Datasets:

Infi-MM
/

InfiMM-WebMath-40B

Dataset card Data Studio Files Files and versions Community

Split (1)

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

Subsets and Splits

No community queries yet

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

URL stringlengths 15 1.68k	text_list sequencelengths 1 199	image_list sequencelengths 1 199	metadata stringlengths 1.19k 3.08k
https://cran.uni-muenster.de:443/web/packages/dsmisc/readme/README.html	[ "# Data Science Box of Pandora Miscellaneous\n\nStatus", null, "", null, "", null, "", null, "", null, "", null, "lines of R code: 83, lines of test code: 27\n\nVersion\n\n0.3.3 ( 2020-09-11 18:11:12 )\n\nDescription\n\nTool collection for common and not so common data science use cases. This includes custom made algorithms for data management as well as value calculations that are hard to find elsewhere because of their specificity but would be a waste to get lost nonetheless. Currently available functionality: find sub-graphs in an edge list data.frame, find mode or modes in a vector of values, extract (a) specific regular expression group(s), generate ISO time stamps that play well with file names, or generate URL parameter lists by expanding value combinations.\n\nGPL (>= 2)\nPeter Meissner [aut, cre]\n\nCitation\n\n``citation(\"dsmisc\")``\n``Meissner P (2020). dsmisc: Data Science Box of Pandora Miscellaneous. R package version 0.3.3.``\n\nBibTex for citing\n\n``toBibtex(citation(\"dsmisc\"))``\n``````@Manual{,\ntitle = {dsmisc: Data Science Box of Pandora Miscellaneous},\nauthor = {Peter Meissner},\nyear = {2020},\nnote = {R package version 0.3.3},\n}``````\n\nInstallation\n\nStable version from CRAN:\n\n``install.packages(\"dsmisc\")``\n\n## Usage\n\nstarting up …\n\n``library(\"dsmisc\")``\n\n### Graph computations\n\nfind isolated graphs / networks\n\nA graph described by an edgelist with two distinct subgraphs.\n\n``````edges_df <-\ndata.frame(\nnode_1 = c(1:5, 10:8),\nnode_2 = c(2:6, 7,7,7)\n)\n\nedges_df``````\n``````## node_1 node_2\n## 1 1 2\n## 2 2 3\n## 3 3 4\n## 4 4 5\n## 5 5 6\n## 6 10 7\n## 7 9 7\n## 8 8 7``````\n\nFinding subgraphs and grouping them together via subgraph id.\n\n``````edges_df\\$subgraph_id <-\ngraphs_find_subgraphs(\nid_1 = edges_df\\$node_1,\nid_2 = edges_df\\$node_2,\nverbose = 0\n)\n\nedges_df``````\n``````## node_1 node_2 subgraph_id\n## 1 1 2 1\n## 2 2 3 1\n## 3 3 4 1\n## 4 4 5 1\n## 5 5 6 1\n## 6 10 7 2\n## 7 9 7 2\n## 8 8 7 2``````\n\nspeedtest for large graph\n\n``````edges_df <-\ndata.frame(\nnode_1 = sample(x = 1:10000, size = 10^5, replace = TRUE),\nnode_2 = sample(x = 1:10000, size = 10^5, replace = TRUE)\n)\n\nsystem.time({\nedges_df\\$subgraph_id <-\ngraphs_find_subgraphs(\nid_1 = edges_df\\$node_1,\nid_2 = edges_df\\$node_2,\nverbose = 0\n)\n})``````\n``````## user system elapsed\n## 2.96 0.01 3.02``````\n\n### Stats Functions\n\nCalculating the modus from a collection of values\n\n``````# one modus only\nstats_mode(1:10)``````\n``````## Warning in stats_mode(1:10): modus : multimodal but only one value returned (use warn=FALSE to turn this off)\n\n## 1``````\n``````# all values if multiple modi are found\nstats_mode_multi(1:10)``````\n``## 1 2 3 4 5 6 7 8 9 10``\n\n### String Functions\n\n{stringr} / {stringi} packages are cool … but can they do this (actually they can, of cause but with a little more work and cognitive load needed, e.g.: `stringr::str_match(strings, \"([\\\\w])_(?:\\\\d+)\")[, 2]`)?\n\nExtract specific RegEx groups\n\n``````strings <- paste(LETTERS, seq_along(LETTERS), sep = \"_\")\n\n# whole pattern\nstr_group_extract(strings, \"([\\\\w])_(\\\\d+)\")``````\n``````## \"A_1\" \"B_2\" \"C_3\" \"D_4\" \"E_5\" \"F_6\" \"G_7\" \"H_8\" \"I_9\" \"J_10\" \"K_11\" \"L_12\" \"M_13\" \"N_14\" \"O_15\"\n## \"P_16\" \"Q_17\" \"R_18\" \"S_19\" \"T_20\" \"U_21\" \"V_22\" \"W_23\" \"X_24\" \"Y_25\" \"Z_26\"``````\n``````# first group\nstr_group_extract(strings, \"([\\\\w])_(\\\\d+)\", 1)``````\n``## \"A\" \"B\" \"C\" \"D\" \"E\" \"F\" \"G\" \"H\" \"I\" \"J\" \"K\" \"L\" \"M\" \"N\" \"O\" \"P\" \"Q\" \"R\" \"S\" \"T\" \"U\" \"V\" \"W\" \"X\" \"Y\" \"Z\"``\n``````# second group\nstr_group_extract(strings, \"([\\\\w])_(\\\\d+)\", 2)``````\n``````## \"1\" \"2\" \"3\" \"4\" \"5\" \"6\" \"7\" \"8\" \"9\" \"10\" \"11\" \"12\" \"13\" \"14\" \"15\" \"16\" \"17\" \"18\" \"19\" \"20\" \"21\"\n## \"22\" \"23\" \"24\" \"25\" \"26\"``````\n\n### Data.Frame Manipulation\n\nTransform factor columns in a data.frame to character vectors\n\n``````df <-\ndata.frame(\na = 1:2,\nb = factor(c(\"a\", \"b\")),\nc = as.character(letters[3:4]),\nstringsAsFactors = FALSE\n)\nvapply(df, class, \"\")``````\n``````## a b c\n## \"integer\" \"factor\" \"character\"``````\n``````df_df <- df_defactorize(df)\nvapply(df_df, class, \"\")``````\n``````## a b c\n## \"integer\" \"character\" \"character\"``````\n\n### Time Manipulation\n\n``````# current time\ntime_stamp()``````\n``## \"2020-09-11_20_11_33\"``\n``````time_stamp(\nts = as.POSIXct(c(\"2010-01-27 10:23:45\", \"2010-01-27 10:23:45\")),\nsep = c(\"\",\"_\",\"\")\n)``````\n``## \"20100127_102345\" \"20100127_102345\"``\n``````time_stamp(\nts = as.POSIXct(c(\"2010-01-27 10:23:45\", \"2010-01-27 10:23:45\")),\nsep = c(\"\")\n)``````\n``## \"20100127102345\" \"20100127102345\"``\n\n### Web Scraping\n\nprepare multiple URLs via query parameter grid expansion\n\n``web_gen_param_list_expand(id=1:3, lang=c(\"en\", \"de\"))``\n``## \"id=1&lang=en\" \"id=2&lang=en\" \"id=3&lang=en\" \"id=1&lang=de\" \"id=2&lang=de\" \"id=3&lang=de\"``" ]	[ null, "https://api.travis-ci.org/petermeissner/dsmisc.svg", null, "https://ci.appveyor.com/api/projects/status/github/petermeissner/dsmisc", null, "https://codecov.io/gh/petermeissner/dsmisc/branch/master/graph/badge.svg", null, "http://www.r-pkg.org/badges/version/dsmisc", null, "http://cranlogs.r-pkg.org/badges/grand-total/dsmisc", null, "http://cranlogs.r-pkg.org/badges/dsmisc", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6222588,"math_prob":0.89350384,"size":4132,"snap":"2023-14-2023-23","text_gpt3_token_len":1604,"char_repetition_ratio":0.090358526,"word_repetition_ratio":0.075987846,"special_character_ratio":0.45232332,"punctuation_ratio":0.1433869,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9900831,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12],"im_url_duplicate_count":[null,6,null,6,null,6,null,6,null,6,null,6,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-06-10T17:19:54Z\",\"WARC-Record-ID\":\"<urn:uuid:245ec2ea-5104-4db8-aff3-74a1aa5fcc5f>\",\"Content-Length\":\"23959\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c9b2f191-4b30-4ab3-a4a5-a8ab2944f1d2>\",\"WARC-Concurrent-To\":\"<urn:uuid:273a0103-b95d-4029-a379-83ed7d9d170f>\",\"WARC-IP-Address\":\"128.176.130.197\",\"WARC-Target-URI\":\"https://cran.uni-muenster.de:443/web/packages/dsmisc/readme/README.html\",\"WARC-Payload-Digest\":\"sha1:3NVHQOMBELX6KGHCFQW22LLK47JLL4OE\",\"WARC-Block-Digest\":\"sha1:GTBBKXNZL5POO4SXZIXBACIYEHZS7VVE\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224657735.85_warc_CC-MAIN-20230610164417-20230610194417-00508.warc.gz\"}"}
