e0e\", size=0.15) gg <- gg + geom_map(data=droughts, map=map, aes(map_id=id, fill=total), color=\"#0e0e0e\", size=0.15) gg <- gg + scale_fill_gradientn(colours=c(\"#ffffff\", brewer.pal(n=9, name=\"YlOrRd\")), na.value=\"#ffffff\", name=\"% of County\") gg <- gg + labs(title=\"U.S. Areas of Drought (all levels, % county coverage)\") gg <- gg + coord_equal() gg <- gg + theme_map() gg <- gg + theme(legend.position=\"right\") gg <- gg + theme(plot.title=element_text(size=16)) gg ```",
null,
"While that shows Alaska & Hawaii in D3-Albers-style, it would be more convincing if we actually used the FIPS county codes on Alaska & Hawaii, so we’ll riff off the previous post and make a county land-mass area choropleth (since we have the land mass area data available in the GeoJSON file):\n\n``` gg <- ggplot() gg <- gg + geom_map(data=map, map=map, aes(x=long, y=lat, map_id=id, group=group), fill=\"white\", color=\"white\", size=0.15) gg <- gg + geom_map(data=[email protected]data, map=map, aes(map_id=GEOID, fill=log(ALAND)), color=\"white\", size=0.15) gg <- gg + scale_fill_gradientn(colours=c(brewer.pal(n=9, name=\"YlGn\")), na.value=\"#ffffff\", name=\"County LandnMass Area (log)\") gg <- gg + labs(title=\"U.S. County Area Choropleth (log scale)\") gg <- gg + coord_equal() gg <- gg + theme_map() gg <- gg + theme(legend.position=\"right\") gg <- gg + theme(plot.title=element_text(size=16)) gg ```",
null,
"Now, you have one less reason to be envious of the D3 cool kids!\n\nThe code & shapefiles are available on github.\n\nR-bloggers.com offers daily e-mail updates about R news and tutorials about learning R and many other topics. Click here if you're looking to post or find an R/data-science job.\nWant to share your content on R-bloggers? click here if you have a blog, or here if you don't."
] | [
null,
"https://rud.is/dl/drought.svg",
null,
"https://rud.is/dl/area.svg",
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.68954563,"math_prob":0.7941514,"size":5912,"snap":"2019-43-2019-47","text_gpt3_token_len":1666,"char_repetition_ratio":0.102572784,"word_repetition_ratio":0.10730594,"special_character_ratio":0.28907308,"punctuation_ratio":0.12956522,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9723702,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,10,null,10,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-11-22T04:51:30Z\",\"WARC-Record-ID\":\"<urn:uuid:05730ce4-7cac-49e0-94db-8bf76d71df30>\",\"Content-Length\":\"196335\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6aa4daa5-89c5-49bb-a3a6-b689e1c2e8b6>\",\"WARC-Concurrent-To\":\"<urn:uuid:31834a5f-730d-4008-a56d-c67a9ac92993>\",\"WARC-IP-Address\":\"104.24.127.192\",\"WARC-Target-URI\":\"https://www.r-bloggers.com/moving-the-earth-well-alaska-hawaii-with-r/\",\"WARC-Payload-Digest\":\"sha1:7VXP55QRYIGS2VJISLUTMKMKKR4DENKH\",\"WARC-Block-Digest\":\"sha1:LL6BHYJ6L6MQTWXZOL2OM3VSRQIIHZRK\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-47/CC-MAIN-2019-47_segments_1573496671239.99_warc_CC-MAIN-20191122042047-20191122070047-00298.warc.gz\"}"} |
https://instrumentationtools.com/stability-nonlinear-system/ | [
" Stability of Nonlinear System - Inst Tools\n\n# Stability of Nonlinear System\n\nStability of Nonlinear System\n\n1. Stability of a system implies that :\n\na) Small changes in the system input does not result in large change in system output\nb) Small changes in the system parameters does not result in large change in system output\nc) Small changes in the initial conditions does not result in large change in system output\nd) Small changes in the initial conditions result in large change in system output\n\nAnswer: a\n\nExplanation: Stability of the system implies that small changes in the system input, initial conditions, and system parameters does not result in large change in system output.\n\n2. A linear time invariant system is stable if :\n\na) System in excited by the bounded input, the output is also bounded\nb) In the absence of input output tends zero\nc) Both a and b\nd) None of the mentioned\n\nAnswer: c\n\nExplanation: A system is stable only if it is BIBO stable and asymptotic stable.\n\n3. Asymptotic stability is concerned with :\n\na) A system under influence of input\nb) A system not under influence of input\nc) A system under influence of output\nd) A system not under influence of output\n\nAnswer: b\n\nExplanation: Asymptotic stability concerns a free system relative to its transient behavior.\n\n4. Bounded input and Bounded output stability notion concerns with :\n\na) A system under influence of input\nb) A system not under influence of input\nc) A system under influence of output\nd) A system not under influence of output\n\nAnswer: a\n\nExplanation: BIBO stability concerns with the system that has input present.\n\n5. If a system is given unbounded input then the system is:\n\na) Stable\nb) Unstable\nc) Not defined\nd) Linear\n\nAnswer: c\n\nExplanation: If the system is given with the unbounded input then nothing can be clarified for the stability of the system.\n\n6. Linear mathematical model applies to :\n\na) Linear systems\nb) Stable systems\nc) Unstable systems\nd) All of the mentioned\n\nAnswer: b\n\nExplanation: As the output exceeds certain magnitude then the linear mathematical model no longer applies.\n\n7. For non-linear systems stability cannot be determined due to:\n\na) Possible existence of multiple equilibrium states\nb) No correspondence between bounded input and bounded output stability and asymptotic stability\nc) Output may be bounded for the particular bounded input but may not be bounded for the bounded inputs\nd) All of the mentioned\n\nAnswer: d\n\nExplanation: For non-linear systems stability cannot be determined as asymptotic stability and BIBO stability concepts cannot be applied, existence of multiple states and unbounded output for many bounded inputs.\n\n8. If the impulse response in absolutely integrable then the system is :\n\na) Absolutely stable\nb) Unstable\nc) Linear\nd) None of the mentioned\n\nAnswer: a\n\nExplanation: The impulse response must be absolutely integrable for the system to absolutely stable.\n\n9. The roots of the transfer function do not have any effect on the stability of the system.\n\na) True\nb) False\n\nAnswer: b\n\nExplanation: The roots of transfer function also determine the stability of system as they may be real, complex and may have multiplicity of various order.\n\n10. Roots with higher multiplicity on the imaginary axis makes the system :\n\na) Absolutely stable\nb) Unstable\nc) Linear\nd) None of the mentioned\n\nAnswer: b\n\nExplanation: Repetitive roots on the imaginary axis makes the system unstable.\n\n#### Share With Your Friends\n\nSend this to a friend"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.8129829,"math_prob":0.8534029,"size":3330,"snap":"2021-21-2021-25","text_gpt3_token_len":730,"char_repetition_ratio":0.18610944,"word_repetition_ratio":0.24057451,"special_character_ratio":0.2,"punctuation_ratio":0.090016365,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9774294,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-06-17T18:13:54Z\",\"WARC-Record-ID\":\"<urn:uuid:1dc5eb87-fecf-4d22-9fcb-c3277ff81819>\",\"Content-Length\":\"165885\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4b92927f-e766-441b-8375-6571b6135efb>\",\"WARC-Concurrent-To\":\"<urn:uuid:5969761f-a64e-4969-83ea-476aca5845f4>\",\"WARC-IP-Address\":\"172.67.146.161\",\"WARC-Target-URI\":\"https://instrumentationtools.com/stability-nonlinear-system/\",\"WARC-Payload-Digest\":\"sha1:TZV7MUGPQIJIPV7B573NGZPX25YSLXEN\",\"WARC-Block-Digest\":\"sha1:CCDKAWV5B3DCBXKKOYIXE4FNBR5P5DYL\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-25/CC-MAIN-2021-25_segments_1623487630518.38_warc_CC-MAIN-20210617162149-20210617192149-00546.warc.gz\"}"} |
https://ls4-www.cs.tu-dortmund.de/download/buchholz/CMDP/CMDP_Description | [
"# Markov Decision Processes with Uncertain Parameters\n\nMarkov Decision Processes (MDPs) are a commonly used model type to describe decision making in stochastic models. However, usually the parameters of MDPs result from some data or estimates of experts. In both cases parameters are uncertain. This uncertainty has to be taken into account during the computation of policies that describe decisions to be made over time. In this case, the parameters of the MDP are not exactly known, instead a set of MDPs is defined which captures the parameter uncertainty. The goal is then to find a policy that behaves good for all possible realizations of uncertainty. A good behavior is not really well-defined, common interpretations are an optimal policy for the worst possible realization of uncertainty (robust optimization), an optimal policy for the expected behavior (risk neutral stochastic optimization), an optimal policy for the expected behavior plus some guarantee for the worst case (stochastic optimization with some baseline guarantee), etc. In general, the computation of optimal policies for MDPs with uncertain parameters becomes much more complex than the computation of optimal policies for MDPs with known parameters. Many problems are NP-hard. However, often good approximation algorithms can be found to compute acceptable policies sometimes even with an error bound.",
null,
"Queuing Network Example\n\nMDPs with uncertain parameters appear in in various application areas like the control of queuing networks, maintenance problems, routing in computer networks, computer security or computational finance. In the figure above a small control problem for queuing networks is shown. Upon arrival of a new task it has to be decided into which queue the entity is routed. The routing algorithm knows the number of customers in each queue but not the detailed service times. In an MDP setting the rates are known, internal uncertainty is introduced by different realizations of the (exponentially distributed) service and inter arrival times. With uncertain parameters the rates are not exactly known introducing another source of external uncertainty\n\n## Rectangular Parameter Uncertainty\n\nThe basic assumption of rectangular parameter uncertainty is that uncertainty occurs independently for every state-action pair (s,a). A typical example are Bounded Parameter MDPs (BMDPs) where transition probabilities or/and rewards are defined by intervals rather than scalars. For rectangular uncertainty, the robust policy, which maximizes the reward under the worst possible realization of uncertainty, can be computed with polynomial effort. However, the computational effort is still much higher than the effort required to compute optimal policies for MDP with known parameters. In particular, solution approaches based on linear programming cannot be applied for the analysis of BMDPs or related models.",
null,
"BMDP Example\n\nIn our research on MDPs with rectangular uncertainty, mainly BMDPs have been analyzed. The specification of BMDPs with a class of Stochastic Petri Nets has been published in , describes the application of BMDPs for maintenance problems. In numerical methods to compute robust policies for BMDPs are compared and describes the relation between aggregation of large MDPs and the use of BMDPs.\nApproximate and exact methods for two NP-hard problems are considered in the papers and . In the Pareto frontier of policies that are not dominated with respect to their worst, average and best case behavior is approximated. introduces several algorithms to determine policies that are optimal according to one criterion, like the average or worst case, and guarantee a minimal reward for the other criterion.\n\n## Scenario Based Parameter Uncertainty\n\nIn the scenario based approach, uncertainty is represented by finitely many scenarios. This allows one to consider correlations between different parameters of the model or to sample from a set of parameter distributions. The goal is then to find a policy which maximizes the weighted sum of rewards over all scenarios. The resulting optimization problem has shown to be NP-hard .",
null,
"Example of a Concurrent MDPs with two Scenarios\n\nThe class of Concurrent MDPs (CMDPs) has been defined in [2,8]. Paper also presents several methods to compute or approximate optimal policies. The approach is extended to a new class of policies and decision dependent rewards in .\n\n## References\n\n1. Marco Beccuti, Elvio Gilberto Amparore, Susanna Donatelli, Dimitri Scheftelowitsch, Peter Buchholz, Giuliana Franceschinis: Markov Decision Petri Nets with Uncertainty. EPEW 2015: 177-192\n\n2. Dimitri Scheftelowitsch, Peter Buchholz, Vahid Hashemi, Holger Hermanns: Multi-Objective Approaches to Markov Decision Processes with Uncertain Transition Parameters. VALUETOOLS 2017: 44-51\n\n3. Peter Buchholz, Iryna Dohndorf, Alexander Frank, Dimitri Scheftelowitsch: Bounded Aggregation for Continuous Time Markov Decision Processes. EPEW 2017: 19-32\n\n4. Peter Buchholz, Iryna Dohndorf, Dimitri Scheftelowitsch: Analysis of Markov Decision Processes Under Parameter Uncertainty. EPEW 2017: 3-18\n\n5. Dimitri Scheftelowitsch: Markov decision processes with uncertain parameters. Dissertation Technical University of Dortmund, Germany, 2018\n\n6. Peter Buchholz, Iryna Dohndorf, Dimitri Scheftelowitsch: Time-Based Maintenance Models Under Uncertainty. MMB 2018: 3-18\n\n7. Peter Buchholz, Dimitri Scheftelowitsch: Light robustness in the optimization of Markov decision processes with uncertain parameters. Computers & OR 108: 69-81 (2019)\n\n8. Peter Buchholz, Dimitri Scheftelowitsch: Computation of weighted sums of rewards for concurrent MDPs. Math. Meth. of OR 89(1): 1-42 (2019)\n\n9. Peter Buchholz, Dimitri Scheftelowitsch: Concurrent MDPs with Finite Markovian Policies. Accepted for MMB 2020\n\n## Software\n\nA collection of Matlab functions which implements the algorithms from and can be downloaded (please cite the above references if you use the software)."
] | [
null,
"http://ls4-www.cs.tu-dortmund.de/download/buchholz/CMDP/qn.jpg",
null,
"http://ls4-www.cs.tu-dortmund.de/download/buchholz/CMDP/BMDP_pic.jpg",
null,
"http://ls4-www.cs.tu-dortmund.de/download/buchholz/CMDP/CMDP_pic.jpg",
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.85787255,"math_prob":0.76552206,"size":5836,"snap":"2023-14-2023-23","text_gpt3_token_len":1259,"char_repetition_ratio":0.13494512,"word_repetition_ratio":0.043632075,"special_character_ratio":0.19019876,"punctuation_ratio":0.10963115,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.955151,"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\":\"2023-03-26T16:35:15Z\",\"WARC-Record-ID\":\"<urn:uuid:c4674e6a-c7af-4555-b0de-7c96b53a6645>\",\"Content-Length\":\"9909\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:8386f439-f5a5-40e3-ab81-fba714050dd4>\",\"WARC-Concurrent-To\":\"<urn:uuid:a7756281-846d-42cc-89e5-7c399a978a92>\",\"WARC-IP-Address\":\"129.217.231.102\",\"WARC-Target-URI\":\"https://ls4-www.cs.tu-dortmund.de/download/buchholz/CMDP/CMDP_Description\",\"WARC-Payload-Digest\":\"sha1:4GPMCT3BM52EUJDA5WE4DGZUAP5MWH5O\",\"WARC-Block-Digest\":\"sha1:RVKNF3RC73U64ZECLBGQ7L7AMFDPMTYY\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-14/CC-MAIN-2023-14_segments_1679296945473.69_warc_CC-MAIN-20230326142035-20230326172035-00049.warc.gz\"}"} |
https://www.plus2net.com/sql_tutorial/comparison-operators.php | [
"# comparison Operators\n\nOperatorsDESCRIPTION\n=Equal to , returns 1 when both operands are same\n!=Not Equal to , returns 1 when both operands are different\n<>Not Equal to , returns 1 when both operands are different\n<=>Null safe equal to, returns 1 when both operands are same including NULL value\n>Greater than\n>=Greater than or equal to\n<Less than\n<=Less than or equal to\nIN Matching from a set of values\nNOT IN NOT Matching from a set of values\nIS Check against Boolean values\nIS NULLChecking NULL value\nBETWEEN Between a range of values\nSTRCMP String Comparison\nLIKE Pattern matching\nHere are some sample queries using comparison operators of MySQL\n``SELECT * FROM student where mark=85``\nidnameclassmarksex\n2Max RuinThree85male\n8AsruidFive85male\n\nUsing not equal to\n``SELECT * FROM student WHERE class <> 'Six'``\nUsing Less than\n``SELECT * FROM student WHERE mark < 25``\nUsing Less than or equal to\n``SELECT * FROM student WHERE mark <= 25``\nUsing greater than\n``SELECT * FROM student WHERE mark > 50``\nUsing greater than equal to\n``SELECT * FROM student WHERE mark >= 25``\nUsing IN\n``SELECT * FROM `student` WHERE class IN ('Four','Five')``\n\nUsing NOT IN\n``SELECT * FROM `student` WHERE class NOT IN ('Four','Five')``\n\n## Using IS\n\n``SELECT * FROM `plus2_boolean` WHERE mar IS TRUE``\nusing IS NOT\n``SELECT * FROM `plus2_boolean` WHERE jan IS NOT TRUE``\n\n## Using BETWEEN\n\n``SELECT * FROM student WHERE mark BETWEEN 50 AND 60``\nUsing NOT BETWEEN\n``SELECT * FROM student WHERE mark NOT BETWEEN 50 AND 60``\n\n## NULL safe operators <=>\n\nWe can't compare NULL value with NULL value as the meaning of NULL value is absence of any value. Check this table ( table1)\nidfirst_namelast_name\n2AlexJohn\n3RonRon\n4NULLNULL\n``SELECT * FROM table1 WHERE first_name=last_name``\nThe output is here\nidfirst_namelast_name\n3RonRon\nWhy the record with NULL value as first_name and last_name is not included in the output ?\nThis is because we can't compare NULL value with NULL value . Read this output\n``SELECT NULL=NULL``\nOutput of above query is NULL. ( Why ? )\nLet us try one more query\n``SELECT * FROM table1 WHERE first_name <=> last_name``\nThe output is here\nidfirst_namelast_name\n3RonRon\n4NULLNULL\nBy using Null safe operator we can get two records including the row having NULL value in both the columns.\n\n## Using STRCMP\n\nWe can compare strings by using string function STRCMP\n``SELECT STRCMP('plus2net','PLUS2NET')``\nAs both strings are same, so we will get 0 as output.\n\nSQL dump of plus2_boolean table\n\nSQL dump of student3 table\n\nSubscribe to our YouTube Channel here\n\n## Subscribe\n\n* indicates required\nSubscribe to plus2net",
null,
"plus2net.com"
] | [
null,
"https://www.plus2net.com/images/top2.jpg",
null
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https://profiles.doe.mass.edu/mcas/mcasitems2.aspx?grade=04&subjectcode=MTH&linkid=4&orgcode=02230000&fycode=2019&orgtypecode=5& | [
"# Orange\n\nDistricts Schools",
null,
"## 2019 Item by Item Results for GRADE 04 MATHEMATICS\n\n### Number of Students Included: 63\n\n Orange - GRADE 04 MATHEMATICS ITEM INFORMATION PERCENT OF DISTRICT'S POSSIBLE POINTS ITEM TYPE REPORTING CATEGORY STANDARD ITEM DESC POSSIBLE POINTS ORANGE STATE DISTRICT-STATE DIFFERENCE 1 SR OA 4.OA.B.4 Given a set of multiples of a number, determine the number. 1 57% 81% -24 2 SR NF 4.NF.C.5 Add fractions with denominators of 10 and 100. 1 54% 70% -16 3 CR NF 4.NF.C.7 Compare decimals given in tenths and hundredths in a list, order decimals from least to greatest, and determine which decimal from the list is closest in value to a given decimal. 4 36% 46% -10 4 SR NF 4.NF.B.3 Determine which expression has a value that is not equivalent to a given expression. 1 68% 81% -13 5 SA NF 4.NF.C.6 Locate a decimal on a zoom number line. 1 27% 49% -22 6 CR OA 4.OA.A.2 Write an equation with a symbol for the unknown number to represent a word problem involving multiplicative comparison and then multiply to solve problems. 4 50% 67% -17 7 SR NF 4.NF.A.2 Identify the correct comparisons of two fractions that are represented by visual fraction models. 1 14% 40% -26 8 SR MD 4.MD.B.4 Solve a word problem with addition of fractions by using data from a dot plot. 1 24% 51% -27 9 SR GE 4.G.A.2 Identify shapes that have at least one obtuse angle and justify why a shape is a right triangle. 2 68% 77% -9 10 SR MD 4.MD.A.1 Convert dimensions measured in yards to feet. 1 56% 68% -12 11 SA NT 4.NBT.A.1 In a given multi-digit number, recognize that the value of a digit is 10 times the value of the digit to its right. 1 16% 43% -27 12 SA NT 4.NBT.A.2 Write the standard form of a number given in word form. 1 87% 90% -3 13 SR GE 4.G.A.3 Recognize a line of symmetry for a two-dimensional figure and identify how many lines of symmetry can be drawn on the figure. 1 35% 55% -20 14 SR MD 4.MD.C.7 Determine an angle measure given the measures of two adjacent angles and the sum of all three angle measures. 1 29% 51% -22 15 SA OA 4.OA.A.3 Solve a multi-step word problem involving addition and division of whole numbers. 1 41% 51% -10 16 SR NT 4.NBT.A.3 Round multi-digit whole numbers to the nearest ten, hundred, and thousand. 1 40% 43% -3 17 SR MD 4.MD.C.6 Determine measures of given angles shown on protractors. 1 52% 69% -17 18 SA NF 4.NF.B.4 Solve a word problem by multiplying a fraction by a whole number. 1 37% 54% -17 19 SR NT 4.NBT.B.4 Determine the difference of two five-digit numbers. 1 54% 76% -22 20 SR MD 4.MD.A.3 Given the length and the width of a rectangle, determine its area. 1 37% 69% -32 21 SR NF 4.NF.B.3 Solve a word problem involving subtraction of a given fraction from one whole. 1 89% 93% -4 22 SR GE 4.G.A.1 Identify an acute angle. 1 90% 91% -1 23 SR GE 4.G.A.3 Identify one, two, or three or more lines of symmetry for four different figures. 1 10% 34% -24 24 SR OA 4.OA.C.5 Choose the statement that correctly identifies a feature of a given shape pattern. 1 49% 52% -3 25 SR NT 4.NBT.A.2 Compare multi-digit whole numbers given in word form and in number form. 1 54% 75% -21 26 SA NT 4.NBT.B.4 Determine the sum of a five-digit number and a four-digit number. 1 76% 80% -4 27 SR MD 4.MD.C.5 Determine the measure of an angle that turns through a portion of a circle. 1 24% 47% -23 28 SA NT 4.NBT.B.6 Solve a word problem by dividing a four-digit number by a one-digit number. 1 30% 45% -15 29 SA NF 4.NF.B.4 Use a visual fraction model to represent the product of a whole number and a unit fraction. 1 51% 69% -18 30 SR OA 4.OA.B.4 Identify multiples of a given number. 1 89% 89% 0 31 SR NF 4.NF.A.1 Identify a pair of equivalent fractions represented by a picture. 1 43% 63% -20 32 CR NT 4.NBT.B.5 Solve word problems by multiplying whole numbers: two digits by one digit, two digits by two digits, and four digits by one digit. 4 42% 53% -11 33 SR NF 4.NF.B.3 Determine which expression has a value that is equivalent to a given fraction. 1 90% 95% -5 34 SA NF 4.NF.C.6 Write a fraction with a denominator of 100 as a decimal. 1 59% 68% -9 35 CR MD 4.MD.A.2 Use a ruler to measure given objects to the nearest centimeter and solve word problems involving multiplication and addition of measurements and the conversion of meters to centimeters. 4 42% 46% -4 36 SR NF 4.NF.A.1 Determine which fraction is equivalent to a given fraction using a picture. 1 65% 74% -9 37 SR NF 4.NF.C.7 Determine which decimal is greater than a number shown on a visual model and is less than 1. 1 43% 60% -17 38 SA OA 4.OA.A.1 Write a multiplication equation to represent a word comparison and a word comparison to represent a multiplication equation. 2 58% 64% -6 39 SR OA 4.OA.C.5 Solve a word problem by determining additional terms of a given pattern. 1 49% 65% -16 40 SR GE 4.G.A.1 Identify whether specified line segments and angles can be found in a given figure. 1 30% 49% -19"
] | [
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"https://profiles.doe.mass.edu/images/btn.gif",
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.73236316,"math_prob":0.98746395,"size":5178,"snap":"2021-31-2021-39","text_gpt3_token_len":1717,"char_repetition_ratio":0.14476228,"word_repetition_ratio":0.020971302,"special_character_ratio":0.38972577,"punctuation_ratio":0.14214876,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98143494,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-08-01T08:15:37Z\",\"WARC-Record-ID\":\"<urn:uuid:50c1001a-a8e7-46ab-9a58-2aa9915cc7e5>\",\"Content-Length\":\"99883\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:eb14ab15-7d1f-4a89-b24b-5b7541466b55>\",\"WARC-Concurrent-To\":\"<urn:uuid:413ab225-aaf9-460b-aec3-6c5c9761ce9b>\",\"WARC-IP-Address\":\"170.63.127.48\",\"WARC-Target-URI\":\"https://profiles.doe.mass.edu/mcas/mcasitems2.aspx?grade=04&subjectcode=MTH&linkid=4&orgcode=02230000&fycode=2019&orgtypecode=5&\",\"WARC-Payload-Digest\":\"sha1:W645726UXV2WSHMP7ME26OXAZ33S76GU\",\"WARC-Block-Digest\":\"sha1:LTUZRF3YB6GIC6I4CTCGTZWSHLOOMDZ7\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-31/CC-MAIN-2021-31_segments_1627046154163.9_warc_CC-MAIN-20210801061513-20210801091513-00379.warc.gz\"}"} |
https://dojo.domo.com/discussion/52942/formula-not-summarizing-in-analyzer | [
"# Formula not summarizing in analyzer\n\nHello Dojo,\n\nI have a calculated field I am trying to apply to a time series chart that does not seem to want to summarize. The formula changes based on one of the variables - objective.\n\n```case when `Objective` = 'CLICKS' then\n\n(case when (sum(`Clicks`) / sum(`Impressions`)) < .0082 then 0\nwhen (sum(`Clicks`) / sum(`Impressions`)) < .0098 then 1\nwhen (sum(`Clicks`) / sum(`Impressions`)) < .0107 then 2\nelse 3 end)\n\nwhen `Objective` LIKE 'ENGAGEMENT%' then\n\n(case when (sum(`Engagements`) / sum(`Impressions`)) < .2203 then 0\nwhen (sum(`Engagements`) / sum(`Impressions`)) < .2644 then 1\nwhen (sum(`Engagements`) / sum(`Impressions`)) < .2864 then 2\nelse 3 end)\n\nwhen `Objective` = 'VIDEO VIEWS' then\n\n(case when (sum(`Video Views`) / sum(`Impressions`)) < .0489 then 0\nwhen (sum(`Video Views`) / sum(`Impressions`)) < .0587 then 1\nwhen (sum(`Video Views`) / sum(`Impressions`)) < .0636 then 2\nelse 3 end)\n\nwhen `Objective` = 'REACH' then\n\n(case when sum(`Reach`) < 1527494 then 0\nwhen sum(`Reach`) < 1680243 then 1\nwhen sum(`Reach`) < 1985742 then 2\nelse 3 end) end\n\n```\n\nWhen I add this formula to my chart and try to trend it by date, each of the dates repeats. It looks to repeat for each objective. I would like this score to show the summarized score for all objectives. Oddly enough, the data table at the bottom shows what I want, but in analyzer it repeats.\n\nData table at bottom:\n\nAnalyzer table:\n\nLet me know if anyone has any ideas.\n\n• Check to see if you have any fields in the Sorting section of the Analyzer. That will throw of how Domo can aggregate the data in the card. Also, check the Date Range Filter and what it is grouping by.\n\n**Make sure to",
null,
"any users posts that helped you.\n• There is nothing in sorting, and i am grouping by month.\n\n• If you add your objective column to the table card, will that show that there is a month \"repeating\" because there is a different objective type?\n\n**Make sure to",
null,
"any users posts that helped you.\n• yes that is correct.\n\n• My first suggestion would be to do the calculation in Magic ETL, but that may not work for you depending on how you want the card to function as far as filtering\n\nYou might try restructuring your case statement and see if that does the trick. If you can get your objective within your division calculation so that your are only dividing once, that might work. Sorry, I don't any good sample data to test this out with.\n\n**Make sure to",
null,
"any users posts that helped you.\n• @JustinB by building your aggregation INSIDE the CASE statement you're applying the CASE statement after aggregation. (i know that sounds like i said the same thing twice...\n\npoint being, what you're asking for is \"after i aggregate the data, i want to substitute the results with a number and then i want to aggregate again.\"\n\nbut you can't... because you already aggregated.\n\nwhen you put Objective on the Axis, it should look like your 'CASE statement is working' but as soon as you take it off, it will look like 'it isn't working.' and again, that's because you're expecting an aggregation AFTER CASE.\n\nIF Clicks and Impressions are on the same row, and it's appropriate to rate each row of data as Clicks / Impressions then you can rewrite your BM as\n\n```sum(\ncase\nwhen objective = ... AND clicks / impressions = .75 then 0\nwhen objective = ... AND clicks / impressions = .82 then 1\n)\n```\n\nNote this evaluates and assigns a score per ROW not per DAY.\n\nIf you want to assign a row per day, you have to pre-aggregate as @MarkSnodgrass suggests.\n\nJae Wilson\nCheck out my Domo Training YouTube Channel\n\n**Say \"Thanks\" by clicking the heart in the post that helped you.\n**Please mark the post that solves your problem by clicking on \"Accept as Solution\""
] | [
null,
"https://dojo.domo.com/resources/emoji/heart.png",
null,
"https://dojo.domo.com/resources/emoji/heart.png",
null,
"https://dojo.domo.com/resources/emoji/heart.png",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.8841088,"math_prob":0.89938325,"size":4305,"snap":"2022-05-2022-21","text_gpt3_token_len":1195,"char_repetition_ratio":0.13833992,"word_repetition_ratio":0.105058365,"special_character_ratio":0.28385597,"punctuation_ratio":0.095525995,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9785236,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-23T04:59:36Z\",\"WARC-Record-ID\":\"<urn:uuid:de1faf1f-cca9-4b5b-a552-14300ba1d561>\",\"Content-Length\":\"101428\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:97c2e2fe-3f99-43dd-9365-c4a81f172f4c>\",\"WARC-Concurrent-To\":\"<urn:uuid:5d5b1909-8931-49aa-9337-891c29d3c954>\",\"WARC-IP-Address\":\"162.159.128.79\",\"WARC-Target-URI\":\"https://dojo.domo.com/discussion/52942/formula-not-summarizing-in-analyzer\",\"WARC-Payload-Digest\":\"sha1:3KXL3SYAKTUL24NQZNH6KXIL66DI33LP\",\"WARC-Block-Digest\":\"sha1:XZKTHH6DMZVUIGHX3RLPF4LPWSB2LYZY\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662555558.23_warc_CC-MAIN-20220523041156-20220523071156-00707.warc.gz\"}"} |
https://metanumbers.com/32805 | [
"# 32805 (number)\n\n32,805 (thirty-two thousand eight hundred five) is an odd five-digits composite number following 32804 and preceding 32806. In scientific notation, it is written as 3.2805 × 104. The sum of its digits is 18. It has a total of 9 prime factors and 18 positive divisors. There are 17,496 positive integers (up to 32805) that are relatively prime to 32805.\n\n## Basic properties\n\n• Is Prime? No\n• Number parity Odd\n• Number length 5\n• Sum of Digits 18\n• Digital Root 9\n\n## Name\n\nShort name 32 thousand 805 thirty-two thousand eight hundred five\n\n## Notation\n\nScientific notation 3.2805 × 104 32.805 × 103\n\n## Prime Factorization of 32805\n\nPrime Factorization 38 × 5\n\nComposite number\nDistinct Factors Total Factors Radical ω(n) 2 Total number of distinct prime factors Ω(n) 9 Total number of prime factors rad(n) 15 Product of the distinct prime numbers λ(n) -1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) 0 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 32,805 is 38 × 5. Since it has a total of 9 prime factors, 32,805 is a composite number.\n\n## Divisors of 32805\n\n1, 3, 5, 9, 15, 27, 45, 81, 135, 243, 405, 729, 1215, 2187, 3645, 6561, 10935, 32805\n\n18 divisors\n\n Even divisors 0 18 10 8\nTotal Divisors Sum of Divisors Aliquot Sum τ(n) 18 Total number of the positive divisors of n σ(n) 59046 Sum of all the positive divisors of n s(n) 26241 Sum of the proper positive divisors of n A(n) 3280.33 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 181.122 Returns the nth root of the product of n divisors H(n) 10.0005 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors\n\nThe number 32,805 can be divided by 18 positive divisors (out of which 0 are even, and 18 are odd). The sum of these divisors (counting 32,805) is 59,046, the average is 32,80.,333.\n\n## Other Arithmetic Functions (n = 32805)\n\n1 φ(n) n\nEuler Totient Carmichael Lambda Prime Pi φ(n) 17496 Total number of positive integers not greater than n that are coprime to n λ(n) 8748 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 3519 Total number of primes less than or equal to n r2(n) 8 The number of ways n can be represented as the sum of 2 squares\n\nThere are 17,496 positive integers (less than 32,805) that are coprime with 32,805. And there are approximately 3,519 prime numbers less than or equal to 32,805.\n\n## Divisibility of 32805\n\n m n mod m 2 3 4 5 6 7 8 9 1 0 1 0 3 3 5 0\n\nThe number 32,805 is divisible by 3, 5 and 9.\n\n• Deficient\n\n• Polite\n\n• Frugal\n• Regular\n\n## Base conversion (32805)\n\nBase System Value\n2 Binary 1000000000100101\n3 Ternary 1200000000\n4 Quaternary 20000211\n5 Quinary 2022210\n6 Senary 411513\n8 Octal 100045\n10 Decimal 32805\n12 Duodecimal 16b99\n20 Vigesimal 4205\n36 Base36 pb9\n\n## Basic calculations (n = 32805)\n\n### Multiplication\n\nn×y\n n×2 65610 98415 131220 164025\n\n### Division\n\nn÷y\n n÷2 16402.5 10935 8201.25 6561\n\n### Exponentiation\n\nny\n n2 1076168025 35303692060125 1158137618032400625 37992704559552902503125\n\n### Nth Root\n\ny√n\n 2√n 181.122 32.012 13.4581 8.00181\n\n## 32805 as geometric shapes\n\n### Circle\n\n Diameter 65610 206120 3.38088e+09\n\n### Sphere\n\n Volume 1.4788e+14 1.35235e+10 206120\n\n### Square\n\nLength = n\n Perimeter 131220 1.07617e+09 46393.3\n\n### Cube\n\nLength = n\n Surface area 6.45701e+09 3.53037e+13 56819.9\n\n### Equilateral Triangle\n\nLength = n\n Perimeter 98415 4.65994e+08 28410\n\n### Triangular Pyramid\n\nLength = n\n Surface area 1.86398e+09 4.16058e+12 26785.2"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.6316796,"math_prob":0.99480385,"size":4580,"snap":"2023-14-2023-23","text_gpt3_token_len":1809,"char_repetition_ratio":0.12521853,"word_repetition_ratio":0.020558003,"special_character_ratio":0.4558952,"punctuation_ratio":0.079345085,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99846506,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-06-05T02:54:40Z\",\"WARC-Record-ID\":\"<urn:uuid:6d292611-f4f7-4ff4-be2c-dfdd43f896ff>\",\"Content-Length\":\"40827\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:5ba8e136-1612-4ef5-9ba5-20a79cfaf837>\",\"WARC-Concurrent-To\":\"<urn:uuid:f0a3f315-2fc8-413e-b312-baf4d0b26fe2>\",\"WARC-IP-Address\":\"46.105.53.190\",\"WARC-Target-URI\":\"https://metanumbers.com/32805\",\"WARC-Payload-Digest\":\"sha1:CJ44B2NCPZ4MYSR7SCLGFKLSHXXZGRLX\",\"WARC-Block-Digest\":\"sha1:HPY73M3IBO3V5ZN6RN22MRJFFFHSHYU5\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224650620.66_warc_CC-MAIN-20230605021141-20230605051141-00375.warc.gz\"}"} |
https://zh.cppreference.com/w/cpp/types/bad_typeid | [
"##### 操作\n\n< cpp | types\n\nC++\n 语言 标准库头文件 自立与有宿主实现 具名要求 语言支持库 概念库 (C++20) 诊断库 工具库 字符串库 容器库 迭代器库 范围库 (C++20) 算法库 数值库 输入/输出库 本地化库 正则表达式库 (C++11) 原子操作库 (C++11) 线程支持库 (C++11) 文件系统库 (C++17) 技术规范\n\n(C++11)\n\n pair tuple(C++11) apply(C++17) make_from_tuple(C++17)\n optional(C++17) any(C++17) variant(C++17)\nswap 、 forward 与 move\n(C++14)\n(C++11)\n(C++11)\n\n(C++17)\n(C++17)\n\n(C++11)\n(C++17)\n(C++17)\n\n ptrdiff_t size_t max_align_t(C++11) byte(C++17)\n nullptr_t(C++11) offsetof NULL\n\nC 数值极限接口\n\n type_info type_index(C++11)\n\n is_void(C++11) is_null_pointer(C++14) is_array(C++11) is_pointer(C++11) is_enum(C++11) is_union(C++11) is_class(C++11) is_function(C++11)\n is_object(C++11) is_scalar(C++11) is_compound(C++11) is_integral(C++11) is_floating_point(C++11) is_fundamental(C++11) is_arithmetic(C++11)\n\n is_const(C++11) is_volatile(C++11) is_empty(C++11) is_polymorphic(C++11) is_final(C++14) is_abstract(C++11) is_aggregate(C++17) is_trivial(C++11)\n is_trivially_copyable(C++11) is_standard_layout(C++11) is_literal_type(C++11)(C++20 前) is_pod(C++11)(C++20 中弃用) is_signed(C++11) is_unsigned(C++11) is_bounded_array(C++20) is_unbounded_array(C++20)\n\n(C++17)\n\n is_same(C++11) is_base_of(C++11) is_convertibleis_nothrow_convertible(C++11)(C++20) is_layout_compatible(C++20) is_corresponding_member(C++20)\n alignment_of(C++11) rank(C++11) extent(C++11) is_invocableis_invocable_ris_nothrow_invocableis_nothrow_invocable_r(C++17)(C++17)(C++17)(C++17)\n\n aligned_storage(C++11) aligned_union(C++11) decay(C++11) remove_cvref(C++20) enable_if(C++11) void_t(C++17)\n conditional(C++11) common_type(C++11) common_reference(C++20) underlying_type(C++11) result_ofinvoke_result(C++11)(C++20 前)(C++17) type_identity(C++20)\n\n 定义于头文件 class bad_typeid : public std::exception;",
null,
"## 目录\n\n### [编辑]成员函数\n\n (构造函数) 构造新的 bad_typeid 对象 (公开成员函数)\n\n## 继承自 std::exception\n\n### 成员函数\n\n (析构函数)[虚] 析构该异常对象 (std::exception 的虚公开成员函数) [编辑] what[虚] 返回解释性字符串 (std::exception 的虚公开成员函数) [编辑]\n\n### [编辑]示例\n\n#include <iostream>\n#include <typeinfo>\n\nstruct S { // 类型必须是多态\nvirtual void f();\n};\n\nint main()\n{\nS* p = nullptr;\ntry {\nstd::cout << typeid(*p).name() << '\\n';\n}\nAttempted a typeid of NULL pointer!"
