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https://fr.maplesoft.com/support/help/Maple/view.aspx?path=OrderBasis	[ "", null, "OrderBasis - Maple Help\n\nOrderBasis\n\ncompute an order basis", null, "Calling Sequence OrderBasis([f1, f2, ..., fn], x, N, [d1, d2, ..., dn])", null, "Parameters\n\n f1, ..., fn - expressions; represent the functions to be approximated x - variable appearing in the fis N - (optional) non-negative integer; specify the order of approximation. You must specify at least one of N or d1, ..., dn. d1, ..., dn - (optional) non-negative integers; specify the degree bounds. You must specify at least one of N or d1, ..., dn.", null, "Description\n\n • The OrderBasis([f1, ..., fn], x, N, [d1, ..., dn]) command computes an order basis for the functions f1, ..., fn with respect to the variable x, the degrees d1, ..., dn, and the order N. It finds all polynomial coefficients that provide an identity of the form\n\n$\\mathrm{f1}\\left(x\\right)\\mathrm{v1}\\left(x\\right)+\\dots +\\mathrm{fn}\\left(x\\right)\\mathrm{vn}\\left(x\\right)=0$\n\n up to a certain number of terms and with the degree of each vi bounded. This is similar to what the IntegerRelations[PSLQ] algorithm does for finding integer relations for floating-point numbers.\n • More precisely, given functions fi assumed to have a series expansion about 0, the OrderBasis function returns a matrix whose columns provide a basis for the (mathematical) module defined by\n\n$L=\\left\\{\\left[\\mathrm{v1}\\left(x\\right),...,\\mathrm{vn}\\left(x\\right)\\right]\|\\mathrm{f1}\\left(x\\right)\\mathrm{v1}\\left(x\\right)+...+\\mathrm{fn}\\left(x\\right)\\mathrm{vn}\\left(x\\right)=\\mathrm{O}\\left({x}^{N}\\right),\\mathrm{degree}\\left(\\mathrm{v1}\\right)\\le \\mathrm{d1},...,\\mathrm{degree}\\left(\\mathrm{vn}\\right)\\le \\mathrm{dn}\\right\\}$\n\n • That is, for every vector v of polynomials in L there exist n polynomials $\\mathrm{a1},\\mathrm{a2},\\mathrm{#mo\\left(…\\right)},\\mathrm{an}$\n\n$v=\\mathrm{a1}\\left(x\\right)\\mathrm{column}\\left(M,1\\right)+\\mathrm{a2}\\left(x\\right)\\mathrm{column}\\left(M,2\\right)+\\dots +\\mathrm{an}\\left(x\\right)\\mathrm{column}\\left(M,n\\right).$\n\n Here the degree of $\\mathrm{ai}$ is bounded by $\\mathrm{di}-\\mathrm{degree}\\left({M}_{i,i}\\right)$.\n • If there are three arguments with the third argument as a positive integer N, that is, OrderBasis([f1, ..., fn], x, N), then the degree bounds d1, ..., dn are assumed to be N, ..., N.\n • If there are three arguments with the third argument as a list, that is, OrderBasis([f1, ..., fn], x, [d1, ..., dn]), then the order is determined by ${\\mathrm{dn}}_{1}+\\dots +{\\mathrm{dn}}_{n}+n-1$.", null, "Examples\n\n > $F≔\\left[1+{x}^{2}-{x}^{7}+{x}^{12},\\mathrm{sin}\\left(x\\right),\\mathrm{exp}\\left(x\\right)\\right]:$\n > $M≔\\mathrm{OrderBasis}\\left(F,x,8,\\left[3,1,2\\right]\\right)$\n ${M}{≔}\\left[\\begin{array}{ccc}{{x}}^{{4}}{+}\\frac{{68238360}}{{4251353}}{}{{x}}^{{3}}{+}\\frac{{511942344}}{{4251353}}{}{{x}}^{{2}}{+}\\frac{{971729136}}{{4251353}}{}{x}{-}\\frac{{2669976}}{{4251353}}& \\frac{{2011699}}{{12754059}}{}{{x}}^{{3}}{-}\\frac{{23128}}{{4251353}}{}{{x}}^{{2}}{-}\\frac{{4252654}}{{4251353}}{}{x}{+}\\frac{{34692}}{{4251353}}& \\frac{{5533799}}{{12754059}}{}{{x}}^{{3}}{+}\\frac{{17049452}}{{4251353}}{}{{x}}^{{2}}{+}\\frac{{33708898}}{{4251353}}{}{x}{-}\\frac{{66060}}{{4251353}}\\\\ \\frac{{829819404}}{{4251353}}{+}\\frac{{1293611160}{}{x}}{{4251353}}& {{x}}^{{2}}{-}\\frac{{141659}}{{8502706}}{}{x}{+}\\frac{{8421469}}{{8502706}}& \\frac{{68785145}}{{8502706}}{+}\\frac{{93799511}{}{x}}{{8502706}}\\\\ \\frac{{2669976}}{{4251353}}{-}\\frac{{1804218516}{}{x}}{{4251353}}& {-}\\frac{{34692}}{{4251353}}{+}\\frac{{153223}{}{x}}{{8502706}}& {{x}}^{{2}}{-}\\frac{{136335061}}{{8502706}}{}{x}{+}\\frac{{66060}}{{4251353}}\\end{array}\\right]$ (1)\n\nEach column of $M$ has order 8.\n\n > $\\mathrm{map}\\left(\\mathrm{series},\\mathrm{map}\\left(\\mathrm{expand},\\mathrm{Matrix}\\left(1,3,F\\right)·M\\right),x,8\\right)$\n $\\left[\\begin{array}{ccc}{O}{}\\left({{x}}^{{8}}\\right)& {O}{}\\left({{x}}^{{8}}\\right)& {O}{}\\left({{x}}^{{8}}\\right)\\end{array}\\right]$ (2)\n > $\\mathrm{map}\\left(\\mathrm{degree},M,x\\right)$\n $\\left[\\begin{array}{ccc}{4}& {3}& {3}\\\\ {1}& {2}& {1}\\\\ {1}& {1}& {2}\\end{array}\\right]$ (3)\n\nImplies that a basis for all $\\left[\\mathrm{v1},\\mathrm{v2},\\mathrm{v3}\\right]$ satisfying $\\mathrm{v1}{F}_{1}+\\mathrm{v2}{F}_{2}+\\mathrm{v3}{F}_{3}$ with $\\mathrm{degree}\\left(\\mathrm{v1}\\right)\\le 3,\\mathrm{degree}\\left(\\mathrm{v2}\\right)\\le 1,\\mathrm{degree}\\left(\\mathrm{v3}\\right)\\le 2$ is a constant * column(M,3).\n\nIn the next example, OrderBasis(F,x,8) is the same as OrderBasis(F,x,8,[8,8,8]).\n\n > $M≔\\mathrm{OrderBasis}\\left(F,x,8\\right)$\n ${M}{≔}\\left[\\begin{array}{ccc}{{x}}^{{3}}{-}\\frac{{69384}}{{2011699}}{}{{x}}^{{2}}{-}\\frac{{12757962}}{{2011699}}{}{x}{+}\\frac{{104076}}{{2011699}}& {-}\\frac{{40543788}}{{2011699}}{}{{x}}^{{2}}{-}\\frac{{105266112}}{{2011699}}{}{x}{+}\\frac{{464712}}{{2011699}}& \\frac{{8097740}}{{2011699}}{}{{x}}^{{2}}{+}\\frac{{21486216}}{{2011699}}{}{x}{-}\\frac{{76416}}{{2011699}}\\\\ \\frac{{12754059}}{{2011699}}{}{{x}}^{{2}}{-}\\frac{{424977}}{{4023398}}{}{x}{+}\\frac{{25264407}}{{4023398}}& {{x}}^{{3}}{+}\\frac{{32425320}}{{2011699}}{}{{x}}^{{2}}{-}\\frac{{95498640}}{{2011699}}{}{x}{-}\\frac{{30079248}}{{2011699}}& {-}\\frac{{5533799}}{{2011699}}{}{{x}}^{{2}}{+}\\frac{{22284705}}{{2011699}}{}{x}{+}\\frac{{10793304}}{{2011699}}\\\\ {-}\\frac{{104076}}{{2011699}}{+}\\frac{{459669}{}{x}}{{4023398}}& {-}\\frac{{464712}}{{2011699}}{+}\\frac{{135810072}{}{x}}{{2011699}}& {{x}}^{{2}}{-}\\frac{{32355936}}{{2011699}}{}{x}{+}\\frac{{76416}}{{2011699}}\\end{array}\\right]$ (4)\n\nEach column of $M$ has order 8.\n\n > $\\mathrm{map}\\left(\\mathrm{series},\\mathrm{map}\\left(\\mathrm{expand},\\mathrm{Matrix}\\left(1,3,F\\right)·M\\right),x,8\\right)$\n $\\left[\\begin{array}{ccc}{O}{}\\left({{x}}^{{8}}\\right)& {O}{}\\left({{x}}^{{8}}\\right)& {O}{}\\left({{x}}^{{8}}\\right)\\end{array}\\right]$ (5)", null, "References\n\n Beckermann, B., and Labahn, G. \"Fraction-Free Computation of Matrix Rational Interpolants and Matrix GCDs.\" SIAM Journal on Matrix Analysis and Applications. Vol. 22 No. 1. (2000): 114-144.\n Beckermann, B. and Labahn, G. \"A Uniform Approach for the Fast Computation of Matrix-Type Pade Approximants.\" SIAM Journal on Matrix Analysis and Applications. Vol. 15 No. 3. (1994): 804-823." ]	[ null, "https://bat.bing.com/action/0", null, "https://fr.maplesoft.com/support/help/Maple/arrow_down.gif", null, "https://fr.maplesoft.com/support/help/Maple/arrow_down.gif", null, "https://fr.maplesoft.com/support/help/Maple/arrow_down.gif", null, "https://fr.maplesoft.com/support/help/Maple/arrow_down.gif", null, "https://fr.maplesoft.com/support/help/Maple/arrow_down.gif", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.58843946,"math_prob":0.99998856,"size":3519,"snap":"2022-27-2022-33","text_gpt3_token_len":1329,"char_repetition_ratio":0.13570413,"word_repetition_ratio":0.11253197,"special_character_ratio":0.43535095,"punctuation_ratio":0.2513158,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99950147,"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,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-06-25T13:05:28Z\",\"WARC-Record-ID\":\"<urn:uuid:f2f08d12-5ef7-441d-a79b-f3a870ed743d>\",\"Content-Length\":\"328747\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:65208a30-2595-4386-a4b3-c37093d0c186>\",\"WARC-Concurrent-To\":\"<urn:uuid:1ad83378-37b0-45c8-8fe9-958f03d97ec8>\",\"WARC-IP-Address\":\"199.71.183.28\",\"WARC-Target-URI\":\"https://fr.maplesoft.com/support/help/Maple/view.aspx?path=OrderBasis\",\"WARC-Payload-Digest\":\"sha1:B42AJSCTNNPJLQUENKY37F62I4GLRWWN\",\"WARC-Block-Digest\":\"sha1:NEX6QOXS5JLLKCF4FZHKKMURKW6SVLW3\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656103035636.10_warc_CC-MAIN-20220625125944-20220625155944-00627.warc.gz\"}"}
https://docs.google.com/document/d/e/2PACX-1vSCNs4MfLKgfaJLQLmHrXD6Eij4HMmza-q043hFejd-zA5Ho6qHHpaXHsLRDEcbLTB0Y21-DfTz9PJt/pub	[ "Algebra II 1st Quarter 3rd Quarter Equations & Inequalities Rational Exponents and Radical Functions a. Evaluate, Simplify, & Solve Linear & Absolute Value a. Evaluate nth Roots and Rational Exponents Equations & Inequalities b. Perform Function Operations and Composition c. Graph Square Root and Cube Root Functions d. Solve Radical Equations Linear Equations & Functions a. Represent Relations and Functions b. Find Slope and Rate of Change Exponential and Logarithmic Functions c. Graph Equations of Lines a. Graph Exponential Growth & Decay Functions d. Draw Scatter Plots & Best Fitting Lines b. Evaluate and Graph Logarithmic Functions e. Graph Linear Inequalities in Two variables d. Solve Exponential and Logarithmic Functions Linear Systems and Matrices Counting Methods and Probability a. Solve Linear Systems by Graphing and Algebraically a. Apply Counting Principle & Permutations b. Graph and Solve Linear Inequalities b. Use Combinations and the Binomial Theorem c. Perform Basic Matrix Operations c. Define and Use Probability d. Multiply Matrices d. Find Probability of Disjoint and Overlapping Events e. Evaluate Determinants and Apply Cramer's Rule e. Find Probabilities of Independent and Dependent f. Use Inverse Matrices to Solve Linear Systems Events f. Construct & Interpret Binomial Distributions 2nd Quarter Quadratic Functions and Factoring 4th Quarter a. Graph Quadratic Functions Data Analysis and Statistics b. Solve Quadratic Equations by Factoring a. Find Measures of Central Tendency & Dispersion c. Perform Operations with Complex Numbers b. Use Normal Distributions d. Solve Quadratic Equations by Completing the Square c. Select & Draw Conclusions from Samples e. Solve Quadratic Equations by Using the Quadratic Formula f. Graph and Solve Quadratic Inequalities Sequences & Series a. Define & Use Sequences and Series Polynomials & Polynomial Functions b. Analyze Arithmetic Sequences & Series a. Use Properties of Exponents c. Analyze Geometric Sequences & Series b. Add, Subtract, & Multiply Polynomials d. Find Sums of Infinite Geometric Series c. Factor and Solve Polynomial Equations e. Use Recursive Rules with Sequences d. Find Rational Zeros" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6923163,"math_prob":0.9943007,"size":2186,"snap":"2019-13-2019-22","text_gpt3_token_len":520,"char_repetition_ratio":0.16590284,"word_repetition_ratio":0.0,"special_character_ratio":0.17978042,"punctuation_ratio":0.13239437,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9984514,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-03-25T04:03:37Z\",\"WARC-Record-ID\":\"<urn:uuid:e8a7129e-0cdd-4532-8f1b-ffe0a206ea8f>\",\"Content-Length\":\"37209\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0521de48-1533-4065-acb3-42c904714572>\",\"WARC-Concurrent-To\":\"<urn:uuid:dda7572a-58b8-4f15-968e-30e82d5ade44>\",\"WARC-IP-Address\":\"172.217.7.238\",\"WARC-Target-URI\":\"https://docs.google.com/document/d/e/2PACX-1vSCNs4MfLKgfaJLQLmHrXD6Eij4HMmza-q043hFejd-zA5Ho6qHHpaXHsLRDEcbLTB0Y21-DfTz9PJt/pub\",\"WARC-Payload-Digest\":\"sha1:O5QQAM3SBPTNUC6RYJUDNF7IU3HMIDGL\",\"WARC-Block-Digest\":\"sha1:HU253TQ65FBXLMKD7PYLEZ25SEIFLGW3\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-13/CC-MAIN-2019-13_segments_1552912203548.81_warc_CC-MAIN-20190325031213-20190325053213-00110.warc.gz\"}"}
https://discourse.bokeh.org/t/set-upper-lower-bounds-individually/1917	[ "", null, "# set upper/lower bounds individually\n\nHello,\n\n@bryevdv says there’s a way to accomplish this, but I can’t find any clues in the docs:\n\nSetting both limits of an axis is easy:\n\n``````p = figure(x_range=[1, 5])\nor p.set(x_range=[1,5])\n\n``````\n\nSetting lower bound only could be done though using (nonexisting) `p.get_x_range()` but as discussed in #4371 it is not possible to get calculated values of the `x_range` in python because the calculation is done on the client side.\n\nIt’d be great if one could set only one limit manually and let bokeh calculate the other one for example using this notation:\n\n``````p = figure(x_range=[1, None])\n\n``````\n\n(it doesn’t work right now).\n\nHi,\n\nIf you want any auto-ranging at all, then the Plot's range objects need to be DataRange1d. These are what are added by default. However, when you provide a tuple (or list) like this:\n\np = figure(x_range=[1, 5])\n\nThat is a just a shorthand convenience or setting a different kind of range object, a Range1d, which does not do any sort of auto-ranging. It's just a fixed start and end tuple, basically.\n\nSo if you want some auto-ranging, there needs to be a DataRange1d. So there are two options:\n\n* update the default ones that figure creates, or\n* create data ranges explicitly by hand\n\nThose two options look roughly like:\n\np = figure()\np.x_range.start = 1\n\nor\n\np = figure(x_range=DataRange1d(start=1)\n\nIt's conceivable that\n\np = figure(x_range=[1, None])\n\ncould be made to do the above \"automagically\" however it would first merit some discussion. There's already a way to accomplish it without more \"magic\" (which is often harder to document).\n\nThanks,\n\nBryan\n\n···\n\nOn Jan 24, 2017, at 10:04 PM, [email protected] wrote:\n\nHello,\n\n@bryevdv says there's a way to accomplish this, but I can't find any clues in the docs:\n\nSetting both limits of an axis is easy:\n\np = figure(x_range=[1, 5])\nor p.set(x_range=[1,5])\n\nSetting lower bound only could be done though using (nonexisting) p.get_x_range() but as discussed in #4371 it is not possible to get calculated values of the x_range in python because the calculation is done on the client side.\n\nIt'd be great if one could set only one limit manually and let bokeh calculate the other one for example using this notation:\n\np = figure(x_range=[1, None])\n\n(it doesn't work right now).\n\n--\nYou received this message because you are subscribed to the Google Groups \"Bokeh Discussion - Public\" group.\nTo unsubscribe from this group and stop receiving emails from it, send an email to [email protected].\nTo post to this group, send email to [email protected].\nTo view this discussion on the web visit https://groups.google.com/a/continuum.io/d/msgid/bokeh/a18d6a46-47d8-438d-b51c-a0df03808c96%40continuum.io." ]	[ null, "https://discourse-uploads.bokeh.org/original/2X/f/f503a01092bbf1758cf8db3ec9ce14a0b0412566.svg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8810243,"math_prob":0.7247124,"size":2108,"snap":"2020-34-2020-40","text_gpt3_token_len":543,"char_repetition_ratio":0.10313688,"word_repetition_ratio":0.0060790274,"special_character_ratio":0.26233396,"punctuation_ratio":0.13411765,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9844775,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-20T05:52:09Z\",\"WARC-Record-ID\":\"<urn:uuid:42a6f6ec-4588-4568-ac36-d46995e969b2>\",\"Content-Length\":\"17060\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:cd754839-8be1-4d9c-a005-5d010cfb70cb>\",\"WARC-Concurrent-To\":\"<urn:uuid:7fbeca75-fe6d-42ad-af85-13cf215b01a0>\",\"WARC-IP-Address\":\"104.24.108.228\",\"WARC-Target-URI\":\"https://discourse.bokeh.org/t/set-upper-lower-bounds-individually/1917\",\"WARC-Payload-Digest\":\"sha1:6XNZPOIZ3FOPHN4WJ7E2JLMTNJ744BP3\",\"WARC-Block-Digest\":\"sha1:I6BRX4B2JMTOPRDI7RY76B5E45BP3FCW\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600400193391.9_warc_CC-MAIN-20200920031425-20200920061425-00233.warc.gz\"}"}
https://programmerah.com/python-run-error-typeerror-hog-got-an-unexpected-keyword-argument-visualise-34200/	[ "# Python Run Error: TypeError: hog() got an unexpected keyword argument ‘visualise‘”\n\nRunning Python code reports an error “typeerror: hog() got an unexpected keyword argument ‘visualise'”\n\nFD, hog_ image = hog(image, orientations=8, pixels_ per_ cell=(12, 12),\ncells_ per_ Block = (1, 1), visualise = true) can be normal by changing visualise to visualize, that is (changing the letter S to Z):\n\n`````` fd, hog_image = hog(image, orientations=8, pixels_per_cell=(12, 12),\ncells_per_block=(1, 1), visualize=True)``````" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.5076426,"math_prob":0.80178666,"size":2095,"snap":"2021-31-2021-39","text_gpt3_token_len":527,"char_repetition_ratio":0.13582018,"word_repetition_ratio":0.020477816,"special_character_ratio":0.25202864,"punctuation_ratio":0.15864022,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96754193,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-28T00:53:08Z\",\"WARC-Record-ID\":\"<urn:uuid:a6c963c1-d47f-4bfb-a6e2-c214fcb9040b>\",\"Content-Length\":\"35409\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a677738b-5a73-4ed2-8c0c-feafdb89219d>\",\"WARC-Concurrent-To\":\"<urn:uuid:5c1fd337-7798-409d-b06d-d1298bf99e4f>\",\"WARC-IP-Address\":\"172.67.214.245\",\"WARC-Target-URI\":\"https://programmerah.com/python-run-error-typeerror-hog-got-an-unexpected-keyword-argument-visualise-34200/\",\"WARC-Payload-Digest\":\"sha1:IGSKIFLWHGPBMG7WQA55QT6SIVQOLEDO\",\"WARC-Block-Digest\":\"sha1:JEJJGELKUC7TTIZGIMOVBIX7JQIQZ2AD\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780058589.72_warc_CC-MAIN-20210928002254-20210928032254-00442.warc.gz\"}"}
https://www.indiabix.com/civil-engineering/hydraulics/discussion-3756	[ "# Civil Engineering - Hydraulics - Discussion\n\nDiscussion Forum : Hydraulics - Section 2 (Q.No. 46)\n46.\nA cylinder 3 m in diameter and 4 m long retains water one side as shown in the below figure. If the weight of the cylinder is 2000 kgf, the vertical reaction at A is", null, "14,137 kgf\n5,863 kgf\n20,000 kgf\n18,000 kgf.\nExplanation:\nNo answer description is available. Let's discuss.\nDiscussion:\n13 comments Page 1 of 2.\n\nJENISH POUDEL said: 1 month ago\nReaction = vertical force by water on A+2000kg\nVertical force = wt of water in a volume[volume here is vertically upward projected portion of water without the semicylindrical portion]\nVertical force = 1000 * vol = 1000 * [3 * 1.4 * 4 - 0.5 * 3.14 * 3^(2) * 4/4 = 1000 * [18 - 14.137].\n= 3863kg force.\nThen the reaction = 3863 + 2000 = 5863kg.\n\nRakesh roushan said: 2 years ago\nThank you for explaining @Nushi.\n\nAadil bhat said: 3 years ago\n@Nungshi Jr.\n\nYes, you are right. Thanks.\n\nNushi said: 5 years ago\nVertical reaction = wt Of cylinder - vertical Force.\nVertical force= specific weight * volume,\n= 1000 * &pie; 1.5^2 4/2.\n= 14137 kgf.\n\nRa= 20000-14137 = 5863 kgf.\n(2)\n\nNungshi Jr said: 5 years ago\nReaction at B = horizontal force (Fh).\nFh= specific wt * area * y.\n= 1000 * 3 * 4 * 3/2,\n= 18000 kgf.\n\nBasavaraj said: 5 years ago\nF(verticle) = 3.142 * R^2 * L * 9.81.\n\nKumar Adarsh said: 5 years ago\nYes, right @Baleno.\n\nAnshu said: 5 years ago" ]	[ null, "https://www.indiabix.com/_files/images/civil-engineering/hydraulics/159-7.237-1.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6800268,"math_prob":0.97576326,"size":2231,"snap":"2023-40-2023-50","text_gpt3_token_len":755,"char_repetition_ratio":0.14638527,"word_repetition_ratio":0.424821,"special_character_ratio":0.3814433,"punctuation_ratio":0.16299559,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97357786,"pos_list":[0,1,2],"im_url_duplicate_count":[null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-10T19:57:03Z\",\"WARC-Record-ID\":\"<urn:uuid:f173e144-4161-4db1-8534-5a9e272ea156>\",\"Content-Length\":\"47179\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:fd06946b-ba0a-49fb-96e1-372afceb1ecc>\",\"WARC-Concurrent-To\":\"<urn:uuid:51aa5a6d-573c-4a93-804e-58f8a30540fd>\",\"WARC-IP-Address\":\"34.100.254.150\",\"WARC-Target-URI\":\"https://www.indiabix.com/civil-engineering/hydraulics/discussion-3756\",\"WARC-Payload-Digest\":\"sha1:2VVY4YVJFH3OASSHYSOGXITUE7D7PQT2\",\"WARC-Block-Digest\":\"sha1:JRMHMLU2DHWDF2HYP6EPRUVC4V4F5MMT\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679102637.84_warc_CC-MAIN-20231210190744-20231210220744-00248.warc.gz\"}"}
https://assumptionsofphysics.org/problems/005-BetterQuantumStateSpace	[ "## #005: Find a better mathematical characterization for quantum states\n\nCategory: Quantum mechanics - Tags: Vector spaces, Function spaces\n\nFind a better physically motivated characterization for the state space of quantum mechanics.\n\nMathematical problem. The standard way to represent quantum states is using vectors in Hilbert spaces. The requirements for a Hilbert space can be broken up into the following components:\n\n• Vector space\n• + normed (normed vector spaces)\n• + complete under the norm (Banach space)\n• + every closed linear subspace is the range of a projection (Hilbert space) (see here) The completion under the norm seems the only non-physical requirement.\n\nOn the other hand, the Schwartz_space is a dense subset of $$L^2$$, which seems better suited as:\n\n• It is closed under Fourier transform\n• It has finite expectations for all polynomials of position and momentum\n• It is dense over $$L^2$$ In fact, requiring the second feature means recovering the Schwartz space.\n\nDoes the Schwartz space satisfy all other characteristics of a Hilbert space, except the closure under the norm? If we just drop the closure under the norm, what do we lose?\n\nPhysical significance. If we look at the list of defining properties of a Hilbert space, completeness is the only one that does not make physical sense. The linearity of the normed vector space can be understood as coming from linearity of probability space; the existence of projections is the requirement of being able to identify states (i.e. a measurement that outputs 1 if the state matches and 0 if it doesn’t). The completeness would mean that the limit of a sequence of state preparation always leads to a state, but this is not the case: we can (in principle) prepare states with narrower and narrower spatial distribution, but not zero spatial distribution (delta Dirac). The idea would be that the requirement of completeness makes the mathematical space nicer to work with, but not physically meaningful.\n\nNotes. Even listing all problems with Hilbert spaces may be useful.\n\nFor example, a related problem with Hilbert spaces ($$L^2 specifically$$ see Adrian Heathcote - Unbounded operators and the incompleteness of quantum mechanics) is that self-adjoint operators that are defined on the whole space must be bounded. This means that unbounded operators must not be defined on all states: there must be states for which the average position is not well-defined. Again, note that this is not true for the Schwartz space: the position is unbounded (there is no maximum value for position) but all states have a well defined average position." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9074526,"math_prob":0.974806,"size":2608,"snap":"2022-27-2022-33","text_gpt3_token_len":534,"char_repetition_ratio":0.12327189,"word_repetition_ratio":0.0,"special_character_ratio":0.20015338,"punctuation_ratio":0.08695652,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99061096,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-08-18T16:57:58Z\",\"WARC-Record-ID\":\"<urn:uuid:66a3703c-cb6e-47ea-b56f-bb0898499b80>\",\"Content-Length\":\"10767\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:76170541-8eee-4020-bf0b-571fdabe409e>\",\"WARC-Concurrent-To\":\"<urn:uuid:8ce8b44a-e2b4-43f1-9f37-1fc41b797866>\",\"WARC-IP-Address\":\"185.199.108.153\",\"WARC-Target-URI\":\"https://assumptionsofphysics.org/problems/005-BetterQuantumStateSpace\",\"WARC-Payload-Digest\":\"sha1:L32Z5ON7R6MVOHII7FCRHEYTULQ37EQK\",\"WARC-Block-Digest\":\"sha1:KBS4LXBE4WHKM2M7WX3XFT6MYGIGOVFI\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-33/CC-MAIN-2022-33_segments_1659882573242.55_warc_CC-MAIN-20220818154820-20220818184820-00206.warc.gz\"}"}
https://hvacrschool.com/acfm-scfm-baseball-dents/	[ "## ACFM, SCFM, & Baseball dents", null, "This is a VERY in-depth look at ACFM vs. SCFM and why it matters to airflow measurement from Steven Mazzoni. Thanks, Steve!\n\nImagine your job is to figure out how fast baseballs were traveling before they hit a sheet-rock wall. The only method you have is to measure the depth of the dent left in the wall. Suppose, at 60 mph, the ball leaves a ¼”-deep dent. At 80 mph, it leaves a ½”-dent, and so forth. No problem. All you have to do is measure the dents, and you can derive the speed (velocity).\n\nBut it’s more complicated than that. You discover that some of the balls are a bit lighter than others. Otherwise, they are all identical. What does this mean? The lighter balls leave behind a shallower dent than the heavy ones, even if they traveled at the same velocity before hitting the wall. Obviously, more is needed than just the depth of the dents. The weight of the balls must also be factored in. Suppose you can weigh the balls in addition to measuring the depth of the dent they leave. You come up with an equation that considers the ball’s weight and depth of the dent and solves for its velocity.\n\nSomething similar to the baseballs is happening when we measure airflow. To determine the airflow (cfm, or ft3/min) in a duct, all we need to find out is its average velocity (ft/min) and the duct area (ft2). Measuring the air’s velocity (duct traverse) is the tricky part. A pitot tube and manometer measure the speed of the air flowing in a duct. At a faster speed or velocity, more force is imparted to the column of water in the manometer. The pressure difference (velocity pressure or VP) determines the air’s velocity in feet/minute.\n\nHowever, like the baseballs, air’s density isn’t always the same. Thus, the force it imparts to the column of water when traveling at a given velocity changes if its density changes. “Heavy” air will lift a column of water to a higher level (velocity pressure, in inches of water) on a manometer than “light” air will, even though it's moving at the exact same velocity. Thus, the velocity pressure and the air’s density must be factored in before we can determine its velocity.\n\nWhat factors determine the air’s density? Mainly its temperature and the barometric pressure. Warm air is lighter (less dense) than cold air. Air at higher barometric pressures near sea level is denser than air at lower pressures (high altitudes). The air’s moisture content also plays a minor role. Moist air (high humidity) at a given temperature is lighter than dry air at the same temperature.\n\nThe flow of air (volumetric) is usually expressed in cfm (ft3/min). To be more specific, actual cfm (ACFM) and standard cfm (SCFM) are used. ACFM & SCFM have been defined as follows:", null, "Air is at “standard conditions” when its density is @ 0.075 lb/ft3. We can thus conclude a couple of key points. First, if the airflow measurement is taken at or near standard conditions, the ACFM and the SCFM will have the exact same value. Second, if the reading were taken on air at a significantly different density, ACFM and SCFM would have two different values.\n\nLet’s work through an example duct traverse at a high elevation and temperature to show how to determine ACFM & SCFM. Suppose a 4-point duct traverse has been taken at the following conditions. A pitot tube was used to obtain velocity pressures (VP), but these have not yet been converted to velocity (ft/min). Let’s keep it simple and assume a 1.0 ft2 duct.\n\n Elevation: 4,000 ft Barometric pressure: 25.84” Hg Duct temperature: 120°F Duct area: 12” x 12” = 1.0 ft2 Actual air density: 0.059 lb/ft3 Standard air density: 0.075 lb/ft3 Actual velocity pressure (VP) readings: 0.020” WC 0.025” WC 0.030” WC 0.035” WC\n\nNow, what do we do with these four velocity pressure readings? We need to convert them to velocity using one of the equations below. The “4,005” equation is only valid for air at standard density. The “1,096” equation works at any density.", null, "Here is where it gets interesting. Which density should we use to convert the VP readings to velocity to determine ACFM & SCFM? The actual density (0.059 lb/ft3), or standard density (0.075 lb/ft3)? We’ll explore two options.\n\n• Option 1: Calculate the actual average duct velocity using the actual density of the air measured.\n\nThen, multiply average velocity by the duct area in ft2. The result will be in ACFM.\n\nCalculate ACFM Using Option 1:", null, "0.020” WC = 638 ft/min 0.025” WC = 713 ft/min 0.030” WC = 782 ft/min 0.035” WC = 844 ft/min Avg = 744 ft/min", null, "• Determine SCFM for our example using one of these two methods:\n• Method A: Determine the mass flow rate of the ACFM. From that, determine what volumetric flow at standard conditions would result in the same mass flow. The result will be in SCFM.", null, "• Method B: Multiply the ACFM by the ratio of the actual density to standard density. The result will be in SCFM.", null, "• Method A & B both result in @ 585 SCFM.\n• Option 2: Even though we realize the actual density at the traverse was not standard, calculate using the standard density. Multiply by the area in ft2. Then take the result and apply a correction factor to determine ACFM & SCFM. Calculate velocity and flow using the same VPs from the non-standard density traverse but using the standard density 4,005 formula:", null, "0.020” WC = 566 ft/min 0.025” WC = 633 ft/min 0.030” WC = 694 ft/min 0.035” WC = 749 ft/min Avg = 661 ft/min", null, "• Is this 661 “cfm” the ACFM? No. Is it the SCFM? No. Obviously, it falls in between the 744 ACFM and 585 SCFM we calculated above. What is it, then? It is a value that, when corrected, can get us to the true ACFM & SCFM.\n• Determine a unique correction factor for our example as follows. Notice the square root function:", null, "• Now what? Use this correction factor to convert the “uncorrected” 661 cfm to ACFM as follows:", null, "• Next, use the same correction factor to convert the “uncorrected” 661 cfm to SCFM as follows:", null, "Conclusions: Consider the type of instrument you are using to measure the differential pressure coming from a pitot tube. Velocity pressure readings from inclined manometers and simple differential pressure instruments will need the correct math applied. Electronic ones may be able to correct for local density and display the actual velocity.\n\n• Both Option 1 & 2 resulted in the same ACFM & SCFM values.\n• In Option 1, we used the actual local density to determine the actual average duct velocity and the ACFM. From the ACFM, we calculated the SCFM based on either the mass flow (Method A) or the ratio of actual density to standard density (Method B).\n• In Option 2, standard density was used to calculate a “reference cfm.” This reference cfm did not reflect reality but was used to calculate ACFM & SCFM. A correction factor had to be calculated (square root of the ratio of the two densities) and used to convert the reference cfm to ACFM and SCFM. This method is similar to assuming all the baseballs are the heavy ones and calculating a reference speed based on that incorrect premise. Then, you must correct the result based on the actual weight of the baseball.\n• To avoid confusion, it seems best to use Option 1 and Method B when working with air under non-standard conditions. At least then, the calculation gives you the ACFM directly. SCFM can be calculated easily based on the ratio of the two densities. No other correction factors are needed.\n\n—Steven Mazzoni\n\nHVAC/R Instructor\n\n##", null, "", null, "Related Tech Tips", null, "Venting for High efficiency Gas Furnaces - Part 1 Materials\nThis article was written by senior furnace tech Benoît (Ben) Mongeau. Ben hails from the frozen tundra of Ontario, Canada, where high-efficiency gas furnaces are commonplace. While some codes and practices may be different from the US, I find that most of it is common sense and translates pretty well. One glaring difference between Canada […]", null, "The House is the Biggest Duct\nThis article was inspired by a podcast episode about the house being the most underappreciated duct with Joe Medosch. You can listen to that podcast HERE. We probably think about sheet metal, flex duct, or the ever-controversial duct board when we think about ducts. It’s probably shiny and out of sight in most homes. But […]", null, "Is Liquid Incompressible?\nCompressibility is the ability of a substance to be squeezed into a smaller volume. It is the change in volume and increase in density that results from an increase in pressure. The subject of compression should be familiar to HVAC techs. After the return air passes over the boiling refrigerant in the evaporator coils, the […]\n\nThis site uses Akismet to reduce spam. Learn how your comment data is processed." ]	[ null, "data:image/svg+xml,%3Csvg%20xmlns=%22http://www.w3.org/2000/svg%22%20viewBox=%220%200%20794%20530%22%3E%3C/svg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns=%22http://www.w3.org/2000/svg%22%20viewBox=%220%200%20749%20171%22%3E%3C/svg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns=%22http://www.w3.org/2000/svg%22%20viewBox=%220%200%20753%20329%22%3E%3C/svg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns=%22http://www.w3.org/2000/svg%22%20viewBox=%220%200%20526%20567%22%3E%3C/svg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns=%22http://www.w3.org/2000/svg%22%20viewBox=%220%200%20644%2080%22%3E%3C/svg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns=%22http://www.w3.org/2000/svg%22%20viewBox=%220%200%20652%20420%22%3E%3C/svg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns=%22http://www.w3.org/2000/svg%22%20viewBox=%220%200%20746%20158%22%3E%3C/svg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns=%22http://www.w3.org/2000/svg%22%20viewBox=%220%200%20593%20102%22%3E%3C/svg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns=%22http://www.w3.org/2000/svg%22%20viewBox=%220%200%20608%2086%22%3E%3C/svg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns=%22http://www.w3.org/2000/svg%22%20viewBox=%220%200%20631%20396%22%3E%3C/svg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns=%22http://www.w3.org/2000/svg%22%20viewBox=%220%200%20758%20117%22%3E%3C/svg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns=%22http://www.w3.org/2000/svg%22%20viewBox=%220%200%20532%20221%22%3E%3C/svg%3E", null, "https://hvacrschool.com/wp-content/themes/hvacrschool/assets/svg/tips.svg", null, "data:image/svg+xml,%3Csvg%20xmlns=%22http://www.w3.org/2000/svg%22%20viewBox=%220%200%20210%20140%22%3E%3C/svg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns=%22http://www.w3.org/2000/svg%22%20viewBox=%220%200%20210%20140%22%3E%3C/svg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns=%22http://www.w3.org/2000/svg%22%20viewBox=%220%200%20210%20140%22%3E%3C/svg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns=%22http://www.w3.org/2000/svg%22%20viewBox=%220%200%20210%20140%22%3E%3C/svg%3E", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.902279,"math_prob":0.9683151,"size":7477,"snap":"2022-27-2022-33","text_gpt3_token_len":1853,"char_repetition_ratio":0.1411749,"word_repetition_ratio":0.022053232,"special_character_ratio":0.24903037,"punctuation_ratio":0.11439842,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98836154,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-08-13T09:00:26Z\",\"WARC-Record-ID\":\"<urn:uuid:73446cf9-06cd-41eb-b406-76d412cab428>\",\"Content-Length\":\"388109\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:034d2b26-f0e7-438d-8eaa-919a69ae5479>\",\"WARC-Concurrent-To\":\"<urn:uuid:68fa92e8-5651-422a-ba3c-54b3ca69e603>\",\"WARC-IP-Address\":\"35.208.143.255\",\"WARC-Target-URI\":\"https://hvacrschool.com/acfm-scfm-baseball-dents/\",\"WARC-Payload-Digest\":\"sha1:WU4KD252X2JPMEH2VM27IDHXPYCEHILR\",\"WARC-Block-Digest\":\"sha1:3I3PHAXV7ZFLFLB2AJX3J5DALKXSRIVZ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-33/CC-MAIN-2022-33_segments_1659882571911.5_warc_CC-MAIN-20220813081639-20220813111639-00408.warc.gz\"}"}
http://sosmath.com/algebra/solve/solve3/s32/s3211/s3211.html	[ "", null, "## SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE(S)", null, "Note:\n\n•", null, "if and only if", null, "•", null, "if and only if a + b = 3 or a + b = -3\n\n• Step1: Isolate the absolute value expression.\n\n• Step 2: Set the quantity inside the absolute value notation equal to + and - the quantity on the other side of the equation.\n\n• Step 3: Solve for the unknown in both equations.\n\n• Step 4: Check your answer analytically or graphically.\n\nSolve for x in the following equation.\n\nIf you would like to see the answers and the solutions, click on Solution.\n\nProblem 3.2a :", null, "Solution\n\nProblem 3.2b :", null, "Solution\n\nProblem 3.2c :", null, "Solution\n\nIf you would like to go back to the equation table of contents, click on Contents.", null, "[Algebra] [Trigonometry]\n[Geometry] [Differential Equations]\n[Calculus] [Complex Variables] [Matrix Algebra]", null, "S.O.S MATHematics home page\n\nDo you need more help? Please post your question on our S.O.S. Mathematics CyberBoard.", null, "Author:Nancy Marcus" ]	[ null, "http://sosmath.com/logos001.gif", null, "http://sosmath.com/gif/bar.gif", null, "http://sosmath.com/algebra/solve/solve3/s32/s3211/img2.gif", null, "http://sosmath.com/algebra/solve/solve3/s32/s3211/img3.gif", null, "http://sosmath.com/algebra/solve/solve3/s32/s3211/img4.gif", null, "http://sosmath.com/algebra/solve/solve3/s32/s3211/img5.gif", null, "http://sosmath.com/algebra/solve/solve3/s32/s3211/img6.gif", null, "http://sosmath.com/algebra/solve/solve3/s32/s3211/img7.gif", null, "http://sosmath.com/gif/bar.gif", null, "http://sosmath.com/gif/lighthouse.gif", null, "http://sosmath.com/gif/sailbar.gif", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7275007,"math_prob":0.9804579,"size":984,"snap":"2019-13-2019-22","text_gpt3_token_len":279,"char_repetition_ratio":0.113265306,"word_repetition_ratio":0.01183432,"special_character_ratio":0.2703252,"punctuation_ratio":0.15544042,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9961724,"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,1,null,1,null,1,null,1,null,1,null,1,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-03-21T12:44:29Z\",\"WARC-Record-ID\":\"<urn:uuid:1f40e44e-80cc-4617-ba6c-23ef33ce5031>\",\"Content-Length\":\"6406\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e4ba8ae9-16ed-4111-b386-3438ed54ab32>\",\"WARC-Concurrent-To\":\"<urn:uuid:2ed8f0a4-8daa-4017-90b0-a22118ca381a>\",\"WARC-IP-Address\":\"69.13.193.154\",\"WARC-Target-URI\":\"http://sosmath.com/algebra/solve/solve3/s32/s3211/s3211.html\",\"WARC-Payload-Digest\":\"sha1:JF4HZOGWMQGILBIIDCPGY3B6NW7XT5XX\",\"WARC-Block-Digest\":\"sha1:C6YFM2WAD77JX63XFECRKQU2N3KOG4MB\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-13/CC-MAIN-2019-13_segments_1552912202523.0_warc_CC-MAIN-20190321112407-20190321134407-00167.warc.gz\"}"}
http://www.dev-hq.net/javascript/3--variables-and-maths	[ "# JavaScript: Variables and Maths\n\n## Variables\n\nBefore we talk about how to create variables in JavaScript, let's first make sure that we all know what variables are. I usually think of a variable like a box - we can create a box whenever we like, and then we can put things in it, see what's in it, and even change what's in it.\n\nAlthough in other programming languages we often have to specify what data our 'box' (variable) can hold - JavaScript does all this hard work for us, and we can choose what kind of data our variable can hold, simply by how we specify the value we set it to. If we want a combination of different characters/letters (like a string of words or something), we specify the value that we set the variable to in either single or double quotes - whereas if we want to set the value to an integer (a whole number), then we can simply set the variable to the number we want to set it to. With this theory out of the way, let's actually learn how to create variables!\n\nThe first keyword that we use to create variables in JavaScript, is the `var` keyword, which stands for variable. For a number of applications you can actually exclude this keyword and it'll work just fine, but the keyword always makes sure that you are creating a new variable rather than setting the value of an already-existing one in the cases where this matters (if you don't have a clue what I'm talking about, you'll see soon enough). After this keyword (optionally in most cases, as discussed), we specify the variable's name so we can reference it in our code, and if we just want to create an 'empty box' then we can just put our semicolon here to end the variable creation. This process of creating a variable is called the variable declaration. For example the following would create an empty variable called 'VariableOne':\n\n ```1 ``` ``````var VariableOne; ``````\n\nTo assign values to this variable we can write its name, followed by an equals sign, followed by the value we want to set it to (and remember, this can be any data-type you like). So if we wanted to create a variable called 'Greeting' and then set it to the string of text, \"Hello!\", then we might do something like the following:\n\n ```1 2 ``` ``````var Greeting; Greeting = \"Hello!\"; ``````\n\nWhen we first set a variable to a value, this is called the initialization. Also note that we can set the variable to a different value wherever we like by simply using its name, and using the equals operator as we have above. So we could change the value of 'Greeting' again later on in our JavaScript document with something like `Greeting = \"Hiya!\";`. We can also get the value of the variable wherever we want by simply typing its name - so if we wanted to combine this with the alert function that we learnt in previous lessons to output the value of 'Greeting', we can just write the variable name in the `alert` function's parameters. In the following example, we will set the new variable, 'Greeting', to something, output that in an `alert`, then set the variable to something else, and `alert` that:\n\n ```1 2 3 4 5 ``` ``````var Greeting; Greeting = \"Hello!\"; alert(Greeting); Greeting = \"Hi!\"; alert(Greeting); ``````\n\nNote that we could actually combine the first two lines of our JavaScript so that we declare the variable and initialize it at the same time, to create a more condensed and neat piece of JavaScript which looks something like the following:\n\n ```1 2 3 4 ``` ``````var Greeting = \"Hello!\"; alert(Greeting); Greeting = \"Hi!\"; alert(Greeting); ``````\n\nIf you put all of the above in the 'script.js' file of the project folder that we set up previously, you should see that the pop-up boxes output exactly what we expected, \"Hello!\" and then \"Hi!\"!\n\nIf you want to just quickly test this simply script without setting up the whole project - there is an excellent service available called JSFiddle which is super awesome. I've embedded the code from this tutorial in a JSFiddle iframe below (you can run it by clicking the run button in the iframe) for quick testing.\n\n## Mathematical Operations\n\nSo the next part of this tutorial, is all about mathematical operations. Luckily for us, these are extremely simple in JavaScript. There are 4 main, simple mathematical operators:\n\n ```1 2 ``` ``````var myVariable = 5; alert(myVariable + 5); ``````\n ```1 2 ``` ``````var myVariable = 5; var VariableTwo = myVariable * 5; ``````\nI think the usage of mathematical operators is generally pretty straightforward, so I'll leave the rest of finding out to you! Try messing about with operators in different places, and if you're feeling up for a little bit of a challenge, try creating a basic script in which 2 variables contain different lengths of triangle sides, and the third side is calculated using the Pythagoras' Theorem (Hint: As well as using the operators we've just covered, you're going to need to utilise the `sqrt` method of the `Math` object to square root values!)." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.90488476,"math_prob":0.9495489,"size":4978,"snap":"2022-27-2022-33","text_gpt3_token_len":1100,"char_repetition_ratio":0.14636108,"word_repetition_ratio":0.013348165,"special_character_ratio":0.22097228,"punctuation_ratio":0.08615384,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98213816,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-06-30T20:13:11Z\",\"WARC-Record-ID\":\"<urn:uuid:274cc932-7d0c-4ad9-814e-e329212e9a71>\",\"Content-Length\":\"17248\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:055720dc-91ad-419d-ad89-5e0fdfb85f53>\",\"WARC-Concurrent-To\":\"<urn:uuid:f1c672e9-8148-46b1-a35f-9f4665298482>\",\"WARC-IP-Address\":\"45.79.8.208\",\"WARC-Target-URI\":\"http://www.dev-hq.net/javascript/3--variables-and-maths\",\"WARC-Payload-Digest\":\"sha1:QC4262SNNYLU53DQNMB4ZL7O6X5H6JLB\",\"WARC-Block-Digest\":\"sha1:6MMQG42I6QSZDYL2XJRZWZ3C55H5JJKD\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656103877410.46_warc_CC-MAIN-20220630183616-20220630213616-00631.warc.gz\"}"}
https://math.stackexchange.com/questions/2372624/a-question-about-electrical-energy-in-a-network	[ "# A question about electrical energy in a network\n\nLet $G=(V,E)$ be a network. Each arc $e$ has a resistance $r_e>0$. Let $f_e$ be the current flowing though $e=(u,v)$. By Ohm's law we know that a voltage $\\phi$ is induced on the nodes and $f_e = \\frac{\\phi_u - \\phi_v}{r_e}$. We define the electical energy of the network as $\\mathcal{E}_r(f) = \\sum_e f_e^2 r_e$. Note that $\\phi$ is a mapping from the node set to $\\mathbb{R}$. Given a real number $x$, define $E_x=\\{e=(u,v)\\in E : \\min(\\phi_u,\\phi_v)\\leq x\\leq \\max(\\phi_u,\\phi_v)\\}$. Also $F_x=\\sum_{e\\in E_x}f_e$. Now show that $\\int_{\\mathbb{R}}F(x)dx = \\mathcal{E}_r(f)$. I think this follows from the definition of integration, but can not find the connection. I am asking this question question in relation to max-flow computation using electrical flows.\n\n## 1 Answer\n\nNote that the energy can also be written as $\\sum_e \\Delta \\phi(e)^2/r_e$. (To a physicist, this is the familiar $P=IV=I^2 R=V^2/R$ formula, but you don't need to know anything about electromagnetism to get this.) Now each edge contributes to the integral of $F$ on an interval of length $\\Delta \\phi(e)$, and contributes $f_e=\\Delta \\phi(e)/r_e$ there. Multiplying that gives that the contribution of each edge to the integral is $\\Delta \\phi(e)^2/r_e$; summing over edges gives the desired result.\n\n• Can you be more specific? Are you using the definition of Riemann integration somehow? – Sudipta Roy Jul 26 '17 at 19:10\n• @SudiptaRoy Not really. The point is that $e \\in E_x$ if and only if $x \\in [\\min \\{ \\phi_u,\\phi_v \\},\\max \\{ \\phi_u,\\phi_v \\}]$. This interval has length $\\Delta \\phi(e)$. The contribution of $e$ to $F$ on this interval is $\\Delta \\phi(e)/r_e$. So you multiply the length of the interval by the contribution to $F$ to get the contribution of $e$ to $\\int F$. I'm not sure about sign issues, though (is $f_e$ selected to be positive?) – Ian Jul 26 '17 at 19:21" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.80465347,"math_prob":0.99988806,"size":1900,"snap":"2021-04-2021-17","text_gpt3_token_len":589,"char_repetition_ratio":0.119198315,"word_repetition_ratio":0.0,"special_character_ratio":0.32210526,"punctuation_ratio":0.10485934,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.0000077,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-04-20T03:33:03Z\",\"WARC-Record-ID\":\"<urn:uuid:f887c3cd-c9cd-4141-9ad8-88676dbfb71a>\",\"Content-Length\":\"161718\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c9a11aa2-d3fe-4568-a876-078a5ff05396>\",\"WARC-Concurrent-To\":\"<urn:uuid:a10be98c-627d-4cd4-a464-12d5ae4f8004>\",\"WARC-IP-Address\":\"151.101.65.69\",\"WARC-Target-URI\":\"https://math.stackexchange.com/questions/2372624/a-question-about-electrical-energy-in-a-network\",\"WARC-Payload-Digest\":\"sha1:OUVZRJX3JUIZVBIK66MOKJRD6WFXFYDP\",\"WARC-Block-Digest\":\"sha1:35BYH6MCF7Q6K2HTQKM7DRMIF5VAXAKJ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-17/CC-MAIN-2021-17_segments_1618039375537.73_warc_CC-MAIN-20210420025739-20210420055739-00249.warc.gz\"}"}