https://leanprover-community.github.io/mathlib_docs/ring_theory/witt_vector/witt_polynomial.html	[ "# mathlibdocumentation\n\nring_theory.witt_vector.witt_polynomial\n\n# Witt polynomials #\n\nTo endow witt_vector p R with a ring structure, we need to study the so-called Witt polynomials.\n\nFix a base value p : ℕ. The p-adic Witt polynomials are an infinite family of polynomials indexed by a natural number n, taking values in an arbitrary ring R. The variables of these polynomials are represented by natural numbers. The variable set of the nth Witt polynomial contains at most n+1 elements {0, ..., n}, with exactly these variables when R has characteristic 0.\n\nThese polynomials are used to define the addition and multiplication operators on the type of Witt vectors. (While this type itself is not complicated, the ring operations are what make it interesting.)\n\nWhen the base p is invertible in R, the p-adic Witt polynomials form a basis for mv_polynomial ℕ R, equivalent to the standard basis.\n\n## Main declarations #\n\n• witt_polynomial p R n: the n-th Witt polynomial, viewed as polynomial over the ring R\n• X_in_terms_of_W p R n: if p is invertible, the polynomial X n is contained in the subalgebra generated by the Witt polynomials. X_in_terms_of_W p R n is the explicit polynomial, which upon being bound to the Witt polynomials yields X n.\n• bind₁_witt_polynomial_X_in_terms_of_W: the proof of the claim that bind₁ (X_in_terms_of_W p R) (W_ R n) = X n\n• bind₁_X_in_terms_of_W_witt_polynomial: the converse of the above statement\n\n## Notation #\n\nIn this file we use the following notation\n\n• p is a natural number, typically assumed to be prime.\n• R and S are commutative rings\n• W n (and W_ R n when the ring needs to be explicit) denotes the nth Witt polynomial" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7497128,"math_prob":0.9728251,"size":2714,"snap":"2021-43-2021-49","text_gpt3_token_len":769,"char_repetition_ratio":0.21254613,"word_repetition_ratio":0.035196688,"special_character_ratio":0.25829035,"punctuation_ratio":0.108949415,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9989238,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-18T01:36:05Z\",\"WARC-Record-ID\":\"<urn:uuid:f2c8d861-9c4a-48d2-a8c6-c23d20bff725>\",\"Content-Length\":\"433859\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:27cf96df-06df-4d4b-880c-cf92d078d541>\",\"WARC-Concurrent-To\":\"<urn:uuid:b5359218-ae6b-43de-ac9f-bedabed2ceef>\",\"WARC-IP-Address\":\"185.199.108.153\",\"WARC-Target-URI\":\"https://leanprover-community.github.io/mathlib_docs/ring_theory/witt_vector/witt_polynomial.html\",\"WARC-Payload-Digest\":\"sha1:6NDI2LFBKXPL3QSYV7NBNHPVLOBTVH7O\",\"WARC-Block-Digest\":\"sha1:7TALRKXFHKODWGIM775XPB6DMMHCIM37\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323585186.33_warc_CC-MAIN-20211018000838-20211018030838-00336.warc.gz\"}"}
https://mathoverflow.net/questions/331350/interior-smooth-regularity	[ "# Interior smooth regularity\n\nI recently read the PDE book of L. Evans, and in its chapter 6 some kinds of regularities of second-order elliptic equations were discussed. My question is about its proof of interior smooth regularity (thm 3 in Ch. 6.3.1).\n\nThe theorem asserts that if a second-order elliptic PDE $$Lu=f$$ has smooth coefficients and admits an $$H^1$$ weak solution $$u$$ on a bounded domain $$U\\subseteq \\mathbb R^n,$$ then $$u$$ is smooth.\n\nIn the statement of the theorem, no condition is assumed about $$\\partial U,$$ but in the book, the author would like to apply the general Sobolev inequality to assure $$u\\in C^\\infty(U)$$ if $$u\\in H^m_{\\text{loc}}(U)$$ for all $$m\\in\\mathbb N,$$ which can be obtained by the theorem 6 in its chapter 5.6.3, but with $$\\partial U$$ is $$C^1.$$\n\nMy problem is whether the regular assumption on the boundary is necessary. However, without the condition $$\\partial U$$ being $$C^1,$$ I only know some Sobolev inequality about $$W^{k,p}_0(U).$$ I am not sure if these are sufficient to derive the desired conclusion (since I don't know the behavior of $$u$$ near the boundary a priori). Perhaps there are alternatives to this problem, or the conclusion is just wrong without the boundary assumption?\n\nThanks in advance!\n\n## 2 Answers\n\nI assume that you require $$f\\in C^\\infty(U)$$. You do not need regularity of the boundary of $$U\\subset \\mathbb{R}^N$$. The condition $$u\\in H^m_{loc}(U)$$ is equivalent with $$\\widetilde{\\phi u}\\in H^m(\\mathbb{R}^N)$$, for any $$\\phi\\in C^\\infty_0(U)$$. Here $$\\widetilde{g}$$ denotes the extension of the function $$g:U\\to\\mathbb{R}$$ by zero outside $$U$$. Apply the Sobolev embedding theorems to $$\\widetilde{\\phi u}$$.\n\nI strongly recommend opening Brezis' book on functional anaylsis and pde's.\n\n• Thanks! You are right that I forgot to say $f$ is smooth. This is the answer I am looking for! Is this a common technique as dealing with such a problem? – tommy xu3 May 12 at 11:50\n• Yes. For another approach in the general case check Sec 10.3.2. of these notes www3.nd.edu/~lnicolae/Lectures.pdf – Liviu Nicolaescu May 12 at 12:12\n• This helps me a lot, and thanks for your suggestions about good references! – tommy xu3 May 12 at 12:24\n\nIf I understand your question correctly, you speak about interior regularity. Let me quote a classical result for linear elliptic equations with $$C^\\infty$$ coefficients, even true for pseudo-differential equations.\n\nLet $$P$$ be an elliptic differential operator with $$C^\\infty$$ coefficients in an open subset $$\\Omega$$ of $$\\mathbb R^N$$. Then for $$u$$ a distribution on $$\\Omega$$, $$Pu\\in C^\\infty(\\Omega)\\Longrightarrow u\\in C^\\infty(\\Omega).$$ You may refine that result in the Sobolev scale with $$Pu\\in H^s_{loc}(\\Omega)\\Longrightarrow u\\in H^{s+m}_{loc}(\\Omega),$$ where $$m$$ is the order of $$P$$. If you like the wave-front-set, you have $$WF(Pu)\\subset WF(u)\\subset WF(Pu)\\cup \\text{char}P,$$ and in the elliptic case $$\\text{char}P=\\emptyset$$. You can also formulate a result on the $$H^s$$ wave-front-set.\n\n• Thank you! So this result doesn't require any assumption on the boundary of $\\Omega?$ – tommy xu3 May 12 at 11:04\n• No, you do not need any assumption on the boundary for this result. – Bazin May 12 at 16:43\n• Thank you. I will also try to see more general theorems like what you mentioned! – tommy xu3 May 17 at 4:53" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.94867235,"math_prob":0.9995548,"size":1209,"snap":"2019-13-2019-22","text_gpt3_token_len":318,"char_repetition_ratio":0.09460581,"word_repetition_ratio":0.0,"special_character_ratio":0.254756,"punctuation_ratio":0.103174604,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9999428,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-05-20T06:03:27Z\",\"WARC-Record-ID\":\"<urn:uuid:c2282a46-ac7b-404f-94c8-79b69b6b3d11>\",\"Content-Length\":\"127788\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d8b89509-798b-4803-b773-7ed93d4f9bca>\",\"WARC-Concurrent-To\":\"<urn:uuid:94b61760-25d2-4b12-b59d-69d9762cb659>\",\"WARC-IP-Address\":\"151.101.65.69\",\"WARC-Target-URI\":\"https://mathoverflow.net/questions/331350/interior-smooth-regularity\",\"WARC-Payload-Digest\":\"sha1:7Y5WIKLSCCJVMD66EXZKYXDDVVO7QDKC\",\"WARC-Block-Digest\":\"sha1:NPZCDBNYJKNK5CHLBOMMLFG5EVFRHVKX\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-22/CC-MAIN-2019-22_segments_1558232255562.23_warc_CC-MAIN-20190520041753-20190520063753-00366.warc.gz\"}"}