] | [
null,
"http://upload.cppreference.com/mwiki/images/6/69/std-bad_typeid-inheritance.svg",
null
] | {"ft_lang_label":"__label__zh","ft_lang_prob":0.6636745,"math_prob":0.99693805,"size":287,"snap":"2019-51-2020-05","text_gpt3_token_len":150,"char_repetition_ratio":0.19787987,"word_repetition_ratio":0.0,"special_character_ratio":0.26480836,"punctuation_ratio":0.27083334,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99498665,"pos_list":[0,1,2],"im_url_duplicate_count":[null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-01-21T07:24:32Z\",\"WARC-Record-ID\":\"<urn:uuid:a5d99d29-fb86-47ab-abdf-842b3155dc22>\",\"Content-Length\":\"89192\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:09fd7cb7-487f-44cb-891d-d23d394a3290>\",\"WARC-Concurrent-To\":\"<urn:uuid:bd992d84-ab40-4da4-9d0d-5b8e9a61796b>\",\"WARC-IP-Address\":\"74.114.90.46\",\"WARC-Target-URI\":\"https://zh.cppreference.com/w/cpp/types/bad_typeid\",\"WARC-Payload-Digest\":\"sha1:PJP3LCJYEEOER7L4L6UNWWCD4IL32UWF\",\"WARC-Block-Digest\":\"sha1:3ONDLAQOR4VSDXQ6ABYILZCKPMXVRRGR\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-05/CC-MAIN-2020-05_segments_1579250601615.66_warc_CC-MAIN-20200121044233-20200121073233-00525.warc.gz\"}"} |
https://tutorialspoint.dev/language/java/for-each-loop-in-java | [
"# For-each loop in Java\n\nPrerequisite: Decision making in Java\n\nFor-each is another array traversing technique like for loop, while loop, do-while loop introduced in Java5.\n\n• It starts with the keyword for like a normal for-loop.\n• Instead of declaring and initializing a loop counter variable, you declare a variable that is the same type as the base type of the array, followed by a colon, which is then followed by the array name.\n• In the loop body, you can use the loop variable you created rather than using an indexed array element.\n• It’s commonly used to iterate over an array or a Collections class (eg, ArrayList)\n\nSyntax:\n\n```for (type var : array)\n{\nstatements using var;\n}\n```\n\nis equivalent to:\n\n```for (int i=0; i<arr.length; i++)\n{\ntype var = arr[i];\nstatements using var;\n}\n```\n `// Java program to illustrate ` `// for-each loop ` `class` `For_Each ` `{ ` ` ``public` `static` `void` `main(String[] arg) ` ` ``{ ` ` ``{ ` ` ``int``[] marks = { ``125``, ``132``, ``95``, ``116``, ``110` `}; ` ` ` ` ``int` `highest_marks = maximum(marks); ` ` ``System.out.println(``\"The highest score is \"` `+ highest_marks); ` ` ``} ` ` ``} ` ` ``public` `static` `int` `maximum(``int``[] numbers) ` ` ``{ ` ` ``int` `maxSoFar = numbers[``0``]; ` ` ` ` ``// for each loop ` ` ``for` `(``int` `num : numbers) ` ` ``{ ` ` ``if` `(num > maxSoFar) ` ` ``{ ` ` ``maxSoFar = num; ` ` ``} ` ` ``} ` ` ``return` `maxSoFar; ` ` ``} ` `} `\n\nOutput:\n\n```The highest score is 132\n```\n\nLimitations of for-each loop\n\n1. For-each loops are not appropriate when you want to modify the array:\n```for (int num : marks)\n{\n// only changes num, not the array element\nnum = num*2;\n}\n```\n2. For-each loops do not keep track of index. So we can not obtain array index using For-Each loop\n```for (int num : numbers)\n{\nif (num == target)\n{\nreturn ???; // do not know the index of num\n}\n}\n```\n3. For-each only iterates forward over the array in single steps\n```// cannot be converted to a for-each loop\nfor (int i=numbers.length-1; i>0; i--)\n{\nSystem.out.println(numbers[i]);\n}\n```\n4. For-each cannot process two decision making statements at once\n```// cannot be easily converted to a for-each loop\nfor (int i=0; i<numbers.length; i++)\n{\nif (numbers[i] == arr[i])\n{ ...\n}\n}\n```\n\nRelated Articles:\nFor-each in C++ vs Java\nIterator vs For-each in Java\n\n## tags:\n\nJava java-basics Java"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.68069553,"math_prob":0.9510821,"size":2191,"snap":"2021-21-2021-25","text_gpt3_token_len":576,"char_repetition_ratio":0.12345679,"word_repetition_ratio":0.025252525,"special_character_ratio":0.28890917,"punctuation_ratio":0.14084508,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99460006,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-05-15T15:16:24Z\",\"WARC-Record-ID\":\"<urn:uuid:01ba33ea-41b8-4239-88ae-d3deca2411b0>\",\"Content-Length\":\"23924\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:cce37966-bc5a-4b56-8a75-20adff164790>\",\"WARC-Concurrent-To\":\"<urn:uuid:e13974bd-9b2d-4ea5-bca7-91ad180bf4cd>\",\"WARC-IP-Address\":\"104.21.79.77\",\"WARC-Target-URI\":\"https://tutorialspoint.dev/language/java/for-each-loop-in-java\",\"WARC-Payload-Digest\":\"sha1:JR2NKT2VV3RK7QCA6ELSASBPXQOKQ6U4\",\"WARC-Block-Digest\":\"sha1:PG7WILGTGW4XIUZTLUUAZIOJGFULJIED\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-21/CC-MAIN-2021-21_segments_1620243991370.50_warc_CC-MAIN-20210515131024-20210515161024-00406.warc.gz\"}"} |
https://artofproblemsolving.com/wiki/index.php?title=2015_AMC_8_Problems/Problem_19&oldid=73091 | [
"# 2015 AMC 8 Problems/Problem 19\n\nA triangle with vertices as",
null,
"$A=(1,3)$,",
null,
"$B=(5,1)$, and",
null,
"$C=(4,4)$ is plotted on a",
null,
"$6\\times5$ grid. What fraction of the grid is covered by the triangle?",
null,
"$\\textbf{(A) }\\frac{1}{6} \\qquad \\textbf{(B) }\\frac{1}{5} \\qquad \\textbf{(C) }\\frac{1}{4} \\qquad \\textbf{(D) }\\frac{1}{3} \\qquad \\textbf{(E) }\\frac{1}{2}$",
null,
"$[asy] draw((1,0)--(1,5),linewidth(.5)); draw((2,0)--(2,5),linewidth(.5)); draw((3,0)--(3,5),linewidth(.5)); draw((4,0)--(4,5),linewidth(.5)); draw((5,0)--(5,5),linewidth(.5)); draw((6,0)--(6,5),linewidth(.5)); draw((0,1)--(6,1),linewidth(.5)); draw((0,2)--(6,2),linewidth(.5)); draw((0,3)--(6,3),linewidth(.5)); draw((0,4)--(6,4),linewidth(.5)); draw((0,5)--(6,5),linewidth(.5)); draw((0,0)--(0,6),EndArrow); draw((0,0)--(7,0),EndArrow); draw((1,3)--(4,4)--(5,1)--cycle); label(\"y\",(0,6),W); label(\"x\",(7,0),S); label(\"A\",(1,3),dir(210)); label(\"B\",(5,1),SE); label(\"C\",(4,4),dir(100)); [/asy]$\n\n## Solution\n\nThe area of",
null,
"$\\triangle ABC$ is equal to half the product of its base and height. By the Pythagorean Theorem, we find its height is",
null,
"$\\sqrt{1^2+2^2}=\\sqrt{5}$, and its base is",
null,
"$\\sqrt{2^2+4^2}=\\sqrt{20}$. We multiply these and divide by 2 to find the of the triangle is",
null,
"$\\frac{\\sqrt{5 \\cdot 20}}2=\\frac{\\sqrt{100}}2=\\frac{10}2=5$. Since the grid has an area of",
null,
"$30$, the fraction of the grid covered by the triangle is",
null,
"$\\frac 5{30}=\\boxed{\\textbf{(A) }\\frac{1}{6}}$.\n\n## See Also\n\n 2015 AMC 8 (Problems • Answer Key • Resources) Preceded byProblem 18 Followed byProblem 20 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 All AJHSME/AMC 8 Problems and Solutions\n\nThe problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.",
null,
"Invalid username\nLogin to AoPS"
] | [
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"https://latex.artofproblemsolving.com/6/8/e/68e8c6017962feb4293fbab0bba51887ba571656.png ",
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"https://latex.artofproblemsolving.com/f/7/0/f704a5156f7020d34e532d60908b4ca2a03b521d.png ",
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"https://latex.artofproblemsolving.com/0/3/2/0326fb9b83a664bec4bab910587f802f51202267.png ",
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"https://latex.artofproblemsolving.com/8/c/3/8c3a2d2224f7d163b46d702132425d47828bf538.png ",
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"https://latex.artofproblemsolving.com/d/7/c/d7c102e6d465673a7871e64ea35e2c43eeabc419.png ",
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"https://latex.artofproblemsolving.com/6/f/4/6f4c5aeca5c4636b8eec4391a024e89c4e304d17.png ",
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"https://latex.artofproblemsolving.com/4/5/d/45d8abcd96938150b1cef6c8c01f8a3f5fba7623.png ",
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"https://latex.artofproblemsolving.com/6/5/1/651ba418a810d971dbc8a326d49a71fe1541fae0.png ",
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"https://latex.artofproblemsolving.com/e/0/d/e0d56888852146e06fa5e4c793a6a1e6fb4e3fbb.png ",
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"https://wiki-images.artofproblemsolving.com//8/8b/AMC_logo.png",
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.85274166,"math_prob":0.9999509,"size":822,"snap":"2021-21-2021-25","text_gpt3_token_len":248,"char_repetition_ratio":0.13202934,"word_repetition_ratio":0.0,"special_character_ratio":0.35036495,"punctuation_ratio":0.07453416,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99983764,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-06-15T06:42:08Z\",\"WARC-Record-ID\":\"<urn:uuid:7af5f503-7edf-4d17-9fff-d884107d5b87>\",\"Content-Length\":\"41461\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9bf819c6-5c0b-437f-a03d-de41af8f810e>\",\"WARC-Concurrent-To\":\"<urn:uuid:23396986-68d1-4b73-af54-cae7811dd1be>\",\"WARC-IP-Address\":\"172.67.69.208\",\"WARC-Target-URI\":\"https://artofproblemsolving.com/wiki/index.php?title=2015_AMC_8_Problems/Problem_19&oldid=73091\",\"WARC-Payload-Digest\":\"sha1:JPBQLKNTR6VNYC2SLAXZ6ZYVSQ5JRF7C\",\"WARC-Block-Digest\":\"sha1:APLJ5CJSHF2UR3PXZBJ2KZP6PMZI77O3\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-25/CC-MAIN-2021-25_segments_1623487617599.15_warc_CC-MAIN-20210615053457-20210615083457-00596.warc.gz\"}"} |
http://git.kamailio.org/gitlist/index.php/sip-router/blob/00f45c49667caf6e62eb89e14a76c81b8c053964/qvalue.h | [
"```/*\n* \\$Id\\$\n*\n* Handling of the q value\n*\n* Copyright (C) 2004 FhG FOKUS\n*\n* This file is part of ser, a free SIP server.\n*\n* ser is free software; you can redistribute it and/or modify\n* the Free Software Foundation; either version 2 of the License, or\n* (at your option) any later version\n*\n* For a license to use the ser software under conditions\n* other than those described here, or to purchase support for this\n* [email protected]\n*\n* ser is distributed in the hope that it will be useful,\n* but WITHOUT ANY WARRANTY; without even the implied warranty of\n* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n* GNU General Public License for more details.\n*\n* You should have received a copy of the GNU General Public License\n* along with this program; if not, write to the Free Software\n* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA\n*\n* History\n* ------\n* 2004-04-25 created (janakj)\n*/\n\n#ifndef _QVALUE_H\n#define _QVALUE_H 1\n\n#include <string.h>\n\n/*\n* The q value expresses the priority of a URI within a set of URIs\n* (Contact header field in the same SIP message or dset array in\n* ser. The higher is the q value of a URI the higher is the priority\n* of the URI.\n*\n* The q value is usually expressed as a floating point number with\n* limited number of decimal digits, for example 0.346. RFC3261 allows\n* 0-3 decimal digits.\n*\n* To speed things up we represent the q value as integer number, it\n* is then easier to handle/print the value. To convert float into\n* integer we multiply the q value by 1000, i.e.\n* (float)0.567 == (int)567. In the opposite direction, values\n* higher or equal to 1000 are converted to 1.0 and values below or\n* equal to 0 are converted to 0.\n*\n* Value Q_UNSPECIFIED (which is in fact -1) has a special meaning, it\n* means that the q value is not known and the parameter should not be\n* printed when printing Contacts, implementations will then use\n* implementation specific pre-defined values.\n*/\n\ntypedef int qvalue_t;\n\n/*\n* Use this if the value of q is not specified\n*/\n#define Q_UNSPECIFIED ((qvalue_t)-1)\n\n#define MAX_Q ((qvalue_t)1000)\n#define MIN_Q ((qvalue_t)0)\n\n#define MAX_Q_STR \"1\"\n#define MAX_Q_STR_LEN (sizeof(MAX_Q_STR) - 1)\n\n#define MIN_Q_STR \"0\"\n#define MIN_Q_STR_LEN (sizeof(MIN_Q_STR) - 1)\n\n#define Q_PREFIX \"0.\"\n#define Q_PREFIX_LEN (sizeof(Q_PREFIX) - 1)\n\n/*\n* Calculate the length of printed q\n*/\nstatic inline size_t len_q(qvalue_t q)\n{\nif (q == Q_UNSPECIFIED) {\nreturn 0;\n} else if (q >= MAX_Q) {\nreturn MAX_Q_STR_LEN;\n} else if (q <= MIN_Q) {\nreturn MIN_Q_STR_LEN;\n} else if (q % 100 == 0) {\nreturn Q_PREFIX_LEN + 1;\n} else if (q % 10 == 0) {\nreturn Q_PREFIX_LEN + 2;\n} else {\nreturn Q_PREFIX_LEN + 3;\n}\n}\n\n/*\n* Convert qvalue_t to double\n*/\nstatic inline double q2double(qvalue_t q)\n{\nif (q == Q_UNSPECIFIED) {\nreturn -1;\n} else {\nreturn (double)((double)q / (double)1000);\n}\n}\n\n/*\n* Convert double to qvalue_t\n*/\nstatic inline qvalue_t double2q(double q)\n{\nif (q == -1) {\nreturn Q_UNSPECIFIED;\n} else {\nreturn q * 1000;\n}\n}\n\n/*\n* Convert q value to string\n*/\nstatic inline char* q2str(qvalue_t q, unsigned int* len)\n{\nstatic char buf[sizeof(\"0.123\")];\nchar* p;\n\np = buf;\nif (q == Q_UNSPECIFIED) {\n/* Do nothing */\n} else if (q >= MAX_Q) {\nmemcpy(p, MAX_Q_STR, MAX_Q_STR_LEN);\np += MAX_Q_STR_LEN;\n} else if (q <= MIN_Q) {\nmemcpy(p, MIN_Q_STR, MIN_Q_STR_LEN);\np += MIN_Q_STR_LEN;\n} else {\nmemcpy(p, Q_PREFIX, Q_PREFIX_LEN);\np += Q_PREFIX_LEN;\n\n*p++ = q / 100 + '0';\nq %= 100;\nif (!q) goto end;\n\n*p++ = q / 10 + '0';\nq %= 10;\nif (!q) goto end;\n\n*p++ = q + '0';\n}\nend:\n*p = '\\0';\nif (len) {\n*len = p - buf;\n}\nreturn buf;\n}\n\n/*\n* Convert string representation of q parameter in qvalue_t\n*/\nint str2q(qvalue_t* q, char* s, int len);\n\n#endif /* _QVALUE_H */\n```"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.592456,"math_prob":0.9881926,"size":3873,"snap":"2020-34-2020-40","text_gpt3_token_len":1124,"char_repetition_ratio":0.13388473,"word_repetition_ratio":0.059972107,"special_character_ratio":0.3488252,"punctuation_ratio":0.12536024,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9877435,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-08-05T02:41:56Z\",\"WARC-Record-ID\":\"<urn:uuid:1cdbbee6-16b8-4a76-86d8-651f2eea86c4>\",\"Content-Length\":\"41499\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:022ffc31-c0d8-47f2-95a2-e6e755ae4d48>\",\"WARC-Concurrent-To\":\"<urn:uuid:a5ab9b94-821a-4efb-8218-16f1f943746c>\",\"WARC-IP-Address\":\"193.22.119.66\",\"WARC-Target-URI\":\"http://git.kamailio.org/gitlist/index.php/sip-router/blob/00f45c49667caf6e62eb89e14a76c81b8c053964/qvalue.h\",\"WARC-Payload-Digest\":\"sha1:IWIMHFNDXNETJ5H7TRIL6Q5BHXFNKQNM\",\"WARC-Block-Digest\":\"sha1:4UO2E2EIWAX3JDD4XRBQPX2HYDS3E3T7\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-34/CC-MAIN-2020-34_segments_1596439735906.77_warc_CC-MAIN-20200805010001-20200805040001-00578.warc.gz\"}"} |
https://support.nag.com/numeric/nl/nagdoc_28.6/clhtml/f01/f01fqc.html | [
"# NAG CL Interfacef01fqc (complex_gen_matrix_pow)\n\nSettings help\n\nCL Name Style:\n\n## 1Purpose\n\nf01fqc computes an abitrary real power ${A}^{p}$ of a complex $n×n$ matrix $A$.\n\n## 2Specification\n\n #include\n void f01fqc (Integer n, Complex a[], Integer pda, double p, NagError *fail)\nThe function may be called by the names: f01fqc or nag_matop_complex_gen_matrix_pow.\n\n## 3Description\n\nFor a matrix $A$ with no eigenvalues on the closed negative real line, ${A}^{p}$ ($p\\in ℝ$) can be defined as\n $Ap= exp(plog(A))$\nwhere $\\mathrm{log}\\left(A\\right)$ is the principal logarithm of $A$ (the unique logarithm whose spectrum lies in the strip $\\left\\{z:-\\pi <\\mathrm{Im}\\left(z\\right)<\\pi \\right\\}$).\n${A}^{p}$ is computed using the Schur–Padé algorithm described in Higham and Lin (2011) and Higham and Lin (2013).\nThe real number $p$ is expressed as $p=q+r$ where $q\\in \\left(-1,1\\right)$ and $r\\in ℤ$. Then ${A}^{p}={A}^{q}{A}^{r}$. The integer power ${A}^{r}$ is found using a combination of binary powering and, if necessary, matrix inversion. The fractional power ${A}^{q}$ is computed using a Schur decomposition and a Padé approximant.\nHigham N J (2008) Functions of Matrices: Theory and Computation SIAM, Philadelphia, PA, USA\nHigham N J and Lin L (2011) A Schur–Padé algorithm for fractional powers of a matrix SIAM J. Matrix Anal. Appl. 32(3) 1056–1078\nHigham N J and Lin L (2013) An improved Schur–Padé algorithm for fractional powers of a matrix and their Fréchet derivatives SIAM J. Matrix Anal. Appl. 34(3) 1341–1360\n\n## 5Arguments\n\n1: $\\mathbf{n}$Integer Input\nOn entry: $n$, the order of the matrix $A$.\nConstraint: ${\\mathbf{n}}\\ge 0$.\n2: $\\mathbf{a}\\left[\\mathit{dim}\\right]$Complex Input/Output\nNote: the dimension, dim, of the array a must be at least ${\\mathbf{pda}}×{\\mathbf{n}}$.\nThe $\\left(i,j\\right)$th element of the matrix $A$ is stored in ${\\mathbf{a}}\\left[\\left(j-1\\right)×{\\mathbf{pda}}+i-1\\right]$.\nOn entry: the $n×n$ matrix $A$.\nOn exit: if ${\\mathbf{fail}}\\mathbf{.}\\mathbf{code}=$ NE_NOERROR, the $n×n$ matrix $p$th power, ${A}^{p}$. Alternatively, if ${\\mathbf{fail}}\\mathbf{.}\\mathbf{code}=$ NE_NEGATIVE_EIGVAL, contains an $n×n$ non-principal power of $A$.\n3: $\\mathbf{pda}$Integer Input\nOn entry: the stride separating matrix row elements in the array a.\nConstraint: ${\\mathbf{pda}}\\ge {\\mathbf{n}}$.\n4: $\\mathbf{p}$double Input\nOn entry: the required power of $A$.\n5: $\\mathbf{fail}$NagError * Input/Output\nThe NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).\n\n## 6Error Indicators and Warnings\n\nNE_ALLOC_FAIL\nDynamic memory allocation failed.\nSee Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.\nOn entry, argument $⟨\\mathit{\\text{value}}⟩$ had an illegal value.\nNE_INT\nOn entry, ${\\mathbf{n}}=⟨\\mathit{\\text{value}}⟩$.\nConstraint: ${\\mathbf{n}}\\ge 0$.\nNE_INT_2\nOn entry, ${\\mathbf{pda}}=⟨\\mathit{\\text{value}}⟩$ and ${\\mathbf{n}}=⟨\\mathit{\\text{value}}⟩$.\nConstraint: ${\\mathbf{pda}}\\ge {\\mathbf{n}}$.\nNE_INTERNAL_ERROR\nAn internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.\nSee Section 7.5 in the Introduction to the NAG Library CL Interface for further information.\nNE_NEGATIVE_EIGVAL\n$A$ has eigenvalues on the negative real line. The principal $p$th power is not defined so a non-principal power is returned.\nNE_NO_LICENCE\nYour licence key may have expired or may not have been installed correctly.\nSee Section 8 in the Introduction to the NAG Library CL Interface for further information.\nNE_SINGULAR\n$A$ is singular so the $p$th power cannot be computed.\nNW_SOME_PRECISION_LOSS\n${A}^{p}$ has been computed using an IEEE double precision Padé approximant, although the arithmetic precision is higher than IEEE double precision.\n\n## 7Accuracy\n\nFor positive integer $p$, the algorithm reduces to a sequence of matrix multiplications. For negative integer $p$, the algorithm consists of a combination of matrix inversion and matrix multiplications.\nFor a normal matrix $A$ (for which ${A}^{\\mathrm{H}}A=A{A}^{\\mathrm{H}}$) and non-integer $p$, the Schur decomposition is diagonal and the algorithm reduces to evaluating powers of the eigenvalues of $A$ and then constructing ${A}^{p}$ using the Schur vectors. This should give a very accurate result. In general however, no error bounds are available for the algorithm.\n\n## 8Parallelism and Performance\n\nf01fqc is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.\nf01fqc makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.\nPlease consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this function. Please also consult the Users' Note for your implementation for any additional implementation-specific information.\n\nThe cost of the algorithm is $O\\left({n}^{3}\\right)$. The exact cost depends on the matrix $A$ but if $p\\in \\left(-1,1\\right)$ then the cost is independent of $p$. $O\\left(4×{n}^{2}\\right)$ complex allocatable memory is required by the function.\nIf estimates of the condition number of ${A}^{p}$ are required then f01kec should be used.\n\n## 10Example\n\nThis example finds ${A}^{p}$ where $p=0.2$ and\n $A = ( 2i+ 3i+0 2i+0 1+3i 2+i 1i+0 1i+0 2+2i 2+i 2+2i 2i 2+4i 3i+ 2+2i 3i+0 1i+0 ) .$\n\n### 10.1Program Text\n\nProgram Text (f01fqce.c)\n\n### 10.2Program Data\n\nProgram Data (f01fqce.d)\n\n### 10.3Program Results\n\nProgram Results (f01fqce.r)"
] | [
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.80907863,"math_prob":0.99813193,"size":3839,"snap":"2023-40-2023-50","text_gpt3_token_len":863,"char_repetition_ratio":0.124119945,"word_repetition_ratio":0.06644518,"special_character_ratio":0.21125293,"punctuation_ratio":0.13478261,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99979573,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-21T22:02:54Z\",\"WARC-Record-ID\":\"<urn:uuid:427388f0-82e9-4db2-af35-cfde715c62d8>\",\"Content-Length\":\"30165\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:5ffe99f1-8b46-450e-a619-c5c94302841d>\",\"WARC-Concurrent-To\":\"<urn:uuid:e48b1e7f-71cc-4dcd-bbdc-2554ce337b5f>\",\"WARC-IP-Address\":\"78.129.168.4\",\"WARC-Target-URI\":\"https://support.nag.com/numeric/nl/nagdoc_28.6/clhtml/f01/f01fqc.html\",\"WARC-Payload-Digest\":\"sha1:BFJGAIMH3ONQEQHWDWWJAHGLM5HIU3LY\",\"WARC-Block-Digest\":\"sha1:FSR4SN7UFZTXFHIV6N7MFTRE4VC7RT4G\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233506045.12_warc_CC-MAIN-20230921210007-20230922000007-00203.warc.gz\"}"} |
https://eccc.weizmann.ac.il/report/2012/171/ | [
"",
null,
"",
null,
"Under the auspices of the Computational Complexity Foundation (CCF)",
null,
"",
null,
"",
null,
"",
null,
"",
null,
"REPORTS > DETAIL:\n\n### Paper:\n\nTR12-171 | 3rd December 2012 02:16\n\n#### From Information to Exact Communication",
null,
"TR12-171\nAuthors: Mark Braverman, Ankit Garg, Denis Pankratov, Omri Weinstein\nPublication: 3rd December 2012 05:55\nKeywords:\n\nAbstract:\n\nWe develop a new local characterization of the zero-error information complexity function for two party communication problems, and use it to compute the exact internal and external information complexity of the 2-bit AND function: $IC(AND,0) = C_{\\wedge}\\approx 1.4923$ bits, and $IC^{ext}(AND,0) = \\log_2 3 \\approx 1.5839$ bits. This leads to a tight (upper and lower bound) characterization of the communication complexity of the set intersection problem on subsets of $\\{1,\\ldots,n\\}$, whose randomized communication complexity tends to $C_{\\wedge}\\cdot n\\pm o(n)$ as the error tends to zero.\n\nThe information-optimal protocol we present has an infinite number of rounds. We show this is necessary by proving that the rate of convergence of the r-round information cost of AND to $IC(AND,0)=C_\\wedge$ behaves like $\\Theta(1/r^2)$, i.e. that the r-round information complexity of AND is $C_\\wedge+\\Theta(1/r^2)$.\n\nWe leverage the tight analysis obtained for the information complexity of AND to calculate and prove the exact communication complexity of the set disjointness function $Disj_n(X,Y) = \\neg \\vee_{i=1}^{n} AND(x_i,y_i)$ with error tending to 0, which turns out to be $= C_{DISJ}\\cdot n \\pm o(n)$, where $C_{DISJ}\\approx 0.4827$. Our rate of convergence results imply that an optimal protocol for set disjointness will have to use $\\omega(1)$ rounds of communication, since every $r$-round protocol will be sub-optimal by at least $\\Omega(n/r^2)$ bits of communication.\n\nWe also obtain the tight bound of $\\frac{2}{\\ln 2}k\\pm o(k)$ on the communication complexity of disjointness of sets of size $\\le k$. An asymptotic bound of $\\Theta(k)$ was previously shown by Hastad and Wigderson.\n\nISSN 1433-8092 | Imprint"
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"https://eccc.weizmann.ac.il/resources/gf/rss.png",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.8378596,"math_prob":0.98764044,"size":1764,"snap":"2019-51-2020-05","text_gpt3_token_len":454,"char_repetition_ratio":0.15852273,"word_repetition_ratio":0.007936508,"special_character_ratio":0.2585034,"punctuation_ratio":0.082840234,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99915385,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-14T05:05:43Z\",\"WARC-Record-ID\":\"<urn:uuid:d3c6a832-1b04-4be9-b89c-fcdc5da414d2>\",\"Content-Length\":\"21309\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9da27d02-65b3-468c-b226-98553b91aacc>\",\"WARC-Concurrent-To\":\"<urn:uuid:264dec1b-c235-4d5d-a544-93905b275880>\",\"WARC-IP-Address\":\"132.77.150.87\",\"WARC-Target-URI\":\"https://eccc.weizmann.ac.il/report/2012/171/\",\"WARC-Payload-Digest\":\"sha1:NZ7BCI3XJK7POU3BDNLIDRKT4KVHHRI7\",\"WARC-Block-Digest\":\"sha1:KCLJXCGL3GGBR7SONWDZHIFBCF52RHQQ\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575540584491.89_warc_CC-MAIN-20191214042241-20191214070241-00228.warc.gz\"}"} |
https://physics.stackexchange.com/questions/486534/does-the-pressure-from-a-water-tank-increases-as-the-altitude-increases/486764 | [
"# Does the pressure from a water tank increases as the altitude increases?\n\nIf a solenoid valve is placed right after water tank's water tap does the water pressure changes if the water tank is lifted to 3 meters?\nThe context is this: the electric valve is functional only if the water pressure surpasses 0.6 bar.\n\nAnd a second question: from other sources I found out that 1000 liters of water create a 1 bar pressure. Does this pressure is the same at the water tap exit?",
null,
"• 1000 liters of water in a puddle on a floor exerts very little hydrostatic pressure, but that same amount of water in a tall column (e.g., a water tower) will exert a great deal of pressure. It's the height of the water column that matters - you can't convert a volume of water into an estimate of pressure without knowing something about the geometry. Not sure if that 1000L=1 bar rule of thumb is for the specific device pictured, but it's not a general rule. – Nuclear Wang Jun 17 '19 at 14:20\n• @NuclearWang from other sources I found out that 1 meter depth of water can exert 0.98 bar. In this case, the minimum length of the tube before the tap should be 10 meters to reach 1 bar. – George I. Jun 17 '19 at 15:45\n\nAs mentioned in the other answer and a comment, it is the height of the water column above the tap that determines the pressure. (That means if you lift the whole tank, including the valve, the pressure will not change.) The shape of the water doesn't matter, so you could have the cubic tank with a thin tube of, say, 3 m length downwards, and the pressure would correspond to a height of $$3 \\text{ m} + (\\text{height in the tank})$$.\nSpecifically, in a body of water, at a depth $$d$$ below the surface, the pressure is $$p=\\rho\\cdot g \\cdot d\\,$$ where $$\\rho=1000\\text{ kg}/\\text{m}^3$$ is the density and $$g=9.81\\text{ m}/\\text{s}^2$$ is gravitational acceleration. (These are values for pure (drinking) water and at sea level. For salt water, $$\\rho$$ is higher, and higher up on a mountain $$g$$ is lower, but you can probably ignore that. You can also approximate $$g=10\\text{ m}/\\text{s}^2$$ for easier calculation.)\nHence, one meter of water gives $$p\\approx1000\\text{ kg}/\\text{m}^3 \\cdot 1\\text{ m}\\cdot 10\\text{ m}/\\text{s}^2=10\\,000 \\text{ N}/\\text{m}^2=0.1 \\text{ bar}$$. So for $$0.6 \\text{ bar}$$, you would need $$6\\text {m}$$ of water."