https://www.geeksforgeeks.org/set-list-java/?ref=rp	[ "Related Articles\nSet to List in Java\n• Difficulty Level : Easy\n• Last Updated : 11 Dec, 2018\n\nGiven a set (HashSet or TreeSet) of strings in Java, convert it into a list (ArrayList or LinkedList) of strings.\n\n```Input : Set hash_Set = new HashSet();\nhash_Set.add(\"Geeks\");\nhash_Set.add(\"For\");\nOutput : ArrayList or Linked List with\nfollowing content\n{\"Geeks\", \"for\"}\n```\n\n## Recommended: Please try your approach on {IDE} first, before moving on to the solution.\n\nMethod 1 (Simple)\nWe simply create an list. We traverse the given set and one by one add elements to the list.\n\n `// Java program to demonstrate conversion of``// Set to array using simple traversal``import` `java.util.;`` ` `class` `Test {`` ``public` `static` `void` `main(String[] args) {`` ` ` ``// Creating a hash set of strings`` ``Set s = ``new` `HashSet();`` ``s.add(``\"Geeks\"``);`` ``s.add(``\"for\"``);`` ` ` ``int` `n = s.size();`` ``List aList = ``new` `ArrayList(n);`` ``for` `(String x : s)`` ``aList.add(x);`` ` ` ``System.out.println(``\"Created ArrayList is\"``);`` ``for` `(String x : aList)`` ``System.out.println(x);`` ` ` ``// We can created LinkedList same way`` ``}``}`\nOutput:\n```Created ArrayList is\nGeeks\nfor\n```\n\nMethod 2 (Using ArrayList or LinkedList Constructor)\n\n `// Java program to demonstrate conversion of``// Set to list using constructor``import` `java.util.;`` ` `class` `Test {`` ``public` `static` `void` `main(String[] args) {`` ` ` ``// Creating a hash set of strings`` ``Set s = ``new` `HashSet();`` ``s.add(``\"Geeks\"``);`` ``s.add(``\"for\"``);`` ` ` ``// Creating an array list using constructor`` ``List aList = ``new` `ArrayList(s);`` ` ` ``System.out.println(``\"Created ArrayList is\"``);`` ``for` `(String x : aList)`` ``System.out.println(x);`` ` ` ``System.out.println(``\"Created LinkedList is\"``);`` ``List lList = ``new` `LinkedList(s); `` ``for` `(String x : lList)`` ``System.out.println(x); `` ``}``}`\nOutput:\n\n```Created ArrayList is\nGeeks\nfor\nCreated LinkedList is\nGeeks\nfor\n```\n\nMethod 3 (Using addAll method)\n\n `// Java program to demonstrate conversion of``// Set to array using addAll() method.``import` `java.util.;`` ` `class` `Test {`` ``public` `static` `void` `main(String[] args) {`` ` ` ``// Creating a hash set of strings`` ``Set s = ``new` `HashSet();`` ``s.add(``\"Geeks\"``);`` ``s.add(``\"for\"``);`` ` ` ``List aList = ``new` `ArrayList();`` ``aList.addAll(s);`` ` ` ``System.out.println(``\"Created ArrayList is\"``);`` ``for` `(String x : aList)`` ``System.out.println(x);`` ` ` ``List lList = ``new` `LinkedList();`` ``lList.addAll(s);`` ` ` ``System.out.println(``\"Created LinkedList is\"``);`` ``for` `(String x : lList)`` ``System.out.println(x); `` ``}``}`\nOutput:\n```Created ArrayList is\nGeeks\nfor\nCreated LinkedList is\nGeeks\nfor\n```\n\nMethod 4 (Using stream in Java)\nWe use stream in Java to convert given set to steam, then stream to list. This works only in Java 8 or versions after that.\n\n `// Java program to demonstrate conversion of``// Set to list using stream``import` `java.util.;``import` `java.util.stream.*;`` ` `class` `Test {`` ``public` `static` `void` `main(String[] args) {`` ` ` ``// Creating a hash set of strings`` ``Set s = ``new` `HashSet();`` ``s.add(``\"Geeks\"``);`` ``s.add(``\"for\"``);`` ` ` ``List aList = s.stream().collect(Collectors.toList());`` ` ` ``for` `(String x : aList)`` ``System.out.println(x);`` ``}``}`\nOutput:\n```Geeks\nfor\n```\n\nAttention reader! Don’t stop learning now. Get hold of all the important Java Foundation and Collections concepts with the Fundamentals of Java and Java Collections Course at a student-friendly price and become industry ready. To complete your preparation from learning a language to DS Algo and many more, please refer Complete Interview Preparation Course.\n\nMy Personal Notes arrow_drop_up" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.511208,"math_prob":0.58710086,"size":3204,"snap":"2021-04-2021-17","text_gpt3_token_len":789,"char_repetition_ratio":0.1490625,"word_repetition_ratio":0.41004184,"special_character_ratio":0.26841447,"punctuation_ratio":0.184765,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9727873,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-04-21T08:58:56Z\",\"WARC-Record-ID\":\"<urn:uuid:05616957-884a-4151-9e74-6452bdfc7bb1>\",\"Content-Length\":\"102260\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e207d9cc-4224-4b21-8825-0f6d93ac536e>\",\"WARC-Concurrent-To\":\"<urn:uuid:f6a0efc7-1ea8-47f5-8da4-8e9dbc9a5937>\",\"WARC-IP-Address\":\"23.62.230.73\",\"WARC-Target-URI\":\"https://www.geeksforgeeks.org/set-list-java/?ref=rp\",\"WARC-Payload-Digest\":\"sha1:ZWNFV4V5NCPXZSJXI2PSHFWO4CE3V7QE\",\"WARC-Block-Digest\":\"sha1:U24TUDPNPXKAYZMVJTDSFMPVCPRGGCGV\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-17/CC-MAIN-2021-17_segments_1618039526421.82_warc_CC-MAIN-20210421065303-20210421095303-00243.warc.gz\"}"}
https://collaborate.princeton.edu/en/publications/an-application-of-filtering-theory-to-parameter-identification-us	[ "# An application of filtering theory to parameter identification using stochastic mechanics\n\nJ. G.B. Beumee, Herschel Albert Rabitz\n\nResearch output: Contribution to journalArticle\n\n2 Scopus citations\n\n### Abstract\n\nAn estimation method for unknown parameters in the initial conditions and the potential of a quantal system using the stochastic interpretation of quantum mechanics and some results in system theory are presented. According to this interpretation the possible trajectories of a particle through coordinate space may be represented by the realization of a stochastic process that satisfies a stochastic differential equation. The drift term in this equation is derived from the wave function and consequently contains all unknown parameters in the initial conditions and the potential. The main assumption of the paper is that a continuous sequence of position measurements on the trajectory of the particle can be identified with a realization of this stochastic process over the corresponding period of time. An application of the stochastic filtering theorems subsequently provides a minimum variance estimate of the unknown parameters in the drift conditional on this continuous sequence of measurements. As simple illustrations, this method is used to obtain estimates for the initial momentum of a free particle given measurements on its trajectory and to construct an estimator for the unknown parameters in a harmonic potential. It is shown that an optimal estimator exists if the stochastic processes are associated with a wave function from a potential of the Rellich type. In addition the a posteriori probability density of the parameters in the quantal system is calculated, assuming that all parameters involved prescribe a Rellich potential.\n\nOriginal language English (US) 1787-1794 8 Journal of Mathematical Physics 28 8 https://doi.org/10.1063/1.527820 Published - Jan 1 1987\n\n### All Science Journal Classification (ASJC) codes\n\n• Statistical and Nonlinear Physics\n• Mathematical Physics" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8225528,"math_prob":0.7553264,"size":1860,"snap":"2020-34-2020-40","text_gpt3_token_len":334,"char_repetition_ratio":0.12823276,"word_repetition_ratio":0.02919708,"special_character_ratio":0.17741935,"punctuation_ratio":0.034843206,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9823664,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-27T14:39:49Z\",\"WARC-Record-ID\":\"<urn:uuid:086a34f8-3dd9-4d58-82d4-1abb59b5d8de>\",\"Content-Length\":\"47644\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:cbef2b30-e5b1-48bb-ab5a-71e81209ffc6>\",\"WARC-Concurrent-To\":\"<urn:uuid:c93b28ba-9068-4cab-8781-c2357f46e84b>\",\"WARC-IP-Address\":\"3.90.122.189\",\"WARC-Target-URI\":\"https://collaborate.princeton.edu/en/publications/an-application-of-filtering-theory-to-parameter-identification-us\",\"WARC-Payload-Digest\":\"sha1:FTAOJVCM3ZIQZIX324EYPYVCFQY3XW7W\",\"WARC-Block-Digest\":\"sha1:G5SMNQEIFSVZNSCOUZ2AWMANUURDASJS\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600400279782.77_warc_CC-MAIN-20200927121105-20200927151105-00376.warc.gz\"}"}
https://support.systemweaver.se/en/support/solutions/articles/31000141814-managing-test-execution-time-in-a-test-model	[ "If there is a need to manage test execution time, using an Integer attribute and a Computed attribute could be one solution.\n\nIn our example, the execution time is the time required for performing an individual Test Case and the set-up time required for the complete Test.\n\nAn 'Execution time' [5TCE] integer attribute is set as a default attribute on Test Case and Test with a scale of minutes. The value is stored on Test rather than Test Specification (which would make it easier to reuse the value, along with the Test Specification) because the set-up time depends on the test environment which is under the Test level. Using the same argument, the 'Execution time' ought to be a node/part attribute of the Test Case, under the Test (or maybe Test Specification) but this would make the solution a bit more difficult to manage, since such attributes would require editing using a special grid view.\n\nThe total of 'Execution time' is calculated by a Computed attribute 'Total execution time' [5TTE], which summarizes the time on Test Suite level (including all sub Test suits) and Tests/Test Cases:\n\n`/ISSS/ISES/ISSP/ITEC[@5TCE > 0].Select(@5TCE).Sum + /ISSS/ISES[@5TCE > 0].Select(@5TCE).Sum `\n\nNote: The condition [@5TCE > 0] is required since the sum would otherwise potentially be calculated over 'nil' values for those attributes that have no value, which would result in a 'nil' sum. If the attribute is introduced before the first Test Case is created, this condition is not needed as the attribute would have a default value of 0 min.\n\nAn alternative method is to present the Total execution time in the h:m format:\n\n`minutes := /ISSS/ISES/ISSP/ITEC[@5TCE > 0].Select(@5TCE).Sum + /ISSS/ISES[@5TCE > 0].Select(@5TCE).Sum; hours := minutes.Div( 60); minute:= minutes - (hours * 60); hours.ToString + \":\" + minute.ToString `\n\nThis method, however, displays 1 hour + 3 minutes as: \"1:3\".\n\nThe following method displays the time as \"1:03\":\n\n`minutes := /ISSS/ISES/ISSP/ITEC[@5TCE > 0].Select(@5TCE).Sum + /ISSS/ISES[@5TCE > 0].Select(@5TCE).Sum; hours := minutes.Div( 60); minute:= minutes - (hours 60); textminute := if minute < 10 then \"0\" + minute.ToString else minute.ToString; hours.ToString + \":\" + textminute `\n\n# Result", null, "" ]	[ null, "https://s3.amazonaws.com/cdn.freshdesk.com/data/helpdesk/attachments/production/31004638902/original/E6OSq6tkls7TjpDbzCn4PiWioKiH-AQBsw", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.82675153,"math_prob":0.89663726,"size":2223,"snap":"2023-40-2023-50","text_gpt3_token_len":577,"char_repetition_ratio":0.15141957,"word_repetition_ratio":0.093294464,"special_character_ratio":0.26675662,"punctuation_ratio":0.1438515,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9785981,"pos_list":[0,1,2],"im_url_duplicate_count":[null,7,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-09T14:13:21Z\",\"WARC-Record-ID\":\"<urn:uuid:43912a93-8e30-499d-a7f7-77a53c8672dd>\",\"Content-Length\":\"36961\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2570694e-7673-4239-bc3e-6fe8422ca396>\",\"WARC-Concurrent-To\":\"<urn:uuid:5f698e40-93e0-4d6b-bec7-e520161b2737>\",\"WARC-IP-Address\":\"34.232.242.102\",\"WARC-Target-URI\":\"https://support.systemweaver.se/en/support/solutions/articles/31000141814-managing-test-execution-time-in-a-test-model\",\"WARC-Payload-Digest\":\"sha1:AFX65YLMAJOTTK6WGQXED2TJBP4GKG2O\",\"WARC-Block-Digest\":\"sha1:JDKPXTMSEGKFAPZZSMRFRM4FINP2KVJF\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100912.91_warc_CC-MAIN-20231209134916-20231209164916-00537.warc.gz\"}"}
https://favtutor.com/blogs/machine-learning-algorithms-for-beginners	[ "# Machine Learning Algorithms for Beginners [Guide]\n\nAs a human being can recognize faces and detect images using cognitive skills, with technological advancement, it is now even possible for machines to perform activities that a human can do and even more!\n\nFrom the beginning of their lives, humans collect data and analyze it to find patterns, our brains are trained in this way to have cognitive skills and interpret data. Likewise, computers can be trained to find a pattern in the data and make appropriate predictions, this is called machine learning. Based on what kind of predictions the models make, there are different machine learning algorithms.\n\nIn this guide, we are going to discuss various types of machine learning algorithms for beginners. There are two types of datasets on which algorithms can be trained, one which has prediction or labeled data and another which has only raw data with no actual prediction values to train your model on. The former is a category of supervised learning where your models train on known predictions whereas the latter is unsupervised learning, where the model trains on undetected and unlabeled data. Let’s discuss these algorithms in detail!\n\n## Supervised learning\n\nSupervised learning is a category of machine learning algorithms where you have input factors (x) and an output variable (Y) and you utilize an algorithm to create a mapping from the input to the output variable.\n\nY = f(X)\n\nThe objective is to create an efficient and well-defined function that can create predictions as the output on inputting unseen data.\n\nSupervised learning can be further structured into regression and classification problems.\n\n1. Regression: It is an algorithm that predicts a continuous real value. Eg. Predicting gold prices. There are many different types of regression algorithms. The three most common are listed below:\n• Linear Regression\n• Polynomial Regression\n2. Classification: It is an algorithm that predicts class. Eg. Predicting if the patient is suffering from heart disease or not. Classification problems can be solved with a numerous number of algorithms. Suitable algorithms can be chosen depending upon the data and the structure of the data. Here are a few popular classification algorithms:\n• Logistic Regression\n• K-Nearest Neighbor\n• Support Vector Machines\n• Naive Bayes\n3. Common supervised learning algorithms, which can be used for regression and classification algorithms problems:\n• Decision Trees\n• Random Forest\n\n## Regression Algorithms\n\nRegression problems are unique, as they anticipate that the model should output a real continuous value. For example, predicting stock prices, home loan prices, classifying if the website can be hacked, etc.\n\n### 1) Linear Regression\n\nIn a simple linear regression algorithm, we create predictions from a single variable. The output attribute is known as the target variable and is alluded to as Y. The input parameter is known as the predictor variable and is alluded to as X. When we consider only one input parameter, the algorithm is known as simple linear regression.\n\n“Linear Regression fits a linear model with coefficients w = (w1, …, wp) to minimize the residual sum of squares between the observed targets in the dataset, and the targets predicted by the linear approximation.”\n\nAfter creating the test and training data, train the model using scikit learn library.\n\n```# Fitting Simple Linear Regression to the Training set\nfrom sklearn.linear_model import LinearRegression\nregressor = LinearRegression()\nregressor.fit(X_train, y_train)\n\n# Predicting the Test set results\ny_pred = regressor.predict(X_test)\n```\n\nThe sample plot for the training data following simple linear regression is:", null, "### 2) Polynomial Regression\n\nIn polynomial regression, the input and output variables are mapped in the nth degree of the polynomial. Polynomial Regression doesn't need the connection between the input and output variables to be linear according to the data, this is the basic difference between Linear and Polynomial Regression.\n\nThe code below illustrates how you can train a polynomial regression model using python:\n\n```# Fitting Linear Regression to the dataset\nfrom sklearn.linear_model import LinearRegression\nlin_reg = LinearRegression()\nlin_reg.fit(X, y)\n\n# Fitting Polynomial Regression to the dataset\nfrom sklearn.preprocessing import PolynomialFeatures\npoly_reg = PolynomialFeatures(degree = 4)\nX_poly = poly_reg.fit_transform(X)\npoly_reg.fit(X_poly, y)\nlin_reg_2 = LinearRegression()\nlin_reg_2.fit(X_poly, y)\n\n# Predicting a new result with Linear Regression\nlin_reg.predict([[6.5]])\n```\n\nPlots for linear regression and polynomial regression:", null, "", null, "## Classification Algorithms\n\n### 3) Logistic regression\n\nLogistic regression algorithms are used for classification problems. We use a logistic function to generate predictions that is why it is known as Logistic regression.\n\nAnother name for the logistic function is the sigmoid function, sigmoid function or activation function is used to convert the output into categorical discrete value. It’s an S-shaped curve that inputs a real-valued number and maps it into a value between 0 and 1. The logistic regression equation is:\n\n1/(1 + e-value)", null, "After creating and scaling the training and test dataset we can fit our training data to the model and create model predictions on the test data. And create a confusion matrix.\n\n```# Feature Scaling\nfrom sklearn.preprocessing import StandardScaler\nsc = StandardScaler()\nX_train = sc.fit_transform(X_train)\nX_test = sc.transform(X_test)\n\n# Fitting Logistic Regression to the Training set\nfrom sklearn.linear_model import LogisticRegression\nclassifier = LogisticRegression(random_state = 0)\nclassifier.fit(X_train, y_train)\n\n# Predicting the Test set results\ny_pred = classifier.predict(X_test)\n\n# Making the Confusion Matrix\nfrom sklearn.metrics import confusion_matrix\ncm = confusion_matrix(y_test, y_pred)\n```\n\nThe decision boundary and scatter plot for the training data predicting if the user will purchase the commodity based on the data from social media advertisement, looks like this:", null, "The model can overfit if the input parameters are highly correlated like linear regression, to cure this we can map pairwise correlations between inputs by removing the highly correlated inputs.\n\n### 4) K-Nearest Neighbor algorithm\n\nKNN is used for both regression and classification problems. However, it is vastly used for classification problems. K-nearest neighbors (KNN) algorithm uses ‘feature similarity’ to create the prediction values of new data points. This implies that new data points are assigned new values based on points in the training set. The working of the algorithm-\n\n• Step 1: Creating training and test data.\n• Step 2: We choose the value of K i.e. the nearest data points. K can be any integer. N− For each point in the test data do the following:\n• 2.1: Calculate the distance between test data and each value of training data using any of the methods namely: Euclidean, Manhattan, or Hamming distance. Euclidean distance is the most common method.\n• 2.2: Sort the distance in ascending order.\n• 2.3: The algorithm chooses the top K rows from the sorted array.\n• 2.4: It will assign a class to the test point based on the most frequent class of these rows.\n\nThe training data is fit into the KNN model and predictions are created using test data and create confusion matrix:\n\n```# Feature Scaling\nfrom sklearn.preprocessing import StandardScaler\nsc = StandardScaler()\nX_train = sc.fit_transform(X_train)\nX_test = sc.transform(X_test)\n\n# Fitting K-NN to the Training set\nfrom sklearn.neighbors import KNeighborsClassifier\nclassifier = KNeighborsClassifier(n_neighbors = 5, metric = 'minkowski', p = 2)\nclassifier.fit(X_train, y_train)\n\n# Predicting the Test set results\ny_pred = classifier.predict(X_test)\n\n# Making the Confusion Matrix\nfrom sklearn.metrics import confusion_matrix\ncm = confusion_matrix(y_test, y_pred)\n```\n\nThe plot of the training data and labels with decision boundary according to the KNN classification algorithm:", null, "### 5) Support Vector machines - Kernel SVM\n\nThe aim of support vector machine algorithms is to find a hyperplane in an N-dimensional space where N is the number of features that are used to distinctly classify data.\n\nThere are many different methods or hyperplanes to separate the two classes of data points. Our aim is to find a hyperplane with a maximum distance between data points of both classes. Maximizing the margin distance enhances the efficiency of the model and predicts with more confidence.\n\nThe code to scale and fit the training data is:\n\n```# Feature Scaling\nfrom sklearn.preprocessing import StandardScaler\nsc = StandardScaler()\nX_train = sc.fit_transform(X_train)\nX_test = sc.transform(X_test)\n\n# Fitting Kernel SVM to the Training set\nfrom sklearn.svm import SVC\nclassifier = SVC(kernel = 'rbf', random_state = 0)\nclassifier.fit(X_train, y_train)\n\n# Predicting the Test set results\ny_pred = classifier.predict(X_test)\n\n# Making the Confusion Matrix\nfrom sklearn.metrics import confusion_matrix\ncm = confusion_matrix(y_test, y_pred)\n```\n\nThe plot of the training data and labels with decision boundary according to the SVM classification algorithm:", null, "### 6) Naïve Bayes Algorithm\n\nNaïve Bayes Classifier is one of the straightforward and best Classification algorithms which helps in building the fast machine learning models which will make quick predictions.\n\nIt is a probabilistic classifier, which suggests it predicts the idea of the probability of an object. Some popular examples of the Naïve Bayes Algorithm are spam filters, sentimental analysis, and classifying articles.\n\nThe algorithm follows the following equation:\n\nP(h\|d) = (P(d\|h) * P(h)) / P(d)\n\nAnd this is how we fit the data to the naive Bayes model:\n\n```# Fitting Naive Bayes to the Training set\nfrom sklearn.naive_bayes import GaussianNB\nclassifier = GaussianNB()\nclassifier.fit(X_train, y_train)\n\n# Predicting the Test set results\ny_pred = classifier.predict(X_test)\n\n# Making the Confusion Matrix\nfrom sklearn.metrics import confusion_matrix\ncm = confusion_matrix(y_test, y_pred)\n```\n\nNaive Bayes is often extended to real-valued attributes, most ordinarily by assuming a normal distribution.\n\nThis extension of naive Bayes is named Gaussian Naive Bayes. The Gaussian (or Normal distribution) is the easiest method because we only need to estimate the mean and therefore the variance from our training data.\n\nThe plot of decision boundary for a gaussian naive Bayes algorithm on training data:", null, "## Common Supervised learning Algorithms\n\n### 7) Decision Tree Algorithm\n\nThe decision tree as the name suggests works on the principle of conditions. It is efficient and has strong algorithms used for predictive analysis. It has mainly attributed that include internal nodes, branches, and a terminal node.\n\nEvery internal node holds a “test” on an attribute, branches hold the conclusion of the test and every leaf node means the class label. It is used for both classifications as well as regression which are both supervised learning algorithms. Decisions trees are extremely delicate to the information they are prepared on — little changes to the preparation set can bring about fundamentally different tree structures.\n\nTrees answer consecutive roles that send us down a specific use of the tree given we have the answer. The model acts with \"if this then that\" conditions, at last, yielding a particular outcome. The code to fit the training data to the decision tree classification model:\n\n```# Feature Scaling\nfrom sklearn.preprocessing import StandardScaler\nsc = StandardScaler()\nX_train = sc.fit_transform(X_train)\nX_test = sc.transform(X_test)\n\n# Fitting Decision Tree Classification to the Training set\nfrom sklearn.tree import DecisionTreeClassifier\nclassifier = DecisionTreeClassifier(criterion = 'entropy', random_state = 0)\nclassifier.fit(X_train, y_train)\n\n# Predicting the Test set results\ny_pred = classifier.predict(X_test)\n\n# Making the Confusion Matrix\nfrom sklearn.metrics import confusion_matrix\ncm = confusion_matrix(y_test, y_pred)\n```\n\nThe plot showing the decision boundary for the decision tree classification algorithm for the training data.", null, "### 8) Random Forest Algorithm\n\nRandom forest, as its name suggests, comprises an enormous amount of individual decision trees that work as a group or as they say, an ensemble. Every individual decision tree in the random forest lets out a class prediction and the class with the most votes is considered as the model's prediction.\n\nRandom forest uses this by permitting every individual tree to randomly sample from the dataset with replacement, bringing about various trees. This is known as bagging. You can refer to a detailed tutorial on Random forest classifier by making a project on credit card fraud detection using machine learning.\n\nFitting the training data:\n\n```# Feature Scaling\nfrom sklearn.preprocessing import StandardScaler\nsc = StandardScaler()\nX_train = sc.fit_transform(X_train)\nX_test = sc.transform(X_test)\n\n# Fitting Random Forest Classification to the Training set\nfrom sklearn.ensemble import RandomForestClassifier\nclassifier = RandomForestClassifier(n_estimators = 10, criterion = 'entropy', random_state = 0)\nclassifier.fit(X_train, y_train)\n\n# Predicting the Test set results\ny_pred = classifier.predict(X_test)\n\n# Making the Confusion Matrix\nfrom sklearn.metrics import confusion_matrix\ncm = confusion_matrix(y_test, y_pred)\n```\n\nThe plot for the training data for the random forest classification. You can notice that the plot somewhat looks like the plot for the decision tree but with better accuracy of the decision boundary.", null, "## Unsupervised Learning\n\nAn unsupervised learning algorithm is training a model on data that is neither classified nor labeled and allowing the algorithm to find patterns in the data without guidance. The algorithm groups the unsorted information according to patterns without any prior training of the model on any data.\n\nUnlike supervised learning, no labels are provided in the data that means no training is done for the model. Therefore models are restricted to find the hidden structure in unlabeled data by our-self.\n\nIn this guide, we’ll discuss the two most prominent unsupervised learning algorithms, namely K-mean clustering and Principal component analysis.\n\n### 9) K-means clustering Algorithm\n\nK-Means Clustering is an Unsupervised Learning algorithm, which groups the unlabeled dataset into different clusters. Here K is the number of predefined clusters that are needed to train the model, as if K=2, there will be two clusters, and for K=3, there will be three clusters, and so on.\n\n“It is an iterative algorithm that divides the unlabeled dataset into k different clusters in such a way that each dataset belongs to only one group that has similar properties.”\n\nTo choose the optimal number of clusters for the model, we use the elbow method:\n\n1. It trains the K-means clustering model on the given dataset with different K values (ranges from 1-10).\n2. For each value of K, calculate the WCSS value.\n3. The plot between calculated WCSS values and the number of clusters K.\n4. The steep bend or a point of the plot looks like an arm, that point is considered as the best value of K.\n\nThe WCSS curve looks like this:", null, "From the curve, we deduce that the most suitable number of clusters (K) is 5. Hence the code to fit an unlabeled data by finding the number of clusters using the elbow method to a K-mean clustering model is:\n\n```# Using the elbow method to find the optimal number of clusters\nfrom sklearn.cluster import KMeans\nwcss = []\nfor i in range(1, 11):\nkmeans = KMeans(n_clusters = i, init = 'k-means++', random_state = 42)\nkmeans.fit(X)\nwcss.append(kmeans.inertia_)\nplt.plot(range(1, 11), wcss)\nplt.title('The Elbow Method')\nplt.xlabel('Number of clusters')\nplt.ylabel('WCSS')\nplt.show()\n\n# Fitting K-Means to the dataset\nkmeans = KMeans(n_clusters = 5, init = 'k-means++', random_state = 42)\ny_kmeans = kmeans.fit_predict(X)\n```\n\nThe number of clusters and the data segmentation and centroid of the clusters created by the model is:", null, "### 10) Principal Component Analysis\n\nThe main purpose of PCA is to decrease the complexity of the model. PCA simplifies the model and improves model performance. In cases of the datasets which have a lot of features we just extract much fewer independent variables that explain the variance the most.\n\nThe principal component analysis is used to extract linear composites of the observed variables. Factor analysis is basically a formal model predicting observed variables from theoretical latent factors from the dataset. We use PCA to maximize the total variance to find distinguishable patterns, and Factor analysis to maximize the shared variance for latent constructs or variables.\n\n## Reinforcement Learning\n\nReinforcement learning is used to make a sequence of decisions. The model learns to achieve a goal for an uncertain, potentially complex dataset. The concept of reinforcement learning is very similar to a game. The model uses a trial and error method to solve the problem. To achieve the goal the model gets either rewards or penalties for the actions it performs. Its primary goal of the model is to maximize the total reward.\n\nThere are two types of Reinforcement:\n\n### Positive Reinforcement\n\nIt is when an event occurs due to a particular behavior and resulting in an increase in the strength and the frequency of the behavior. Consequently, it has a positive effect on the behavior of the model.\n\n• Maximizes Performance\n• Sustain Change for a long period of time\n\n• Too much Reinforcement can lead to an overload of states which can diminish the results.\n\n### Negative Reinforcement\n\nIt is defined as the strengthening of behavior because a negative condition is stopped or avoided.\n\n• Increases Behavior\n• Provide defiance to a minimum standard of performance\n\n• It facilitates enough to meet up the minimum behavior\n\n## Conclusion\n\nNow that you know all about machine learning algorithms, you can start working with machine learning projects to apply your knowledge to real-world problems.\n\nMachine learning is all about handling and processing the data and speculating the best machine learning algorithm to train your model to get optimal results. Python libraries like scikit-learn make it pretty easy to train your data without working out the actual mathematics behind the machine learning algorithm but understanding the algorithm to its core is what makes you a good data scientist.\n\nWe have covered 10 of the most prominent machine learning algorithms for beginners in this tutorial. Hope this article helps you create a clear understanding of the buzzword nowadays. That’s right Machine Learning.\n\nHappy Learning :)\n\n### FavTutor - 24x7 Live Coding Help from Expert Tutors!", null, "" ]	[ null, "https://favtutor.com/resources/images/uploads/mceu_98910096311608112565080.png", null, "https://favtutor.com/resources/images/uploads/mceu_58019826121608112854682.png", null, "https://favtutor.com/resources/images/uploads/mceu_31138775731608112950920.png", null, "https://favtutor.com/resources/images/uploads/mceu_75735761041608113265265.png", null, "https://favtutor.com/resources/images/uploads/mceu_48646141951608113425324.png", null, "https://favtutor.com/resources/images/uploads/mceu_83842499671608113668883.png", null, "https://favtutor.com/resources/images/uploads/mceu_34916476381608113822065.png", null, "https://favtutor.com/resources/images/uploads/mceu_91987944291608113996880.png", null, "https://favtutor.com/resources/images/uploads/mceu_779345047101608114169831.png", null, "https://favtutor.com/resources/images/uploads/mceu_918675748111608114295034.png", null, "https://favtutor.com/resources/images/uploads/mceu_218915888121608114495166.png", null, "https://favtutor.com/resources/images/uploads/mceu_710559578131608114649954.png", null, "https://favtutor.com/resources/images/uploads/apurva_sharma_writer.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.85006326,"math_prob":0.9610382,"size":18668,"snap":"2023-40-2023-50","text_gpt3_token_len":3698,"char_repetition_ratio":0.1577904,"word_repetition_ratio":0.10117146,"special_character_ratio":0.19562888,"punctuation_ratio":0.096190475,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9986844,"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,3,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-22T21:43:20Z\",\"WARC-Record-ID\":\"<urn:uuid:0c7bc0ba-9b5a-45dc-9c87-7535b7446248>\",\"Content-Length\":\"73617\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:23119a15-b3e7-4fd4-8cef-f9857812acd3>\",\"WARC-Concurrent-To\":\"<urn:uuid:72a4c739-17c0-4c27-93a7-418e60067905>\",\"WARC-IP-Address\":\"172.67.190.139\",\"WARC-Target-URI\":\"https://favtutor.com/blogs/machine-learning-algorithms-for-beginners\",\"WARC-Payload-Digest\":\"sha1:6A4MVEJKARBPTOYNQKGUDUNRI2LS6HCE\",\"WARC-Block-Digest\":\"sha1:YN6J3IYO66NBZ7J46QXSLZAZZ37ILXFE\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233506423.70_warc_CC-MAIN-20230922202444-20230922232444-00322.warc.gz\"}"}
https://symbolaris.com/orbital/Orbital-doc/api/orbital/math/UnivariatePolynomial.html	[ "Orbital library\n\norbital.math Interface UnivariatePolynomial\n\nAll Superinterfaces:\nArithmetic, Euclidean, Function, Functor, MathFunctor, Normed, Polynomial\n\npublic interface UnivariatePolynomial\nextends Euclidean, Polynomial, Function\n\n(Univariate) polynomial p∈R[X].\n\nLet R be a commutative ring with 1. The polynomial ring over R in one variable X is\n\nR[X] := {∑i∈N aiXi = (ai)i∈N ¦ ai=0 p.t. i∈N ∧ ∀i∈N ai∈R}\nwith the convolution as multiplication. It is an associative, graded R-algebra, and as commutative or unital as R. R[X] inherits the properties of being an integrity domain, factorial (a unique factorization domain), Noetherian from R. Additionally, if R is an integrity domain, then R[X]× = R×.\n\nThe polynomial ring over a field in one variable even is Euclidean.\n\nAuthor:\nAndré Platzer\nPolynomial, ValueFactory.polynomial(Arithmetic[]), ValueFactory.polynomial(Object), ValueFactory.asPolynomial(Vector), NumericalAlgorithms.polynomialInterpolation(Matrix)\n\nNested Class Summary\n\nNested classes/interfaces inherited from interface orbital.math.functional.Function\nFunction.Composite\n\nNested classes/interfaces inherited from interface orbital.logic.functor.Functor\nFunctor.Specification\n\nNested classes/interfaces inherited from interface orbital.logic.functor.Functor\nFunctor.Specification\n\nField Summary\n\nFields inherited from interface orbital.logic.functor.Function\ncallTypeDeclaration\n\nMethod Summary\n\njava.lang.Object apply(java.lang.Object a)\nEvaluate this polynomial at a.\nInteger degree()\nGet the degree of this polynomial.\nArithmetic get(int i)\nGet the coefficient of Xi.\nArithmetic[] getCoefficients()\nReturns an array containing all the coefficients of this polynomial.\nVector getCoefficientVector()\nReturns a vector view of all the coefficients of this polynomial.\njava.util.ListIterator iterator()\nReturns an iterator over all coefficients (up to degree).\nUnivariatePolynomial modulo(UnivariatePolynomial g)\n\nUnivariatePolynomial multiply(UnivariatePolynomial b)\n\nUnivariatePolynomial quotient(UnivariatePolynomial g)\n\nUnivariatePolynomial subtract(UnivariatePolynomial b)\n\nMethods inherited from interface orbital.math.Euclidean\nmodulo, quotient\n\nMethods inherited from interface orbital.math.Polynomial\nadd, degrees, degreeValue, get, indexSet, indices, monomials, multiply, rank, subtract\n\nMethods inherited from interface orbital.math.functional.Function\nderive, integrate\n\nMethods inherited from interface orbital.logic.functor.Functor\nequals, hashCode, toString\n\nMethods inherited from interface orbital.logic.functor.Functor\nequals, hashCode, toString\n\nMethod Detail\n\ndegree\n\nInteger degree()\nGet the degree of this polynomial.\n\nThis is the Euclidean degree function δ and also the graduation function for polynomials. 0 is an element of undefined or all or none degrees. So for 0 we should return null (or Integer.MIN_VALUE, but this is not recommended).\n\nSpecified by:\ndegree in interface Euclidean\nSpecified by:\ndegree in interface Polynomial\nReturns:\ndeg(this) = max {i∈N ¦ ai≠0}\n\nget\n\nArithmetic get(int i)\nGet the coefficient of Xi. Convenience method for Polynomial.get(Arithmetic).\n\nReturns:\nai if i≤deg(this), or 0 if i>deg(this).\n\niterator\n\njava.util.ListIterator iterator()\nReturns an iterator over all coefficients (up to degree).\n\nSpecified by:\niterator in interface Polynomial\nPostconditions:\nalways (RES.succeedes(#next()))\n\napply\n\njava.lang.Object apply(java.lang.Object a)\nEvaluate this polynomial at a. Using the \"Einsetzungshomomorphismus\".\n\nSpecified by:\napply in interface Function\nSpecified by:\napply in interface Polynomial\nParameters:\na - generic Object as argument\nReturns:\nf(a) = f(X)\|X=a = (f(X) mod (X-a))\n\nsubtract\n\nUnivariatePolynomial subtract(UnivariatePolynomial b)\n\nmultiply\n\nUnivariatePolynomial multiply(UnivariatePolynomial b)\n\nquotient\n\nUnivariatePolynomial quotient(UnivariatePolynomial g)\n\nmodulo\n\nUnivariatePolynomial modulo(UnivariatePolynomial g)\n\ngetCoefficients\n\nArithmetic[] getCoefficients()\nReturns an array containing all the coefficients of this polynomial.\n\nReturns:\na new array containing all our coefficients.\nObject.clone()\nPostconditions:\nRES[i]==get(i) ∧ RES.length==degree()+1 ∧ RES!=RES\n\ngetCoefficientVector\n\nVector getCoefficientVector()\nReturns a vector view of all the coefficients of this polynomial.\n\nPostconditions:\nRES[i]==get(i) ∧ RES.length==degree()+1\n\nOrbital library\n1.3.0: 11 Apr 2009" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.5881129,"math_prob":0.7894298,"size":3337,"snap":"2022-05-2022-21","text_gpt3_token_len":750,"char_repetition_ratio":0.21542154,"word_repetition_ratio":0.17368421,"special_character_ratio":0.18849266,"punctuation_ratio":0.17706238,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99944013,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-26T05:40:14Z\",\"WARC-Record-ID\":\"<urn:uuid:758b9eeb-b601-40e5-9055-7ed9566509db>\",\"Content-Length\":\"30218\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0bfc0726-2f1a-4bc8-b1db-c7cd2e81b2c2>\",\"WARC-Concurrent-To\":\"<urn:uuid:e651133a-d57c-41d7-adcd-21afe0340139>\",\"WARC-IP-Address\":\"5.175.14.99\",\"WARC-Target-URI\":\"https://symbolaris.com/orbital/Orbital-doc/api/orbital/math/UnivariatePolynomial.html\",\"WARC-Payload-Digest\":\"sha1:V73WV4WRTJHIHL4EVAAW7KOBQV33HMIH\",\"WARC-Block-Digest\":\"sha1:4GSCZPTRTOWOQMQLVS6P4WX6YXAOTUON\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320304915.53_warc_CC-MAIN-20220126041016-20220126071016-00479.warc.gz\"}"}
https://www.stat.math.ethz.ch/pipermail/r-devel/2011-September/062105.html	[ "# [Rd] array extraction\n\nrobin hankin hankin.robin at gmail.com\nWed Sep 28 00:12:26 CEST 2011\n\n```thank you Simon.\n\nI find a[M] working to be unexpected, but consistent with (a close\n\nCan we reproduce a[,M]?\n\n[I would expect this to extract a[,j,k] where M[j,k] is TRUE]\n\ntry this:\n\n> a <- array(1:30,c(3,5,2))\n> M <- matrix(1:10,5,2) %% 3==1\n> a[M]\n 1 4 7 10 11 14 17 20 21 24 27 30\n\nThis is not doing what I would want a[,M] to do.\n\nI'll checkout afill() right now....\n\nbest wishes\n\nRobin\n\nOn Wed, Sep 28, 2011 at 10:39 AM, Simon Knapp <sleepingwell at gmail.com> wrote:\n> a[M] gives the same as your `cobbled together' code.\n>\n> On Wed, Sep 28, 2011 at 6:35 AM, robin hankin <hankin.robin at gmail.com>\n> wrote:\n>>\n>> hello everyone.\n>>\n>> Look at the following R idiom:\n>>\n>> a <- array(1:30,c(3,5,2))\n>> M <- (matrix(1:15,c(3,5)) %% 4) < 2\n>> a[M,] <- 0\n>>\n>> Now, I think that \"a[M,]\" has an unambiguous meaning (to a human).\n>> However, the last line doesn't work as desired, but I expected it\n>> to...and it recently took me an indecent amount of time to debug an\n>> analogous case. Just to be explicit, I would expect a[M,] to extract\n>> a[i,j,] where M[i,j] is TRUE. (Extract.Rd is perfectly clear here, and R\n>> is\n>> behaving as documented).\n>>\n>> The best I could cobble together was the following:\n>>\n>> ind <- which(M,arr.ind=TRUE)\n>> n <- 3\n>> ind <-\n>> cbind(kronecker(ind,rep(1,dim(a)[n])),rep(seq_len(dim(a)[n]),nrow(ind)))\n>> a[ind] <- 0\n>>\n>>\n>> but the intent is hardly clear, certainly compared to \"a[M,]\"\n>>\n>> I've been pondering how to implement such indexing, and its\n>> generalization.\n>>\n>> Suppose 'a' is a seven-dimensional array, and M1 a matrix and M2 a\n>> three-dimensional array (both Boolean). Then \"a[,M1,,M2]\" is a\n>> natural generalization of the above. I would want a[,M1,,M2] to\n>> extract a[i1,i2,i3,i4,i5,i6,i7] where M1[i2,i3] and M[i5,i6,i7] are\n>> TRUE.\n>>\n>> One would need all(dim(a)[2:3] == dim(M1)) and all(dim(a)[5:7] ==\n>> dim(M2)) for consistency.\n>>\n>> Can any R-devel subscribers advise?\n>>\n>>\n>>\n>>\n>> --\n>> Robin Hankin\n>> Uncertainty Analyst\n>> hankin.robin at gmail.com\n>>\n>> ______________________________________________\n>> R-devel at r-project.org mailing list\n>> https://stat.ethz.ch/mailman/listinfo/r-devel\n>\n>\n\n--\nRobin Hankin\nUncertainty Analyst\nhankin.robin at gmail.com\n\n```" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.866812,"math_prob":0.6502647,"size":2394,"snap":"2023-14-2023-23","text_gpt3_token_len":789,"char_repetition_ratio":0.116736405,"word_repetition_ratio":0.010025063,"special_character_ratio":0.39807853,"punctuation_ratio":0.20036429,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95094883,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-03-29T09:40:40Z\",\"WARC-Record-ID\":\"<urn:uuid:03a45087-a11a-401d-a8a5-d8925a80fce5>\",\"Content-Length\":\"6174\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:bd5d4c80-d872-450a-9436-02b044142189>\",\"WARC-Concurrent-To\":\"<urn:uuid:21887038-247f-498c-94ea-72042a183a61>\",\"WARC-IP-Address\":\"129.132.119.195\",\"WARC-Target-URI\":\"https://www.stat.math.ethz.ch/pipermail/r-devel/2011-September/062105.html\",\"WARC-Payload-Digest\":\"sha1:RG42PLMBQDC2P5CKVQLYNTVH7YG56T5F\",\"WARC-Block-Digest\":\"sha1:HOC554R2RADOKGE5QEFJKFKMPNNETMPR\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-14/CC-MAIN-2023-14_segments_1679296948965.80_warc_CC-MAIN-20230329085436-20230329115436-00340.warc.gz\"}"}
https://www.programiz.com/javascript/library/array/entries	[ "", null, "# Javascript Array entries()\n\nIn this tutorial, you will learn about the JavaScript Array entries() method with the help of examples.\n\nThe `entries()` method returns a new Array Iterator object containing key/value pairs for each array index.\n\n### Example\n\n``````// defining an array named alphabets\nconst alphabets = [\"A\", \"B\", \"C\"];\n\n// array iterator object that contains\n// key-value pairs for each index in the array\nlet iterator = alphabets.entries();\n\n// iterating through key-value pairs in the array\nfor (let entry of iterator) {\nconsole.log(entry);\n}\n\n// Output:\n// [ 0, 'A' ]\n// [ 1, 'B' ]\n// [ 2, 'C' ]``````\n\n## entries() Syntax\n\nThe syntax of the `entries()` method is:\n\n``arr.entries()``\n\nHere, arr is an array.\n\n## entries() Parameters\n\nThe `entries()` method does not take any parameters.\n\n## entries() Return Value\n\n• Returns a new `Array` iterator object.\n\nNote: The `entries()` method does not change the original array.\n\n## Example 1: Using entries() Method\n\n``````// defining an array\nconst languages = [\"Java\", \"C\", \"C++\", \"Python\"];\n\n// array iterator object that contains\n// key-value pairs for each index in the array\nlet iterator = languages.entries();\n\n// looping through key-value pairs in the array\nfor (let entry of iterator) {\nconsole.log(entry);\n}``````\n\nOutput\n\n```[ 0, 'Java' ]\n[ 1, 'C' ]\n[ 2, 'C++' ]\n[ 3, 'Python' ]```\n\nIn the above example, we have used the `entries()` method to get an Array iterator object of the key/value pair of each index in the language array.\n\nWe have then looped through iterator that prints the key/value pairs of each index.\n\n## Example 2: Using next() Method in Array Iterator Object\n\nArray Iterator object has a built-in method called `next()` which is used to get the next value in the object.\n\nInstead of looping through the iterator, we can get the key/value pairs using `next().value`. For example:\n\n``````// defining an array\nconst symbols = [\"#\", \"\\$\", \"\"];\n\n// Array iterator object that holds key/value pairs\nlet iterator = symbols.entries();\n\n// using built-in next() method in Array iterator object\nconsole.log(iterator.next().value);\nconsole.log(iterator.next().value);\nconsole.log(iterator.next().value);``````\n\nOutput\n\n```[ 0, '#' ]\n[ 1, '\\$' ]\n[ 2, '' ]```" ]	[ null, "https://www.facebook.com/tr", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.5218504,"math_prob":0.68074167,"size":2030,"snap":"2022-27-2022-33","text_gpt3_token_len":503,"char_repetition_ratio":0.1786772,"word_repetition_ratio":0.1590214,"special_character_ratio":0.29014778,"punctuation_ratio":0.16535433,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.978538,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-07-01T13:31:18Z\",\"WARC-Record-ID\":\"<urn:uuid:72d5a143-a099-478c-8443-ba5928d9d121>\",\"Content-Length\":\"90108\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7ef7107d-4028-4fc2-a372-32146875029d>\",\"WARC-Concurrent-To\":\"<urn:uuid:5b71d4c7-ae97-4ec8-b730-d838f89d5a09>\",\"WARC-IP-Address\":\"174.138.49.232\",\"WARC-Target-URI\":\"https://www.programiz.com/javascript/library/array/entries\",\"WARC-Payload-Digest\":\"sha1:R7OWWHI65NQFYYA7NTWKMRHCAPH4MS5L\",\"WARC-Block-Digest\":\"sha1:Z55WLEMRGILORAYT2HKVZFZMIMVG7PRL\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656103941562.52_warc_CC-MAIN-20220701125452-20220701155452-00178.warc.gz\"}"}
https://tripprivacy.com/minutes-in-day/	[ "# Minutes in day\n\n## How Many Minutes in a Day?\n\nA day consists of 24 hours and 1 hour consists of 60 minutes\nSo:\n24 x 60 = 1440 minutes\nThere are 1440 minutes in a day\n\nEssential Life Hacks To Save You Ti...\nEssential Life Hacks To Save You Time!\n\n### Convert minutes to day\n\nday =min * 0.00069444\n\nTo convert minutes into a day, you need to divide the number of minutes by 1440.\n\nNUMBER OF DAYS (DAYS) = NUMBER OF MINUTES / 1440\n\nFor example, in order to find out how many days are in 10080 minutes, you need 10080/1440 = 7 days.\n\n### Convert day to minutes\n\nTo convert a day to minutes, multiply the number of days by 1440.\n\nNUMBER OF MINUTES = NUMBER OF DAYS (DAYS) * 1440\n\nFor example, in order to find out how many minutes are in 2 days, you need 2 * 1440 = 2880 minutes.\n\nMinutes\nA minute is a unit of time that is equal to 60 seconds or 1/60 of an hour. In the universal coordinated time standard, a minute in rare cases can be equal to 59 or 61 seconds.\n\nDays\nA day (symbol: “d”) is a unit of time that is equal to 24 hours or 86,400 seconds. Officially, this is an off-system unit, but it can also be used in the International System of Units. In addition to the fact that a day is 86,400 seconds, this indicator is also used to determine some other periods of time based on the rotation of the Earth on its axis.\n\nThe year has 365 days, which means that it has = 365 * 1440 = 525,600 minutes per year.\n\nAnd in the year 12 months, which means that the average minutes per month = 525600 / 12 = 43800 minutes per month.\n\n## Units of Time\n\nMeasurement The time unit used to express time. Represents the continuous sequence of events. The units of time measurement in the metric system popular unit.\n\nMinutes in day\nScroll to top" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.90836746,"math_prob":0.96208864,"size":1579,"snap":"2022-40-2023-06","text_gpt3_token_len":429,"char_repetition_ratio":0.13460317,"word_repetition_ratio":0.07096774,"special_character_ratio":0.31158963,"punctuation_ratio":0.097345136,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9867983,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-10-02T19:22:23Z\",\"WARC-Record-ID\":\"<urn:uuid:d8266190-25e4-407c-b2e1-16d58628db84>\",\"Content-Length\":\"138492\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b161d328-dbb5-467c-a16f-f5db43b61566>\",\"WARC-Concurrent-To\":\"<urn:uuid:f0d309c5-d203-4e68-928f-03a43a535ab1>\",\"WARC-IP-Address\":\"52.86.133.10\",\"WARC-Target-URI\":\"https://tripprivacy.com/minutes-in-day/\",\"WARC-Payload-Digest\":\"sha1:MQ5WZBBRZ7HSCUBZ5UMTAJGERKH2AKKY\",\"WARC-Block-Digest\":\"sha1:EP776E3HRLIDJIJ2SBH5Q6FMZPYKYQNW\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030337339.70_warc_CC-MAIN-20221002181356-20221002211356-00228.warc.gz\"}"}