http://forums.wolfram.com/mathgroup/archive/2008/Nov/msg00414.html	[ "", null, "", null, "", null, "", null, "", null, "", null, "", null, "Re: Reduce[a^x + b^x - 2 == 0, x]\n\n• To: mathgroup at smc.vnet.net\n• Subject: [mg93654] Re: Reduce[a^x + b^x - 2 == 0, x]\n• From: \"sjoerd.c.devries at gmail.com\" <sjoerd.c.devries at gmail.com>\n• Date: Thu, 20 Nov 2008 04:57:27 -0500 (EST)\n• References: <gg0qcu\\$9j\\[email protected]>\n\n```It seems the equation is not solvable in an algebraic way. However, I\ngive you one solution: x=0. Depending on a and b there may be one\nother solution.\n\nYou should probably try to solve this numerically.\n\nCheers -- Sjoerd\n\nOn Nov 19, 12:39 pm, \"Severin Posta\" <seve... at km1.fjfi.cvut.cz> wrote:\n> If I put\n>\n> Reduce[a^x + b^x - 2 == 0, x]\n>\n> into Mathematica 6.0.0 Win32, I get no result. System is running computat=\nion\n> several days - probably forever :)\n>\n> S.\n\n```\n\n• Prev by Date: FFT in Mathematica\n• Next by Date: Re: List of Month Names\n• Previous by thread: Reduce[a^x + b^x - 2 == 0, x]\n• Next by thread: Re: Reduce[a^x + b^x - 2 == 0, x]" ]	[ null, "http://forums.wolfram.com/mathgroup/images/head_mathgroup.gif", null, "http://forums.wolfram.com/mathgroup/images/head_archive.gif", null, "http://forums.wolfram.com/mathgroup/images/numbers/2.gif", null, "http://forums.wolfram.com/mathgroup/images/numbers/0.gif", null, "http://forums.wolfram.com/mathgroup/images/numbers/0.gif", null, "http://forums.wolfram.com/mathgroup/images/numbers/8.gif", null, "http://forums.wolfram.com/mathgroup/images/search_archive.gif", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7926654,"math_prob":0.8798185,"size":745,"snap":"2019-35-2019-39","text_gpt3_token_len":273,"char_repetition_ratio":0.10121457,"word_repetition_ratio":0.10606061,"special_character_ratio":0.38120806,"punctuation_ratio":0.24064171,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9925847,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-09-18T15:18:44Z\",\"WARC-Record-ID\":\"<urn:uuid:97fb53f8-4041-4645-a113-c70b27293b42>\",\"Content-Length\":\"42450\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9cac0a55-d769-4746-9a02-0b8b76147ca5>\",\"WARC-Concurrent-To\":\"<urn:uuid:ebee6c27-6d40-478b-a61c-27330f705e38>\",\"WARC-IP-Address\":\"140.177.205.73\",\"WARC-Target-URI\":\"http://forums.wolfram.com/mathgroup/archive/2008/Nov/msg00414.html\",\"WARC-Payload-Digest\":\"sha1:WPKSZWJFLJEY6JKNBCV3FKQNVGNWKEFQ\",\"WARC-Block-Digest\":\"sha1:BT4KA4XHTACWRVAQS3DMWO3ZRE76N7OI\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-39/CC-MAIN-2019-39_segments_1568514573289.83_warc_CC-MAIN-20190918131429-20190918153429-00368.warc.gz\"}"}
http://plasmasturm.org/log/kolmoguni/	[ "# Real as can be, after all?\n\nThursday, 13 Feb 2014\n\nIt is possible to consider that the value of π is not infinite because it is recursively enumerable. You can make as many correct digits as you like using finite means. I think some scientists are thinking this means that π doesn’t “actually” have an infinite number of digits, because there are simple rules for getting as many as you need, without limit.\n\nHowever, there is another arena well known to physicists where an “actual infinity” is much harder to exorcise, and that is the randomness that seems to be built in at a basic level in quantum mechanics. It is now known, thanks to recent results, that it is possible to certify that a sequence of bits produced by quantum processes are truly, irreducibly random. It is also known that it is not possible to compute an irreducibly random sequence of indefinite length using a program of finite size. So as far as I can see, this means that the universe is not any sort of computer, because if it were it would not be possible to physically certify that a random sequence is random.\n\nIf my layman’s understanding is correct, the result is essentially that the Kolmogorov complexity of the universe was shown to be at least “equivalent” to the “size” of the universe, which rules out the possibility of it being the result of computation. (Contrasting with the fact that π can be computed because, even though it is a non-repeating infinite series in the decimal system, its Kolmogorov complexity is yet very modest. (That is not hard to conceive. A trivial way to create a non-repeating infinite series is to emit a series of 1s separated by an always-increasing number of 0s. Cycle length: ∞; Kolmogorov complexity: ~0.))\n\nIf this is correct, and true, I find it very exciting. I always found the concept of the universe as a kind of simulation profoundly unsatisfying, due to the infinite regress that is immediately invoked: is that computer itself simulated, in turn? If so, does the chain end? If it does, why/how there? It all seems like multiplication of entities that achieves nothing in exchange for opening up unlimited arbitrariness potential." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.97361875,"math_prob":0.87431103,"size":2134,"snap":"2021-43-2021-49","text_gpt3_token_len":462,"char_repetition_ratio":0.11032864,"word_repetition_ratio":0.0,"special_character_ratio":0.20431115,"punctuation_ratio":0.100961536,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97760415,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-22T13:01:58Z\",\"WARC-Record-ID\":\"<urn:uuid:ffbf183b-7d95-4b31-8c51-9e343b16db17>\",\"Content-Length\":\"4104\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4164b949-0fe8-4e1f-aae8-7a554d243d45>\",\"WARC-Concurrent-To\":\"<urn:uuid:59fdb177-902d-4af9-936b-69aff43652a9>\",\"WARC-IP-Address\":\"79.140.42.73\",\"WARC-Target-URI\":\"http://plasmasturm.org/log/kolmoguni/\",\"WARC-Payload-Digest\":\"sha1:QHJYPII6SMGT5OOSCXLEY7BWIQXX6EJG\",\"WARC-Block-Digest\":\"sha1:6Q7BTYAYBJDU7PP4IWPEYM7X5PAN2ZUL\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323585507.26_warc_CC-MAIN-20211022114748-20211022144748-00372.warc.gz\"}"}
https://www.answers.com/Q/How_many_quarts_are_in_a_pound	[ "# How many quarts are in a pound?\n\nA quart is a unit of volume, and a pound is a unit of weight, so there is no direct conversion of the two. If we know what substance we are talking about (such as water, for example) we could then ask how much a quart of water weighs (about two pounds, but I am estimating)." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9560183,"math_prob":0.9971805,"size":1944,"snap":"2019-35-2019-39","text_gpt3_token_len":486,"char_repetition_ratio":0.20670103,"word_repetition_ratio":0.07197943,"special_character_ratio":0.24794239,"punctuation_ratio":0.101149425,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9724114,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-08-17T10:41:25Z\",\"WARC-Record-ID\":\"<urn:uuid:61a5ef2b-cb5c-4042-bd7e-d3283ce7acd2>\",\"Content-Length\":\"161234\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9b7cf734-08ca-4534-a1d3-8e1419211f3f>\",\"WARC-Concurrent-To\":\"<urn:uuid:8224b7b8-1ff7-48b7-b2ca-8bc2775a52b8>\",\"WARC-IP-Address\":\"151.101.248.203\",\"WARC-Target-URI\":\"https://www.answers.com/Q/How_many_quarts_are_in_a_pound\",\"WARC-Payload-Digest\":\"sha1:O224AYSD7JV3O5S32HXFPEVDTSGRUX3J\",\"WARC-Block-Digest\":\"sha1:NMK7WEWIF2I6U4WNFIKKN5MVBZQ3FB2T\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-35/CC-MAIN-2019-35_segments_1566027312128.3_warc_CC-MAIN-20190817102624-20190817124624-00325.warc.gz\"}"}