] | [
null,
"https://i.stack.imgur.com/2s4Wl.jpg",
null
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https://rdrr.io/cran/bspmma/man/bf1.html | [
"# bf1: Generate Chains for Computation of Bayes Factors In bspmma: Bayesian Semiparametric Models for Meta-Analysis\n\n## Description\n\nGenerate nine matrices of MCMC output under the ordinary Dirichlet model, for nine fixed values of the precision parameter M. This MCMC output is needed for computing Bayes factors.\n\n## Usage\n\n `1` ```bf1(data,seed=1,ncycles=2000,d=c(.1,.1,0,1000),K=10,burnin=1000) ```\n\n## Arguments\n\n `data` is a two-column matrix with a row for each study in the meta-analysis. The first column is the log of estimate of relative risk, often a log(odds ratio). The second column is the true or estimated standard error of the log(odds ratio). `seed` is the value of the seed for starting the random number generator, which will be used before each of the nine calls to the function `dirichlet.o`. `ncycles` is the number of cycles of the Markov chain. `d` is a vector of length four with the values of the hyperparameters, in order, the location and scale of the Gamma inverse prior, mean and variance multiplier for the normal prior on mu. `K` is the number of summands to include when one uses Sethuraman's (1994) representation for getting the parameter eta = mean(F). If you do not intend to use this parameter, then take K small, say K=10. `burnin` is the number of Markov chain cycles to drop.\n\n## Details\n\nDoss (2012) describes a method for estimating Bayes factors for many M values in a Dirichlet mixing model; the method requires judicious selection of multiple hyperparameter points at which to estimate the posterior distribution by MCMC under the ordinary Dirichlet model. The function `bf1` is used for estimating Bayes factors for conditional vs.\\ ordinary Dirichlet models, and for comparing values of M in the conditional model or in the ordinary model, for a range of the precision parameter M which cover the range of values of interest in most practical problems. The function `bf1` generates the MCMC output for a hard-wired selection of hyperparameters which work well to give low-variance estimates of Bayes factors of interest in practice. Chains are generated for nine values of the Dirichlet precision parameter M: .25, .5, 1, 2, 4, 8, 16, 32, and 64. The rest of the Dirichlet model is specified by the parameters of the normal/inverse Gamma prior, which by default are d = (.1,.1,0,1000).\n\n## Value\n\nList with nine matrix components. Each matrix has nr rows and nc columns, where nr= `ncycles` - `burnin`, nc= (number of studies) +4 for the row label, the individual study parameter values, and the three overall parameters, mu, tau, and eta.\n\n## References\n\nDoss, Hani (2012). “Hyperparameter and model selection for nonparametric Bayes problems via Radon-Nikodym derivatives.” Statistica Sinica, 22, 1–26.\n\nSethuraman, J. (1994). “A constructive definition of Dirichlet priors.” Statistica Sinica 4, 639–650.\n\n## Examples\n\n ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21``` ```## Not run: ## Set up the data. data(breast.17) # the breast cancer dataset breast.data <- as.matrix(breast.17) # put data in matrix object ## Default values ncycles=2000, burnin=1000, seed=1 ## CPU time is given from a run of the R command system.time() on an ## Intel \\$2.8\\$ GHz Q\\$9550\\$ running Linux chain1.list <- bf1(breast.data) # 40.5 secs ## Next get a second set of 9 chains, with a different seed chain2.list <- bf2(breast.data, seed=2) # 40.4 secs ## Perhaps save for another time. save(chain1.list,chain2.list,file=\"breast-rdat-2lists-1000\",compress=TRUE) ## later session load(\"breast-rdat-2lists-1000\") ## End(Not run) ```\n\nbspmma documentation built on Jan. 14, 2019, 1:04 a.m."
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.69187963,"math_prob":0.9105464,"size":3469,"snap":"2019-13-2019-22","text_gpt3_token_len":939,"char_repetition_ratio":0.11919192,"word_repetition_ratio":0.008726004,"special_character_ratio":0.2643413,"punctuation_ratio":0.13669065,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9879193,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-03-21T16:30:26Z\",\"WARC-Record-ID\":\"<urn:uuid:a50fc629-0d04-445a-b90d-45dfb99f9fc1>\",\"Content-Length\":\"67844\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:62878a4a-e263-4d66-af75-84fa44769726>\",\"WARC-Concurrent-To\":\"<urn:uuid:cd1c4b37-f787-4756-99c2-abab14651d9e>\",\"WARC-IP-Address\":\"104.28.7.171\",\"WARC-Target-URI\":\"https://rdrr.io/cran/bspmma/man/bf1.html\",\"WARC-Payload-Digest\":\"sha1:NPQLOL2D46DWXIS2ZKRQ3VR7VPLWOLW2\",\"WARC-Block-Digest\":\"sha1:2T7DLJQ2BQ3J2RTCP5UUB3GOBDCXWTA2\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-13/CC-MAIN-2019-13_segments_1552912202526.24_warc_CC-MAIN-20190321152638-20190321174638-00232.warc.gz\"}"} |
http://dulue.club/random-question-game-math/ | [
"# Random Question Game Math",
null,
"Random question game math mathnasium.",
null,
"Random question game math the best ideas come from randomly staring off into space at midnight finally brought this random idea to life the kiddos loved our math review game today mathway limits.",
null,
"Random question game math fraction and mixed number math bingo math review games bundle all operations mathematics building columbia.",
null,
"Random question game math the exam in question mathematics degree.",
null,
"Random question game math pick a number questions questions to ask random questions this or math playground duck life 5.",
null,
"Random question game math ask me please i love these things for some reason mathway.",
null,
"Random question game math how to do this math question math games for kids.",
null,
"Random question game math mathway app.",
null,
"Random question game math numbers swat 2 mathnasium cost.",
null,
"Random question game math maths bash on the app store math calculator that shows work.",
null,
"Random question game math game theory mathematics table normal form table illustrates the concept of a or entry mathletics hack.",
null,
"Random question game math on twitter creating own integer math questions using card shuffler and challenging their partner to a game math integers math playground duck life.",
null,
"Random question game math generating random whole numbers in in a specific range stack overflow mathnasium scarsdale.",
null,
"Random question game math these are interesting so please ask away questions game random questions to mathletics usa."
] | [
null,
"http://dulue.club/wp-content/uploads//2018/11/random-question-game-math-mathnasium.jpg",
null,
"http://dulue.club/wp-content/uploads//2018/11/random-question-game-math-the-best-ideas-come-from-randomly-staring-off-into-space-at-midnight-finally-brought-this-random-idea-to-life-the-kiddos-loved-our-math-review-game-today-mathway-limits.jpg",
null,
"http://dulue.club/wp-content/uploads//2018/11/random-question-game-math-fraction-and-mixed-number-math-bingo-math-review-games-bundle-all-operations-mathematics-building-columbia.jpg",
null,
"http://dulue.club/wp-content/uploads//2018/11/random-question-game-math-the-exam-in-question-mathematics-degree.jpg",
null,
"http://dulue.club/wp-content/uploads//2018/11/random-question-game-math-pick-a-number-questions-questions-to-ask-random-questions-this-or-math-playground-duck-life-5.jpg",
null,
"http://dulue.club/wp-content/uploads//2018/11/random-question-game-math-ask-me-please-i-love-these-things-for-some-reason-mathway.jpg",
null,
"http://dulue.club/wp-content/uploads//2018/11/random-question-game-math-how-to-do-this-math-question-math-games-for-kids.jpg",
null,
"http://dulue.club/wp-content/uploads//2018/11/random-question-game-math-mathway-app.jpg",
null,
"http://dulue.club/wp-content/uploads//2018/11/random-question-game-math-numbers-swat-2-mathnasium-cost.jpg",
null,
"http://dulue.club/wp-content/uploads//2018/11/random-question-game-math-maths-bash-on-the-app-store-math-calculator-that-shows-work.jpg",
null,
"http://dulue.club/wp-content/uploads//2018/11/random-question-game-math-game-theory-mathematics-table-normal-form-table-illustrates-the-concept-of-a-or-entry-mathletics-hack.jpg",
null,
"http://dulue.club/wp-content/uploads//2018/11/random-question-game-math-on-twitter-creating-own-integer-math-questions-using-card-shuffler-and-challenging-their-partner-to-a-game-math-integers-math-playground-duck-life.jpg",
null,
"http://dulue.club/wp-content/uploads//2018/11/random-question-game-math-generating-random-whole-numbers-in-in-a-specific-range-stack-overflow-mathnasium-scarsdale.jpg",
null,
"http://dulue.club/wp-content/uploads//2018/11/random-question-game-math-these-are-interesting-so-please-ask-away-questions-game-random-questions-to-mathletics-usa.jpg",
null
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https://commons.ph/tag/addition/ | [
"# addition",
null,
"## Grade 6 Math | Addition IV (without regrouping)\n\nAddition (usually signified by the plus symbol +) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division. The addition of two whole numbers results in the total amount or sum of… Read More »Grade 6 Math | Addition IV (without regrouping)",
null,
"## Grade 6 Math | Addition III (without regrouping)\n\nAddition (usually signified by the plus symbol +) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division. The addition of two whole numbers results in the total amount or sum of… Read More »Grade 6 Math | Addition III (without regrouping)",
null,
"## Grade 6 Math | Addition II (with regrouping)\n\nAddition (usually signified by the plus symbol +) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division. The addition of two whole numbers results in the total amount or sum of… Read More »Grade 6 Math | Addition II (with regrouping)",
null,
"## Grade 6 Math | Addition I (with regrouping)\n\nAddition (usually signified by the plus symbol +) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division. The addition of two whole numbers results in the total amount or sum of… Read More »Grade 6 Math | Addition I (with regrouping)",
null,
"## Grade 1 Math | Addition (Compilation)\n\nAddition (usually signified by the plus symbol +) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division. The addition of two whole numbers results in the total amount or sum of… Read More »Grade 1 Math | Addition (Compilation)",
null,
"## Grade 1 Math | Addition VI (Missing Addend)\n\nAddition (usually signified by the plus symbol +) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division. The addition of two whole numbers results in the total amount or sum of… Read More »Grade 1 Math | Addition VI (Missing Addend)",
null,
"## Grade 1 Math | Addition V (Column)\n\nAddition (usually signified by the plus symbol +) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division. The addition of two whole numbers results in the total amount or sum of… Read More »Grade 1 Math | Addition V (Column)"
] | [
null,
"https://cdn.commons.ph/wp-content/uploads/2021/01/Untitled-design-12-930x620.png",
null,
"https://cdn.commons.ph/wp-content/uploads/2021/01/Untitled-design-11-930x620.png",
null,
"https://cdn.commons.ph/wp-content/uploads/2021/01/Untitled-design-10-930x620.png",
null,
"https://cdn.commons.ph/wp-content/uploads/2021/01/Untitled-design-9-930x620.png",
null,
"https://cdn.commons.ph/wp-content/uploads/2020/12/enjoy-930x620.png",
null,
"https://cdn.commons.ph/wp-content/uploads/2020/12/Untitled-design-20-930x620.png",
null,
"https://cdn.commons.ph/wp-content/uploads/2020/12/Untitled-design-17-930x620.png",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.8875294,"math_prob":0.90315145,"size":344,"snap":"2021-04-2021-17","text_gpt3_token_len":76,"char_repetition_ratio":0.12941177,"word_repetition_ratio":0.11320755,"special_character_ratio":0.20930232,"punctuation_ratio":0.05263158,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9986991,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"im_url_duplicate_count":[null,1,null,1,null,1,null,1,null,2,null,2,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-04-13T16:40:08Z\",\"WARC-Record-ID\":\"<urn:uuid:288967d6-5f05-46ff-b62c-f6199407f3cc>\",\"Content-Length\":\"60126\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9b5dab35-e4d1-4d67-ab45-57a0d858978b>\",\"WARC-Concurrent-To\":\"<urn:uuid:4e3152f1-79fb-47cf-bc5c-437d35c6eb5b>\",\"WARC-IP-Address\":\"23.94.27.251\",\"WARC-Target-URI\":\"https://commons.ph/tag/addition/\",\"WARC-Payload-Digest\":\"sha1:SWLIG3RZVMRYSEW35DFIJIMQ3CB3TEHO\",\"WARC-Block-Digest\":\"sha1:D7V52W3KPGTZ4W54XI3S2UETO5KWVHCM\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-17/CC-MAIN-2021-17_segments_1618038073437.35_warc_CC-MAIN-20210413152520-20210413182520-00189.warc.gz\"}"} |
https://shellcodes.org/Perl/Perl%E5%9F%BA%E7%A1%80%E7%AC%94%E8%AE%B0.html | [
"# Perl 基础笔记\n\n## 1 开发环境\n\n• 编辑器：Emacs+cperl-mode。设置 cperl-mode 样式：M-x customize-group RET cperl-faces RET。\n• Perlbrew：管理本机多个版本的 Perl，可以在不同版本间切换。官网：https://perlbrew.pl/\n\n### 1.1 帮助文档\n\nperldoc 的使用：\n\n-v 参数可以查看内置变量的帮助文档，往往这些难记的变量不好用搜索引擎检索，如：\n\n$perldoc -v '$\\'\n\n\n-f 参数查看函数的帮助文档，如：\n\n$perldoc -f print -m 参数查看模块的源码： $ perldoc -m File::Basename\n\n\n## 2 标量\n\n### 2.1 数字\n\nPerl 的数字表示：1、1.0、-1、0、421_559（下划线为了便于阅读）。\n\nprint 0xfff, \"\\n\"; # 十六进制\nprint 0777, \"\\n\"; # 八进制\nprint 0b1111; # 二进制\nprint 0xffff_ffff; # 十进制外的数字同样也可以用下划线分割出距离\n\n\n### 2.2 数字运算操作\n\nPerl 支持基本的四则运算：+、-、*、/，同时还支持取模（%）、幂（**）运算。\n\nprint 0xff + 1; # => 256\n\n\nPerl 也支持自加和自减运算：\n\n$i++;$i--;\n\n\n### 2.3 字符串\n\n$msg = \"hello world\"; print \"$msg\";\n\n\nPerl 不限制字符串长度，最长可以耗尽内存，最短则叫作空字符串。对于长字符串，Perl 支持 heredoc：\n\nmy $html = <<HERE; <html> <head> <title>test</title> </head> <body> </body> </html> HERE print$html;\n\n\n#### 2.3.1 Unicode\n\nuse utf8;\n\n\nprint length \"我是你爸爸\"; # => 15\n\n\nuse utf8;\nprint length \"我是你爸爸\"; # => 5\n\n\n#### 2.3.2 字符串操作\n\nprint 'hello' . ' ' . 'world'; # => hello world\n# 如果配合数字使用，结果为字符串\nprint 123 . 'abc'; # => 123abc\n\n\nprint 'A' x 3; # => AAA\nprint 1 x 3; # => 111，等同重复三次字符串“1”\n\n\nmy $str = \"hello world\"; my @words = split / /,$str;\nprint @words; # => hello\nprint @words; # => world\n\n\n# uc 函数提供转换成大写字母\nprint uc \"hi\"; # => HI\n# lc 函数提供转换成小写字母\nprint lc \"HI\"; # => hi\n\n\n#### 2.3.3 字符和数字的转换\n\n'4' * '2'; # => 8\n'4' + '1'; # => 5\n'4' - '1'; # => 3\n'4' / '2'; # => 2\n'123abc' * 2; # => 246，非数字部分的”abc“会被忽略\n'abc' * 2; # => 0，没有数字就取值为 0\n\n\n### 2.4 undef 和 defined\n\n$a = undef; 当数字遇到 undef 时，赋值为0： $i += 10;\nprint $i; # => 10 字符串遇到 undef 时，赋值为空字符串： $msg .= \"hello\";\nprint $msg; # => hello 可以用 defined 函数来判断值是否为 undef，比如直接读取到文件尾（EOF）时就返回 undef。 例，检查脚本参数： if (not defined$ARGV) {\nexit;\n}\n\n\n## 3 常量和变量\n\nPerl 变量以“$”开头，区分大小写，只能包含下划线、数字和字母，且不能以数字开头。如果启用了 utf8 指令，也可以用 Unicode 字符做变量名。 $msg = \"hello world\";\n\n\n### 3.1 双目运算\n\n$a = 1;$b = 2;\n$c = 3;$d = 4;\n$e = 'hello';$a += 1; # 等同 $a =$a + 1\n$b -= 2; # 等同$b = $b - 2$c *= 3; # 等同 $c =$c * 3\n$d /= 4; # 等同$d = $d / 4$e .= ' world'; # 等同 $e =$e + ' world'\n\n\n### 3.2 字符串中引用变量\n\n$hello = 'hello';$world = 'world';\n\nprint \"$hello$world\\n\";\nprint \"${hello}${world}\";\n\n\n### 3.3 常量\n\nuse constant PI => 3.1415926;\nprint PI;\n\n\n## 5 流程控制\n\n### 5.1 逻辑判断\n\nPerl 没有布尔类型，标量仅在以下情况下为”假“，其余情况为”真“：\n\n• 数字0；\n• 当值为字符串时，空字符串和'0'为假；\n• undef；\n• 空 list。\n\nPerl 的逻辑判断和大多脚本语言的不同，字符串和数字有两套语法：\n\n'1' == '1'\n\n\nPerl 的逻辑操作符：\n\n&&：逻辑AND\n\n||：逻辑OR\n\n!：逻辑NOT\n\n\n### 5.2 if，elsif，else\n\nif (...) {\n...\n}\n\n# 或：\n\nif (...) {\n...\n} else {\n...\n}\n\n\nif (...) {\n...\n} elsif (...) {\n...\n} elsif (...) {\n...\n} else {\n...\n}\n\n\n### 5.4 ?:\n\n 表达式 ? 如果为真 : 如果为假\n\n\n### 5.5 given-when\n\nuse 5.010001;\n\ngiven($ARGV) { when ('-h') {print 'help'} when ('-a') {print '-a'} default {print 'default'} } ### 5.6 do do 语句能让多个表达式组合成一个表达式，如简化 if..elsif 判断赋值。如下代码，没有 do 的情况： my$code_type;\n\nif ($code == 'LEFTCTRL') {$code_type = 'left';\n} elsif ($code == 'ENTER') {$code_type = 'enter';\n} elsif ($code == 'BACKSPACE') {$code_type = 'backspace';\n}\n\n\nmy $code_type = do { if ($code == 'LEFTCTRL') {'left'}\nelsif ($code == 'ENTER') {'enter'} elsif ($code == 'BACKSPACE') {'backspace'}\n}\n\n\n## 6 循环\n\n### 6.1 while\n\nwhile (...) {\n...\n}\n\n\n### 6.2 foreach\n\nforeach $i (1..10) { print \"$i\\n\";\n}\n\n\nforeach $i (ls /etc) { print \"$i\";\n}\n\n\nforeach 的控制变量（如上面两个例子中的变量 i），会在 foreach 结束后恢复变量的值，如果值不存在就是 undef。如：\n\n$i = 100; foreach$i (1..10) {\n$i .= \"\\n\"; } print$i; # 输出：100\n\n\nforeach 还可以省略控制变量，改用”$_“代替： foreach (1..10) { print \"$_\\n\";\n}\n\n\n### 6.3 for\n\nfor (初始化; 测试条件; 递增) {\n...\n}\n\n\nfor ($i = 0;$i < 100; $i++) { print$i;\n}\n\n\nfor (;;) {\n...\n}\n\n\nPerl 会根据括号中的表达来决定代码执行意图，如果括号里没有分号，就说明是 foreach 循环，如：\n\nfor (1..10) {\nprint;\n}\n\n\n### 6.4 until\n\nwhile 的相反语句，只有表达式不为真时才执行块中的代码。\n\n### 6.5 循环控制\n\n#### 6.5.1 last\n\n# 打印标准输入的内容\nwhile(<STDIN>) {\n# 一旦遇到__END__，说明输入结束\nif (/__END__/) {\nlast;\n}\nprint;\n}\n\n\n#### 6.5.2 next\n\nfor (1..100) {\nnext if ($_ % 2 == 1); print \"$_\\n\";\n}\n\n\n#### 6.5.3 redo\n\n$i = 0; foreach (\"Perl\", \"Python\", \"Ruby\", \"Scheme\") {$i++;\n\n}\n}\n\n\n## 7 列表和数组\n\n### 7.1 初始化数组\n\n$books = 'Learning Perl';$books = 'Intermediate Perl';\n\n\n@books = ('Learning Perl', 'Intermediate Perl'); # ()表示空数组\n$books; 也可用 qw(…) 语法来省略字符串的引号，Perl 会将元素按空白字符分割： @books = qw(a b c);$books;\n\n\nqw 的定界符并不固定，也可指定成其他的，如：\n\nqw( a b c );\nqw{ a b c };\nqw< a b c >;\nqw/ a b c /;\nqw# a b c #;\nqw! a b c !;\n\n\nqw! a b c \\! !;\n\n\n($a,$b, $c) = (1, 2, 3); # 实质执行了 3 次赋值操作 print$a, $b,$c;\n\n\n@a = (1, 2, 3);\n@b = @a; # 复制数组\n$a = 10; # 不会改变数组 a 的内容 print$a, ' ', $b; ### 7.2 数组长度 my @languages = qw(Perl Ruby Lisp Python Go); print scalar @languages; # 方法1：用 scalar my$count = @languages; # 方法2：直接赋值\nprint $count; print$#languages + 1; # 方法3：最后一个元素的下标加 1 就是数组大小\n\n\n### 7.3 数组索引\n\n$books;$books; # 超出索引范围返回 undef，而不会报异常\n\n\n$#books可取出最后一个元素的下标： $books[$#books]; 或者用负数做下标： $books[-1]; # 倒数第一个元素\n$books[-2]; # 倒数第二个元素 Perl还支持按范围生成数组： @a = (1 .. 3); @b = (a .. z); ### 7.4 数组操作 push @a = (1 .. 3); push(@a, 4); print$a[-1]; # 输出：4\n\n\nunshift 和 push 操作方向相反。\n\n@a = (1 .. 3);\nunshift(@a, 0);\nprint $a; # 输出：0 pop pop 操作在空数组上则返回 undef。pop 示例代码： @a = (1 .. 3);$last = pop(@a);\nprint $last; # 输出：3 print$a[-1]; # 输出： 2\n\n\nshift 和 pop 操作方向相反。\n\n@a = (1 .. 3);\n$item = shift(@a); print$item; # 输出：1\nprint $a; # 输出：2 splice 返回部分数组元素并从原始数组中删除。 splice 接受四个参数： • 参数1：数组； • 参数2：删除的起始位置； • 参数3：可选参数。删除的长度； • 参数4：把参数 4 数组内容替换到原来数组被删除的位置。 @a = (1 .. 10); splice(@a, 8, 1); # 删除元素 9 foreach$item (@a) {\nprint $item; } # 输出：1234567810 指定参数 4，把新元素替换到原来数组被删除的位置： @a = (1 .. 10); splice(@a, 8, 1, qw(a b c)); # 将a、b、c替换到元素 9 的位置上 foreach$item (@a) {\nprint $item; } # 输出：12345678abc10 字符串中插入数组 @list = qw{a b c}; print @list; # 输出：a b c 注意的是，如果要把 E-mail 地址作为邮箱，要么用单引号字符，要么转义”@“。 reverse：逆转数组 @a = (1..5); print reverse @a; # 输出54321 sort：排序数组 @a = (5, 4, 3, 2, 1); print sort @a; # 输出12345 map：对项逐一应用 print map {$_ + 1} (1, 2, 3); # => 234\n\n\ngrep：过滤元素\n\nmy @new = grep $_ > 10, (10, 20, 1, 3, 11, 28); ### 7.5 数组切片 open IN, \"< /etc/passwd\"; while(<IN>) { my @line = split /:/; print \"@line[0, 4]\\n\"; } ### 7.6 遍历数组 my @languages = qw(Perl Python Ruby Lisp); for my$lang (@languages) {\nprint $lang, \"\\n\"; } 也可以像 C 语言中那样，按下标遍历： my @languages = qw(Perl Python Ruby Lisp); for my$i (0 .. @languages) {\nprint $languages[$i], \"\\n\";\n}\n\n\n## 8 hash 表\n\nuse 5.010;\n\n# 定义Hash表以“%”开头\n%a_hash = (\n'a' => 1,\n'b' => 2\n);\n\nsay $a_hash{'a'}; # 访问 key$a_hash{'c'} = 3; # 修改键值\nsay %a_hash; # 访问整个 hash 表\n\n\nif (!exists $a_hash{\"c\"}) { print \"不存在\"; } 从 hash 表中删除键值 %a_hash = ( 'a' => 1, 'b' => 2, 'c' => 3 ); delete$a_hash{'c'};\nprint keys %a_hash;\n\n\nkeys 和 values 函数\n\nkeys 函数返回 hash 表所有 key；values 函数返回 hash 表所有的 value：\n\nsay keys %a_hash; # => ab\nsay values %a_hash; # => 12\n\n\n%a_hash = (\n'a' => 1,\n'b' => 2\n);\n\nwhile (($k,$v) = each %a_hash) {\nprintf \"key: %s, value: %s\\n\", $k,$v;\n}\n\n\n%ENV\n\n%ENV 保存了当前的环境变量，例如输出 PATH 环境变量：\n\nprint $ENV{\"PATH\"}; ## 9 输入输出 print 用于打印消息。print 默认不打印换行符，如需默认打印换行符，就设置$\\ 的值：\n\n$\\ = \"\\n\"; print \"hello world\"; print 打印数组时，如果数组是在字符串中引用，打印时会有空格分离： @a = qw /a b c/; print @a; # 输出：abc print \"@a\"; # 输出：a b c 如需格式化输出，请用 printf 函数。 printf 打印数组： @users = qw(user1 user2 user3);$format = \"users are: @users\";\nprintf $format, @users;$format = \"users are: \" . (\"%s \" x @items); # 后面是重复 @items 元素个数多少次\nprintf $format, @users; Perl5.10 开始增加了一个新函数——say，say 输出时会带上换行符： use 5.010; # 必须启用 5.10 的特性才可以 say \"hello\"; say \"world\"; ### 9.1 输出 Perl 警告信息 要打开 Perl 的警告，可在 perl 命令加上 -w 参数： $ perl -w hello.pl\n\n\nuse warnings;\n\n\nuse diagnostics;\n\n\n$perl -Mdiagnostics hello.pl ### 9.2 标准输入 <STDIN> 用于获取用户的标准输入。 例，逐行打印标准输入的文本： # foreach 版，Perl 会先把内容放到数组里循环，所以不建议用 foreach$line (<STDIN>) {\nprint $line; } # while 版才是逐行读取，不会预先读取 while (<STDIN>) { print$_;\n}\n\n\n#### 9.2.1 chomp\n\nforeach $line (<STDIN>) { chomp($line);\nprint $line; } 精简版： foreach (<STDIN>) { chomp; # chomp 默认作用在$_ 上\nprint $_; } ### 9.3 钻石（<>）读取 Perl 为了更适应 Unix 风格，发明了“<>”操作符，当程序指定多个输入源作为参数时，Perl 会逐一读取文件，如果其中一个参数是“-”，Perl 会从标准输入中读取： while(<>) { print$_;\n}\n\n\n$echo hi | ./test.pl /etc/passwd /etc/hosts - 这等同把 /etc/passwd、/etc/hosts 和标准输入的内容合并在了一起。 #### 9.3.1 接受脚本参数 参数存在 @ARGV 数组中： foreach (@ARGV) { print$_, \"\\n\";\n}\n\n\n@ARGV = qw# /etc/passwd #;\n\nforeach (<>) {\nprint $_, \"\\n\"; } ### 9.4 文件句柄 open 操作符用来打开其他文件句柄。 示例： open f, \"/etc/hosts\"; foreach$line (<f>) {\nprint $line; } 关闭文件句柄用 close 操作符： close f; #### 9.4.1 读、写和追加模式 Perl 里用“<”、“>”和“>>”分别表示读、取和追加，完整示例如下： open PASSWD, \"</etc/passwd\"; # 读取模式 open OUT, \">out\"; # 写入模式 open LOG, \">>log\"; # 追加模式 while(<PASSWD>) { print$_;\n}\n\n### 向文件中写或追加数据时，用 print、printf 和 say 函数，指定句柄即可\nprint OUT \"hello world\"; # print 指定输出句柄参数时不用加逗号\nsay LOG \"test1\"; # say 指定句柄的规则和 print 一样\nsay LOG \"test2\";\n\nclose PASSWD;\nclose OUT;\nclose LOG;\n\n\nopen IN, \"/etc/passwd\";\nmy $lines = join '', <IN>; print$lines;\n\n\n#### 9.4.2 处理错误\n\n$f = open F, \"<not_exists\"; if (!$f) {\ndie \"打开文件失败\";\n}\n\nclose F;\n\n\ndie 和 warn 会打印出错误信息已经行号，不同的是 die 函数输出错误后会结束程序的运行。\n\n#### 9.4.3 改进文件句柄\n\nopen my $f, \">\", \"a\"; print${f} \"hello world\\n\";\nclose $f; 这也是最推荐的方法，标量还可以作为参数传递。 #### 9.4.4 字符串句柄 open 除了新建一个文件句柄，也可以打开一个字符串句柄，并不断地向字符串句柄写数据： open my$f, \">\", \\my $str; print${f} \"hello world\\n\";\nprint ${f} \"hehe\\n\"; print${f} \"just test\";\nclose $f; print$str;\n\n\n#### 9.4.5 临时改变句柄\n\nmy $str; { local *STDOUT; open STDOUT, '>', \\$str;\n\nprint \"hehe\";\nclose STDOUT;\n}\n\nprint $str; local 关键字和 my 不一样的是，local 只是临时改变标量的指向；my 是创建新的标量。 #### 9.4.6 另一种方式逐行遍历字符串 也可以让字符串作为句柄输入，这样便可逐行遍历： my$str = \"1\\n22\\n333\\n4444\\n\";\n\nopen $f, \"<\", \\$str;\n\nwhile (<$f>) { print; } #### 9.4.7 文件目录句柄 opendir my$dir, \"/etc\" or die \"open error\";\n\nforeach my $file (readdir($dir)) {\nprint \"$file\\n\"; } #### 9.4.8 将文件全部内容读入到字符串 { local$/ = undef;\nopen F, \"/etc/hosts\" or die \"open file error\";\n$content = <F>; close F; } print$content;\n\n\n## 10 子程序\n\nPerl 中，函数叫作“子程序”，用 sub 关键字定义，例：\n\nsub hello {\nprint \"hello world\";\n}\n\n\nhello; # 如果不加括号不影响表达式含义，可省掉括号\nhello();\n&hello; # 旧风格\n\n\n### 10.1 传递参数\n\nPerl 把参数自动存入 @_ 数组中，可直接访问，如：\n\nsub say_msg {\nprint $_; } say_msg 'hello world'; 每次调用子程序，都会分配一个私有的 @_ 数组，所以不用担心被覆盖。 判断参数个数： sub say_msg { if (@_ != 1) { print '参数错误'; return; } print$_;\n}\n\n\n### 10.2 定义私有变量\n\nsub test {\n$n += 1; } &test; # n = 1 &test; # n = 2 &test; # n = 3 print$n; # => 3\n\n\nsub say_msg {\nmy($msg) = @_; # msg 作用于仅限 say_msg 子程序中 print$msg;\n}\n\nsay_msg 'hello world';\n\n\nmy 也可以用在其他代码块中，如 foreach：\n\nforeach (1 .. 10) {\nmy($i) =$_;\nprint $i; } 这里的变量 i 作用域范围仅限 foreach 中。 如果需要先声明私有的、持续的变量（比如在用了 strict 时编译器会提示变量未声明），就用 state 关键字，这是 Perl 5.10 新增的： use 5.010; sub test { state$n = 0;\n$n += 1; } test; test; print test; # 输出：3 ### 10.3 原型匹配 sub test($;) {\nprint @_;\n}\n\ntest; # 报错：Not enough arguments for main::test\ntest \"hi\";\n\n\n## 11 更多 Perl 结构\n\n### 11.1 表达式修饰\n\n# 逻辑判断\nprint \"hello\" if 1 > 2;\n# 遍历数组\nprint($_) foreach (1, 2, 3); # 循环$i = 0;\nprint ($i += 1) while$i < 10;\n$i = 0; print ($i += 1) until $i > 10; ### 11.2 裸块 裸块就是单独的一对花括号之间的内容，它可以有自己的作用域： { my$i = 100;\nprint $i; #$i 的作用域仅限于裸块之内\n}\n\n\n## 12 正则表达式\n\nopen IN, \"< /etc/passwd\";\n\n# “/../”会去从 $_ 搜索匹配 while(<IN>) { if (/bash/) { print$_;\n}\n}\n\n\n### 12.1 unicode 属性\n\nuse utf8; # 前面说过，必须要启用 utf8，Perl 才会把字符串作为 unicode\n\n$_ = 'ӏ'; if (/\\p{Block: Cyrillic}/) { print \"yes\"; } ### 12.2 正则修饰符 /i：忽略大小写 $_ = \"hello World\";\nprint /world/i;\n\n\n/x：允许在正则中插入空白\n\n$_ = \"192.168.1.1\"; print /\\d{1,3} \\. \\d{1,3} \\. \\d{1,3} \\. \\d{1,3}/x; /x模式下同时也允许注释存在： $_ = \"192.168.1.1\";\nprint /\n\\d{1,3} \\. # A 段\n\\d{1,3} \\. # B 段\n\\d{1,3} \\. # C 段\n\\d{1,3} # D 段\n/x;\n\n\n\\A和\\z\n\n\\A指定开头字符，只有匹配对象是指定的字符开头，才会继续匹配下去；\\z指定结尾字符。\n\n### 12.3 =~\n\n# 否则它的值可能是上一个表达式捕获的\n}\n}\n\n\n#### 12.4.2 捕获变量\n\n$&：保存实际匹配到的部分$：保存匹配到的字符串之前的内容\n\n}\n}\n\n\n## 13 智能匹配：~~\n\n%a = ('Perl' => 1,\n'Python' => 2);\n\nprint %a ~~ /Py/;\n\n\n@a = (1, 2, 3);\n@b = (1, 2, 3);\nprint @a ~~ @b;\n\n\n## 14 异常捕获\n\nPerl 中可用 eval 作为异常捕获，将有可能会发生异常的代码块放在 eval 中执行，如果执行顺利，eval 就返回代码块最后一条的执行结果，否则返回 undef。在 eval 中发生严重错误都不会导致整个程序崩溃：\n\nmy $result = eval { 1/0; # 这里不会导致 Perl 崩溃 }; print$result;\n\n\n{\nlocal [email protected]; # 不影响其他层次的错误消息捕获\n\nmy $result = eval { 1/0; }; print [email protected]; } eval 还有另外一种用法，如果传递的是字符串，则执行字符串表达的代码。当说 eval 不安全的时候，请区别对待。 ## 15 文件测试 Perl 中有丰富的文件测试符，如用 -e 测试文件是否存在： die \"file not exists\" if ! -e '/etc/passwd'; 要查看完整的清单，可用命令：perldoc -f -X，注意 -X 并非 perldoc 的参数。 ## 16 引用 引用是指让某个变量指向某个数据结构。 my @list = (1, 2, 3); my$p = \\@list; # $p 指向列表地址 $p 指保存了 @list 的内存地址，如果要取 @list 的元素，需要做解引用操作，语法：\n\n@{$p}; # 指向整个数组${$p}; # 指向具体的某个元素，当然用 @{$p} 也可以访问具体元素\n\n# 也可以去掉大括号：\n@$p;$$p; 要使用循环遍历引用对象，直接解引整个数组即可： foreach$i (@{$p}) { print$i;\n}\n\n\nmy %hash = ('a' => 1, 'b' => 2);\nmy $p = \\%hash; print %{$p}{'a'};\nprint ${$p}{'a'};\n\nwhile (($k,$v) = each %{$p}) { print \"$k, $v\\n\"; } 对于解引用，还可以用箭头来简化语法，使代码变得更整洁： my @list = (1, 2, 3); my$p = \\@list;\n\nprint $p->; ### 16.1 检查引用类型 ref 函数可以用于检查引用类型： my @list = (1, 2, 3); my %hash = ('a' => 1, 'b' => 2); my$p1 = \\@list;\nmy $p2 = \\%hash; print ref$p1; # => ARRAY\nprint ref $p2; # => HASH ### 16.2 匿名数组引用 匿名数组，是保存了指向某个数组的内存地址，如： my$ref;\n\n{\n@list = (1, 2, 3, 'a', 'b', 'c');\n$ref = \\@list; } print$ref;\n\n\nprint $ref->; 用法2: my$ref = [1, 2, 3];\nprint $ref->; ### 16.3 匿名hash表 和匿名数组相似。创建方法： my$ref = {\n'a' => 1,\n'b' => 2,\n'c' => 3\n};\n\nprint $ref; 使用匿名 hash 有一点要注意，因为语法用的大括号，而代码块也用的大括号，有时需要显示区分： 告诉编译器此处为匿名 hash：+{ ... } 告诉编译器此处为代码块：{; ... } ### 16.4 子程序引用 也可以让变量指向子程序的内存位置，对子程序进行引用： sub say { my$msg = shift;\nprint \"$msg\\n\"; } my$sub_ref = \\&say;\n&{$sub_ref}(\"hi\"); 对$sub_ref 解引用操作还有更优美的方式：\n\n$sub_ref->(\"hi\"); 既然子程序可以引用，那么就可以创建匿名子程序： my$say = sub {\nmy $msg = shift; print \"$msg\\n\";\n};\n\n$say->(\"hi\"); ## 17 模块 corelist 命令可以帮助查看系统中已有的 Perl 模块，如： $ corelist /File::/\n\n\n$corelist // 要查看模块的文档，就可借助 perldoc 了。如下，查看 :Basename 的帮助文档： $ perldoc File::Basename\n\n\n### 17.1 模块引入\n\n#### 17.1.1 use\n\nuse File::Basename;\nprint basename(\"/etc/passwd\");\n\n\nuse 函数导入默认的子程序，也可指定只导入哪些子程序：\n\nuse File::Basename qw(basename);\nprint basename(\"/etc/passwd\");\n\n\nuse File::Basename ();\nprint File::Basename::basename(\"/etc/passwd\");\n\n\n#### 17.1.2 do\n\ndo 语句的另一个用法，当传递给 do 语句的参数是字符串时，Perl 将字符串当作是其他 Perl 文件来导入，如：\n\ndo \"Hello.pm\";\n\n\n#### 17.1.3 require\n\nrequire 还有两个特性：\n\n1、导入的文件出现任何语法错误，Perl 都会被中止；\n\n2、导入的文件的最后一个表达式必须返回真值，所以很多文件最后一行代码是一个“1”。\n\n### 17.2 命名空间\n\npackage Hello;\n\nsub say {\nmy $msg = shift; print \"$msg\\n\";\n}\n\n1\n\n\nHello::say(\"hello world\");\n\n\n#### 17.2.1 package 作用域\n\npackage 作用域是在 package 指令之后，带代码块的作用域中：\n\n{\npackage Hello;\n\nsub say {\nprint \"in Hello package\\n\";\n}\n}\n\nsub say {\nprint \"in main\\n\";\n}\n\nsay; # 输出：in main\nHello::say # 输出：package Hello\n\n\npackage Hello {\nsub say {\nprint \"in Hello package\\n\";\n}\n}\n\nsub say {\nprint \"in main\\n\";\n}\n\nsay; # 输出：in main\nHello::say # 输出：package Hello;\n\n\n## 18 CPAN\n\nCPAN 包含了丰富的 Perl 库。\n\ncpan> m /HTTP/\n\n\ncpan [模块名]\n\n\\$ cpan HTTP::Server::Simple\n\ncpan> install HTTP::Server::Simple\n`"
] | [
null
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https://download.racket-lang.org/releases/5.93/doc/reference/procedures.html | [
"#### 4.17Procedures\n\n procedure v : any/c\nReturns #t if v is a procedure, #f otherwise.\n\n procedure(apply proc v ... lst #: kw-arg ...) → any proc : procedure? v : any/c lst : list? kw-arg : any/c",
null,
"The apply Function in The Racket Guide introduces apply.\n\nApplies proc using the content of (list* v ... lst) as the (by-position) arguments. The #:<kw> kw-arg sequence is also supplied as keyword arguments to proc, where #:<kw> stands for any keyword.\n\nThe given proc must accept as many arguments as the number of vs plus length of lst, it must accept the supplied keyword arguments, and it must not require any other keyword arguments; otherwise, the exn:fail:contract exception is raised. The given proc is called in tail position with respect to the apply call.\n\nExamples:\n\n > (apply + '(1 2 3)) 6 > (apply + 1 2 '(3)) 6 > (apply + '()) 0 > (apply sort (list (list '(2) '(1)) <) #:key car) '((1) (2))\n\n procedure(compose proc ...) → procedure? proc : procedure?\n procedure(compose1 proc ...) → procedure? proc : procedure?\nReturns a procedure that composes the given functions, applying the last proc first and the first proc last. The compose function allows the given functions to consume and produce any number of values, as long as each function produces as many values as the preceding function consumes, while compose1 restricts the internal value passing to a single value. In both cases, the input arity of the last function and the output arity of the first are unrestricted, and they become the corresponding arity of the resulting composition (including keyword arguments for the input side).\n\nWhen no proc arguments are given, the result is values. When exactly one is given, it is returned.\n\nExamples:\n\n > ((compose1 - sqrt) 10) -3.1622776601683795 > ((compose1 sqrt -) 10) 0+3.1622776601683795i > ((compose list split-path) (bytes->path #\"/a\" 'unix)) '(# # #f)\n\nNote that in many cases, compose1 is preferred. For example, using compose with two library functions may lead to problems when one function is extended to return two values, and the preceding one has an optional input with different semantics. In addition, compose1 may create faster compositions.\n\n procedure(procedure-rename proc name) → procedure? proc : procedure? name : symbol?\nReturns a procedure that is like proc, except that its name as returned by object-name (and as printed for debugging) is name.\n\nThe given name is used for printing an error message if the resulting procedure is applied to the wrong number of arguments. In addition, if proc is an accessor or mutator produced by struct, make-struct-field-accessor, or make-struct-field-mutator, the resulting procedure also uses name when its (first) argument has the wrong type. More typically, however, name is not used for reporting errors, since the procedure name is typically hard-wired into an internal check.\n\n procedure(procedure->method proc) → procedure? proc : procedure?\nReturns a procedure that is like proc except that, when applied to the wrong number of arguments, the resulting error hides the first argument as if the procedure had been compiled with the 'method-arity-error syntax property.\n\nprocedure\n\n (procedure-closure-contents-eq? proc1 proc2) → boolean?\nproc1 : procedure?\nproc2 : procedure?\nCompares the contents of the closures of proc1 and proc2 for equality by comparing closure elements pointwise using eq?\n\n##### 4.17.1Keywords and Arity\n\nprocedure\n\n (keyword-apply proc kw-lst kw-val-lst v ... lst #: kw-arg ...) → any\nproc : procedure?\nkw-lst : (listof keyword?)\nkw-val-lst : list?\nv : any/c\nlst : list?\nkw-arg : any/c",