https://socratic.org/questions/58e3251f7c01491e20de705d	[ "# For the 1/2 cell sf(MnO_4^(-)+8H^(+)+5erightleftharpoonsMn^(2+)+7H_2O) the value of sf(E^(@)=+1.51V). What is the value for E if sf([MnO_4^(-)]=0.0001M) and sf([Mn^(2+)]=0.0005M) ?\n\nApr 7, 2017\n\n$\\textsf{E = + 1.50 \\textcolor{w h i t e}{x} V}$\n\n#### Explanation:\n\nBefore the calculation it is helpful to make a prediction for the electrode potential using Le Chatelier's Principle:\n\nThe 1/2 cell reaction is:\n\nstackrel(color(white)(xxxxxxxxxxxxxxxxxxxxxxxxxxxxx))(color(blue)(larr)\n\n$\\textsf{M n {O}_{4}^{-} + 8 {H}^{+} + 5 e r i g h t \\le f t h a r p \\infty n s M {n}^{2 +} + 4 {H}_{2} O}$\n\nsf(color(red)(0.0001Mcolor(white)(xxxxxxxxx)0.0005M)\n\n$\\textsf{{E}^{\\circ} = + 1.51 \\textcolor{w h i t e}{x} V}$\n\nYou can see that the concentration of $\\textsf{M n {O}_{4}^{-}}$ has been reduced relative to the concentration of $\\textsf{M {n}^{2 +}}$.\n\nAccording to Le Chatelier we would predict that the position of equilibrium will shift to the left to oppose that change, as shown by the blue arrow.\n\nYou can see from the 1/2 equation that this will tend to push out more electrons so we would expect the electrode potential to be less positive.\n\nWe can calculate this using The Nernst Equation:\n\nsf(E=E^(@)-(RT)/(zF)ln(([red])/([\"ox\"]))\n\nAt 298K this simplifies to:\n\n$\\textsf{E = {E}^{\\circ} + \\frac{0.05916}{z} \\log \\left(\\frac{\\left[\\text{ox}\\right]}{\\left[red\\right]}\\right)}$\n\nWhere z is the number of moles of electrons transferred.\n\nThis becomes:\n\nsf(E=E^@+(0.05916)/(5)log(([MnO_4^-][H^+]^8)/([Mn^(2+)]))\n\nSince we are at pH = 0 we can say that $\\textsf{\\left[{H}^{+}\\right] = 1 \\textcolor{w h i t e}{x} M}$\n\nThis becomes:\n\nsf(E=E^@+(0.05916)/(5)log(([MnO_4^-])/([Mn^(2+)]))\n\nPutting in the numbers:\n\nsf(E=+1.51+(0.05916)/(5)log((0.0001)/(0.0005))\n\n$\\textsf{E = + 1.51 - 0.00827 = + 1.50 \\textcolor{w h i t e}{x} V}$\n\nAs you can see, this is in accordance with our prediction. The potential of the electrode has been made slightly less positive.\n\nPut simply, reducing the concentration of Mn(VII) relative to Mn(II) has made the Mn(VII) slightly less effective as an oxidising agent." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8590879,"math_prob":0.99984443,"size":1226,"snap":"2022-27-2022-33","text_gpt3_token_len":325,"char_repetition_ratio":0.10638298,"word_repetition_ratio":0.0,"special_character_ratio":0.25856444,"punctuation_ratio":0.09166667,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9998018,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-08-19T02:44:29Z\",\"WARC-Record-ID\":\"<urn:uuid:7ee162df-e6ac-4576-8eaa-52abc61a54cf>\",\"Content-Length\":\"37811\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f90c5c99-a315-458a-b73b-8800c7ea9655>\",\"WARC-Concurrent-To\":\"<urn:uuid:90456f33-894f-4e97-bce6-17efa7e2fa3d>\",\"WARC-IP-Address\":\"216.239.38.21\",\"WARC-Target-URI\":\"https://socratic.org/questions/58e3251f7c01491e20de705d\",\"WARC-Payload-Digest\":\"sha1:7JX7SVKU7EHROOUZMJKM2NKLHS4Q2VOW\",\"WARC-Block-Digest\":\"sha1:QKRTTKJDEEROYTQMCAZZFDFIO5BP5N24\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-33/CC-MAIN-2022-33_segments_1659882573540.20_warc_CC-MAIN-20220819005802-20220819035802-00105.warc.gz\"}"}
https://support.nag.com/numeric/nl/nagdoc_24/nagdoc_fl24/html/f01/f01crf.html	[ "F01 Chapter Contents\nF01 Chapter Introduction\nNAG Library Manual\n\n# NAG Library Routine DocumentF01CRF\n\nNote: before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.\n\n## 1 Purpose\n\nF01CRF transposes a rectangular matrix in-situ.\n\n## 2 Specification\n\n SUBROUTINE F01CRF ( A, M, N, MN, MOVE, LMOVE, IFAIL)\n INTEGER M, N, MN, MOVE(LMOVE), LMOVE, IFAIL REAL (KIND=nag_wp) A(MN)\n\n## 3 Description\n\nF01CRF requires that the elements of an $m$ by $n$ matrix $A$ are stored consecutively by columns in a one-dimensional array. It reorders the elements so that on exit the array holds the transpose of $A$ stored in the same way. For example, if $m=4$ and $n=3$, on entry the array must hold:\n $a11 a21 a31 a41 a12 a22 a32 a42 a13 a23 a33 a43$\nand on exit it holds\n $a11 a12 a13 a21 a22 a23 a31 a32 a33 a41 a42 a43.$\nCate E G and Twigg D W (1977) Algorithm 513: Analysis of in-situ transposition ACM Trans. Math. Software 3 104–110\n\n## 5 Parameters\n\n1: A(MN) – REAL (KIND=nag_wp) arrayInput/Output\nOn entry: the elements of the $m$ by $n$ matrix $A$, stored by columns.\nOn exit: the elements of the transpose matrix, also stored by columns.\n2: M – INTEGERInput\nOn entry: $m$, the number of rows of the matrix $A$.\n3: N – INTEGERInput\nOn entry: $n$, the number of columns of the matrix $A$.\n4: MN – INTEGERInput\nOn entry: $n$, the value $m×n$.\n5: MOVE(LMOVE) – INTEGER arrayWorkspace\n6: LMOVE – INTEGERInput\nOn entry: the dimension of the array MOVE as declared in the (sub)program from which F01CRF is called.\nSuggested value: ${\\mathbf{LMOVE}}=\\left(m+n\\right)/2$.\nConstraint: ${\\mathbf{LMOVE}}\\ge 1$.\n7: IFAIL – INTEGERInput/Output\nOn entry: IFAIL must be set to $0$, $-1\\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.\nFor environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$. When the value $-\\mathbf{1}\\text{ or }\\mathbf{1}$ is used it is essential to test the value of IFAIL on exit.\nOn exit: ${\\mathbf{IFAIL}}={\\mathbf{0}}$ unless the routine detects an error or a warning has been flagged (see Section 6).\n\n## 6 Error Indicators and Warnings\n\nIf on entry ${\\mathbf{IFAIL}}={\\mathbf{0}}$ or $-{\\mathbf{1}}$, explanatory error messages are output on the current error message unit (as defined by X04AAF).\nErrors or warnings detected by the routine:\n${\\mathbf{IFAIL}}=1$\n On entry, ${\\mathbf{MN}}\\ne {\\mathbf{M}}×{\\mathbf{N}}$.\n${\\mathbf{IFAIL}}=2$\n On entry, ${\\mathbf{LMOVE}}\\le 0$.\n${\\mathbf{IFAIL}}<0$\nA serious error has occurred. Check all subroutine calls and array sizes. Seek expert help.\n\n## 7 Accuracy\n\nExact results are produced.\n\nThe time taken by F01CRF is approximately proportional to $mn$.\n\n## 9 Example\n\nThis example transposes a $7$ by $3$ matrix and prints out, for convenience, its transpose.\n\n### 9.1 Program Text\n\nProgram Text (f01crfe.f90)\n\n### 9.2 Program Data\n\nProgram Data (f01crfe.d)\n\n### 9.3 Program Results\n\nProgram Results (f01crfe.r)" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.75193465,"math_prob":0.99123836,"size":2457,"snap":"2023-40-2023-50","text_gpt3_token_len":646,"char_repetition_ratio":0.11699959,"word_repetition_ratio":0.028235294,"special_character_ratio":0.25111926,"punctuation_ratio":0.15226337,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99735254,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-11-30T05:09:40Z\",\"WARC-Record-ID\":\"<urn:uuid:f6f5b687-a152-4fa5-b242-f9a2dc3d8740>\",\"Content-Length\":\"14999\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:29dd7a25-58f7-44ab-9da9-980ba70f9bd2>\",\"WARC-Concurrent-To\":\"<urn:uuid:455ab42d-1065-4f9f-8d16-62f61f344a0c>\",\"WARC-IP-Address\":\"78.129.168.4\",\"WARC-Target-URI\":\"https://support.nag.com/numeric/nl/nagdoc_24/nagdoc_fl24/html/f01/f01crf.html\",\"WARC-Payload-Digest\":\"sha1:4NXFGVJKOEHXXPRZVQPMLSENELIAAAYR\",\"WARC-Block-Digest\":\"sha1:XV6ALIUSB2MEVTI3MHCAST5OQQK4YQMW\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100164.87_warc_CC-MAIN-20231130031610-20231130061610-00003.warc.gz\"}"}
https://www.maplesoft.com/support/help/maple/view.aspx?path=Student%2FLinearAlgebra%2FLinearSolveTutor	[ "", null, "LinearSolveTutor - Maple Help\n\nStudent[LinearAlgebra][LinearSolveTutor] - interactive solution of linear systems", null, "Calling Sequence LinearSolveTutor(M) LinearSolveTutor(M, v)", null, "Parameters\n\n M - Matrix v - Vector", null, "Description\n\n • The LinearSolveTutor(M) command allows you to interactively solve the system of equations represented by the Matrix M. The Matrix is interpreted as an augmented matrix whose last column specifies the right-hand side. It returns the solution as a column Vector.\n • The LinearSolveTutor(M, v) command allows you to interactively solve the system $M·x=v$. It returns the solution as a column Vector.\n • For both calling sequences, you must choose whether to use Gaussian elimination (producing the row echelon form of the Matrix) or Gauss-Jordan elimination (producing the reduced row echelon form of the Matrix). To make a selection, click the corresponding button on the initially displayed Maplet application.\n • Floating-point numbers in M or v are converted to rationals before computation begins.\n • The dimensions of the Matrix must be no greater than 5x5.", null, "Examples\n\n > $\\mathrm{with}\\left(\\mathrm{Student}\\left[\\mathrm{LinearAlgebra}\\right]\\right):$\n > $M≔⟨⟨1,2,0⟩\|⟨2,3,2⟩\|⟨0,2,1⟩\|⟨3,5,5⟩⟩$\n ${M}{≔}\\left[\\begin{array}{cccc}{1}& {2}& {0}& {3}\\\\ {2}& {3}& {2}& {5}\\\\ {0}& {2}& {1}& {5}\\end{array}\\right]$ (1)\n > $v≔⟨5,4,2⟩$\n ${v}{≔}\\left[\\begin{array}{c}{5}\\\\ {4}\\\\ {2}\\end{array}\\right]$ (2)\n > $\\mathrm{LinearSolveTutor}\\left(M\\right)$\n > $\\mathrm{LinearSolveTutor}\\left(M,v\\right)$", null, "See Also" ]	[ null, "https://bat.bing.com/action/0", null, "https://www.maplesoft.com/support/help/maple/arrow_down.gif", null, "https://www.maplesoft.com/support/help/maple/arrow_down.gif", null, "https://www.maplesoft.com/support/help/maple/arrow_down.gif", null, "https://www.maplesoft.com/support/help/maple/arrow_down.gif", null, "https://www.maplesoft.com/support/help/maple/arrow_down.gif", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.71988386,"math_prob":0.99702597,"size":1455,"snap":"2021-43-2021-49","text_gpt3_token_len":377,"char_repetition_ratio":0.16678153,"word_repetition_ratio":0.10404624,"special_character_ratio":0.195189,"punctuation_ratio":0.12195122,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99765146,"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,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-12-01T00:44:20Z\",\"WARC-Record-ID\":\"<urn:uuid:3602032b-ab32-4f20-a8fd-523a75f56ad9>\",\"Content-Length\":\"152517\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9f37a9c1-0816-4f42-8307-cdfd412e9665>\",\"WARC-Concurrent-To\":\"<urn:uuid:e3293946-d0ff-43ef-a515-0ac77bc3f3a3>\",\"WARC-IP-Address\":\"199.71.183.28\",\"WARC-Target-URI\":\"https://www.maplesoft.com/support/help/maple/view.aspx?path=Student%2FLinearAlgebra%2FLinearSolveTutor\",\"WARC-Payload-Digest\":\"sha1:I2OJLPMF3QSNVXLXNLL65AILNLA6LKCB\",\"WARC-Block-Digest\":\"sha1:GI4BSJOE552TF65VBVWXCYVUYOP6DZXN\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964359082.76_warc_CC-MAIN-20211130232232-20211201022232-00104.warc.gz\"}"}
https://www.npmjs.com/package/speedy-vision	[ "# npm\n\n## speedy-vision", null, "0.9.0-wip • Public • Published\n\n# speedy-vision.js\n\nBuild real-time stuff with speedy-vision.js, a GPU-accelerated Computer Vision library for JavaScript.", null, "## Features\n\n• Feature detection\n• Harris corner detector\n• FAST feature detector\n• ORB feature descriptor\n• Feature tracking\n• KLT feature tracker\n• LK optical flow\n• Feature matching\n• Soon\n• Geometric transformations\n• Homography matrix\n• Affine transform\n• Image processing\n• Convert to greyscale\n• Convolution\n• Gaussian blur, box & median filters\n• Image normalization & warping\n• Image pyramids\n• Linear Algebra\n• Beautiful matrix algebra with a fluent interface\n• Efficient computations with WebAssembly\n• Systems of linear equations\n• QR decomposition\n\n... and more in development!\n\nThere are plenty of demos available!\n\n## Author\n\nspeedy-vision.js is developed by Alexandre Martins, a computer scientist from Brazil. It is released under the Apache-2.0 license.\n\nIf my work is of value to you, make a donation. Thank you.\n\nFor general enquiries, contact me at `alemartf` `at` `gmail` `dot` `com`.\n\n## Demos\n\nTry the demos and take a look at their source code:\n\n## Installation\n\nDownload the latest release of speedy-vision.js and include it in the `<head>` section of your HTML page:\n\n`<script src=\"dist/speedy-vision.min.js\"></script>`\n\nOnce you import the library, the `Speedy` object will be exposed. Check out the Hello World demo for a working example.\n\n## Motivation\n\nDetecting features in an image is an important step of many computer vision algorithms. Traditionally, the computationally expensive nature of this process made it difficult to bring interactive Computer Vision applications to the web browser. The framerates were unsatisfactory for a compelling user experience. Speedy, a short name for speedy-vision.js, is a JavaScript library created to address this issue.\n\nSpeedy's real-time performance in the web browser is possible thanks to its efficient WebGL2 backend and to its GPU implementations of fast computer vision algorithms. With an easy-to-use API, Speedy is an excellent choice for real-time computer vision projects involving tasks such as: object detection in videos, pose estimation, Simultaneous Location and Mapping (SLAM), and others.\n\n## The Pipeline\n\nThe pipeline is a central concept in Speedy. It's a powerful structure that lets you organize the computations that take place in the GPU. It's a very flexible, yet conceptually simple, way of working with computer vision and image processing. Let's define a few things:\n\n• A pipeline is a network of nodes in which data flows downstream from one or more sources to one or more sinks.\n• Nodes have input and/or output ports. A node with no input ports is called a source. A node with no output ports is called a sink. A node with both input and output ports transforms the input data in some way and writes the results to its output port(s).\n• A link connects an output port of a node to an input port of another node. Two nodes are said to be connected if there is a link connecting their ports. Data flows from one node to another by means of a link. An input port may only be connected to a single output port, but an output port may be connected to multiple input ports.\n• Input ports expect data of a certain type (e.g., an image). Output ports hold data of a certain type. Two ports may only be connected if their types match.\n• Ports may impose additional constraints on the data passing through them. For example, an input port may expect an image and also impose the constraint that this image must be greyscale.\n• Different nodes may have different parameters. These parameters can be adjusted and are meant to modify the output of the nodes in some way.\n• Nodes and their ports have names. An input port is typically called `\"in\"`. An output port is typically called `\"out\"`. These names can vary, e.g., if a node has more than one input / output port. Speedy automatically assigns names to the nodes, but you can assign your own names as well.\n\nThe picture below shows a visual representation of a pipeline that converts an image or video to greyscale. Data gets into the pipeline via the image source. It is then passed to the Convert to greyscale node. Finally, a greyscale image goes into the image sink, where it gets out of the pipeline.", null, "Here's a little bit of code:\n\n```// Load an image\nconst img = document.querySelector('img');\n\n// Create the pipeline and the nodes\nconst pipeline = Speedy.Pipeline();\nconst source = Speedy.Image.Source();\nconst sink = Speedy.Image.Sink();\nconst greyscale = Speedy.Filter.Greyscale();\n\n// Set the media source\nsource.media = media; // media is a SpeedyMedia object\n\n// Connect the nodes\nsource.output().connectTo(greyscale.input());\ngreyscale.output().connectTo(sink.input());\n\n// Specify the nodes to initialize the pipeline\npipeline.init(source, sink, greyscale);\n\n// Run the pipeline\nconst { image } = await pipeline.run(); // image is a SpeedyMedia\n\n// Create a <canvas> to display the result\nconst canvas = document.createElement('canvas');\ncanvas.width = image.width;\ncanvas.height = image.height;\ndocument.body.appendChild(canvas);\n\n// Display the result\nconst ctx = canvas.getContext('2d');\nctx.drawImage(media.source, 0, 0);```\n\nSpeedy provides many types of nodes. You can connect these nodes in a way that is suitable to your application, and Speedy will bring back the results you ask for.\n\n## API Reference\n\n### Media routines\n\nA `SpeedyMedia` object encapsulates a media object: an image, a video, a canvas or a bitmap.\n\n`Speedy.load(source: HTMLImageElement \| HTMLVideoElement \| HTMLCanvasElement \| ImageBitmap, options?: object): SpeedyPromise<SpeedyMedia>`\n\nTells Speedy to load `source`. The `source` parameter may be an image, a video, a canvas or a bitmap.\n\n###### Arguments\n• `source: HTMLImageElement \| HTMLVideoElement \| HTMLCanvasElement \| ImageBitmap`. The media source.\n• `options: object, optional`. Additional options for advanced configuration. See SpeedyMedia.options for details.\n###### Returns\n\nA `SpeedyPromise<SpeedyMedia>` that resolves as soon as the media source is loaded.\n\n###### Example\n```window.onload = async function() {\nlet image = document.getElementById('my-image'); // <img id=\"my-image\" src=\"...\">\n}```\n##### Speedy.camera()\n\n`Speedy.camera(width?: number, height?: number): SpeedyPromise<SpeedyMedia>`\n\n`Speedy.camera(constraints: MediaStreamConstraints): SpeedyPromise<SpeedyMedia>`\n\nLoads a camera stream into a new `SpeedyMedia` object. This is a wrapper around `navigator.mediaDevices.getUserMedia()`, provided for your convenience.\n\n###### Arguments\n• `width: number, optional`. The ideal width of the stream. The browser will use this value or a close match. Defaults to `640`.\n• `height: number, optional`. The ideal height of the stream. The browser will use this value or a close match. Defaults to `360`.\n• `constraints: MediaStreamConstraints`. A MediaStreamConstraints dictionary to be passed to `getUserMedia()` for complete customization.\n###### Returns\n\nA `SpeedyPromise<SpeedyMedia>` that resolves as soon as the media source is loaded with the camera stream.\n\n###### Example\n```// Display the contents of a webcam\nconst media = await Speedy.camera();\nconst canvas = createCanvas(media.width, media.height);\nconst ctx = canvas.getContext('2d');\n\nfunction render()\n{\nctx.drawImage(media.source, 0, 0);\nrequestAnimationFrame(render);\n}\n\nrender();\n}\n\nfunction createCanvas(width, height)\n{\nconst canvas = document.createElement('canvas');\n\ncanvas.width = width;\ncanvas.height = height;\ndocument.body.appendChild(canvas);\n\nreturn canvas;\n}```\n##### SpeedyMedia.release()\n\n`SpeedyMedia.release(): null`\n\nReleases internal resources associated with this `SpeedyMedia`.\n\n###### Returns\n\nReturns `null`.\n\n#### Media properties\n\n##### SpeedyMedia.source\n\n`SpeedyMedia.source: HTMLImageElement \| HTMLVideoElement \| HTMLCanvasElement \| ImageBitmap, read-only`\n\nThe media source associated with the `SpeedyMedia` object.\n\n##### SpeedyMedia.type\n\n`SpeedyMedia.type: string, read-only`\n\nThe type of the media source. One of the following: `\"image\"`, `\"video\"`, `\"canvas\"`, `\"bitmap\"`.\n\n##### SpeedyMedia.width\n\n`SpeedyMedia.width: number, read-only`\n\nThe width of the media source, in pixels.\n\n##### SpeedyMedia.height\n\n`SpeedyMedia.height: number, read-only`\n\nThe height of the media source, in pixels.\n\n##### SpeedyMedia.size\n\n`SpeedyMedia.size: SpeedySize, read-only`\n\nThe size of the media, in pixels.\n\n##### SpeedyMedia.options\n\n`SpeedyMedia.options: object, read-only`\n\n##### SpeedyMedia.clone()\n\n`SpeedyMedia.clone(): SpeedyPromise<SpeedyMedia>`\n\nClones the `SpeedyMedia` object.\n\n###### Returns\n\nA `SpeedyPromise` that resolves to a clone of the `SpeedyMedia` object.\n\n###### Example\n`const clone = await media.clone();`\n##### SpeedyMedia.toBitmap()\n\n`SpeedyMedia.toBitmap(): SpeedyPromise<ImageBitmap>`\n\nConverts the media to an `ImageBitmap`.\n\n###### Returns\n\nA `SpeedyPromise` that resolves to an `ImageBitmap`.\n\n### Pipeline\n\n#### Basic routines\n\n##### Speedy.Pipeline.Pipeline()\n\n`Speedy.Pipeline.Pipeline(): SpeedyPipeline`\n\nCreates a new, empty pipeline.\n\n###### Returns\n\nA new `SpeedyPipeline` object.\n\n##### SpeedyPipeline.init()\n\n`SpeedyPipeline.init(...nodes: ...SpeedyPipelineNode): SpeedyPipeline`\n\nInitializes a pipeline with the specified `nodes`.\n\n###### Arguments\n• `...nodes: ...SpeedyPipelineNode`. The list of nodes that belong to the pipeline.\n###### Returns\n\nThe pipeline itself.\n\n###### Example\n```const pipeline = Speedy.Pipeline(); // create the pipeline and the nodes\nconst source = Speedy.Image.Source();\nconst sink = Speedy.Image.Sink();\nconst greyscale = Speedy.Filter.Greyscale();\n\nsource.media = media; // set the media source\n\nsource.output().connectTo(greyscale.input()); // connect the nodes\ngreyscale.output().connectTo(sink.input());\n\npipeline.init(source, sink, greyscale); // add the nodes to the pipeline```\n##### SpeedyPipeline.release()\n\n`SpeedyPipeline.release(): null`\n\nReleases the resources associated with `this` pipeline.\n\n###### Returns\n\nReturns `null`.\n\n##### SpeedyPipeline.run()\n\n`SpeedyPipeline.run(): SpeedyPromise<object>`\n\nRuns `this` pipeline.\n\n###### Returns\n\nReturns a `SpeedyPromise` that resolves to an object whose keys are the names of the sinks of the pipeline and whose values are the data exported by those sinks.\n\n###### Example\n`const { sink1, sink2 } = await pipeline.run();`\n##### SpeedyPipeline.node()\n\n`SpeedyPipeline.node(name: string): SpeedyPipelineNode \| null`\n\nFinds a node by its `name`.\n\n###### Arguments\n• `name: string`. Name of the target node.\n###### Returns\n\nReturns a `SpeedyPipelineNode` that has the specified `name` and that belongs to `this` pipeline, or `null` if there is no such node.\n\n##### SpeedyPipelineNode.input()\n\n`SpeedyPipelineNode.input(portName?: string): SpeedyPipelineNodePort`\n\nThe input port of `this` node whose name is `portName`.\n\n###### Arguments\n• `portName: string, optional`. The name of the port you want to access. Defaults to `\"in\"`.\n###### Returns\n\nThe requested input port.\n\n##### SpeedyPipelineNode.output()\n\n`SpeedyPipelineNode.output(portName?: string): SpeedyPipelineNodePort`\n\nThe output port of `this` node whose name is `portName`.\n\n###### Arguments\n• `portName: string, optional`. The name of the port you want to access. Defaults to `\"out\"`.\n###### Returns\n\nThe requested output port.\n\n##### SpeedyPipelineNodePort.connectTo()\n\n`SpeedyPipelineNodePort.connectTo(port: SpeedyPipelineNodePort): void`\n\nCreates a link connecting `this` port to another `port`.\n\n#### Basic properties\n\n##### SpeedyPipelineNode.name\n\n`SpeedyPipelineNode.name: string, read-only`\n\nThe name of the node.\n\n##### SpeedyPipelineNode.fullName\n\n`SpeedyPipelineNode.fullName: string, read-only`\n\nA string that exhibits the name and the type of the node.\n\n##### SpeedyPipelineNodePort.name\n\n`SpeedyPipelineNodePort.name: string, read-only`\n\nThe name of the port.\n\n##### SpeedyPipelineNodePort.node\n\n`SpeedyPipelineNodePort.node: SpeedyPipelineNode, read-only`\n\nThe node to which `this` port belongs.\n\n#### Basic nodes\n\n##### Speedy.Image.Source()\n\n`Speedy.Image.Source(name?: string): SpeedyPipelineNodeImageInput`\n\nCreates an image source with the specified name. If the name is not specified, Speedy will automatically generate a name for you.\n\n###### Parameters\n• `media: SpeedyMedia`. The media to be imported into the pipeline.\n###### Ports\nPort name Data type Description\n`\"out\"` Image An image corresponding to the `media` of this node.\n##### Speedy.Image.Sink()\n\n`Speedy.Image.Sink(name?: string): SpeedyPipelineNodeImageOutput`\n\nCreates an image sink with the specified name. If the name is not specified, Speedy will call this node `\"image\"`. A `SpeedyMedia` object will be exported from the pipeline.\n\n###### Ports\nPort name Data type Description\n`\"in\"` Image An image to be exported from the pipeline.\n\n### Image processing\n\n#### Image basics\n\n##### Speedy.Image.Pyramid()\n\n`Speedy.Image.Pyramid(name?: string): SpeedyPipelineNodeImagePyramid`\n\nGenerate a Gaussian pyramid. A pyramid is a texture with mipmaps.\n\nPort name Data type Description\n`\"in\"` Image Input image.\n`\"out\"` Image Gaussian pyramid.\n##### Speedy.Image.Multiplexer()\n\n`Speedy.Image.Multiplexer(name?: string): SpeedyPipelineNodeImageMultiplexer`\n\nAn image multiplexer receives two images as input and outputs one of the them.\n\n###### Parameters\n• `port: number`. Which input image should be redirected to the output: `0` or `1`? Defaults to `0`.\n###### Ports\nPort name Data type Description\n`\"in0\"` Image First image.\n`\"in1\"` Image Second image.\n`\"out\"` Image Either the first or the second image, depending on the value of `port`.\n##### Speedy.Image.Buffer()\n\n`Speedy.Image.Buffer(name?: string): SpeedyPipelineNodeImageBuffer`\n\nAn image buffer outputs at time t the input image received at time t-1. It's useful for tracking.\n\nNote: an image buffer cannot be used to store a pyramid at this time.\n\n###### Parameters\n• `frozen: boolean`. A frozen buffer discards the input, effectively increasing the buffering time. Defaults to `false`.\n###### Ports\nPort name Data type Description\n`\"in\"` Image Input image at time t.\n`\"out\"` Image Output image: the input image at time t-1.\n##### Speedy.Image.Mixer()\n\n`Speedy.Image.Mixer(name?: string): SpeedyPipelineNodeImageMixer`\n\nAn image mixer combines two images, image0 and image1, as follows:\n\noutput = `alpha` * image0 + `beta` * image1 + `gamma`\n\nThe above expression will be computed for each pixel of the resulting image and then clamped to the [0,1] interval. The dimensions of the resulting image will be the dimensions of the larger of the input images.\n\nNote: Both input images must have the same format. If they're colored, the above expression will be evaluated in each color channel independently.\n\nTip: if you pick an `alpha` between 0 and 1, set `beta` to `1 - alpha` and set `gamma` to 0, you'll get a nice alpha blending effect.\n\n###### Parameters\n• `alpha: number`. A scalar value. Defaults to 0.5.\n• `beta: number`. A scalar value. Defaults to 0.5.\n• `gamma: number`. A scalar value. Defaults to 0.0.\n###### Ports\nPort name Data type Description\n`\"in0\"` Image Input image: the image0 above\n`\"in1\"` Image Input image: the image1 above\n`\"out\"` Image Output image\n\n#### Image filters\n\n##### Speedy.Filter.Greyscale()\n\n`Speedy.Filter.Greyscale(name?: string): SpeedyPipelineNodeGreyscale`\n\nConvert an image to greyscale.\n\n###### Ports\nPort name Data type Description\n`\"in\"` Image Input image.\n`\"out\"` Image The input image converted to greyscale.\n##### Speedy.Filter.SimpleBlur()\n\n`Speedy.Filter.SimpleBlur(name?: string): SpeedyPipelineNodeSimpleBlur`\n\nBlur an image using a box filter.\n\n###### Parameters\n• `kernelSize: SpeedySize`. The size of the convolution kernel: from 3x3 to 15x15. Defaults to 5x5.\n###### Ports\nPort name Data type Description\n`\"in\"` Image Input image.\n`\"out\"` Image The input image, blurred.\n##### Speedy.Filter.GaussianBlur()\n\n`Speedy.Filter.SimpleBlur(name?: string): SpeedyPipelineNodeGaussianBlur`\n\nBlur an image using a Gaussian filter.\n\n###### Parameters\n• `kernelSize: SpeedySize`. The size of the convolution kernel: from 3x3 to 15x15. Defaults to 5x5.\n• `sigma: SpeedyVector2`. The sigma of the Gaussian function in both x and y axes. If set to the zero vector, Speedy will automatically pick a sigma according to the selected `kernelSize`. Defaults to (0,0).\n###### Ports\nPort name Data type Description\n`\"in\"` Image Input image.\n`\"out\"` Image The input image, blurred.\n##### Speedy.Filter.MedianBlur()\n\n`Speedy.Filter.MedianBlur(name?: string): SpeedyPipelineNodeMedianBlur`\n\nMedian filter.\n\n###### Parameters\n• `kernelSize: SpeedySize`. One of the following: 3x3, 5x5 or 7x7. Defaults to 5x5.\n###### Ports\nPort name Data type Description\n`\"in\"` Image A greyscale image.\n`\"out\"` Image The result of the median blur.\n###### Example\n```const median = Speedy.Filter.MedianBlur();\nmedian.kernelSize = Speedy.Size(7,7);```\n##### Speedy.Filter.Convolution()\n\n`Speedy.Filter.Convolution(name?: string): SpeedyPipelineNodeConvolution`\n\nCompute the convolution of an image using a 2D kernel.\n\n###### Parameters\n• `kernel: SpeedyMatrixExpr`. A 3x3, 5x5 or 7x7 matrix.\n###### Ports\nPort name Data type Description\n`\"in\"` Image Input image.\n`\"out\"` Image The result of the convolution.\n###### Example\n```// Sharpening an image\nconst sharpen = Speedy.Filter.Convolution();\nsharpen.kernel = Speedy.Matrix(3, 3, [\n0,-1, 0,\n-1, 5,-1,\n0,-1, 0\n]);```\n##### Speedy.Filter.Normalize()\n\n`Speedy.Filter.Normalize(name?: string): SpeedyPipelineNodeNormalize`\n\nNormalize the intensity values of the input image to the [`minValue`, `maxValue`] interval.\n\n###### Parameters\n• `minValue: number`. A value in [0,255].\n• `maxValue: number`. A value in [0,255] greater than or equal to `minValue`.\n###### Ports\nPort name Data type Description\n`\"in\"` Image Greyscale image.\n`\"out\"` Image Normalized image.\n##### Speedy.Filter.Nightvision()\n\n`Speedy.Filter.Nightvision(name?: string): SpeedyPipelineNodeNightvision`\n\nNightvision filter for local contrast stretching and brightness control.\n\n###### Parameters\n• `gain: number`. A value in [0,1]: the larger the number, the higher the contrast. Defaults to `0.5`.\n• `offset: number`. A value in [0,1] that controls the brightness. Defaults to `0.5`.\n• `decay: number`. A value in [0,1] specifying a contrast decay from the center of the image. Defaults to zero (no decay).\n• `quality: string`. Quality level: `\"high\"`, `\"medium\"` or `\"low\"`. Defaults to `\"medium\"`.\n###### Ports\nPort name Data type Description\n`\"in\"` Image Input image.\n`\"out\"` Image Output image.\n\n#### General transformations\n\n##### Speedy.Transform.Resize()\n\n`Speedy.Transform.Resize(name?: string): SpeedyPipelineNodeResize`\n\nResize an image.\n\n###### Parameters\n• `size: SpeedySize`. The size of the output image, in pixels. If set to zero, `scale` will be used to determine the size of the output. Defaults to zero.\n• `scale: SpeedyVector2`. The size of the output image relative to the size of the input image. This parameter is only applied if `size` is zero. Defaults to (1,1), meaning: keep the original size.\n• `method: string`. Resize method. One of the following: `\"bilinear\"` (bilinear interpolation) or `\"nearest\"` (nearest neighbors). Defaults to `\"bilinear\"`.\n###### Ports\nPort name Data type Description\n`\"in\"` Image Input image.\n`\"out\"` Image Resized image.\n##### Speedy.Transform.PerspectiveWarp()\n\n`Speedy.Transform.PerspectiveWarp(name?: string): SpeedyPipelineNodePerspectiveWarp`\n\nWarp an image using a homography matrix.\n\n###### Parameters\n• `transform: SpeedyMatrixExpr`. A 3x3 perspective transformation. Defaults to the identity matrix.\n###### Ports\nPort name Data type Description\n`\"in\"` Image Input image.\n`\"out\"` Image Warped image.\n\n### Keypoints and descriptors\n\nA keypoint is a small patch in an image that is somehow distinctive. For example, a small patch with significant intensity changes in both x and y axes (i.e., a \"corner\") is distinctive. If we pick two \"similar\" images, we should be able to locate a set of keypoints in each of them and then match those keypoints based on their similarity.\n\nA descriptor is a mathematical object that somehow describes a keypoint. Two keypoints are considered to be \"similar\" if their descriptors are \"similar\". Speedy works with binary descriptors, meaning that keypoints are described using bit vectors of fixed length.\n\nThere are different ways to detect and describe keypoints. For example, in order to detect a keypoint, you may take a look at the pixel intensities around a point or perhaps study the image derivatives. You may describe a keypoint by comparing the pixel intensities of the image patch in a special way. Additionally, it's possible to conceive a way to describe a keypoint in such a way that, if you rotate the patch, the descriptor stays roughly the same. This is called rotational invariance and is usually a desirable property for a descriptor.\n\nSpeedy offers different options for processing keypoints in multiple ways. A novelty of this work is that Speedy's implementations have been either adapted from the literature or conceived from scratch to work on the GPU. Therefore, keypoint processing is done in parallel and is often very fast.\n\n#### Keypoint basics\n\n##### SpeedyKeypoint\n\nA `SpeedyKeypoint` object represents a keypoint.\n\n###### SpeedyKeypoint.position\n\n`SpeedyKeypoint.position: SpeedyPoint2`\n\nThe position of the keypoint in the image.\n\n###### SpeedyKeypoint.x\n\n`SpeedyKeypoint.x: number`\n\nThe x position of the keypoint in the image. A shortcut to `position.x`.\n\n###### SpeedyKeypoint.y\n\n`SpeedyKeypoint.y: number`\n\nThe y position of the keypoint in the image. A shortcut to `position.y`.\n\n###### SpeedyKeypoint.lod\n\n`SpeedyKeypoint.lod: number`\n\nThe level-of-detail (pyramid level) from which the keypoint was extracted, starting from zero. Defaults to `0.0`.\n\n###### SpeedyKeypoint.scale\n\n`SpeedyKeypoint.scale: number`\n\nThe scale of the keypoint. This is equivalent to 2 ^ lod. Defaults to `1.0`.\n\n###### SpeedyKeypoint.rotation\n\n`SpeedyKeypoint.rotation: number`\n\nThe orientation angle of the keypoint, in radians. Defaults to `0.0`.\n\n###### SpeedyKeypoint.score\n\n`SpeedyKeypoint.score: number`\n\nThe score is a measure associated with the keypoint. Although different detection methods employ different measurement strategies, the larger the score, the \"better\" the keypoint is considered to be. The score is always a positive value.\n\n###### SpeedyKeypoint.descriptor\n\n`SpeedyKeypoint.descriptor: SpeedyKeypointDescriptor \| null, read-only`\n\nThe descriptor associated with the keypoint, if it exists.\n\n##### SpeedyKeypointDescriptor\n\nA `SpeedyKeypointDescriptor` represents a keypoint descriptor.\n\n###### SpeedyKeypointDescriptor.data\n\n`SpeedyKeypointDescriptor.data: Uint8Array, read-only`\n\nThe bytes of the keypoint descriptor.\n\n###### SpeedyKeypointDescriptor.size\n\n`SpeedyKeypointDescriptor.size: number, read-only`\n\nThe size of the keypoint descriptor, in bytes.\n\n###### SpeedyKeypointDescriptor.toString()\n\n`SpeedyKeypointDescriptor.toString(): string`\n\nReturns a string representation of the keypoint descriptor.\n\n##### SpeedyTrackedKeypoint\n\nA `SpeedyTrackedKeypoint` is a `SpeedyKeypoint` with the following additional properties:\n\n###### SpeedyTrackerKeypoint.flow\n\n`SpeedyTrackedKeypoint.flow: SpeedyVector2`\n\nA displacement vector associated with the tracked keypoint.\n\n##### Speedy.Keypoint.Source()\n\n`Speedy.Keypoint.Source(name?: string): SpeedyPipelineNodeKeypointSource`\n\nCreates a source of keypoints. Only the position, score and scale of the provided keypoints will be imported to the pipeline. Descriptors, if present, will be lost.\n\n###### Parameters\n• `keypoints: SpeedyKeypoint[]`. The keypoints you want to import.\n• `capacity: number`. The maximum number of keypoints that can be imported to the GPU. If you have an idea of how many keypoints you expect (at most), use a tight bound to make processing more efficient. The default capacity is `2048`. It can be no larger than `8192`.\n###### Ports\nPort name Data type Description\n`\"out\"` Keypoints The imported set of keypoints.\n##### Speedy.Keypoint.Sink()\n\n`Speedy.Keypoint.Sink(name?: string): SpeedyPipelineNodeKeypointSink`\n\nCreates a sink of keypoints using the specified name. If the name is not specified, Speedy will call this node `\"keypoints\"`. An array of `SpeedyKeypoint` objects will be exported from the pipeline.\n\n###### Parameters\n• `turbo: boolean`. Accelerate GPU-CPU transfers. You'll get the data from the previous frame. Defaults to `false`.\n• `includeDiscarded: boolean`. Set discarded keypoints (e.g., by a tracker) to `null` in the exported set. Defaults to `false`, meaning that discarded keypoints will simply be dropped from the exported set rather than being set to `null`.\n###### Ports\nPort name Data type Description\n`\"in\"` Keypoints A set of keypoints to be exported from the pipeline.\n##### Speedy.Keypoint.SinkOfTrackedKeypoints()\n\n`Speedy.Keypoint.SinkOfTrackedKeypoints(name?: string): SpeedyPipelineNodeTrackedKeypointSink`\n\nCreates a sink of tracked keypoints using the specified name. If the name is not specified, Speedy will call this node `\"keypoints\"`. An array of `SpeedyTrackedKeypoint` objects will be exported from the pipeline.\n\n###### Parameters\n\nThe same as `SpeedyPipelineNodeKeypointSink`.\n\n###### Ports\nPort name Data type Description\n`\"in\"` Keypoints A set of keypoints to be exported from the pipeline.\n`\"flow\"` Vector2 A set of displacement vectors associated with each keypoint.\n##### Speedy.Keypoint.Clipper()\n\n`Speedy.Keypoint.Clipper(name?: string): SpeedyPipelineNodeKeypointClipper`\n\nClips a set of keypoints, so that it outputs no more than a fixed quantity of them. When generating the output, it will choose the \"best\" keypoints according to their score metric. The keypoint clipper is a very useful tool to reduce processing time, since it can discard \"bad\" keypoints regardless of the sensitivity of their detector. The clipping must be applied before computing any descriptors.\n\n###### Parameters\n• `size: number`. A positive integer. No more than this number of keypoints will be available in the output.\n###### Ports\nPort name Data type Description\n`\"in\"` Keypoints A set of keypoints.\n`\"out\"` Keypoints A set of at most `size` keypoints.\n##### Speedy.Keypoint.BorderClipper()\n\n`Speedy.Keypoint.BorderClipper(name?: string): SpeedyPipelineNodeKeypointBorderClipper`\n\nRemoves all keypoints within a specified border of the edge of an image. The border is specified in pixels as an ordered pair of integers: the first is the size of the horizontal border and the second is the size of the vertical border.\n\n###### Parameters\n• `imageSize: SpeedySize`. Image size, in pixels.\n• `borderSize: SpeedyVector2`. Border size in both x and y axes. Defaults to zero, meaning that no clipping takes place.\n###### Ports\nPort name Data type Description\n`\"in\"` Keypoints A set of keypoints.\n`\"out\"` Keypoints The clipped set of keypoints.\n##### Speedy.Keypoint.Mixer()\n\n`Speedy.Keypoint.Mixer(name?: string): SpeedyPipelineNodeKeypointMixer`\n\nMixes (merges) two sets of keypoints.\n\n###### Ports\nPort name Data type Description\n`\"in0\"` Keypoints A set of keypoints.\n`\"in1\"` Keypoints Another set of keypoints.\n`\"out\"` Keypoints The union of the two input sets.\n##### Speedy.Keypoint.Buffer()\n\n`Speedy.Keypoint.Buffer(name?: string): SpeedyPipelineNodeKeypointBuffer`\n\nA keypoint buffer outputs at time t the keypoints received at time t-1.\n\n###### Parameters\n• `frozen: boolean`. A frozen buffer discards the input, effectively increasing the buffering time. Defaults to `false`.\n###### Ports\nPort name Data type Description\n`\"in\"` Keypoints A set of keypoints at time t.\n`\"out\"` Keypoints The set of keypoints received at time t-1.\n##### Speedy.Keypoint.Multiplexer()\n\n`Speedy.Keypoint.Multiplexer(name?: string): SpeedyPipelineNodeKeypointMultiplexer`\n\nA keypoint multiplexer receives two sets of keypoints as input and outputs one of the them.\n\n###### Parameters\n• `port: number`. Which input set of keypoints should be redirected to the output: `0` or `1`? Defaults to `0`.\n###### Ports\nPort name Data type Description\n`\"in0\"` Image First set of keypoints.\n`\"in1\"` Image Second set of keypoints.\n`\"out\"` Image Either the first or the second set of keypoints, depending on the value of `port`.\n##### Speedy.Keypoint.Transformer()\n\n`Speedy.Keypoint.Transformer(name?: string): SpeedyPipelineNodeKeypointTransformer`\n\nApplies a transformation matrix to a set of keypoints.\n\n###### Parameters\n• `transform: SpeedyMatrix`. A 3x3 homography matrix. Defaults to the identity matrix.\n###### Ports\nPort name Data type Description\n`\"in\"` Keypoints A set of keypoints.\n`\"out\"` Keypoints A transformed set of keypoints.\n##### Speedy.Keypoint.SubpixelRefiner()\n\n`Speedy.Keypoint.SubpixelRefiner(name?: string): SpeedyPipelineNodeKeypointSubpixelRefiner`\n\nRefines the position of a set of keypoints down to the subpixel level.\n\nNote 1: filter the image to reduce the noise before working at the subpixel level.\n\nNote 2: if there are keypoints in multiple scales, make sure to provide a pyramid as input.\n\nNote 3: the position of the keypoints is stored as fixed-point. This representation may introduce a loss of accuracy (~0.1 pixel). This is probably enough already, but if you need higher accuracy, ignore the output keypoints and work with the displacement vectors instead. These are encoded as floating-point. In addition, use the upsampling methods.\n\n###### Parameters\n• `method: string`. The method to be used to compute the subpixel displacement. See the table below.\n• `maxIterations: number`. The maximum number of iterations used by methods `\"bicubic-upsample\"` and `\"bilinear-upsample\"`. Defaults to 6.\n• `epsilon: number`. The threshold used to determine when the subpixel displacement has reached convergence. Used with methods `\"bicubic-upsample\"` and `\"bilinear-upsample\"`. Defaults to 0.1 pixel.\n\nTable of methods:\n\nMethod Description\n`\"quadratic1d\"` Maximize a 1D parabola fit to a corner strength function. This is the default method.\n`\"taylor2d\"` Maximize a second-order 2D Taylor expansion of a corner strength function. Method `\"quadratic1d\"` seems to perform slightly better than this, but your mileage may vary.\n`\"bicubic-upsample\"` Iteratively upsample the image using bicubic interpolation in order to maximize a corner strength function. Repeat until convergence or until a maximum number of iterations is reached.\n`\"bilinear-upsample\"` Analogous to bicubic upsample, but this method uses bilinear interpolation instead.\n###### Ports\nPort name Data type Description\n`\"image\"` Image An image or pyramid from which you extracted the keypoints.\n`\"keypoints\"` Keypoints Input set of keypoints.\n`\"out\"` Keypoints Subpixel-refined output set of keypoints.\n`\"displacements\"` Vector2 Displacement vectors (output).\n##### Speedy.Keypoint.DistanceFilter()\n\n`Speedy.Keypoint.DistanceFilter(name?: string): SpeedyPipelineNodeKeypointDistanceFilter`\n\nGiven a set of pairs of keypoints, discard all pairs whose distance is above a user-defined threshold. This is useful for implementing bidirectional optical-flow.\n\nThe pairs of keypoints are provided as two separate sets, \"in\" and \"reference\". Keypoints that are kept will have their data extracted from the \"in\" set.\n\n###### Parameters\n• `threshold: number`. Distance threshold, given in pixels.\n###### Ports\nPort name Data type Description\n`\"in\"` Keypoints A set of keypoints.\n`\"reference\"` Keypoints A reference set of keypoints.\n`\"out\"` Keypoints Filtered set of keypoints.\n##### Speedy.Keypoint.HammingDistanceFilter()\n\n`Speedy.Keypoint.HammingDistanceFilter(name?: string): SpeedyPipelineNodeKeypointHammingDistanceFilter`\n\nGiven a set of pairs of keypoints with descriptors, discard all pairs whose Hamming distance between their descriptors is above a user-defined threshold.\n\nThe pairs of keypoints are provided as two separate sets, \"in\" and \"reference\". Keypoints that are kept will have their data extracted from the \"in\" set.\n\n###### Parameters\n• `threshold: number`. Distance threshold, an integer.\n###### Ports\nPort name Data type Description\n`\"in\"` Keypoints A set of keypoints.\n`\"reference\"` Keypoints A reference set of keypoints.\n`\"out\"` Keypoints Filtered set of keypoints.\n##### Speedy.Keypoint.Shuffler()\n\n`Speedy.Keypoint.Shuffler(name?: string): SpeedyPipelineNodeKeypointShuffler`\n\nShuffles the input keypoints, optionally clipping the output set.\n\n###### Parameters\n• `maxKeypoints: number`. Maximum number of keypoints of the output set. If unspecified, the number of keypoints of the output set will be the number of keypoints of the input set.\n###### Ports\nPort name Data type Description\n`\"in\"` Keypoints A set of keypoints.\n`\"out\"` Keypoints The input set of keypoints, shuffled and possibly clipped.\n\n#### Keypoint detection\n\nThe following nodes expect greyscale images as input. They output a set of keypoints.\n\n##### Speedy.Keypoint.Detector.FAST()\n\n`Speedy.Keypoint.Detector.FAST(name?: string): SpeedyPipelineNodeFASTKeypointDetector`\n\nFAST keypoint detector. Speedy implements the FAST-9,16 variant of the algorithm.\n\nTo use the multi-scale version of the algorithm, pass a pyramid as input, set the number of levels you want to scan and optionally set the scale factor. After scanning all levels and performing non-maximum suppression, the scale of the keypoints will be set by means of interpolation using the scale that maximizes a response measure and its adjacent scales.\n\n###### Parameters\n• `threshold: number`. An integer between `0` and `255`, inclusive. The larger the number, the \"stronger\" your keypoints will be. The smaller the number, the more keypoint you will get. Numbers between `20` and `50` are usually meaningful.\n• `levels: number`. The number of pyramid levels you want to use. Defaults to `1` (i.e., no pyramid is used). When using a pyramid, a value such as `7` is a reasonable choice.\n• `scaleFactor: number`. The scale factor between two consecutive levels of the pyramid. This is a value between `1` (exclusive) and `2` (inclusive). Defaults to the square root of two. This is applicable only when using a pyramid.\n• `capacity: number`. The maximum number of keypoints that can be detected by this node. The default capacity is `2048`. It can be no larger than `8192`.\n###### Ports\nPort name Data type Description\n`\"in\"` Image Greyscale image or pyramid.\n`\"out\"` Keypoints Detected keypoints.\n##### Speedy.Keypoint.Detector.Harris()\n\n`Speedy.Keypoint.Detector.Harris(name?: string): SpeedyPipelineNodeHarrisKeypointDetector`\n\nHarris corner detector. Speedy implements the Shi-Tomasi corner response for best results.\n\nTo use the multi-scale version of the algorithm, pass a pyramid as input, set the number of levels you want to scan and optionally set the scale factor. After scanning all levels and performing non-maximum suppression, the scale of the keypoints will be set by means of interpolation using the scale that maximizes a response measure and its adjacent scales.\n\n###### Parameters\n• `quality: number`. A value between `0` and `1` representing the minimum \"quality\" of the returned keypoints. Speedy will discard any keypoint whose score is lower than the specified percentage of the maximum keypoint score found in the image. A typical value for this parameter is `0.10` (10%).