https://www.mathworks.com/help/matlab/ref/quadv.html?refresh=true	[ "Documentation\n\n`quadv` is not recommended. Use `integral` with the `'ArrayValued'` option instead.\n\n## Syntax\n\n```Q = quadv(fun,a,b) Q = quadv(fun,a,b,tol) Q = quadv(fun,a,b,tol,trace) [Q,fcnt] = quadv(...) ```\n\n## Description\n\n`Q = quadv(fun,a,b)` approximates the integral of the complex array-valued function `fun` from `a` to `b` to within an error of `1.e-6` using recursive adaptive Simpson quadrature. `fun` is a function handle. The function `Y = fun(x)` should accept a scalar argument `x` and return an array result `Y`, whose components are the integrands evaluated at `x`. Limits `a` and `b` must be finite.\n\nParameterizing Functions explains how to provide addition parameters to the function `fun`, if necessary.\n\n`Q = quadv(fun,a,b,tol)` uses the absolute error tolerance `tol` for all the integrals instead of the default, which is `1.e-6`.\n\n### Note\n\nThe same tolerance is used for all components, so the results obtained with `quadv` are usually not the same as those obtained with `quad` on the individual components.\n\n`Q = quadv(fun,a,b,tol,trace)` with non-zero `trace` shows the values of ```[fcnt a b-a Q(1)]``` during the recursion.\n\n`[Q,fcnt] = quadv(...)` returns the number of function evaluations.\n\n• The `quad` function might be most efficient for low accuracies with nonsmooth integrands.\n\n• The `quadl` function might be more efficient than `quad` at higher accuracies with smooth integrands.\n\n• The `quadgk` function might be most efficient for high accuracies and oscillatory integrands. It supports infinite intervals and can handle moderate singularities at the endpoints. It also supports contour integration along piecewise linear paths.\n\n• The `quadv` function vectorizes `quad` for an array-valued `fun`.\n\n• If the interval is infinite, $\\left[a,\\infty \\right)$, then for the integral of `fun(x)` to exist, `fun(x)` must decay as `x` approaches infinity, and `quadgk` requires it to decay rapidly. Special methods should be used for oscillatory functions on infinite intervals, but `quadgk` can be used if `fun(x)` decays fast enough.\n\n• The `quadgk` function will integrate functions that are singular at finite endpoints if the singularities are not too strong. For example, it will integrate functions that behave at an endpoint `c` like `log\|x-c\|` or `\|x-c\|p` for ```p >= -1/2```. If the function is singular at points inside `(a,b)`, write the integral as a sum of integrals over subintervals with the singular points as endpoints, compute them with `quadgk`, and add the results.\n\n## Examples\n\nFor the parameterized array-valued function `myarrayfun`, defined by\n\n```function Y = myarrayfun(x,n) Y = 1./((1:n)+x);```\n\nthe following command integrates `myarrayfun`, for the parameter value n = 10 between a = 0 and b = 1:\n\n`Qv = quadv(@(x)myarrayfun(x,10),0,1);`\n\nThe resulting array `Qv` has 10 elements estimating ```Q(k) = log((k+1)./(k))```, for `k = 1:10`.\n\nThe entries in `Qv` are slightly different than if you compute the integrals using `quad` in a loop:\n\n```for k = 1:10 Qs(k) = quadv(@(x)myscalarfun(x,k),0,1); end```\n\nwhere `myscalarfun` is:\n\n```function y = myscalarfun(x,k) y = 1./(k+x);```" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7029684,"math_prob":0.9963878,"size":3120,"snap":"2019-51-2020-05","text_gpt3_token_len":858,"char_repetition_ratio":0.14634146,"word_repetition_ratio":0.008048289,"special_character_ratio":0.23942308,"punctuation_ratio":0.14376996,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99842274,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-08T03:52:23Z\",\"WARC-Record-ID\":\"<urn:uuid:c98f1d80-5720-4e57-bf5b-2c319d06ccac>\",\"Content-Length\":\"70680\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:bc60f48c-3d04-4976-beb0-17891906af40>\",\"WARC-Concurrent-To\":\"<urn:uuid:ef7c09a8-e2aa-4f93-8762-ed4ef0341457>\",\"WARC-IP-Address\":\"23.5.129.95\",\"WARC-Target-URI\":\"https://www.mathworks.com/help/matlab/ref/quadv.html?refresh=true\",\"WARC-Payload-Digest\":\"sha1:2QH26LGQTY2JFL7BLQIAUJSZXFQMABBV\",\"WARC-Block-Digest\":\"sha1:TGBT44Z36VPN2ZGEC5KS7SKNB32KAON5\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575540504338.31_warc_CC-MAIN-20191208021121-20191208045121-00492.warc.gz\"}"}
http://gluon-ts.mxnet.io/master/api/gluonts/gluonts.mx.distribution.html	[ "# gluonts.mx.distribution package¶\n\nclass gluonts.mx.distribution.Distribution[source]\n\nBases: object\n\nA class representing probability distributions.\n\nproperty all_dim\n\nNumber of overall dimensions.\n\narg_names: Tuple = None\nproperty args\nproperty batch_dim\n\nNumber of batch dimensions, i.e., length of the batch_shape tuple.\n\nproperty batch_shape\n\nLayout of the set of events contemplated by the distribution.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape, and computing log_prob (or loss more in general) on such sample will yield a tensor of shape batch_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\ncdf(x: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nReturns the value of the cumulative distribution function evaluated at x\n\ncrps(x: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nCompute the continuous rank probability score (CRPS) of x according to the distribution.\n\nParameters\n\nx – Tensor of shape (batch_shape, event_shape).\n\nReturns\n\nTensor of shape batch_shape containing the CRPS score, according to the distribution, for each event in x.\n\nReturn type\n\nTensor\n\nproperty event_dim\n\nNumber of event dimensions, i.e., length of the event_shape tuple.\n\nThis is 0 for distributions over scalars, 1 over vectors, 2 over matrices, and so on.\n\nproperty event_shape\n\nShape of each individual event contemplated by the distribution.\n\nFor example, distributions over scalars have event_shape = (), over vectors have event_shape = (d, ) where d is the length of the vectors, over matrices have event_shape = (d1, d2), and so on.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\nis_reparameterizable = False\nlog_prob(x: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nCompute the log-density of the distribution at x.\n\nParameters\n\nx – Tensor of shape (batch_shape, event_shape).\n\nReturns\n\nTensor of shape batch_shape containing the log-density of the distribution for each event in x.\n\nReturn type\n\nTensor\n\nloss(x: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nCompute the loss at x according to the distribution.\n\nBy default, this method returns the negative of log_prob. For some distributions, however, the log-density is not easily computable and therefore other loss functions are computed.\n\nParameters\n\nx – Tensor of shape (batch_shape, event_shape).\n\nReturns\n\nTensor of shape batch_shape containing the value of the loss for each event in x.\n\nReturn type\n\nTensor\n\nproperty mean\n\nTensor containing the mean of the distribution.\n\nprob(x: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nCompute the density of the distribution at x.\n\nParameters\n\nx – Tensor of shape (batch_shape, event_shape).\n\nReturns\n\nTensor of shape batch_shape containing the density of the distribution for each event in x.