null,
"The apply Function in The Racket Guide introduces keyword-apply.\n\nLike apply, but kw-lst and kw-val-lst supply by-keyword arguments in addition to the by-position arguments of the vs and lst, and in addition to the directly supplied keyword arguments in the #:<kw> kw-arg sequence, where #:<kw> stands for any keyword.\n\nThe given kw-lst must be sorted using keyword<?. No keyword can appear twice in kw-lst or in both kw-list and as a #:<kw>, otherwise, the exn:fail:contract exception is raised. The given kw-val-lst must have the same length as kw-lst, otherwise, the exn:fail:contract exception is raised. The given proc must accept all of the keywords in kw-lst plus the #:<kw>s, it must not require any other keywords, and it must accept as many by-position arguments as supplied via the vs and lst; otherwise, the exn:fail:contract exception is raised.\n\nExamples:\n\n (define (f x #:y y #:z [z 10]) (list x y z))\n> (keyword-apply f '(#:y) '(2) '(1))\n\n'(1 2 10)\n\n> (keyword-apply f '(#:y #:z) '(2 3) '(1))\n\n'(1 2 3)\n\n> (keyword-apply f #:z 7 '(#:y) '(2) '(1))\n\n'(1 2 7)\n\n procedure proc : procedure?\n\n procedure v : any/c\nA valid arity a is one of the following:\n\n• An exact non-negative integer, which means that the procedure accepts a arguments, only.\n\n• A arity-at-least instance, which means that the procedure accepts (arity-at-least-value a) or more arguments.\n\n• A list containing integers and arity-at-least instances, which means that the procedure accepts any number of arguments that can match one of the elements of a.\n\nThe result of procedure-arity is always normalized in the sense of normalized-arity?.\n\nExamples:\n\n > (procedure-arity cons) 2 > (procedure-arity list) (arity-at-least 0) > (arity-at-least? (procedure-arity list)) #t > (arity-at-least-value (procedure-arity list)) 0 > (arity-at-least-value (procedure-arity (lambda (x . y) x))) 1 > (procedure-arity (case-lambda [(x) 0] [(x y) 1])) '(1 2)\n\n procedure(procedure-arity-includes? proc k [kws-ok?]) → boolean? proc : procedure? k : exact-nonnegative-integer? kws-ok? : any/c = #f\nReturns #t if the procedure can accept k by-position arguments, #f otherwise. If kws-ok? is #f, the result is #t only if proc has no required keyword arguments.\n\nExamples:\n\n > (procedure-arity-includes? cons 2) #t > (procedure-arity-includes? display 3) #f > (procedure-arity-includes? (lambda (x #:y y) x) 1) #f > (procedure-arity-includes? (lambda (x #:y y) x) 1 #t) #t\n\n procedure(procedure-reduce-arity proc arity) → procedure? proc : procedure? arity : procedure-arity?\nReturns a procedure that is the same as proc (including the same name returned by object-name), but that accepts only arguments consistent with arity. In particular, when procedure-arity is applied to the generated procedure, it returns a value that is equal? to arity.\n\nIf the arity specification allows arguments that are not in (procedure-arity proc), the exn:fail:contract exception is raised. If proc accepts keyword argument, either the keyword arguments must be all optional (and they are not accepted in by the arity-reduced procedure) or arity must be the empty list (which makes a procedure that cannot be called); otherwise, the exn:fail:contract exception is raised.\n\nExamples:\n\n> (define my+ (procedure-reduce-arity + 2))\n> (my+ 1 2)\n\n3\n\n> (my+ 1 2 3)\n\n+: arity mismatch;\n\nthe expected number of arguments does not match the given\n\nnumber\n\nexpected: 2\n\ngiven: 3\n\narguments...:\n\n1\n\n2\n\n3\n\nprocedure\n\n(procedure-keywords proc)\n (listof keyword?) (or/c (listof keyword?) #f)\nproc : procedure?\nReturns information about the keyword arguments required and accepted by a procedure. The first result is a list of distinct keywords (sorted by keyword<?) that are required when applying proc. The second result is a list of distinct accepted keywords (sorted by keyword<?), or #f to mean that any keyword is accepted. When the second result is a list, every element in the first list is also in the second list.\n\nExamples:\n\n> (procedure-keywords +)\n '() '()\n> (procedure-keywords (lambda (#:tag t #:mode m) t))\n '(#:mode #:tag) '(#:mode #:tag)\n> (procedure-keywords (lambda (#:tag t #:mode [m #f]) t))\n '(#:tag) '(#:mode #:tag)\n\nprocedure\n\n(make-keyword-procedure proc [plain-proc]) procedure?\n\nproc : (((listof keyword?) list?) () #:rest list? . ->* . any)\n plain-proc : procedure? = (lambda args (apply proc null null args))\nReturns a procedure that accepts all keyword arguments (without requiring any keyword arguments).\n\nWhen the procedure returned by make-keyword-procedure is called with keyword arguments, then proc is called; the first argument is a list of distinct keywords sorted by keyword<?, the second argument is a parallel list containing a value for each keyword, and the remaining arguments are the by-position arguments.\n\nWhen the procedure returned by make-keyword-procedure is called without keyword arguments, then plain-proc is called—possibly more efficiently than dispatching through proc. Normally, plain-proc should have the same behavior as calling proc with empty lists as the first two arguments, but that correspondence is in no way enforced.\n\nThe result of procedure-arity and object-name on the new procedure is the same as for plain-proc. See also procedure-reduce-keyword-arity and procedure-rename.\n\nExamples:\n\n (define show (make-keyword-procedure (lambda (kws kw-args . rest) (list kws kw-args rest))))\n> (show 1)\n\n'(() () (1))\n\n> (show #:init 0 1 2 3 #:extra 4)\n\n'((#:extra #:init) (4 0) (1 2 3))\n\n (define show2 (make-keyword-procedure (lambda (kws kw-args . rest) (list kws kw-args rest)) (lambda args (list->vector args))))\n> (show2 1)\n\n'#(1)\n\n> (show2 #:init 0 1 2 3 #:extra 4)\n\n'((#:extra #:init) (4 0) (1 2 3))\n\nprocedure\n\n (procedure-reduce-keyword-arity proc arity required-kws allowed-kws) → procedure?\nproc : procedure?\narity : procedure-arity?\nrequired-kws : (listof keyword?)\nallowed-kws :\n (or/c (listof keyword?) #f)\nLike procedure-reduce-arity, but constrains the keyword arguments according to required-kws and allowed-kws, which must be sorted using keyword<? and contain no duplicates. If allowed-kws is #f, then the resulting procedure still accepts any keyword, otherwise the keywords in required-kws must be a subset of those in allowed-kws. The original proc must require no more keywords than the ones listed in required-kws, and it must allow at least the keywords in allowed-kws (or it must allow all keywords if allowed-kws is #f).\n\nExamples:\n\n (define orig-show (make-keyword-procedure (lambda (kws kw-args . rest) (list kws kw-args rest))))\n (define show (procedure-reduce-keyword-arity orig-show 3 '(#:init) '(#:extra #:init)))\n> (show #:init 0 1 2 3 #:extra 4)\n\n'((#:extra #:init) (4 0) (1 2 3))\n\n> (show 1)\n\n...t/private/kw.rkt:196:14: arity mismatch;\n\nthe expected number of arguments does not match the given\n\nnumber\n\nexpected: 3 plus an argument with keyword #:init plus an\n\noptional argument with keyword #:extra\n\ngiven: 1\n\narguments...:\n\n1\n\n> (show #:init 0 1 2 3 #:extra 4 #:more 7)\n\napplication: procedure does not expect an argument with\n\ngiven keyword\n\nprocedure: ...t/private/kw.rkt:196:14\n\ngiven keyword: #:more\n\narguments...:\n\n1\n\n2\n\n3\n\n#:extra 4\n\n#:init 0\n\n#:more 7\n\nstruct\n\n (struct arity-at-least (value) #:extra-constructor-name make-arity-at-least)\nvalue : exact-nonnegative-integer?\nA structure type used for the result of procedure-arity. See also procedure-arity?.\n\n value\nA structure type property to identify structure types whose instances can be applied as procedures. In particular, when procedure? is applied to the instance, the result will be #t, and when an instance is used in the function position of an application expression, a procedure is extracted from the instance and used to complete the procedure call.\n\nIf the prop:procedure property value is an exact non-negative integer, it designates a field within the structure that should contain a procedure. The integer must be between 0 (inclusive) and the number of non-automatic fields in the structure type (exclusive, not counting supertype fields). The designated field must also be specified as immutable, so that after an instance of the structure is created, its procedure cannot be changed. (Otherwise, the arity and name of the instance could change, and such mutations are generally not allowed for procedures.) When the instance is used as the procedure in an application expression, the value of the designated field in the instance is used to complete the procedure call. (This procedure can be another structure that acts as a procedure; the immutability of procedure fields disallows cycles in the procedure graph, so that the procedure call will eventually continue with a non-structure procedure.) That procedure receives all of the arguments from the application expression. The procedure’s name (see object-name), arity (see procedure-arity), and keyword protocol (see procedure-keywords) are also used for the name, arity, and keyword protocol of the structure. If the value in the designated field is not a procedure, then the instance behaves like (case-lambda) (i.e., a procedure which does not accept any number of arguments). See also procedure-extract-target.\n\nProviding an integer proc-spec argument to make-struct-type is the same as both supplying the value with the prop:procedure property and designating the field as immutable (so that a property binding or immutable designation is redundant and disallowed).\n\nExamples:\n\n > (struct annotated-proc (base note) #:property prop:procedure (struct-field-index base))\n > (define plus1 (annotated-proc (lambda (x) (+ x 1)) \"adds 1 to its argument\"))\n> (procedure? plus1)\n\n#t\n\n> (annotated-proc? plus1)\n\n#t\n\n> (plus1 10)\n\n11\n\n> (annotated-proc-note plus1)\n\nWhen the prop:procedure value is a procedure, it should accept at least one non-keyword argument. When an instance of the structure is used in an application expression, the property-value procedure is called with the instance as the first argument. The remaining arguments to the property-value procedure are the arguments from the application expression (including keyword arguments). Thus, if the application expression provides five non-keyword arguments, the property-value procedure is called with six non-keyword arguments. The name of the instance (see object-name) and its keyword protocol (see procedure-keywords) are unaffected by the property-value procedure, but the instance’s arity is determined by subtracting one from every possible non-keyword argument count of the property-value procedure. If the property-value procedure cannot accept at least one argument, then the instance behaves like (case-lambda).\n\nProviding a procedure proc-spec argument to make-struct-type is the same as supplying the value with the prop:procedure property (so that a specific property binding is disallowed).\n\nExamples:\n\n > (struct fish (weight color) #:mutable #:property prop:procedure (lambda (f n) (let ([w (fish-weight f)]) (set-fish-weight! f (+ n w)))))\n> (define wanda (fish 12 'red))\n> (fish? wanda)\n\n#t\n\n> (procedure? wanda)\n\n#t\n\n> (fish-weight wanda)\n\n12\n\n> (for-each wanda '(1 2 3))\n> (fish-weight wanda)\n\n18\n\nIf the value supplied for the prop:procedure property is not an exact non-negative integer or a procedure, the exn:fail:contract exception is raised.\n\n procedure type : struct-type?\nReturns #t if instances of the structure type represented by type are procedures (according to procedure?), #f otherwise.\n\n procedure(procedure-extract-target proc) → (or/c #f procedure?) proc : procedure?\nIf proc is an instance of a structure type with property prop:procedure, and if the property value indicates a field of the structure, and if the field value is a procedure, then procedure-extract-target returns the field value. Otherwise, the result is #f.\n\nWhen a prop:procedure property value is a procedure, the procedure is not returned by procedure-extract-target. Such a procedure is different from one accessed through a structure field, because it consumes an extra argument, which is always the structure that was applied as a procedure. Keeping the procedure private ensures that is it always called with a suitable first argument.\n\n value\nA structure type property that is used for reporting arity-mismatch errors when a structure type with the prop:procedure property is applied to the wrong number of arguments. The value of the prop:arity-string property must be a procedure that takes a single argument, which is the misapplied structure, and returns a string. The result string is used after the word “expects,” and it is followed in the error message by the number of actual arguments.\n\nArity-mismatch reporting automatically uses procedure-extract-target when the prop:arity-string property is not associated with a procedure structure type.\n\nExamples:\n\n > (struct evens (proc) #:property prop:procedure (struct-field-index proc) #:property prop:arity-string (lambda (p) \"an even number of arguments\"))\n > (define pairs (evens (case-lambda [() null] [(a b . more) (cons (cons a b) (apply pairs more))])))\n> (pairs 1 2 3 4)\n\n'((1 . 2) (3 . 4))\n\n> (pairs 5)\n\n#<procedure>: arity mismatch;\n\nthe expected number of arguments does not match the given\n\nnumber\n\nexpected: an even number of arguments\n\ngiven: 1\n\narguments...:\n\n5\n\n value\nA structure type property that is used with checked-procedure-check-and-extract, which is a hook to allow the compiler to improve the performance of keyword arguments. The property can only be attached to a structure type without a supertype and with at least two fields.\n\nprocedure\n\n (checked-procedure-check-and-extract type v proc v1 v2) → any/c\ntype : struct-type?\nv : any/c\nproc : (any/c any/c any/c . -> . any/c)\nv1 : any/c\nv2 : any/c\nExtracts a value from v if it is an instance of type, which must have the property prop:checked-procedure. If v is such an instance, then the first field of v is extracted and applied to v1 and v2; if the result is a true value, the result is the value of the second field of v.\n\nIf v is not an instance of type, or if the first field of v applied to v1 and v2 produces #f, then proc is applied to v, v1, and v2, and its result is returned by checked-procedure-check-and-extract.\n\n##### 4.17.2Reflecting on Primitives\n\nA primitive procedure is a built-in procedure that is implemented in low-level language. Not all procedures of racket/base are primitives, but many are. The distinction is mainly useful to other low-level code.\n\n procedure v : any/c\nReturns #t if v is a primitive procedure, #f otherwise.\n\n procedure(primitive-closure? v) → boolean v : any/c\nReturns #t if v is internally implemented as a primitive closure rather than a simple primitive procedure, #f otherwise.\n\n procedure prim : primitive?\nReturns the arity of the result of the primitive procedure prim (as opposed to the procedure’s input arity as returned by procedure-arity). For most primitives, this procedure returns 1, since most primitives return a single value when applied.\n\n (require racket/function) package: base\nThe bindings documented in this section are provided by the racket/function and racket libraries, but not racket/base.\n\n procedure(identity v) → any/c v : any/c\nReturns v.\n\n procedure(const v) → procedure? v : any\nReturns a procedure that accepts any arguments (including keyword arguments) and returns v.\n\nExamples:\n\n > ((const 'foo) 1 2 3) 'foo > ((const 'foo)) 'foo\n\n syntax(thunk body ...+)\n syntax(thunk* body ...+)\nThe thunk form creates a nullary function that evaluates the given body. The thunk* form is similar, except that the resulting function accepts any arguments (including keyword arguments).\n\nExamples:\n\n (define th1 (thunk (define x 1) (printf \"~a\\n\" x)))\n> (th1)\n\n1\n\n> (th1 'x)\n\nth1: arity mismatch;\n\nthe expected number of arguments does not match the given\n\nnumber\n\nexpected: 0\n\ngiven: 1\n\narguments...:\n\n'x\n\n> (th1 #:y 'z)\n\napplication: procedure does not accept keyword arguments\n\nprocedure: th1\n\narguments...:\n\n#:y 'z\n\n (define th2 (thunk* (define x 1) (printf \"~a\\n\" x)))\n> (th2)\n\n1\n\n> (th2 'x)\n\n1\n\n> (th2 #:y 'z)\n\n1\n\n procedure(negate proc) → procedure? proc : procedure?\nReturns a procedure that is just like proc, except that it returns the not of proc’s result.\n\nExamples:\n\n > (filter (negate symbol?) '(1 a 2 b 3 c)) '(1 2 3) > (map (negate =) '(1 2 3) '(1 1 1)) '(#f #t #t)\n\n procedure(curry proc) → procedure? proc : procedure? (curry proc v ...+) → any/c proc : procedure? v : any/c\nReturns a procedure that is a curried version of proc. When the resulting procedure is first applied, unless it is given the maximum number of arguments that it can accept, the result is a procedure to accept additional arguments.\n\nExamples:\n\n > ((curry list) 1 2) # > ((curry cons) 1) # > ((curry cons) 1 2) '(1 . 2)\n\nAfter the first application of the result of curry, each further application accumulates arguments until an acceptable number of arguments have been accumulated, at which point the original proc is called.\n\nExamples:\n\n > (((curry list) 1 2) 3) '(1 2 3) > (((curry list) 1) 3) '(1 3) > ((((curry foldl) +) 0) '(1 2 3)) 6\n\nA function call (curry proc v ...) is equivalent to ((curry proc) v ...). In other words, curry itself is curried.\n\nThe curry function provides limited support for keyworded functions: only the curry call itself can receive keyworded arguments to be propagated eventually to proc.\n\nExamples:\n\n> (map ((curry +) 10) '(1 2 3))\n\n'(11 12 13)\n\n> (map (curry + 10) '(1 2 3))\n\n'(11 12 13)\n\n> (map (compose (curry * 2) (curry + 10)) '(1 2 3))\n\n'(22 24 26)\n\n> (define foo (curry (lambda (x y z) (list x y z))))\n> (foo 1 2 3)\n\n'(1 2 3)\n\n> (((((foo) 1) 2)) 3)\n\n'(1 2 3)\n\n procedure(curryr proc) → procedure? proc : procedure? (curryr proc v ...+) → any/c proc : procedure? v : any/c\nLike curry, except that the arguments are collected in the opposite direction: the first step collects the rightmost group of arguments, and following steps add arguments to the left of these.\n\nExample:\n\n > (map (curryr list 'foo) '(1 2 3)) '((1 foo) (2 foo) (3 foo))\n\n procedure(normalized-arity? arity) → boolean? arity : any/c\nA normalized arity has one of the following forms:\n• the empty list;\n\n• an exact non-negative integer;\n\n• an arity-at-least instance;\n\n• a list of two or more strictly increasing, exact non-negative integers; or\n\n• a list of one or more strictly increasing, exact non-negative integers followed by a single arity-at-least instance whose value is greater than the preceding integer by at least 2.\n\nEvery normalized arity is a valid procedure arity and satisfies procedure-arity?. Any two normalized arity values that are arity=? must also be equal?.\n\nExamples:\n\n > (normalized-arity? (arity-at-least 1)) #t > (normalized-arity? (list (arity-at-least 1))) #f > (normalized-arity? (list 0 (arity-at-least 2))) #t > (normalized-arity? (list (arity-at-least 2) 0)) #f > (normalized-arity? (list 0 2 (arity-at-least 3))) #f\n\n procedure(normalize-arity arity) → (and/c normalized-arity? (lambda (x) (arity=? x arity))) arity : procedure-arity?\n\nExamples:\n\n > (normalize-arity 1) 1 > (normalize-arity (list 1)) 1 > (normalize-arity (arity-at-least 2)) (arity-at-least 2) > (normalize-arity (list (arity-at-least 2))) (arity-at-least 2) > (normalize-arity (list 1 (arity-at-least 2))) (arity-at-least 1) > (normalize-arity (list (arity-at-least 2) 1)) (arity-at-least 1) > (normalize-arity (list (arity-at-least 2) 3)) (arity-at-least 2) > (normalize-arity (list 3 (arity-at-least 2))) (arity-at-least 2) > (normalize-arity (list (arity-at-least 6) 0 2 (arity-at-least 4))) (list 0 2 (arity-at-least 4))\n\n procedure(arity=? a b) → boolean? a : procedure-arity? b : procedure-arity?\nReturns #true if procedures with arity a and b accept the same numbers of arguments, and #false otherwise. Equivalent to both (and (arity-includes? a b) (arity-includes? b a)) and (equal? (normalize-arity a) (normalize-arity b)).\n\nExamples:\n\n > (arity=? 1 1) #t > (arity=? (list 1) 1) #t > (arity=? 1 (list 1)) #t > (arity=? 1 (arity-at-least 1)) #f > (arity=? (arity-at-least 1) 1) #f > (arity=? 1 (arity-at-least 1)) #f > (arity=? (arity-at-least 1) (list 1 (arity-at-least 2))) #t > (arity=? (list 1 (arity-at-least 2)) (arity-at-least 1)) #t > (arity=? (arity-at-least 1) (list 1 (arity-at-least 3))) #f > (arity=? (list 1 (arity-at-least 3)) (arity-at-least 1)) #f > (arity=? (list 0 1 2 (arity-at-least 3)) (list (arity-at-least 0))) #t > (arity=? (list (arity-at-least 0)) (list 0 1 2 (arity-at-least 3))) #t > (arity=? (list 0 2 (arity-at-least 3)) (list (arity-at-least 0))) #f > (arity=? (list (arity-at-least 0)) (list 0 2 (arity-at-least 3))) #f\n\n procedure a : procedure-arity? b : procedure-arity?\nReturns #true if procedures with arity a accept any number of arguments that procedures with arity b accept.\n\nExamples:\n\n > (arity-includes? 1 1) #t > (arity-includes? (list 1) 1) #t > (arity-includes? 1 (list 1)) #t > (arity-includes? 1 (arity-at-least 1)) #f > (arity-includes? (arity-at-least 1) 1) #t > (arity-includes? 1 (arity-at-least 1)) #f > (arity-includes? (arity-at-least 1) (list 1 (arity-at-least 2))) #t > (arity-includes? (list 1 (arity-at-least 2)) (arity-at-least 1)) #t > (arity-includes? (arity-at-least 1) (list 1 (arity-at-least 3))) #t > (arity-includes? (list 1 (arity-at-least 3)) (arity-at-least 1)) #f > (arity-includes? (list 0 1 2 (arity-at-least 3)) (list (arity-at-least 0))) #t > (arity-includes? (list (arity-at-least 0)) (list 0 1 2 (arity-at-least 3))) #t > (arity-includes? (list 0 2 (arity-at-least 3)) (list (arity-at-least 0))) #f > (arity-includes? (list (arity-at-least 0)) (list 0 2 (arity-at-least 3))) #t"
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https://www.realnfo.com/ee/Electrical-Circuit-Analysis/Transformer/Types-of-Transformers | [
"# Types of Transformers",
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"Transformers are available in many different shapes and sizes. Some of the more common types include the power transformer, audio transformer, IF (intermediate-frequency) transformer, and RF (radiofrequency) transformer. Each is designed to fulfill a particular requirement in a specific area of application. The symbols for some of the basic types of transformers are shown in Fig. 1.",
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"Fig. 1: Transformer symbols.\nThe method of construction varies from one transformer to another. Two of the many different ways in which the primary and secondary coils can be wound around an iron core are shown in Fig. 2. In either case, the core is made of laminated sheets of ferromagnetic material separated by an insulator to reduce the eddy current losses. The sheets themselves will also contain a small percentage of silicon to increase the electrical resistivity of the material and further reduce the eddy current losses.",
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"Fig. 2: Types of ferromagnetic core construction.\n\n### Split Bobbin Transformer\n\nA variation of the core-type transformer know as split bobbin appears in Fig. 3. This transformer is designed for low-profile (the 2.5-VA size has a maximum height of only 0.65 in.) applications in power, control, and instrumentation applications. There are actually two transformers on the same core, with the primary and secondary of each wound side by side.",
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"",
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"Fig. 3: Split bobbin, low-profile power transformer.\nThe schematic representation appears in the same figure. Each set of terminals on the left can accept 115 V at 50 or 60 Hz, whereas each side of the output will provide 230 V at the same frequency. Note the dot convention, as described earlier in the chapter.\n\n### Autotransformer\n\nThe autotransformer [Fig. 4(b)] is a type of power transformer that, instead of employing the two-circuit principle (complete isolation between coils), has one winding common to both the input and the output circuits.",
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"",
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"Fig. 4: (a) Two-circuit transformer; (b) autotransformer.\nThe induced voltages are related to the turns ratio in the same manner as that described for the two-circuit transformer. If the proper connection is used, a two-circuit power transformer can be employed as an autotransformer. The advantage of using it as an autotransformer is that a larger apparent power can be transformed. This can be demonstrated by the two-circuit transformer of Fig. 4(a), shown in Fig. 4(b) as an autotransformer.\nFor the two-circuit transformer, note that\n$$S = ( {1 \\over 20}A)(120 V) = 6 VA$$\nwhereas for the autotransformer, $$S = (1 {1 \\over 20}A)(120 V) = 126 VA$$, which is many times that of the two-circuit transformer. Note also that the current and voltage of each coil are the same as those for the two-circuit configuration. The disadvantage of the autotransformer is obvious: loss of the isolation between the primary and secondary circuits.\n\n### Pulse Transformer\n\nA pulse transformer designed for printed-circuit applications where high-amplitude, long-duration pulses must be transferred without saturation appears in Fig. 5. Turns ratios are available from 1: 1 to 5: 1 at maximum line voltages of 240 V rms at 60 Hz.",
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"Fig. 5: Pulse transformers.\nThe upper unit is for printed-circuit applications with isolated dual primaries, whereas the lower unit is the bobbin variety with a single primary winding.\n\n## Do you want to say or ask something?\n\nOnly 250 characters are allowed. Remaining: 250"
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https://www.enchantedlearning.com/math/multiply/ | [
"EnchantedLearning.com is a user-supported site.\nAs a bonus, site members have access to a banner-ad-free version of the site, with print-friendly pages.\n\n More Math Activities EnchantedLearning.comMultiplication Printouts",
null,
"The following are multiplication printouts.",
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"Generate Printable Multiplication Worksheets:One Digit x One DigitYou can generate printable multiplication worksheets (one page of questions and one page of answers) with 8, 10 or 12 problems. Every time you click, you get a new worksheet, with a new set of questions and answers. For subscribers only.",
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"Generate Printable Multiplication Worksheets:One Digit x One Digit, Vertical FormatYou can generate printable multiplication worksheets (one page of questions and one page of answers) with 16 or 20 problems. Every time you click, you get a new worksheet, with a new set of questions and answers. For subscribers only.",
null,
"Early Multiplication PrintablesPrintable worksheets and short books that introduce the concept of multiplication to students. The idea of multiplication is developed as the addition of groups of numbers.",
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"Early MultiplicationAdding Groups of NumbersAdd groups of items to develop the idea of multiplication as the addition of groups of numbers. Printout #1. Or go to the answers. Printout #2. Or go to the answers. Printout #3. Or go to the answers. Printout #4. Or go to the answers. Printout #5. Or go to the answers. Printout #6. Or go to the answers. Printout #7. Or go to the answers. Printout #8. Or go to the answers. Printout #9. Or go to the answers.",
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"Early Multiplication: Count by 2s, 3s, 4s... 9sCount by twos, threes, fours, ... and then write how many objects are in that many groups groups, for example, \"How many legs are on all the bugs?\" Count by 2s. Or go to the answers. Count by 3s. Or go to the answers. Count by 4s. Or go to the answers. Count by 5s. Or go to the answers. Count by 6s. Or go to the answers. Count by 7s. Or go to the answers. Count by 8s. Or go to the answers. Count by 9s. Or go to the answers.",
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"Early MultiplicationDraw Groups of Shapes #1Draw groups of shapes and write equations that describe them. For example, \"Draw 2 groups of 3 circles. 2 x 2 = 4\" Printout #1. Or go to the answers. Printout #2. Or go to the answers. Printout #3. Or go to the answers.",
null,
"Multiplication: Match Groups of NumbersMatch groups of numbers, for example, match \"2 groups of 3\"to \"2 x 3\" to \"2 threes.\" Or go to the answers.",
null,
"Multiplication: Match Groups of Numbers #2Match groups of numbers, for example, match \"2 groups of 3\"to \"2 x 3\" to \"2 threes.\" Or go to the answers. Multiplication Table 1-12Print a multiplication table of the numbers 1 to 12.",
null,
"Multiplication ChartWrite many equations in which axb=c, like 3x2=6. 1 Digit times 1 DigitMultiply two one-digit numbers. 2 Digits times 1 DigitMultiply two-digit numbers times one-digit numbers. 2 Digits times 2 DigitsMultiply two two-digit numbers.",
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"Multiplying Integers:3 Digits times 2 DigitsMultiply a three-digit number by a two-digit number.",
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"Multiplying Numbers Path-o-Math Puzzles: 2 by 3Make a path through each number matrix so that the product of the numbers is equal to the given answer. Use only horizontal and vertical trails. You may not have to use all the numbers, and don't use a number more than once. Puzzle #1, or the answers Puzzle #2, or the answers Puzzle #3, or the answers Puzzle #4, or the answers Puzzle #5, or the answers Multiplying Decimals",
null,
"Each worksheet has decimal numbers to multiply.",
null,