\n• `levels: number`. The number of pyramid levels you want to use. Defaults to `1` (i.e., no pyramid is used). When using a pyramid, a value such as `7` is a reasonable choice.\n• `scaleFactor: number`. The scale factor between two consecutive levels of the pyramid. This is a value between `1` (exclusive) and `2` (inclusive). Defaults to the square root of two. This is applicable only when using a pyramid.\n• `capacity: number`. The maximum number of keypoints that can be detected by this node. The default capacity is `2048`. It can be no larger than `8192`.\n###### Ports\nPort name Data type Description\n`\"in\"` Image Greyscale image or pyramid.\n`\"out\"` Keypoints Detected keypoints.\n\n#### Keypoint description\n\n##### Speedy.Keypoint.Descriptor.ORB()\n\n`Speedy.Keypoint.Descriptor.ORB(name?: string): SpeedyPipelineNodeORBKeypointDescriptor`\n\nORB descriptors. In order to improve robustness to noise, apply a Gaussian filter to the image before computing the descriptors.\n\n###### Ports\nPort name Data type Description\n`\"image\"` Image Input image. Must be greyscale.\n`\"keypoints\"` Keypoints Input keypoints.\n`\"out\"` Keypoints Keypoints with descriptors.\n###### Example\n```/\n\nThis is our pipeline:\n\nImage ---> Convert to ---> Image ------> FAST corner -----> Keypoint ---> ORB ----------> Keypoint\nSource greyscale Pyramid detector Clipper descriptors Sink\n\| ^\n\| \|\n+-------------------------> Gaussian ---------------------------+\nBlur\n/\n\nconst pipeline = Speedy.Pipeline();\nconst source = Speedy.Image.Source();\nconst greyscale = Speedy.Filter.Greyscale();\nconst pyramid = Speedy.Image.Pyramid();\nconst fast = Speedy.Keypoint.Detector.FAST();\nconst blur = Speedy.Filter.GaussianBlur();\nconst clipper = Speedy.Keypoint.Clipper();\nconst descriptor = Speedy.Keypoint.Descriptor.ORB();\nconst sink = Speedy.Keypoint.Sink();\n\nsource.media = media;\nblur.kernelSize = Speedy.Size(9, 9);\nblur.sigma = Speedy.Vector2(2, 2);\nfast.threshold = 50;\nfast.levels = 8; // pyramid levels\nfast.scaleFactor = 1.19; // approx. 2^0.25\nclipper.size = 800; // up to how many features?\n\nsource.output().connectTo(greyscale.input());\n\ngreyscale.output().connectTo(pyramid.input());\npyramid.output().connectTo(fast.input());\nfast.output().connectTo(clipper.input());\nclipper.output().connectTo(descriptor.input('keypoints'));\n\ngreyscale.output().connectTo(blur.input());\nblur.output().connectTo(descriptor.input('image'));\n\ndescriptor.output().connectTo(sink.input());\n\npipeline.init(source, greyscale, pyramid, blur, fast, clipper, descriptor, sink);```\n\n#### Keypoint tracking\n\nKeypoint tracking is the process of tracking keypoints across a sequence of images. It allows you to get a sense of how keypoints are moving in time - i.e., how fast they are moving and where they are going.\n\nSpeedy uses sparse optical-flow algorithms to track keypoints in a video. Applications of optical-flow are numerous: you may get a sense of how objects are moving in a scene, estimate how the camera itself is moving, detect a transition in a film (a cut between two shots), and so on.\n\n##### Speedy.Keypoint.Tracker.LK()\n\n`Speedy.Keypoint.Tracker.LK(name?: string): SpeedyPipelineNodeLKKeypointTracker`\n\nPyramid-based LK optical-flow.\n\n###### Parameters\n• `windowSize: SpeedySize`. The size of the window to be used by the feature tracker. The algorithm will read neighbor pixels to determine the motion of a keypoint. You must specify a square window. Typical sizes include: 7x7, 11x11, 15x15 (use positive odd integers). Defaults to 11x11.\n• `levels: number`. Specifies how many pyramid levels will be used in the computation. The more levels you use, the faster the motions you can capture. Defaults to `3`.\n• `discardThreshold: number`. A threshold used to discard keypoints that are not \"good\" candidates for tracking. The higher the value, the more keypoints will be discarded. Defaults to `0.0001`.\n• `numberOfIterations: number`. Maximum number of iterations for computing the local optical-flow on each level of the pyramid. Defaults to `30`.\n• `epsilon: number`. An accuracy threshold used to stop the computation of the local optical-flow of any level of the pyramid. The local optical-flow is computed iteratively and in small increments. If the length of an increment is too small, we discard it. This property defaults to `0.01`.\n###### Ports\nPort name Data type Description\n`\"previousImage\"` Image Input image at time t-1. Must be greyscale.\n`\"nextImage\"` Image Input image at time t. Must be greyscale.\n`\"previousKeypoints\"` Keypoints Input keypoints at time t-1.\n`\"out\"` Keypoints Output keypoints at time t.\n`\"flow\"` Vector2 Flow vectors (output) at time t.\n\nNote: you need to provide pyramids as input if `levels > 1`.\n\nSoon!\n\n### Portals\n\nPortals let you create loops within a pipeline. They also let you transfer data between different pipelines.\n\nA portal is defined by a set of nodes: a portal sink and one or more portal sources. The portal sink receives data from a node of a pipeline, which is then read by the portal source(s). The portal source(s) feed(s) one or more pipelines. The portal nodes may or may not belong to the same pipeline.\n\n#### Image Portals\n\n##### Speedy.Image.Portal.Source()\n\n`Speedy.Image.Portal.Source(name?: string): SpeedyPipelineNodeImagePortalSource`\n\nCreate a source of an Image Portal.\n\n###### Parameters\n• `source: SpeedyPipelineNodeImagePortalSink`. A sink of an Image Portal.\n###### Ports\nPort name Data type Description\n`\"out\"` Image An image.\n##### Speedy.Image.Portal.Sink()\n\n`Speedy.Image.Portal.Sink(name?: string): SpeedyPipelineNodeImagePortalSink`\n\nCreate a sink of an Image Portal.\n\nNote: pyramids can't travel through portals at this time.\n\n###### Ports\nPort name Data type Description\n`\"in\"` Image An image.\n\n#### Keypoint Portals\n\n##### Speedy.Keypoint.Portal.Source()\n\n`Speedy.Keypoint.Portal.Source(name?: string): SpeedyPipelineNodeKeypointPortalSource`\n\nCreate a source of a Keypoint Portal.\n\n###### Parameters\n• `source: SpeedyPipelineNodeKeypointPortalSink`. A sink of a Keypoint Portal.\n###### Ports\nPort name Data type Description\n`\"out\"` Keypoints A set of keypoints.\n##### Speedy.Keypoint.Portal.Sink()\n\n`Speedy.Keypoint.Portal.Sink(name?: string): SpeedyPipelineNodeKeypointPortalSink`\n\nCreate a sink of a Keypoint Portal.\n\n###### Ports\nPort name Data type Description\n`\"in\"` Keypoints A set of keypoints.\n\n### Linear Algebra\n\nMatrix computations play a crucial role in computer vision applications. Speedy includes its own implementation of numerical linear algebra algorithms.\n\nMatrix operations are specified using a fluent interface that has been crafted to be easy to use and to mirror how we write matrix algebra using pen-and-paper.\n\nSince numerical algorithms may be computationally demanding, Speedy uses WebAssembly for extra performance. Most matrix-related routines are written in C language. Matrices are stored in column-major format. Typed Arrays are used for storage.\n\nThere are two basic classes you need to be aware of: `SpeedyMatrix` and `SpeedyMatrixExpr`. The latter represents a symbolic expression, whereas the former represents an actual matrix with data. A `SpeedyMatrix` is a `SpeedyMatrixExpr`. A `SpeedyMatrixExpr` may be evaluated to a `SpeedyMatrix`.\n\n#### Creating new matrices\n\n##### Speedy.Matrix()\n\n`Speedy.Matrix(rows: number, columns: number, entries?: number[]): SpeedyMatrix`\n\n`Speedy.Matrix(expr: SpeedyMatrixExpr): SpeedyMatrix`\n\nFirst form: create a new matrix with the specified size and entries.\n\nSecond form: synchronously evaluate a matrix expression and store the result in a new matrix.\n\n###### Arguments\n• `rows: number`. The number of rows of the matrix.\n• `columns: number, optional`. The number of columns of the matrix. If not specified, it will be set to `rows` (i.e., you'll get a square matrix).\n• `entries: number[], optional`. The elements of the matrix in column-major format. The length of this array must be `rows * columns`.\n• `expr: SpeedyMatrixExpr`. The matrix expression to be evaluated.\n###### Returns\n\nA new `SpeedyMatrix`.\n\n###### Example\n```//\n// We use the column-major format to specify\n// the elements of the new matrix. For example,\n// to create the 2x3 matrix (2 rows, 3 columns)\n// below, we first specify the elements of the\n// first column, then the elements of the second\n// column, and finally the elements of the third\n// column.\n//\n// M = [ 1 3 5 ]\n// [ 2 4 6 ]\n//\nconst mat = Speedy.Matrix(2, 3, [\n1,\n2,\n3,\n4,\n5,\n6\n]);\n\n// Alternatively, we may write the data in\n// column-major format in a compact form:\nconst mat1 = Speedy.Matrix(2, 3, [\n1, 2, // first column\n3, 4, // second column\n5, 6 // third column\n]);\n\n// Print the matrices to the console\nconsole.log(mat.toString());\nconsole.log(mat1.toString());```\n##### Speedy.Matrix.Zeros()\n\n`Speedy.Matrix.Zeros(rows: number, columns?: number): SpeedyMatrix`\n\nCreate a new matrix filled with zeros.\n\n###### Arguments\n• `rows: number`. The number of rows of the matrix.\n• `columns: number, optional`. The number of columns of the matrix. If not specified, it will be set to `rows` (square matrix).\n###### Returns\n\nA new `rows` x `columns` `SpeedyMatrix` filled with zeros.\n\n###### Example\n```// A 3x3 matrix filled with zeros\nconst zeros = Speedy.Matrix.Zeros(3);```\n##### Speedy.Matrix.Ones()\n\n`Speedy.Matrix.Ones(rows: number, columns?: number): SpeedyMatrix`\n\nCreate a new matrix filled with ones.\n\n###### Arguments\n• `rows: number`. The number of rows of the matrix.\n• `columns: number, optional`. The number of columns of the matrix. If not specified, it will be set to `rows` (square matrix).\n###### Returns\n\nA new `rows` x `columns` `SpeedyMatrix` filled with ones.\n\n##### Speedy.Matrix.Eye()\n\n`Speedy.Matrix.Eye(rows: number, columns?: number): SpeedyMatrix`\n\nCreate a new matrix with ones on the main diagonal and zeros elsewhere.\n\n###### Arguments\n• `rows: number`. The number of rows of the matrix.\n• `columns: number, optional`. The number of columns of the matrix. If not specified, it will be set to `rows` (identity matrix).\n###### Returns\n\nA new `SpeedyMatrix` with the specified configuration.\n\n###### Example\n```// A 3x3 identity matrix\nconst eye = Speedy.Matrix.Eye(3);```\n\n#### Matrix properties\n\n##### SpeedyMatrixExpr.rows\n\n`SpeedyMatrixExpr.rows: number, read-only`\n\nThe number of rows of the matrix expression.\n\n##### SpeedyMatrixExpr.columns\n\n`SpeedyMatrixExpr.columns: number, read-only`\n\nThe number of columns of the matrix expression.\n\n##### SpeedyMatrixExpr.dtype\n\n`SpeedyMatrixExpr.dtype: string, read-only`\n\nThe constant `\"float32\"`.\n\n##### SpeedyMatrix.data\n\n`SpeedyMatrix.data: ArrayBufferView, read-only`\n\nData storage.\n\n##### SpeedyMatrix.step\n\n`SpeedyMatrix.step0: number, read-only`\n\n`SpeedyMatrix.step1: number, read-only`\n\nStorage steps. The (`i`, `j`) entry of the matrix is stored at `data[i * step0 + j * step1]`.\n\n`SpeedyMatrix.read(): number[]`\n\nRead the entries of the matrix.\n\n###### Returns\n\nAn array containing the entries of the matrix in column-major format.\n\n###### Example\n```const mat = Speedy.Matrix(2, 2, [\n1,\n2,\n3,\n4\n]);\n\nconsole.log(entries); // [ 1, 2, 3, 4 ]```\n##### SpeedyMatrix.at()\n\n`SpeedyMatrix.at(row: number, column: number): number`\n\nRead a single entry of the matrix.\n\n###### Arguments\n• `row: number`. Index of the row of the desired element (0-based).\n• `column: number`. Index of the column of the desired element (0-based).\n###### Returns\n\nThe requested entry of the matrix, or a NaN if the entry is outside bounds.\n\n###### Example\n```const A = Speedy.Matrix(2, 2, [\n1,\n2,\n3,\n4\n]);\n\nconst a00 = A.at(0, 0); // first row, first column\nconst a10 = A.at(1, 0); // second row, first column\nconst a01 = A.at(0, 1); // first row, second column\nconst a11 = A.at(1, 1); // second row, second column\n\nconsole.log([ a00, a10, a01, a11 ]); // [ 1, 2, 3, 4 ]```\n##### SpeedyMatrixExpr.toString()\n\n`SpeedyMatrixExpr.toString(): string`\n\nConvert a matrix expression to a string. Entries will only be included if `this` expression is a `SpeedyMatrix`.\n\n###### Returns\n\nA string representation of the matrix expression.\n\n#### Writing to the matrices\n\n##### SpeedyMatrix.setTo()\n\n`SpeedyMatrix.setTo(expr: SpeedyMatrixExpr): SpeedyPromise<SpeedyMatrix>`\n\nEvaluate a matrix expression and store the result in `this` matrix.\n\n###### Arguments\n• `expr: SpeedyMatrixExpr`. A matrix expression.\n###### Returns\n\nA `SpeedyPromise` that resolves to `this` matrix after evaluating `expr`.\n\n###### Example\n```//\n//\n// A = [ 1 3 ] B = [ 4 2 ]\n// [ 2 4 ] [ 3 1 ]\n//\n// We'll set C to the sum A + B\n//\nconst matA = Speedy.Matrix(2, 2, [\n1, 2,\n3, 4\n]);\nconst matB = Speedy.Matrix(2, 2, [\n4, 3,\n2, 1\n]);\n\n// Set C = A + B\nconst matC = Speedy.Matrix.Zeros(2, 2);\nawait matC.setTo(matA.plus(matB));\n\n//\n// Print the result:\n//\n// C = [ 5 5 ]\n// [ 5 5 ]\n//\nconsole.log(matC.toString());```\n##### SpeedyMatrix.fill()\n\n`SpeedyMatrix.fill(value: number): SpeedyPromise<SpeedyMatrix>`\n\nFill `this` matrix with a scalar.\n\n###### Arguments\n• `value: number`. Scalar value.\n###### Returns\n\nA `SpeedyPromise` that resolves to `this` matrix.\n\n###### Example\n```// Create a 5x5 matrix filled with twos\nconst twos = Speedy.Matrix.Zeros(5);\nawait twos.fill(2);```\n\n#### Synchronous writing\n\nSpeedy provides synchronous writing methods for convenience.\n\n`Speedy.Matrix.ready(): SpeedyPromise<void>`\n\nThis method lets you know that the matrix routines are initialized and ready to be used (the WebAssembly routines need to be loaded before usage). You should only use the synchronous writing methods when the matrix routines are ready.\n\n###### Returns\n\nA `SpeedyPromise` that resolves immediately if the matrix routines are already initialized, or as soon as they are initialized.\n\n##### SpeedyMatrix.setToSync()\n\n`SpeedyMatrix.setToSync(expr: SpeedyMatrixExpr): SpeedyMatrix`\n\nSynchronously evaluate a matrix expression and store the result in `this` matrix.\n\n###### Arguments\n• `expr: SpeedyMatrixExpr`. A matrix expression.\n###### Returns\n\nReturns `this` matrix after setting it to the result of `expr`.\n\n###### Example\n```Speedy.Matrix.ready().then(() => {\nconst mat = Speedy.Matrix.Eye(3); // I := identity matrix\nconst pot = 3; // power-of-two\n\nfor(let i = 0; i < pot; i++)\nmat.setToSync(mat.plus(mat)); // mat := mat + mat\n\nconsole.log(mat.toString()); // mat will be (2^pot) * I\n});```\n##### SpeedyMatrix.fillSync()\n\n`SpeedyMatrix.fillSync(value: number): SpeedyMatrix`\n\nSynchronously fill `this` matrix with a scalar.\n\n###### Arguments\n• `value: number`. Scalar value.\n###### Returns\n\nReturns `this` matrix after filling it with the provided `value`.\n\n#### Access by block\n\nSpeedy lets you work with blocks of matrices. This is a very handy feature! Blocks share memory with the originating matrices. If you modify the entries of a block of a matrix M, you'll modify the corresponding entries of M. Columns and rows are examples of blocks.\n\n##### SpeedyMatrix.block()\n\n`SpeedyMatrix.block(firstRow: number, lastRow: number, firstColumn: number, lastColumn: number): SpeedyMatrix`\n\nExtract a `lastRow - firstRow + 1` x `lastColumn - firstColumn + 1` block from the matrix. All indices are 0-based. They are all inclusive. The memory of the matrix is shared with the block.\n\n###### Arguments\n• `firstRow: number`. Index of the first row (0-based).\n• `lastRow: number`. Index of the last row (0-based). Use `lastRow >= firstRow`.\n• `firstColumn: number`. Index of the first column (0-based).\n• `lastColumn: number`. Index of the last column (0-based). Use `lastColumn >= firstColumn`.\n###### Returns\n\nA new `SpeedyMatrix` representing the specified block.\n\n###### Example\n```//\n// We'll create the following 4x4 matrix:\n// (a dot represents a zero)\n//\n// [ 5 5 5 . ]\n// [ 5 5 5 . ]\n// [ 5 5 5 . ]\n// [ . . . . ]\n//\nconst mat = Speedy.Matrix.Zeros(4);\nawait mat.block(0, 2, 0, 2).fill(5);\nconsole.log(mat.toString());```\n##### SpeedyMatrix.column()\n\n`SpeedyMatrix.column(index: number): SpeedyMatrix`\n\nExtract a column of the matrix.\n\n###### Arguments\n• `index: number`. Index of the column (0-based).\n###### Returns\n\nA new `SpeedyMatrix` representing the specified column.\n\n###### Example\n```const mat = Speedy.Matrix(2, 3, [\n1,\n2,\n3,\n4,\n5,\n6\n]);\n\nconst firstColumn = mat.column(0); // [1, 2]^T\nconst secondColumn = mat.column(1); // [3, 4]^T\nconst thirdColumn = mat.column(2); // [5, 6]^T\n\nconsole.log(firstColumn.toString());\nconsole.log(secondColumn.toString());\nconsole.log(thirdColumn.toString());```\n##### SpeedyMatrix.row()\n\n`SpeedyMatrix.row(index: number): SpeedyMatrix`\n\nExtract a row of the matrix.\n\n###### Arguments\n• `index: number`. Index of the row (0-based).\n###### Returns\n\nA new `SpeedyMatrix` representing the specified row.\n\n###### Example\n```//\n// We'll create the following matrix:\n// [ 0 0 0 0 ]\n// [ 1 1 1 1 ]\n// [ 2 2 2 2 ]\n// [ 0 0 0 0 ]\n//\nconst mat = Speedy.Matrix.Zeros(4);\nawait mat.row(1).fill(1);\nawait mat.row(2).fill(2);\nconsole.log(mat.toString());```\n##### SpeedyMatrix.diagonal()\n\n`SpeedyMatrix.diagonal(): SpeedyMatrix`\n\nExtract the main diagonal of `this` matrix as a column vector.\n\n###### Returns\n\nA new `SpeedyMatrix` representing the main diagonal of `this` matrix.\n\n###### Example\n```//\n// We'll create the following matrix:\n// (a dot represents a zero)\n//\n// [ 5 . . . . ]\n// [ . 5 . . . ]\n// [ . . 5 . . ]\n// [ . . . . . ]\n// [ . . . . . ]\n//\nconst mat = Speedy.Matrix.Zeros(5); // create a 5x5 matrix filled with zeros\nconst submat = mat.block(0, 2, 0, 2); // extract 3x3 submatrix at the \"top-left\"\nconst diag = submat.diagonal(); // extract the diagonal of the submatrix\n\nawait diag.fill(5); // fill the diagonal of the submatrix with a constant\nconsole.log(mat.toString()); // print the entire matrix\n\n// Alternatively, we may use this compact form:\nawait mat.block(0, 2, 0, 2).diagonal().fill(5);```\n\n#### Elementary operations\n\n##### SpeedyMatrixExpr.transpose()\n\n`SpeedyMatrixExpr.transpose(): SpeedyMatrixExpr`\n\nTranspose `this` matrix expression.\n\n###### Returns\n\nA `SpeedyMatrixExpr` representing the tranpose of `this` matrix expression.\n\n###### Example\n```// Create a 2x3 matrix\nconst mat = Speedy.Matrix(2, 3, [\n1, 2, // first column\n3, 4, // second column\n5, 6 // third column\n]);\n\n// We'll store the transpose of mat in matT\nconst matT = Speedy.Matrix.Zeros(mat.columns, mat.rows);\nawait matT.setTo(mat.transpose());\n\n// Print the matrix and its transpose\nconsole.log(mat.toString());\nconsole.log(matT.toString());```\n##### SpeedyMatrixExpr.plus()\n\n`SpeedyMatrixExpr.plus(expr: SpeedyMatrixExpr): SpeedyMatrixExpr`\n\nCompute the sum between `this` matrix expression and `expr`. Both expressions must have the same shape.\n\n###### Arguments\n• `expr: SpeedyMatrixExpr`. Another matrix expression.\n###### Returns\n\nA `SpeedyMatrixExpr` representing the sum between `this` matrix expression and `expr`.\n\n###### Example\n```const matA = Speedy.Matrix(3, 3, [\n1, 2, 3,\n4, 5, 6,\n7, 8, 9\n]);\nconst ones = Speedy.Matrix.Ones(3);\n\n// set B = A + 1\nconst matB = Speedy.Matrix.Zeros(3);\nawait matB.setTo(matA.plus(ones));```\n##### SpeedyMatrixExpr.minus()\n\n`SpeedyMatrixExpr.minus(expr: SpeedyMatrixExpr): SpeedyMatrixExpr`\n\nCompute the difference between `this` matrix expression and `expr`. Both expressions must have the same shape.\n\n###### Arguments\n• `expr: SpeedyMatrixExpr`. Another matrix expression.\n###### Returns\n\nA `SpeedyMatrixExpr` representing the difference between `this` matrix expression and `expr`.\n\n##### SpeedyMatrixExpr.times()\n\n`SpeedyMatrixExpr.times(expr: SpeedyMatrixExpr): SpeedyMatrixExpr`\n\n`SpeedyMatrixExpr.times(scalar: number): SpeedyMatrixExpr`\n\nMatrix multiplication.\n\nIn the first form, compute the matrix multiplication between `this` matrix expression and `expr`. The shape of `expr` must be compatible with the shape of `this` matrix expression.\n\nIn the second form, multiply `this` matrix expression by a `scalar`.\n\n###### Arguments\n• `expr: SpeedyMatrixExpr`. Matrix expression.\n• `scalar: number`. A number.\n###### Returns\n\nA `SpeedyMatrixExpr` representing the result of the multiplication.\n\n###### Example\n```const col = Speedy.Matrix(3, 1, [0, 5, 2]);\nconst row = Speedy.Matrix(1, 3, [1, 2, 3]);\n\nconst dot = row.times(col); // 1x1 matrix expression: inner product\nconst out = col.times(row); // 3x3 matrix expression: outer product\nconst len = col.transpose().times(col); // 1x1 matrix expression: squared length of col\n\nconst mat = Speedy.Matrix.Zeros(1);\nawait mat.setTo(len); // evaluate len\nconsole.log(mat.read()); // 29 = 00 + 55 + 22```\n##### SpeedyMatrixExpr.compMult()\n\n`SpeedyMatrixExpr.compMult(expr: SpeedyMatrixExpr): SpeedyMatrixExpr`\n\nCompute the component-wise multiplication between `this` matrix expression and `expr`. Both matrices must have the same shape.\n\n###### Arguments\n• `expr: SpeedyMatrixExpr`. Matrix expression.\n###### Returns\n\nA `SpeedyMatrixExpr` representing the component-wise multiplication.\n\n##### SpeedyMatrixExpr.inverse()\n\n`SpeedyMatrixExpr.inverse(): SpeedyMatrixExpr`\n\nCompute the inverse of `this` matrix expression. Make sure it's square.\n\n###### Returns\n\nA `SpeedyMatrixExpr` representing the inverse of `this` matrix expression.\n\n##### SpeedyMatrixExpr.ldiv()\n\n`SpeedyMatrixExpr.ldiv(expr: SpeedyMatrixExpr): SpeedyMatrixExpr`\n\nLeft division `this` \\ `expr`. This is equivalent to solving a system of linear equations Ax = b, where A is `this` and b is `expr` (in a least squares sense if A is not square). The number of rows of `this` must be greater or equal than its number of columns. `expr` must be a column vector.\n\n###### Arguments\n• `expr: SpeedyMatrixExpr`. Matrix expression.\n###### Returns\n\nA `SpeedyMatrixExpr` representing the left division.\n\n#### Systems of equations\n\n##### Speedy.Matrix.solve()\n\n`Speedy.Matrix.solve(solution: SpeedyMatrix, A: SpeedyMatrix, b: SpeedyMatrix, options?: object): SpeedyPromise<SpeedyMatrix>`\n\nSolve a system of linear equations Ax = b for x, the `solution`, where `A` is a n x n square matrix, `b` is a n x 1 column vector and `solution` is a n x 1 column vector of unknowns. n is the number of equations and the number of unknowns.\n\n###### Arguments\n• `solution: SpeedyMatrix`. The output column vector.\n• `A: SpeedyMatrix`. A square matrix.\n• `b: SpeedyMatrix`. A column vector.\n• `options: object, optional`. Options to be passed to the solver. Available keys:\n• `method: string`. One of the following: `\"qr\"`. Defaults to `\"qr\"`.\n###### Returns\n\nA `SpeedyPromise` that resolves to `solution`.\n\n###### Example\n```//\n// We'll solve the following system of equations:\n// y - z = 9\n// y + z = 6\n//\n// Let's write it in matrix form:\n// [ 1 -1 ] [ y ] = [ 9 ]\n// [ 1 1 ] [ z ] [ 6 ]\n//\n// The code below solves Ax = b for x, where\n// x = (y, z) is the column vector of unknowns.\n//\nconst A = Speedy.Matrix(2, 2, [\n1, 1, // first column\n-1, 1 // second column\n]);\nconst b = Speedy.Matrix(2, 1, [\n9, 6 // column vector\n]);\n\n// Solve Ax = b for x\nconst solution = Speedy.Matrix.Zeros(2, 1);\nawait Speedy.Matrix.solve(solution, A, b);\n\n// get the result\nconsole.log(solution.read()); // [ 7.5, -1.5 ]```\n##### Speedy.Matrix.ols()\n\n`Speedy.Matrix.ols(solution: SpeedyMatrix, A: SpeedyMatrix, b: SpeedyMatrix): SpeedyPromise<SpeedyMatrix>`\n\nOrdinary least squares.\n\nGiven an overdetermined system of linear equations Ax = b, where `A` is a m x n matrix, `b` is a m x 1 column vector and `solution` x is a n x 1 column vector of unknowns, find a `solution` x that minimizes the Euclidean norm of the residual b - Ax.\n\nm is the number of equations and n is the number of unknowns. We require m >= n.\n\n###### Arguments\n• `solution: SpeedyMatrix`. The output column vector.\n• `A: SpeedyMatrix`. A matrix.\n• `b: SpeedyMatrix`. A column vector.\n• `options: object, optional`. Options to be passed to the solver. Available keys:\n• `method: string`. One of the following: `\"qr\"`. Defaults to `\"qr\"`.\n###### Returns\n\nA `SpeedyPromise` that resolves to `solution`.\n\n#### Matrix factorization\n\n##### Speedy.Matrix.qr()\n\n`Speedy.Matrix.qr(Q: SpeedyMatrix, R: SpeedyMatrix, A: SpeedyMatrix, options?: object): SpeedyPromise<void>`\n\nCompute a QR decomposition of a m x n matrix `A` using Householder reflectors. `Q` will be orthogonal and `R` will be upper-triangular. We require m >= n.\n\n###### Arguments\n• `Q: SpeedyMatrix`. Output matrix (m x n if reduced, m x m if full).\n• `R: SpeedyMatrix`. Output matrix (n x n if reduced, m x n if full).\n• `A: SpeedyMatrix`. The matrix to be decomposed.\n• `options: object, optional`. A configuration object that accepts the following keys:\n• `mode: string`. Either `\"full\"` or `\"reduced\"`. Defaults to `\"reduced\"`.\n###### Returns\n\nReturns a `SpeedyPromise` that resolves as soon as the computation is complete.\n\n###### Example\n```// We'll find a QR decomposition of this matrix\nconst A = Speedy.Matrix(3, 3, [\n0, 1, 0, // first column\n1, 1, 0, // second column\n1, 2, 3, // third column\n]);\n\n// Compute a QR decomposition of A\nconst Q = Speedy.Matrix.Zeros(3, 3);\nconst R = Speedy.Matrix.Zeros(3, 3);\nawait Speedy.Matrix.qr(Q, R, A);\n\n// Print the result\nconsole.log(Q.toString());\nconsole.log(R.toString());\n\n// Check the answer (A = QR)\nconst QR = await Speedy.Matrix.Zeros(Q.rows, R.columns).setTo(Q.times(R));\nconsole.log(QR.toString());```\n\n### Geometric transformations\n\n#### Perspective transformation\n\n##### Speedy.Matrix.applyPerspectiveTransform()\n\n`Speedy.Matrix.applyPerspectiveTransform(dest: SpeedyMatrix, src: SpeedyMatrix, transform: SpeedyMatrix): SpeedyPromise<SpeedyMatrix>`\n\nApply a perspective `transform` to a set of 2D points described by `src` and store the results in `dest`.\n\n###### Arguments\n• `dest: SpeedyMatrix`. A 2 x n output matrix.\n• `src: SpeedyMatrix`. A 2 x n matrix encoding a set of n points, one per column.\n• `transform: SpeedyMatrix`. A 3x3 homography matrix.\n###### Returns\n\nA `SpeedyPromise` that resolves to `dest`.\n\n###### Example\n```const transform = Speedy.Matrix(3, 3, [\n3, 0, 0, // first column\n0, 2, 0, // second column\n2, 1, 1, // third column\n]);\n\nconst src = Speedy.Matrix(2, 4, [\n0, 0,\n1, 0,\n1, 1,\n0, 1,\n]);\n\nconst dest = Speedy.Matrix.Zeros(src.rows, src.columns);\nawait Speedy.Matrix.applyPerspectiveTransform(dest, src, transform);\nconsole.log(dest.toString());\n\n//\n// Result:\n// [ 2 5 5 2 ]\n// [ 1 1 3 3 ]\n//```\n##### Speedy.Matrix.perspective()\n\n`Speedy.Matrix.perspective(homography: SpeedyMatrix, src: SpeedyMatrix, dest: SpeedyMatrix): SpeedyPromise<SpeedyMatrix>`\n\nCompute a `homography` matrix using four correspondences of points.\n\n###### Arguments\n• `homography: SpeedyMatrix`. A 3x3 output matrix.\n• `src: SpeedyMatrix`. A 2x4 matrix with the coordinates of four points (one per column) representing the corners of the source space.\n• `dest: SpeedyMatrix`. A 2x4 matrix with the coordinates of four points (one per column) representing the corners of the destination space.\n###### Returns\n\nA `SpeedyPromise` that resolves to `homography`.\n\n###### Example\n```const src = Speedy.Matrix(2, 4, [\n0, 0, // first point\n1, 0, // second point\n1, 1, // third point\n0, 1, // fourth point\n]);\n\nconst dest = Speedy.Matrix(2, 4, [\n0, 0,\n3, 0,\n3, 2,\n0, 2,\n]);\n\nconst homography = Speedy.Matrix.Zeros(3, 3);\nawait Speedy.Matrix.perspective(homography, src, dest);\n\nconsole.log(homography.toString());```\n##### Speedy.Matrix.findHomography()\n\n`Speedy.Matrix.findHomography(homography: SpeedyMatrix, src: SpeedyMatrix, dest: SpeedyMatrix, options?: object): SpeedyPromise<SpeedyMatrix>`\n\nCompute a `homography` matrix using a set of n >= 4 correspondences of points, possibly with noise.\n\n###### Arguments\n• `homography: SpeedyMatrix`. A 3x3 output matrix.\n• `src: SpeedyMatrix`. A 2 x n matrix with the coordinates of n points (one per column) representing the corners of the source space.\n• `dest: SpeedyMatrix`. A 2 x n matrix with the coordinates of n points (one per column) representing the corners of the destination space.\n• `options: object, optional`. A configuration object.\n• `method: string`. The method to be employed to compute the homography (see the table of methods below).\n\nTable of methods:\n\nMethod Description\n`\"default\"` Normalized Direct Linear Transform (DLT). All points will be used to estimate the homography. Use this method if your data set is not polluted with outliers.\n`\"pransac\"` PRANSAC is a variant of RANSAC with bounded runtime that is designed for real-time tasks. It is able to reject outliers in the data set.\n\nTable of parameters:\n\nParameter Supported methods Description\n`reprojectionError: number` `\"pransac\"` A threshold, measured in pixels, that lets Speedy decide if a data point is an inlier or an outlier for a given model. A data point is an inlier for a given model if the model maps its `src` coordinates near its `dest` coordinates (i.e., if the Euclidean distance is not greater than the threshold). A data point is an outlier if it's not an inlier. Defaults to 3 pixels.\n`mask: SpeedyMatrix` `\"pransac\"` An optional output matrix of shape 1 x n. Its i-th entry will be set to 1 if the i-th data point is an inlier for the best model found by the method, or 0 if it's an outlier.\n`numberOfHypotheses: number` `\"pransac\"` A positive integer specifying the number of models that will be generated and tested. The best model found by the method will be refined and then returned. If your inlier ratio is \"high\", this parameter can be set to a \"low\" number, making the algorithm run even faster. Defaults to 500.\n`bundleSize: number` `\"pransac\"` A positive integer specifying the number of data points to be tested against all viable models before the set of viable models gets cut in half, over and over again. Defaults to 100.\n###### Returns\n\nA `SpeedyPromise` that resolves to `homography`.\n\n###### Example\n```//\n// Map random points\n// from [0,100] x [0,100]\n// to [200,600] x [200,600]\n//\nconst numPoints = 50;\nconst noiseLevel = 2;\n\nconst transform = x => 4x + 200; // simulated model\nconst randCoord = () => 100 * Math.random(); // in [0, 100)\nconst randNoise = () => (Math.random() - 0.5) * noiseLevel;\n\nconst srcCoords = new Array(numPoints * 2).fill(0).map(() => randCoord());\nconst dstCoords = srcCoords.map(x => transform(x) + randNoise());\n\nconst src = Speedy.Matrix(2, numPoints, srcCoords);\nconst dst = Speedy.Matrix(2, numPoints, dstCoords);\n\nconst homography = Speedy.Matrix.Zeros(3, 3);\nawait Speedy.Matrix.findHomography(homography, src, dst, {\nmethod: \"pransac\",\nreprojectionError: 1\n});\n\nconsole.log('homography:', homography.toString());\n\n// Now let's test the homography using a few test points.\n// The points need to be mapped in line with our simulated model (see above)\nconst tstCoords = Speedy.Matrix(2, 5, [\n0, 0,\n100, 0,\n100, 100,\n0, 100,\n50, 50,\n]);\n\nconst chkCoords = Speedy.Matrix.Zeros(2, 5);\nawait Speedy.Matrix.applyPerspectiveTransform(chkCoords, tstCoords, homography);\nconsole.log(chkCoords.toString());```\n\n#### Affine transformation\n\n##### Speedy.Matrix.applyAffineTransform()\n\n`Speedy.Matrix.applyAffineTransform(dest: SpeedyMatrix, src: SpeedyMatrix, transform: SpeedyMatrix): SpeedyPromise<SpeedyMatrix>`\n\nApply an affine `transform` to a set of 2D points described by `src` and store the results in `dest`.\n\n###### Arguments\n• `dest: SpeedyMatrix`. A 2 x n output matrix.\n• `src: SpeedyMatrix`. A 2 x n matrix encoding a set of n points, one per column.\n• `transform: SpeedyMatrix`. A 2x3 affine transformation matrix.\n###### Returns\n\nA `SpeedyPromise` that resolves to `dest`.\n\n###### Example\n```const transform = Speedy.Matrix(2, 3, [\n3, 0, // first column\n0, 2, // second column\n2, 1, // third column\n]);\n\nconst src = Speedy.Matrix(2, 4, [\n0, 0,\n1, 0,\n1, 1,\n0, 1,\n]);\n\nconst dest = Speedy.Matrix.Zeros(src.rows, src.columns);\nawait Speedy.Matrix.applyAffineTransform(dest, src, transform);\nconsole.log(dest.toString());\n\n//\n// Result:\n// [ 2 5 5 2 ]\n// [ 1 1 3 3 ]\n//```\n##### Speedy.Matrix.affine()\n\n`Speedy.Matrix.affine(transform: SpeedyMatrix, src: SpeedyMatrix, dest: SpeedyMatrix): SpeedyPromise<SpeedyMatrix>`\n\nCompute an `affine` transform using three correspondences of points.\n\n###### Arguments\n• `transform: SpeedyMatrix`. A 2x3 output matrix.\n• `src: SpeedyMatrix`. A 2x3 matrix with the coordinates of three points (one per column) representing the corners of the source space.\n• `dest: SpeedyMatrix`. A 2x3 matrix with the coordinates of three points (one per column) representing the corners of the destination space.\n###### Returns\n\nA `SpeedyPromise` that resolves to `transform`.\n\n###### Example\n```const src = Speedy.Matrix(2, 3, [\n0, 0, // first point\n1, 0, // second point\n1, 1, // third point\n]);\n\nconst dest = Speedy.Matrix(2, 3, [\n0, 0,\n3, 0,\n3, 2,\n]);\n\nconst transform = Speedy.Matrix.Zeros(2, 3);\nawait Speedy.Matrix.affine(transform, src, dest);\n\nconsole.log(transform.toString());```\n##### Speedy.Matrix.findAffineTransform()\n\n`Speedy.Matrix.findAffineTransform(transform: SpeedyMatrix, src: SpeedyMatrix, dest: SpeedyMatrix, options?: object): SpeedyPromise<SpeedyMatrix>`\n\nCompute an affine `transform` using a set of n >= 3 correspondences of points, possibly with noise.\n\n###### Arguments\n• `transform: SpeedyMatrix`. A 2x3 output matrix.\n• `src: SpeedyMatrix`. A 2 x n matrix with the coordinates of n points (one per column) representing the corners of the source space.\n• `dest: SpeedyMatrix`. A 2 x n matrix with the coordinates of n points (one per column) representing the corners of the destination space.\n• `options: object, optional`. A configuration object.\n• `method: string`. The method to be employed to compute the affine transform (see the table of methods below).\n\nTable of methods:\n\nTable of parameters:\n\n###### Returns\n\nA `SpeedyPromise` that resolves to `transform`.\n\n### Geometric Utilities\n\n#### 2D Vectors\n\n##### Speedy.Vector2()\n\n`Speedy.Vector2(x: number, y: number): SpeedyVector2`\n\nCreates a new 2D vector with the given coordinates.\n\n###### Arguments\n• `x: number`. The x-coordinate of the vector.\n• `y: number`. The y-coordinate of the vector.\n###### Returns\n\nA new `SpeedyVector2` instance.\n\n###### Example\n`const zero = Speedy.Vector2(0, 0);`\n##### Speedy.Vector2.Sink()\n\n`Speedy.Vector2.Sink(name?: string): SpeedyPipelineNodeVector2Sink`\n\nCreates a sink of 2D vectors using the specified name. If the name is not specified, Speedy will call this node `\"vec2\"`. An array of `SpeedyVector2` objects will be exported from the pipeline.\n\n###### Parameters\n• `turbo: boolean`. Accelerate GPU-CPU transfers. You'll get the data from the previous frame. Defaults to `false`.\n###### Ports\nPort name Data type Description\n`\"in\"` Vector2 A set of 2D vectors to be exported from the pipeline.\n##### SpeedyVector2.x\n\n`SpeedyVector2.x: number`\n\nThe x-coordinate of the vector.\n\n##### SpeedyVector2.y\n\n`SpeedyVector2.y: number`\n\nThe y-coordinate of the vector.\n\n##### SpeedyVector2.plus()\n\n`SpeedyVector2.plus(offset: SpeedyVector2): SpeedyVector2`\n\n###### Returns\n\nA new vector corresponding to `this` + `offset`.\n\n##### SpeedyVector2.minus()\n\n`SpeedyVector2.minus(offset: SpeedyVector2): SpeedyVector2`\n\nVector subtraction.\n\n###### Returns\n\nA new vector corresponding to `this` - `offset`.\n\n##### SpeedyVector2.times()\n\n`SpeedyVector2.times(scalar: number): SpeedyVector2`\n\nMultiply a vector by a scalar.\n\n###### Returns\n\nA new vector corresponding to `this` * `scalar`.\n\n##### SpeedyVector2.length()\n\n`SpeedyVector2.length(): number`\n\nComputes the length of the vector (Euclidean norm).\n\n###### Returns\n\nThe length of the vector.\n\n###### Example\n```const v = Speedy.Vector2(3, 4);\n\nconsole.log('Coordinates', v.x, v.y);\nconsole.log('Length', v.length()); // 5```\n##### SpeedyVector2.normalized()\n\n`SpeedyVector2.normalized(): SpeedyVector2`\n\nReturns a normalized version of this vector.\n\n###### Returns\n\nA new vector with the same direction as the original one and with length equal to one.\n\n##### SpeedyVector2.dot()\n\n`SpeedyVector2.dot(v: SpeedyVector2): number`\n\nDot product.\n\n###### Arguments\n• `v: SpeedyVector2`. A vector.\n###### Returns\n\nThe dot product between the two vectors.\n\n##### SpeedyVector2.distanceTo()\n\n`SpeedyVector2.distanceTo(v: SpeedyVector2): number`\n\nComputes the distance between two vectors.\n\n###### Arguments\n• `v: SpeedyVector2`. A vector.\n###### Returns\n\nThe Euclidean distance between the two vectors.\n\n###### Example\n```const u = Speedy.Vector2(1, 0);\nconst v = Speedy.Vector2(5, 0);\n\nconsole.log(u.distanceTo(v)); // 4```\n##### SpeedyVector2.toString()\n\n`SpeedyVector2.toString(): string`\n\nGet a string representation of the vector.\n\n###### Returns\n\nA string representation of the vector.\n\n##### SpeedyVector2.equals()\n\n`SpeedyVector2.equals(v: SpeedyVector2): boolean`\n\nEquality comparison.\n\n###### Returns\n\nReturns `true` if the coordinates of `this` are equal to the coordinates of `v`, or `false` otherwise.\n\n#### 2D Points\n\n##### Speedy.Point2()\n\n`Speedy.Point2(x: number, y: number): SpeedyPoint2`\n\nCreates a new 2D point with the given coordinates.\n\n###### Arguments\n• `x: number`. The x-coordinate of the point.\n• `y: number`. The y-coordinate of the point.\n###### Returns\n\nA new `SpeedyPoint2` instance.\n\n###### Example\n`const p = Speedy.Point2(5, 10);`\n##### SpeedyPoint2.x\n\n`SpeedyPoint2.x: number`\n\nThe x-coordinate of the point.\n\n##### SpeedyPoint2.y\n\n`SpeedyPoint2.y: number`\n\nThe y-coordinate of the point.\n\n##### SpeedyPoint2.plus()\n\n`SpeedyPoint2.plus(v: SpeedyVector2): SpeedyPoint2`\n\nAdds a vector to this point.\n\n###### Arguments\n• `v: SpeedyVector2`. A 2D vector.\n###### Returns\n\nA new `SpeedyPoint2` instance corresponding to this point translated by `v`.\n\n##### SpeedyPoint2.minus()\n\n`SpeedyPoint2.minus(p: SpeedyPoint2): SpeedyVector2`\n\nSubtracts point `p` from this.\n\n###### Arguments\n• `p: SpeedyPoint2`. A 2D point.\n###### Returns\n\nA new `SpeedyVector2` instance such that `p` plus that vector equals this point.\n\n##### SpeedyPoint2.equals()\n\n`SpeedyPoint2.equals(p: SpeedyPoint2): boolean`\n\nEquality comparison.\n\n###### Returns\n\nReturns `true` if the coordinates of `this` are equal to the coordinates of `p`, or `false` otherwise.\n\n#### 2D Size\n\n##### Speedy.Size()\n\n`Speedy.Size(width: number, height: number): SpeedySize`\n\nCreates a new object that represents the size of a rectangle.\n\n###### Arguments\n• `width: number`. A non-negative number.\n• `height: number`. A non-negative number.\n###### Returns\n\nA new `SpeedySize` instance.\n\n###### Example\n`const size = Speedy.Size(640, 360);`\n##### SpeedySize.width\n\n`SpeedySize.width: number`\n\nWidth property.\n\n##### SpeedySize.height\n\n`SpeedySize.height: number`\n\nHeight property.\n\n##### SpeedySize.equals()\n\n`SpeedySize.equals(anotherSize: SpeedySize): boolean`\n\nChecks if two size objects have the same dimensions.\n\n###### Returns\n\nReturns `true` if the dimensions of `this` and `anotherSize` are equal.\n\n##### SpeedySize.toString()\n\n`SpeedySize.toString(): string`\n\nConvert to string.\n\n###### Returns\n\nA string representation of the object.\n\n### Extras\n\n#### Promises\n\nSpeedy includes its own implementation of Promises, called SpeedyPromises. SpeedyPromises can interoperate with standard ES6 Promises and are based on the Promises/A+ specification. The main difference between SpeedyPromises and standard ES6 Promises is that, under certain circunstances, SpeedyPromises can be made to run faster than ES6 Promises.\n\nSpeedyPromises are specially beneficial when you have a chain of them. When (and if) their \"turbocharged\" mode is invoked, they will adopt a special (non-standard) behavior and skip the microtask queue when settling promises in a chain. This will save you a few milliseconds. While \"a few milliseconds\" doesn't sound much in terms of standard web development, for a real-time library such as Speedy it means a lot. Simply put, we're squeezing out performance. SpeedyPromises are used internally by the library.\n\n##### Speedy.Promise\n\n`Speedy.Promise: Function`\n\nUsed to create a new `SpeedyPromise` object.\n\n###### Example\n```let promise = new Speedy.Promise((resolve, reject) => {\nsetTimeout(resolve, 2000);\n});\n\npromise.then(() => {\nconsole.log(`The SpeedyPromise is now fulfilled.`);\n}).catch(() => {\nconsole.log(`The SpeedyPromise is now rejected.`);\n}).finally(() => {\nconsole.log(`The SpeedyPromise is now settled.`);\n});```\n\n#### Settings\n\n##### Speedy.Settings.powerPreference\n\n`Speedy.Settings.powerPreference: \"default\" \| \"low-power\" \| \"high-performance\"`\n\nExperimental. The desired power preference for the WebGL context. This option should be set before creating any pipelines. The browser uses this setting as a hint to balance rendering performance and battery life (especially on mobile devices).\n\n##### Speedy.Settings.gpuPollingMode\n\n`Speedy.Settings.gpuPollingMode: \"raf\" \| \"asap\"`\n\nExperimental. GPU polling mode. `\"asap\"` has slightly better performance than `\"raf\"`, at the cost of higher CPU usage.\n\n#### Utilities\n\n##### Speedy.version\n\n`Speedy.version: string, read-only`\n\nThe version of the library.\n\n##### Speedy.fps\n\n`Speedy.fps: number, read-only`\n\nSpeedy includes a frames per second (FPS) counter for testing purposes. It will be created as soon as you access it.\n\n###### Example\n`console.log(Speedy.fps);`\n##### Speedy.isSupported()\n\n`Speedy.isSupported(): boolean`\n\nChecks if Speedy is supported in this machine & browser.\n\n###### Returns\n\nReturns a boolean telling whether or not Speedy is supported in the client environment.\n\n###### Example\n```if(!Speedy.isSupported())\nalert('This application is not supported in this browser. Please use a different browser.');```\n\n## Keywords\n\n### Install\n\n`npm i speedy-vision`\n\n### Repository\n\ngithub.com/alemart/speedy-vision\n\n### Homepage\n\ngithub.com/alemart/speedy-vision\n\n0\n\n0.9.0-wip" ]	[ null, "https://static.npmjs.com/255a118f56f5346b97e56325a1217a16.svg", null, "https://raw.githubusercontent.com/alemart/speedy-vision/HEAD/assets/demo-bestfeatures.gif", null, "https://raw.githubusercontent.com/alemart/speedy-vision/HEAD/assets/network-example.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6297927,"math_prob":0.89117736,"size":73349,"snap":"2023-14-2023-23","text_gpt3_token_len":18779,"char_repetition_ratio":0.20252232,"word_repetition_ratio":0.2508162,"special_character_ratio":0.236145,"punctuation_ratio":0.21603547,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97268456,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,null,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-03-23T01:28:36Z\",\"WARC-Record-ID\":\"<urn:uuid:1cddf49b-c6cf-4dd1-827b-5b1a7ef7105c>\",\"Content-Length\":\"312530\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:cd4a98a9-3ac4-43e4-8ade-fcc12a48285c>\",\"WARC-Concurrent-To\":\"<urn:uuid:fcdf253c-618e-4724-b801-ee460de2c397>\",\"WARC-IP-Address\":\"104.16.92.83\",\"WARC-Target-URI\":\"https://www.npmjs.com/package/speedy-vision\",\"WARC-Payload-Digest\":\"sha1:GENYH7BMT34UF3IC5EBWK2KWI2IZT2LK\",\"WARC-Block-Digest\":\"sha1:KEE64YRFNFV4KK2GDFXYP76NRZOL7NEH\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-14/CC-MAIN-2023-14_segments_1679296944606.5_warc_CC-MAIN-20230323003026-20230323033026-00267.warc.gz\"}"}