\n\nReturn type\n\nTensor\n\nquantile(level: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nCalculates quantiles for the given levels.\n\nParameters\n\nlevel – Level values to use for computing the quantiles. level should be a 1d tensor of level values between 0 and 1.\n\nReturns\n\nQuantile values corresponding to the levels passed. The return shape is\n\n(num_levels, …DISTRIBUTION_SHAPE…),\n\nwhere DISTRIBUTION_SHAPE is the shape of the underlying distribution.\n\nReturn type\n\nquantiles\n\nsample(num_samples: Optional[int] = None, dtype=<class 'numpy.float32'>) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nDraw samples from the distribution.\n\nIf num_samples is given the first dimension of the output will be num_samples.\n\nParameters\n• num_samples – Number of samples to to be drawn.\n\n• dtype – Data-type of the samples.\n\nReturns\n\nA tensor containing samples. This has shape (batch_shape, eval_shape) if num_samples = None and (num_samples, batch_shape, eval_shape) otherwise.\n\nReturn type\n\nTensor\n\nsample_rep(num_samples: Optional[int] = None, dtype=<class 'numpy.float32'>) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\nslice_axis(axis: int, begin: int, end: Optional[int]) → gluonts.mx.distribution.distribution.Distribution[source]\nproperty stddev\n\nTensor containing the standard deviation of the distribution.\n\nproperty variance\n\nTensor containing the variance of the distribution.\n\nclass gluonts.mx.distribution.DistributionOutput[source]\n\nClass to construct a distribution given the output of a network.\n\ndistr_cls: type = None\ndistribution(distr_args, loc: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol, None] = None, scale: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol, None] = None) → gluonts.mx.distribution.distribution.Distribution[source]\n\nConstruct the associated distribution, given the collection of constructor arguments and, optionally, a scale tensor.\n\nParameters\n• distr_args – Constructor arguments for the underlying Distribution type.\n\n• loc – Optional tensor, of the same shape as the batch_shape+event_shape of the resulting distribution.\n\n• scale – Optional tensor, of the same shape as the batch_shape+event_shape of the resulting distribution.\n\ndomain_map(F, args: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol])[source]\n\nConverts arguments to the right shape and domain. The domain depends on the type of distribution, while the correct shape is obtained by reshaping the trailing axis in such a way that the returned tensors define a distribution of the right event_shape.\n\nproperty event_dim\n\nNumber of event dimensions, i.e., length of the event_shape tuple, of the distributions that this object constructs.\n\nproperty event_shape\n\nShape of each individual event contemplated by the distributions that this object constructs.\n\nproperty value_in_support\n\nA float that will have a valid numeric value when computing the log-loss of the corresponding distribution. By default 0.0. This value will be used when padding data series.\n\nclass gluonts.mx.distribution.StudentTOutput[source]\nargs_dim: Dict[str, int] = {'mu': 1, 'nu': 1, 'sigma': 1}\ndistr_cls\n\nalias of StudentT\n\nclassmethod domain_map(F, mu, sigma, nu)[source]\n\nConverts arguments to the right shape and domain. The domain depends on the type of distribution, while the correct shape is obtained by reshaping the trailing axis in such a way that the returned tensors define a distribution of the right event_shape.\n\nproperty event_shape\n\nShape of each individual event contemplated by the distributions that this object constructs.\n\nclass gluonts.mx.distribution.StudentT(mu: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], sigma: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], nu: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], F=None)[source]\n\nStudent’s t-distribution.\n\nParameters\n• mu – Tensor containing the means, of shape (batch_shape, event_shape).\n\n• sigma – Tensor containing the standard deviations, of shape (batch_shape, event_shape).\n\n• nu – Nonnegative tensor containing the degrees of freedom of the distribution, of shape (batch_shape, event_shape).\n\n• F\n\nproperty F\narg_names = None\nproperty args\nproperty batch_shape\n\nLayout of the set of events contemplated by the distribution.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape, and computing log_prob (or loss more in general) on such sample will yield a tensor of shape batch_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\nproperty event_dim\n\nNumber of event dimensions, i.e., length of the event_shape tuple.\n\nThis is 0 for distributions over scalars, 1 over vectors, 2 over matrices, and so on.\n\nproperty event_shape\n\nShape of each individual event contemplated by the distribution.\n\nFor example, distributions over scalars have event_shape = (), over vectors have event_shape = (d, ) where d is the length of the vectors, over matrices have event_shape = (d1, d2), and so on.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\nis_reparameterizable = False\nlog_prob(x: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nCompute the log-density of the distribution at x.\n\nParameters\n\nx – Tensor of shape (batch_shape, event_shape).\n\nReturns\n\nTensor of shape batch_shape containing the log-density of the distribution for each event in x.\n\nReturn type\n\nTensor\n\nproperty mean\n\nTensor containing the mean of the distribution.\n\nsample(num_samples: Optional[int] = None, dtype=<class 'numpy.float32'>) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nDraw samples from the distribution.\n\nIf num_samples is given the first dimension of the output will be num_samples.\n\nParameters\n• num_samples – Number of samples to to be drawn.\n\n• dtype – Data-type of the samples.\n\nReturns\n\nA tensor containing samples. This has shape (batch_shape, eval_shape) if num_samples = None and (num_samples, batch_shape, eval_shape) otherwise.\n\nReturn type\n\nTensor\n\nproperty stddev\n\nTensor containing the standard deviation of the distribution.\n\nclass gluonts.mx.distribution.GammaOutput[source]\nargs_dim: Dict[str, int] = {'alpha': 1, 'beta': 1}\ndistr_cls\n\nalias of Gamma\n\nclassmethod domain_map(F, alpha, beta)[source]\n\nMaps raw tensors to valid arguments for constructing a Gamma distribution.\n\nParameters\n• F\n\n• alpha – Tensor of shape (batch_shape, 1)\n\n• beta – Tensor of shape (batch_shape, 1)\n\nReturns\n\nTwo squeezed tensors, of shape (batch_shape): both have entries mapped to the positive orthant.\n\nReturn type\n\nTuple[Tensor, Tensor]\n\nproperty event_shape\n\nShape of each individual event contemplated by the distributions that this object constructs.\n\nproperty value_in_support\n\nA float that will have a valid numeric value when computing the log-loss of the corresponding distribution. By default 0.0. This value will be used when padding data series.\n\nclass gluonts.mx.distribution.Gamma(alpha: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], beta: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol])[source]\n\nGamma distribution.\n\nParameters\n• alpha – Tensor containing the shape parameters, of shape (batch_shape, event_shape).\n\n• beta – Tensor containing the rate parameters, of shape (batch_shape, event_shape).