"Multiplication Follow-the-Arrows Puzzles Do multiplication problems along the paths according to the arrows until you get to the end. You should get to the same final answer three different ways. Puzzle #1, or the answers Puzzle #2, or the answers Puzzle #3, or the answers Puzzle #4, or the answers Puzzle #5, or the answers",
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"Multiplication of Fractions Follow-the-Arrows Puzzles Do multiplication of fractions along the paths according to the arrows until you get to the end. You should get to the same final answer three different ways. Puzzle #1, or the answers Puzzle #2, or the answers Puzzle #3, or the answers Puzzle #4, or the answers Puzzle #5, or the answers",
null,
"LCM, GCFFactor two numbers into primes, then use a Venn diagram to compute their least common multiple (LCM) and greatest common factor (GCF). Multiplying Fractions",
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"Multiply the fractions.",
null,
"Multiples and LCM:Printable WorksheetsWrite multiples of numbers, then determine their least common multiple (LCM). Worksheet #1, or the answers Worksheet #2, or the answers Worksheet #3, or the answers Worksheet #4, or the answers Worksheet #5, or the answers\n\n +, - EnchantedLearning.comMath x, ÷\n A B C D E F G H I J K L M N O P Q R S T U V W X Y Z\n Number Line Fractions Decimals Measurement Rounding Graphs\n\nEnchanted Learning®\nOver 35,000 Web Pages\nSample Pages for Prospective Subscribers, or click below\n\n Overview of Site What's New Enchanted Learning Home Monthly Activity Calendar Books to Print Site Index K-3 Crafts K-3 Themes Little ExplorersPicture dictionary PreK/K Activities Rebus Rhymes Stories Writing Cloze Activities Essay Topics Newspaper Writing Activities Parts of Speech Fiction The Test of Time Biology Animal Printouts Biology Label Printouts Biomes Birds Butterflies Dinosaurs Food Chain Human Anatomy Mammals Plants Rainforests Sharks Whales Physical Sciences: K-12 Astronomy The Earth Geology Hurricanes Landforms Oceans Tsunami Volcano Languages Dutch French German Italian Japanese (Romaji) Portuguese Spanish Swedish Geography/History Explorers Flags Geography Inventors US History Other Topics Art and Artists Calendars College Finder Crafts Graphic Organizers Label Me! Printouts Math Music Word Wheels\n\n## Enchanted Learning Search\n\n Search the Enchanted Learning website for:"
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https://www.hackmath.net/en/word-math-problems/mathematical-olympiad?tag_id=49 | [
"# Mathematical Olympiad + area - math problems\n\n#### Number of problems found: 10\n\n• MO Z8–I–6 2018",
null,
"In the KLMN trapeze, KL has a 40 cm base and an MN of 16 cm. Point P lies on the KL line so that the NP segment divides the trapezoid into two parts with the same area. Find the length of the KP line.\n• Equilateral triangle ABC",
null,
"In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near the point C, and the point M lies in the one-third of the side of the AC side closer to the point A. Find what part of the ABC triangle cont\n• MO8-Z8-I-5 2017",
null,
"Identical rectangles ABCD and EFGH are positioned such that their sides are parallel to the same. The points I, J, K, L, M and N are the intersections of the extended sides, as shown. The area of the BNHM rectangle is 12 cm2, the rectangle MBCK area is 63\n• Trapezoid MO-5-Z8",
null,
"ABCD is a trapezoid that lime segment CE is divided into a triangle and parallelogram, as shown. Point F is the midpoint of CE, DF line passes through the center of the segment BE, and the area of the triangle CDE is 3 cm2. Determine the area of the trape\n• Octahedron - sum",
null,
"On each wall of a regular octahedron is written one of the numbers 1, 2, 3, 4, 5, 6, 7 and 8, wherein on different sides are different numbers. For each wall John make the sum of the numbers written of three adjacent walls. Thus got eight sums, which also\n• Mr. Zucchini",
null,
"Mr. Zucchini had a rectangular garden whose perimeter is 28 meters. The garden's content area filled just four square beds, whose dimensions in meters are expressed in whole numbers. Determine what size could have a garden. Find all the possibilities and\n• Hexagon - MO",
null,
"The picture shows the ABCD square, the EFGD square and the HIJD rectangle. Points J and G lie on the side CD and is true |DJ|\n• MO - triangles",
null,
"On the AB and AC sides of the triangle ABC lies successive points E and F, on segment EF lie point D. The EF and BC lines are parallel and is true this ratio FD:DE = AE:EB = 2:1. The area of ABC triangle is 27 hectares and line segments EF, AD, and DB seg\n• Katy MO",
null,
"Kate drew triangle ABC. The middle of the line segment AB has marked as X and the center of the side AC as Y. On the side BC wants to find the point Z such that the content area of a 4gon AXZY was greatest. What part of the triangle ABC can maximally occu\n• Square grid",
null,
"Square grid consists of a square with sides of length 1 cm. Draw in it at least three different patterns such that each had a content of 6 cm2 and circumference 12 cm and that their sides is in square grid.\n\nWe apologize, but in this category are not a lot of examples.\nDo you have an exciting math question or word problem that you can't solve? Ask a question or post a math problem, and we can try to solve it.\n\nWe will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.\n\nMathematical Olympiad - math problems. Area - math problems."
] | [
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"https://www.hackmath.net/thumb/63/t_7663.jpg",
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"https://www.hackmath.net/thumb/75/t_5375.jpg",
null,
"https://www.hackmath.net/thumb/62/t_4962.jpg",
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"https://www.hackmath.net/thumb/54/t_4154.jpg",
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"https://www.hackmath.net/thumb/80/t_2480.jpg",
null,
"https://www.hackmath.net/thumb/2/t_2402.jpg",
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"https://www.hackmath.net/thumb/30/t_2330.jpg",
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"https://www.hackmath.net/thumb/84/t_2284.jpg",
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"https://www.hackmath.net/thumb/52/t_2152.jpg",
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https://howkgtolbs.com/convert/6.41-kg-to-lbs | [
"# 6.41 kg to lbs - 6.41 kilograms into pounds\n\nDo you need to learn how much is 6.41 kg equal to lbs and how to convert 6.41 kg to lbs? You couldn’t have chosen better. You will find in this article everything you need to make kilogram to pound conversion - theoretical and also practical. It is also needed/We also want to point out that all this article is devoted to one amount of kilograms - exactly one kilogram. So if you need to know more about 6.41 kg to pound conversion - read on.\n\nBefore we go to the more practical part - this is 6.41 kg how much lbs conversion - we want to tell you a little bit of theoretical information about these two units - kilograms and pounds. So let’s start.\n\nHow to convert 6.41 kg to lbs? 6.41 kilograms it is equal 14.1316309942 pounds, so 6.41 kg is equal 14.1316309942 lbs.\n\n## 6.41 kgs in pounds\n\nWe will begin with the kilogram. The kilogram is a unit of mass. It is a basic unit in a metric system, that is International System of Units (in abbreviated form SI).\n\nAt times the kilogram could be written as kilogramme. The symbol of this unit is kg.\n\nThe kilogram was defined first time in 1795. The kilogram was defined as the mass of one liter of water. First definition was simply but impractical to use.\n\nLater, in 1889 the kilogram was defined by the International Prototype of the Kilogram (in short form IPK). The IPK was prepared of 90% platinum and 10 % iridium. The IPK was in use until 2019, when it was switched by a new definition.\n\nToday the definition of the kilogram is build on physical constants, especially Planck constant. The official definition is: “The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6.62607015×10−34 when expressed in the unit J⋅s, which is equal to kg⋅m2⋅s−1, where the metre and the second are defined in terms of c and ΔνCs.”\n\nOne kilogram is equal 0.001 tonne. It is also divided into 100 decagrams and 1000 grams.\n\n## 6.41 kilogram to pounds\n\nYou know some information about kilogram, so now we can go to the pound. The pound is also a unit of mass. We want to underline that there are more than one kind of pound. What does it mean? For example, there are also pound-force. In this article we want to concentrate only on pound-mass.\n\nThe pound is in use in the British and United States customary systems of measurements. To be honest, this unit is used also in other systems. The symbol of the pound is lb or “.\n\nThe international avoirdupois pound has no descriptive definition. It is just equal 0.45359237 kilograms. One avoirdupois pound can be divided into 16 avoirdupois ounces or 7000 grains.\n\nThe avoirdupois pound was implemented in the Weights and Measures Act 1963. The definition of the pound was written in first section of this act: “The yard or the metre shall be the unit of measurement of length and the pound or the kilogram shall be the unit of measurement of mass by reference to which any measurement involving a measurement of length or mass shall be made in the United Kingdom; and- (a) the yard shall be 0.9144 metre exactly; (b) the pound shall be 0.45359237 kilogram exactly.”\n\n### How many lbs is 6.41 kg?\n\n6.41 kilogram is equal to 14.1316309942 pounds. If You want convert kilograms to pounds, multiply the kilogram value by 2.2046226218.\n\n### 6.41 kg in lbs\n\nThe most theoretical part is already behind us. In this part we want to tell you how much is 6.41 kg to lbs. Now you learned that 6.41 kg = x lbs. So it is high time to know the answer. Let’s see:\n\n6.41 kilogram = 14.1316309942 pounds.\n\nIt is an exact outcome of how much 6.41 kg to pound. You can also round off this result. After it your result will be exactly: 6.41 kg = 14.102 lbs.\n\nYou know 6.41 kg is how many lbs, so have a look how many kg 6.41 lbs: 6.41 pound = 0.45359237 kilograms.\n\nOf course, in this case you may also round off this result. After rounding off your result is as following: 6.41 lb = 0.45 kgs.\n\nWe are also going to show you 6.41 kg to how many pounds and 6.41 pound how many kg results in tables. Look:\n\nWe will begin with a table for how much is 6.41 kg equal to pound.\n\n### 6.41 Kilograms to Pounds conversion table\n\nKilograms (kg) Pounds (lb) Pounds (lbs) (rounded off to two decimal places)\n6.41 14.1316309942 14.1020\nNow look at a chart for how many kilograms 6.41 pounds.\n\nPounds Kilograms Kilograms (rounded off to two decimal places\n6.41 0.45359237 0.45\n\nNow you learned how many 6.41 kg to lbs and how many kilograms 6.41 pound, so it is time to move on to the 6.41 kg to lbs formula.\n\n### 6.41 kg to pounds\n\nTo convert 6.41 kg to us lbs you need a formula. We are going to show you two versions of a formula. Let’s start with the first one:\n\nNumber of kilograms * 2.20462262 = the 14.1316309942 outcome in pounds\n\nThe first formula will give you the most accurate outcome. In some situations even the smallest difference could be significant. So if you need a correct outcome - first formula will be the best solution to know how many pounds are equivalent to 6.41 kilogram.\n\nSo let’s move on to the second version of a formula, which also enables conversions to learn how much 6.41 kilogram in pounds.\n\nThe second version of a formula is down below, let’s see:\n\nNumber of kilograms * 2.2 = the outcome in pounds\n\nAs you can see, the second formula is simpler. It can be the best solution if you want to make a conversion of 6.41 kilogram to pounds in easy way, for instance, during shopping. Just remember that final result will be not so exact.\n\nNow we want to learn you how to use these two formulas in practice. But before we are going to make a conversion of 6.41 kg to lbs we are going to show you another way to know 6.41 kg to how many lbs without any effort.\n\n### 6.41 kg to lbs converter\n\nAnother way to know what is 6.41 kilogram equal to in pounds is to use 6.41 kg lbs calculator. What is a kg to lb converter?\n\nConverter is an application. Calculator is based on longer formula which we showed you above. Due to 6.41 kg pound calculator you can effortless convert 6.41 kg to lbs. You only have to enter number of kilograms which you want to convert and click ‘convert’ button. You will get the result in a flash.\n\nSo let’s try to calculate 6.41 kg into lbs using 6.41 kg vs pound calculator. We entered 6.41 as an amount of kilograms. This is the result: 6.41 kilogram = 14.1316309942 pounds.\n\nAs you see, our 6.41 kg vs lbs calculator is easy to use.\n\nNow we can go to our primary topic - how to convert 6.41 kilograms to pounds on your own.\n\n#### 6.41 kg to lbs conversion\n\nWe will start 6.41 kilogram equals to how many pounds calculation with the first formula to get the most accurate result. A quick reminder of a formula:\n\nNumber of kilograms * 2.20462262 = 14.1316309942 the result in pounds\n\nSo what have you do to know how many pounds equal to 6.41 kilogram? Just multiply amount of kilograms, this time 6.41, by 2.20462262. It is exactly 14.1316309942. So 6.41 kilogram is exactly 14.1316309942.\n\nIt is also possible to round off this result, for example, to two decimal places. It gives 2.20. So 6.41 kilogram = 14.1020 pounds.\n\nIt is high time for an example from everyday life. Let’s calculate 6.41 kg gold in pounds. So 6.41 kg equal to how many lbs? As in the previous example - multiply 6.41 by 2.20462262. It is exactly 14.1316309942. So equivalent of 6.41 kilograms to pounds, when it comes to gold, is 14.1316309942.\n\nIn this example it is also possible to round off the result. Here is the outcome after rounding off, in this case to one decimal place - 6.41 kilogram 14.102 pounds.\n\nNow we can move on to examples converted with short formula.\n\n#### How many 6.41 kg to lbs\n\nBefore we show you an example - a quick reminder of shorter formula:\n\nAmount of kilograms * 2.2 = 14.102 the outcome in pounds\n\nSo 6.41 kg equal to how much lbs? And again, you have to multiply number of kilogram, in this case 6.41, by 2.2. Let’s see: 6.41 * 2.2 = 14.102. So 6.41 kilogram is equal 2.2 pounds.\n\nMake another conversion with use of this formula. Now calculate something from everyday life, for instance, 6.41 kg to lbs weight of strawberries.\n\nSo convert - 6.41 kilogram of strawberries * 2.2 = 14.102 pounds of strawberries. So 6.41 kg to pound mass is exactly 14.102.\n\nIf you know how much is 6.41 kilogram weight in pounds and are able to convert it with use of two different versions of a formula, let’s move on. Now we are going to show you these results in tables.\n\n#### Convert 6.41 kilogram to pounds\n\nWe realize that outcomes shown in charts are so much clearer for most of you. We understand it, so we gathered all these outcomes in tables for your convenience. Thanks to this you can quickly compare 6.41 kg equivalent to lbs outcomes.\n\nBegin with a 6.41 kg equals lbs chart for the first version of a formula:\n\nKilograms Pounds Pounds (after rounding off to two decimal places)\n6.41 14.1316309942 14.1020\n\nAnd now let’s see 6.41 kg equal pound table for the second version of a formula:\n\nKilograms Pounds\n6.41 14.102\n\nAs you can see, after rounding off, if it comes to how much 6.41 kilogram equals pounds, the outcomes are the same. The bigger number the more considerable difference. Keep it in mind when you need to do bigger number than 6.41 kilograms pounds conversion.\n\n#### How many kilograms 6.41 pound\n\nNow you know how to convert 6.41 kilograms how much pounds but we will show you something more. Do you want to know what it is? What about 6.41 kilogram to pounds and ounces conversion?\n\nWe want to show you how you can convert it little by little. Begin. How much is 6.41 kg in lbs and oz?\n\nFirst things first - you need to multiply number of kilograms, this time 6.41, by 2.20462262. So 6.41 * 2.20462262 = 14.1316309942. One kilogram is exactly 2.20462262 pounds.\n\nThe integer part is number of pounds. So in this case there are 2 pounds.\n\nTo check how much 6.41 kilogram is equal to pounds and ounces you need to multiply fraction part by 16. So multiply 20462262 by 16. It is 327396192 ounces.\n\nSo final result is exactly 2 pounds and 327396192 ounces. You can also round off ounces, for example, to two places. Then final result will be exactly 2 pounds and 33 ounces.\n\nAs you can see, conversion 6.41 kilogram in pounds and ounces easy.\n\nThe last calculation which we want to show you is conversion of 6.41 foot pounds to kilograms meters. Both of them are units of work.\n\nTo convert it you need another formula. Before we show you this formula, look:\n\n• 6.41 kilograms meters = 7.23301385 foot pounds,\n• 6.41 foot pounds = 0.13825495 kilograms meters.\n\nNow have a look at a formula:\n\nAmount.RandomElement()) of foot pounds * 0.13825495 = the outcome in kilograms meters\n\nSo to calculate 6.41 foot pounds to kilograms meters you need to multiply 6.41 by 0.13825495. It is 0.13825495. So 6.41 foot pounds is equal 0.13825495 kilogram meters.\n\nIt is also possible to round off this result, for example, to two decimal places. Then 6.41 foot pounds will be exactly 0.14 kilogram meters.\n\nWe hope that this calculation was as easy as 6.41 kilogram into pounds conversions.\n\nThis article was a huge compendium about kilogram, pound and 6.41 kg to lbs in conversion. Thanks to this conversion you learned 6.41 kilogram is equivalent to how many pounds.\n\nWe showed you not only how to do a calculation 6.41 kilogram to metric pounds but also two other calculations - to know how many 6.41 kg in pounds and ounces and how many 6.41 foot pounds to kilograms meters.\n\nWe showed you also another way to do 6.41 kilogram how many pounds conversions, this is using 6.41 kg en pound converter. This is the best solution for those of you who do not like calculating on your own at all or this time do not want to make @baseAmountStr kg how lbs calculations on your own.\n\nWe hope that now all of you are able to do 6.41 kilogram equal to how many pounds calculation - on your own or with use of our 6.41 kgs to pounds converter.\n\nIt is time to make your move! Let’s convert 6.41 kilogram mass to pounds in the best way for you.\n\nDo you need to make other than 6.41 kilogram as pounds calculation? For instance, for 5 kilograms? Check our other articles! We guarantee that conversions for other numbers of kilograms are so simply as for 6.41 kilogram equal many pounds.\n\n### How much is 6.41 kg in pounds\n\nTo quickly sum up this topic, that is how much is 6.41 kg in pounds , we prepared for you an additional section. Here you can find the most important information about how much is 6.41 kg equal to lbs and how to convert 6.41 kg to lbs . Have a look.\n\nWhat is the kilogram to pound conversion? To make the kg to lb conversion it is needed to multiply 2 numbers. Let’s see 6.41 kg to pound conversion formula . Have a look:\n\nThe number of kilograms * 2.20462262 = the result in pounds\n\nSo what is the result of the conversion of 6.41 kilogram to pounds? The accurate result is 14.1316309942 lb.\n\nThere is also another way to calculate how much 6.41 kilogram is equal to pounds with another, shortened type of the equation. Have a look.\n\nThe number of kilograms * 2.2 = the result in pounds\n\nSo this time, 6.41 kg equal to how much lbs ? The result is 14.1316309942 pounds.\n\nHow to convert 6.41 kg to lbs in an easier way? It is possible to use the 6.41 kg to lbs converter , which will do whole mathematical operation for you and give you an exact answer .\n\n#### Kilograms [kg]\n\nThe kilogram, or kilogramme, is the base unit of weight in the Metric system. It is the approximate weight of a cube of water 10 centimeters on a side.\n\n#### Pounds [lbs]\n\nA pound is a unit of weight commonly used in the United States and the British commonwealths. A pound is defined as exactly 0.45359237 kilograms."
] | [
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http://pyretis.org/current/examples/examples-tis-1d.html | [
"# TIS in a 1D potential¶\n\nIn this example, you will explore a rare event with the Transition Interface Sampling (TIS) algorithm.\n\nWe will consider a simple 1D potential where a particle is moving. The potential is given by",
null,
"where",
null,
"is the position. By plotting this potential, we see that we have two states (at",
null,
"and",
null,
") separated by a barrier (at",
null,
"):",
null,
"Fig. 18 The potential energy as a function of the position. We have two stable states (at x = -1 and x = 1) separated by a barrier (at x = 0). In addition, three paths are shown. One is reactive while the two others are not able to escape the state at x = -1. Using the TIS method, we can generate such paths which gives information about the reaction rate and the mechanism. The vertical dotted lines show two TIS interfaces.\n\nUsing the TIS algorithm, we will compute the rate constant for the transition between the two states. This particular problem has been considered before by van Erp and we will here try to reproduce these results.\n\nIn order to obtain a rate constant, we will have to obtain both the crossing probability and an initial flux. To obtain to the crossing probability, we need to carry out TIS simulations for each path ensemble we define and in order to obtain the initial flux, we will have to carry out a MD simulation. Below we describe the two kinds of input files we need to create.\n\n## Creating and running the TIS simulations with PyRETIS¶\n\nWe will now create the input file for PyRETIS. We will do this section by section in order to explain the different keywords and settings. The full input file is given at the end of this section.\n\n### Setting up the simulation task¶\n\nThe first thing we will define is the type of simulation we will run. This is done by creating a simulation section.\n\nHere, we are going to do a tis simulation and we will do 20000 steps . Since we will be running a path sampling simulation, we will also need to specify the positions of the interfaces we will be using.\n\nTIS 1D example\n==============\n\nSimulation\n----------\nsteps = 20000\ninterfaces = [-0.9, -0.8, -0.7, -0.6, -0.5, -0.4, -0.3, 1.0]\n\n\n### Setting up the system¶\n\nWe will now set up the system we are going to consider. Here, we will actually define several PyRETIS input sections:\n\n• The system section which defines the units, dimensions and temperature we are considering:\n\nSystem\n------\nunits = reduced\ndimensions = 1\ntemperature = 0.07\n\n• The box section, but since we are here just considering a single particle in a 1D potential, we will simply use a 1D box without periodic boundaries:\n\nBox\n---\nperiodic = [False]\n\n• The particles section which add particles to the system and defines the initial state:\n\nParticles\n---------\nposition = {'file': 'initial.xyz'}\nvelocity = {'generate': 'maxwell',\n'momentum': False,\n'seed': 0}\nmass = {'Ar': 1.0}\nname = ['Ar']\ntype = \n\n\nIn this case, we will read the initial configuration from a file initial.xyz and velocities are generated from a Maxwell distribution. Further, we specify the mass, particle type and we label the particle as Ar. Note that this does not mean that we are simulating Argon, it is just a label used in the output of trajectories.\n\n• The force field and potential sections which setup up the 1D double well potential:\n\nForcefield\n----------\ndescription = 1D double well\n\nPotential\n---------\nclass = DoubleWell\na = 1.0\nb = 2.0\nc = 0.0\n\n\n### Selecting the engine¶\n\nHere, we will make use of a stochastic Langevin engine. We set it up by setting the time step, the friction parameter and whether we are in the high friction limit. The seed given is a seed for the random number generator used by the integrator.\n\nEngine\n------\nclass = Langevin\ntimestep = 0.002\ngamma = 0.3\nhigh_friction = False\nseed = 0\n\n\n### TIS specific settings¶\n\nThe TIS settings control how the TIS algorithm is carried out. Here we set that 50 % of the moves should be shooting moves (keyword freq) and we limit all paths to a maximum length of 20 000 steps. Further, we select aimless shooting and we tell PyRETIS to not set the momentum to zero and to not rescale the energy after drawing new random velocities. We also set allowmaxlength = False which means that for shooting, we determine (randomly) the length of new paths based on the length of the path we are shooting from. The given seed is a seed for the random number generator used by the TIS algorithm.\n\nTIS\n---\nfreq = 0.5\nmaxlength = 20000\naimless = True\nallowmaxlength = False\nzero_momentum = False\nrescale_energy = False\nsigma_v = -1\nseed = 0\n\n\n### Initial path settings¶\n\nThese settings determine how we find the initial path(s). Here, we ask PyRETIS to generate these using the kick method.\n\nInitial-path\n------------\nmethod = kick\n\n\n### Selecting the order parameter¶\n\nFor this system, we simply define the order parameter as the position of the single particle we are simulating.\n\nOrderparameter\n--------------\nclass = Position\ndim = x\nindex = 0\nperiodic = False\n\n\n### Modifying the output¶\n\nTo save some disk space, we will set up the simulation to only write output for trajectories at every 100th step.\n\nOutput\n------\nenergy-file = 100\norder-file = 100\ntrajectory-file = 100\n\n\nTIS 1D example\n==============\n\nSimulation\n----------\nsteps = 20000\ninterfaces = [-0.9, -0.8, -0.7, -0.6, -0.5, -0.4, -0.3, 1.0]\n\nSystem\n------\nunits = reduced\ndimensions = 1\ntemperature = 0.07\n\nBox\n---\nperiodic = [False]\n\nEngine\n------\nclass = Langevin\ntimestep = 0.002\ngamma = 0.3\nhigh_friction = False\nseed = 0\n\nTIS\n---\nfreq = 0.5\nmaxlength = 20000\naimless = True\nallowmaxlength = False\nzero_momentum = False\nrescale_energy = False\nsigma_v = -1\nseed = 0\n\nInitial-path\n------------\nmethod = kick\n\nParticles\n---------\nposition = {'file': 'initial.xyz'}\nvelocity = {'generate': 'maxwell',\n'momentum': False,\n'seed': 0}\nmass = {'Ar': 1.0}\nname = ['Ar']\ntype = \n\nForcefield\n----------\ndescription = 1D double well\n\nPotential\n---------\nclass = DoubleWell\na = 1.0\nb = 2.0\nc = 0.0\n\nOrderparameter\n--------------\nclass = Position\ndim = x\nindex = 0\nperiodic = False\n\nOutput\n------\nenergy-file = 100\norder-file = 100\ntrajectory-file = 100\n\n\n### Running the TIS simulation(s)¶\n\nWe will now run the TIS simulation. Create a new directory and place the input file (let’s call it tis.rst) here. Also, download the initial configuration initial.xyz and place it in the same folder. The TIS simulations are executed in two steps:\n\n1. Input TIS files are created for each path ensemble. This is done by running:\n\npyretisrun -i tis.rst\n\n\nwhich will create files named tis-001.rst, tis-002.rst and so on. Each one of these files defines a TIS simulation for a specific path ensemble.\n\n2. Running the PyRETIS TIS simulations for each path ensemble. The individual TIS simulations can be executed by running:\n\npyretisrun -i tis-001.rst -p -f 001.log\n\n\nand so on. All these TIS simulations are independent and can, in priciple, be executed in parallel.\n\nThe -p option will display a progress bar for your simulation and -f will rename the log file.\n\n### Analysing the TIS results¶\n\nWhen the all the TIS simulations are finished, we can analyse the results. PyRETIS will create a file, out.rst_000, which you can use for the analysis. This is a copy of the input tis.rst with some additional settings for the analysis. For a description of the analysis specific keywords, we refer to the analysis section.\n\nThe analysis itself is performed using:\n\npyretisanalyse -i out.rst_000\n\n\nThis will produce a new folder, report which contains the results from the analysis. If you have latex installed, you can generate a pdf using the file tis_report.tex within the report folder. An example result is shown below.",
null,
"Fig. 19 The crossing probability after running for 20 000 cycles. The numerical value is",
null,
".\n\n## Creating and running the initial flux simulation with PyRETIS¶\n\nThe initial flux simulation measure effective crossings with the first interface. In PyRETIS such a simulation is requested by selecting the md-flux task.\n\nThis can be done by setting the following simulation settings:\n\nSimulation settings\n-------------------\nsteps = 1000000\ninterfaces = [-0.9]\n\n\nThe other sections will be similar to the sections already defined for the TIS simulation, however, we do not need to include the TIS section for the md-flux simulation. The full input file is given below.\n\nMD flux simulation\n==================\n\nSimulation settings\n-------------------\nsteps = 1000000\ninterfaces = [-0.9]\n\nSystem settings\n---------------\nunits = lj\ndimensions = 1\ntemperature = 0.07\n\nEngine settings\n---------------\nclass = Langevin\ntimestep = 0.002\ngamma = 0.3\nhigh_friction = False\nseed = 0\n\nParticles\n---------\nposition = {'file': 'initial.xyz'}\nvelocity = {'generate': 'maxwell',\n'momentum': False,\n'seed': 0}\nmass = {'Ar': 1.0}\nname = ['Ar']\ntype = \n\nForceField settings\n-------------------\ndescription = 1D double well potential\n\nPotential\n---------\nclass = DoubleWell\na = 1.0\nb = 2.0\nc = 0.0\n\nOrderparameter\n--------------\nclass = Position\ndim = x\nindex = 0\nperiodic = False\n\nOutput\n------\nbackup = overwrite\nenergy-file = 1000\norder-file = 1000\ncross-file = 1\ntrajectory-file = -1\n\n\n### Running the md-flux simulation¶\n\nWe will now run the md-flux simulation. Create a new directory and place the input file (let’s call it flux.rst) here. Also, download the initial configuration initial.xyz and place it in the same folder. The md-flux simulation can now be executed using:\n\npyretisrun -i flux.rst -p\n\n\n### Analysing the md-flux results¶\n\nWhen the md-flux simulation has finished, we can analyse the results. PyRETIS will create a file, out.rst, which you can use for the analysis. This is a copy of the input flux.rst with some additional settings for the analysis. For a description of the analysis specific keywords, we refer to the analysis section.\n\nThe analysis itself is performed using:\n\npyretisanalyse -i out.rst\n\n\nThis will produce a new folder, report which contains the results from the analysis. If you have latex installed, you can generate a pdf using the file md_flux_report.tex within the report folder. An example result is shown below.",
null,
"Fig. 20 The running average for the initial flux.\n\n## Improving the statistics¶\n\nWe can improve the statistics by running a longer simulation. Modify the number of steps, from 20000 to 1000000 and re-run the simulation and the analysis. Below we show an example for the crossing probability after performing the additional steps",
null,
"Fig. 21 The crossing probability after running for 1 000 000 steps. The numerical value is",
null,
"."