https://www.cnblogs.com/jpfss/p/9928747.html	[ "# Java泛型详解：<T>和Class<T>的使用。泛型类，泛型方法的详细使用实例\n\n## 一、引入\n\n### 1、泛型是什么\n\n[java] view plain\n1. ArrayList<String> strList = new ArrayList<String>();\n2. ArrayList<Integer> intList = new ArrayList<Integer>();\n3. ArrayList<Double> doubleList = new ArrayList<Double>();\n\n### 2、没有泛型会怎样\n\n[java] view plain\n1. //设置Integer类型的点坐标\n2. class IntegerPoint{\n3. private Integer x ; // 表示X坐标\n4. private Integer y ; // 表示Y坐标\n5. public void setX(Integer x){\n6. this.x = x ;\n7. }\n8. public void setY(Integer y){\n9. this.y = y ;\n10. }\n11. public Integer getX(){\n12. return this.x ;\n13. }\n14. public Integer getY(){\n15. return this.y ;\n16. }\n17. }\n18. //设置Float类型的点坐标\n19. class FloatPoint{\n20. private Float x ; // 表示X坐标\n21. private Float y ; // 表示Y坐标\n22. public void setX(Float x){\n23. this.x = x ;\n24. }\n25. public void setY(Float y){\n26. this.y = y ;\n27. }\n28. public Float getX(){\n29. return this.x ;\n30. }\n31. public Float getY(){\n32. return this.y ;\n33. }\n34. }\n\n[java] view plain\n1. class ObjectPoint{\n2. private Object x ;\n3. private Object y ;\n4. public void setX(Object x){\n5. this.x = x ;\n6. }\n7. public void setY(Object y){\n8. this.y = y ;\n9. }\n10. public Object getX(){\n11. return this.x ;\n12. }\n13. public Object getY(){\n14. return this.y ;\n15. }\n16. }\n\n[java] view plain\n1. ObjectPoint integerPoint = new ObjectPoint();\n2. integerPoint.setX(new Integer(100));\n3. Integer integerX=(Integer)integerPoint.getX();\n\n[java] view plain\n1. integerPoint.setX(new Integer(100));\n\n[java] view plain\n1. Integer integerX=(Integer)integerPoint.getX();\n\n[java] view plain\n1. ObjectPoint floatPoint = new ObjectPoint();\n2. floatPoint.setX(new Float(100.12f));\n3. Float floatX = (Float)floatPoint.getX();\n\n[java] view plain\n1. ObjectPoint floatPoint = new ObjectPoint();\n2. floatPoint.setX(new Float(100.12f));\n3. String floatX = (String)floatPoint.getX();\n\n[java] view plain\n1. String floatX = (String)floatPoint.getX();\n\n## 二、各种泛型定义及使用\n\n### 1、泛型类定义及使用\n\n[java] view plain\n1. //定义\n2. class Point<T>{// 此处可以随便写标识符号\n3. private T x ;\n4. private T y ;\n5. public void setX(T x){//作为参数\n6. this.x = x ;\n7. }\n8. public void setY(T y){\n9. this.y = y ;\n10. }\n11. public T getX(){//作为返回值\n12. return this.x ;\n13. }\n14. public T getY(){\n15. return this.y ;\n16. }\n17. };\n18. //IntegerPoint使用\n19. Point<Integer> p = new Point<Integer>() ;\n20. p.setX(new Integer(100)) ;\n21. System.out.println(p.getX());\n22.\n23. //FloatPoint使用\n24. Point<Float> p = new Point<Float>() ;\n25. p.setX(new Float(100.12f)) ;\n26. System.out.println(p.getX());", null, "（1）、定义泛型：Point<T>\n\n（2）类中使用泛型\n\n[java] view plain\n1. //定义变量\n2. private T x ;\n3. //作为返回值\n4. public T getX(){\n5. return x ;\n6. }\n7. //作为参数\n8. public void setX(T x){\n9. this.x = x ;\n10. }\n（3）使用泛型类\n\n[java] view plain\n1. //IntegerPoint使用\n2. Point<Integer> p = new Point<Integer>() ;\n3. p.setX(new Integer(100)) ;\n4. System.out.println(p.getX());\n5.\n6. //FloatPoint使用\n7. Point<Float> p = new Point<Float>() ;\n8. p.setX(new Float(100.12f)) ;\n9. System.out.println(p.getX());\n\n[java] view plain\n1. Point<String> p = new Point<String>() ;\n\n[java] view plain\n1. //IntegerPoint使用\n2. Point<Integer> p = new Point<Integer>() ;\n3. //FloatPoint使用\n4. Point<Float> p = new Point<Float>() ;\n\n[java] view plain\n1. public class ArrayList<E>{\n2. …………\n3. }\n\n(4）使用泛型实现的优势\n\n（1）、不用强制转换\n\n[java] view plain\n1. //使用Object作为返回值，要强制转换成指定类型\n2. Float floatX = (Float)floatPoint.getX();\n3. //使用泛型时，不用强制转换，直接出来就是String\n4. System.out.println(p.getVar());\n(2)、在settVar()时如果传入类型不对，编译时会报错", null, "### 2、多泛型变量定义及字母规范\n\n（1）、多泛型变量定义\n\n[java] view plain\n1. class MorePoint<T,U>{\n2. }\n\n[java] view plain\n1. class MorePoint<T,U,A,B,C>{\n2. }\n\n[java] view plain\n1. class MorePoint<T,U> {\n2. private T x;\n3. private T y;\n4.\n5. private U name;\n6.\n7. public void setX(T x) {\n8. this.x = x;\n9. }\n10. public T getX() {\n11. return this.x;\n12. }\n13. …………\n14. public void setName(U name){\n15. this.name = name;\n16. }\n17.\n18. public U getName() {\n19. return this.name;\n20. }\n21. }\n22. //使用\n23. MorePoint<Integer,String> morePoint = new MorePoint<Integer, String>();\n24. morePoint.setName(\"harvic\");\n25. Log.d(TAG, \"morPont.getName:\" + morePoint.getName());\n\n（2）、字母规范\n\n[java] view plain\n1. class Point<T>{\n2. …………\n3. }\n\n• E — Element，常用在java Collection里，如：List<E>,Iterator<E>,Set<E>\n• K,V — Key，Value，代表Map的键值对\n• N — Number，数字\n• T — Type，类型，如String，Integer等等\n\n### 3、泛型接口定义及使用\n\n[java] view plain\n1. interface Info<T>{ // 在接口上定义泛型\n2. public T getVar() ; // 定义抽象方法，抽象方法的返回值就是泛型类型\n3. public void setVar(T x);\n4. }\n\n（1）、使用方法一：非泛型类\n\n[java] view plain\n1. class InfoImpl implements Info<String>{ // 定义泛型接口的子类\n2. private String var ; // 定义属性\n3. public InfoImpl(String var){ // 通过构造方法设置属性内容\n4. this.setVar(var) ;\n5. }\n6. @Override\n7. public void setVar(String var){\n8. this.var = var ;\n9. }\n10. @Override\n11. public String getVar(){\n12. return this.var ;\n13. }\n14. }\n15.\n16. public class GenericsDemo24{\n17. public void main(String arsg[]){\n18. InfoImpl i = new InfoImpl(\"harvic\");\n19. System.out.println(i.getVar()) ;\n20. }\n21. };\n\n[java] view plain\n1. class InfoImpl implements Info<String>{\n2. …………\n3. }\n\n[java] view plain\n1. public class GenericsDemo24{\n2. public void main(String arsg[]){\n3. InfoImpl i = new InfoImpl(\"harvic\");\n4. System.out.println(i.getVar()) ;\n5. }\n6. };\n（2）、使用方法二：泛型类\n\n[java] view plain\n1. interface Info<T>{ // 在接口上定义泛型\n2. public T getVar() ; // 定义抽象方法，抽象方法的返回值就是泛型类型\n3. public void setVar(T var);\n4. }\n5. class InfoImpl<T> implements Info<T>{ // 定义泛型接口的子类\n6. private T var ; // 定义属性\n7. public InfoImpl(T var){ // 通过构造方法设置属性内容\n8. this.setVar(var) ;\n9. }\n10. public void setVar(T var){\n11. this.var = var ;\n12. }\n13. public T getVar(){\n14. return this.var ;\n15. }\n16. }\n17. public class GenericsDemo24{\n18. public static void main(String arsg[]){\n19. InfoImpl<String> i = new InfoImpl<String>(\"harvic\");\n20. System.out.println(i.getVar()) ;\n21. }\n22. };\n\n[java] view plain\n1. class InfoImpl<T> implements Info<T>{ // 定义泛型接口的子类\n2. private T var ; // 定义属性\n3. public InfoImpl(T var){ // 通过构造方法设置属性内容\n4. this.setVar(var) ;\n5. }\n6. public void setVar(T var){\n7. this.var = var ;\n8. }\n9. public T getVar(){\n10. return this.var ;\n11. }\n12. }\n\n[java] view plain\n1. public class GenericsDemo24{\n2. public static void main(String arsg[]){\n3. Info<String> i = new InfoImpl<String>(\"harvic\");\n4. System.out.println(i.getVar()) ;\n5. }\n6. };\n\n[java] view plain\n1. class InfoImpl<T,K,U> implements Info<U>{ // 定义泛型接口的子类\n2. private U var ;\n3. private T x;\n4. private K y;\n5. public InfoImpl(U var){ // 通过构造方法设置属性内容\n6. this.setVar(var) ;\n7. }\n8. public void setVar(U var){\n9. this.var = var ;\n10. }\n11. public U getVar(){\n12. return this.var ;\n13. }\n14. }\n\n[java] view plain\n1. public class GenericsDemo24{\n2. public void main(String arsg[]){\n3. InfoImpl<Integer,Double,String> i = new InfoImpl<Integer,Double,String>(\"harvic\");\n4. System.out.println(i.getVar()) ;\n5. }\n6. }\n\n### 4、泛型函数定义及使用\n\n[java] view plain\n1. public class StaticFans {\n2. //静态函数\n3. public static <T> void StaticMethod(T a){\n4. Log.d(\"harvic\",\"StaticMethod: \"+a.toString());\n5. }\n6. //普通函数\n7. public <T> void OtherMethod(T a){\n8. Log.d(\"harvic\",\"OtherMethod: \"+a.toString());\n9. }\n10. }\n\n[java] view plain\n1. //静态方法\n4.\n5. //常规方法\n6. StaticFans staticFans = new StaticFans();\n7. staticFans.OtherMethod(new Integer(123));//使用方法一\n8. staticFans.<Integer>OtherMethod(new Integer(123));//使用方法二", null, "[java] view plain\n\n[java] view plain\n1. StaticFans staticFans = new StaticFans();\n2. staticFans.OtherMethod(new Integer(123));//使用方法一\n3. staticFans.<Integer>OtherMethod(new Integer(123));//使用方法二\n\n[java] view plain\n1. public static <T> List<T> parseArray(String response,Class<T> object){\n2. List<T> modelList = JSON.parseArray(response, object);\n3. return modelList;\n4. }\n\n### 5、其它用法:Class<T>类传递及泛型数组\n\n（1）、使用Class<T>传递泛型类Class对象\n\n[java] view plain\n1. public static List<SuccessModel> parseArray(String response){\n2. List<SuccessModel> modelList = JSON.parseArray(response, SuccessModel.class);\n3. return modelList;\n4. }\n\n[java] view plain\n1. public class SuccessModel {\n2. private boolean success;\n3.\n4. public boolean isSuccess() {\n5. return success;\n6. }\n7.\n8. public void setSuccess(boolean success) {\n9. this.success = success;\n10. }\n11. }\n\n[java] view plain\n1. public static List<SuccessModel> parseArray(String response){\n2. List<SuccessModel> modelList = JSON.parseArray(response, SuccessModel.class);\n3. return modelList;\n4. }\n\n[java] view plain\n1. public static <T> List<T> parseArray(String response,Class<T> object){\n2. List<T> modelList = JSON.parseArray(response, object);\n3. return modelList;\n4. }\n\n[java] view plain\n1. public final class Class<T> implements Serializable {\n2. …………\n3. }\n\n（2）、定义泛型数组\n\n[java] view plain\n1. //定义\n2. public static <T> T[] fun1(T...arg){ // 接收可变参数\n3. return arg ; // 返回泛型数组\n4. }\n5. //使用\n6. public static void main(String args[]){\n7. Integer i[] = fun1(1,2,3,4,5,6) ;\n8. Integer[] result = fun1(i) ;\n9. }\n\n[java] view plain\n1. public static <T> T[] fun1(T...arg){ // 接收可变参数\n2. return arg ; // 返回泛型数组\n3. }\n\n# 下面是我自己实际使用泛型的几个实例。\n\n## 关于泛型类的使用实例\n\nimport lombok.Data; @Datapublic class MultiObject<T> { \t/** * 成功状态 / private boolean success; /* * 异常 / private Exception ex; /* * 数据 / private T obj;\t\tpublic MultiObject() {\t} \t/\t 注意：当传入的泛型是Boolean时，就和第三个构造函数冲突了。\t /\tpublic MultiObject(boolean success) {\t\tthis.success = success;\t}\t\tpublic MultiObject(Exception ex) {\t\tthis.success = false;\t\tthis.ex = ex;\t}\t\tpublic MultiObject(T value) {\t\tthis.success = true;\t\tthis.obj = value;\t}}\n\n1，成功与否。对应属性success。\n2，异常信息。对应属性ex。若是操作正常执行，则就不在意这个属性的值。\n3，我们操作的最终目的对象。对应属性obj。\n\n## 关于泛型方法的使用实例\n\n1，一个是泛型表示某一个类型的参数。为的传递某一类的参数对象\n2，另一个则是传递的不是参数，而是代表Class，某一个类。\n\n /* * 将Json字符串信息转换成对应的Java对象 * * @param json json字符串对象 * @param c 对应的类型 / public static <T> T parseJsonToObj(String json, Class<T> c) { try { JSONObject jsonObject = JSONObject.parseObject(json); return JSON.toJavaObject(jsonObject, c); } catch (Exception e) { LOG.error(e.getMessage()); } return null; }\n\nCollector collectorObj = JSONUtils.parseJsonToObj(collector, Collector.class);Flume flume = JSONUtils.parseJsonToObj(flumeJson, Flume.class);Probe probe = JSONUtils.parseJsonToObj(probeJson, Probe.class);\n\n /* * @param dest 目的集合 * @param source 源集合 * @param <T> 集合参数的类型 */ private static <T> void listAddAllAvoidNPE(List<T> dest, List<T> source) { if (source == null) { return; } dest.addAll(source); } private static <T> void listAddAvoidNull(List<T> dest, T source) { if (source == null) { return; } dest.add(source); }\n\n\tList<ProbeObject> list = Lists.newArrayList();\tlistAddAllAvoidNPE(list, decoder.getProperties());\n\nposted @ 2018-11-08 14:10 星朝阅读(71761) 评论(8编辑收藏" ]	[ null, "https://img-blog.csdn.net/20151116222626759", null, "https://img-blog.csdn.net/20151116222950942", null, "https://img-blog.csdn.net/20151117082843103", null ]	{"ft_lang_label":"__label__zh","ft_lang_prob":0.95732635,"math_prob":0.8375387,"size":7518,"snap":"2020-34-2020-40","text_gpt3_token_len":5266,"char_repetition_ratio":0.08810221,"word_repetition_ratio":0.0631068,"special_character_ratio":0.1915403,"punctuation_ratio":0.09744214,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96792406,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,5,null,5,null,5,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-27T09:41:32Z\",\"WARC-Record-ID\":\"<urn:uuid:5f582840-87b3-4339-b7b7-94c5d38682c0>\",\"Content-Length\":\"376372\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7682d426-db1c-4f72-8ce4-bdc963c2f08a>\",\"WARC-Concurrent-To\":\"<urn:uuid:4d6681d3-02ea-4d36-8e33-6d8ad3fd42eb>\",\"WARC-IP-Address\":\"118.31.180.41\",\"WARC-Target-URI\":\"https://www.cnblogs.com/jpfss/p/9928747.html\",\"WARC-Payload-Digest\":\"sha1:W762WVSXB4QBOQFDKMYHNLHX3MDGLZ6V\",\"WARC-Block-Digest\":\"sha1:DOOF4T37IIPRAVJVHPIOIVFZKS5H72OM\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600400274441.60_warc_CC-MAIN-20200927085848-20200927115848-00240.warc.gz\"}"}
http://alexminnaar.com/2015/02/14/deep-learning-basics.html	[ "Alex Minnaar\n\n## Deep Learning Basics: Neural Networks, Backpropagation and Stochastic Gradient Descent\n\n14 Feb 2015\n\nIn the last couple of years Deep Learning has received a great deal of press. This press is not without warrant - Deep Learning has produced stat-of-the-art results in many computer vision and speech processing tasks. However, I believe that the press has given people the impression that Deep Learning is some kind of imprenetrable, esoteric field that can only be understood by academics. In this blog post I want to try to erase that impression and provide a practical overview of some of Deep Learning’s basic concepts.\n\nAt its core, Deep Learning is a class of of neural network models. That is, a model with an input layer, an output layer, and an arbitrary number of hidden layers. These layers are made up of neurons or neural units. They are called neurons because they share some similarities with the behaviour of the neurons present in the human brain (though this comparison has drawn a lot of criticism from neuroscientists). For our purposes, we can think of a neuron as a nonlinear function of the weighted sum of its inputs. Since the neuron is really the most basic part of any Deep Learning model it is a good place to start.\n\n## The Single Neuron Model\n\nA neuron is a function that maps an input vector $$\\{x_1,...,x_K\\}$$ to a scalar output $$y$$ via a weight vector $$\\{w_1,...,w_K\\}$$ and a nonlinear function $$f$$.", null, "The function $$f$$ takes a weighted sum of the inputs and returns $$y$$.\n\n$y=f(\\sum_{i=0}^Kw_ix_i)=f(\\mathbf{w^Tx})$\n\nOften an additional element is added to the input vector that is always equal to $$1$$ with a corresponding additional weight element which acts as a bias. The function $$f$$ is called the link function which provides the nonlinearity between the input and output. A common choice for this link function is the logistic function which is defined as\n\n$f(u)=\\frac{1}{1+e^{u}}$\n\nWith the appropriate substitutions the final formula for the single neuron model becomes\n\n$y=\\frac{1}{1+e^{\\mathbf{w^Tx}}}$\n\nIf you plot the logistic function,", null, "you can see that it is smooth and differentiable and bound between $$0$$ and 1\\$. We shall see that these are two important properties. The derivative of the logistic function is simply\n\n$\\frac{d f(u)}{d u}=f(u)(1-f(u))=f(u)f(-u)$\n\nThis derivative will be used when we learn the weight vector $$\\bf{w}$$ via stochastic gradient descent.\n\nLike any optimization problem, our goal is to minimize an objective function. Traditionally, the objective function measures the difference between the actual output $$t$$ and the predicted output $$f(\\mathbf{w^Tx})$$. In this case we will be using the squared loss function\n\n$E=\\frac{1}{2}(t - y)^2=\\frac{1}{2}(t-f(\\mathbf{w^Tx}))^2$\n\nWe want to find the weights $$\\mathbf{w}$$ such that the above objective is minimized. We do this with stochastic gradient descent (SGD). In SGD we iteratively update our weight parameters in the direction of the gradient of the loss function until we have reached a minimum. Unlike traditional gradient descent, we do not use the entire dataset to compute the gradient at each iteration. Instead, at each iteration we randomly select a single data point from our dataset and move in the direction of the gradient with respect to that data point. Obviously this is only an approximation of the true gradient but it can be proven that we will eventually reach the minimum by following this noisey gradient. There are several advantages to using stochastic gradient descent over traditional gradient descent.\n\n1. Gradient descent requires loading the entire dataset into main memory. If your dataset is large this can be problematic. Stochastic gradient descent only requires one data point at a time (or sometimes a minibatch of data points) which is much less memory intensive.\n2. Most datasets have redundancy in them. Traditional gradient descent requires one full pass over the data until an update is made. Due to redundancy, a meaningful update can often be made without iterating over the entire dataset as with stochastic gradient descent.\n3. As a consequence of the previous point, stochastic gradient descent can often converge faster than traditional gradient descent. It is also guaranteed to find the global minimum if the loss function is convex.\n\nOur objective function $$E$$ is already defined in terms of a single data point so let’s procede to compute its gradient with respect to an aribtrary element of our weight vector $$w_i$$.\n\n\\begin{align} \\frac{\\partial E}{\\partial w_i} &= \\frac{\\partial E}{\\partial y} \\cdot \\frac{\\partial y}{\\partial u} \\cdot\\frac{\\partial u}{\\partial w_i} \\\\ &= (y-t) \\cdot y(1-y) \\cdot x_i \\end{align}\n\nNow we are able to obtain the stochastic gradient descent update equation (in vector notation)\n\n$\\mathbf{w}^{new}=\\mathbf{w}^{old}- \\eta \\cdot (y-t) \\cdot y(1-y) \\cdot \\mathbf{x}$\n\nWhere $$\\eta>0$$ is the step size. As stated previously, $$(\\mathbf{x},y)$$ data points are sequentially fed into this update equation until the weights $$\\mathbf{w}$$ converge to their optimal value. This is how we use stochastic gradient descent to learn the weights for the single neuron model.\n\nWhat we just did is also known as logistic regression and if we had replaced our logistic function with a unit step function we would have made what is known as a perceptron! Now let’s extend this relatively simple model to something a bit more complex…\n\n## The Neural Network\n\nA neural network consists of an input layer, output layer, and hidden layer. Our input layer consists of the input vector $$\\mathbf{x}=\\{x_1,...,x_K\\}$$. The hidden layer consists of a vector of $$N$$ neurons $$\\mathbf{h}=\\{h_1,...,h_N\\}$$. Finally there is an output layer with one neuron for every element of the output vector $$\\mathbf{y}=\\{y_1,...,y_M\\}$$. Every element in the input layer is connected to every neuron in the hidden layer with $$w_{ki}$$ indicating the weight associated with the connection between the $$k^{th}$$ input element and the $$i^{th}$$ hidden neuron. The same connection structure is present between the hidden and output layers with $$w'_{ij}$$ indicating the weight associated with the connection between the $$i^{th}$$ hidden neuron and the $$j^{th}$$ output neuron. This network structure is better illustrated in the below diagram.", null, "It is helpful to think of the weight $$w_{ki}$$ as the the $$(k,i)^{th}$$ entry in a $$K \\times N$$ weight matrix $$\\mathbf{W}$$ and similarly weight $$w'_{ij}$$ as the $$(i,j)^{th}$$ entry in a $$N \\times M$$ weight matrix $$\\mathbf{W'}$$. The output of each neuron in the hidden and output layer is computed in the exact same way as before. It is simply the logistic function applied to the weighted sum of the neuron’s inputs. For example, the output of an arbitrary neuron in the hidden layer $$h_i$$ is\n\n$h_i=f(u_i)=f(\\sum^K_{k=1}w_{ki}x_k)$\n\nand similarly for the output of an arbitrary output neuron $$y_j$$ is\n\n$y_j=f(u'_j)=f(\\sum^N_{i=1}w'_{ij}h_i)$\n\nThe objective function is also the same as before except now it is summed over all elements in the output layer.\n\n$E=\\frac{1}{2}\\sum^M_{j=1}(y_j-t_j)^2$\n\nUnlike before, we need to construct update equations for both sets of weights - the input-to-hidden layer weights $$w_{ki}$$ and the hidden-to-output weights $$w'_{ij}$$. In order to do this we need to compute the gradient of our objective function $$E$$ with respect to $$w_{ki}$$ as well as the gradient with respect to $$w'_{ij}$$. We must start with the gradient with respect to $$w'_{ij}$$ (the hidden-to-output weights) and we shall see why later. In order to compute $$\\frac{\\partial E}{\\partial{w'_{ij}}}$$ we must recall our high-school calculus, specifically the chain rule. From the chain rule, we must first take the derivative of $$E$$ with respect to $$y'_j$$. Then we must take the derivative of $$y_j$$ (i.e. the logistic function) with respect to $$w'_{ij}$$ which needs yet another application of the chain rule. We first take the derivative of the logistic function with respect to its input $$u'_j$$, then finally we can take the derivative of this input with respect to $$w'_{ij}$$ and we arrive at our desired value. This process is clearly defined below.\n\nFrom the chain rule,\n\n$\\frac{\\partial E}{\\partial w'_{ij}}=\\frac{\\partial E}{\\partial y_j} \\cdot \\frac{\\partial y_j}{\\partial u'_j} \\cdot \\frac{\\partial u'_j}{\\partial w'_{ij}}$\n\nThe derivative of $$E$$ with respect to $$y_j$$ is simply,\n\n$\\frac{\\partial E}{\\partial y_j}=y_j-t_j$\n\nFrom the last section we saw that the derivative of the logistic function $$f$$ with respect to its input $$u$$ is $$f(u)(1-f(u))$$. If we apply this we get,\n\n$\\frac{\\partial y_j}{\\partial u'_j}=y_j(1-y_j)$\n\nwhere $$y_j=f(u'_j)$$. Next we compute the derivative of $$u'_j=\\sum^N_{i=1}w'_{ij}h_i$$ with respect to a particular $$w'_{ij}$$ which is simply $$h_i$$. So, after making the appropriate subsitutions, we get\n\n$\\frac{\\partial E}{\\partial w'_{ij}}=(y_j-t_j) \\cdot y_j(1-y_j) \\cdot h_i$\n\nWith this gradient we can construct the update equation for $$w'_{ij}$$\n\n$w'^{new}_{ij}=w'^{old}_{ij} - \\eta \\cdot (y_j-t_j) \\cdot y_j(1-y_j) \\cdot h_i$\n\nNow let’s turn our attention to the gradient of the objective function with respect to the input-to-hidden weights $$w_{ki}$$. As we shall see, this gradient has already been partially computed when we computed the previous gradient.\n\nUsing the chain rule, the full gradient is\n\n$\\frac{\\partial E}{\\partial w_{ki}}=\\sum^M_{j=1}(\\frac{\\partial E}{\\partial y_j}\\cdot \\frac{\\partial y_j}{\\partial u'_j} \\cdot \\frac{\\partial u'_j}{\\partial h_i} )\\cdot \\frac{\\partial h_i}{\\partial u_i} \\cdot \\frac{\\partial u_i}{\\partial w_{ki}}$\n\nThe sum is due to the fact that the hidden unit that $$w_{ki}$$ connects to is itself connected to every output unit, thus each of these gradients need to be taken into account as well. We have already computed both $$\\frac{\\partial E}{\\partial y_j}$$ and $$\\frac{\\partial y_j}{\\partial u'_j}$$ which means that\n\n$\\frac{\\partial E}{\\partial y_j}\\cdot \\frac{\\partial y_j}{\\partial u'_j} = (y_j-t_j) \\cdot y_j(1-y_j)$\n\nNow we need to compute the remaining derivatives $$\\frac{\\partial u'_j}{\\partial h_i}$$, $$\\frac{\\partial h_i}{\\partial u_i}$$, and $$\\frac{\\partial u_i}{\\partial w_{ki}}$$. So let’s do just that.\n\n$\\frac{\\partial u'_j}{\\partial h_i}=\\frac{\\partial \\sum^N_{i=1}w'_{ij}h_i}{\\partial h_i}=w'_{ij}$\n\nand, again using the derivative of the logistic function\n\n$\\frac{\\partial h_i}{\\partial u_i}=h_i(1-h_i)$\n\nand finally\n\n$$\\frac{\\partial u_i}{\\partial w_{ki}}=\\frac{\\partial \\sum^K_{k=1}w_{ki}x_k}{\\partial w_{ki}}=x_k$$ƒ\n\nAfter making the appropriate substitutions we arrive at the gradient\n\n$\\frac{\\partial E}{\\partial w_{ki}}=\\sum^M_{j=1}[(y_j-t_j) \\cdot y_j(1-y_j) \\cdot w'_{ij}] \\cdot h_i(1-h_i) \\cdot x_k$\n\nAnd the update equation becomes\n\n$w^{new}_{ki}=w^{old}_{ki} - \\eta \\cdot \\sum^M_{j=1}[(y_j-t_j) \\cdot y_j(1-y_j) \\cdot w'_{ij}] \\cdot h_i(1-h_i) \\cdot x_k$\n\nThis process is known as backpropagation because we begin with the final output error $$y_j-t_j$$ for the output neuron $$j$$ and this error gets propagated backwards throughout the network in order to update the weights.\n\n## Wrapping Everything Up\n\nIn this blog post we started with the simple single neuron model and we learned the model weights by computing the gradient of the objective function and using it in the stochastic gradient descent update equation. Then we moved on to the slightly more complicated neural network model. In this case we computed the required gradients using a procedure known as backpropagation and we again used these gradients in the SGD update equations. True Deep Learning models either contain many more hidden layers or neurons in different configurations but they still adhere to the basic principles described here. Hopefully this post has made Deep Learning seem like a more understandable and less daunting field of machine learning." ]	[ null, "http://alexminnaar.com/assets/neuron.png", null, "http://alexminnaar.com/assets/logistic.png", null, "http://alexminnaar.com/assets/neural_network.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.84297603,"math_prob":0.99936646,"size":11936,"snap":"2022-40-2023-06","text_gpt3_token_len":3077,"char_repetition_ratio":0.16694602,"word_repetition_ratio":0.0328341,"special_character_ratio":0.26918566,"punctuation_ratio":0.062075216,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9999881,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,3,null,3,null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-02-07T05:55:24Z\",\"WARC-Record-ID\":\"<urn:uuid:f5dbd1ad-39a2-482f-8e36-61374a8b92d3>\",\"Content-Length\":\"16616\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:16613117-eed9-4075-ac29-d487c033bf86>\",\"WARC-Concurrent-To\":\"<urn:uuid:91e29f11-361f-4c05-8896-51f7a89b4158>\",\"WARC-IP-Address\":\"185.199.108.153\",\"WARC-Target-URI\":\"http://alexminnaar.com/2015/02/14/deep-learning-basics.html\",\"WARC-Payload-Digest\":\"sha1:EJWWF7PF3QCERIS5VRCQ7AV5X6X6GOKV\",\"WARC-Block-Digest\":\"sha1:FNNFHEVCCJ376MPTU56RQI4GJSKH35RL\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-06/CC-MAIN-2023-06_segments_1674764500384.17_warc_CC-MAIN-20230207035749-20230207065749-00015.warc.gz\"}"}
https://numpy.org.cn/user/c-info/python-as-glue.html	[ "# # 使用Python作为粘合剂\n\nThere is no conversation more boring than the one where everybody agrees.\n\n— Michel de Montaigne\n\nDuct tape is like the force. It has a light side, and a dark side, and it holds the universe together.\n\n— Carl Zwanzig\n\n## # f2py\n\nF2py允许您自动构建一个扩展模块，该模块与Fortran 77/90/95代码中的例程相连。它能够解析Fortran 77/90/95代码并自动为它遇到的子程序生成Python签名，或者你可以通过构造一个接口定义文件（或修改f2py生成的文件）来指导子程序如何与Python接口。）。\n\n### # 创建基本扩展模块的源\n\nC\nC\nDOUBLE COMPLEX A()\nDOUBLE COMPLEX B()\nDOUBLE COMPLEX C()\nINTEGER N\nDO 20 J = 1, N\nC(J) = A(J)+B(J)\n20 CONTINUE\nEND\n\n\nf2py -m add add.f\n\n\n### # 创建编译的扩展模块\n\nf2py -c -m add add.f\n\n\n>>> import add\nRequired arguments:\na : input rank-1 array('D') with bounds ()\nb : input rank-1 array('D') with bounds ()\nc : input rank-1 array('D') with bounds ()\nn : input int\n\n\n### # 改善基本界面\n\n>>> add.zadd([1,2,3], [1,2], [3,4], 1000)\n\n\nf2py -h add.pyf -m add add.f\n\n\nsubroutine zadd(a,b,c,n) ! in :add:add.f\ndouble complex dimension() :: a\ndouble complex dimension() :: b\ndouble complex dimension() :: c\ninteger :: n\n\n\nsubroutine zadd(a,b,c,n) ! in :add:add.f\ndouble complex dimension(n) :: a\ndouble complex dimension(n) :: b\ndouble complex intent(out),dimension(n) :: c\ninteger intent(hide),depend(a) :: n=len(a)\n\n\nintent指令，intent（out）用于告诉c作为输出变量的f2py，并且应该在传递给底层代码之前由接口创建。intent（hide）指令告诉f2py不允许用户指定变量n，而是从大小中获取它a。depend（a）指令必须告诉f2py n的值取决于输入a（因此在创建变量a之前它不会尝试创建变量n）。\n\nf2py -c add.pyf add.f95\n\n\n>>> import add\nRequired arguments:\na : input rank-1 array('D') with bounds (n)\nb : input rank-1 array('D') with bounds (n)\nReturn objects:\nc : rank-1 array('D') with bounds (n)\n\n\n>>> add.zadd([1,2,3],[4,5,6])\narray([ 5.+0.j, 7.+0.j, 9.+0.j])\n\n\n### # 在Fortran源中插入指令\n\nC\nC\nCF2PY INTENT(OUT) :: C\nCF2PY INTENT(HIDE) :: N\nCF2PY DOUBLE COMPLEX :: A(N)\nCF2PY DOUBLE COMPLEX :: B(N)\nCF2PY DOUBLE COMPLEX :: C(N)\nDOUBLE COMPLEX A()\nDOUBLE COMPLEX B()\nDOUBLE COMPLEX C()\nINTEGER N\nDO 20 J = 1, N\nC(J) = A(J) + B(J)\n20 CONTINUE\nEND\n\n\nf2py -c -m add add.f\n\n\n### # 过滤示例\n\nSUBROUTINE DFILTER2D(A,B,M,N)\nC\nDOUBLE PRECISION A(M,N)\nDOUBLE PRECISION B(M,N)\nINTEGER N, M\nCF2PY INTENT(OUT) :: B\nCF2PY INTENT(HIDE) :: N\nCF2PY INTENT(HIDE) :: M\nDO 20 I = 2,M-1\nDO 40 J=2,N-1\nB(I,J) = A(I,J) +\n$(A(I-1,J)+A(I+1,J) +$ A(I,J-1)+A(I,J+1) )0.5D0 +\n$(A(I-1,J-1) + A(I-1,J+1) +$ A(I+1,J-1) + A(I+1,J+1))0.25D0\n40 CONTINUE\n20 CONTINUE\nEND\n\n\nf2py -c -m filter filter.f\n\n\n### # 从Python中调用f2py\n\nf2py程序是用Python编写的，可以在代码中运行，以便在运行时编译Fortran代码，如下所示：\n\nfrom numpy import f2py\n\n\n### # 自动扩展模块生成\n\ndef configuration(parent_package='', top_path=None)\nfrom numpy.distutils.misc_util import Configuration\nconfig = Configuration('f2py_examples',parent_package, top_path)\nreturn config\n\nif __name__ == '__main__':\nfrom numpy.distutils.core import setup\nsetup(*configuration(top_path='').todict())\n\n\npip install .\n\n\n## # 用Cython\n\nCythonopen in new window是Python方言的编译器，它为速度添加（可选）静态类型，并允许将C或C ++代码混合到模块中。它生成C或C ++扩展，可以在Python代码中编译和导入。\n\nfrom Cython.Distutils import build_ext\nfrom distutils.extension import Extension\nfrom distutils.core import setup\nimport numpy\n\nsetup(name='mine', description='Nothing',\next_modules=[Extension('filter', ['filter.pyx'],\ninclude_dirs=[numpy.get_include()])],\ncmdclass = {'build_ext':build_ext})\n\n\n### # Cython中的复杂添加\n\ncimport cython\ncimport numpy as np\nimport numpy as np\n\n# We need to initialize NumPy.\nnp.import_array()\n\n#@cython.boundscheck(False)\ncdef double complex[:] a = in1.ravel()\ncdef double complex[:] b = in2.ravel()\n\nout = np.empty(a.shape, np.complex64)\ncdef double complex[:] c = out.ravel()\n\nfor i in range(c.shape):\nc[i].real = a[i].real + b[i].real\nc[i].imag = a[i].imag + b[i].imag\n\nreturn out\n\n\n### # Cython中的图像过滤器\n\ncimport numpy as np\nimport numpy as np\n\nnp.import_array()\n\ndef filter(img):\ncdef double[:, :] a = np.asarray(img, dtype=np.double)\nout = np.zeros(img.shape, dtype=np.double)\ncdef double[:, ::1] b = out\n\ncdef np.npy_intp i, j\n\nfor i in range(1, a.shape - 1):\nfor j in range(1, a.shape - 1):\nb[i, j] = (a[i, j]\n+ .5 ( a[i-1, j] + a[i+1, j]\n+ a[i, j-1] + a[i, j+1])\n+ .25 * ( a[i-1, j-1] + a[i-1, j+1]\n+ a[i+1, j-1] + a[i+1, j+1]))\n\nreturn out\n\n\nimport image\nout = image.filter(img)\n\n\n### # Cython结论\n\nCython是几个科学Python库的首选扩展机制，包括Scipy，Pandas，SAGE，scikit-image和scikit-learn，以及XML处理库LXML。语言和编译器维护良好。\n\n1. 在编写自定义算法时，有时在包装现有C库时，需要熟悉C语言。特别是，当使用C内存管理（malloc和朋友）时，很容易引入内存泄漏。但是，只是编译重命名的Python模块.pyx 已经可以加快速度，并且添加一些类型声明可以在某些代码中提供显着的加速。\n2. 很容易在Python和C之间失去一个清晰的分离，这使得重用你的C代码用于其他非Python相关项目变得更加困难。\n3. Cython生成的C代码难以阅读和修改（并且通常编译有令人烦恼但无害的警告）。\n\nCython生成的扩展模块的一大优势是它们易于分发。总之，Cython是一个非常强大的工具，可以粘合C代码或快速生成扩展模块，不应该被忽视。它对于不能或不会编写C或Fortran代码的人特别有用。\n\n## # ctypes\n\nctypesopen in new window 是一个包含在stdlib中的Python扩展模块，它允许您直接从Python调用共享库中的任意函数。这种方法允许您直接从Python接口C代码。这开辟了大量可供Python使用的库。然而，缺点是编码错误很容易导致丑陋的程序崩溃（就像C中可能发生的那样），因为对参数进行的类型或边界检查很少。当数组数据作为指向原始内存位置的指针传入时尤其如此。那么你应该负责子程序不会访问实际数组区域之外的内存。但，\n\n1. 有一个共享的库。\n2. 加载共享库。\n3. 将python对象转换为ctypes理解的参数。\n4. 使用ctypes参数从库中调用函数。\n\n### # 加载共享库\n\n• 必须以特殊方式编译共享库（例如，使用-shared带有gcc 的标志）。\n• 在某些平台（例如 Windows）上，共享库需要一个.def文件，该文件指定要导出的函数。例如，mylib.def文件可能包含：\nLIBRARY mylib.dll\nEXPORTS\ncool_function1\ncool_function2\n\n\nPython distutils中没有标准的方法来以跨平台的方式创建标准共享库（扩展模块是Python理解的“特殊”共享库）。因此，在编写本书时，ctypes的一大缺点是难以以跨平台的方式分发使用ctypes的Python扩展并包含您自己的代码，这些代码应编译为用户系统上的共享库。\n\n### # 加载共享库\n\nlib = ctypes.cdll[<full_path_name>]\n\n\nNumPy提供称为ctypeslib.load_library（名称，路径）的便利功能。此函数采用共享库的名称（包括任何前缀，如'lib'但不包括扩展名）和共享库所在的路径。它返回一个ctypes库对象，或者OSError如果找不到库则引发一个或者ImportError如果ctypes模块不可用则引发一个。（Windows用户：使用加载的ctypes库对象 load_library总是在假定cdecl调用约定的情况下加载。请参阅下面的ctypes文档ctypes.windll和/或ctypes.oledll 了解在其他调用约定下加载库的方法）。\n\n### # 转换参数\n\nPython int / long，字符串和unicode对象会根据需要自动转换为等效的ctypes参数None对象也会自动转换为NULL指针。必须将所有其他Python对象转换为特定于ctypes的类型。围绕此限制有两种方法允许ctypes与其他对象集成。\n\n1. 不要设置函数对象的argtypes属性，并_as_parameter_为要传入的对象定义方法。该 _as_parameter_方法必须返回一个Python int，它将直接传递给函数。\n2. 将argtypes属性设置为一个列表，其条目包含具有名为from_param的类方法的对象，该类方法知道如何将对象转换为ctypes可以理解的对象（具有该_as_parameter_属性的int / long，字符串，unicode或对象）。\n\nNumPy使用两种方法，优先选择第二种方法，因为它可以更安全。ndarray的ctypes属性返回一个对象，该对象具有一个_as_parameter_返回整数的属性，该整数表示与之关联的ndarray的地址。因此，可以将此ctypes属性对象直接传递给期望指向ndarray中数据的指针的函数。调用者必须确保ndarray对象具有正确的类型，形状，并且设置了正确的标志，否则如果传入指向不适当数组的数据指针则会导致令人讨厌的崩溃。\n\nndarray的ctypes属性还赋予了额外的属性，这些属性在将有关数组的其他信息传递给ctypes函数时可能很方便。属性数据形状步幅可以提供与数据区域，形状和数组步幅相对应的ctypes兼容类型。data属性返回c_void_p表示指向数据区域的指针。shape和strides属性各自返回一个ctypes整数数组（如果是0-d数组，则返回None表示NULL指针）。数组的基本ctype是与平台上的指针大小相同的ctype整数。还有一些方法 data_as({ctype})，和shape_as()strides_as()。它们将数据作为您选择的ctype对象返回，并使用您选择的基础类型返回shape / strides数组。为方便起见，该ctypeslib模块还包含c_intp一个ctypes整数数据类型，其大小c_void_p与平台上的大小相同（如果未安装ctypes，则其值为None）。\n\n### # 调用函数\n\nlib = numpy.ctypeslib.load_library('mylib','.')\nfunc1 = lib.cool_function1 # or equivalently\nfunc1 = lib['cool_function1']\n\n\nfunc1.restype = None\n\n\nndpointerdtype = Nonendim = Noneshape = Noneflags = None\n\nNone不检查具有该值的关键字参数。指定关键字会强制在转换为与ctypes兼容的对象时检查ndarray的该方面。dtype关键字可以是任何被理解为数据类型对象的对象。ndim关键字应为整数，shape关键字应为整数或整数序列。flags关键字指定传入的任何数组所需的最小标志。这可以指定为逗号分隔要求的字符串，指示需求位OR'd在一起的整数，或者从flags的flags属性返回的flags对象。具有必要要求的数组。\n\n### # 完整的例子\n\n/* Add arrays of contiguous data /\ntypedef struct {double real; double imag;} cdouble;\ntypedef struct {float real; float imag;} cfloat;\nvoid zadd(cdouble a, cdouble b, cdouble c, long n)\n{\nwhile (n--) {\nc->real = a->real + b->real;\nc->imag = a->imag + b->imag;\na++; b++; c++;\n}\n}\n\n\nvoid cadd(cfloat a, cfloat b, cfloat c, long n)\n{\nwhile (n--) {\nc->real = a->real + b->real;\nc->imag = a->imag + b->imag;\na++; b++; c++;\n}\n}\nvoid dadd(double a, double b, double c, long n)\n{\nwhile (n--) {\nc++ = a++ + b++;\n}\n}\nvoid sadd(float a, float b, float c, long n)\n{\nwhile (n--) {\nc++ = a++ + b++;\n}\n}\n\n\ncode.c文件还包含以下功能dfilter2d\n\n/\n* Assumes b is contiguous and has strides that are multiples of\n* sizeof(double)\n/\nvoid\ndfilter2d(double a, double b, ssize_t astrides, ssize_t dims)\n{\nssize_t i, j, M, N, S0, S1;\nssize_t r, c, rm1, rp1, cp1, cm1;\n\nM = dims; N = dims;\nS0 = astrides/sizeof(double);\nS1 = astrides/sizeof(double);\nfor (i = 1; i < M - 1; i++) {\nr = iS0;\nrp1 = r + S0;\nrm1 = r - S0;\nfor (j = 1; j < N - 1; j++) {\nc = jS1;\ncp1 = j + S1;\ncm1 = j - S1;\nb[iN + j] = a[r + c] +\n(a[rp1 + c] + a[rm1 + c] +\na[r + cp1] + a[r + cm1])0.5 +\n(a[rp1 + cp1] + a[rp1 + cm1] +\na[rm1 + cp1] + a[rm1 + cp1])0.25;\n}\n}\n}\n\n\ngcc -o code.so -shared code.c\n\n\n__all__ = ['add', 'filter2d']\n\nimport numpy as np\nimport os\n\n_path = os.path.dirname('__file__')\nfor name in _typedict.keys():\nval = getattr(lib, name)\nval.restype = None\n_type = _typedict[name]\nval.argtypes = [np.ctypeslib.ndpointer(_type,\nflags='aligned, contiguous'),\nnp.ctypeslib.ndpointer(_type,\nflags='aligned, contiguous'),\nnp.ctypeslib.ndpointer(_type,\nflags='aligned, contiguous,'\\\n'writeable'),\nnp.ctypeslib.c_intp]\n\n\nlib.dfilter2d.restype=None\nlib.dfilter2d.argtypes = [np.ctypeslib.ndpointer(float, ndim=2,\nflags='aligned'),\nnp.ctypeslib.ndpointer(float, ndim=2,\nflags='aligned, contiguous,'\\\n'writeable'),\nctypes.POINTER(np.ctypeslib.c_intp),\nctypes.POINTER(np.ctypeslib.c_intp)]\n\n\ndef select(dtype):\nif dtype.char in ['?bBhHf']:\nelif dtype.char in ['F']:\nelif dtype.char in ['DG']:\nelse:\nreturn func, ntype\n\n\ndef add(a, b):\nrequires = ['CONTIGUOUS', 'ALIGNED']\na = np.asanyarray(a)\nfunc, dtype = select(a.dtype)\na = np.require(a, dtype, requires)\nb = np.require(b, dtype, requires)\nc = np.empty_like(a)\nfunc(a,b,c,a.size)\nreturn c\n\n\ndef filter2d(a):\na = np.require(a, float, ['ALIGNED'])\nb = np.zeros_like(a)\nlib.dfilter2d(a, b, a.ctypes.strides, a.ctypes.shape)\nreturn b\n\n\n### # ctypes结论\n\n• 从Python代码中清除C代码的分离\n• 除了Python和C之外，无需学习新的语法\n• 允许重复使用C代码\n• 可以使用简单的Python包装器获取为其他目的编写的共享库中的功能并搜索库。\n• 通过ctypes属性轻松与NumPy集成\n• 使用ndpointer类工厂进行完整的参数检查\n\n• 由于缺乏在distutils中构建共享库的支持，很难分发使用ctypes创建的扩展模块（但我怀疑这会随着时间的推移而改变）。\n• 您必须拥有代码的共享库（没有静态库）。\n• 很少支持C ++代码及其不同的库调用约定。你可能需要一个围绕C ++代码的C包装器来与ctypes一起使用（或者只是使用Boost.Python）。\n\n## # 您可能会觉得有用的其他工具\n\n### # SIP\n\nSIP是另一种用于包装特定于Python的C / C ++库的工具，似乎对C ++有很好的支持。Riverbank Computing开发了SIP，以便为QT库创建Python绑定。必须编写接口文件以生成绑定，但接口文件看起来很像C / C ++头文件。虽然SIP不是一个完整的C ++解析器，但它理解了相当多的C ++语法以及它自己的特殊指令，这些指令允许修改Python绑定的完成方式。它还允许用户定义Python类型和C / C ++结构和类之间的映射。\n\n### # 提升Python\n\nBoost是C ++库的存储库，Boost.Python是其中一个库，它提供了一个简洁的接口，用于将C ++类和函数绑定到Python。Boost.Python方法的神奇之处在于它完全在纯C ++中工作而不引入新语法。许多C ++用户报告称，Boost.Python可以无缝地结合两者的优点。我没有使用过Boost.Python，因为我不是C ++的大用户，并且使用Boost来包装简单的C子例程通常都是过度杀戮。它的主要目的是使Python中的C ++类可用。因此，如果您有一组需要完全集成到Python中的C ++类，请考虑学习并使用Boost.Python。\n\n### # PyFort\n\nPyFort是一个很好的工具，可以将Fortran和类似Fortran的C代码包装到Python中，并支持数值数组。它由着名计算机科学家Paul Dubois编写，是Numeric（现已退休）的第一个维护者。值得一提的是希望有人会更新PyFort以使用NumPy数组，现在支持Fortran或C风格的连续数组。" ]	[ null ]	{"ft_lang_label":"__label__zh","ft_lang_prob":0.86248666,"math_prob":0.95853794,"size":19310,"snap":"2023-14-2023-23","text_gpt3_token_len":12074,"char_repetition_ratio":0.08955765,"word_repetition_ratio":0.1010101,"special_character_ratio":0.21196271,"punctuation_ratio":0.18123586,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9859268,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-06-09T04:05:51Z\",\"WARC-Record-ID\":\"<urn:uuid:af2cda2b-7d6b-43a8-a4f0-a11484499295>\",\"Content-Length\":\"158480\",\"Content-Type\":\"application/http; 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https://zbmath.org/authors/?q=ai:zariski.oscar	[ "## Zariski, Oscar\n\nCompute Distance To:\n Author ID: zariski.oscar", null, "Published as: Zariski, Oscar; Zariski, O.; Zariski, Oskar more...less External Links: MacTutor · MGP · Wikidata · Math-Net.Ru · GND · IdRef Awards: Wolf Prize (1981)\n Documents Indexed: 139 Publications since 1924, including 19 Books Biographic References: 8 Publications Co-Authors: 7 Co-Authors with 17 Joint Publications 79 Co-Co-Authors\nall top 5\n\n### Co-Authors\n\n 116 single-authored 6 Samuel, Pierre 3 Muhly, Harry Townsend 3 Mumford, David Bryant 2 Abhyankar, Shreeram Shankar 2 Artin, Michael 2 Barber, Sherburne F. 2 Cohen, Irvin Sol 2 Kmety, Francois 2 Schilling, Otto Franz Georg 2 Teissier, Bernard 1 Falb, Peter L. 1 Hironaka, Heisuke 1 Lipman, Joseph 1 Mazur, Barry 1 Merle, Michel\nall top 5\n\n### Serials\n\n 42 American Journal of Mathematics 13 Annals of Mathematics. Second Series 12 Bulletin of the American Mathematical Society 8 Transactions of the American Mathematical Society 8 Proceedings of the National Academy of Sciences of the United States of America 3 Atti della Accademia Nazionale dei Lincei, Rendiconti, VI. Serie 3 Ergebnisse der Mathematik und ihrer Grenzgebiete 3 Mathematicians of Our Time 2 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 2 Bulletin des Sciences Mathématiques. Deuxième Série 2 Illinois Journal of Mathematics 2 Atti della Accademia Nazionale dei Lincei. Serie Ottava. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali 2 Graduate Texts in Mathematics 1 Uspekhi Matematicheskikh Nauk [N. S.] 1 Annales de l’Institut Fourier 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Memoirs of the American Mathematical Society 1 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Paris 1 Periodico di Matematiche. IV. Serie 1 Memoirs of the College of Science, University of Kyoto, Series A 1 Rendiconti del Circolo Matematico di Palermo 1 Rendiconti Di Matematica e Delle Sue Applicazioni, V. Serie 1 Lecture Notes in Mathematics 1 Princeton Mathematical Series 1 University Lecture Series 1 Rendiconti del Seminario Matematico delle Facoltá di Scienze della R. Universitá di Roma, II. Serie 1 Memorie della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali. 6. Serie 1 Accademia dei Lincei, Rendiconti, V. Serie 1 Revista Matemática Hispano-Americana. II. Seria 1 Classics in Mathematics\nall top 5\n\n### Fields\n\n 28 Algebraic geometry (14-XX) 10 Commutative algebra (13-XX) 3 Field theory and polynomials (12-XX) 2 Several complex variables and analytic spaces (32-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Number theory (11-XX) 1 Geometry (51-XX) 1 Manifolds and cell complexes (57-XX)\n\n### Citations contained in zbMATH Open\n\n105 Publications have been cited 3,334 times in 2,674 Documents Cited by Year\nCommutative algebra. Vol. II. Zbl 0121.27801\nZariski, Oscar; Samuel, Pierre\n1960\nCommutative algebra. Vol. 1. With the cooperation of I. S. Cohen. Zbl 0081.26501\nZariski, Oscar; Samuel, Pierre\n1958\nCommutative algebra. Vol. II. Reprint of the 1958-1960 Van Nostrand edition. Zbl 0322.13001\nZariski, Oscar; Samuel, Pierre\n1976\nCommutative algebra. Vol. II. Übersetzung aus dem Englischen von E. S. Golod, S. P. Demuškin und A. N. Tyurin. Unter Redaktion von A. I. Uzkov. (Коммутативная алгтебра. Том II.) Zbl 0121.27901\nZariski, O.; Samuel, P.\n1963\nThe theorem of Riemann-Roch for high multiples of an effective divisor on an algebraic surface. Zbl 0124.37001\nZariski, Oscar\n1962\nStudies in equisingularity. I: Equivalent singularities of plane algebroid curves. Zbl 0132.41601\nZariski, O.\n1965\nCommutative Algebra. Vol. 1. With the cooperation of I. S. Cohen. 2nd ed. Zbl 0313.13001\nZariski, Oscar; Samuel, Pierre\n1975\nOn the problem of existence of algebraic functions of two variables possessing a given branch curve. JFM 55.0806.01\nZariski, O.\n1929\nAlgebraic surfaces. With appendices by S.S. Abhyankar, J. Lipman, and D. Mumford. 2nd suplemented ed. Zbl 0219.14020\nZariski, O.\n1971\nSome open questions in the theory of singularities. Zbl 0236.14002\nZariski, Oscar\n1971\nStudies in equisingularity. II: Equisingularity in codimension 1 (and characteristic zero). Zbl 0146.42502\nZariski, O.\n1965\nCommutative algebra. Vol. 1. Übersetzung aus dem Englischen von O.N. Vvedenskii, S.P. Demuskin und A.N. Tjurin. Zbl 0112.02902\nZariski, O.; Samuel, P.\n1963\nThe reduction of the singularities of an algebraic surface. JFM 65.1399.03\nZariski, O.\n1939\nStudies in equisingularity. III: Saturation of local rings and equisingularity. Zbl 0189.21405\nZariski, O.\n1968\nLocal uniformization on algebraic varieties. JFM 66.1327.02\nZariski, O.\n1940\nOn the purity of the branch locus of algebraic functions. Zbl 0087.35703\nZariski, Oscar\n1958\nIntroduction to the problem of minimal models in the theory of algebraic surfaces. Zbl 0093.33904\nZariski, Oscar\n1958\nInterprétations algébrico-géométriques du quatorzième problème de Hilbert. Zbl 0056.39602\nZariski, O.\n1954\nOn the topology of algebroid singularities. JFM 58.0614.02\nZariski, O.\n1932\nThe concept of a simple point of an abstract algebraic variety. Zbl 0031.26101\nZariski, Oscar\n1947\nThe reduction of the singularities of an algebraic surface. Zbl 0021.25303\nZariski, Oscar\n1939\nFoundations of a general theory of birational correspondences. Zbl 0061.33004\nZariski, Oscar\n1943\nPolynomial ideals defined by infinitely near base points. Zbl 0018.20101\nZariski, Oscar\n1938\nLe problème des modules pour les branches planes. Redige par Francois Kmety et Michel Merle. Avec un appendice de Bernard Teissier. Zbl 0317.14004\nZariski, Oscar\n1973\nThe compactness of the Riemann manifold of an abstract field of algebraic functions. Zbl 0063.08390\nZariski, Oscar\n1944\nReduction of the singularities of algebraic three dimensional varieties. Zbl 0063.08361\nZariski, Oscar\n1944\nOn Castelnuovo’s criterion of rationality P$$_a$$=P$$_2$$=0 of an algebraic surface. Zbl 0085.36203\nZariski, Oscar\n1958\nOn the irregularity of cyclic multiple planes. Zbl 0001.40301\nZariski, Oscar\n1931\nLocal uniformization on algebraic varieties. Zbl 0025.21601\nZariski, Oscar\n1940\nAlgebraic surfaces. Zbl 0010.37103\nZariski, O.\n1935\nAlgebraic surfaces. JFM 61.0704.01\nZariski, O.\n1935\nCharacterization of plane algebroid curves whose module of differentials has maxim torsion. Zbl 0144.20201\nZariski, O.\n1966\nDimension-theoretic characterization of maximal irreducible algebraic systems of plane nodal curves of a given order n and with a given number d of nodes. Zbl 0516.14023\nZariski, Oscar\n1982\nOn the topology of algebroid singularities. Zbl 0004.36902\nZariski, Oscar\n1932\nA simplified proof for the resolution of singularities of an algebraic surface. Zbl 0063.08389\nZariski, Oscar\n1942\nThe topological discriminant group of a Riemann surface of genus p. Zbl 0016.32502\nZariski, Oscar\n1937\nPolynomial ideals defined by infinitely near base points. JFM 64.0079.01\nZariski, O.\n1938\nThe problem of minimal models in the theory of algebraic surfaces. Zbl 0085.36202\nZariski, Oscar\n1958\nGeneral theory of saturation and of saturated local rings. II: Saturated local rings of dimension 1. Zbl 0228.13007\nZariski, Oscar\n1971\nLe problème des modules pour les branches planes. Cours donné au Centre de Mathématiques de l’École Polytechnique. Nouvelle éd. revue par l’auteur. Rédigé par François Kmety et Michel Merle. Avec un appendice de Bernard Teissier. Zbl 0592.14010\nZariski, Oscar\n1986\nA theorem on the Poincaré group of an algebraic hypersurface. Zbl 0016.04102\nZariski, Oscar\n1937\nPencils on an algebraic variety and a new proof of a theorem of Bertini. Zbl 0025.21502\nZariski, Oscar\n1941\nTheory and applications of holomorpic functions on algebraic varieties over arbitrary ground fields. Zbl 0045.24001\nZariski, Oscar\n1951\nComplete linear systems on normal varieties and a generalization of a lemma of Enriques-Severi. Zbl 0047.14803\nZariski, Oscar\n1952\nThe theorem of Bertini on variable singular points of a linear system of varieties. Zbl 0061.33101\nZariski, Oscar\n1944\nOn the Poincaré group of rational plane curves. Zbl 0014.32801\nZariski, Oscar\n1936\nAnalytical irreducibility of normal varieties. Zbl 0037.22701\nZariski, Oscar\n1948\nThe topological discriminant group of a Riemann surface of genus $$p$$. JFM 63.0338.02\nZariski, O.\n1937\nAn introduction to the theory of algebraic surfaces. Zbl 0177.49001\nZariski, O.\n1969\nThe moduli problem for plane branches. With an appendix by Bernard Teissier. Transl. from the French by Ben Lichtin. Zbl 1107.14021\nZariski, Oscar\n2006\nOn the linear connection index of the algebraic surfaces $$z^n=f(x,y)$$. JFM 55.0806.02\nZariski, O.\n1929\nContributions to the problem of equisingularity. Zbl 0204.54503\nZariski, O.\n1970\nA new proof of Hilbert’s Nullstellensatz. Zbl 0032.26001\nZariski, Oscar\n1947\nOn the Poincaré group of rational plane curves. JFM 62.0758.02\nZariski, O.\n1936\nA fundamental lemma from the theory of holomorphic functions on an algebraic variety. Zbl 0039.03301\nZariski, Oscar\n1949\nPencils on an algebraic variety and a new proof of a theorem of Bertini. JFM 67.0618.01\nZariski, O.\n1941\nSome results in the arithmetic theory of algebraic varieties. JFM 65.0118.02\nZariski, O.\n1939\nExceptional singularities of an algebroid surface and their reduction. Zbl 0168.18903\nZariski, O.\n1967\nA theorem on the Poincaré group of an algebraic hypersurface. JFM 63.0621.03\nZariski, O.\n1937\nFoundations of a general theory of equisingularity on r-dimensional algebroid and algebraic varieties, of embedding dimension r+1. Zbl 0417.14008\nZariski, Oscar\n1979\nOn a theorem of Eddington. JFM 58.0105.02\nZariski, O.\n1932\nSur la normalité analytique des variétés normales. Zbl 0044.26601\nZariski, Oscar\n1950\nScientific report on the Second Summer Institute, Several Complex Variables. Part III: Algebraic sheaf theory. Zbl 0074.15703\nZariski, Oskar\n1956\nSome results in the arithmetic theory of algebraic varieties. Zbl 0020.39101\nZariski, Oscar\n1939\nOn the irregularity of cyclic multiple planes. JFM 57.0440.03\nZariski, O.\n1931\nGeneral theory of saturation and of saturated local rings. I: Saturation of complete local domains of dimension one having arbitrary coefficient fields (of characteristic zero). Zbl 0226.13013\nZariski, Oscar\n1971\nOn equimultiple subvarieties of algebroid hypersurfaces. Zbl 0304.14008\nZariski, Oscar\n1975\nGeneral theory of saturation and of saturated local rings. III: Saturation in arbitrary dimension and, in particular, saturation of algebroid hypersurfaces. Zbl 0306.13009\nZariski, Oscar\n1975\nAlgebraic varieties over ground fields of characteristic zero. Zbl 0022.30501\nZariski, Oscar\n1940\nA simple analytical proof of a fundamental property of birational transformations. Zbl 0037.16401\nZariski, Oscar\n1949\nAlgebraic surfaces: with appendices by S. S. Abhyankar, J. Lipman and D. Mumford. Reprint of the 2nd suppl. ed. 1971. Zbl 0845.14021\nZariski, Oscar\n1995\nNormal varieties and birational correspondences. Zbl 0063.08388\nZariski, Oscar\n1942\nA fundamental inequality in the theory of extensions of valuations. Zbl 0079.05601\nCohen, I. S.; Zariski, Oscar\n1957\nSull’ impossibilità di risolvere parametricamente per radicali un’equazione algebrica $$f (x,y) = 0$$ di genere $$p > 6$$ a moduli generali. JFM 52.0652.05\nZariski, O.\n1926\nCollected papers. Vol. III: Topology of curves and surfaces, and special topics in the theory of algebraic varieties. Edited and with an introduction by M. Artin and B. Mazur. Zbl 0446.14001\nZariski, Oscar\n1978\nGeneralized weight properties of the resultant of $$n + 1$$ polynomials in $$n$$ indeterminates. JFM 63.0047.01\nZariski, O.\n1937\nApplicazioni geometriche della teoria delle valutazioni. Zbl 0055.38801\nZariski, Oscar\n1954\nReducible exceptional curves of the first kind. JFM 61.0707.01\nBarber, S. F.; Zariski, O.\n1935\nOn the non-existence of curves of order 8 with 16 cusps. JFM 57.0823.03\nZariski, O.\n1931\nOn a theorem of Severi. JFM 54.0698.01\nZariski, O.\n1928\nCollected papers. Vol. I: Foundations of algebraic geometry and resolution of singularities. Edited by H. Hironaka and D. Mumford. Zbl 0234.14001\nZariski, Oscar\n1972\nReducible exceptional curves of the first kind. Zbl 0010.37104\nBarber, S. F.; Zariski, Oscar\n1935\nGeneralized weight properties of the resultant of $$n+1$$ polynomials in $$n$$ indeterminates. Zbl 0016.10001\nZariski, Oscar\n1937\nHilbert’s characteristic function and the arithmetic genus of an algebraic variety. Zbl 0041.08403\nMuhly, H. T.; Zariski, O.\n1950\nGeneralized semi-local rings. Zbl 0063.08392\nZariski, Oscar\n1946\nSplitting of valuations in extensions of local domains. I. Zbl 0064.27204\nAbhyankar, Shreeram; Zariski, Oscar\n1955\nThe connectedness theorem for birational transformations. Zbl 0087.35601\nZariski, Oscar\n1957\nCollected papers. Volume II: Holomorphic functions and linear systems. Ed. by M. Artin and D. Mumford. Zbl 0564.14001\nZariski, Oscar\n1973\nAlgebraic varieties over ground fields of characteristic zero. JFM 66.0792.01\nZariski, O.\n1940\nOn the irregularity of cyclic multiple planes. JFM 57.0830.13\nZariski, O.\n1931\nOn hyperelliptic $$\\varTheta$$-functions with rational characteristics. JFM 54.0410.05\nZariski, O.\n1928\nSopra una classe di equazioni algebriche contenenti linearmente un parametro e risolubili per radicali. JFM 52.0653.01\nZariski, O.\n1926\nOn algebraic equations containing linearly a parameter and solvable by radicals. (Sulle equazioni algebriche contenenti linearmente un parametro e risolubili per radicali.) JFM 50.0048.02\nZariski, O.\n1924\nOn differentials in function fields. Zbl 0100.03402\nZariski, Oscar; Falb, Peter\n1961\nLa risoluzione delle singolarita delle superficie algebriche immerse. I, II. Zbl 0105.14301\nZariski, O.\n1961\nA new operation (’saturation’) on local rings and applications to classification of singularities. Zbl 0154.20805\nZariski, O.