\n\n• F\n\nproperty F\narg_names = None\nproperty args\nproperty batch_shape\n\nLayout of the set of events contemplated by the distribution.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape, and computing log_prob (or loss more in general) on such sample will yield a tensor of shape batch_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\nproperty event_dim\n\nNumber of event dimensions, i.e., length of the event_shape tuple.\n\nThis is 0 for distributions over scalars, 1 over vectors, 2 over matrices, and so on.\n\nproperty event_shape\n\nShape of each individual event contemplated by the distribution.\n\nFor example, distributions over scalars have event_shape = (), over vectors have event_shape = (d, ) where d is the length of the vectors, over matrices have event_shape = (d1, d2), and so on.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\nis_reparameterizable = False\nlog_prob(x: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nCompute the log-density of the distribution at x.\n\nParameters\n\nx – Tensor of shape (batch_shape, event_shape).\n\nReturns\n\nTensor of shape batch_shape containing the log-density of the distribution for each event in x.\n\nReturn type\n\nTensor\n\nproperty mean\n\nTensor containing the mean of the distribution.\n\nsample(num_samples: Optional[int] = None, dtype=<class 'numpy.float32'>) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nDraw samples from the distribution.\n\nIf num_samples is given the first dimension of the output will be num_samples.\n\nParameters\n• num_samples – Number of samples to to be drawn.\n\n• dtype – Data-type of the samples.\n\nReturns\n\nA tensor containing samples. This has shape (batch_shape, eval_shape) if num_samples = None and (num_samples, batch_shape, eval_shape) otherwise.\n\nReturn type\n\nTensor\n\nproperty stddev\n\nTensor containing the standard deviation of the distribution.\n\nclass gluonts.mx.distribution.BetaOutput[source]\nargs_dim: Dict[str, int] = {'alpha': 1, 'beta': 1}\ndistr_cls\n\nalias of Beta\n\nclassmethod domain_map(F, alpha, beta)[source]\n\nMaps raw tensors to valid arguments for constructing a Beta distribution.\n\nParameters\n• F\n\n• alpha – Tensor of shape (batch_shape, 1)\n\n• beta – Tensor of shape (batch_shape, 1)\n\nReturns\n\nTwo squeezed tensors, of shape (batch_shape): both have entries mapped to the positive orthant.\n\nReturn type\n\nTuple[Tensor, Tensor]\n\nproperty event_shape\n\nShape of each individual event contemplated by the distributions that this object constructs.\n\nproperty value_in_support\n\nA float that will have a valid numeric value when computing the log-loss of the corresponding distribution. By default 0.0. This value will be used when padding data series.\n\nclass gluonts.mx.distribution.Beta(alpha: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], beta: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol])[source]\n\nBeta distribution.\n\nParameters\n• alpha – Tensor containing the alpha shape parameters, of shape (batch_shape, event_shape).\n\n• beta – Tensor containing the beta shape parameters, of shape (batch_shape, event_shape).\n\n• F\n\nproperty F\narg_names = None\nproperty args\nproperty batch_shape\n\nLayout of the set of events contemplated by the distribution.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape, and computing log_prob (or loss more in general) on such sample will yield a tensor of shape batch_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\nproperty event_dim\n\nNumber of event dimensions, i.e., length of the event_shape tuple.\n\nThis is 0 for distributions over scalars, 1 over vectors, 2 over matrices, and so on.\n\nproperty event_shape\n\nShape of each individual event contemplated by the distribution.\n\nFor example, distributions over scalars have event_shape = (), over vectors have event_shape = (d, ) where d is the length of the vectors, over matrices have event_shape = (d1, d2), and so on.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\nis_reparameterizable = False\nlog_prob(x: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nCompute the log-density of the distribution at x.\n\nParameters\n\nx – Tensor of shape (batch_shape, event_shape).\n\nReturns\n\nTensor of shape batch_shape containing the log-density of the distribution for each event in x.\n\nReturn type\n\nTensor\n\nproperty mean\n\nTensor containing the mean of the distribution.\n\nsample(num_samples: Optional[int] = None, dtype=<class 'numpy.float32'>) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nDraw samples from the distribution.\n\nIf num_samples is given the first dimension of the output will be num_samples.\n\nParameters\n• num_samples – Number of samples to to be drawn.\n\n• dtype – Data-type of the samples.\n\nReturns\n\nA tensor containing samples. This has shape (batch_shape, eval_shape) if num_samples = None and (num_samples, batch_shape, eval_shape) otherwise.\n\nReturn type\n\nTensor\n\nproperty stddev\n\nTensor containing the standard deviation of the distribution.\n\nproperty variance\n\nTensor containing the variance of the distribution.\n\nclass gluonts.mx.distribution.GaussianOutput[source]\nargs_dim: Dict[str, int] = {'mu': 1, 'sigma': 1}\ndistr_cls\n\nalias of Gaussian\n\nclassmethod domain_map(F, mu, sigma)[source]\n\nMaps raw tensors to valid arguments for constructing a Gaussian distribution.\n\nParameters\n• F\n\n• mu – Tensor of shape (batch_shape, 1)\n\n• sigma – Tensor of shape (batch_shape, 1)\n\nReturns\n\nTwo squeezed tensors, of shape (batch_shape): the first has the same entries as mu and the second has entries mapped to the positive orthant.\n\nReturn type\n\nTuple[Tensor, Tensor]\n\nproperty event_shape\n\nShape of each individual event contemplated by the distributions that this object constructs.\n\nclass gluonts.mx.distribution.Gaussian(mu: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], sigma: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol])[source]\n\nGaussian distribution.\n\nParameters\n• mu – Tensor containing the means, of shape (batch_shape, event_shape).\n\n• std – Tensor containing the standard deviations, of shape (batch_shape, event_shape).\n\n• F\n\nproperty F\narg_names = None\nproperty args\nproperty batch_shape\n\nLayout of the set of events contemplated by the distribution.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape, and computing log_prob (or loss more in general) on such sample will yield a tensor of shape batch_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\ncdf(x)[source]\n\nReturns the value of the cumulative distribution function evaluated at x\n\nproperty event_dim\n\nNumber of event dimensions, i.e., length of the event_shape tuple.\n\nThis is 0 for distributions over scalars, 1 over vectors, 2 over matrices, and so on.\n\nproperty event_shape\n\nShape of each individual event contemplated by the distribution.\n\nFor example, distributions over scalars have event_shape = (), over vectors have event_shape = (d, ) where d is the length of the vectors, over matrices have event_shape = (d1, d2), and so on.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\nis_reparameterizable = True\nlog_prob(x: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nCompute the log-density of the distribution at x.\n\nParameters\n\nx – Tensor of shape (batch_shape, event_shape).