] | [
null,
"http://pyretis.org/current/_images/math/35fc4d2774f38b69ac8afe2a65b0b307ac26a3ad.png",
null,
"http://pyretis.org/current/_images/math/888f7c323ac0341871e867220ae2d76467d74d6e.png",
null,
"http://pyretis.org/current/_images/math/627dd8ffb57945e8ded86de9ceb1fef4fb3cd983.png",
null,
"http://pyretis.org/current/_images/math/23ec360a99998552bf72f9d9020b82cecb309848.png",
null,
"http://pyretis.org/current/_images/math/c34170440d4046a9b3e1ef2635a2f5d6a529a421.png",
null,
"http://pyretis.org/current/_images/1dpot.png",
null,
"http://pyretis.org/current/_images/prob1.png",
null,
"http://pyretis.org/current/_images/math/3fd92afa21fa622a497247c8169cbf9e5cd3857d.png",
null,
"http://pyretis.org/current/_images/flux.png",
null,
"http://pyretis.org/current/_images/prob2.png",
null,
"http://pyretis.org/current/_images/math/f889b5e399a9f00fd51f7be90dbb296633653f9d.png",
null
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https://www.aqua-calc.com/calculate/volume-to-weight/substance/n-coma-n-dimethylformamide | [
"# Weight of N,N-Dimethylformamide\n\n## n,n-dimethylformamide: convert volume to weight\n\n### Weight of 1 cubic centimeter of N,N-Dimethylformamide\n\n carat 4.72 ounce 0.03 gram 0.94 pound 0 kilogram 0 tonne 9.45 × 10-7 milligram 944.5\n\n#### How many moles in 1 cubic centimeter of N,N-Dimethylformamide?\n\nThere are 12.92 millimoles in 1 cubic centimeter of N,N-Dimethylformamide\n\n### The entered volume of N,N-Dimethylformamide in various units of volume\n\n centimeter³ 1 milliliter 1 foot³ 3.53 × 10-5 oil barrel 6.29 × 10-6 Imperial gallon 0 US cup 0 inch³ 0.06 US fluid ounce 0.03 liter 0 US gallon 0 meter³ 1 × 10-6 US pint 0 metric cup 0 US quart 0 metric tablespoon 0.07 US tablespoon 0.07 metric teaspoon 0.2 US teaspoon 0.2\n• 1 cubic meter of N,N-Dimethylformamide weighs 944.5 kilograms [kg]\n• 1 cubic foot of N,N-Dimethylformamide weighs 58.96321 pounds [lbs]\n• N,N-Dimethylformamide weighs 0.9445 gram per cubic centimeter or 944.5 kilogram per cubic meter, i.e. density of n,N-Dimethylformamide is equal to 944.5 kg/m³; at 25°C (77°F or 298.15K) at standard atmospheric pressure. In Imperial or US customary measurement system, the density is equal to 58.96 pound per cubic foot [lb/ft³], or 0.546 ounce per cubic inch [oz/inch³] .\n• Melting Point (MP), N,N-Dimethylformamide changes its state from solid to liquid at -60.3°C (-76.54°F or 212.85K)\n• Boiling Point (BP), N,N-Dimethylformamide changes its state from liquid to gas at 152.8°C (307.04°F or 425.95K)\n• Molecular formula: HCON(CH3)2\n\nElements: Carbon (C), Hydrogen (H), Nitrogen (N), Oxygen (O)\n\nMolecular weight: 73.095 g/mol\n\nMolar volume: 77.39 cm³/mol\n\nCAS Registry Number (CAS RN): 68-12-2\n\n• Bookmarks: [ weight to volume | volume to weight | price | mole to volume and weight | density ]\n• For instance, calculate how many ounces, pounds, milligrams, grams, kilograms or tonnes of a selected substance in a liter, gallon, fluid ounce, cubic centimeter or in a cubic inch. This page computes weight of the substance per given volume, and answers the question: How much the substance weighs per volume.\n\n#### Foods, Nutrients and Calories\n\nWATERMELON JELLY SLICES, UPC: 077890362129 contain(s) 333 calories per 100 grams or ≈3.527 ounces [ price ]\n\n#### Gravels, Substances and Oils\n\nCaribSea, Freshwater, Super Naturals, Gemstone Creek weighs 1 537.77 kg/m³ (95.99984 lb/ft³) with specific gravity of 1.53777 relative to pure water. Calculate how much of this gravel is required to attain a specific depth in a cylindricalquarter cylindrical or in a rectangular shaped aquarium or pond [ weight to volume | volume to weight | price ]\n\nSodium carbonate monohydrate [Na2CO3 ⋅ H2O] weighs 2 250 kg/m³ (140.46291 lb/ft³) [ weight to volume | volume to weight | price | mole to volume and weight | density ]\n\nVolume to weightweight to volume and cost conversions for Refrigerant R-124, liquid (R124) with temperature in the range of -40°C (-40°F) to 82.23°C (180.014°F)\n\n#### Weights and Measurements\n\nA dyne per square inch is a unit of pressure where a force of one dyne (dyn) is applied to an area of one square inch.\n\nThe frequency is defined as an interval of time, during which a physical system, e.g. electrical current or a wave, performs a full oscillation and returns to its original momentary state, in both sign (direction) and in value, is called the oscillation period of this physical system.\n\noz t/ft³ to kg/in³ conversion table, oz t/ft³ to kg/in³ unit converter or convert between all units of density measurement.\n\n#### Calculators\n\nWeight to Volume conversions for sands, gravels and substrates"
] | [
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.8431271,"math_prob":0.98446304,"size":1526,"snap":"2020-45-2020-50","text_gpt3_token_len":403,"char_repetition_ratio":0.108409986,"word_repetition_ratio":0.048,"special_character_ratio":0.2712975,"punctuation_ratio":0.102389075,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96613675,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-10-26T15:38:04Z\",\"WARC-Record-ID\":\"<urn:uuid:a1e2718f-a2aa-409d-bca7-672594355e2a>\",\"Content-Length\":\"25855\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2abc876e-fa03-4b26-ba84-8253731d8807>\",\"WARC-Concurrent-To\":\"<urn:uuid:d455a9da-0e3b-468c-90a5-e57d21793187>\",\"WARC-IP-Address\":\"69.46.0.75\",\"WARC-Target-URI\":\"https://www.aqua-calc.com/calculate/volume-to-weight/substance/n-coma-n-dimethylformamide\",\"WARC-Payload-Digest\":\"sha1:OQ7LGYH3FOQJOIJJR2UIWPGYYEZJQ33F\",\"WARC-Block-Digest\":\"sha1:3OXM7LGM2EPMDETMZ32NEL6SBVJJUJVA\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-45/CC-MAIN-2020-45_segments_1603107891428.74_warc_CC-MAIN-20201026145305-20201026175305-00282.warc.gz\"}"} |
https://www.rjr-verschueren.be/19-10-40306-expression-of-critical-spped-of-a-ball-mill-ppt.html | [
" expression of critical spped of a ball mill ppt\n\n## expression of critical spped of a ball mill ppt\n\n#### ball mill working principle - YouTube\n\nMay 08, 2015· Great Wall ball grinding mill process ball grinding mill working principle 3D our website:, our email:[email protected]\n\n#### derivation for the critical speed of ball mill\n\nderivation of the expression for critical speed of a ball mill. The modelling of the mechanical alloying process in a planetary ball milling have been analysed and the calculated ball trajectory is compared with in-situ conventional ball mills a critical speed exists above which a reduced grinding action is …\n\n#### Derive An Expression For The Critical Speed Of A Ball Mill\n\nderive the equation of critical speed of ball mill. derivation of expression for critical speed of ball mill. derivation of expression for critical speed of ball mill. ball milling: abrasive wear and impactive wear. per cent of critical speed and higher, cataracting will be . distribution requires the derivation of the number densi- equation (9) then yields the following expression for the.\n\n#### Expression Of Critical Spped Of A Ball Mill Ppt - cz-eu.eu\n\nExpression Of Critical Spped Of A Ball Mill Ppt. expression of critical spped of a ball mill. meaning of critical speed of the mill - BINQ Mining. 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Ball Mills Mine EngineerCom ball mill critical speed derivation,If the peripheral speed of the mill is too great, it begins to act like a centrifuge and the balls do not fall back, but stay on the perimeter of the mill The point where the mill becomes a centrifuge is called the \"Critical Speed\", and dragThe second is air drag, which ...\n\n#### expression of critical spped of a ball mill - lese-fair.de\n\nMill Speed - Critical Speed - Paul O. Abbe. No matter how large or small a mill, ball mill, ceramic lined mill, pebble mill, jar mill or laboratory jar rolling mill, its rotational speed is important to proper and efficient mill operation. ...\n\n#### TECHNICAL NOTES 8 GRINDING R. P. King - Mineral Tech\n\nFigures 8.5 for the popular mill types. 3 c is the mill speed measured as a fraction of the critical speed. More reliable models for the prediction of the power drawn by ball, semi-autogenous and fully autogenous mills have been developed by Morrell and by Austin. (Morrell, S. Power draw of wet tumbling mills …\n\n#### expression of critical spped of a ball mill ppt\n\nIf the peripheral speed of the mill is too great, it begins to act like a centrifuge and the balls do not fall back, but stay on the perimeter of the mill. The point where the mill becomes a centrifuge is called the \"Critical Speed\" and ball mills usually operate at 65% to 75% of the critical speed. Ball Mills are generally used to grind\n\n#### expression of critical spped of a ball mill ppt\n\nexpression of critical spped of a ball mill thingsyoulove.nl. expression of critical spped of a ball mill ppt. expression of critical spped of a ball mill ppt. attritors and ball mills how they work robert e. schilling, in this presentation we will discuss the principle of the attritor and its the critical speed of a ball mill is calculated as 54.19 divided by the square root ofderive ...\n\n#### Ball mill - slideshare.net\n\nApr 24, 2015· • Weight of the balls: With a heavy discharge of balls,we get a fine product.We can increase the weight of the charge by increasing the number of balls or by using a ball material of high density • Speed & rotation of Ball mill: low speeds,the balls simply roll over one another and little grinding is obtained while at very high speeds the ...\n\n#### Derive An E Pression For The Critical Speed Of A Ball Mill\n\nderive the equation of critical speed of ball mill. derivation of expression for critical speed of ball mill. derivation of expression for critical speed of ball mill. ball milling: abrasive wear and impactive wear. per cent of critical speed and higher, cataracting will be . distribution requires the derivation of the number densi- equation (9) then yields the following expression for the.\n\n#### derive an expression for calculating the critical speed of ...\n\nderive an expression for the critical speed of a ball mill. derive expression of critical speed of ball mill - ibsmorgin- derive an expression for the critical speed of a ball mill,derive expression of critical speed of ball mill ALL; Ball Mill,Derivation of flux equation, ball mill, critical speed of ball mill, ultra fine grinders, .radius of ball and mill in critical speedball mill critical ...\n\n#### Maintenance Of Ball Mills Ppt - greenrevolution.org.in\n\nball mills ppt, powerpoint presentation. ball milling ppt slides, powerpoint presentations for download review of ball milling matthew king 2/4/04 talk outline overview of ball milling parameters.Grinding in titan group maintenance cost. equivalent or better cement quality than tube mill cement. energy saving."
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.8595407,"math_prob":0.9498202,"size":8734,"snap":"2019-51-2020-05","text_gpt3_token_len":1867,"char_repetition_ratio":0.31981674,"word_repetition_ratio":0.27882037,"special_character_ratio":0.21559423,"punctuation_ratio":0.13290398,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.977378,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-16T13:31:49Z\",\"WARC-Record-ID\":\"<urn:uuid:ecde4813-b39c-4b71-8207-9f6c9e2473b4>\",\"Content-Length\":\"37019\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:77ae4f5f-3c5f-41b7-a9db-62fc65df3647>\",\"WARC-Concurrent-To\":\"<urn:uuid:92129e49-20a9-48a5-b673-04d799f7d1e8>\",\"WARC-IP-Address\":\"104.27.145.209\",\"WARC-Target-URI\":\"https://www.rjr-verschueren.be/19-10-40306-expression-of-critical-spped-of-a-ball-mill-ppt.html\",\"WARC-Payload-Digest\":\"sha1:L526J7SERGZZU67HMGGI6XZSV7FEYZFS\",\"WARC-Block-Digest\":\"sha1:ACLPMYKLTTSBZUXFE36IB4IASS37MLIS\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575540565544.86_warc_CC-MAIN-20191216121204-20191216145204-00261.warc.gz\"}"} |
https://www.nagwa.com/en/worksheets/213183472903/ | [
"# Worksheet: Reaction Rates\n\nIn this worksheet, we will practice calculating reaction rates using variables such as concentration, pressure, conductivity, and optical absorption.\n\nQ1:\n\nAmmonia decomposes into hydrogen and nitrogen at high temperature. The rate of decomposition of ammonia is found to be M/s.\n\nWrite a balanced chemical equation for this reaction.\n\n• A\n• B\n• C\n• D\n• E\n\nWhat is the rate of formation of nitrogen?\n\n• A M/s\n• B M/s\n• C M/s\n• D M/s\n• E M/s\n\nWhat is the rate of formation of hydrogen?\n\n• A M/s\n• B M/s\n• C M/s\n• D M/s\n• E M/s\n\nQ2:\n\nAqueous hydrogen peroxide () decomposes into oxygen and water. The rate of decomposition of hydrogen peroxide is found to be M/h.\n\nWrite a balanced chemical equation for this reaction.\n\n• A\n• B\n• C\n• D\n• E\n\nWhat is the rate of formation of water?\n\n• A M/h\n• B M/h\n• C M/h\n• D M/h\n• E M/h\n\nWhat is the rate of formation of oxygen?\n\n• A M/h\n• B M/h\n• C M/h\n• D M/h\n• E M/h\n\nQ3:\n\nThe equilibrium for the ionization of the ion, a weak acid used in some household cleaners, is shown. For a mixture of and at equilibrium, the following are the concentrations:\n\n• ,\n• ,\n• .\n\nWhat is the equilibrium constant for this reaction under these conditions?\n\n• A M/s\n• B M/s\n• C M/s\n• D M/s\n• E M/s\n\nQ4:\n\nDinitrogen pentoxide decomposes in chloroform to form nitrogen dioxide and oxygen, as shown. The decomposition is a first-order reaction with a rate constant of min−1 at . Calculate the rate of reaction in molars per second when [] = 0.400 M.\n\n• A M/s\n• B M/s\n• C M/s\n• D M/s\n• E M/s\n\nQ5:\n\nA reaction begins at a time and is monitored over a period of time, , by measuring the reactant concentration, , at fixed time intervals. How is the average rate of reaction for this time period calculated from a graph of against ?\n\n• ABy calculating the total area under the graph between and\n• BBy calculating the gradient of the tangent at\n• CBy fitting a polynomial function to the curve and evaluating the derivative of this function at\n• DBy calculating the gradient of the tangent at\n• EBy dividing the change in between and by\n\nQ6:\n\nA reaction begins at a time and is monitored over a period of time, , by measuring the reactant concentration, , at fixed time intervals. How is the instantaneous rate at calculated from a graph of against ?\n\n• ABy dividing the change in between and by\n• BBy calculating the total area under the graph between and\n• CBy calculating the gradient of the tangent at\n• DBy fitting a polynomial function to the curve and evaluating the derivative of this function at\n• EBy calculating the gradient of the tangent at"
] | [
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.91568273,"math_prob":0.98102176,"size":1964,"snap":"2019-51-2020-05","text_gpt3_token_len":499,"char_repetition_ratio":0.15153061,"word_repetition_ratio":0.55497384,"special_character_ratio":0.24694501,"punctuation_ratio":0.08142494,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9997943,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-16T00:41:33Z\",\"WARC-Record-ID\":\"<urn:uuid:7a29fdb5-df3e-4696-872b-62a212ad8f4a>\",\"Content-Length\":\"98194\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4e923ab5-0c9f-4694-ac45-13fa83f61b19>\",\"WARC-Concurrent-To\":\"<urn:uuid:5619c9ad-39a1-47c8-8d12-6bb25e3c5b8b>\",\"WARC-IP-Address\":\"23.21.22.97\",\"WARC-Target-URI\":\"https://www.nagwa.com/en/worksheets/213183472903/\",\"WARC-Payload-Digest\":\"sha1:RH3RLGAG5DZEHUX64MKWH5ENGUEE7WKT\",\"WARC-Block-Digest\":\"sha1:LQ3KPWGEWHTQVFN6LH5GSIZWOZRHEANQ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575541310970.85_warc_CC-MAIN-20191215225643-20191216013643-00257.warc.gz\"}"} |
https://windycitysealsinc.com/glossary/coefficient-of-expansion/ | [
"## Coefficient of Expansion\n\nThe coefficient of linear expansion is the ratio of the change in length per degree to the length at 0 Celsius. The coefficient of surface expansion is two (2) times the linear coefficient. The coefficient of volume expansion (for solids) is three (3) times the linear coefficient. The coefficient of volume expansion for liquids is the ratio of the change in volume per degree to the volume at 0 Celsius.\n\nShare\nThis"
] | [
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.88916934,"math_prob":0.9657795,"size":405,"snap":"2023-40-2023-50","text_gpt3_token_len":82,"char_repetition_ratio":0.18952619,"word_repetition_ratio":0.24242425,"special_character_ratio":0.20493828,"punctuation_ratio":0.054054055,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9969161,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-10-01T08:43:37Z\",\"WARC-Record-ID\":\"<urn:uuid:b57c8eb8-7d5a-4ad7-9e08-807c2451a487>\",\"Content-Length\":\"53803\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9aca6ab8-788f-429d-89af-1afca16f3345>\",\"WARC-Concurrent-To\":\"<urn:uuid:44f311b1-63c6-4ed1-82c7-06f4bf5a11d1>\",\"WARC-IP-Address\":\"35.223.208.123\",\"WARC-Target-URI\":\"https://windycitysealsinc.com/glossary/coefficient-of-expansion/\",\"WARC-Payload-Digest\":\"sha1:EE6LE7PNXCWQLIVXGFHSPYOJIMEWGXMX\",\"WARC-Block-Digest\":\"sha1:TFGVJFO62QNSV3CEC2W5IT3LYQ2PSSG5\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510810.46_warc_CC-MAIN-20231001073649-20231001103649-00241.warc.gz\"}"} |
https://www.colorhexa.com/e30020 | [
"# #e30020 Color Information\n\nIn a RGB color space, hex #e30020 is composed of 89% red, 0% green and 12.5% blue. Whereas in a CMYK color space, it is composed of 0% cyan, 100% magenta, 85.9% yellow and 11% black. It has a hue angle of 351.5 degrees, a saturation of 100% and a lightness of 44.5%. #e30020 color hex could be obtained by blending #ff0040 with #c70000. Closest websafe color is: #cc0033.\n\n• R 89\n• G 0\n• B 13\nRGB color chart\n• C 0\n• M 100\n• Y 86\n• K 11\nCMYK color chart\n\n#e30020 color description : Pure (or mostly pure) red.\n\n# #e30020 Color Conversion\n\nThe hexadecimal color #e30020 has RGB values of R:227, G:0, B:32 and CMYK values of C:0, M:1, Y:0.86, K:0.11. Its decimal value is 14876704.\n\nHex triplet RGB Decimal e30020 `#e30020` 227, 0, 32 `rgb(227,0,32)` 89, 0, 12.5 `rgb(89%,0%,12.5%)` 0, 100, 86, 11 351.5°, 100, 44.5 `hsl(351.5,100%,44.5%)` 351.5°, 100, 89 cc0033 `#cc0033`\nCIE-LAB 47.546, 73.717, 50.125 31.941, 16.439, 2.858 0.623, 0.321, 16.439 47.546, 89.145, 34.214 47.546, 152.773, 29.048 40.546, 69.664, 24.203 11100011, 00000000, 00100000\n\n# Color Schemes with #e30020\n\n• #e30020\n``#e30020` `rgb(227,0,32)``\n• #00e3c3\n``#00e3c3` `rgb(0,227,195)``\nComplementary Color\n• #e30092\n``#e30092` `rgb(227,0,146)``\n• #e30020\n``#e30020` `rgb(227,0,32)``\n• #e35100\n``#e35100` `rgb(227,81,0)``\nAnalogous Color\n• #0092e3\n``#0092e3` `rgb(0,146,227)``\n• #e30020\n``#e30020` `rgb(227,0,32)``\n• #00e351\n``#00e351` `rgb(0,227,81)``\nSplit Complementary Color\n• #0020e3\n``#0020e3` `rgb(0,32,227)``\n• #e30020\n``#e30020` `rgb(227,0,32)``\n• #20e300\n``#20e300` `rgb(32,227,0)``\nTriadic Color\n• #c300e3\n``#c300e3` `rgb(195,0,227)``\n• #e30020\n``#e30020` `rgb(227,0,32)``\n• #20e300\n``#20e300` `rgb(32,227,0)``\n• #00e3c3\n``#00e3c3` `rgb(0,227,195)``\nTetradic Color\n• #970015\n``#970015` `rgb(151,0,21)``\n• #b00019\n``#b00019` `rgb(176,0,25)``\n• #ca001c\n``#ca001c` `rgb(202,0,28)``\n• #e30020\n``#e30020` `rgb(227,0,32)``\n• #fd0024\n``#fd0024` `rgb(253,0,36)``\n• #ff1738\n``#ff1738` `rgb(255,23,56)``\n• #ff314e\n``#ff314e` `rgb(255,49,78)``\nMonochromatic Color\n\n# Alternatives to #e30020\n\nBelow, you can see some colors close to #e30020. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #e30059\n``#e30059` `rgb(227,0,89)``\n• #e30046\n``#e30046` `rgb(227,0,70)``\n• #e30033\n``#e30033` `rgb(227,0,51)``\n• #e30020\n``#e30020` `rgb(227,0,32)``\n• #e3000d\n``#e3000d` `rgb(227,0,13)``\n• #e30600\n``#e30600` `rgb(227,6,0)``\n• #e31900\n``#e31900` `rgb(227,25,0)``\nSimilar Colors\n\n# #e30020 Preview\n\nText with hexadecimal color #e30020\n\nThis text has a font color of #e30020.\n\n``<span style=\"color:#e30020;\">Text here</span>``\n#e30020 background color\n\nThis paragraph has a background color of #e30020.\n\n``<p style=\"background-color:#e30020;\">Content here</p>``\n#e30020 border color\n\nThis element has a border color of #e30020.\n\n``<div style=\"border:1px solid #e30020;\">Content here</div>``\nCSS codes\n``.text {color:#e30020;}``\n``.background {background-color:#e30020;}``\n``.border {border:1px solid #e30020;}``\n\n# Shades and Tints of #e30020\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, #0b0002 is the darkest color, while #fff7f8 is the lightest one.\n\n• #0b0002\n``#0b0002` `rgb(11,0,2)``\n• #1f0004\n``#1f0004` `rgb(31,0,4)``\n• #320007\n``#320007` `rgb(50,0,7)``\n• #46000a\n``#46000a` `rgb(70,0,10)``\n• #5a000d\n``#5a000d` `rgb(90,0,13)``\n• #6d000f\n``#6d000f` `rgb(109,0,15)``\n• #810012\n``#810012` `rgb(129,0,18)``\n• #950015\n``#950015` `rgb(149,0,21)``\n• #a80018\n``#a80018` `rgb(168,0,24)``\n• #bc001a\n``#bc001a` `rgb(188,0,26)``\n• #cf001d\n``#cf001d` `rgb(207,0,29)``\n• #e30020\n``#e30020` `rgb(227,0,32)``\n• #f70023\n``#f70023` `rgb(247,0,35)``\nShade Color Variation\n• #ff0b2e\n``#ff0b2e` `rgb(255,11,46)``\n• #ff1f3e\n``#ff1f3e` `rgb(255,31,62)``\n• #ff324f\n``#ff324f` `rgb(255,50,79)``\n• #ff4660\n``#ff4660` `rgb(255,70,96)``\n• #ff5a71\n``#ff5a71` `rgb(255,90,113)``\n• #ff6d82\n``#ff6d82` `rgb(255,109,130)``\n• #ff8193\n``#ff8193` `rgb(255,129,147)``\n• #ff95a4\n``#ff95a4` `rgb(255,149,164)``\n• #ffa8b4\n``#ffa8b4` `rgb(255,168,180)``\n• #ffbcc5\n``#ffbcc5` `rgb(255,188,197)``\n• #ffcfd6\n``#ffcfd6` `rgb(255,207,214)``\n• #ffe3e7\n``#ffe3e7` `rgb(255,227,231)``\n• #fff7f8\n``#fff7f8` `rgb(255,247,248)``\nTint Color Variation\n\n# Tones of #e30020\n\nA tone is produced by adding gray to any pure hue. In this case, #7a696b is the less saturated color, while #e30020 is the most saturated one.\n\n• #7a696b\n``#7a696b` `rgb(122,105,107)``\n• #836065\n``#836065` `rgb(131,96,101)``\n• #8c575f\n``#8c575f` `rgb(140,87,95)``\n• #944f58\n``#944f58` `rgb(148,79,88)``\n• #9d4652\n``#9d4652` `rgb(157,70,82)``\n• #a63d4c\n``#a63d4c` `rgb(166,61,76)``\n• #af3446\n``#af3446` `rgb(175,52,70)``\n• #b72c3f\n``#b72c3f` `rgb(183,44,63)``\n• #c02339\n``#c02339` `rgb(192,35,57)``\n• #c91a33\n``#c91a33` `rgb(201,26,51)``\n• #d2112d\n``#d2112d` `rgb(210,17,45)``\n• #da0926\n``#da0926` `rgb(218,9,38)``\n• #e30020\n``#e30020` `rgb(227,0,32)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #e30020 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://math.hecker.org/2012/11/18/linear-algebra-and-its-applications-exercise-2-5-10/ | [
"## Linear Algebra and Its Applications, Exercise 2.5.10\n\nExercise 2.5.10. Given the incidence matrix",
null,
"$A = \\begin{bmatrix} -1&1&0&0 \\\\ -1&0&1&0 \\\\ 0&1&0&-1 \\\\ 0&0&-1&1 \\end{bmatrix}$\n\ndraw the graph corresponding to the matrix, and state whether or not it is a tree and the rows are linearly independent. Demonstrate that removing a row produces a spanning tree, and describe the subspace of which the remaining rows form a basis.\n\nAnswer: The incidence matrix has four nodes, corresponding to the columns, and four edges, corresponding to the rows. The nodes can be arranged in the form of a square. Put node 1 in the upper left corner of the square. Edge 1 runs from node 1 to node 2; put node 2 in the lower left corner of the square, so that edge 2 forms the left side of the square. Edge 2 runs from node 1 to node 3; put node 3 in the upper right corner of the square, so that edge 2 forms the top side of the square.\n\nPut the remaining node 4 in the lower right corner of the square. Edge 3 runs from node 4 to node 2, and thus forms the bottom side of the square. Edge 4 runs from node 3 to node 4, and thus forms the right side of the square.\n\nSince the four edges form a loop (in the shape of a square) the graph is not a tree. Also, the rows are not linearly independent, since the first row minus the sum of the second and third rows equals the fourth row:",
null,
"$\\begin{bmatrix} -1 \\\\ 1 \\\\ 0 \\\\ 0 \\end{bmatrix} - \\left( \\begin{bmatrix} -1 \\\\ 0 \\\\ 1 \\\\ 0 \\end{bmatrix} + \\begin{bmatrix} 0 \\\\ 1 \\\\ 0 \\\\ -1 \\end{bmatrix} \\right)$",
null,
"$= \\begin{bmatrix} -1 \\\\ 1 \\\\ 0 \\\\ 0 \\end{bmatrix} - \\begin{bmatrix} -1 \\\\ 1 \\\\ 1 \\\\ -1 \\end{bmatrix} = \\begin{bmatrix} 0 \\\\ 0 \\\\ -1 \\\\ 1 \\end{bmatrix}$\n\nIf we remove the fourth row and the corresponding edge (i.e., the bottom side of the square) then the resulting three edges form a spanning tree, since they touch all four nodes and have no loops. The remaining three rows are linearly independent and form a basis for the row space",
null,
"$\\mathcal R(A^T)$.\n\nNOTE: This continues a series of posts containing worked out exercises from the (out of print) book Linear Algebra and Its Applications, Third Edition",
null,
"by Gilbert Strang.\n\nIf you find these posts useful I encourage you to also check out the more current Linear Algebra and Its Applications, Fourth Edition",
null,
", Dr Strang’s introductory textbook Introduction to Linear Algebra, Fourth Edition",
null,
"and the accompanying free online course, and Dr Strang’s other books",
null,
".\n\nThis entry was posted in linear algebra. Bookmark the permalink.\n\n### 1 Response to Linear Algebra and Its Applications, Exercise 2.5.10\n\n1.",
null,
"Filipe says:\n\nVery good!\nPost these questions: 2.5.12, 2.5.16 and 2.6.4, 2.6.10, 2.6.16.\nI didn’t get to do."