\n1966\nThe elusive concept of equisingularity and related questions. Zbl 0422.14006\nZariski, Oscar\n1977\nAddendum to my paper ”Foundations of a general theory of equisingularity on r-dimensional algebroid and algebraic varieties, of embedding dimension r+1”. Zbl 0455.14004\nZariski, Oscar\n1980\nOn the problem of irreducibility of the algebraic system of irreducible plane curves of a given order and having a given number of nodes. Zbl 0597.14022\nZariski, Oscar\n1983\nSome open questions in the theory of singularities. Zbl 0241.14003\nZariski, Oscar\n1972\nThe moduli problem for plane branches. With an appendix by Bernard Teissier. Transl. from the French by Ben Lichtin. Zbl 1107.14021\nZariski, Oscar\n2006\nAlgebraic surfaces: with appendices by S. S. Abhyankar, J. Lipman and D. Mumford. Reprint of the 2nd suppl. ed. 1971. Zbl 0845.14021\nZariski, Oscar\n1995\nLe problème des modules pour les branches planes. Cours donné au Centre de Mathématiques de l’École Polytechnique. Nouvelle éd. revue par l’auteur. Rédigé par François Kmety et Michel Merle. Avec un appendice de Bernard Teissier. Zbl 0592.14010\nZariski, Oscar\n1986\nOn the problem of irreducibility of the algebraic system of irreducible plane curves of a given order and having a given number of nodes. Zbl 0597.14022\nZariski, Oscar\n1983\nDimension-theoretic characterization of maximal irreducible algebraic systems of plane nodal curves of a given order n and with a given number d of nodes. Zbl 0516.14023\nZariski, Oscar\n1982\nAddendum to my paper ”Foundations of a general theory of equisingularity on r-dimensional algebroid and algebraic varieties, of embedding dimension r+1”. Zbl 0455.14004\nZariski, Oscar\n1980\nFoundations of a general theory of equisingularity on r-dimensional algebroid and algebraic varieties, of embedding dimension r+1. Zbl 0417.14008\nZariski, Oscar\n1979\nCollected papers. Vol. III: Topology of curves and surfaces, and special topics in the theory of algebraic varieties. Edited and with an introduction by M. Artin and B. Mazur. Zbl 0446.14001\nZariski, Oscar\n1978\nThe elusive concept of equisingularity and related questions. Zbl 0422.14006\nZariski, Oscar\n1977\nCommutative algebra. Vol. II. Reprint of the 1958-1960 Van Nostrand edition. Zbl 0322.13001\nZariski, Oscar; Samuel, Pierre\n1976\nCommutative Algebra. Vol. 1. With the cooperation of I. S. Cohen. 2nd ed. Zbl 0313.13001\nZariski, Oscar; Samuel, Pierre\n1975\nOn equimultiple subvarieties of algebroid hypersurfaces. Zbl 0304.14008\nZariski, Oscar\n1975\nGeneral theory of saturation and of saturated local rings. III: Saturation in arbitrary dimension and, in particular, saturation of algebroid hypersurfaces. Zbl 0306.13009\nZariski, Oscar\n1975\nLe problème des modules pour les branches planes. Redige par Francois Kmety et Michel Merle. Avec un appendice de Bernard Teissier. Zbl 0317.14004\nZariski, Oscar\n1973\nCollected papers. Volume II: Holomorphic functions and linear systems. Ed. by M. Artin and D. Mumford. Zbl 0564.14001\nZariski, Oscar\n1973\nCollected papers. Vol. I: Foundations of algebraic geometry and resolution of singularities. Edited by H. Hironaka and D. Mumford. Zbl 0234.14001\nZariski, Oscar\n1972\nSome open questions in the theory of singularities. Zbl 0241.14003\nZariski, Oscar\n1972\nAlgebraic surfaces. With appendices by S.S. Abhyankar, J. Lipman, and D. Mumford. 2nd suplemented ed. Zbl 0219.14020\nZariski, O.\n1971\nSome open questions in the theory of singularities. Zbl 0236.14002\nZariski, Oscar\n1971\nGeneral theory of saturation and of saturated local rings. II: Saturated local rings of dimension 1. Zbl 0228.13007\nZariski, Oscar\n1971\nGeneral theory of saturation and of saturated local rings. I: Saturation of complete local domains of dimension one having arbitrary coefficient fields (of characteristic zero). Zbl 0226.13013\nZariski, Oscar\n1971\nContributions to the problem of equisingularity. Zbl 0204.54503\nZariski, O.\n1970\nAn introduction to the theory of algebraic surfaces. Zbl 0177.49001\nZariski, O.\n1969\nStudies in equisingularity. III: Saturation of local rings and equisingularity. Zbl 0189.21405\nZariski, O.\n1968\nExceptional singularities of an algebroid surface and their reduction. Zbl 0168.18903\nZariski, O.\n1967\nCharacterization of plane algebroid curves whose module of differentials has maxim torsion. Zbl 0144.20201\nZariski, O.\n1966\nA new operation (’saturation’) on local rings and applications to classification of singularities. Zbl 0154.20805\nZariski, O.\n1966\nStudies in equisingularity. I: Equivalent singularities of plane algebroid curves. Zbl 0132.41601\nZariski, O.\n1965\nStudies in equisingularity. II: Equisingularity in codimension 1 (and characteristic zero). Zbl 0146.42502\nZariski, O.\n1965\nCommutative algebra. Vol. II. Übersetzung aus dem Englischen von E. S. Golod, S. P. Demuškin und A. N. Tyurin. Unter Redaktion von A. I. Uzkov. (Коммутативная алгтебра. Том II.) Zbl 0121.27901\nZariski, O.; Samuel, P.\n1963\nCommutative algebra. Vol. 1. Übersetzung aus dem Englischen von O.N. Vvedenskii, S.P. Demuskin und A.N. Tjurin. Zbl 0112.02902\nZariski, O.; Samuel, P.\n1963\nThe theorem of Riemann-Roch for high multiples of an effective divisor on an algebraic surface. Zbl 0124.37001\nZariski, Oscar\n1962\nOn differentials in function fields. Zbl 0100.03402\nZariski, Oscar; Falb, Peter\n1961\nLa risoluzione delle singolarita delle superficie algebriche immerse. I, II. Zbl 0105.14301\nZariski, O.\n1961\nCommutative algebra. Vol. II. Zbl 0121.27801\nZariski, Oscar; Samuel, Pierre\n1960\nCommutative algebra. Vol. 1. With the cooperation of I. S. Cohen. Zbl 0081.26501\nZariski, Oscar; Samuel, Pierre\n1958\nOn the purity of the branch locus of algebraic functions. Zbl 0087.35703\nZariski, Oscar\n1958\nIntroduction to the problem of minimal models in the theory of algebraic surfaces. Zbl 0093.33904\nZariski, Oscar\n1958\nOn Castelnuovo’s criterion of rationality P$$_a$$=P$$_2$$=0 of an algebraic surface. Zbl 0085.36203\nZariski, Oscar\n1958\nThe problem of minimal models in the theory of algebraic surfaces. Zbl 0085.36202\nZariski, Oscar\n1958\nA fundamental inequality in the theory of extensions of valuations. Zbl 0079.05601\nCohen, I. S.; Zariski, Oscar\n1957\nThe connectedness theorem for birational transformations. Zbl 0087.35601\nZariski, Oscar\n1957\nScientific report on the Second Summer Institute, Several Complex Variables. Part III: Algebraic sheaf theory. Zbl 0074.15703\nZariski, Oskar\n1956\nSplitting of valuations in extensions of local domains. I. Zbl 0064.27204\nAbhyankar, Shreeram; Zariski, Oscar\n1955\nInterprétations algébrico-géométriques du quatorzième problème de Hilbert. Zbl 0056.39602\nZariski, O.\n1954\nApplicazioni geometriche della teoria delle valutazioni. Zbl 0055.38801\nZariski, Oscar\n1954\nLe problème de la réduction des singularités d’une variété algébrique. Zbl 0055.38802\nZariski, O.\n1954\nComplete linear systems on normal varieties and a generalization of a lemma of Enriques-Severi. Zbl 0047.14803\nZariski, Oscar\n1952\nThe fundamental ideas of abstract algebraic geometry. Zbl 0049.22701\nZariski, Oscar\n1952\nTheory and applications of holomorpic functions on algebraic varieties over arbitrary ground fields. Zbl 0045.24001\nZariski, Oscar\n1951\nSur la normalité analytique des variétés normales. Zbl 0044.26601\nZariski, Oscar\n1950\nHilbert’s characteristic function and the arithmetic genus of an algebraic variety. Zbl 0041.08403\nMuhly, H. T.; Zariski, O.\n1950\nA fundamental lemma from the theory of holomorphic functions on an algebraic variety. Zbl 0039.03301\nZariski, Oscar\n1949\nA simple analytical proof of a fundamental property of birational transformations. Zbl 0037.16401\nZariski, Oscar\n1949\nAnalytical irreducibility of normal varieties. Zbl 0037.22701\nZariski, Oscar\n1948\nThe concept of a simple point of an abstract algebraic variety. Zbl 0031.26101\nZariski, Oscar\n1947\nA new proof of Hilbert’s Nullstellensatz. Zbl 0032.26001\nZariski, Oscar\n1947\nGeneralized semi-local rings. Zbl 0063.08392\nZariski, Oscar\n1946\nThe compactness of the Riemann manifold of an abstract field of algebraic functions. Zbl 0063.08390\nZariski, Oscar\n1944\nReduction of the singularities of algebraic three dimensional varieties. Zbl 0063.08361\nZariski, Oscar\n1944\nThe theorem of Bertini on variable singular points of a linear system of varieties. Zbl 0061.33101\nZariski, Oscar\n1944\nFoundations of a general theory of birational correspondences. Zbl 0061.33004\nZariski, Oscar\n1943\nA simplified proof for the resolution of singularities of an algebraic surface. Zbl 0063.08389\nZariski, Oscar\n1942\nNormal varieties and birational correspondences. Zbl 0063.08388\nZariski, Oscar\n1942\nPencils on an algebraic variety and a new proof of a theorem of Bertini. Zbl 0025.21502\nZariski, Oscar\n1941\nPencils on an algebraic variety and a new proof of a theorem of Bertini. JFM 67.0618.01\nZariski, O.\n1941\nLocal uniformization on algebraic varieties. JFM 66.1327.02\nZariski, O.\n1940\nLocal uniformization on algebraic varieties. Zbl 0025.21601\nZariski, Oscar\n1940\nAlgebraic varieties over ground fields of characteristic zero. Zbl 0022.30501\nZariski, Oscar\n1940\nAlgebraic varieties over ground fields of characteristic zero. JFM 66.0792.01\nZariski, O.\n1940\nThe reduction of the singularities of an algebraic surface. JFM 65.1399.03\nZariski, O.\n1939\nThe reduction of the singularities of an algebraic surface. Zbl 0021.25303\nZariski, Oscar\n1939\nSome results in the arithmetic theory of algebraic varieties. JFM 65.0118.02\nZariski, O.\n1939\nSome results in the arithmetic theory of algebraic varieties. Zbl 0020.39101\nZariski, Oscar\n1939\nThe resolution of singularities of an algebraic curve. Zbl 0020.16001\nMuhly, H. T.; Zariski, O.\n1939\nPolynomial ideals defined by infinitely near base points. Zbl 0018.20101\nZariski, Oscar\n1938\nPolynomial ideals defined by infinitely near base points. JFM 64.0079.01\nZariski, O.\n1938\nThe topological discriminant group of a Riemann surface of genus p. Zbl 0016.32502\nZariski, Oscar\n1937\nA theorem on the Poincaré group of an algebraic hypersurface. Zbl 0016.04102\nZariski, Oscar\n1937\nThe topological discriminant group of a Riemann surface of genus $$p$$. JFM 63.0338.02\nZariski, O.\n1937\nA theorem on the Poincaré group of an algebraic hypersurface. JFM 63.0621.03\nZariski, O.\n1937\nGeneralized weight properties of the resultant of $$n + 1$$ polynomials in $$n$$ indeterminates. JFM 63.0047.01\nZariski, O.\n1937\nGeneralized weight properties of the resultant of $$n+1$$ polynomials in $$n$$ indeterminates. Zbl 0016.10001\nZariski, Oscar\n1937\nOn the Poincaré group of rational plane curves. Zbl 0014.32801\nZariski, Oscar\n1936\nOn the Poincaré group of rational plane curves. JFM 62.0758.02\nZariski, O.\n1936\nA topological proof of the Riemann-Roch theorem on an algebraic curve. Zbl 0013.07602\nZariski, Oscar\n1936\nAlgebraic surfaces. Zbl 0010.37103\nZariski, O.\n1935\nAlgebraic surfaces. JFM 61.0704.01\nZariski, O.\n1935\nReducible exceptional curves of the first kind. JFM 61.0707.01\nBarber, S. F.; Zariski, O.\n1935\nReducible exceptional curves of the first kind. Zbl 0010.37104\nBarber, S. F.; Zariski, Oscar\n1935\nOn the topology of algebroid singularities. JFM 58.0614.02\nZariski, O.\n1932\nOn the topology of algebroid singularities. Zbl 0004.36902\nZariski, Oscar\n1932\nOn a theorem of Eddington. JFM 58.0105.02\nZariski, O.\n1932\nOn the irregularity of cyclic multiple planes. Zbl 0001.40301\nZariski, Oscar\n1931\nOn the irregularity of cyclic multiple planes. JFM 57.0440.03\nZariski, O.\n1931\nOn the non-existence of curves of order 8 with 16 cusps. JFM 57.0823.03\nZariski, O.\n1931\nOn the irregularity of cyclic multiple planes. JFM 57.0830.13\nZariski, O.\n1931\nOn the non-existence of curves of order 8 with 16 cusps. Zbl 0001.22604\nZariski, Oscar\n1931\nOn the problem of existence of algebraic functions of two variables possessing a given branch curve. JFM 55.0806.01\nZariski, O.\n1929\nOn the linear connection index of the algebraic surfaces $$z^n=f(x,y)$$. JFM 55.0806.02\nZariski, O.\n1929\n...and 5 more Documents\nall top 5\n\n### Cited by 2,252 Authors\n\n 55 Heinzer, William J. 32 Cutkosky, Steven Dale 29 Abhyankar, Shreeram Shankar 29 Ratliff, Louis J. jun. 26 Gilmer, Robert W. jun. 22 Artal Bartolo, Enrique 18 Kuhlmann, Franz-Viktor 17 Olberding, Bruce M. 16 Dobbs, David Earl 16 Rush, David E. 14 Eyral, Christophe 14 Fontana, Marco 14 Nobile, Augusto 13 Galindo Pastor, Carlos 13 Mordeson, John N. 13 Oka, Mutsuo 13 Warner, Seth 12 Cogolludo Agustín, José Ignacio 11 Sampaio, José Edson 11 Spivakovsky, Mark 11 Tokunaga, Hiro-o 10 Lê Dûng Tráng 10 Parusiński, Adam 10 Piltant, Olivier 10 Spirito, Dario 10 Teicher, Mina 10 Teissier, Bernard 9 Campillo, Antonio 9 Ciliberto, Ciro 9 Finocchiaro, Carmelo Antonio 9 Gonçalves, Daciberg Lima 9 Greco, Silvio 9 Guaschi, John 9 Hernandes, Marcelo Escudeiro 9 Kang, Ming-Chang 9 Verma, Jugal Kishore 9 Villamayor Uriburu, Orlando Eugenio 9 Yau, Stephen Shing-Toung 8 Degtyarev, Alex 8 García Barroso, Evelia Rosa 8 González Pérez, Pedro Daniel 8 Gurjar, Rajendra Vasant 8 Marchionna, Ermanno 8 Monserrat, Francisco 8 Reguera, Ana-José 8 Shustin, Eugenii Isaakovich 8 Vasconcelos, Wolmer V. 7 Boucksom, Sébastien 7 Brown, William C. 7 Chistov, Alexandre L. 7 Favre, Charles 7 Greuel, Gert-Martin 7 Jonsson, Mattias 7 Kim, Mee-Kyoung 7 Kiyek, Karl-Heinz 7 Küronya, Alex 7 Libgober, Anatoly S. 7 Mott, Joe Leonard 7 O’Carroll, Liam 7 Ohm, Jack 7 Popescu-Pampu, Patrick 7 Vogel, Wolfgang 6 Becker, Joseph A. 6 Debremaeker, Raymond 6 Guerville-Ballé, Benoît 6 Harbourne, Brian 6 Hauser, Herwig 6 Hefez, Abramo 6 Hochster, Melvin 6 Kaliman, Shulim I. 6 Kleiman, Steven Lawrence 6 Kuhlmann, Norbert 6 Kulikov, Viktor Stepanovich 6 Kuroda, Shigeru 6 Loper, Kenneth Alan 6 Luengo, Ignacio 6 Ngô Viêt Trung 6 Noh, Sunsook 6 Nuño-Ballesteros, Juan José 6 Pfister, Gerhard 6 Risler, Jean-Jacques 6 Schicho, Josef 6 Van Tuyl, Adam 6 Zaidenberg, Mikhail G. 6 Zariski, Oscar 5 Alling, Norman Larrabee 5 Amram, Meirav 5 Baldassarri Ghezzo, Santuzza 5 Bouchiba, Samir 5 Butts, Hubert S. 5 Cossart, Vincent 5 Daigle, Daniel 5 Delgado, Felix 5 Eakin, Paul M. jun. 5 Granja, Angel 5 Grifo, Eloísa 5 Guo, Kunyu 5 Herrmann, Manfred 5 Herzog, Jürgen 5 Huneke, Craig L. ...and 2,152 more Authors\nall top 5\n\n### Cited in 291 Serials\n\n 236 Journal of Algebra 183 Transactions of the American Mathematical Society 154 Proceedings of the American Mathematical Society 147 Mathematische Annalen 139 Journal of Pure and Applied Algebra 80 Communications in Algebra 80 Mathematische Zeitschrift 77 Inventiones Mathematicae 63 Compositio Mathematica 54 Manuscripta Mathematica 50 Archiv der Mathematik 43 Advances in Mathematics 40 Annales de l’Institut Fourier 37 Annali di Matematica Pura ed Applicata. Serie Quarta 37 Rendiconti del Seminario Matematico della Università di Padova 35 Bulletin de la Société Mathématique de France 32 Journal of Symbolic Computation 27 Bulletin of the American Mathematical Society 24 Duke Mathematical Journal 23 Proceedings of the Japan Academy. Series A 22 Mathematical Proceedings of the Cambridge Philosophical Society 21 Publications Mathématiques 20 Israel Journal of Mathematics 20 Linear Algebra and its Applications 19 Mathematical Notes 19 Bulletin of the American Mathematical Society. New Series 18 Nagoya Mathematical Journal 18 Topology and its Applications 17 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 17 Journal of Algebraic Geometry 16 International Journal of Mathematics 16 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 16 Journal of Mathematical Sciences (New York) 15 Journal of Algebra and its Applications 14 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 14 Algebra and Logic 14 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 13 Rocky Mountain Journal of Mathematics 13 Monatshefte für Mathematik 13 Comptes Rendus. Mathématique. Académie des Sciences, Paris 12 Journal of Number Theory 12 Rendiconti del Circolo Matemàtico di Palermo. Serie II 12 Rendiconti del Seminario Matemàtico e Fisico di Milano 11 Journal für die Reine und Angewandte Mathematik 11 Michigan Mathematical Journal 11 Bulletin de la Société Mathématique de France. Supplément. Mémoires 10 Transformation Groups 10 Journal of Commutative Algebra 9 Fuzzy Sets and Systems 9 Journal of the Mathematical Society of Japan 9 Results in Mathematics 9 Tôhoku Mathematical Journal. Second Series 9 Annali della Scuola Normale Superiore di Pisa. Scienze Fisiche e Matematiche. III. Ser 8 Czechoslovak Mathematical Journal 8 Functional Analysis and its Applications 8 Siberian Mathematical Journal 8 Journal of Knot Theory and its Ramifications 8 European Journal of Mathematics 7 Arkiv för Matematik 7 Acta Mathematica 7 Geometriae Dedicata 7 Journal of Soviet Mathematics 7 Memoirs of the American Mathematical Society 7 Revista Matemática Iberoamericana 7 Applicable Algebra in Engineering, Communication and Computing 7 Finite Fields and their Applications 7 Revista Matemática Complutense 7 Proceedings of the Japan Academy 6 Astronomische Nachrichten 6 Bulletin of the Australian Mathematical Society 6 Journal of Mathematical Analysis and Applications 6 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 6 Kodai Mathematical Journal 6 Mathematische Nachrichten 6 Proceedings of the Edinburgh Mathematical Society. Series II 6 Publications of the Research Institute for Mathematical Sciences, Kyoto University 6 Computer Aided Geometric Design 6 Geometry & Topology 6 Journal of Singularities 5 Archive for History of Exact Sciences 5 Discrete Mathematics 5 Mathematics of Computation 5 Beiträge zur Algebra und Geometrie 5 Algebra Universalis 5 Mathematica Slovaca 5 Osaka Journal of Mathematics 5 Journal of the American Mathematical Society 5 International Journal of Algebra and Computation 5 Designs, Codes and Cryptography 5 Expositiones Mathematicae 5 St. Petersburg Mathematical Journal 5 Selecta Mathematica. New Series 5 Annals of Mathematics. Second Series 5 Algebraic & Geometric Topology 5 Bulletin of the Brazilian Mathematical Society. New Series 4 Communications in Mathematical Physics 4 Acta Mathematica Vietnamica 4 Collectanea Mathematica 4 Journal of Differential Equations 4 Mathematika ...and 191 more Serials\nall top 5\n\n### Cited in 55 Fields\n\n 1,212 Algebraic geometry (14-XX) 926 Commutative algebra (13-XX) 362 Several complex variables and analytic spaces (32-XX) 216 Field theory and polynomials (12-XX) 149 Number theory (11-XX) 149 Group theory and generalizations (20-XX) 143 Associative rings and algebras (16-XX) 107 Manifolds and cell complexes (57-XX) 49 Computer science (68-XX) 42 Linear and multilinear algebra; matrix theory (15-XX) 42 Nonassociative rings and algebras (17-XX) 41 Mathematical logic and foundations (03-XX) 37 Global analysis, analysis on manifolds (58-XX) 34 Functional analysis (46-XX) 32 Algebraic topology (55-XX) 30 Dynamical systems and ergodic theory (37-XX) 27 Category theory; homological algebra (18-XX) 27 Functions of a complex variable (30-XX) 26 Combinatorics (05-XX) 26 Convex and discrete geometry (52-XX) 26 Differential geometry (53-XX) 22 Systems theory; control (93-XX) 21 Topological groups, Lie groups (22-XX) 21 Information and communication theory, circuits (94-XX) 18 History and biography (01-XX) 18 Numerical analysis (65-XX) 17 Order, lattices, ordered algebraic structures (06-XX) 17 Ordinary differential equations (34-XX) 16 General algebraic systems (08-XX) 13 $$K$$-theory (19-XX) 13 Real functions (26-XX) 13 General topology (54-XX) 13 Quantum theory (81-XX) 12 Approximations and expansions (41-XX) 12 Geometry (51-XX) 11 Operator theory (47-XX) 9 Special functions (33-XX) 8 Partial differential equations (35-XX) 7 Difference and functional equations (39-XX) 5 Relativity and gravitational theory (83-XX) 4 Measure and integration (28-XX) 4 Integral transforms, operational calculus (44-XX) 4 Mechanics of particles and systems (70-XX) 3 Potential theory (31-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Abstract harmonic analysis (43-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 2 Statistics (62-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 General and overarching topics; collections (00-XX) 1 Sequences, series, summability (40-XX) 1 Mechanics of deformable solids (74-XX) 1 Operations research, mathematical programming (90-XX) 1 Biology and other natural sciences (92-XX) 1 Mathematics education (97-XX)\n\n### Wikidata Timeline\n\nThe data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata." ]	[ null, "https://zbmath.org/static/feed-icon-14x14.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.5836077,"math_prob":0.7562529,"size":34921,"snap":"2022-40-2023-06","text_gpt3_token_len":11044,"char_repetition_ratio":0.20852306,"word_repetition_ratio":0.5131034,"special_character_ratio":0.2956101,"punctuation_ratio":0.18743502,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9555474,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-09-24T17:00:47Z\",\"WARC-Record-ID\":\"<urn:uuid:9482df51-3f55-47a6-a98d-49f717d47468>\",\"Content-Length\":\"401352\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f9ca4624-e419-4d8f-ae9e-69bb9c2e976d>\",\"WARC-Concurrent-To\":\"<urn:uuid:14f9dfa5-deda-4a24-9fc1-772cfba0f7bd>\",\"WARC-IP-Address\":\"141.66.194.2\",\"WARC-Target-URI\":\"https://zbmath.org/authors/?q=ai:zariski.oscar\",\"WARC-Payload-Digest\":\"sha1:4P2XQR6GPQP76NTOAOZZWWLWONSO7QUS\",\"WARC-Block-Digest\":\"sha1:AHXUOFZ72PPZ22P3KDWQNND5RHBYRZ45\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030331677.90_warc_CC-MAIN-20220924151538-20220924181538-00494.warc.gz\"}"}
https://www.magiwise.com/addition-and-subtraction/	[ "Select Page", null, "## Plus and Minus app", null, "## Learn the fundamental of addition and subtraction with numbers.\n\nThe app includes excellent instructions alternated with 59 interactive exercises to practice addition and subtraction with numbers up to 20.\nOur “Plus & Minus”-app is ideal to support any maths method, in which you start adding and subtracting numbers.\n\nTopics which are covered in this app, are:\n\n• The line with numbers.\n• Addition and subtraction to the number 5.\n• Addition and subtraction with 5, 10, 15 and 20.\n• Addition and subtraction to the number 20.\n• To split numbers.\n• Calculating with a bus and train.\n• Adding and subtracting with dozens.", null, "### The line with numbers\n\nA number line is a line that displays all the integers in order from low to high. First, you practise with up to 5 then finally up to 20. To understand the concept of the number line, you first get short exercises, where you have to add each time the correct number omitted on the line.", null, "### To split numbers\n\nYou learn to divide numbers with short exercises. You have to break the number into two other values, which together forms the first number. In this way, you will learn the concept of adding and subtracting of numbers.", null, "### Splitting by using a train as an example\n\nAs soon as you understand the concept of dividing numbers, we will count with numbers above five. You will work with a train as an example, where you have to place cubes on the wagon. In this way, you will learn that 4 + 2 is actually 5 + 1.", null, "### Practice addition and subtraction with passengers at the bus stop\n\nAfter the train, you get the sums with buses. For example: ‘ A bus drives away with twenty passengers. One passenger leaves the bus at the next stop. How many passengers are on the bus? ‘", null, "" ]	[ null, "https://www.magiwise.com/wp-content/uploads/2018/12/AppIconE006-nl.svg", null, "https://i0.wp.com/www.magiwise.com/wp-content/uploads/2019/05/E006-P-en-07.png", null, "https://i0.wp.com/www.magiwise.com/wp-content/uploads/2019/05/E006-en-01.png", null, "https://i0.wp.com/www.magiwise.com/wp-content/uploads/2019/05/E006-en-02.png", null, "https://i0.wp.com/www.magiwise.com/wp-content/uploads/2019/05/E006-en-04.png", null, "https://i0.wp.com/www.magiwise.com/wp-content/uploads/2019/05/E006-04-nl.png", null, "https://i0.wp.com/www.magiwise.com/wp-content/uploads/2018/11/logo.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9361361,"math_prob":0.8856221,"size":1729,"snap":"2023-40-2023-50","text_gpt3_token_len":384,"char_repetition_ratio":0.17855072,"word_repetition_ratio":0.032051284,"special_character_ratio":0.22498554,"punctuation_ratio":0.110787176,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99600554,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"im_url_duplicate_count":[null,5,null,2,null,2,null,2,null,2,null,2,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-29T17:51:48Z\",\"WARC-Record-ID\":\"<urn:uuid:89aa2be8-e8e9-4a21-8038-263b92734309>\",\"Content-Length\":\"230847\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:fa819163-f2b5-4ff7-9cbc-1016083d35be>\",\"WARC-Concurrent-To\":\"<urn:uuid:8a36bd44-a044-4d1a-b8ac-09bc8fb5a3f4>\",\"WARC-IP-Address\":\"141.138.168.124\",\"WARC-Target-URI\":\"https://www.magiwise.com/addition-and-subtraction/\",\"WARC-Payload-Digest\":\"sha1:7IDWFIO4FOK4OW46HNEDY3A3MYIDUPA2\",\"WARC-Block-Digest\":\"sha1:OKSOTMKYN42ZC3FMTQ55E4R6BRRRW4ZE\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510520.98_warc_CC-MAIN-20230929154432-20230929184432-00191.warc.gz\"}"}
https://www.onlinemathlearning.com/percentage-p5.html	[ "", null, "# Percentage\n\nVideos, worksheets, games and activities to help students learn about percentage in Singapore Math.\nIntroduction to Percentage\nFind out what a percentage is using examples.\nPercentages and Fractions\nHow are percentages and fractions related? How to convert percentages to fractions and fractions to percentages?\n\nPercentage and Decimal\nDetailed example to explain the relation between percentage and decimal, and converting percentage to decimal and decimal to percentage.\nPercentage (1): Practice Exercise\nConversion of fractions to percentages\n\nPercentage (1): More Practical Exercise Question 3\nExample: 65% of the children prefer cycling to walking. Two-fifths of those who prefer cycling are girls. What percentage of the children are girls who prefer walking to cycling?\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.", null, "", null, "" ]	[ null, "https://www.onlinemathlearning.com/objects/default_image.gif", null, "https://www.onlinemathlearning.com/objects/default_image.gif", null, "https://www.onlinemathlearning.com/objects/default_image.gif", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8631142,"math_prob":0.8566696,"size":985,"snap":"2021-04-2021-17","text_gpt3_token_len":184,"char_repetition_ratio":0.19877675,"word_repetition_ratio":0.0,"special_character_ratio":0.17563452,"punctuation_ratio":0.103658535,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99241376,"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\":\"2021-01-25T05:04:24Z\",\"WARC-Record-ID\":\"<urn:uuid:51cd146f-3660-4fa9-9733-582a4d4111ba>\",\"Content-Length\":\"46671\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2fd69c9f-e24b-4194-a27f-0de506ee6711>\",\"WARC-Concurrent-To\":\"<urn:uuid:83dfa1dd-3f84-49e4-8dda-a189197f023b>\",\"WARC-IP-Address\":\"173.247.219.45\",\"WARC-Target-URI\":\"https://www.onlinemathlearning.com/percentage-p5.html\",\"WARC-Payload-Digest\":\"sha1:3KJ4KK634KWUF6MTQ5KUBSVHE77DFLPE\",\"WARC-Block-Digest\":\"sha1:ZTYSOLNJGPNBLECNPXWDKEGTSN4NAZFQ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-04/CC-MAIN-2021-04_segments_1610703564029.59_warc_CC-MAIN-20210125030118-20210125060118-00605.warc.gz\"}"}
https://www.getsetcoupon.com/npv-discount-rate-table/	[ "Filter Type:\nFilter Time:\n\n## PRESENT VALUE TABLE\n\nActived: Thursday Feb 13, 2020\n\n› See more: Promo codes\n\n## Leases Discount rates - KPMG\n\nActived: Friday Feb 14, 2020\n\n› See more: Discount codes\n\nOffer Details: The discount rate affects the amount of the lessee’s lease liabilities – and . a host of key financial ratios. The new standard brings forward definitions of discount rates from the current leases standard. But applying these old definitions in the new world of on-balance sheet lease accounting will be tough, especially for lessees. They now need to . determine discount rates for most See more ...\n\n## NPV calculation - Illinois Institute of Technology\n\nActived: Saturday Feb 15, 2020\n\n› See more: Discount codes\n\nOffer Details: NPV Calculation – basic concept PV(Present Value): PV is the current worth of a future sum of money or stream of cash flows given a specified rate of return. Future cash flows are discounted at the discount rate, and the higher the discount rate, the lower the present value of the future cash flows. See more ...\n\n## Difference Between NPV and IRR (with Comparison Chart\n\nActived: Thursday Feb 13, 2020\n\n› See more: Discount codes\n\nOffer Details: The aggregate of all present value of the cash flows of an asset, immaterial of positive or negative is known as Net Present Value. Internal Rate of Return is the discount rate at which NPV = 0. The calculation of NPV is made in absolute terms as compared to IRR which is computed in percentage terms. See more ...\n\n## NPV Calculator - calculate Net Present Value\n\nActived: Wednesday Feb 12, 2020\n\n› See more: Discount codes\n\nOffer Details: If you wonder how to calculate the Net Present Value (NPV) by yourself or using an Excel spreadsheet, all you need is the formula: where r is the discount rate and t is the number of cash flow periods, C 0 is the initial investment while C t is the return during period t. See more ...\n\n## Business Smarts - Sample Module for Corporate Financial\n\nActived: Saturday Feb 15, 2020\n\n› See more: Discount codes\n\nOffer Details: 2) A project with a 3 year life and a cost of $28,000 generates revenues of$8,000 in year 1, $12,000 in year 2, and$17,000 in year 3. If the discount rate is 4%, what is the NPV of the project? See more ...\n\n## Discount Factor Calculator - miniwebtool.com\n\nActived: Wednesday Feb 12, 2020\n\n› See more: Discount codes\n\nOffer Details: Discount Rate: % Number of Compounding Periods: About Discount Factor Calculator . The Discount Factor Calculator is used to calculate the discount factor, which is the factor by which a future cash flow must be multiplied in order to obtain the present value. Discount Factor Calculation Formula. The discount factor is calculated in the following way, where P(T) is the discount factor, r the See more ...\n\n## Valuing Pharmaceutical Assets: When to Use NPV vs rNPV\n\nActived: Friday Feb 14, 2020\n\n› See more: Discount codes\n\nOffer Details: The NPV approach requires the use of different discount rates in an attempt to approximate the evolving probability of technical and regulatory success. Each new NPV calculation and discount rate can only provide insight about the net present value and risk at a single point in time. For example, the NPV calculation with a 33.4% discount rate See more ...\n\n## Calculate the Net Present Value - NPV \| PrepLounge.com\n\nActived: Friday Feb 14, 2020\n\n› See more: Discount codes\n\nOffer Details: By increasing the discount rate, the NPV of future earnings will shrink. Discount rates for quite secure cash-streams vary between 1% and 3%, but for most companies, you use a discount rate between 4% - 10% and for a speculative start-up investment, the applied interest rate could reach up to 40%. See more ...\n\n## Mid Period Discounting with the NPV Function\n\nActived: Saturday Feb 15, 2020\n\n› See more: Discount codes\n\nOffer Details: taking the present value of each cash flow then adding them up. If you use the NPV including the initial cash flow you will understate the true NPV. Getting the IRR for the half year assumptions is a little trickier. The easiest way is to use the NPV formula above with the half year adjustment, make the discount rate (.1 in example) a variable See more ...\n\n## NPV (net present value) - Valuation - Moneyterms\n\nActived: Friday Feb 14, 2020\n\n› See more: Promo codes\n\nOffer Details: A net present value (NPV) includes all cash flows including initial cash flows such as the cost of purchasing an asset, whereas a present value does not. The simple present value is useful where the negative cash flow is an initial one-off, as when buying a security (see DCF valuation for more detail) See more ...\n\n## How to Evaluate Two Projects by Evaluating the Net Present\n\nActived: Saturday Feb 15, 2020\n\n› See more: Discount codes\n\nOffer Details: Does the Net Present Value of Future Cash Flows Increase or Decrease as the Discount Rate Increases? Share on Facebook The net present value method has become one of the most popular tools for evaluating capital projects because it reduces each project to a single figure: the total estimated value of the project, expressed in today's dollars. See more ...\n\n## NPV Profile \| Excel with Excel Master\n\nActived: Wednesday Feb 12, 2020\n\n› See more: Promo codes\n\nOffer Details: An NPV Profile or Net Present Value Profile is a graph that looks like this:. The horizontal axis shows various values of r or the cost of capital and the vertical axis shows the Net Present Values (NPV) at those values of r. The point at which the line or curve crosses the horizontal axis is the estimate of the Internal Rate of Return or IRR.. To prepare an NPV Profile we need to have set up See more ...\n\n## A Refresher on Net Present Value\n\nActived: Tuesday Feb 11, 2020\n\n› See more: Promo codes\n\nOffer Details: “Net present value is the present value of the cash flows at the required rate of return of your project compared to your initial investment,” says Knight. In practical terms, it’s a method See more ...\n\n## Calculate NPV with a Series of Future Cash Flows - dummies\n\nActived: Friday Feb 14, 2020\n\n› See more: Promo codes\n\nOffer Details: Compute the net present value of a series of annual net cash flows. To determine the present value of these cash flows, use time value of money computations with the established interest rate to convert each year’s net cash flow from its future value back to its present value. Then add these present values together. See more ...\n\n## Excel formula: NPV formula for net present value \| Exceljet\n\nActived: Saturday Feb 15, 2020\n\n› See more: Promo codes\n\nOffer Details: How this formula works. Net Present Value (NPV) is the present value of expected future cash flows minus the initial cost of investment. The NPV function in Excel only calculates the present value of uneven cashflows, so the initial cost must be handled explicitly. See more ...\n\n## Net Present Value Calculator\n\nActived: Saturday Feb 15, 2020\n\n› See more: Discount codes\n\nOffer Details: Calculator Use. Calculate the net present value (NPV) of a series of future cash flows.More specifically, you can calculate the present value of uneven cash flows (or even cash flows). See Present Value Cash Flows Calculator for related formulas and calculations.. Interest Rate (discount rate per period) This is your expected rate of return on the cash flows for the length of one period. See more ...\n\n## Let's Talk About Net Present Value and - Bloomberg.com\n\nActived: Friday Feb 14, 2020\n\n› See more: Discount codes\n\nOffer Details: hyperbolic discounting,” the idea being that the discount rate in your personal present-value calculation might start out low but rises sharply after a year or two before settling down again in See more ...\n\n## Appendix: Present Value Tables - GitHub Pages\n\nActived: Thursday Feb 13, 2020\n\n› See more: Promo codes\n\n## NPV Profile \| Definition \| Example\n\nActived: Friday Feb 14, 2020\n\n› See more: Discount codes\n\nOffer Details: NPV profile of a project or investment is a graph of the project’s net present value corresponding to different values of discount rates. The NPV values are plotted on the Y-axis and the WACC is plotted on the X-axis. The NPV profile shows how NPV changes in response to changing cost of capital. See more ..." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8926355,"math_prob":0.89759004,"size":24110,"snap":"2020-10-2020-16","text_gpt3_token_len":5917,"char_repetition_ratio":0.2325977,"word_repetition_ratio":0.15635179,"special_character_ratio":0.24807134,"punctuation_ratio":0.16087408,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96016127,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-02-18T08:14:32Z\",\"WARC-Record-ID\":\"<urn:uuid:98d5918e-6aff-46e1-bb6d-85ce5109bf16>\",\"Content-Length\":\"85294\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2fa2857b-8e38-437c-82da-8e5207d1a199>\",\"WARC-Concurrent-To\":\"<urn:uuid:21a88506-8253-4e21-83d5-06b54af5d302>\",\"WARC-IP-Address\":\"104.27.143.51\",\"WARC-Target-URI\":\"https://www.getsetcoupon.com/npv-discount-rate-table/\",\"WARC-Payload-Digest\":\"sha1:22PHGVA42OI3GHUF7M2SF6CRWFGLJ4M5\",\"WARC-Block-Digest\":\"sha1:FJA3QKQMM7ZUPK5Q2QT55Z3ZQPTTITU5\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-10/CC-MAIN-2020-10_segments_1581875143635.54_warc_CC-MAIN-20200218055414-20200218085414-00078.warc.gz\"}"}
https://nanohub.org/courses/SOE	[ "## nanoHUB-U: The Science, Art, and Practice of Analyzing Experimental Data and Designing Experiments\n\nBrought to you by:\n\n### nanoHUB-U\n\nLecture 1: Collecting and Plotting Data\n\n• Origin of data, Field Acceleration vs. Statistical Inference\n• Nonparametric information\n• Preparing data for projection: Hazen formula\n• Preparing data for projection: Kaplan formula\n\nLecture 2: Physical vs Empirical Distribution\n\n• Physical vs. empirical distribution\n• Properties of classical distribution function\n• Moment-based fitting of data\n\nLecture 3: Model Selection/Goodness of Fit\n\n• The problem of matching data with theoretical distribution\n• Parameter extractions: Moments, linear regression, maximum likelihood\n• Goodness of fit: Residual, Pearson, Cox, Akika\n\nLecture 4: Scaling Theory of Design of Experiments\n\n• Buckingham PI Theorem\n• An Illustrative Example\n• Recall the scaling theory of HCI, NBTI, and TDDB\n\nLecture 5: Design of Experiments\n\n• Single factor and full factorial method\n• Orthogonal vector analysis: Taguchi/Fisher model\n• Correlation in dependent parameters" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.69992816,"math_prob":0.6880696,"size":1065,"snap":"2022-40-2023-06","text_gpt3_token_len":250,"char_repetition_ratio":0.11875589,"word_repetition_ratio":0.013422819,"special_character_ratio":0.18967137,"punctuation_ratio":0.14457831,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96508515,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-09-28T03:16:33Z\",\"WARC-Record-ID\":\"<urn:uuid:08e63c0c-96fe-47c5-a189-eaf294bd6e96>\",\"Content-Length\":\"37327\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:27d1e600-931e-4a15-a897-6a28246fb94c>\",\"WARC-Concurrent-To\":\"<urn:uuid:7f45abb0-0759-48dc-bb3a-5e58138f8e81>\",\"WARC-IP-Address\":\"132.249.202.76\",\"WARC-Target-URI\":\"https://nanohub.org/courses/SOE\",\"WARC-Payload-Digest\":\"sha1:YT277TAOMQDNDOYOAR3BZS2LPVLYRCX5\",\"WARC-Block-Digest\":\"sha1:HBOAQWB5F263YFKTCNWVJ5JC7PLNSQX7\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030335059.43_warc_CC-MAIN-20220928020513-20220928050513-00650.warc.gz\"}"}
https://chem.libretexts.org/Ancillary_Materials/Exemplars_and_Case_Studies/Case_Studies/Heat_and_Chemical_Resistant_Silicone_Rubber/Silicones_6._(CH3)2SiCl2/Silicones_6a._Thermodynamics_and_the_Preparation_of_Silicon	[ "# Silicones 6a. Thermodynamics and the Preparation of Silicon\n\n•", null, "• Contributed by ChemCases\n• Laurence Peterson (Project PI) at Kennesaw State University\n\n## Heat and Chemical Resistant Silicone Rubber\n\nEugene Rochow knew that the elemental silicon was not easy to make in a pure state. He needed pure silicon to make silicones. We need even purer silicon for computer chips and other devices. Consider thermodynamics. The reaction of sand with carbon is the source of silicon. In a high temperature electric arc, we observe:\n\n$\\ce{2C +SiO2 -> 2CO + Si}$\n\nIntuitively this scheme seems rather unattractive - two of nature's seemingly most stable materials in a chemical reaction to reduce sand and oxidize carbon. Intuitively this scheme seems attractive, too. We learned in thermodynamics that the universe seems to want to go to a disordered state of what we called high entropy. Gases, like CO, represented ideal products of chemical reactions. Gases disperse, gases can have a huge number of configurations, gases are highly disordered, gases have high entropy.\n\nBut we learned in thermodynamics that if a process had high positive enthalpy - was not spontaneous at room temperature, we could only make the process go forward if the entropy was positive and we raised the temperature. It is the Free Energy, G, that must be negative if we want a process to proceed.\n\nHere is the thermodynamic data on the four reactants and products, along with data for CO2.\n\nC SiO2 CO Si CO2\nStandard Enthalpy kJ/mol 0 -911 -110 0 -394\nStandard Free Energy kJ/mol 0 -856 -137 0 -394\nStandard Entropy J/Kmol 6 42 198 19 214\n\nFor 298 degrees Kelvin:\n\n$\\ce{2C +SiO2 -> 2CO + Si}$\n\nΔH0 = 2(-110) - (-911) = 691kJ/mol - highly unfavored\n\nΔS0 = [2(198) + (19)] - (6 + 42) = 367 J/mol.K = 0.367 kJ/mol.K - highly favored\n\nbut ΔG0 is what counts for spontaneity.\n\nΔG0 = 2(-137) - (-856) = 586kJ/mol highly unfavored at 25 degrees Celsius.\n\nWell, what temperature would be required to, let's say, reach equilibrium in this system? At equilibrium, G = 0. So let's calculate a theoretical temperature for an equilibrium :\n\nΔG = ΔH - TΔS\n\n0 = 691 - T(.367)\n\nT = 1850 degrees Kelvin\n\nThe electric arc furnace is what's required for this process. And the process will only go to equilibrium. Thus the silicon is certain to be contaminated with the two other solid materials, sand and carbon. Additional processing is required to make pure silicon metal - processes that take advantage of the low intermolecular forces between nonpolar SiCl4 molecules:\n\n$\\ce{Si + 2Cl2 -> SiCl4}$\n\nSilicon tetrachloride is a liquid with a unique boiling point. It can be purified easily by boiling it from the solid silicon and gaseous chlorine. The pure silicon tetrachloride is then converted back to now pure silicon for electronic devices.\n\nExercise $$\\PageIndex{1}$$\n\nWe might expect that an alternate reaction for the preparation of silicon would be:\n\n$\\ce{C + SiO2 -> Si + CO2}$\n\nFrom the thermodynamic data above, determine ΔG for this potential reaction. Compare your data with the CO producing reaction.\n\n1. At what temperature might this reaction be expected to occur?\n2. Which process is favored from the ΔG calculations?\n3. By comparing the temperatures at equilibrium of the CO and CO2 producing reactions, which reaction do you predict DOES occur more readily.\n4. Which process gives the higher system entropy?\n\n5. How does the entropy affect the preferred chemical pathway?" ]	[ null, "https://chem.libretexts.org/@api/deki/files/126375/Peterson.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8869693,"math_prob":0.9440636,"size":3371,"snap":"2021-43-2021-49","text_gpt3_token_len":848,"char_repetition_ratio":0.114939116,"word_repetition_ratio":0.0070921984,"special_character_ratio":0.2622367,"punctuation_ratio":0.10243902,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.970167,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-18T22:38:42Z\",\"WARC-Record-ID\":\"<urn:uuid:cb4f0e7d-f5d0-4e85-bcfe-272ad3196a51>\",\"Content-Length\":\"100306\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:66f63486-c294-4dc7-a895-5fb70f81e46e>\",\"WARC-Concurrent-To\":\"<urn:uuid:84f285e0-e779-43d0-87f3-344dfed3a195>\",\"WARC-IP-Address\":\"99.86.230.108\",\"WARC-Target-URI\":\"https://chem.libretexts.org/Ancillary_Materials/Exemplars_and_Case_Studies/Case_Studies/Heat_and_Chemical_Resistant_Silicone_Rubber/Silicones_6._(CH3)2SiCl2/Silicones_6a._Thermodynamics_and_the_Preparation_of_Silicon\",\"WARC-Payload-Digest\":\"sha1:GHPYRCZMNASVLFKYE52SVFOUSN4J7V3W\",\"WARC-Block-Digest\":\"sha1:3IM3L7J7KU2DTUVHFEGABFJBPR4LXIIB\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323585215.14_warc_CC-MAIN-20211018221501-20211019011501-00704.warc.gz\"}"}
https://kupdf.net/download/instruction-templates-of-microprocessor-8086_597a3717dc0d608303043371_pdf	[ "# Instruction Templates of Microprocessor 8086\n\n#### Description\n\n8086 Instruction Template Need for Instruction Template 8085 has 246 opcodes. The opcodes can be printed on an A4 size paper. 8086 has about 13000 opcodes. A book of about 60 pages is needed for printing the opcodes. Concept of Template In 8085, MOV r1, r2 (ex. MOV A, B) has the following template. 0\n\n1\n\n3-bit r1 code\n\n3-bit Register code 000 001 010 011 100 101 110 111\n\n3-bit r2 code\n\nRegister B C D E H L M A\n\nEx. 1: Code for\n\nMOV A, 01 11 1 7\n\nB is 000 = 78H 8\n\nEx.2: Code for\n\nMOV M, D is 01 11 0 010 = 72H 7 2\n\nUsing the template for MOV r1, r2 we can generate opcodes of 26 = 64 opcodes. 8086 Template for data transfer between REG and R/M 1 0 0 0\n\n1\n\n0 D\n\nW\n\nMOD 2 bits\n\nREG 3 bits\n\nR/M 3 bits\n\nREG = A register of 8086 (8-bit or 16-bits) (except Segment registers, IP, and Flags registers) Thus REG = AL/ BL/ CL/ DL/ AH/ BH/ CH/ DH/ AX/ BX/ CX/ DX/ SI/ DI/ BP/ SP R/ M = Register (as defined above) or Memory contents (8-bits or 16-bits) W = 1 means Word operation W = 0 means Byte operation\n\nD = 1 means REG is Destination register D = 0 means REG is source register MOD = 00 means R/M specifies Memory with no displacement MOD = 01 means R/M specifies Memory with 8-bit displacement MOD = 10 means R/M specifies Memory with 16-bit displacement MOD = 11 means R/M specifies a Register 3-bit Register code 000 001 010 011 100 101 110 111\n\nRegister name When W = 1 When W = 0 AX AL CX CL DX DL BX BL SP AH BP CH SI DH DI BH\n\nAid to remember:\n\nALl Children Drink Bournvita (AL, CL, DL, BL) SPecial Beverages SIamese DrInk (SP, BP, SI, DI)\n\nCase of MOD = 11 Example: Code for MOV AX, BX treated as ‘Move from BX to destination register AX’\n\n1 0 0 0\n\n1\n\n0\n\nD 1\n\n8\n\nW 1 Word operation\n\nMOD 11\n\nB\n\nREG 00 0 AX is destination C\n\nR/M 011 BX\n\n= 8B C3H\n\n3\n\nExample: Alternative code for MOV AX, BX treating it as ‘Move from source register BX to register AX’\n\n1 0 0 0\n\n8\n\n1\n\nD 0 0\n\nW 1 Word operation 9\n\nMOD 11\n\nD\n\nREG 01 1 BX is source\n\nR/M 000 AX\n\n= 89 D8H\n\n8\n\nThere are 2 possible opcodes for MOV AX, BX as we can choose either AX or BX as REG.\n\nExample: Code for MOV AL, BH treated as ‘Move from BL to destination register AL’\n\n1 0 0 0\n\n1\n\nD 0 1\n\n8\n\nW 0 Byte operation\n\nMOD 11\n\nA\n\nREG 00 0 AL is destination\n\nR/M 111 BH\n\nC\n\n= 8A C7H\n\n7\n\nExample: Alternative code for MOV AL, BH treating it as ‘Move from source register BH to register AL’\n\n1 0 0 0\n\n8\n\n1\n\nD 0 0\n\nW 0 Byte operation\n\nMOD 11\n\n8\n\nREG 11 1 BH is source\n\nF\n\nR/M 000 AL\n\n= 88 F8H\n\n8\n\nThere are 2 possible opcodes for MOV AL, BH as we can choose either AL or BH as REG. Case of MOD = 00, 01 or 10 R/M\n\n000 001 010 011 100 101 110 111\n\nMOD = 00 No Displacement [SI+BX] [DI+BX] [SI+BP] [DI+BP] [SI] [DI] [BP] Direct Addressing [BX]\n\nMOD = 01 8-bit signed displacement d8 [SI+BX+d8] [DI+BX+d8] [SI+BP+d8] [DI+BP+d8] [SI+d8] [DI+d8] [BP+d8]\n\nMOD = 10 16-bit signed displacement d16 [SI+BX+d16] [DI+BX+d16] [SI+BP+d16] [DI+BP+d16] [SI+d16] [DI+d16] [BP+d16]\n\n[BX+d8]\n\n[BX+d16]\n\nThe table shows 24 memory addressing modes i.e. 24 different ways of accessing data stored in memory. Aid to remember: SubInspector DIxit is a BoXer ( [SI+BX] and [DI]+[BX] ) SubInspector DIxit knows to control BP ( [SI+BP] and [DI]+[BP] ) He says’ SImple DIet DIRECTs a BoXer' ( [SI], [DI], Direct addressing, [BX] )\n\nEx: Code for MOV CL, [SI]\n\n1 0 0 0\n\n1\n\nD 1\n\n0\n\n8\n\nW 0 Byte operation\n\nMOD REG R/M 00 00 1 100 No CL is [SI] Disp. destination 0 C\n\nA\n\n= 8A 0CH\n\nNote that there is a unique opcode for MOV CL, [SI] as CL only can be REG. Ex: Code for MOV 46H[BP], DX D 1 0 0 0 1 0 0\n\n8\n\nW 1 Word operation\n\nMOD REG R/M d8 01 01 0 110 46H 8-bit DX is [BP+d8] Disp. source 5 6\n\n9\n\n= 89 56 46H\n\nNote that there is a unique opcode for MOV 46H[BP], DX as DX only can be REG. Ex: Code for MOV 0F246H[BP], DX\n\n1\n\n0\n\n0\n\n0\n\n1\n\nD 0 0\n\n8\n\nW 1 Word operation 9\n\nMOD 10 16-bit Disp. 9\n\nREG 01 0 DX is source\n\nR/M 110 [BP+d16]\n\nd16 F2 46H\n\n6\n\n= 89 96 F2 46H Stored as 89 96 46 F2H in Little Endian\n\nNote that there is a unique opcode for MOV 0F246H[BP], DX as DX only can be REG.\n\nEx: Code for MOV [BP], DX\n\n1 0 0 0 1 0\n\n8\n\nD 0\n\nW 1 Word operation 9\n\nMOD REG R/M d8 01 01 0 110 00H 8-bit DX is [BP+d8] Disp. source 5 6\n\nNote that MOV [BP], DX is treated as MOV 00H[BP], DX before coding.\n\n= 89 56 00H\n\nEx: Code for MOV BX, DS:1234H\n\n1 0 0 0 1 0\n\nD\n\nW\n\nMOD\n\nREG\n\nR/M\n\n1\n\n1\n\n00\n\n01 1\n\n110\n\nWord operation 8\n\nB\n\nNo BX is Disp. Dest. 1" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7320869,"math_prob":0.96504664,"size":4527,"snap":"2023-14-2023-23","text_gpt3_token_len":1759,"char_repetition_ratio":0.124474905,"word_repetition_ratio":0.16109422,"special_character_ratio":0.40048596,"punctuation_ratio":0.07637017,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96987325,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-03-23T02:43:24Z\",\"WARC-Record-ID\":\"<urn:uuid:568136aa-b927-4182-8a75-4f6e7ee994c1>\",\"Content-Length\":\"29386\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:72a7322f-2a71-4f55-9684-19836c15a469>\",\"WARC-Concurrent-To\":\"<urn:uuid:a0ac8621-2274-45c5-afee-9be5bb626638>\",\"WARC-IP-Address\":\"172.67.149.121\",\"WARC-Target-URI\":\"https://kupdf.net/download/instruction-templates-of-microprocessor-8086_597a3717dc0d608303043371_pdf\",\"WARC-Payload-Digest\":\"sha1:L7RQGCNUW3H3QC2AZWYFDEMKKBPYJ7XQ\",\"WARC-Block-Digest\":\"sha1:RA7V376JYPPAHIMHKCEXZWCL4SIBUYIC\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-14/CC-MAIN-2023-14_segments_1679296944606.5_warc_CC-MAIN-20230323003026-20230323033026-00098.warc.gz\"}"}