\n\nReturns\n\nTensor of shape batch_shape containing the log-density of the distribution for each event in x.\n\nReturn type\n\nTensor\n\nproperty mean\n\nTensor containing the mean of the distribution.\n\nquantile(level: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nCalculates quantiles for the given levels.\n\nParameters\n\nlevel – Level values to use for computing the quantiles. level should be a 1d tensor of level values between 0 and 1.\n\nReturns\n\nQuantile values corresponding to the levels passed. The return shape is\n\n(num_levels, …DISTRIBUTION_SHAPE…),\n\nwhere DISTRIBUTION_SHAPE is the shape of the underlying distribution.\n\nReturn type\n\nquantiles\n\nsample(num_samples: Optional[int] = None, dtype=<class 'numpy.float32'>) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nDraw samples from the distribution.\n\nIf num_samples is given the first dimension of the output will be num_samples.\n\nParameters\n• num_samples – Number of samples to to be drawn.\n\n• dtype – Data-type of the samples.\n\nReturns\n\nA tensor containing samples. This has shape (batch_shape, eval_shape) if num_samples = None and (num_samples, batch_shape, eval_shape) otherwise.\n\nReturn type\n\nTensor\n\nsample_rep(num_samples: Optional[int] = None, dtype=<class 'numpy.float32'>) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\nproperty stddev\n\nTensor containing the standard deviation of the distribution.\n\nclass gluonts.mx.distribution.LaplaceOutput[source]\nargs_dim: Dict[str, int] = {'b': 1, 'mu': 1}\ndistr_cls\n\nalias of Laplace\n\nclassmethod domain_map(F, mu, b)[source]\n\nConverts arguments to the right shape and domain. The domain depends on the type of distribution, while the correct shape is obtained by reshaping the trailing axis in such a way that the returned tensors define a distribution of the right event_shape.\n\nproperty event_shape\n\nShape of each individual event contemplated by the distributions that this object constructs.\n\nclass gluonts.mx.distribution.Laplace(mu: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], b: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol])[source]\n\nLaplace distribution.\n\nParameters\n• mu – Tensor containing the means, of shape (batch_shape, event_shape).\n\n• b – Tensor containing the distribution scale, of shape (batch_shape, event_shape).\n\n• F\n\nproperty F\narg_names = None\nproperty args\nproperty batch_shape\n\nLayout of the set of events contemplated by the distribution.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape, and computing log_prob (or loss more in general) on such sample will yield a tensor of shape batch_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\ncdf(x: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nReturns the value of the cumulative distribution function evaluated at x\n\nproperty event_dim\n\nNumber of event dimensions, i.e., length of the event_shape tuple.\n\nThis is 0 for distributions over scalars, 1 over vectors, 2 over matrices, and so on.\n\nproperty event_shape\n\nShape of each individual event contemplated by the distribution.\n\nFor example, distributions over scalars have event_shape = (), over vectors have event_shape = (d, ) where d is the length of the vectors, over matrices have event_shape = (d1, d2), and so on.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\nis_reparameterizable = True\nlog_prob(x: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nCompute the log-density of the distribution at x.\n\nParameters\n\nx – Tensor of shape (batch_shape, event_shape).\n\nReturns\n\nTensor of shape batch_shape containing the log-density of the distribution for each event in x.\n\nReturn type\n\nTensor\n\nproperty mean\n\nTensor containing the mean of the distribution.\n\nquantile(level: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nCalculates quantiles for the given levels.\n\nParameters\n\nlevel – Level values to use for computing the quantiles. level should be a 1d tensor of level values between 0 and 1.\n\nReturns\n\nQuantile values corresponding to the levels passed. The return shape is\n\n(num_levels, …DISTRIBUTION_SHAPE…),\n\nwhere DISTRIBUTION_SHAPE is the shape of the underlying distribution.\n\nReturn type\n\nquantiles\n\nsample_rep(num_samples=None, dtype=<class 'numpy.float32'>) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\nproperty stddev\n\nTensor containing the standard deviation of the distribution.\n\nclass gluonts.mx.distribution.MultivariateGaussian(mu: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], L: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], F=None)[source]\n\nMultivariate Gaussian distribution, specified by the mean vector and the Cholesky factor of its covariance matrix.\n\nParameters\n• mu – mean vector, of shape (…, d)\n\n• L – Lower triangular Cholesky factor of covariance matrix, of shape (…, d, d)\n\n• F – A module that can either refer to the Symbol API or the NDArray API in MXNet\n\nproperty F\narg_names = None\nproperty batch_shape\n\nLayout of the set of events contemplated by the distribution.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape, and computing log_prob (or loss more in general) on such sample will yield a tensor of shape batch_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\nproperty event_dim\n\nNumber of event dimensions, i.e., length of the event_shape tuple.\n\nThis is 0 for distributions over scalars, 1 over vectors, 2 over matrices, and so on.\n\nproperty event_shape\n\nShape of each individual event contemplated by the distribution.\n\nFor example, distributions over scalars have event_shape = (), over vectors have event_shape = (d, ) where d is the length of the vectors, over matrices have event_shape = (d1, d2), and so on.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\nis_reparameterizable = True\nlog_prob(x: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nCompute the log-density of the distribution at x.\n\nParameters\n\nx – Tensor of shape (batch_shape, event_shape).\n\nReturns\n\nTensor of shape batch_shape containing the log-density of the distribution for each event in x.\n\nReturn type\n\nTensor\n\nproperty mean\n\nTensor containing the mean of the distribution.\n\nsample_rep(num_samples: Optional[int] = None, dtype=<class 'numpy.float32'>) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nDraw samples from the multivariate Gaussian distributions. Internally, Cholesky factorization of the covariance matrix is used:\n\nsample = L v + mu,\n\nwhere L is the Cholesky factor, v is a standard normal sample.\n\nParameters\n• num_samples – Number of samples to be drawn.\n\n• dtype – Data-type of the samples.\n\nReturns\n\nTensor with shape (num_samples, …, d).\n\nReturn type\n\nTensor\n\nproperty variance\n\nTensor containing the variance of the distribution.\n\nclass gluonts.mx.distribution.MultivariateGaussianOutput(dim: int)[source]\ndistr_cls = None\ndomain_map(F, mu_vector, L_vector)[source]\n\nConverts arguments to the right shape and domain. The domain depends on the type of distribution, while the correct shape is obtained by reshaping the trailing axis in such a way that the returned tensors define a distribution of the right event_shape.\n\nproperty event_shape\n\nShape of each individual event contemplated by the distributions that this object constructs.