] | [
null,
"https://s0.wp.com/latex.php",
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"https://s0.wp.com/latex.php",
null,
"https://s0.wp.com/latex.php",
null,
"https://s0.wp.com/latex.php",
null,
"http://www.assoc-amazon.com/e/ir",
null,
"http://www.assoc-amazon.com/e/ir",
null,
"http://www.assoc-amazon.com/e/ir",
null,
"https://www.assoc-amazon.com/e/ir",
null,
"https://2.gravatar.com/avatar/8194a68d095d670f636f6ad7c9ddf985",
null
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https://countingpennies.savingadvice.com/2008/12/ | [
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Array\n(\n => 119.82.83.238\n)\n\n => Array\n(\n => 106.212.128.138\n)\n\n => Array\n(\n => 139.167.237.36\n)\n\n => Array\n(\n => 222.124.40.250\n)\n\n => Array\n(\n => 134.56.185.169\n)\n\n => Array\n(\n => 54.255.226.31\n)\n\n => Array\n(\n => 137.97.162.31\n)\n\n => Array\n(\n => 95.185.21.191\n)\n\n => Array\n(\n => 171.61.168.151\n)\n\n => Array\n(\n => 137.97.184.4\n)\n\n => Array\n(\n => 106.203.151.202\n)\n\n => Array\n(\n => 39.37.137.0\n)\n\n => Array\n(\n => 45.118.166.66\n)\n\n => Array\n(\n => 14.248.105.100\n)\n\n => Array\n(\n => 106.215.61.185\n)\n\n => Array\n(\n => 202.83.57.179\n)\n\n => Array\n(\n => 89.187.182.176\n)\n\n => Array\n(\n => 49.249.232.198\n)\n\n => Array\n(\n => 132.154.95.236\n)\n\n => Array\n(\n => 223.233.83.230\n)\n\n => Array\n(\n => 183.83.153.14\n)\n\n => Array\n(\n => 125.63.72.210\n)\n\n => Array\n(\n => 207.174.202.11\n)\n\n => Array\n(\n => 119.95.88.59\n)\n\n => Array\n(\n => 122.170.14.150\n)\n\n => Array\n(\n => 45.118.166.75\n)\n\n => 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Array\n(\n => 119.81.105.2\n)\n\n => Array\n(\n => 49.36.128.114\n)\n\n => Array\n(\n => 213.200.31.93\n)\n\n => Array\n(\n => 2.50.15.110\n)\n\n => Array\n(\n => 120.29.104.67\n)\n\n => Array\n(\n => 223.225.32.221\n)\n\n => Array\n(\n => 14.248.67.195\n)\n\n => Array\n(\n => 119.155.36.13\n)\n\n => Array\n(\n => 101.50.95.104\n)\n\n => Array\n(\n => 104.236.205.233\n)\n\n => Array\n(\n => 122.164.36.150\n)\n\n => Array\n(\n => 157.45.93.209\n)\n\n => Array\n(\n => 182.77.118.100\n)\n\n => Array\n(\n => 182.74.134.218\n)\n\n => Array\n(\n => 183.82.128.146\n)\n\n => Array\n(\n => 112.196.170.234\n)\n\n => Array\n(\n => 122.173.230.178\n)\n\n => Array\n(\n => 122.164.71.199\n)\n\n => Array\n(\n => 51.79.19.31\n)\n\n => Array\n(\n => 58.65.222.20\n)\n\n => Array\n(\n => 103.27.203.97\n)\n\n => Array\n(\n => 111.88.7.242\n)\n\n => Array\n(\n => 14.171.232.77\n)\n\n => Array\n(\n => 46.101.22.182\n)\n\n => Array\n(\n => 103.94.219.19\n)\n\n => Array\n(\n => 139.190.83.30\n)\n\n => Array\n(\n => 223.190.27.184\n)\n\n => Array\n(\n => 182.185.183.34\n)\n\n => Array\n(\n => 91.74.181.242\n)\n\n => Array\n(\n => 222.252.107.14\n)\n\n => Array\n(\n => 137.97.8.28\n)\n\n => Array\n(\n => 46.101.16.229\n)\n\n => Array\n(\n => 122.53.254.229\n)\n\n => Array\n(\n => 106.201.17.180\n)\n\n => Array\n(\n => 123.24.170.129\n)\n\n => Array\n(\n => 182.185.180.79\n)\n\n => Array\n(\n => 223.190.17.4\n)\n\n => Array\n(\n => 213.108.105.1\n)\n\n => Array\n(\n => 171.22.76.9\n)\n\n => Array\n(\n => 202.66.178.164\n)\n\n => Array\n(\n => 178.62.97.171\n)\n\n => Array\n(\n => 167.179.110.209\n)\n\n => Array\n(\n => 223.230.147.172\n)\n\n => Array\n(\n => 76.218.195.160\n)\n\n => Array\n(\n => 14.189.186.178\n)\n\n => Array\n(\n => 157.41.45.143\n)\n\n => Array\n(\n => 223.238.22.53\n)\n\n => Array\n(\n => 111.88.7.244\n)\n\n => Array\n(\n => 5.62.57.19\n)\n\n => Array\n(\n => 106.201.25.216\n)\n\n => Array\n(\n => 117.217.205.33\n)\n\n => Array\n(\n => 111.88.7.215\n)\n\n => Array\n(\n => 106.201.13.77\n)\n\n => Array\n(\n => 50.7.93.29\n)\n\n => Array\n(\n => 123.201.70.112\n)\n\n => Array\n(\n => 39.42.108.226\n)\n\n => Array\n(\n => 27.5.198.29\n)\n\n => Array\n(\n => 223.238.85.187\n)\n\n => Array\n(\n => 171.49.176.32\n)\n\n => Array\n(\n => 14.248.79.242\n)\n\n => Array\n(\n => 46.219.211.183\n)\n\n => Array\n(\n => 185.244.212.251\n)\n\n => Array\n(\n => 14.102.84.126\n)\n\n => Array\n(\n => 106.212.191.52\n)\n\n => Array\n(\n => 154.72.153.203\n)\n\n => Array\n(\n => 14.175.82.64\n)\n\n => Array\n(\n => 141.105.139.131\n)\n\n => Array\n(\n => 182.156.103.98\n)\n\n => Array\n(\n => 117.217.204.75\n)\n\n => Array\n(\n => 104.140.83.115\n)\n\n => Array\n(\n => 119.152.62.8\n)\n\n => Array\n(\n => 45.125.247.94\n)\n\n => Array\n(\n => 137.97.37.252\n)\n\n => Array\n(\n => 117.217.204.73\n)\n\n => Array\n(\n => 14.248.79.133\n)\n\n => Array\n(\n => 39.37.152.52\n)\n\n => Array\n(\n => 103.55.60.54\n)\n\n => Array\n(\n => 102.166.183.88\n)\n\n => Array\n(\n => 5.62.60.162\n)\n\n => Array\n(\n => 5.62.60.163\n)\n\n => Array\n(\n => 160.202.38.131\n)\n\n => Array\n(\n => 106.215.20.253\n)\n\n => Array\n(\n => 39.37.160.54\n)\n\n => Array\n(\n => 119.152.59.186\n)\n\n => Array\n(\n => 183.82.0.164\n)\n\n => Array\n(\n => 41.90.54.87\n)\n\n => Array\n(\n => 157.36.85.158\n)\n\n => Array\n(\n => 110.37.229.162\n)\n\n => Array\n(\n => 203.99.180.148\n)\n\n => Array\n(\n => 117.97.132.91\n)\n\n => Array\n(\n => 171.61.147.105\n)\n\n => Array\n(\n => 14.98.147.214\n)\n\n => Array\n(\n => 209.234.253.191\n)\n\n => Array\n(\n => 92.38.148.60\n)\n\n => Array\n(\n => 178.128.104.139\n)\n\n => Array\n(\n => 212.154.0.176\n)\n\n => Array\n(\n => 103.41.24.141\n)\n\n => Array\n(\n => 2.58.194.132\n)\n\n => Array\n(\n => 180.190.78.169\n)\n\n => Array\n(\n => 106.215.45.182\n)\n\n => Array\n(\n => 125.63.100.222\n)\n\n => Array\n(\n => 110.54.247.17\n)\n\n => Array\n(\n => 103.26.85.105\n)\n\n => Array\n(\n => 39.42.147.3\n)\n\n => Array\n(\n => 137.97.51.41\n)\n\n => Array\n(\n => 71.202.72.27\n)\n\n => Array\n(\n => 119.155.35.10\n)\n\n => Array\n(\n => 202.47.43.120\n)\n\n => Array\n(\n => 183.83.64.101\n)\n\n => Array\n(\n => 182.68.106.141\n)\n\n => Array\n(\n => 171.61.187.87\n)\n\n => Array\n(\n => 178.162.198.118\n)\n\n => Array\n(\n => 115.97.151.218\n)\n\n => Array\n(\n => 196.207.184.210\n)\n\n => Array\n(\n => 198.16.70.51\n)\n\n => Array\n(\n => 41.60.237.33\n)\n\n => Array\n(\n => 47.11.86.26\n)\n\n => Array\n(\n => 117.217.201.183\n)\n\n => Array\n(\n => 203.192.241.79\n)\n\n => Array\n(\n => 122.165.119.85\n)\n\n => Array\n(\n => 23.227.142.218\n)\n\n => Array\n(\n => 178.128.104.221\n)\n\n => Array\n(\n => 14.192.54.163\n)\n\n => Array\n(\n => 139.5.253.218\n)\n\n => Array\n(\n => 117.230.140.127\n)\n\n => Array\n(\n => 195.114.149.199\n)\n\n => Array\n(\n => 14.239.180.220\n)\n\n => Array\n(\n => 103.62.155.94\n)\n\n => Array\n(\n => 118.71.97.14\n)\n\n => Array\n(\n => 137.97.55.163\n)\n\n => Array\n(\n => 202.47.49.198\n)\n\n => Array\n(\n => 171.61.177.85\n)\n\n => Array\n(\n => 137.97.190.224\n)\n\n => Array\n(\n => 117.230.34.142\n)\n\n => Array\n(\n => 103.41.32.5\n)\n\n => Array\n(\n => 203.90.82.237\n)\n\n => Array\n(\n => 125.63.124.238\n)\n\n => Array\n(\n => 103.232.128.78\n)\n\n => Array\n(\n => 106.197.14.227\n)\n\n => Array\n(\n => 81.17.242.244\n)\n\n => Array\n(\n => 81.19.210.179\n)\n\n => Array\n(\n => 103.134.94.98\n)\n\n => Array\n(\n => 110.38.0.86\n)\n\n => Array\n(\n => 103.10.224.195\n)\n\n => Array\n(\n => 45.118.166.89\n)\n\n => Array\n(\n => 115.186.186.68\n)\n\n => Array\n(\n => 138.197.129.237\n)\n\n => Array\n(\n => 14.247.162.52\n)\n\n => Array\n(\n => 103.255.4.5\n)\n\n => Array\n(\n => 14.167.188.254\n)\n\n => Array\n(\n => 5.62.59.54\n)\n\n => Array\n(\n => 27.122.14.80\n)\n\n => Array\n(\n => 39.53.240.21\n)\n\n => Array\n(\n => 39.53.241.243\n)\n\n => Array\n(\n => 117.230.130.161\n)\n\n => Array\n(\n => 118.71.191.149\n)\n\n => Array\n(\n => 5.188.95.54\n)\n\n => Array\n(\n => 66.45.250.27\n)\n\n => Array\n(\n => 106.215.6.175\n)\n\n => Array\n(\n => 27.122.14.86\n)\n\n => Array\n(\n => 103.255.4.51\n)\n\n => Array\n(\n => 101.50.93.119\n)\n\n => Array\n(\n => 137.97.183.51\n)\n\n => Array\n(\n => 117.217.204.185\n)\n\n => Array\n(\n => 95.104.106.82\n)\n\n => Array\n(\n => 5.62.56.211\n)\n\n => Array\n(\n => 103.104.181.214\n)\n\n => Array\n(\n => 36.72.214.243\n)\n\n => Array\n(\n => 5.62.62.219\n)\n\n => Array\n(\n => 110.36.202.4\n)\n\n => Array\n(\n => 103.255.4.253\n)\n\n => Array\n(\n => 110.172.138.61\n)\n\n => Array\n(\n => 159.203.24.195\n)\n\n => Array\n(\n => 13.229.88.42\n)\n\n => Array\n(\n => 59.153.235.20\n)\n\n => Array\n(\n => 171.236.169.32\n)\n\n => Array\n(\n => 14.231.85.206\n)\n\n => Array\n(\n => 119.152.54.103\n)\n\n => Array\n(\n => 103.80.117.202\n)\n\n => Array\n(\n => 223.179.157.75\n)\n\n => Array\n(\n => 122.173.68.249\n)\n\n => Array\n(\n => 188.163.72.113\n)\n\n => Array\n(\n => 119.155.20.164\n)\n\n => Array\n(\n => 103.121.43.68\n)\n\n => Array\n(\n => 5.62.58.6\n)\n\n => Array\n(\n => 203.122.40.154\n)\n\n => Array\n(\n => 222.254.96.203\n)\n\n => Array\n(\n => 103.83.148.167\n)\n\n => Array\n(\n => 103.87.251.226\n)\n\n => Array\n(\n => 123.24.129.24\n)\n\n => Array\n(\n => 137.97.83.8\n)\n\n => Array\n(\n => 223.225.33.132\n)\n\n => Array\n(\n => 128.76.175.190\n)\n\n => Array\n(\n => 195.85.219.32\n)\n\n => Array\n(\n => 139.167.102.93\n)\n\n => Array\n(\n => 49.15.198.253\n)\n\n => Array\n(\n => 45.152.183.172\n)\n\n => Array\n(\n => 42.106.180.136\n)\n\n => Array\n(\n => 95.142.120.9\n)\n\n => Array\n(\n => 139.167.236.4\n)\n\n => Array\n(\n => 159.65.72.167\n)\n\n => Array\n(\n => 49.15.89.2\n)\n\n => Array\n(\n => 42.201.161.195\n)\n\n => Array\n(\n => 27.97.210.38\n)\n\n => Array\n(\n => 171.241.45.19\n)\n\n => Array\n(\n => 42.108.2.18\n)\n\n => Array\n(\n => 171.236.40.68\n)\n\n => Array\n(\n => 110.93.82.102\n)\n\n => Array\n(\n => 43.225.24.186\n)\n\n => Array\n(\n => 117.230.189.119\n)\n\n => Array\n(\n => 124.123.147.187\n)\n\n => Array\n(\n => 216.151.184.250\n)\n\n => Array\n(\n => 49.15.133.16\n)\n\n => Array\n(\n => 49.15.220.74\n)\n\n => Array\n(\n => 157.37.221.246\n)\n\n => Array\n(\n => 176.124.233.112\n)\n\n => Array\n(\n => 118.71.167.40\n)\n\n => Array\n(\n => 182.185.213.161\n)\n\n => Array\n(\n => 47.31.79.248\n)\n\n => Array\n(\n => 223.179.238.192\n)\n\n => Array\n(\n => 79.110.128.219\n)\n\n => Array\n(\n => 106.210.42.111\n)\n\n => Array\n(\n => 47.247.214.229\n)\n\n => Array\n(\n => 193.0.220.108\n)\n\n => Array\n(\n => 1.39.206.254\n)\n\n => Array\n(\n => 123.201.77.38\n)\n\n => Array\n(\n => 115.178.207.21\n)\n\n => Array\n(\n => 37.111.202.92\n)\n\n => Array\n(\n => 49.14.179.243\n)\n\n => Array\n(\n => 117.230.145.171\n)\n\n => Array\n(\n => 171.229.242.96\n)\n\n => Array\n(\n => 27.59.174.209\n)\n\n => Array\n(\n => 1.38.202.211\n)\n\n => Array\n(\n => 157.37.128.46\n)\n\n => Array\n(\n => 49.15.94.80\n)\n\n => Array\n(\n => 123.25.46.147\n)\n\n => Array\n(\n => 117.230.170.185\n)\n\n => Array\n(\n => 5.62.16.19\n)\n\n => Array\n(\n => 103.18.22.25\n)\n\n => Array\n(\n => 103.46.200.132\n)\n\n => Array\n(\n => 27.97.165.126\n)\n\n => Array\n(\n => 117.230.54.241\n)\n\n => Array\n(\n => 27.97.209.76\n)\n\n => Array\n(\n => 47.31.182.109\n)\n\n => Array\n(\n => 47.30.223.221\n)\n\n => Array\n(\n => 103.31.94.82\n)\n\n => Array\n(\n => 103.211.14.45\n)\n\n => Array\n(\n => 171.49.233.58\n)\n\n => Array\n(\n => 65.49.126.95\n)\n\n => Array\n(\n => 69.255.101.170\n)\n\n => Array\n(\n => 27.56.224.67\n)\n\n => Array\n(\n => 117.230.146.86\n)\n\n => Array\n(\n => 27.59.154.52\n)\n\n => Array\n(\n => 132.154.114.10\n)\n\n => Array\n(\n => 182.186.77.60\n)\n\n => Array\n(\n => 117.230.136.74\n)\n\n => Array\n(\n => 43.251.94.253\n)\n\n => Array\n(\n => 103.79.168.225\n)\n\n => Array\n(\n => 117.230.56.51\n)\n\n => Array\n(\n => 27.97.187.45\n)\n\n => Array\n(\n => 137.97.190.61\n)\n\n => Array\n(\n => 193.0.220.26\n)\n\n => Array\n(\n => 49.36.137.62\n)\n\n => Array\n(\n => 47.30.189.248\n)\n\n => Array\n(\n => 109.169.23.84\n)\n\n => Array\n(\n => 111.119.185.46\n)\n\n => Array\n(\n => 103.83.148.246\n)\n\n => Array\n(\n => 157.32.119.138\n)\n\n => Array\n(\n => 5.62.41.53\n)\n\n => Array\n(\n => 47.8.243.236\n)\n\n => Array\n(\n => 112.79.158.69\n)\n\n => Array\n(\n => 180.92.148.218\n)\n\n => Array\n(\n => 157.36.162.154\n)\n\n => Array\n(\n => 39.46.114.47\n)\n\n => Array\n(\n => 117.230.173.250\n)\n\n => Array\n(\n => 117.230.155.188\n)\n\n => Array\n(\n => 193.0.220.17\n)\n\n => Array\n(\n => 117.230.171.166\n)\n\n => Array\n(\n => 49.34.59.228\n)\n\n => Array\n(\n => 111.88.197.247\n)\n\n => Array\n(\n => 47.31.156.112\n)\n\n => Array\n(\n => 137.97.64.180\n)\n\n => Array\n(\n => 14.244.227.18\n)\n\n => Array\n(\n => 113.167.158.8\n)\n\n => Array\n(\n => 39.37.175.189\n)\n\n => Array\n(\n => 139.167.211.8\n)\n\n => Array\n(\n => 73.120.85.235\n)\n\n => Array\n(\n => 104.236.195.72\n)\n\n)\n```\nArchive for December, 2008: Counting Pennies\n << Back to all Blogs Login or Create your own free blog Layout: Blue and Brown (Default) Author's Creation\nHome > Archive: December, 2008",
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"# Archive for December, 2008\n\n## Winter Cleaning?\n\nDecember 28th, 2008 at 04:49 am\n\nToday I just got bitten by the cleaning bug. I packed up most of my Holiday decorations except for the Tree. I like looking at it so I'm going to wait a couple of more days to take it down. But everything else is packed away. Speaking of Holiday stuff. I bought Christmas wrapping paper on sale at Cost Plus Market for \\$0.50 EACH. Original Price was \\$2.99. That's crazy. But I kept my cool and only bought 3 that I really liked. So I have some for next year. I'm trying really hard not to overspend next year or any year after that.\n\nBack to cleaning, I dumped all my magazine before Dec in the recycle. I organized all my paperwork into binders with labels and everything I need at easy access. I even saved all my photos on my computer to disk just in case something happens to my computer.\n\nAnd I did a bunch of other little things. I figure I better ring in the New Year right.\n\nI got a sewing machine from my Grandma for Christmas. I love it. She couldn't have picked a more perfect gift for me. And I don't even remember ever mentioning secretly wanting one. Now I can make all my crafty stuff. I already put it to good use and sewed a tote bag, two to be exact. And the best part yet, my grandma also had big box of fabric pieces that she was going to throw out. Now I have all this fabric for free! Talk about providing hours of entertainment for free, lol.\n\nMy goal this week is to spend less than \\$50. I think this is doable. I mean I already filled up gas Yesterday so I won't be needing gas for at least another week and a half. I don't spend any money on food because I eat breakfast at home and I take my lunch everyday and dinner is usually on the table once I get home. I love Grandma's house, hehe(but can't wait to get on my own!). And that's pretty much it. I can't see whatelse I would spend money on this upcoming week but we shall see. Bills don't count because I have already planned for those to come out once my paycheck hits. Trying to cut back on the non-essential spending. So far so good.\n\n## Updated Numbers\n\nDecember 24th, 2008 at 07:06 am\n\nEh, I figured I might as well do it now or I'm never going to do it. My overdo update.\n\nOuch. Okay so now that I have a job for the time being I'm able to rebuild my savings.\n\nSo here it goes\n\nSavings #1 10,149.00\nSavings #2 1,260.00\nSavings #3 380.00\n\nIRA 1550.00\n401k(which is now a Roll-over IRA from previous job) - 1089.00 (lost from that huge stock market plunge back in september)\n\nCC debt 1,195.00 YIKES\nStudent Loan 14,320.00\n\nso for the time being i get paid weekly.\nMy paycheck varies because of the amount of overtime that I work. But I'm automatically transferring \\$50 to Savings #1, \\$75 to Savings #2, \\$25 to Savings #3 every paycheck. The rest goes towards CC debt and other bill money. I know I could just pay off my Credit Card debt in one swoop. But since I'm only working contract I really want to keep my savings in tact just in case I don't have work once this contract ends.\n\nQuick question. I don't know if anyone knows the answer to this. Since I moved to another state and is now working in another state. I have to file 2 tax returns right? Since I lived in Virginia for most of the year, I file Virginia first right? And then California?\n\n## My Goals.\n\nDecember 22nd, 2008 at 06:30 am\n\nSo I think I have some 2009 goals. I'm not into making resolutions because to be honest I never keep them. But, if I just make goals, for some reason I have more motivation to complete them. I had goals for 2008, they sort of went out the window once I decided to move across country. But for 2009 I see no such drastic changes for the most part.\n\n1. To land a PERMANENT full-time job. I'm doing the contract thing right now because, hey it's something which is better than nothing.\n\n2. To have my own place by the end of the year. Most like rent because I want to be able to put down a good size down payment on a place, but I need my own space.\n\n3. To build back up my savings. Particularly Savings #2&3. \\$3000 for Savings #2 and \\$1500 for #3 by the end of the year.\n\n4. To have \\$12,000 in Savings #1\n\n5. To have my student loan down to \\$11,500 by the end of the year. It is around 14,000 I believe. I have to double check.\n\n6. To have no credit card debt, right now I have a balance because of Christmas. But once I get it paid off no more credit card debt.\n\n7. To finish my accounting classes\n\n8. ????\n\nI'll have to finish this up later because I can't think right now, I'm so sleepy. So I'll have to think of 3 more to round it off to 10 goals for 2009. And then I also need to update my stats.\n\n## Yikes it's been AWHILE!\n\nDecember 11th, 2008 at 05:09 am\n\nGeez, I didn't realize how much time has past since I last posted.\n\nWell I've been busy moving. I moved at the end of September to the Bay Area in California. It's been quite an adjustment, more than I thought it would be. I am getting use to it as everyday passes by. At least now I'm not quite so worried about getting lost. I didn't work for almost 2 months. So my finance took quite a hit. I haven't quite hit below \\$10,000 on savings yet. I'll have to update my stats soon. But luckily I was able to land a temp job in the mean time as an Sales Auditor. Basically I reconcile this company's sales for their stores. I will be temping with this company until the end of January possibly February. But hey at least I'm working now and I'm finally getting stuff to put on my resume.\n\nIt's a good thing that I'm staying with family for the time being. But I really am motivated to hurry up and get on my feet and get on my own.\n\nI'm also started taking an accounting class at UC Berkeley online. It's through their continuing education program. This way I'm getting more accounting background to add to my finance degree. It an entire accounting certificate program. At least this will keep me until I get the funds to go to grad school and get my MBA.\n\nBut yeah, so far so good. I'll have to update everything soon, maybe this weekend once I have more time to sit down and get everything together again. Still unpacking yet hehe."
] | [
null,
"https://www.savingadvice.com/blogs/images/search/top_left.php",
null,
"https://www.savingadvice.com/blogs/images/search/top_right.php",
null,
"https://www.savingadvice.com/blogs/images/search/bottom_left.php",
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.9763667,"math_prob":0.9933937,"size":6153,"snap":"2020-10-2020-16","text_gpt3_token_len":1546,"char_repetition_ratio":0.09351114,"word_repetition_ratio":0.0099502485,"special_character_ratio":0.26263613,"punctuation_ratio":0.110869564,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99692523,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-04-02T13:19:42Z\",\"WARC-Record-ID\":\"<urn:uuid:afb72e0b-9cb2-40dd-b932-3e958c3c7fd6>\",\"Content-Length\":\"121799\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:8f1e5bad-7f86-4f48-85d6-b74503b3320a>\",\"WARC-Concurrent-To\":\"<urn:uuid:f9ac8beb-b022-4642-a09b-6fd650b492f0>\",\"WARC-IP-Address\":\"173.231.200.26\",\"WARC-Target-URI\":\"https://countingpennies.savingadvice.com/2008/12/\",\"WARC-Payload-Digest\":\"sha1:HONOUVF3VFMJDDYTAX4UM3V43TSDVMZF\",\"WARC-Block-Digest\":\"sha1:TCUG4YU7LS6YSWZPZ4NPPCBJF6H5BGSF\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-16/CC-MAIN-2020-16_segments_1585370506959.34_warc_CC-MAIN-20200402111815-20200402141815-00528.warc.gz\"}"} |
https://republicofsouthossetia.org/question/write-an-equation-in-slope-intercept-form-of-the-line-that-is-perpendicular-to-y-2-5-and-passes-15163245-98/ | [
"## Write an equation, in slope-intercept form, of the line that is perpendicular to y = 2x – 5 and passes through the point (2, -3).\n\nQuestion\n\nWrite an equation, in slope-intercept form, of the line that is perpendicular to y = 2x – 5 and passes through the point (2, -3).\n\nin progress 0\n3 weeks 2021-09-08T06:23:01+00:00 1 Answer 0"
] | [
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https://howchoo.com/math/how-to-factor | [
"## What is a factor?\n\nA factor of a number divides that number. It can be multiplied by another factor to equal the target number.\n\nFor example, the factors of 12 are:\n\n1, 2, 3, 4, 6, & 12\n\nBy definition, you can multiply any of these factors by some other factor to equal 12.\n\n1 x 12 = 12 2 x 6 = 12 3 x 4 = 12\n\nThe numbers on the left are all the factors of 12.\n\n## Every number has at least 2 factors\n\nThis may be obvious, but each number can be divided by 1 and itself.\n\nIf we wanted to find all of the factors of 12, we could start with 12 and 1.\n\n## From 2 to n / 2 test each number to see if it is a factor\n\nTo find the factors of 12, we already know that 1 and 12 are factors.\n\nNext, we know that (besides 12) no number higher than 6 (12 / 2) can be a factor. So we can start at 2 and test each number up to 6 to see if is a factor of 12.\n\n2) 12 / 2 = 6 yes 3) 12 / 3 = 4 yes 4) 12 / 4 = 3 yes 5) 12 / 5 = 2.4 no 6) 12 / 6 = 2 yes\n\nSo to 1 and 12 we can add 2, 3, 4 and 6.\n\n2 minutes\n\nLearn how to divide fractions in a few simple steps."
] | [
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] | {"ft_lang_label":"__label__en","ft_lang_prob":0.90416074,"math_prob":0.9994834,"size":898,"snap":"2021-21-2021-25","text_gpt3_token_len":314,"char_repetition_ratio":0.16331096,"word_repetition_ratio":0.009259259,"special_character_ratio":0.38864142,"punctuation_ratio":0.112068966,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99971706,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-05-19T00:47:03Z\",\"WARC-Record-ID\":\"<urn:uuid:59aaed56-95ca-4092-9a09-c825a4ac7192>\",\"Content-Length\":\"547967\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:83434f92-ac10-427c-8d4a-5c340d0247cc>\",\"WARC-Concurrent-To\":\"<urn:uuid:d034b027-ef4e-4694-92ae-335add2d8e15>\",\"WARC-IP-Address\":\"151.101.194.133\",\"WARC-Target-URI\":\"https://howchoo.com/math/how-to-factor\",\"WARC-Payload-Digest\":\"sha1:AKL4PBHMM6ALVMQ6OKXMFNNDIYKISO5D\",\"WARC-Block-Digest\":\"sha1:SADE5WPJ4HJGX5CPM56DA3QVN4GXN66Q\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-21/CC-MAIN-2021-21_segments_1620243989874.84_warc_CC-MAIN-20210518222121-20210519012121-00180.warc.gz\"}"} |
https://www.tutorialspoint.com/check-if-a-number-can-be-expressed-as-a-b-in-cplusplus | [
"# Check if a number can be expressed as a^b in C++\n\nC++Server Side ProgrammingProgramming\n\nHere we will check whether we can represent a number like ab or not. Suppose a number 125 is present. This can be represented as 53. Another number 91 cannot be represented as power of some integer value.\n\n## Algorithm\n\nisRepresentPower(num):\nBegin\nif num = 1, then return true\nfor i := 2, i2 <= num, increase i by 1, do\nval := log(a)/log(i)\nif val – int(val) < 0.0000000001, then return true\ndone\nreturn false\nEnd\n\n## Example\n\nLive Demo\n\n#include<iostream>\n#include<cmath>\nusing namespace std;\nbool isRepresentPower(int num) {\nif (num == 1)\nreturn true;\nfor (int i = 2; i * i <= num; i++) {\ndouble val = log(num) / log(i);\nif ((val - (int)val) < 0.00000001)\nreturn true;\n}\nreturn false;\n}\nint main() {\nint n = 125;\ncout << (isRepresentPower(n) ? \"Can be represented\" : \"Cannot be represented\");\n}\n\n## Output\n\nCan be represented"
] | [
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https://e-eduanswers.com/mathematics/question12696250 | [
" What is the quotient (х3 + 6х2 + 11х + 6) divided by (х2 + 4х + 3)?",
null,
"",
null,
"# What is the quotient (х3 + 6х2 + 11х + 6) divided by (х2 + 4х + 3)?",
null,
"### Similar questions",
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"",
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"Do you know the correct answer?\nWhat is the quotient (х3 + 6х2 + 11х + 6) divided by (х2 + 4х + 3)?...\n\n### Questions in other subjects:",
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"Total solved problems on the site: 13538348"
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https://clojure-south.com/core-logic/ | [
"# Core.logic – From solving puzzles to finding proofs\n\n### Description\n\nFor this presentation I want to follow the steps of two books from the The Little Schemer series: The Reasoned Schemer and The Little Prover. The Little Prover examples are build upon J-Bob, a proof assistant based on the ACL2 (A Computational Logic for Applicative Common Lisp”) theorem prover. For this talk I’ll be using a port for clojure made by juxtin, called clj-bob.Logic programming depends on logic variables (or lvars, variables that can take sereval values, but only one at a time), a set of constraints (expressions that limit the values the lvars may assume) and a solution engine in order to find a value that satisfies the logic expression as a whole.The idea is to work on a specific (unsolvable) puzzle from the book GEB (Gödel, Escher, Bach) and work through it on one side from core.logic, using it as a rule system in which we define, declaratively, the rules of the system and try to solve it making attempts to find a value that satisfies this set of rules. On the other side, we will use the proof assistant in order to validate wether the “proof” for this unsolvability is really a proof.\n\nFor this talk I’ll be using a port for clojure made by juxtin, called clj-bob.Logic programming depends on logic variables (or lvars, variables that can take sereval values, but only one at a time), a set of constraints (expressions that limit the values the lvars may assume) and a solution engine in order to find a value that satisfies the logic expression as a whole.The idea is to work on a specific (unsolvable) puzzle from the book GEB (Gödel, Escher, Bach) and work through it on one side from core.logic, using it as a rule system in which we define, declaratively, the rules of the system and try to solve it making attempts to find a value that satisfies this set of rules.\nOn the other side, we will use the proof assistant in order to validate wether the “proof” for this unsolvability is really a proof.\n\n### Speakers\n\nErick Santana\nInsatiable learner, solver of puzzles and designer of fun.\nI have become passionate about Lisp after reading the article “Beating the Averages”, started to understand it after reading “The Little Schemer” and have used it professionally while working at Nubank."