http://medicalopensource.net/mcs/wifi-trh-arduino.html	[ "Lawrence Technological University\nCollege of Arts and Science\nDepartment of Mathematics and Computer Science\n\n## WiFi and the Arduino\n\n### by John M. Miller M.D.\n\nThe experiment on this page may not be a good \"starter\" Arduino Uno project. There were two main problem areas:\n\n1. Many other serial devices are easy to use with the Arduino Wire library. The Sensirion devices are non standard and have no working Arduino style library that I could find. The interface I made was patterned after the Sensirion data sheets and non-Arduino sample code.\n2. Using the WiFi Web server with the small Uno variable space (which is also shared with the stack) worked better when I stored most of the HTML strings in the flash memory, program space. This brings up the issue of C pointers, which many beginners would prefer to avoid.\n\nThis page is an experiment in measuring temperature and humidity using a digital sensor with the Arduino platform. The results are monitored remotely on a home WiFi network. The parts:\n\n1. Arduino Uno\n2. Sensirion's SHT10 Digital Humidity Sensor assembled as Emartee's Digital Temperature & Humidity Sensor module, Product ID 42049\n3. Emartee's TLG10UA03 Wifi module and Arduino shield kit, Product ID 42121\n4. Disk drive power cord from a defunct PC power supply.\n\nAssembled, the remote sensor looks like this", null, "Before using our hardware setup, we have to intialize the flash memory on the WiFi module so it will connect to the password protected network we have picked for our experiment. In general the Emartee document: WiFi_test_v2.pdf (available on the Emartee site through their link to Google Docs) was followed. Except after using the Arduino IDE Serial Monitor to send the escape sequence of \"+++\" (in order to force the WiFi module to exit \"Auto Work Mode\" and accept AT configuration commands) we continue configuration still using the Serial Monitor because there was no Window's machine handy to run the supplied configuration program. Here is a session, verifying all the settings that were changed manually with AT commands, using\n\n• The Arduino IDE Serial Monitor,\n• The USB-TTL module, jumper set to use 3.3 volts,\n• The supplied 4-wire cable,\n• The USB-TTL Driver PL-2303 Mac OS X Universal Binary Driver v1.4.0 (DMG file format), Prolific Edition For Mac OS X 10.7 Lion and 10.6 Snow Leopard (32-bit and 64-bit kernel) and\n• The AT commands detailed in pages 75 to 99 of the Emartee document: User Manual-03_ENGLISH.pdf (available on the Emartee site through their link to Google Docs.)\n```(Set for \"no line ending\")\n(Sent +++ with no line ending) to exit into AT command mode.\n+OK\n(Set for \"cr line ending\")\n(Sent at+ with cr line ending) to test command mode.\n+OK\n(Sent at+e with cr line ending) to begin echo of commands sent.\n+OK\n\nat+ssid\n+OK=\"2WIRE148\"\n\nat+encry\n+OK=3 3 seems faster than 6 at joining.\n\nat+key\n+OK=1,0,\"0123456789\"\n\nat+wscan\n+OK=c0830a255691,0,1,1,\"2WIRE596\",86\n00304409384a,0,4,1,\"Greenview Observatory3\",58\n00235140dba1,0,5,1,\"2WIRE674\",82\n00173f9288c1,0,10,0,\"Belkin_G_Plus_MIMO_180170\",84\n640f28108449,0,10,1,\"2WIRE148\",29\n\nat+qver\n+OK=H0.00.00.0000,F1.02.01@ 17:23:31 Dec 16 2010\n\nat+wjoin\n+OK=640f28108449,0,10,1,\"2WIRE148\",37\n\nat+lkstt\n+OK=1,\"192.168.1.66\",\"255.255.255.0\",\"192.168.1.254\",\"192.168.1.254\"\n\nat+nip\n+OK=0\n\nat+uart\n+OK=115200,0,0,0\n\nat+webs\n+OK=1,80\n\nfinally: at+pmtf records changes in flash memory.\nat+z resets module so will come back up in auto work mode.\n```\n\nThe rest of the initialization was done via the WiFi interface exactly the same as in the Emartee module test procedure -- including setting the port to 8090.\n\nTesting the server code I found that without using a `Content-Length:` header the browser would wait about 5 minutes for the reply to end under HTTP 1.1. Here is the code running on the Arduino: (Uploading using the Arduino IDE produces an error unless the jumper plugs that connect the WiFi module to the Arduino Tx and Rx pins are removed temporarily.)\n\n```// wifi_trh\n// March 8, 2012\n// Libraries:\n#include <avr/pgmspace.h>\n#include <PString.h>\n// Notes:\n/* Uploading this program with the Arduino IDE, when the Wifi Shield\nis attached to the Arduino, requires removing the 2 jumper plugs\non the shield that connect the Wifi module's and Arduino's Tx and Rx\npins.\n/\n/ Temperature and Humidity are measured with digital results using\nEmartee's Digital Temperature & Humidity Sensor module, Product ID: 42049\n/\n/ Read temperature and humidity values from an SHT10 sensor.\nCoefficients for adjusting for temperature and non-linearity\nare from Sensirion SHT1x datasheet Version 4.3 May 2010.\nUsed coefficients for 3.5 volts as nearest to VDD of 3.3 volts.\n/\n/ SHT10 module connections:\nFunction SHT10 SHT Module Wire Arduino `\nGround 1 3 Black Gnd\nData 2 4 Red D10\nClock 3 1 Yellow D11\nVDD +3.3V 4 2 Black/Red +3.3v\n/\n/ Results are served with Emartee's TLG10UA03 WiFi module which\nwas purchased, with a nice shield that makes the wiring easier\nand a USB converter that makes initialization easier, as a kit\n-- Product ID: 42121\n/\n/ With a little JavaScript, the time-stamp for the served measurements\nis left to the client Web browser.\n/\n// #defines for SHT10:\n// Pins:\n#define DATA_PIN 10\n#define CLOCK_PIN 11\n// Commands:\n#define TEMPERATURE 3\n#define HUMIDITY 5\n#define WRITE_STATUS 6\n#define SOFT_RESET 0x1e\n// Delays in microseconds:\n#define PLATEAU 40\n#define HOLD 20\n#define MAX_MEASUREMENT_WAIT 4000\n#define MAX_RETRIES 1\n// Constant strings in flash/program memory:\n\"<title>Temperature and Relative Humidity \"\n\"from Arduino Uno WiFi Server</title>\\n\";\nprog_char html1_sr[] PROGMEM = \"<meta name=\\\"send receive\\\" content=\\\"\";\nprog_char html1_se[] PROGMEM = \"<meta name=\\\"serial errors\\\" content=\\\"\";\nprog_char html1_rth[] PROGMEM = \"<meta name=\\\"raw data t,h\\\" content=\\\"\";\nprog_char html1_ms[] PROGMEM = \"<meta name=\\\"wait time\\\" content=\\\"\";\n\"<h1>Squawk's Weather Station</h1>\\n\";\nprog_char html3[] PROGMEM = \"<h3><script type=\\\"text/javascript\\\">\\n\"\n\"var d = new Date();\\n\"\n\"document.write(d.toString());\\n\"\n\"</script></h3>\\n\";\nprog_char html3_t[] PROGMEM = \"<p>Temperature: \";\nprog_char html3_h[] PROGMEM = \"<p>Relative Humidity: \";\nprog_char html3_na[] PROGMEM = \"<p>Temperature and Humidity not available. \"\nprog_char html4[] PROGMEM = \"</body>\\n</html>\\n\";\n// Other constant strings:\nconst char meta_end[] = \"\\\" />\\n\";\n// Globals:\nunsigned long started;\nunsigned long elapsed;\nint raw_temperature;\nint raw_humidity;\nfloat temp_C;\nfloat temp_F;\nfloat humidity;\nint retries;\nchar buffer;\nchar buffer_sr;\nchar buffer_se;\nchar buffer_rth;\nchar buffer_ms;\nchar buffer_t;\nchar buffer_h;\n// Debugging traces for reporting in META tags:\nPString serial_errors(buffer_se,sizeof(buffer_se));\nPString raw_th(buffer_rth,sizeof(buffer_rth));\nPString millisec(buffer_ms,sizeof(buffer_ms));\n// The actual reply temperature and relative humidity.\nPString t(buffer_t,sizeof(buffer_t));\nPString h(buffer_h,sizeof(buffer_h));\n// Conversion coefficients from SHT1x datasheet Version 4.3 May 2010\nconst float D1 = -39.7; // for 14 Bit @ 3.5V\nconst float D2 = 0.01; // for 14 Bit DEGC\nconst float C1 = -2.0468; // for 12 Bit\nconst float C2 = 0.0367; // for 12 Bit\nconst float C3 = -0.0000015955; // for 12 Bit\nconst float T1 = 0.01; // for 14 Bit\nconst float T2 = 0.00008; // for 14 Bit\n// Subroutines:\nvoid start_transmission()\n{\n// ____ _____\n// CLOCK_PIN ____\| \|____\| \|____\n// ______ _______\n// DATA_PIN \|__________\|\npinMode(DATA_PIN,OUTPUT);\ndigitalWrite(DATA_PIN,HIGH);\ndigitalWrite(CLOCK_PIN,LOW);\ndelayMicroseconds(PLATEAU);\ndigitalWrite(CLOCK_PIN,HIGH);\ndelayMicroseconds(HOLD);\ndigitalWrite(DATA_PIN,LOW);\ndelayMicroseconds(HOLD);\ndigitalWrite(CLOCK_PIN,LOW);\ndelayMicroseconds(PLATEAU);\ndigitalWrite(CLOCK_PIN,HIGH);\ndelayMicroseconds(HOLD);\ndigitalWrite(DATA_PIN,HIGH);\ndelayMicroseconds(HOLD);\ndigitalWrite(CLOCK_PIN,LOW);\ndelayMicroseconds(PLATEAU);\n}\nvoid serial_reset()\n// This reset has not been tested!\n{\npinMode(DATA_PIN,OUTPUT);\ndigitalWrite(DATA_PIN,HIGH);\ndigitalWrite(CLOCK_PIN,LOW);\nfor (int i = 0;i < 9;i++) {\ndelayMicroseconds(HOLD);\ndigitalWrite(CLOCK_PIN,HIGH);\ndelayMicroseconds(HOLD);\ndigitalWrite(CLOCK_PIN,LOW);\n}\nretries++;\n}\nvoid bit_out(int d)\n{\ndigitalWrite(DATA_PIN,d);\ndelayMicroseconds(HOLD);\ndigitalWrite(CLOCK_PIN,HIGH);\ndelayMicroseconds(PLATEAU);\ndigitalWrite(CLOCK_PIN,LOW);\ndelayMicroseconds(HOLD);\ndigitalWrite(DATA_PIN,LOW);\n}\nint bit_in()\n{\ndelayMicroseconds(HOLD);\ndigitalWrite(CLOCK_PIN,HIGH);\ndelayMicroseconds(HOLD);\ndelayMicroseconds(HOLD);\ndigitalWrite(CLOCK_PIN,LOW);\ndelayMicroseconds(HOLD);\nreturn d;\n}\n{\npinMode(DATA_PIN,INPUT); // Assume was in DATA_PIN output mode.\ndigitalWrite(DATA_PIN,HIGH); // Pullup DATA_PIN.\nreturn bit_in();\n}\nvoid send_ack(boolean ack)\n{\npinMode(DATA_PIN,OUTPUT); // Assume was in DATA_PIN input mode.\n// ____ __\n// DATA_PIN \|________\| Case where ack is true.\n// ____\n// CLOCK_PIN ______\| \|____\ndelayMicroseconds(PLATEAU);\nbit_out(ack ? LOW : HIGH);\npinMode(DATA_PIN,INPUT); // Restore to DATA_PIN input mode.\ndigitalWrite(DATA_PIN,HIGH); // Restore pullup.\n}\n{\nint b,i;\nfor(b = 0,i = 0x80;i;i >>= 1) { if ( bit_in() == HIGH) b \|= i; }\nsend_ack(ack);\nreturn b;\n}\nint send_byte(int b)\n{\nfor (int i = 0x80;i > 0;i >>= 1) { bit_out( (i & b) ? HIGH : LOW); }\nreturn ack;\n}\nint get_measurement(int measurement)\n{\nint m = -1;\nwhile (retries <= MAX_RETRIES) {\nstart_transmission();\nif (send_byte(measurement) == HIGH) {\nserial_errors.print(\"A\");\nserial_errors.print(measurement);\nserial_reset();\ncontinue;\n}\n// Wait during measurement.\ndelayMicroseconds(PLATEAU);\nstarted = millis();\nwhile ((elapsed = millis() - started) < MAX_MEASUREMENT_WAIT) {\nmillisec.print(elapsed);\nmillisec.print(\"\|\");\nbreak;\n}\n}\nif (elapsed >= MAX_MEASUREMENT_WAIT) {\nmillisec.print(elapsed);\nserial_errors.print(\"T\");\nserial_errors.print(measurement);\nserial_reset();\ncontinue;\n}\nm = m 256 + read_byte(false); // Skip CRC by sending HIGH acknowledgment.\nbreak;\n}\nreturn m;\n}\n\nvoid setup()\n{\nstrlen_P(html1_sr) +\nstrlen_P(html1_se) +\nstrlen_P(html1_rth) +\nstrlen_P(html1_ms) +\nstrlen_P(html2) +\nstrlen_P(html3) +\nstrlen_P(html4) +\nstrlen(meta_end) * 4;\nSerial.begin(115200);\npinMode(CLOCK_PIN,OUTPUT);\ndigitalWrite(CLOCK_PIN,LOW);\npinMode(DATA_PIN,INPUT);\ndigitalWrite(DATA_PIN,HIGH);\n}\nvoid loop()\n{\nboolean blankLine = true;\n// Initialize debugging traces and the result:\nserial_errors.begin();\nraw_th.begin();\nmillisec.begin();\nt.begin();\nh.begin();\nretries = 0;\nwhile(1){\nif (Serial.available()) {\nif (c == '\\n' && blankLine) { // End of an HTTP request.\n// Read the current values from the SHT10.\nraw_temperature = get_measurement(TEMPERATURE);\nraw_humidity = get_measurement(HUMIDITY);\nraw_th.print(raw_temperature);\nraw_th.print(\",\");\nraw_th.print(raw_humidity);\n// Report the measurements only if both are good.\nif (raw_temperature >= 0 && raw_humidity >= 0) {\ntemp_C = (raw_temperature * D2) + D1;\ntemp_F = temp_C * 9.0 / 5.0 + 32.0;\nfloat adj_humidity = C1 + C2 * raw_humidity +\nC3 * raw_humidity * raw_humidity;\nhumidity = (temp_C - 25.0 ) * (T1 + T2 * raw_humidity) + adj_humidity;\nt.print(temp_C,1);\nt.print(\" °C, \");\nt.print(temp_F,1);\nt.print(\" °F\\n\");\nh.print(humidity,1);\nh.print(\"%\\n\");\nserial_errors.length() +\nraw_th.length() +\nmillisec.length() +\nstrlen_P(html3_t) + t.length() +\nstrlen_P(html3_h) + h.length();\n} else {\nserial_errors.length() +\nraw_th.length() +\nmillisec.length() +\nstrlen_P(html3_na);\n}\nSerial.print(\"HTTP/1.1 200 OK\\r\\n\");\nSerial.print(\"Content-Type: text/html\\r\\n\");\nSerial.print(\"Content-Length: \");\nSerial.print(\"\\n\\n\");\n// Send body of the reply:\nstrcpy_P(buffer,html1);\nSerial.print(buffer);\nstrcpy_P(buffer,html1_sr);\nSerial.print(buffer);\nSerial.print(meta_end);\nstrcpy_P(buffer,html1_se);\nSerial.print(buffer);\nSerial.print(serial_errors);\nSerial.print(meta_end);\nstrcpy_P(buffer,html1_rth);\nSerial.print(buffer);\nSerial.print(raw_th);\nSerial.print(meta_end);\nstrcpy_P(buffer,html1_ms);\nSerial.print(buffer);\nSerial.print(millisec);\nSerial.print(meta_end);\nstrcpy_P(buffer,html2);\nSerial.print(buffer);\nstrcpy_P(buffer,html3);\nSerial.print(buffer);\nif (raw_temperature >= 0 && raw_humidity >= 0) {\nstrcpy_P(buffer,html3_t);\nSerial.print(buffer);\nSerial.print(t);\nstrcpy_P(buffer,html3_h);\nSerial.print(buffer);\nSerial.print(h);\n} else {\nstrcpy_P(buffer,html3_na);\nSerial.print(buffer);\n}\nstrcpy_P(buffer,html4);\nSerial.print(buffer);\nbreak;\n} else if (c == '\\n') { // && !blankLine\nblankLine = true; // So start a new line.\n} else if (c != '\\r') {\nblankLine = false; // Line is not blank.\n}\n}\n}\n}\n```\n\nAs seen from a client Web Browser:", null, "Viewing the source code of that reply:\n\n```<html>\n<title>Temperature and Relative Humidity from Arduino Uno WiFi Server</title>\n<meta name=\"serial errors\" content=\"\" />\n<meta name=\"raw data t,h\" content=\"6255,1101\" />\n<meta name=\"wait time\" content=\"221\|63\|\" />" ]	[ null, "http://medicalopensource.net/mcs/wifi-trh.jpg", null, "http://medicalopensource.net/mcs/wifi-reply.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6030546,"math_prob":0.82799727,"size":13873,"snap":"2020-10-2020-16","text_gpt3_token_len":3749,"char_repetition_ratio":0.13620304,"word_repetition_ratio":0.024581006,"special_character_ratio":0.31514454,"punctuation_ratio":0.2110849,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95279473,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,2,null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-02-20T01:51:51Z\",\"WARC-Record-ID\":\"<urn:uuid:f4ed9299-6270-4c7b-8a44-c5b560836ddc>\",\"Content-Length\":\"20243\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:dcbd6f14-cd9a-40f0-b607-eb6e9ff82967>\",\"WARC-Concurrent-To\":\"<urn:uuid:0188d88f-8578-4353-9fc7-1192e2a25995>\",\"WARC-IP-Address\":\"192.34.56.95\",\"WARC-Target-URI\":\"http://medicalopensource.net/mcs/wifi-trh-arduino.html\",\"WARC-Payload-Digest\":\"sha1:AD4EFRXC2LPKZNLUYXRMJ6EPPIFVABIP\",\"WARC-Block-Digest\":\"sha1:HCFJ7WSHN4UAVLG3QEUTDZXISB7XKUIF\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-10/CC-MAIN-2020-10_segments_1581875144498.68_warc_CC-MAIN-20200220005045-20200220035045-00015.warc.gz\"}"}
https://www.codespeedy.com/model-evaluation-metrics-in-regression-models-with-python/	[ "# Model Evaluation Metrics in Regression Models with Python\n\nIn this tutorial, we are going to see some evaluation metrics used for evaluating Regression models. Whenever a Machine Learning model is being constructed it should be evaluated such that the efficiency of the model is determined, It helps us to find a good model for our prediction by evaluating the model. In such a note, we are going to see some Evaluation metrics for Regression models like Logistic, Linear regression, and SVC regression.\n\n### Evaluation metrics – Introduction\n\nGenerally, we use a common term called the accuracy to evaluate our model which compares the output predicted by the machine and the original data available. Consider the below formula for accuracy,\n\nAccuracy=(Total no. of correct predictions /Total no. of data used for testing)*100\n\nThis gives the rough idea of evaluation metrics but it is not the correct strategy to evaluate the model. We have some defined metrics especially for Regression models which we will see below.\n\n### Regression Models Evaluation metrics\n\nThe SkLearn package in python provides various models and important tools for machine learning model development. Where it provides some regression model evaluation metrics in the form of functions that are callable from the sklearn package.\n\n• Max_error\n• Mean Absolute Error\n• Mean Squared Error\n• Median Squared Error\n• R Squared\n\nAbove are the available metrics provided from sklearn we will see them in detail with implementation,\n\n1. Max_error\nIt calculates the maximum error present between the original data and predicted data,\nWhere it compares and finds out data that has the maximum difference and produces the output. Consider the code segment below which illustrates the max_error function from the\n\n```from sklearn.metrics import max_error\noriginal_data = [8, 4, 7, 1]\npredicted_data = [4, 2, 7, 1]\nmax_error(original_data,predicted_data)```\n```Output:\n4```\n\nFrom the above code, the original data is compared with predicted data, where the maximum difference occurred between data 8 and 4 so the output is the difference between them (i.e 4).\nThe best output possible here is 0.\n\n2. Mean Absolute Error\nIt is given by the formula below,", null, "Where the difference between data is taken and the average of it is found out and returned as output. The implementation of it is shown in the below code segment.\n\n```from sklearn.metrics import mean_absolute_error\noriginal_data = [3, 5, 2, 7]\npredicted_data = [2, 0, 2, 8]\nmean_absolute_error(y_true, y_pred)```\n```Output:\n1.75```\n\nLet us do some calculations here, the difference between these data is 1,5,0,1 (i.e 1+5+0+1) which gives you 7. Then the average is taken where n=4, so 7/4 gives you (1.75).\nThe best score here would be 0.\n\n3. Mean Squared Error\nIt is as similar to the above metric wherein Mean Squared Error we will be calculating the square of the difference between the predicted and the original data. The formula is given below,", null, "The difference value is calculated and it is squared and means is obtained as the result. Let us see an implementation of it,\n\n```from sklearn.metrics import mean_squared_error\noriginal_data = [3, 5, 2, 7]\npredicted_data = [2, 0, 2, 8]\nmean_squared_error(original_data,predicted_data)```\n\nThe same inputs similar to above mean absolute error is given to this mean squared error, where the difference in the data is ( 1 square+5 square+0 square+1 square) = 27 and mean is (27/4) which gives the output.\n\n```Output:\n6.75```\n\nThe ideal output is 0 and this suits to identify a very large error in the prediction compared to the mean absolute error.\n\n4. Median Absolute Error\nThis finds the median value of the absolute difference between the original and the predicted data. It is famous for its consistency towards robust to outliers. It helps us to know about the outliers present in the dataset.\n\n```from sklearn.metrics import median_absolute_error\noriginal_data = [3, 5, 2, 7]\npredicted_data = [3, 1, 2, 5]\nmedian_absolute_error(original_data,predicted_data)```\n```Output:\n1.0```\n\nLet formulate it! , the output of the above code segment is the median(0,4,0,2) that is obviously 1. The best value is 0.\n\n5. R Squared\nThis is the most important evaluation metric in the regression evaluation where it gives us an understanding of how well the data get fit towards the regression line. This helps us to find the relationship between the independent variable towards the dependent variable.\n\n```from sklearn.metrics import r2_score\noriginal_data = [8, 5, 1, 6]\npredicted_data= [7, 8, 2, 3]\nr2_score(original_data,predicted_data)```\n```Output:\n0.23076923076923073```\n\nIt is calculated by the below formula,", null, "where the SSRes is the sum of the square of the difference between the actual value and the predicted value.SSTotal is the sum of the square of the difference between the actual value and the mean of the actual value.\n\nThese are various Regression evaluation metrics available, Hope this tutorial helps!!!\n\n### One response to “Model Evaluation Metrics in Regression Models with Python”\n\n1. Naveen Kumar says:\n\nSuper It Was Very Useful .Right blog I Was Searching For…..!" ]	[ null, "https://codespeedy.com/wp-content/uploads/2019/12/Mean-Absolute-Error-equation.png", null, "https://codespeedy.com/wp-content/uploads/2019/12/Mean-Squared-Error-Equation.png", null, "https://codespeedy.com/wp-content/uploads/2019/12/R-Squared-Equation.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8455886,"math_prob":0.9886897,"size":4999,"snap":"2020-34-2020-40","text_gpt3_token_len":1125,"char_repetition_ratio":0.14734735,"word_repetition_ratio":0.061712846,"special_character_ratio":0.2284457,"punctuation_ratio":0.12673056,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9994358,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,1,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-29T08:56:57Z\",\"WARC-Record-ID\":\"<urn:uuid:a33338d7-c9b4-4bf3-b262-b2dabca1be97>\",\"Content-Length\":\"39342\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:715772b8-1bde-47d1-b446-8d365369e17d>\",\"WARC-Concurrent-To\":\"<urn:uuid:e7ea0277-f856-4f71-acd5-46725d406499>\",\"WARC-IP-Address\":\"194.1.147.77\",\"WARC-Target-URI\":\"https://www.codespeedy.com/model-evaluation-metrics-in-regression-models-with-python/\",\"WARC-Payload-Digest\":\"sha1:ELYS3QBYEXCD4AXB3RZ4TOU6DZXZL4DB\",\"WARC-Block-Digest\":\"sha1:C2JNL2FKB3WNGN7NMTORRQ3HVEHAK3ZK\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600401632671.79_warc_CC-MAIN-20200929060555-20200929090555-00426.warc.gz\"}"}
https://www.physicsoverflow.org/tag/hamiltonian-formalism	[ "# Recent questions tagged hamiltonian-formalism", null, "The Hamiltonian formalism is a formalism in Classical Mechanics. Besides Lagrangian Mechanics, it is an effective way of reformulating classical mechanics in a simple way. Very useful in Quantum Mechanics, specifically the Heisenberg and Schrodinger formulations. Unlike Lagrangian Mechanics, this formalism relies on a \"Hamiltonian\" instead of a Lagrangian, which differs from the Lagrangian through a Legendre transformation.\n\n# The Hamiltonian\n\nThe Hamiltonian can be interpreted as an “energy input”, as opposed to a Lagrangian, which is the \"energy output\". The Euclidean Hamiltonian, which is used in Classical Mechanics is given by:\n\n$$H = \\frac{{{p^2}}}{{2m}} + U$$\n\nThe Euclidean Lagrangian, on the other hand, has a minus instead of a plus. Notice that\n\n$$L + H = p\\frac{{{\\text{d}}x}}{{{\\text{d}}t}}$$\n\nThis shows that the two are related by a Legendre transformation.\n\n# The Poisson Bracket relationships and the Dynamic Hamiltonian Relationships\n\nThe Poisson Bracket relations are algebraic relationships between phase space variables, and without the presence of any dynamical Lagrangian or Hamiltonian. Thus, the Poisson Bracket relations would obviously (to someone with a basic knowledge of Lagrangian Mechanics) be :\n\n$$\\begin{gathered} \\{ {{p_i},{x_j}} \\} = {\\delta _{ij}} \\\\ \\{ {{p_i},{p_j}} \\} = 0 \\\\ \\{ {{x_i},{x_j}} \\} = 0 \\\\ \\end{gathered}$$\n\nThe Dynamical Relationships, however, are obviously changed. It is clear that the new relationshipjs are that:\n\n$$\\begin{gathered} \\frac{{\\partial H}}{{\\partial {\\mathbf{x}}}} = - \\frac{{{\\text{d}}{\\mathbf{p}}}}{{{\\text{d}}t}} \\\\ \\frac{{\\partial H}}{{\\partial {\\mathbf{p}}}} = \\frac{{{\\text{d}}{\\mathbf{x}}}}{{{\\text{d}}t}} \\\\ \\end{gathered}$$\n\nCompare this to the dynamical Lagrangian Relations:\n\n$$\\begin{gathered} \\frac{{\\partial L}}{{\\partial {\\mathbf{x}}}} = \\frac{{{\\text{d}}{\\mathbf{p}}}}{{{\\text{d}}t}} \\\\ \\frac{{\\partial L}}{{\\partial {\\mathbf{p}}}} = \\frac{{{\\text{d}}{\\mathbf{x}}}}{{{\\text{d}}t}} \\\\ \\end{gathered}$$\n\nThe central equation of Hamiltonian Mechanics is the Hamilton Equation:\n\n$$\\frac{{{\\text{d}}A}}{{{\\text{d}}t}} = \\{A,H \\}$$\n+ 1 like - 0 dislike\n+ 0 like - 0 dislike\n+ 0 like - 0 dislike\n+ 1 like - 0 dislike\n+ 2 like - 0 dislike\n+ 5 like - 0 dislike\n+ 1 like - 0 dislike\n+ 1 like - 0 dislike\n+ 3 like - 0 dislike\n+ 6 like - 0 dislike\n+ 1 like - 0 dislike\n+ 1 like - 0 dislike\n+ 5 like - 0 dislike\n+ 3 like - 0 dislike" ]	[ null, "https://www.physicsoverflow.org/qa-theme/OverSnow/images/rss.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.802869,"math_prob":0.99927694,"size":2102,"snap":"2021-04-2021-17","text_gpt3_token_len":601,"char_repetition_ratio":0.15538608,"word_repetition_ratio":0.007662835,"special_character_ratio":0.30066603,"punctuation_ratio":0.09309309,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99924994,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-01-21T10:40:25Z\",\"WARC-Record-ID\":\"<urn:uuid:8e06b6ce-2ca0-405f-a5b2-e09547bf1251>\",\"Content-Length\":\"138003\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:bac1c432-c192-4e60-9d15-6c513e54eb54>\",\"WARC-Concurrent-To\":\"<urn:uuid:04dd87d6-3f49-4ec6-aff1-00176880c258>\",\"WARC-IP-Address\":\"129.70.43.86\",\"WARC-Target-URI\":\"https://www.physicsoverflow.org/tag/hamiltonian-formalism\",\"WARC-Payload-Digest\":\"sha1:BYYXKMZJBVD7AN4Y74TGSA4RKN2243TZ\",\"WARC-Block-Digest\":\"sha1:D2EOCLF7LKJAAMCT7ZTXAZ3WSPTXGKIR\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-04/CC-MAIN-2021-04_segments_1610703524743.61_warc_CC-MAIN-20210121101406-20210121131406-00629.warc.gz\"}"}
https://cs.stackexchange.com/questions/2814/sums-of-landau-terms-revisited	[ "# Sums of Landau terms revisited\n\nI asked a (seed) question about sums of Landau terms before, trying to gauge the dangers of abusing asymptotics notation in arithmetics, with mixed success.\n\nNow, over here our recurrence guru JeffE does essentially this:\n\n$\\qquad \\displaystyle \\sum_{i=1}^n \\Theta\\left(\\frac{1}{i}\\right) = \\Theta(H_n)$\n\nWhile the end result is correct, I think this is wrong. Why? If we add in all the existence of constants implied (only the upper bound), we have\n\n$\\qquad \\displaystyle \\sum_{i=1}^n c_i \\cdot \\frac{1}{i} \\leq c \\cdot H_n$.\n\nNow how do we compute $c$ from $c_1, \\dots, c_n$? The answer is, I believe, that we can not: $c$ has to bound for all $n$ but we get more $c_i$ as $n$ grows. We don't know anything about them; $c_i$ may very well depend on $i$, so we can not assume a bound: a finite $c$ may not exist.\n\nIn addition, there is this subtle issue of which variable goes to infinity on the left-hand side -- $i$ or $n$? Both? If $n$ (for the sake of compatibility), what is the meaning of $\\Theta(1/i)$, knowing that $1 \\leq i \\leq n$? Does it not only mean $\\Theta(1)$? If so, we can't bound the sum better than $\\Theta(n)$.\n\nSo, where does that leave us? It it a blatant mistake? A subtle one? Or is it just the usual abuse of notation and we should not look at $=$ signs like this one out of context? Can we formulate a (rigorously) correct rule to evalutate (certain) sums of Landau terms?\n\nI think that the main question is: what is $i$? If we consider it constant (as it is inside the scope of the sum) we can easily build counterexamples. If it is not constant, I have no idea how to read it.\n\n• This question on math.SE is a good read about arithmetics with Landau terms in general. – Raphael Jul 18 '12 at 15:36\n• From the link you gave, the equality can be seen to be either a subset relation or an \"is in\" relation (i.e. $\\in$). For $\\Theta$ you're just saying it's bounded above and below by a constant. Why not choose $c = \\min(c_1, c_2, \\cdots, c_n)$ and $C = \\max(c_1, c_2, \\cdots, c_n)$? – user834 Jul 18 '12 at 17:33\n• Hang on there, Bucky. I didn't write any summation with a Theta in it. I wrote a recurrence with a Theta in it. Do you really interpret the recurrence \"$t(n) = \\Theta(1/n) + t(n-1)$\" as something other than \"There is a function $f \\in \\Theta_{x\\to \\infty}(x\\mapsto 1/x)$ such that $t(n) = f(n) + t(n-1)$\"? – JeffE Jul 19 '12 at 16:06\n• @Raphael No, the recurrence is not mathematically the same as the sum, for precisely the reason you describe! The recurrence has exactly one Theta term in it, which unambiguously refers to a single function. – JeffE Jul 20 '12 at 13:41\n• That's not very intuitive — I strongly disagree, but I think it's a matter of taste and experience. – JeffE Jul 20 '12 at 17:01\n\nLooks right to me in the following convention:\n\n$S_n = \\sum_{k=1}^{n} \\Theta(1/k)$ is convenient notation for\n\nThere is an $f(x) \\in \\Theta(1/x)$ (as $x \\to \\infty$) such that\n\n$S_n = \\sum_{k=1}^{n} f(k)$.\n\nThus the $c_i$ (or with the notation in this answer $c_k$) you get, are not really dependent on $k$.\n\nUnder this interpretation, it is indeed true that $S_n = \\Theta(H_n)$.\n\nIn fact, in Jeff's answer, he shows that $T(k+1) = f(k) + T(k)$ where $f \\in \\Theta(1/k)$, so it is consistent with the above interpretation.\n\nThe confusion seems to be arising from mentally \"unrolling\" the $\\sum$ and presuming different functions for each occurrence of $\\Theta$...\n\n• Jup, but every $\\Theta$ can have its own function, and constant. So this convention does only work with context, that is if we know that the Landau terms stem from a somewhat \"uniform\" (in $k$ and $n$) definition of the summands. – Raphael Jul 19 '12 at 11:40\n• @Raphael: It seems meaningless to unroll and then allow different $f_i$: the constants will then depend on the variable! and it becomes an incorrect usage of $\\Theta$, assuming the $\\Theta$ variable is $i$ (or $k$ in above answer). Even if we assume the variable is $n$, it is still looks meaningless to me. – Aryabhata Jul 19 '12 at 15:06\n• In principle, every $\\Theta$ can have its own constant, but in the particular context you describe, it's clear that every $\\Theta$ does not have its own constant. – JeffE Jul 19 '12 at 15:53\n• @JeffE: Right. We can have multiple $\\Theta$ with their own constants, as long as the constants are really constant :-) – Aryabhata Jul 19 '12 at 15:58\n• @JeffE So why don't you just write what you mean but prefer something ambiguous/wrong? Note that my updated answer now proposes a way to do so. I'd appreciate comments on that; downvotes with no reason don't help me understand why people seem to reject my point. – Raphael Jul 20 '12 at 12:10\n\nI think I nailed the problem down. In essence: using Landau terms decouples the variable of the summand function from the sum's running variable. We still (want to) read them as identical, though, therefore the confusion.\n\nTo develop it formally, what does\n\n$\\qquad \\displaystyle S_n \\in \\sum_{i=1}^n \\Theta(f(i)) \\qquad \\qquad\\qquad (1)$\n\nreally mean? Now I assume that these $\\Theta$ let $i$ -- not $n$ -- to infinity; if we let $n \\to \\infty$, every such sum evaluates to $\\Theta(n)$ (if the summands are independent of $n$ and therefore constant) which is clearly wrong. Here is a first giveaway that we to crude things: $i$ is bound (and constant) inside the sum, but we still let it go to infinity?\n\nTranslating $(1)$ (for the upper bound, the lower bound works similarly), we get\n\n$\\qquad \\displaystyle \\exists f_1, \\dots, f_n \\in \\Theta(f).\\ S_n \\leq \\sum_{i=1}^n f_i(i)$\n\nNow it is clear that the sum-$i$ and parameter-$i$ are decoupled: we can easily define the $f_i$ so that they use $i$ as a constant. In the example from the question, we can define $f_i(j) = i \\cdot \\frac{1}{j} \\in \\Theta(1/j)$ and have\n\n$\\qquad \\displaystyle \\sum_{i=0}^n f_i(i) \"=\" \\sum_{i=0}^n \\Theta(1/j) = \\sum_{i=0}^n \\Theta(1/i)$\n\nbut the original sum clearly does not evaluate to something in $\\Theta(H_n) = \\Theta(\\log n)$. Now exchanging $j$ for $i$ -- which is only a renaming -- in the $\\Theta$ may feel strange because $i$ is not independent of $n$ resp. the sum, but if we object to that now, we should never have used $i$ inside the $\\Theta$ in the first place (as that holds the same strangeness).\n\nNote that we did not even exploit that the $f_i$ may also depend on $n$.\n\nTo conclude, the proposed identity is bogus. We can, of course, agree on conventions on how to read such sums as abbreviation of rigorous calculation. However, such conventions will be incompatible with the definition of Landau terms (together with the normal abuse of them), impossible to understand correctly without context and misleading (for beginners) at least -- but that is ultimately a matter of taste (and ruthlessness?).\n\nIt occurred to me that we can also write exactly what we mean and still make use of the convenience of Landau terms. We know that all summands come from one common function, implying that the asymptotic bounds use the same constants. This is lost when we put the $\\Theta$ into the sum. So let us not put it in there and write\n\n$\\qquad \\displaystyle \\sum_{i=1}^n \\frac{2i - 1}{i(i+1)} \\in \\Theta\\left(\\sum_{i=1}^n \\frac{1}{i}\\right) = \\Theta(H_n)$\n\ninstead. Putting the $\\Theta$ outside of the sum results in\n\n• a mathematically correct statement and\n• a simple term inside the $\\Theta$ we can easily deal with (which is what we want here, right?).\n\nSo it seems to me that this is both a correct and a useful way of writing the matter down, and should therefore be preferred over using Landau symbols inside the sum when we mean them outside of it.\n\n• Consider $\\sum_i^n i$. I can define $f_i(n)=i$ (using $i$ as a constant), therefore $\\sum_i^n i = \\sum_i^n O(1) = O(n)$ by your reasoning, right? But this sum is $O(n^2)$. – Xodarap Jul 21 '12 at 19:03\n• @Xodarap: By my reasoning, collapsing the sum like this does not work, because coupling the inner $\\Theta$s (which are not coupled to $i$ nor $n$) to $n$ does change the meaning. – Raphael Jul 21 '12 at 19:24\n• I'm not coupling them to $n$, I'm just using the fact that $\\sum_i^n k = nk$. (And I suppose also the fact that $nO(f)=O(nf)$.) – Xodarap Jul 22 '12 at 1:53\n• @Xodarap: But you don't have one $f$, but one $f_i$ per summand. If the underlying functions $f_i$ use $i$ (as a constant factor), you have to expand that, and the sum ends up being correct. So, clearly, by my reasoning the summing rule you propose does not work as you write. – Raphael Jul 22 '12 at 8:51\n• If I have a sequence $5,1,3,2,\\dots$, each of these are $O(1)$ (provided they don't increase as the series progresses). Would you say that adding $n$ of them will generate a sum $O(n)$? What's the difference if instead of being constants I describe them as constant functions $f_1(x)=5,f_2(x)=1,\\dots$? – Xodarap Jul 22 '12 at 14:03\n\nIf each $c_i$ is a constant, then there is some $c_{max}$ such that $\\forall c_i: c_i\\leq c_{max}$. So clearly $$\\sum c_i f(i) \\leq \\sum c_{max} f(i) = c_{max} \\sum f(i) = O\\left(\\sum f(i)\\right)$$ Same idea for little o.\n\nI think the problem here is that $1/i\\not=\\Theta(1)$. It's $o(1/n)$ (since there is no $\\epsilon$ such that $\\forall i: 1/i>\\epsilon$), so the overall sum will be $no(1/n)=o(1)$. And each term is $O(1)$, meaning the overall sum is $O(n)$. So no tight bounds can be found from this method.\n\n1. Is bounding $\\sum_i^n f(i)$ by doing the little o of each term and the big o of each term then multiplying by $n$ acceptable? (Answer: Yes)\n2. Is there a better method? (Answer: Not that I know of.)\n\nHopefully someone else can answer #2 more clearly.\n\n$\\sum_i^n \\Theta(f(n)) = \\Theta(nf(n))$ ?\n\nTo which the answer is yes. In this case though, each term is not $\\Theta$ of anything, so that approach falls apart.\n\nEDIT 2: You say \"consider $c_i=i$, then there is no $c_{max}$\". Unequivocally true. If you say that $c_i$ is a non-constant function of $i$, then it is, by definition, non-constant.\n\nNote that if you define it this way, then $c_i i$ is not $\\Theta(i)$, it's $\\Theta(i^2)$. Indeed, if you define \"constant\" to mean \"any function of $i$\", then any two functions of $i$ differ by a \"constant\"!\n\nPerhaps this is an easier way to think of it: we have the sequence $1,\\frac{1}{2},\\dots,\\frac{1}{n}$. What's the smallest term in this sequence? Well, it will depend on $n$. So we can't consider the terms as constant.\n\n(Computer scientists are often more familiar with big-O, so it might be more intuitive to ask if $1,\\dots,n$ has a constant largest term.)\n\nTo provide your proof: let $f(i_{min})$ be the smallest value of $f(i)$ in the range $1,\\dots,n$. Then $$\\sum_i^n f(i) \\geq \\sum_i^n f(i_{min}) = n f(i_{min}) = n o(f(n))$$\n\nAn analogous proof can be made for the upper bound.\n\nLastly, you write that $H_n = o(n)$ and as proof give that $H_n = \\Theta(\\log n)$. This is in fact a counter-proof: if $H_n$ is \"bigger\" than $n$, then it can't be \"smaller\" than $\\log n$, which is what's required for it to be $\\Theta(\\log n)$. So it can't be $o(n)$.\n\n• 1) \"..then there is some $c_{max}$ such that...\" -- no, there is not. Consider $(c_i)_{i \\in \\mathbb{N}}$ with $c_i = i$. 2) \"I don't think $H_n=o(n)$\" -- $H_n \\in \\Theta(\\ln n)$ 3) $1/i\\not=\\Theta(1)$. It's $o(1/n)$ -- That is wrong. As $1/i \\geq 1/n$, $1/i \\in \\Omega(1/n)$. 4) \"(Answer: Yes)\" -- as long as I don't see a formal proof of that fact, I don't believe it. Besides, \"multiplying by $n$\" is not what happened in the exhibited case. – Raphael Jul 18 '12 at 21:32\n• I think you are missing the point. Your proof does not work because we may not have the same $f$ in every summand, and not even the same for the same summand but different $n$. I think I nailed it down; I will compose an answer shortly. – Raphael Jul 19 '12 at 11:38\n• I still don't understand what you're saying, so I'm glad you figured it out :-) – Xodarap Jul 19 '12 at 17:50" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9125597,"math_prob":0.9987468,"size":1598,"snap":"2019-51-2020-05","text_gpt3_token_len":461,"char_repetition_ratio":0.08908407,"word_repetition_ratio":0.0,"special_character_ratio":0.28410512,"punctuation_ratio":0.11815562,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9999701,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-12T14:47:50Z\",\"WARC-Record-ID\":\"<urn:uuid:4660ebe3-af8d-4088-8f27-a42cad2b750e>\",\"Content-Length\":\"179843\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a6201ce4-84b1-4ef9-9ea3-7509ebb33f9b>\",\"WARC-Concurrent-To\":\"<urn:uuid:f731eb64-8d46-4121-98c3-390cd968f3c2>\",\"WARC-IP-Address\":\"151.101.129.69\",\"WARC-Target-URI\":\"https://cs.stackexchange.com/questions/2814/sums-of-landau-terms-revisited\",\"WARC-Payload-Digest\":\"sha1:5H26EGDZKYOACKO4SZKFZ3NEUS3NEGK2\",\"WARC-Block-Digest\":\"sha1:XLJ4J6AD6ZCT7FDPNB755XIVTMWOLL2Q\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575540543850.90_warc_CC-MAIN-20191212130009-20191212154009-00281.warc.gz\"}"}
https://in.mathworks.com/matlabcentral/cody/problems/3-find-the-sum-of-all-the-numbers-of-the-input-vector/solutions/1596431	[ "Cody\n\n# Problem 3. Find the sum of all the numbers of the input vector\n\nSolution 1596431\n\nSubmitted on 31 Jul 2018 by Athi\nThis solution is locked. To view this solution, you need to provide a solution of the same size or smaller.\n\n### Test Suite\n\nTest Status Code Input and Output\n1 Pass\nx = 1; y_correct = 1; assert(isequal(vecsum(x),y_correct))\n\n2 Pass\nx = [1 2 3 5]; y_correct = 11; assert(isequal(vecsum(x),y_correct))\n\n3 Pass\nx = [1 2 3 5]; y_correct = 11; assert(isequal(vecsum(x),y_correct))\n\n4 Pass\nx = 1:100; y_correct = 5050; assert(isequal(vecsum(x),y_correct))\n\n### Community Treasure Hunt\n\nFind the treasures in MATLAB Central and discover how the community can help you!\n\nStart Hunting!" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.51876277,"math_prob":0.9958308,"size":607,"snap":"2020-45-2020-50","text_gpt3_token_len":200,"char_repetition_ratio":0.16749585,"word_repetition_ratio":0.17021276,"special_character_ratio":0.35914332,"punctuation_ratio":0.12820514,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9970146,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-10-30T02:25:26Z\",\"WARC-Record-ID\":\"<urn:uuid:daf2b3a4-7d5e-448c-b58f-35c003384fb2>\",\"Content-Length\":\"80659\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:8fb286c8-8158-4ed1-bcba-a952e628f81d>\",\"WARC-Concurrent-To\":\"<urn:uuid:aacec150-d56d-4fe9-a927-1f281fcd6520>\",\"WARC-IP-Address\":\"184.25.198.13\",\"WARC-Target-URI\":\"https://in.mathworks.com/matlabcentral/cody/problems/3-find-the-sum-of-all-the-numbers-of-the-input-vector/solutions/1596431\",\"WARC-Payload-Digest\":\"sha1:WQZNGEYVSDACAHO7O5GZC6A4GHAD5XPJ\",\"WARC-Block-Digest\":\"sha1:GLDLKA3NHDEMQ2PRRTK54ML3RW6GHSJX\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-45/CC-MAIN-2020-45_segments_1603107906872.85_warc_CC-MAIN-20201030003928-20201030033928-00317.warc.gz\"}"}
https://ru.scribd.com/document/249352659/Unit-Planscribd	[ "Вы находитесь на странице: 1из 31\n\n# UNIT PLAN\n\nI. The Setting\nMy unit, entitled 3-D shapes and applications, is intended for a 10th grade\ngeometry class. My class is a heterogeneous mix of 26 students, 16 of which that are\nmales and 10 that are females. Even though this is a standard level geometry class,\nmost of the students are already showing honors level potential. The unit will take\napproximately 9 days; 7 for lessons, 1 for review and 1 for the exam. Each\ninstructional lesson is 50 minutes.\nII. Overview and Rationale for the Unit Overall, this unit should not only provide students the knowledge to work with three\ndimensional shapes, but also be able to apply some of their properties to real life\napplications. Being able to work in three dimensions is the main goal of this unit.\nOften, as most are one dimensional in life, its hard to progress through and enjoy\nthe true beauty of all three dimensions. This unit will also be helpful throughout the\nremainder of the course because we will be making references to 3-D figures I\nregards to proofs. With the visualization out of the way, we can focus our attention\nsolely on the proofs.\nCommon Core standards:\nG.MG.1. Use geometric shapes, their measures, and their properties to\ndescribe objects (e.g., modeling a tree trunk or a human torso as a cylinder).\nG.MG. 2. Apply concepts of density based on area and volume in modeling\nsituations (e.g., persons per square mile, BTUs per cubic foot).\nNCTM standards:\nAnalyze characteristics and properties of two- and\nthree-dimensional geometric shapes and develop\nanalyze properties and determine attributes of two- and three-dimensional\nobjects;\nexplore relationships (including congruence and similarity) among classes of\ntwo- and three- dimensional geometric objects, make and test conjectures\nabout them, and solve problems involving them;\nWhile in mathematics, the common rational for teaching is to prepare them for the next\nlevel of mathematics. In my unit however, I aim to make connections between mathematical\nconcepts and real life. This unit is especially good for my target audience because it takes a new\nlook into the world of three dimensions and the perceptions, or lack thereof, a person can have.\nSince we all live in a three dimensional world, it is hard not to find a relationship between the\n\nmathematics I present and what they will experience in everyday life. Therefore, my rational for\nthis unit is to open their eyes to new perspectives of the world they live in.\nIV. Content Outline\n1. Graphing in three dimensions\n2. Properties of 3-D shapes\na. Cubes\nb. Prisms\nc. Pyramids\nd. Cylinders\ne. Cones\nf. Spheres\n3. Finding surface area\n4. Finding Volume\n5. Cavalieris Principle & Cross sections\n\n(Attatched)\n\n## VII. Assessment procedures\n\nFor each objective that I present, I always give multiple means of assessment to\nensure the objectives are met. Some of the common assessments I used in my lesson\nplan are as follows:\na) Graphic organizers: Used throughout the unit to make comparisons among\nthe different 3-D shapes\nb) Exploration worksheet: With Common Core taking over the mathematics\ncurriculum, it is essential to implement more hands-on learning. With these\nexploration worksheets, I can assess to see if the students are understanding the\nmaterial.\nc) Exit tickets: For all of my exit tickets, I not only assess some of the formulas\nand applications that I teacher, but I also want to make important references to\nactivities that led them to the knowledge they obtained that day\nd) Homework: Homework is presented every day except the day before the\nreview in the hopes that students will get to practice the new material they learned\n\nDay 1\nIntroduction: 2-D shapes in a 3-D world\nDay 1 Objectives:\n1. Students will be able to utilize their knowledge of 2-D shapes in order to graph\nsolids in three dimensions\n2. Students will be able to explain the third dimension in order to discuss\nperceptions of everyday life\nAssessments:\n1. During the course of the lesson, students will be required to graph 3-D objects in\nboth two and three dimensions.\n2. During the exploration activity, students will be required to practice plotting\ncoordinates in three dimensions on a worksheet. The plots will resemble 3-D solids\nthat we will cover in the next couple days.\n3. At the end of class, I will provide an exit ticket that will assess the students\nknowledge of graphing in three dimensions as well as graphing everyday 3-D\nitems in two dimensions.\n4. For homework, the students will create a question sheet for one of their\nclassmates to do next class. While it will once again cover graphing in three\ndimensions, it will be up to each student to play teacher and also provide an answer\nkey to their problem set.\n\nActivities\n1. 3-D shapes in two dimensions: In the first activity, I will have brought in\nrandom household items for the students to observe. Students will be put into\ngroups of four and each given a single item. While they will not be taking any\nmeasurements in this class period, they will be required to draw a perspective of\none angle of the item. In other words, students will be making a sketch (on graph\npaper), from looking at either the back, front, left side or right side of the item.\nAfter each student has chosen an object and drawn a side, we will discuss the\nperceptions of items. More specifically, I may question how only 1 angle and one\nviewpoint can alter ones perception of a solid. You look up in the sky and see a\nfour sided 2-D figure. What shape is it? While most may answer rectangle or\nsquare, the reality is that it is most likely a cube or prism. Unfortunately, with our\nperception on reality, even though we live in a 3 dimensional world, we tend to see\n\nthings in one dimension. Hopefully this activity will open their eyes to a new world\nof mathematics.\n2. Creating the third dimension: In the second activity, not long after the first,\nstudents will take their graphs of one perception and try and manipulate the graphs\ndrawn by the other group members to re-create the original 3-D figure. While this\nactivity will initially seem easy, it is extremely difficult to create a 3-D drawing\nfrom only seeing a few images of the original figure. However, once the students\ncan visualize this image and re-create it, (the best they can) they will start to notice\nsomething they hadnt before when graphing in two dimensions; depth. In order to\nre-create these 3-D objects, there needs to be a third dimension present. I will ask\nthe students the type of orientation needed to create such an abstract image. This\nwill lead us into the next activity in regards to plotting points in three dimensions.\n3. Graphing in three dimensions: For the final activity, I will be guiding the\nstudents in exploring the nature of three dimensions. To do so, I will be showing\nthe students how to plot points on a 3-D graph, and then sending them on their own\nto find points for the 3-D objects we plotted the activity before. Then using a\nregular sheet of graph paper, they will plot the coordinates of the objects and create\nan outline for them. This activity will precede the classwork in the hopes that they\nbuild a deeper understanding of graphing in three dimensions.\nKey Content Outline:\nI. 2-D shapes in a 3-D world\nII. The third dimension\nIII. Graphing in three dimensions\nThis lesson was intended to open the eyes of my students to the true world of three\ndimensions. Even though they have lived in this 3-D world for about 15 years\nalready, they still have a lot to understand in regards to perception. Hopefully,\nespecially for future mathematics, my students understand that it isnt always\nwhat it seems.\nResources:\nNo technology resources\nWill need handouts and graph paper\n\nDay 2\nCubes, Prisms and Pyramids\nDay 2 Objectives:\n1. Students will be able to implement their knowledge of 2-D shapes in order to\ngraph cubes, prisms and pyramids\n2. Students will be able to compare/contrast cubes, prism and solids\n3. Students will be able to construct 3-D mobiles for a cube, prism and pyramid in\norder to further analyze their properties\nAssessments:\n1. During the lesson, students will be filling out graphic organizers to compare the\nthree different types of 3-D solids\n2. Classwork practice will be given for graphing cubes, prisms and pyramids in\nthree dimensions\n3. Students will construct mobiles of cubes, prisms and pyramids\n4. At the end of class, students will be given an exit ticket that will assess their\nknowledge, not only of the continuation of graphing in three dimensions, but more\nimportantly ,the properties of each that make them distinct from each other.\n5. The final assessment will be a homework assignment in which students will\ngraph particular cubes, prism and pyramids. Once again, major comparison\nquestions will also be given to ensure maximum understanding of the different 3-D\nshapes. Students will also be required to start bringing in models of cubes, prisms\nand pyramids from home.\nActivities:\n1. Graphing cubes, prisms and pyramids: The class session will be split up into 6\nsections, each of which covering a 3-D object and either its properties or graphing\nstrategies. For this particular lesson, the graphic organizer will help to drive the\nproperties section of this lesson. The graphing portions will be done by an activity\nin which student will explore, using properties of 2-D figures, graphing cubes,\nprisms and pyramids in three dimensions. A common question I could ask in the\nclasswork is why the coordinates are what they are. More specifically, a cube for\nexample, why are the distances between any two points, when graphing in one\ndimension, the same. If the students were focused during the lecture, the answer is\nsimple. Each measurement is the same because one face of a cube is a square. The\nsame sort of questions could be asked when graphing the prism and pyramid as\nwell.\n\n## 2. Creation of mobiles: The next activity I would lead my class in is the\n\nconstruction of 3-D mobiles. In order to do so, my students will need an\nunderstanding of the properties of cubes, prisms and pyramids. With this\nknowledge, the students will use paper, scissors and pencils to draw two\ndimensional outlines for each three dimensional shape. Then, the students will fold\neach side according to the directions and tape them together to create their figure.\nThis solid will not only be a great tool to remember the properties I future class\nperiods, but I also intend to you use them in the next lesson when we discover\nsurface area.\nKey Content Outline:\nI. Properties of a cube\nII. Graphing a cube\nIII. Properties of a prism\nIV. Graphing a prism\nV. Properties of a pyramid\nVI. Graphing a Pyramid\nThis lesson is intended to introduce the properties of cubes, prisms, and pyramids\nin the hopes of once again having them make connections to the real world. This\nlesson is especially crucial because of the applications we will be covering in the\nnext couple days. It will be extremely hard to find surface area and volume of\nsolids that students have no understanding of.\nResources:\nNo technology resources\nWe will need scissors, tape, paper and handouts\n\n## Day 3: Surface area (Major lesson component)\n\nClass Description\n\nUnit Title\n\nLesson\nTopic\n\n3-D shapes\nSurface\nand\nArea\napplications\n\nType of\nLesson\nDevelopmental\nlesson\n\nMD State Curriculum\nStandard/ MD Common Core\nState Standard\nApply geometric concepts in modeling\nsituations\n1. Use geometric shapes, their measures, and their\nproperties to describe objects (e.g., modeling a tree\ntrunk or a human torso as a cylinder).\n2. Apply concepts of density based on area and volume\nin modeling situations (e.g., persons per square mile,\nBTUs per cubic foot).\n3. Apply geometric methods to solve design problems\n(e.g., designing an object or structure to satisfy physical\nconstraints or minimize cost; working with typographic\ngrid systems based on ratios).\n\nJudges Prior Knowledge (How do you know students are ready to learn the\ncontent in this lesson?)\nI will be discussing two major ideas in this lesson; manipulation of 3-D\nshapes and surface area. To understand the manipulation of 3-D shapes, the\nstudents will need a vast knowledge of the creation of 3-D shapes using 2-D\nshapes. This requirement is fulfilled in my introduction lesson to this unit\non day 1 (This lesson is about day 4 or 5). I will also be including a\nsegment in the drill. To teach the second idea, surface area, students will\nneed to have had previous instruction on the area of 2-D shapes. This type of\nmaterial is usually covered all throughout elementary and middle school. Just\nin case though, I have included a review in my drill as well.\n\nLesson Objective(s):\nObjective 1 SWBAT utilize their knowledge of area to discover\nsurface area of three different 3-D shapes\nObjective 2 SWBAT participate in a hands on activity to find\nthe surface area of common household items\nAssessment(s):\nAssessment for Objective 1 Drill and Opening worksheet\n\n## Is this a formative or summative assessment? Formative\n\nWould you characterize this assessment as a traditional or\nWhy did you select this assessment strategy to measure student\nlearning? It is a review of things they should be confident\nAssessment for Objective 2 Activity completion/ worksheet\nIs this a formative or summative assessment? Formative\nWould you characterize this assessment as a traditional or\nperformance assessment? Performance\nWhy did you select this assessment strategy to measure student\nlearning? The activity allows for student discovery of\nmathematical relationships.\nMaterials Needed for Lesson\nObject from home ( previously instructed)\nModels of 3-D shapes (previously constructed)\nCalculator\nRuler\n\n## Incorporation of Technology (if appropriate)\n\nIf you are using a website, type in the website citation.\nCalculator: To assist the student in calculations\n\nLesson Development\nTeacher\n\nStudents\n\nTime\n\nDrill/Motivational\nActivity\n\nWorksheet\n\n8 minutes\n\nTransition\n\nActivity 1\n\nKey Questions\n\nWhat assumption\nthe area of a two\ndimensional figure\nmore than one two\ndimensional shape?\nWhat seems to be\nthe main\ndifference between\na cube and prism?\nHow does this\naffect the way we\nfind the surface\narea of each?\n\nSo everyone seemed\nto notice that the\nlast figure on the\ndrill was actually a\ncube. Correct? So\neven though I was\nof a 2-D figure, you\nwere actually\nfinding the area of\na cube. We call the\narea of a 3-D shape,\nsurface area\nLecture: Comparing\nthe area of 2-D\nconstructions with\n3-D shapes\n(Worksheet)\nAnticipated\nResponses?\nIt is the sum of\neach two dimensional\nfigure\n\n## The prism is bigger\n\nso the surface area\nis bigger. Since all\nthe sides of the\ncube are the same\nthe surface area is\n6bh. For a prism,\nthe equation would\nbe\nlw+lw+wh+wh+lh+lh.\nCorrection: The\nprism may appear to\nbe bigger in most\ncases but not\nalways. Coincidently\n\n10 minutes\n\nWhat is unique\nsurface area of a\npyramid\n\nTransition\n\n## though, the surface\n\narea of a prism will\nbe bigger than that\nof a cube most of\nthe time. But, do\nnot confuse visual\nrepresentation with\nmathematical\nconcepts. In\nstudents to see and\nbe able to recognize\nthe equation for the\nsurface area of a\nprism: 2(lw+lh+hw)\nIt requires finding\nthe area of\ntriangles and\nsquares.\nMake note: the sides\nof the squares will\nbe the same as the\nbases of each\ntriangle in the\npyramid.\n\nActivity 2\n\n## Now that we know\n\nhow to find the\nsurface area of\ncubes, pyramids and\nprisms, lets go\nKey Questions\nmaterials from home\nDid the formulas for\nsurface area differ for and get into the\ngroups I have\neach object? (i.e was\nassigned on the\nthe way you found\nboard. Hopefully\nsurface area for a\neveryone in the\nshoebox the same way\ngroup has a\nyou found the surface\ndifferent example of\narea of a soda box?)\neach of the 3-D\nfigures we worked\nDid you find any areas\nwhich were close to the with today. While\nyou are doing that,\narea of maybe a\nI will pass around\ndifferent 3-D figure?\n\n25 minutes\n\nmeans?\n\nrulers\n\nTransition\n\n## Finding the Surface\n\narea of household\nitems\nAnticipated\nResponses?\nfound were\ndifferent, but the\nway in which we\nfound them was the\nsame.\n\nSummary/Closure/Revisit\nObjective\nNo, none of the\nvalues were even\nclose. I dont know\nwhat that would mean\nSafety Valve\nthough.\nmean that if you\nopened up the 3-D\nshapes, you would\nfind that the sum of\nthe areas would be\nthe same.\ngentlemen that wraps\nup our lesson on the\nsurface area of\nPyramids, cubes and\nprisms. Can anyone\ntell me what 3-D\nshapes I missed?\nCones, Cylinders and\nSpheres What two\ndimensional shapes\ndo they utilize?\n\n5-7 minutes\n\nCircles. So next\ntime, we will look\nat those shapes in\nparticular and do a\nsimilar activity\nwith more objects\nfrom home.\nExit ticket\n\n## Start to discuss and\n\ndiscover cylinders\nand cones\nReflection on assessment Assume that after you have taught\nthis lesson and assessed student learning you find that students\ndid not meet the objective(s). How would you plan future\ninstruction on this lessons content and skills to ensure\nstudent mastery and application?\nUnfortunately, in regards to Common core standards, the 3-D\nshapes unit is very limited for time and in some cases gets\nthrown all into one week. If I find that students arent meeting\nmy objectives, over the course of two weeks, I would probably\nmake less time for discovery learning and more time for lecture\nbased work. I do not like lecture at all, and in most cases it\nis ineffective, but with the vast number of activities I have\nplanned, the only way students shouldnt be accomplishing my\nobjectives is if they stray too far away from the main objective\nwhen exploring or by the time they finish the activity, the\nobjective is unclear. Regardless though, more lecture seems to\nbe the best solution here.\n\nDay 4\nVolume\n\nDay 4 Objectives:\n1. Students will be able to interpret the theoretical volume in order to calculate the\nvolume of cubes, pyramids and prisms.\n2. Students will be able to participate in a hands on activity in order to calculate\nthe volume of household items that represent cubes, prisms and pyramids\nAssessments:\n1. Fill in the blank lecture notes will handed out at the beginning of class\n2. Before the exploration, students will also be given a worksheet to practice\nfinding the volume of cubes, prisms and pyramids.\n3. During the exploration, students will need to fill out a chart that will showcase\ntheir knowledge of volume by application.\n4. For an exit ticket, students will be required to calculate the volume of cubes,\nprisms and pyramids. However, the questions will be based on real world\napplications. For example, a question might read you want to fill your shoebox up\nwith water to act as a fishbowl. Unfortunately though, your fish requires living in a\nbowl with volume 24inches3. Too much water is ok, but too little will kill him. If\nthe dimensions of the shoebox are 2inches x 5 inches x 4inches, what can we\nconclude about the lifespan of the fish? Should he die anytime soon?\n5. For homework, students will be finding more household items and finding the\nvolume of them as well.\nActivities:\n1. Volume of household items: For this lesson, due to the length of it, there will\nonly be one exploration activity. In this activity, students will be splitting up into\ngroups and measuring the dimensions of common household items that represent\ncubes, prisms and pyramids. With these dimensions, students will calculate the\nvolume of each item and discuss their findings with a partner. Two of each kind of\nsolid should be measured to compare the results. Even though this activity seems\nto be very short and simple, many questions arise when discussing the volume of\nany three dimensional object. The first of which is based similarity and\nproportionality within solids. For example, a good question might ask that prism\ncan clearly hold more volume than the others. What dimensions make this\npossible? Why do you think this is? Also, I may ask the relationship in volumes if\nthe sides were all proportional. In other words, if one prism had dimensions\n\n4x10x8 and the other had 2x5x4, how would one volume compare to the other?\nFinally, in my explanation section, I want to make sure that I express the great deal\nof ease for finding the volume of these shapes in particular. Similar to the way\nsurface area can be hard, volume can easily be just as hard when dealing with more\ncomplex solids.\nKey Content Outline:\nI. What is volume? (Units included)\nII. What is the volume of cube?\nIII. What is the volume of a rectangular prism?\nIV. What is the volume of a pyramid?\nThis lesson is intended to once again give a deeper meaning to an easy concept in\nthree dimensions. Even though volume has most likely been seen in a more applied\nnature to real world applications, I doubt they had the same understanding of\nvolume going into todays lesson. This lesson will also prove to be helpful when\nwe discuss the volume of cones, cylinders and spheres as well. With less time\nhaving to cover the idea of volume, we can take more time for exploration and\napplication\nResources:\nWe will need handouts, household items, rulers and charts\n\nDay 5\nCones and Cylinders\n\nDay 5 Objectives:\n1. Students will be able to relate the applications of circles in order to construct\ncylinders and cones\n2. Students will be able to interpret the height of a cone and cylinder as a\nquadrilateral in order to further understand their surface area\n3. Students will participate in a hands on activity in order to calculate the surface\narea and volume of common household items that represent cones and cylinders\nAssessments:\n1. Students will first be provided a graphic organizer that will be used to\ndistinguish between cones and cylinders\n2. Students will also be given a classwork assignment in which they will graph\ncones and cylinders in three dimensions as well as calculate their volume and\nsurface area\n3. Students will also be given a chart, similar to the ones used for cubes, prisms\nand pyramids. This will be used as a guide for finding the surface area and volume\nof common household items that represent cones and cylinders\n4. An exit ticket will also be given that will assess students knowledge of graphing\ncones and cylinders in three dimensions. In addition, it will look to apply the\nformulas discovered in the exploration.\n5. Finally, a homework assignment will be given that will include application\nproblems of finding both the surface area and volume of cubes, prisms, pyramids,\ncones and cylinders.\n\nActivities:\n1. Constructing a Cylinder: For my first activity, I will have students analyze the\nproperties of a cylinder by manipulating a roll of paper towels. This will be a very\ninnovative activity because it represents the true height of a cylinder. One of the\nbiggest discrepancies in geometry classes is the idea that no one seems to know\nwhere the formula for surface area of a cylinder comes from. With the paper\ntowels, I can literally unravel a single towel and show it to my class. I will ask\nthem first what new shape I have created by opening up the cylinder. Next, I will\nask them what the base and the height are for the new quadrilateral I created.\nWhile the height is simply h, the base can be represented by a variation of a circle.\n\n## More specifically, the base is represented by circumference of the circle at the\n\nbase. This will help lead us into the surface area exploration. Unfortunately, the\nsame type of manipulation cannot occur for the cone.\n2. Surface area/ volume: The surface area and volume activity will be the exact\nsame activity we had done 2 days earlier, except now the students are measuring\ncylinders and cones. Some of the items we will have are ice cream cones, cone\ncups, funnels, tops of soda bottles, soup cans, soda cans, cylindrical boxes, coffee\ncans and cups. Since the formulas have already been given, the actual process of\nfinding all the surface areas and volumes wont be difficult, but it will provide the\nstudents with practice and more real life application.\nKey Content Outline:\nI. Properties of a circle in relation to three dimensions\nII. Properties of a Cylinder\nIII. Properties of a Cone\nIV. Surface area of a Cylinder\nV. Surface area of a Cone\nVI. Volume of a Cylinder\nVII. Volume of a Cone\nThis lesson is intended to provide another dimension to our students knowledge of\nthree dimensional shapes. While cubes and pyramids were harder to find in real\nlife applications, cylinders and cones are found almost anywhere. Now with this\nknowledge, we can cover the last three dimensional shape that utilizes a circle; a\nsphere. This lesson provided some excellent strategies that will be taken over\nwhen we talk about spheres as well.\nResources:\nNo technology resources\nWe will need handouts, a paper towel roll, household items, rulers and charts\n\n## Day 6: Spheres (Major lesson component)\n\nClass Description\nThis is a 10th grade Geometry class. It is simulated by 8\nstudents, 4 of which are male and the other four, female. Though\nthe classroom is quite large and the number of students is quite\nsmall in comparison, I will have them sitting in groups of four\nin the front of the classroom. Each table will have 2 males and\n2 females. Since Jessie and Lydia are my higher level students\n(in mathematics), I will put them at separate tables.\nUnit Title\n\nLesson\nTopic\n\n3-D shapes\nSpheres\nand\napplications\n\nType of\nLesson\nDevelopmental\nLesson\n\nMD State Curriculum\nStandard/ MD Common Core\nState Standard\nApply geometric concepts in modeling\nsituations\n1. Use geometric shapes, their measures, and their\nproperties to describe objects (e.g., modeling a tree\ntrunk or a human torso as a cylinder).\n2. Apply concepts of density based on area and volume\nin modeling situations (e.g., persons per square mile,\nBTUs per cubic foot).\n\n## Judges Prior Knowledge (How do you know students are ready to\n\nlearn the content in this lesson?)\nIn order to understand the significance of finding the surface\narea and volume of a sphere, students must have a vast\nunderstanding of how to find the volume and surface area of\ncubes, pyramids and rectangular prisms. With time constraints, I\nhave elected to only review cubes and rectangular prisms.\nPyramids take a little longer to compute. Also, even though this\nwill be reviewed in lessons before this one, a mastery of\nworking with 2-D shapes and finding their area is crucial to\nunderstanding the shift into 3- dimensions.\n\nLesson Objective(s):\nObjective 1 Students will be able to analyze the major\ncharacteristics of a sphere in order calculate its volume in\nreal world applications.\nObjective 2 Students will manipulate an orange in order to\n\n## develop the surface area of a sphere.\n\nAssessment(s):\nAssessment for Objective 1 PowerPoint Question\nThe distance from the center of Spalding NBA basketball to any\npoint on the ball itself is 3inches. How much air should go\ninto the basketball to fill it up?\nIs this a formative or summative assessment? Formative\nWould you characterize this assessment as a traditional or\nperformance assessment? Performance Assessment\nWhy did you select this assessment strategy to measure student\nlearning? It is a direct way to test the knowledge the students\nwere just given with a real world application.\nAssessment for Objective 2 Orange discovery worksheet\nIs this a formative or summative assessment? Formative\nWould you characterize this assessment as a traditional or\nperformance assessment? Performance Assessment\nWhy did you select this assessment strategy to measure student\nlearning? This hands on activity requires a step by step process\nof discovering the surface area of a sphere. The worksheet\nchronologically takes the students through the thought process\nthey should have when completing this activity. It will be a\ngreat way to make sure they are on track.\n\n## Materials Needed for Lesson\n\nOranges\nPowerPoint slides\nNapkins\n\nNo IEP students in this particular lesson\nIncorporation of Technology (if appropriate)\nIf you are using a website, type in the website citation.\nPowerPoint slides as a guide\n\nTeacher\nKey Questions\nSo a football is a\nsphere right? Can\nanyone give me some\nexamples of spheres?\nDrill/Motivational\nActivity\n\nKey Questions\nWhat makes a cube\ndifferent from a\nrectangular prism? Why\nis its surface area and\nvolume so easy to find?\n\n## Does anyone know why\n\nthe surface area is\nsquared and the volume\nis cubed? Shouldnt\nthey both be cubed\nsince we are in 3dimennsions?\nTransition\n\nLesson Development\nStudents\nAnticipated\nResponses?\nNo!! Balls:\nsoccerball,\ntennisball,\nbaseball etc.\n\nTime\n5 minutes\n\n## See Drill sheet\n\nAnticipated\nResponses?\nSince a cube is\nthe volume and\nsurface area are\ncalculated from\nonly one\nmeasurement. A\nrectangular prism\ncan have up to\nthree different\nsets of dimensions\nto work with.\nNo, surface area is\nsquared because\nonly two things are\nmultiplied at a\ntime. Volume is\ncubed because it is\nbased on\nmultiplication of\n\n10 minutes\n\nthree dimensions.\nActivity 1\n\nKey Questions\n\nSo now that\neveryone seems to\nfeel comfortable\nworking with the\neasier 3-D shapes,\nlets move into a\nmore complex figure\nin spheres.\n\n## What do we call r, the\n\ndistance from the\ncenter of the sphere to Lecture:\nany point on the\nInformation on\nsphere?\nspheres\nHow many faces does a\nsphere have?\n\nAnticipated\nResponses?\n\n## Can anyone show me a\n\nAre there any others?\n\nNone!!\nDoes anyone know or\nremember the volume of\na sphere?\n\n## Students can draw\n\nany line from the\ncenter of the\nsphere to any point\nWhy do you think we use on the sphere\npi and r in our\nitself. Therefore\nequation for volume?\nthere are infinite\nlines that students\ncan give me.\nNo.\nTeacher response:\nAssessment 1: The\nThe volume of a\ndistance from the\nsphere, while\ncenter of Spalding NBA\ndifficult and very\nbasketball to any point arbitrary is 4/3\non the ball itself is\nr3.\n3inches. How much air\nshould go into the\nBecause its based\non a circle.\nup?\nTeacher response:\n\nThats good to\nSurface area is measure note. The volume\nin squares. Why again?\nhas a lot to do\nwith the\naccumulation of\ncircles. When we\nget to surface\narea, we will talk\nTransition\nthat.\n36. There should\nbe no difficulty\nseeing as though it\nis simply a direct\nimplementation of\nthe equation.\n\nActivity 2\n\nKey Questions\nWhat is the area of\neach great circle you\ncreated?\n\nBecause we are\nmultiplying two\nthings at a time.\nEven though it is\nin 3-dimmensions,\nit is based on the\nnumber of items\nbeing multiplies.\n\n## The surface area\n\nof a sphere is not\nonly difficult\nHow many great circles\nbecause it does not\ndid you fill with your\norange peel?\npatterns as the\nother shapes, but\nWhat is the surface\nin most cases,\narea of a sphere being\nstudents will\nrepresented by in this\nforget the equation\nactivity?\nfor surface area\nmore often than\nSo, if you were able to that of volume.\nfill four great\nHopefully this next\ncircles, each of which\nactivity will spark\nhaving area r2, then\nyou interest and\ngive you a\nthe surface area of a\nmemorable\n\n10 minutes\n\nsphere?\n\nexperience.\n\nTransition\nDiscovering the\nsurface area of a\nsphere\nAnticipated\nResponses?\n\nKey Questions\n\nr2\n\n## Before todays lesson,\n\ndid you have any idea\nwhat the surface area\nof a sphere is?\n\n## When you leave class\n\nthough, would you be\nable to explain to\nsomeone what the\nsurface area of a\nsphere means to you?\n\n## The surface area of\n\na sphere is being\nrepresented by the\nnumber of filled\ncircles.\n4r2\n\nSummary/Closure/Revisit So to wrap up\nObjective\ntodays lesson lets\nimportance of\nvisualization and\nwhy it helps to\nunderstand topics\nAnticipated\nResponses?\nSafety Valve\n\nNo, in fact, I\ndont even remember\nThe volume has\nalways been\n\nembedded in my\nbrain. However,\nwith todays\nactivity, I not\nonly feel confident\nusing the equation,\nI feel equally as\ncomfortable\nexplaining it to\nsomeone else.\nSee Exit Ticket w/\nIn todays lesson,\nwe completed both\nobjectives relating\nto the surface area\nand volume of a\nsphere. The\nimportant\ninformation to take\naway is the usage\nof the formulas and\nsome basic\nspheres. These will\ncome back to haunt\nyou later, so do\nnot forget the\nformulas!\nWith a 25 minute\nlesson, yet alone a\nmath lesson, it is\nreally hard to plan\nfor a safety valve.\nHowever, with a bit\nof extra time, I\ncould provide more\nreal world examples\nto drive the\nconcept home for\nthe students.\nReflection on assessment Assume that after you have taught\nthis lesson and assessed student learning you find that students\n\ndid not meet the objective(s). How would you plan future\ninstruction on this lessons content and skills to ensure\nstudent mastery and application?\nIf I were to be informed, through assessment, that my lesson did\nnot coincide with the objectives, regardless of my time frame, I\nneed to find more time to discuss it. Seeing as though my unit\nis 8 days with the initial assumption of 7, I may have that\nextra day to go a little deeper in class. I would however need\nto address this idea ASAP because once this unit is over, it\nwill be very hard to come back to it. We absolutely cannot skip\nit because of its importance. Also, if I wanted to keep the\norange activity, because it worked so well, I can possibly cut\ndown on some lecture and give the students more hands on\nopportunity. That is essentially what Common Core wants in the\nlong run anyway. To ensure students have mastered this concept,\nI will make sure that surface area and volume are hit the\nhardest.\n\nDay 7\nCavalieris Principle\n\nDay 7 Objectives:\n1. Students will be able to manipulate 3-D figures in order to interpret the cross\nsections that they create.\n2. Students will be able to interpret cross sections in order to calculate the volume\nof 3-D shapes using Cavalieris principle\nAssessments:\n1. To introduce the idea of cross sections, I will be leading the students in an\nactivity. A worksheet will be provided to guide the students in their findings.\n2. A practice classwork will also be given for cross sections to ensure students can\nfind cross sections of all 3-D shapes we have discussed thus far (cubes, prisms,\n3. Another exploration worksheet will be given in their discovery of Cavalieris\nprinciple. Even though the activity will cover only spheres, the students will use\nthese worksheets to make predictions of the effects on other 3-D solids.\n4. After the lesson, I will provide an exit ticket that will assess students\nknowledge of cross sections and ensure they are able to apply Cavalieris principle\nto any 3-D solid.\n5. For homework, the students will begin studying for their review the next class.\nIn their studying, they will look over the material taught today and hopefully\npractice it.\n\nActivities:\n1. Cross sections: Before the activity starts, students already have a basic idea of\nwhat cross sections are. Unfortunately though, it is very hard to visualize a cross\nsection of a 3-D solid without actually cutting that solid open yourself. My activity\naims to fill this gap in my students understanding. Using Play-Doh, I will have my\nstudents mold a cone and a cylinder (to the best of their abilities). Using a piece of\nfloss, they will cut their Play-Doh as directed. Their first attempt will be to cut\neach solid horizontally, thus creating similar solids. What the students should\nnotice is that not only are you creating a smaller version of the original solid, but\nyou are also creating 2-D faces from where you cut. These should be circles. This\nidea should also take students back to one of our original lessons where we\nmanipulated three dimensional shapes to graph in two dimensions. Afterwards, I\n\nwill have the students put their 3-D solids back together ( easy with Play-Doh) and\ntry cutting from a different angle. It will be essential to note that this cut will not be\nparallel to the base. With this cut, students will also note that the 2-D shape they\nhave now created is an ellipse, not a circle. The students will continue this process\nfor cubes, prisms and pyramids as well. Then we will look at spheres. For spheres,\nwhich differ from all other 3-D solids, its cross sections are always a circle. This\nwill also be an important idea for the lesson.\n2. Cavalieris principle: The sphere will prove to be a great last example for cross\nsections. As most classes do, I will be introducing Cavalieris principle through the\nmanipulation of spheres. One of the greatest proofs in 3-D geometry involves the\ndiscovery of the volume of a sphere. In this activity, that will be very similar to the\nlast, students will again be finding cross sections, but comparing it to cross sections\nof other 3-D shapes. Cavalieris principle is as follows: If two solids of equal\nheight are cut by a horizontal parallel equidistant from each of the bases, those\nobjects will have the same volume. With that said students can simply make two\nsolids with Ply-Doh, cut both of them equidistant from the bases using floss and\nthen measure the volume of each new solid. They will be the same.\n\n## Key Content Outline:\n\nI. Cross sections\n- Horizontal\n- Diagonal\nII. Cavalieris principle\nThis lesson is intended to relate the students to something they have most likely\nplayed with before; Play-Doh. In one instance, they are doing something fun and\nexciting, but they are also doing mathematics. This material is necessary for the\nstudy session and exam.\nResources:\nNo technology resources\nWe will need Play-Do, handouts and floss\n\nDay 8\nReview\n\nDay 8 Objectives:\n1. Students will be able to utilize their knowledge of 3-D shapes and applications\nin order to compete in a game of Jeopardy.\nAssessments:\n1. A game of Jeopardy will be given to assess students knowledge of cubes,\nprisms, pyramids, cylinders, cones and spheres and their respective applications\n(I.e surface area, volume, dimension in graphing, Cavalieris principle, etc.)\nActivities\n1. Students will compete in a game of Jeopardy in class. As in the common known\ngame show Jeopardy, questions will be given for different point values. The five\ncategories that will be questioned are 2-D shapes in a 3-D world, Cylinders,\ncones and spheres, Cubes, prism and pyramids, Surface Area, and Volume.\nIn regards to the point system, each category will be broken up into point values of\n200,400,600,800 and 1000 respectively. The question topics will be as follows\n2-D shapes Cylinders,\nCubes,\nSurface area Volume\nin a 3-D\ncones and\nprisms and\nworld\nspheres\npyramids\n200\nCube in 2-D Properties\nProperties\nSurface area Def. of\nof a cone\nof a\nof a sphere\nCavalieris\npyramid\nprinciple\n400\nLooking at\nRepresents A jack in\nShortcut to\nVolume of a\n2-D images funnel\nthe box is\nfinding the\nrectangle\nand deciding\nan example surface area and cube\nwhich 3-D\nof this\nof a pyramid\nimages they\nrepresent\n600\nExplain the Properties\nProperties\nApplication Cavalieris\nthird\nof a cylinder of a prism\nto prisms\nprinciple\ndimension\nwas\noriginally\nproven for a\n\n800\n\n1000\n\nGraph a\nrectangular\nprism with\n1x2x3 as the\ndimensions\nGraph a\nsphere with\n\nCross\nCross\nsection is an section of\noval\ncubes and\nrectangles\n\nApplication\nto cylinders\n\nCross\nsection is a\ncircle\nregardless\nof how you\ncut it\n\nApplication\nto cones\n\nCross\nsection of a\npyramid\n\nsphere\nApplication\nfor cones\n\nIf the height\nof a cone is\n4 inches and\nthe height of\na cylinder is\n4 inches, if I\ncreate a\nparallel, 3\ninches from\nthe base, and\nI know the\nvolume of\nthe cylinder\nis 12, what\nis the\nvolume of\nthe cone?\n\n## Key Content Outline:\n\n1. Cubes, Cylinders, Cones, Pyramids, Prisms and Spheres\n2. Surface area\n3. Volume\n4. 2-D and 3-D graphing\n5. Cavaliers principle\nThe intent of this lesson was to prepare my students for the exam next class. In\naddition though, it served as a fun and innovative way to help them remember all\nthe material.\nResources:\n\n## We will need the interactive PowerPoint that utilizes Jeopardy\n\nDay 9\nExam\n\nDay 8 Objectives:\n1. Students will be able to apply their knowledge of 3-D shapes and their\napplications in order to complete an exam\nAssessments:\n1. Students will be given their unit exam today. A few sample questions from each\ntopic are as follows. There are also many forms of questions on todays exam.\nThey include multiple choice, fill in the blank, calculation, matching, graphing and\nshort responses\n2-D objects in a 3-D world\n-(Fill in the blank)If I were to look at a cube from any angle, what two\ndimensional shape should I see?\n-(Graphing)Graph a rectangular prism on the grid provided. Its dimensions are\n2x3x4.\n- (Multiple choice) Which 3-D solids can you manipulate so that at least one side\nis a circle?\na. Sphere\nb. Cone\nc. Cylinder\nd. a and b\ne. a,b and c\nCubes, Pyramids, Prisms, Cones, Spheres and Cylinders\n-(Multiple choice) Which 3-D solid could also be another?\na. Rectangular prism\nb. Cube\nc. Cone\nd. Sphere\ne. None of the above\n- (Short response)What makes pyramids different than both cubes and prisms,\neven though we put them all in the same category?\n- (Matching)Match the following to its appropriate 2-D shape( there can be more\nthan one for each)\n\n1.Prism\n2.Cube\n3.Sphere\n4. Cylinder\n5.Cone\n6. Pyramid\n\na. Square\nb. Rectange\nc. Circle\nd. Triangle\n\nSurface area\n-(Short response)Surface area for cones, cylinders and sphere include a pi. Why?\n- (Fill in the blank)Based on the orange activity, we discovered that our orange\npeel filled _______ circles. The area of each circle was ______.This meant that our\nsurface area was going to be ___________\n- (calculation)Find the surface area of a rectangular prism with dimensions 4x8x3\nVolume\n- (Calculation) The volume of a standard MLB baseball is about 32/ 3 inches3.\nUsing the formula for the volume of a sphere, what is the radius of a standard MLB\nbaseball?\n- (Multiple choice) Whos theorem says that if we have two three dimensional\nsolids that have the same height, and we draw two parallels equidistant from the\nbases, they will have the same volume?\na. Pythagoras\nb. Euclid\nc. Cavalieri\nd. Einstein\n- (Fill in the blank) How much water can I put in a box if my boxes dimensions\nare 5x8x10_______\nActivities\n1. Students will take an exam that will cover 3-D shapes, surface area, volume,\ngraphing and Cavalieris principle.\nKey Content Outline:\n1. Cubes, Cylinders, Cones, Pyramids, Prisms and Spheres\n2. Surface area\n3. Volume\n4. 2-D and 3-D graphing\n5. Cavaliers principle\n\nThe intent of this lesson is to test the knowledge of my students in their ability to\napply formulas of 3-D solids to real world applications\nResources:\nNo technology resources\nWe only need the test itself" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9070546,"math_prob":0.7381651,"size":29137,"snap":"2021-04-2021-17","text_gpt3_token_len":6500,"char_repetition_ratio":0.15587135,"word_repetition_ratio":0.048083466,"special_character_ratio":0.19020489,"punctuation_ratio":0.1224605,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9564898,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-01-16T13:14:57Z\",\"WARC-Record-ID\":\"<urn:uuid:2b2ae300-4395-4efb-bbad-42e5cc2e6431>\",\"Content-Length\":\"565242\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:71d48654-7054-4280-b8b0-0e8f5f8114d3>\",\"WARC-Concurrent-To\":\"<urn:uuid:0780a3d8-e7bc-49d5-8c13-39a127967d84>\",\"WARC-IP-Address\":\"199.232.66.152\",\"WARC-Target-URI\":\"https://ru.scribd.com/document/249352659/Unit-Planscribd\",\"WARC-Payload-Digest\":\"sha1:KOXXO67TOPBFLOQHNOZ7YW2S4YY3CZQ6\",\"WARC-Block-Digest\":\"sha1:ABMWSCDJMHFJ6BYC4P6LR52YW4JWQ4GH\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-04/CC-MAIN-2021-04_segments_1610703506640.22_warc_CC-MAIN-20210116104719-20210116134719-00081.warc.gz\"}"}
https://afternoons-delight.com/qa/quick-answer-what-is-the-principle-of-efficiency.html	[ "", null, "# Quick Answer: What Is The Principle Of Efficiency?\n\n## What is the formula for efficiency?\n\nEfficiency is often measured as the ratio of useful output to total input, which can be expressed with the mathematical formula r=P/C, where P is the amount of useful output (“product”) produced per the amount C (“cost”) of resources consumed..\n\n## What is an example of allocative efficiency?\n\nAllocative efficiency means that the particular mix of goods a society produces represents the combination that society most desires. For example, often a society with a younger population has a preference for production of education, over production of health care.\n\n## What are the two types of efficiency?\n\nProductive efficiency and allocative efficiency are two concepts achieved in the long run in a perfectly competitive market. In fact, these two types of efficiency are the reason we call it a perfectly competitive market.\n\n## What is intertemporal efficiency?\n\nIn deriving these conditions, the paper extends the notion of efficiency to an intertemporal Pareto-optimal concept requiring the maximization of the ith individual’s utility at a point of time subject to the constancy of his utility in all future periods and that of all other individuals during the relevant time span.\n\n## What is known as the efficiency of doing work?\n\nBy working efficiently, more can be produced with the same amount of input (resources)(1). In short, achieving more for lower costs, a higher return and less pressure. Efficiency means ‘doing things in the right way’. 2. Two sorts of efficiency are often referred to, namely static efficiency and dynamic efficiency.\n\n## What do economists mean by efficiency?\n\nDefinition. Economic efficiency is a broad term typically used in microeconomics in order to denote the state of best possible operation of a product or service market. Economic efficiency assumes minimum cost for the production of a good or service, maximum output, and maximum surplus from the operation of the market.\n\n## What creates efficiency?\n\nEfficiency requires reducing the number of unnecessary resources used to produce a given output including personal time and energy. It is a measurable concept that can be determined using the ratio of useful output to total input.\n\n## What is simple machine efficiency?\n\nThe efficiency output of a machine is simply the output work divided by the input work, and is usually multiplied by 100 so that it is expressed as a percent. % efficiency=WoWi×100. Look back at the pictures of the simple machines and think about which would have the highest efficiency.\n\n## Why is efficiency less than 1?\n\nSince a machine does not contain a source of energy, nor can it store energy, from conservation of energy the power output of a machine can never be greater than its input, so the efficiency can never be greater than 1.\n\n## How can I live effectively?\n\nHere are 101 ways to live your life to the fullest:Live every day on a fresh new start. … Be true to who you are. … Quit complaining. … Be proactive. … Rather than think “what if,” think “next time.” Don’t think about the things you can’t change. … Focus on WHAT vs. … Create your own opportunities. … Live consciously each day.More items…\n\n## What is efficiency with example?\n\nEfficiency is defined as the ability to produce something with a minimum amount of effort. An example of efficiency is a reduction in the number of workers needed to make a car. noun.\n\n## What is the unit of efficiency?\n\nThe efficiency is the energy output, divided by the energy input, and expressed as a percentage. A perfect process would have an efficiency of 100%. Wout = the work or energy produced by a process. Units are Joules (J).\n\n## Can you improve work and increase efficiency?\n\nPeople who consistently accomplish their goals by improving work efficiency do so by creating sustainable habits. Develop a routine that puts you in the best possible state to be productive at work. … When you create a routine that makes you feel happy, healthy and clear-minded, your work efficiency will skyrocket.\n\n## Why is efficiency important in the workplace?\n\nEfficiency at the workplace is of utmost importance. It is the key to achieve goals and results and it is the best way to get our projects and tasks done. When we are efficient, we learn how to prioritize tasks and how to delegate those that can be done by somebody else under our supervision.\n\n## What is production efficiency?\n\nProduction efficiency is an economic term describing a level in which an economy or entity can no longer produce additional amounts of a good without lowering the production level of another product. … Productive efficiency similarly means that an entity is operating at maximum capacity.\n\n## How do you calculate work?\n\nWork can be calculated with the equation: Work = Force × Distance. The SI unit for work is the joule (J), or Newton • meter (N • m). One joule equals the amount of work that is done when 1 N of force moves an object over a distance of 1 m.\n\n## What are the types of efficiency?\n\nWhen the term efficiency is used in the field of law and economics, it generally refers to the so-called economic efficiency, which can be subdivided into two types: productive or technical efficiency and allocative efficiency. These categories together form the overall economic efficiency (Coelli et al.\n\n## Can machines be 100% efficient?\n\nIn other words, no machine can be more than 100% efficient. Machines cannot multiply energy or work input. … If a machine were 100% efficient then it can’t have any energy losses to friction, so no friction can be present.\n\n## Is command economy good or bad?\n\nCommand economy advantages include low levels of inequality and unemployment and the common good replacing profit as the primary incentive of production. Command economy disadvantages include lack of competition and lack of efficiency.\n\n## What is work formula?\n\nWe can calculate work by multiplying the force by the movement of the object. W = F × d. Unit. The SI unit of work is the joule (J)\n\n## What is the formula for calculating energy efficiency?\n\nEnergy efficiency is calculated by dividing the energy obtained (useful energy or energy output) by the initial energy (energy input). For example, a refrigerator has an energy efficiency of 20 to 50%, an incandescent bulb about 5%, a LED lamp over 30%, and a wind turbine 59% at most." ]	[ null, "https://mc.yandex.ru/watch/74507773", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.92918205,"math_prob":0.8471171,"size":7036,"snap":"2021-21-2021-25","text_gpt3_token_len":1420,"char_repetition_ratio":0.19553469,"word_repetition_ratio":0.07394958,"special_character_ratio":0.20750426,"punctuation_ratio":0.10421456,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97285545,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-05-08T08:34:41Z\",\"WARC-Record-ID\":\"<urn:uuid:57b5c8cd-bc4d-47a0-b9af-f33050e11a8b>\",\"Content-Length\":\"43340\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:02720481-0cb8-460d-a4f0-0dc6a95a8869>\",\"WARC-Concurrent-To\":\"<urn:uuid:611d7848-6e27-4e00-a761-94e8ba566dcd>\",\"WARC-IP-Address\":\"193.200.75.42\",\"WARC-Target-URI\":\"https://afternoons-delight.com/qa/quick-answer-what-is-the-principle-of-efficiency.html\",\"WARC-Payload-Digest\":\"sha1:RGRLCYUOUWCNVWNIVYD2IAJBWNT2AU6H\",\"WARC-Block-Digest\":\"sha1:LGN3JJ4XCR4N2KCIIJTZVQELYZ4FZVOK\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-21/CC-MAIN-2021-21_segments_1620243988850.21_warc_CC-MAIN-20210508061546-20210508091546-00542.warc.gz\"}"}
https://answers.everydaycalculation.com/compare-fractions/42-3-and-25-24	[ "Solutions by everydaycalculation.com\n\n## Compare 42/3 and 25/24\n\n1st number: 14 0/3, 2nd number: 1 1/24\n\n42/3 is greater than 25/24\n\n#### Steps for comparing fractions\n\n1. Find the least common denominator or LCM of the two denominators:\nLCM of 3 and 24 is 24\n\nNext, find the equivalent fraction of both fractional numbers with denominator 24\n2. For the 1st fraction, since 3 × 8 = 24,\n42/3 = 42 × 8/3 × 8 = 336/24\n3. Likewise, for the 2nd fraction, since 24 × 1 = 24,\n25/24 = 25 × 1/24 × 1 = 25/24\n4. Since the denominators are now the same, the fraction with the bigger numerator is the greater fraction\n5. 336/24 > 25/24 or 42/3 > 25/24\n\nMathStep (Works offline)", null, "Download our mobile app and learn to work with fractions in your own time:" ]	[ null, "https://answers.everydaycalculation.com/mathstep-app-icon.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.84360904,"math_prob":0.99565834,"size":880,"snap":"2021-31-2021-39","text_gpt3_token_len":328,"char_repetition_ratio":0.2089041,"word_repetition_ratio":0.0,"special_character_ratio":0.4431818,"punctuation_ratio":0.07035176,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9940321,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-08-05T18:53:08Z\",\"WARC-Record-ID\":\"<urn:uuid:6572957e-d166-4731-ab82-80b33aff024f>\",\"Content-Length\":\"7799\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:291415a7-55c1-4f72-adef-217aa09a1fa0>\",\"WARC-Concurrent-To\":\"<urn:uuid:5c92ccf2-fd09-45fd-b194-88363e11419b>\",\"WARC-IP-Address\":\"96.126.107.130\",\"WARC-Target-URI\":\"https://answers.everydaycalculation.com/compare-fractions/42-3-and-25-24\",\"WARC-Payload-Digest\":\"sha1:BNEGPLEPS4YKRUJZ4WXDSMKVJWIPLIJI\",\"WARC-Block-Digest\":\"sha1:KAXT5SBAZ2AFNLTDP44F5WUQFMGSRR6Y\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-31/CC-MAIN-2021-31_segments_1627046156141.29_warc_CC-MAIN-20210805161906-20210805191906-00256.warc.gz\"}"}