] | [
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http://users.cs.cf.ac.uk/Dave.Marshall/PERL/node96.html | [
"",
null,
"",
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"",
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"",
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"Next: Example: Using the Translation Up: Some Practical Examples Previous: Using the Match Operator\n\n## Using the Substitution Operator\n\nHere are some handy uses of the match operator:\n\n• If you need to remove white space from the beginning of a string, you can do this:\n\n```s/\\^\\s+//;\n```\n\nThis pattern uses the `\\`s predefined character class to match any whitespace character. The plus sign means to match zero or more white space characters, and the caret means match only at the beginning of the string.\n\n• If you need to remove whitespace from the end of a string, you can do this:\n\n```s/\\s+\\$//;\n```\n\nThis pattern uses the `\\`s predefined character class to match any whitespace character. The plus sign means to match zero or more white space characters, and the dollar sign means match only at the end of the string.\n\n• If you need to add a prefix to a string, you can do this:\n\n```\\$prefix = \"A\";\ns/^(.*)/\\$prefix\\$1/;\n```\n\nWhen the substitution is done, the value in the \\$prefix variable will be added to the beginning of the \\$_ variable. This is done by using variable interpolation and pattern memory. Of course, you also might consider using the string concatenation operator; for instance, \\$_ = \"A\" . \\$_;, which is probably faster.\n\n• If you need to add a suffix to a string, you can do this:\n\n```\\$suffix = \"Z\";\ns/^(.*)/\\$1\\$suffix/;\n```\n\nWhen the substitution is done, the value in the \\$suffix variable will be added to the end of the \\$_ variable. This is done by using variable interpolation and pattern memory. Of course, you also might consider using the string concatenation operator; for instance, \\$_ .= \"Z\";, which is probably faster.\n\n• If you need to reverse the first two words in a string, you can do this:\n\n```s/^\\s*(\\w+)\\W+(\\w+)/\\$2 \\$1/;\n```\n\nThis substitution statement uses the pattern memory variables \\$1 and \\$2 to reverse the first two words in a string. You can use a similar technique to manipulate columns of information, the last two words, or even to change the order of more than two matches.\n\n• If you need to duplicate each character in a string, you can do this:\n\n```s/\\w/\\$& x 2/eg;}\n```\n\nWhen the substitution is done, each character in \\$_ will be repeated. If the original string was \"123abc\", the new string would be \"112233aabbcc\". The e option is used to force evaluation of the replacement string. The \\$& special variable is used in the replacement pattern to reference the matched string, which then is repeated by the string repetition operator.\n\n• If you need to capitalize all the words in a sentence, you can do this:\n\n```s/\\(w+)/\\u\\$1/g;}\n```\n\nWhen the substitution is done, each character in \\$_ will have its first letter capitalized. The /g option means that each word-the `\\`w+ meta-sequence-will be matched and placed in \\$1. Then it will be replaced by `\\`u\\$1. The `\\`u will capitalize whatever follows it; in this case, it's the matched word.\n\n• If you need to insert a string between two repeated characters, you can do this:\n\n```\\$_ = \"!!!!\";\n\\$char = \"!\";\n\\$insert = \"AAA\";\n\ns{\n(\\$char) # look for the specified character.\n(?=\\$char) # look for it again, but don't include\n# it in the matched string, so the next\n} # search also will find it.\n{\n\\$char . \\$insert # concatenate the specified character\n# with the string to insert.\n}xeg; # use extended mode, evaluate the\n# replacement pattern, and match all\n# possible strings.\nprint(\"\\$_\\n\");\n```\n\nThis example uses the extended mode to add comments directly inside the regular expression. This makes it easy to relate the comment directly to a specific pattern element. The match pattern does not directly reflect the originally stated goal of inserting a string between two repeated characters. Instead, the example was quietly restated. The new goal is to substitute all instances of \\$char with \\$char. \\$insert, if \\$char is followed by \\$char. As you can see, the end result is the same. Remember that sometimes you need to think outside the box.\n\n• If you need to do a second level of variable interpolation in the replacement pattern, you can do this:\n\n```\ns/(\\\\\\$\\w+)/\\\\$1/eeg;\n```\n\nThis is a simple example of secondary variable interpolation. If \\$firstVar =\"AAA\" and \\$_ = '\\$firstVar', then \\$_ would be equal to \"AAA\" after the substitution was made. The key is that the replacement pattern is evaluated twice. This technique is very powerful. It can be used to develop error messages used with variable interpolation.\n\n```\\$errMsg = \"File too large\";\n\\$fileName = \"DATA.OUT\";\n\\$_ = 'Error: \\$errMsg for the file named \\$fileName';\ns/(\\\\$\\w+)/\\$1/eeg;\nprint;\n```\n\nWhen this program is run, it will display\n\nError: File too large for the file named DATA.OUT\n\nThe values of the \\$errMsg and \\$fileName variables were interpolated into the replacement pattern as needed.",
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"Next: Example: Using the Translation Up: Some Practical Examples Previous: Using the Match Operator\[email protected]"
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https://www.roadlesstraveledstore.com/how-many-transistors-are-in-a-cmos-nand-gate/ | [
"# How many transistors are in a CMOS NAND gate?\n\n## How many transistors are in a CMOS NAND gate?\n\nCMOS is made up of NMOS and PMOS transistors. A NOT gate requires 2 transistors, 1 NMOS and 1 PMOS. A NAND gate requires 4, a 2 input AND requires 6. A 4 input NAND gate requires 8 transistors, add an inverter and you have 10 transistors.\n\n## What is CMOS NAND gate?\n\nCMOS NAND Gate It consists of two series NMOS transistors between Y and Ground and two parallel PMOS transistors between Y and VDD. If either input A or B is logic 0, at least one of the NMOS transistors will be OFF, breaking the path from Y to Ground. Hence, the output will be logic low.\n\nWhat is level transistor?\n\ntransistor level, not the gate level. ◆ Opens possibility of verifiying a third-party artifact. without access to higher-level representation. ◆ Very hard.\n\nWhat is CMOS level?\n\nCMOS gate circuits have input and output signal specifications that are quite different from TTL. For a CMOS gate operating at a power supply voltage of 5 volts, the acceptable input signal voltages range from 0 volts to 1.5 volts for a “low” logic state, and 3.5 volts to 5 volts for a “high” logic state.\n\n### How many transistors are in a 3 NAND gate?\n\n6 transistors\nAn alternative design for the 3-input NAND gate uses CMOS transistors as building blocks, as shown in Figure 4.2. This circuit needs only 6 transistors, and is symmetric w.r.t. its inputs.\n\n### How is NAND and NOR gate using CMOS technology?\n\nNAND and NOR gate using CMOS Technology. For the design of any circuit with the CMOS technology; We need parallel or series connections of nMOS and pMOS with a nMOS source tied directly or indirectly to ground and a pMOS source tied directly or indirectly to V dd. A basic CMOS structure of any 2-input logic gate can be drawn as follows:\n\nHow big is a NAND NAND gate transistor?\n\nNAND implementation: Therefore, for the 3-ip NAND gate implementation, each PDN n-MOS transistor will be: 3*0.89µm = 2.67µm and each p-MOS transistor in the PUN network will be: 2.23µm NOR implementation: For a 3-ip NOR gate implementation, each PDN n-MOS transistor will be: 0.89µm Each PUN p-MOS transistor will be 3*2.23µm = 6.69µm\n\nHow are transistor levels used in CMOS design?\n\nThe method is based on the use of mixed logic concepts. The input variables should have a designated assertion level (i.e. Assert Low or Assert High). In CMOS designs, two transistor structures (one pmos and one nmos) are required for implementing the functional expression.\n\n#### How are NMOS and PMOS transistors approximated as ideal switches?\n\nThe nmos and pmos transistors are approximated as ideal switches. Included in this paper are examples of several CMOS logic circuits implemented at the transistor level along with a design method for the implementation of CMOS combinational logic circuits.",
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"08/11/2020"
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https://openstax.org/books/elementary-algebra-2e/pages/4-3-graph-with-intercepts | [
"Elementary Algebra 2e\n\n# 4.3Graph with Intercepts\n\nElementary Algebra 2e4.3 Graph with Intercepts\nBe Prepared 4.6\n\nBefore you get started, take this readiness quiz.\n\nSolve: $3·0+4y=−2.3·0+4y=−2.$\nIf you missed this problem, review Example 2.17.\n\n### Identify the x- and y- Intercepts on a Graph\n\nEvery linear equation can be represented by a unique line that shows all the solutions of the equation. We have seen that when graphing a line by plotting points, you can use any three solutions to graph. This means that two people graphing the line might use different sets of three points.\n\nAt first glance, their two lines might not appear to be the same, since they would have different points labeled. But if all the work was done correctly, the lines should be exactly the same. One way to recognize that they are indeed the same line is to look at where the line crosses the x- axis and the y- axis. These points are called the intercepts of the line.\n\n### Intercepts of a Line\n\nThe points where a line crosses the x- axis and the y- axis are called the intercepts of a line.\n\nLet’s look at the graphs of the lines in Figure 4.18.\n\nFigure 4.18 Examples of graphs crossing the x-negative axis.\n\nFirst, notice where each of these lines crosses the $xx$ negative axis. See Figure 4.18.\n\n Figure The line crosses the x- axis at: Ordered pair of this point Figure (a) 3 $(3,0)(3,0)$ Figure (b) 4 $(4,0)(4,0)$ Figure (c) 5 $(5,0)(5,0)$ Figure (d) 0 $(0,0)(0,0)$\nTable 4.24\n\nDo you see a pattern?\n\nFor each row, the y- coordinate of the point where the line crosses the x- axis is zero. The point where the line crosses the x- axis has the form $(a,0)(a,0)$ and is called the x- intercept of a line. The x- intercept occurs when $yy$ is zero.\n\nNow, let’s look at the points where these lines cross the y- axis. See Table 4.25.\n\n Figure The line crosses the y-axis at: Ordered pair for this point Figure (a) 6 $(0,6)(0,6)$ Figure (b) $−3−3$ $(0,−3)(0,−3)$ Figure (c) $−5−5$ $(0,−5)(0,−5)$ Figure (d) 0 $(0,0)(0,0)$\nTable 4.25\n\nWhat is the pattern here?\n\nIn each row, the x- coordinate of the point where the line crosses the y- axis is zero. The point where the line crosses the y- axis has the form $(0,b)(0,b)$ and is called the y- intercept of the line. The y- intercept occurs when $xx$ is zero.\n\n### x- intercept and y- intercept of a line\n\nThe x- intercept is the point $(a,0)(a,0)$ where the line crosses the x- axis.\n\nThe y- intercept is the point $(0,b)(0,b)$ where the line crosses the y- axis.",
null,
"### Example 4.19\n\nFind the x- and y- intercepts on each graph.",
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"Try It 4.37\n\nFind the x- and y- intercepts on the graph.",
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"Try It 4.38\n\nFind the x- and y- intercepts on the graph.",
null,
"### Find the x- and y- Intercepts from an Equation of a Line\n\nRecognizing that the x- intercept occurs when y is zero and that the y- intercept occurs when x is zero, gives us a method to find the intercepts of a line from its equation. To find the x- intercept, let $y=0y=0$ and solve for x. To find the y- intercept, let $x=0x=0$ and solve for y.\n\n### Find the x- and y- Intercepts from the Equation of a Line\n\nUse the equation of the line. To find:\n\n• the x- intercept of the line, let $y=0 y=0$ and solve for $xx$.\n• the y- intercept of the line, let $x=0x=0$ and solve for $yy$.\n\n### Example 4.20\n\nFind the intercepts of $2x+y=62x+y=6$.\n\nTry It 4.39\n\nFind the intercepts of $3x+y=12.3x+y=12.$\n\nTry It 4.40\n\nFind the intercepts of $x+4y=8.x+4y=8.$\n\n### Example 4.21\n\nFind the intercepts of $4x–3y=124x–3y=12$.\n\nTry It 4.41\n\nFind the intercepts of $3x–4y=12.3x–4y=12.$\n\nTry It 4.42\n\nFind the intercepts of $2x–4y=8.2x–4y=8.$\n\n### Graph a Line Using the Intercepts\n\nTo graph a linear equation by plotting points, you need to find three points whose coordinates are solutions to the equation. You can use the x- and y- intercepts as two of your three points. Find the intercepts, and then find a third point to ensure accuracy. Make sure the points line up—then draw the line. This method is often the quickest way to graph a line.\n\n### Example 4.22How to Graph a Line Using Intercepts\n\nGraph $–x+2y=6–x+2y=6$ using the intercepts.\n\nTry It 4.43\n\nGraph $x–2y=4x–2y=4$ using the intercepts.\n\nTry It 4.44\n\nGraph $–x+3y=6–x+3y=6$ using the intercepts.\n\nThe steps to graph a linear equation using the intercepts are summarized below.\n\n### How To\n\n#### Graph a linear equation using the intercepts.\n\n1. Step 1. Find the x- and y- intercepts of the line.\n• Let $y=0y=0$ and solve for $xx$\n• Let $x=0x=0$ and solve for $yy$.\n2. Step 2. Find a third solution to the equation.\n3. Step 3. Plot the three points and check that they line up.\n4. Step 4. Draw the line.\n\n### Example 4.23\n\nGraph $4x–3y=124x–3y=12$ using the intercepts.\n\nTry It 4.45\n\nGraph $5x–2y=105x–2y=10$ using the intercepts.\n\nTry It 4.46\n\nGraph $3x–4y=123x–4y=12$ using the intercepts.\n\n### Example 4.24\n\nGraph $y=5xy=5x$ using the intercepts.\n\nTry It 4.47\n\nGraph $y=4xy=4x$ using the intercepts.\n\nTry It 4.48\n\nGraph $y=−xy=−x$ the intercepts.\n\n### Section 4.3 Exercises\n\n#### Practice Makes Perfect\n\nIdentify the x- and y- Intercepts on a Graph\n\nIn the following exercises, find the x- and y- intercepts on each graph.\n\n139.",
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"Find the x- and y- Intercepts from an Equation of a Line\n\nIn the following exercises, find the intercepts for each equation.\n\n151.\n\n$x+y=4x+y=4$\n\n152.\n\n$x+y=3x+y=3$\n\n153.\n\n$x+y=−2x+y=−2$\n\n154.\n\n$x+y=−5x+y=−5$\n\n155.\n\n$x–y=5x–y=5$\n\n156.\n\n$x–y=1x–y=1$\n\n157.\n\n$x–y=−3x–y=−3$\n\n158.\n\n$x–y=−4x–y=−4$\n\n159.\n\n$x+2y=8x+2y=8$\n\n160.\n\n$x+2y=10x+2y=10$\n\n161.\n\n$3x+y=63x+y=6$\n\n162.\n\n$3x+y=93x+y=9$\n\n163.\n\n$x–3y=12x–3y=12$\n\n164.\n\n$x–2y=8x–2y=8$\n\n165.\n\n$4x–y=84x–y=8$\n\n166.\n\n$5x–y=55x–y=5$\n\n167.\n\n$2x+5y=102x+5y=10$\n\n168.\n\n$2x+3y=62x+3y=6$\n\n169.\n\n$3x–2y=123x–2y=12$\n\n170.\n\n$3x–5y=303x–5y=30$\n\n171.\n\n$y=13x+1y=13x+1$\n\n172.\n\n$y=14x−1y=14x−1$\n\n173.\n\n$y=15x+2y=15x+2$\n\n174.\n\n$y=13x+4y=13x+4$\n\n175.\n\n$y=3xy=3x$\n\n176.\n\n$y=−2xy=−2x$\n\n177.\n\n$y=−4xy=−4x$\n\n178.\n\n$y=5xy=5x$\n\nGraph a Line Using the Intercepts\n\nIn the following exercises, graph using the intercepts.\n\n179.\n\n$–x+5y=10–x+5y=10$\n\n180.\n\n$–x+4y=8–x+4y=8$\n\n181.\n\n$x+2y=4x+2y=4$\n\n182.\n\n$x+2y=6x+2y=6$\n\n183.\n\n$x+y=2x+y=2$\n\n184.\n\n$x+y=5x+y=5$\n\n185.\n\n$x+y=−3x+y=−3$\n\n186.\n\n$x+y=−1x+y=−1$\n\n187.\n\n$x–y=1x–y=1$\n\n188.\n\n$x–y=2x–y=2$\n\n189.\n\n$x–y=−4x–y=−4$\n\n190.\n\n$x–y=−3x–y=−3$\n\n191.\n\n$4x+y=44x+y=4$\n\n192.\n\n$3x+y=33x+y=3$\n\n193.\n\n$2x+4y=122x+4y=12$\n\n194.\n\n$3x+2y=123x+2y=12$\n\n195.\n\n$3x–2y=63x–2y=6$\n\n196.\n\n$5x–2y=105x–2y=10$\n\n197.\n\n$2x–5y=−202x–5y=−20$\n\n198.\n\n$3x–4y=−123x–4y=−12$\n\n199.\n\n$3x–y=−63x–y=−6$\n\n200.\n\n$2x–y=−82x–y=−8$\n\n201.\n\n$y=−2xy=−2x$\n\n202.\n\n$y=−4xy=−4x$\n\n203.\n\n$y=xy=x$\n\n204.\n\n$y=3xy=3x$\n\n#### Everyday Math\n\n205.\n\nRoad trip. Damien is driving from Chicago to Denver, a distance of 1000 miles. The x- axis on the graph below shows the time in hours since Damien left Chicago. The y- axis represents the distance he has left to drive.",
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"1. Find the x- and y- intercepts.\n2. Explain what the x- and y- intercepts mean for Damien.\n206.\n\nRoad trip. Ozzie filled up the gas tank of his truck and headed out on a road trip. The x- axis on the graph below shows the number of miles Ozzie drove since filling up. The y- axis represents the number of gallons of gas in the truck’s gas tank.",
null,
"1. Find the x- and y- intercepts.\n2. Explain what the x- and y- intercepts mean for Ozzie.\n\n#### Writing Exercises\n\n207.\n\nHow do you find the x- intercept of the graph of $3x–2y=63x–2y=6$?\n\n208.\n\nDo you prefer to use the method of plotting points or the method using the intercepts to graph the equation $4x+y=−44x+y=−4$? Why?\n\n209.\n\nDo you prefer to use the method of plotting points or the method using the intercepts to graph the equation $y=23x−2y=23x−2$? Why?\n\n210.\n\nDo you prefer to use the method of plotting points or the method using the intercepts to graph the equation $y=6y=6$? Why?\n\n#### Self Check\n\nAfter completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.",
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"What does this checklist tell you about your mastery of this section? What steps will you take to improve?"
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null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.8992952,"math_prob":0.9994424,"size":5637,"snap":"2020-34-2020-40","text_gpt3_token_len":1404,"char_repetition_ratio":0.23752885,"word_repetition_ratio":0.2857143,"special_character_ratio":0.23860209,"punctuation_ratio":0.1012766,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.000003,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38],"im_url_duplicate_count":[null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-08-13T00:12:36Z\",\"WARC-Record-ID\":\"<urn:uuid:11beec65-bf22-4ea0-9ea0-488e34d88977>\",\"Content-Length\":\"317879\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:de5e512f-2abb-4a7b-841d-9163be486c4e>\",\"WARC-Concurrent-To\":\"<urn:uuid:adeb7c76-5ab9-488c-8fff-79f2164574f7>\",\"WARC-IP-Address\":\"99.84.178.127\",\"WARC-Target-URI\":\"https://openstax.org/books/elementary-algebra-2e/pages/4-3-graph-with-intercepts\",\"WARC-Payload-Digest\":\"sha1:XW5IS6I6BIS3DICGXBW4PKC2AM36NK5T\",\"WARC-Block-Digest\":\"sha1:HYEVIEXYGLJXPIZOI24VHH3HSSVOTJ7J\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-34/CC-MAIN-2020-34_segments_1596439738950.31_warc_CC-MAIN-20200812225607-20200813015607-00441.warc.gz\"}"} |
https://zbmath.org/?q=an:1099.90062 | [
"zbMATH — the first resource for mathematics\n\nStrong semismoothness of the Fischer-Burmeister SDC and SOC complementarity functions. (English) Zbl 1099.90062\nSummary: We show that the Fischer-Burmeister complementarity functions, associated to the semidefinite cone (SDC) and the second order cone (SOC), respectively, are strongly semismooth everywhere. Interestingly enough, the proof relys on a relationship between the singular value decomposition of a nonsymmetric matrix and the spectral decomposition of a symmetric matrix.\n\nMSC:\n 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) 90C22 Semidefinite programming 65F15 Numerical computation of eigenvalues and eigenvectors of matrices 65F18 Numerical solutions to inverse eigenvalue problems\nFull Text:\nReferences:\n Bonnans, J.F., Cominetti, R., Shapiro, A.: Second order optimality conditions based on parabolic second order tangent sets. SIAM J. Optim. 9, 466–493 (1999) · Zbl 0990.90127 Borwein, J.M., Lewis, A.S.: Convex Analysis and Nonlinear Optimization: Theory and Examples. Springer-Verlag, New York, 2000 · Zbl 0953.90001 Chen, J., Chen, X., Tseng, P.: Analysis of nonsmooth vector-valued functions associated with second-order cones. Math. Prog. Series B 101, 95–117 (2004) · Zbl 1065.49013 Chen, X., Qi, H., Tseng, P.: Analysis of nonsmooth symmetric-matrix functions with applications to semidefinite complementarity problems. SIAM J. Optim. 13, 960–985 (2003) · Zbl 1076.90042 Chen, X.,Tseng, P.: Non-interior continuation methods for solving semidefinite complementarity problems. Math. Prog. 95, 431–474 (2003) · Zbl 1023.90046 Chen, X.D., Sun, D., Sun, J.: Complementarity functions and numerical experiments on some smoothing Newton methods for second-order-cone complementarity problems. Comput. Optim. Appl. 25, 39–56 (2003) · Zbl 1038.90084 Chu, M.T.: Inverse eigenvalue problems. SIAM Rev. 40, 1–39 (1998) · Zbl 0915.15008 Fischer, A.: A special Newton-type optimization method. Optimization 24, 269–284 (1992) · Zbl 0814.65063 Fischer, A.: Solution of monotone complementarity problems with locally Lipschitzian functions. Math. Prog. Series B 76, 513–532 (1997) · Zbl 0871.90097 Fukushima, M., Luo, Z.Q., Tseng, P.: Smoothing functions for second-order-cone complementarity problems. SIAM J. Optim. 12, 436–460 (2002) · Zbl 0995.90094 Golub, G.H., Van Loan, C.F.: Matrix Computations. 3rd edn, The Johns Hopkins University Press, Baltimore, USA, 1996 · Zbl 0865.65009 Kanzow, C., Nagel, C.: Semidefinite programs: new search directions, smoothing-type methods. SIAM J. Optim. 13, 1–23 (2002) · Zbl 1029.90052 Pang, J.-S., Qi, L.: Nonsmooth equations: motivation and algorithms. SIAM J. Optim. 3, 443–465 (1993) · Zbl 0784.90082 Qi, L., Sun, J.: A nonsmooth version of Newton’s method. Math. Prog. 58, 353–367 (1993) · Zbl 0780.90090 Sun, D., Sun, J.: Semismooth matrix valued functions. Math. Oper. Res. 27, 150–169 (2002) · Zbl 1082.49501 Sun, D., Sun, J.: Strong semismoothness of eigenvalues of symmetric matrices and its application to inverse eigenvalue problems. SIAM J. Numer. Anal. 40, 2352–2367 (2002) · Zbl 1041.65037 Sun, J., Sun, D., Qi, L.: A squared smoothing Newton method for nonsmooth matrix equations and its applications in semidefinite optimization problems. SIAM J. Optim. 14, 783–806 (2004) · Zbl 1079.90094 Tseng, P.: Merit functions for semidefinite complementarity problems. Math. Prog. 83, 159–185 (1998) · Zbl 0920.90135 Yamashita, N., Fukushima, M.: A new merit function and a descent method for semidefinite complementarity problems. In: M. Fukushima, L. Qi (eds.), Reformulation - Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, Boston, Kluwer Academic Publishers, 1999, pp. 405–420 · Zbl 0969.90087\nThis reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching."
] | [
null
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https://studylib.net/doc/18059861/the-principle-of-conservation-of-energy-in-its-most-gener... | [
"# The Principle of Conservation of Energy In its most general form, the",
null,
"```METR 201: Physical Processes Dr. Dave Dempsey The Principle of Conservation of Energy In its most general form, the Principle of Conservation of Energy says that energy is “conserved”—that is, it can’t be created or destroyed, so that the total amount of energy in any closed system (that is, a system that can’t exchange energy with anything outside the system) doesn’t change. However, energy exists in many forms, and it can change from one form to another. For example, when an object emits radiative energy (which most objects do, all the time), that energy must come at the expense of some other form of energy, and it in fact comes at the expense of an equivalent amount of heat energy in the emitting substance. (Heat is a form of internal energy associated with the random molecular motions of a substance). Similarly, when an object absorbs radiative energy, that energy is converted into an equivalent amount of heat in the object. As another example, when a substance changes phase (from gas, liquid, or solid to one of the other two phases), energy transforms from heat in the substance to an equivalent amount of latent heat (a form of chemical potential energy) in the substance, or vice versa, depending on the direction of the phase change. We can apply the principle of conservation of energy to write a version specific to the heat content of an object, creating a heat budget equation for the object. In it’s most general form, we can write the heat budget equation as: Rate of change of heat content of the object = Sum of rates at which object gains heat −\nby various mechanisms (sum of “sources” of heat) Sum of rates at which object loses heat by various mechanisms (sum of “sinks” of heat) If we apply this general form of the heat budget equation to patch of the earth’s surface (and ignore very small sources and sinks), we get: Rate of change of heat content of the object = Rate of absorption of solar radiative energy + ± Rate of transformation ± of latent heat to/from heat due to phase changes of water Rate of conduction of heat from/to air in contact with it ±\nRate of conduction of heat from/to material below Rate of emission of radiative energy by the surface Rate of absorption of infrared radiation emitted downward by the atmosphere − Rate of absorption of solar radiative energy We can relate the rate of absorption of solar radiation by the surface [(Rsolabs)sfc], the first term on the right-­‐hand side above and a mechanism by which the surface gains heat, to: o the flux or intensity (rate per unit area) of solar radiative energy arriving at the top of the atmosphere on a surface directly facing the sun (that is, perpendicular to the sun’s rays), ( SArrAtm! ,where the symbol ! means “perpendicular to”); o the fraction of that radiation that reaches the surface without being scattered or reflected back to space or absorbed by the atmosphere (that is, transmitted by the atmosphere) (τatm, the transmissivity of the atmosphere); o a factor accounting for the degree of reduction in the intensity of the remaining solar radiation when it strikes the horizontal earth’s surface at an angle and spreads out across it (sin(θsun), where θsun is the angle between the sun’s rays and the horizontal surface, or sun angle); o the fraction of the solar radiation arriving at the surface that the surface absorbs (asfc, the absorptivity of the surface); and o the area of the surface (Asfc) Specifically: (Rsolabs)sfc = SArrAtm! ✕ τatm✕ sin(θsun) ✕ asfc ✕ Asfc (Note that the solar absorption flux at the earth’s surface, (Sabs)sfc = SArrAtm! ✕ τatm✕ sin(θsun) ✕ asfc., and we invoke the generalized relation between any rate and flux: flux = rate/area.) Three categories of things can happen to radiative energy arriving on a surface: (1) it can be scattered or reflected away (without changing form); (2) it can be transmitted (that is, pass through without changing form); or it can be absorbed (and converted into heat). That is, we can write: Flux, rate, or amount Flux, rate, or amount of radiative energy = scattered or reflected striking a surface back by the surface + Flux, rate, or amount transmitted through the surface + Flux, rate, or amount absorbed by the surface Dividing both sides of this equation by the left-­‐hand side (the total flux, rate, or amount of radiative energy striking the surface) gives us: 1 = α + τ + a where α is the albedo (reflectivity) of the surface, τ is the transmissivity of the surface, and a is the absorptivity of the surface, each of which is defined as a fraction of the total flux, rate, or amount of radiative energy arriving at the surface in the first place. For an opaque surface on the surface of the earth, for example (that is, a surface that doesn’t transmit radiative energy, so τsfc = 0), then 1 = αsfc + asfc ! asfc = 1 – αsfc, and we can express the absorptivity in terms of the albedo very simply. Hence, for an opaque surface at the surface of the earth we can write the absorption rate of solar radiation by that surface as: (Rsolabs)sfc = SArrAtm! ✕ τatm✕ sin(θsun) ✕ (1 – αsfc)✕ Asfc Rate of Conduction Conduction is the direct transfer of heat from one object to another that in direct contact with it and at a different temperature, via collisions between the molecules of each substance in random motion. When the faster-­‐moving molecules of the warmer object collide with the slower-­‐moving molecules of the cooler object, the faster molecules slow down and the slower molecules speed up. Because temperature is a measure of the average energy of random molecular motions in a material, this means that the cooler object warms and the warmer object, which loses exactly as much heat as the cooler object gains, cools. The rate at which heat conducts from one object to another is proportional to the temperature difference between them—the bigger the temperature difference between them, the faster heat will conduct from the warmer object to the colder one. Not all objects conduct heat equally well, though. Air, for example, is a poor conductor of heat, and so heat does not conduct through air well. Rock, sand, soil, ice, and liquid water are not great heat conductors, either, but are somewhat better than air. In the atmosphere, we typically ignore heat conduction except between the earth’s surface and the atmosphere, where temperature differences can become large enough to overcome the poor conductivity of the materials involved. Rate of emission of radiative energy For this term (the last term in the conservation equation for heat, representing a sink of heat for an object), we start with the Stefan-­‐\nBoltzmann Law, which states that the intensity of emission of radiative energy (that is, the radiative energy emission flux) of a blackbody ( E(T ) ) is proportional to the absolute temperature of the object (T), raised to the fourth power: E(T ) = ! T 4 A blackbody is an object that absorbs all radiative energy that strikes it (that is, it reflects and transmits no radiation), and emits radiative energy with the theoretically maximum intensity (flux) possible. (The sun acts nearly as a blackbody, for example, and the earth acts as a blackbody for infrared radiation, and while the earth is not a blackbody for solar radiation [clouds reflect visible light well, for example], the earth isn’t hot enough to emit solar radiation so the Stefan-­‐Boltzmann relation still applies to it well. Not all objects act as blackbodies, however, so the Stefan-­‐Boltzmann relation sometimes has to be modified for them, and even when modified it doesn’t apply well to some objects.) Note that the radiative emission flux, E(T ) , is written to emphasize that it is a function of—that is, it depends upon or varies with—the absolute temperature, T. The Greek symbol ! (lower case “sigma”) represents the constant of proportionality between E(T ) and T 4 . In MKS units it has the value of 5.67×10-­‐8(Watts/m2)/K4. E(T ) is a flux, not a rate, so to determine the total rate at which the object loses heat, we have to multiply this by the total surface area of the object, Asfc: Rate of blackbody radiative emission = Asfc ! E(T ) By substituting from the Stefan-­‐Boltzmann relation, we relate this to the object’s absolute temperature: Rate of blackbody radiative emission = Asfc ! ! T 4 This tells us that the warmer an object is, the faster it loses heat by radiative emission. Relating rate of change of heat content to rate of change of temperature of an object: Heat is a form of energy, the total (kinetic) energy of random molecular motions in an object. Temperature is a measure of the average kinetic energy of random molecular motions in a material. Heat and temperature aren’t the same, but they are related. We can relate the rates at which an object’s heat content and temperature change: " T (t2 ) ! T (t1 ) %\nH (t2 ) ! H (t1 )\n= cH m \\$\n'& t2 ! t1\nt2 ! t1\n#\nwhere H (t ) represents the heat content of an object (written to emphasize that is a function of—that is, it depends upon or varies with—time, t); m is the mass of the object; cH is the specific heat of the object; and T (t ) is the temperature of the object (also written to emphasize that it is a function of time). Using common shorthand notational convention for the differences in this relation (the ! , or “difference”), we can also write the relation as: !H (t )\n!T (t )\n= cH m\n!t\n!t\n```"
] | [
null,
"https://s2.studylib.net/store/data/018059861_1-b749162c3ec9af9d0dd47aaf48d7af90-768x994.png",
null
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http://leung.uwaterloo.ca/CHEM/254/254out705.htm | [
"Chemistry 254 Thermodynamics I\n\nLECTURES\n\nTue, Thur @ 8:30-9:50 am, in STC-50\n\nTong Leung - Office: C2-066C (x35826) or Labs: C2-059-066 - Available anytime or by appointment.\n\nTerm tests will be conducted in the class hours.\n\nTEXTBOOKS\n\nCourse and exam materials will be based primarily on Leung’s Lecture Notes Series 254 and handouts provided only in class. It is therefore important that all the lectures are attended. Textbook #1 is the required text of this course while the other textbooks are used as references only.\n\n1. T. Engel, P. Reid, \"Thermodynamics, Statistical Thermodynamics & Kinetics\", Pearson, New York (2006) or later edition [On Reserve QC311.5.E65 2006]\n\n2. D.A. McQuarrie and J.D. Simon, “Physical Chemistry – A Molecular Approach”, University Science Books, Sausalito (1997) [On Reserve QD453.2M394]\n\n3. P.W. Atkins, “Physical Chemistry”, 5th ed., Freeman, New York (1994). Note: 4th edition [On Reserve QD453.2.A88]\n\n4. ANY Physical Chemistry textbook in the Library.\n\nHOMEWORK and MARKS\n\n Assigned problems given on the website and randomly selected for marking 10 % TWO Term Tests (20% each) 40 % ONE Final Exam 50 % Total 100 %\n\nCOURSE OUTLINE\n\nWeek #\n\nText-1\n\n# Topics\n\n1\n\nCh 1\n\nOpener: Scope and course orientation\n\nBasic concepts: System & Universe; Equilibrium; State variables\n\nIdeal gas: equation of state, internal energy, compressibility\n\nReal gas: empirical equations of state, van der Waals gas\n\nSimple one-component phase diagram (PVT) - Isotherm\n\n2\n\nCh 2-3\n\nFirst law: State functions; Work; Heat; U-Energy in transit\n\nIsochoric process; Isobaric process and enthalpy H;\n\nHeat capacities CP & CV\n\nReversible and irreversible processes\n\n3\n\nCh 5\n\nNon-ideality: Joule & Joule-Thomson experiments\n\nSecond law: Spontaneity; Entropy S\n\n4\n\nClausius inequality; Four examples of spontaneous changes\n\n5\n\nThird law: Temperature and absolute zero\n\nApplications of spontaneity: Heat engines; Carnot cycle; Refrigerators\n\nTwo more examples involving S\n\nA\n\n6\n\nMath tutorial: Review of differentials\n\nFree energies: Helmhotz A; Gibbs G; Applications to predicting spontaneity; Examples\n\n7\n\nCh 4\nCh 6\n\nThermo-chemistry\n\nRelations for a system in equilibrium: The six BASIC thermodynamic equations; Gibbs equations; Maxwell relations\n\n8\n\nThe \"magic\" thermodynamic square!\n\nThe need for these equations\n\nGibbs-Helmholz equation\n\n9\n\nRelations for non-equilibrium systems: Extension of Gibbs equations to multi-phase, multi-component systems\n\nPhase and Material equilibria\n\n10\n\nChemical potential; Fugacity; Activity coefficient\n\nEquilibrium constants; van't Hoff equation\n\nB\n\nCatch-up/Wrap-up\n\n Leung’s Lecture Notes C254, University of Waterloo. These notes will not be available on the WEB."
] | [
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