\n\nclass gluonts.mx.distribution.LowrankMultivariateGaussian(dim: int, rank: int, mu: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], D: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], W: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol])[source]\n\nMultivariate Gaussian distribution, with covariance matrix parametrized as the sum of a diagonal matrix and a low-rank matrix\n\n$\\Sigma = D + W W^T$\n\nThe implementation is strongly inspired from Pytorch: https://github.com/pytorch/pytorch/blob/master/torch/distributions/lowrank_multivariate_normal.py.\n\nComplexity to compute log_prob is $$O(dim * rank + rank^3)$$ per element.\n\nParameters\n• dim – Dimension of the distribution’s support\n\n• rank – Rank of W\n\n• mu – Mean tensor, of shape (…, dim)\n\n• D – Diagonal term in the covariance matrix, of shape (…, dim)\n\n• W – Low-rank factor in the covariance matrix, of shape (…, dim, rank)\n\nproperty F\narg_names = None\nproperty batch_shape\n\nLayout of the set of events contemplated by the distribution.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape, and computing log_prob (or loss more in general) on such sample will yield a tensor of shape batch_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\nproperty event_dim\n\nNumber of event dimensions, i.e., length of the event_shape tuple.\n\nThis is 0 for distributions over scalars, 1 over vectors, 2 over matrices, and so on.\n\nproperty event_shape\n\nShape of each individual event contemplated by the distribution.\n\nFor example, distributions over scalars have event_shape = (), over vectors have event_shape = (d, ) where d is the length of the vectors, over matrices have event_shape = (d1, d2), and so on.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\nis_reparameterizable = True\nlog_prob(x: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nCompute the log-density of the distribution at x.\n\nParameters\n\nx – Tensor of shape (batch_shape, event_shape).\n\nReturns\n\nTensor of shape batch_shape containing the log-density of the distribution for each event in x.\n\nReturn type\n\nTensor\n\nproperty mean\n\nTensor containing the mean of the distribution.\n\nsample_rep(num_samples: int = None, dtype=<class 'numpy.float32'>) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nDraw samples from the multivariate Gaussian distribution:\n\n$s = \\mu + D u + W v,$\n\nwhere $$u$$ and $$v$$ are standard normal samples.\n\nParameters\n• num_samples – number of samples to be drawn.\n\n• dtype – Data-type of the samples.\n\nReturns\n\nReturn type\n\ntensor with shape (num_samples, .., dim)\n\nproperty variance\n\nTensor containing the variance of the distribution.\n\nclass gluonts.mx.distribution.LowrankMultivariateGaussianOutput(dim: int, rank: int, sigma_init: float = 1.0, sigma_minimum: float = 0.001)[source]\ndistr_cls = None\ndistribution(distr_args, loc=None, scale=None, *kwargs) → gluonts.mx.distribution.distribution.Distribution[source]\n\nConstruct the associated distribution, given the collection of constructor arguments and, optionally, a scale tensor.\n\nParameters\n• distr_args – Constructor arguments for the underlying Distribution type.\n\n• loc – Optional tensor, of the same shape as the batch_shape+event_shape of the resulting distribution.\n\n• scale – Optional tensor, of the same shape as the batch_shape+event_shape of the resulting distribution.\n\ndomain_map(F, mu_vector, D_vector, W_vector)[source]\nParameters\n• F\n\n• mu_vector – Tensor of shape (…, dim)\n\n• D_vector – Tensor of shape (…, dim)\n\n• W_vector – Tensor of shape (…, dim rank )\n\nReturns\n\nA tuple containing tensors mu, D, and W, with shapes (…, dim), (…, dim), and (…, dim, rank), respectively.\n\nReturn type\n\nTuple\n\nproperty event_shape\n\nShape of each individual event contemplated by the distributions that this object constructs.\n\nget_args_proj(prefix: Optional[str] = None) → gluonts.mx.distribution.distribution_output.ArgProj[source]\nclass gluonts.mx.distribution.MixtureDistributionOutput(distr_outputs: List[gluonts.mx.distribution.distribution_output.DistributionOutput])[source]\ndistr_cls = None\ndistribution(distr_args, loc: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol, None] = None, scale: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol, None] = None, *kwargs) → gluonts.mx.distribution.mixture.MixtureDistribution[source]\n\nConstruct the associated distribution, given the collection of constructor arguments and, optionally, a scale tensor.\n\nParameters\n• distr_args – Constructor arguments for the underlying Distribution type.\n\n• loc – Optional tensor, of the same shape as the batch_shape+event_shape of the resulting distribution.\n\n• scale – Optional tensor, of the same shape as the batch_shape+event_shape of the resulting distribution.\n\nproperty event_shape\n\nShape of each individual event contemplated by the distributions that this object constructs.\n\nget_args_proj(prefix: Optional[str] = None) → gluonts.mx.distribution.mixture.MixtureArgs[source]\nclass gluonts.mx.distribution.MixtureDistribution(mixture_probs: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], components: List[gluonts.mx.distribution.distribution.Distribution], F=None)[source]\n\nA mixture distribution where each component is a Distribution.\n\nParameters\n• mixture_probs – A tensor of mixing probabilities. The entries should all be positive and sum to 1 across the last dimension. Shape: (…, k), where k is the number of distributions to be mixed. All axis except the last one should either coincide with the ones from the component distributions, or be 1 (in which case, the mixing coefficient is shared across the axis).\n\n• components – A list of k Distribution objects representing the mixture components. Distributions can be of different types. Each component’s support should be made of tensors of shape (…, d).\n\n• F – A module that can either refer to the Symbol API or the NDArray API in MXNet\n\nproperty F\narg_names = None\nproperty batch_shape\n\nLayout of the set of events contemplated by the distribution.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape, and computing log_prob (or loss more in general) on such sample will yield a tensor of shape batch_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\ncdf(x: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nReturns the value of the cumulative distribution function evaluated at x\n\nproperty event_dim\n\nNumber of event dimensions, i.e., length of the event_shape tuple.\n\nThis is 0 for distributions over scalars, 1 over vectors, 2 over matrices, and so on.\n\nproperty event_shape\n\nShape of each individual event contemplated by the distribution.\n\nFor example, distributions over scalars have event_shape = (), over vectors have event_shape = (d, ) where d is the length of the vectors, over matrices have event_shape = (d1, d2), and so on.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\nis_reparameterizable = False\nlog_prob(x: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nCompute the log-density of the distribution at x.\n\nParameters\n\nx – Tensor of shape (batch_shape, event_shape).\n\nReturns\n\nTensor of shape batch_shape containing the log-density of the distribution for each event in x.\n\nReturn type\n\nTensor\n\nproperty mean\n\nTensor containing the mean of the distribution.\n\nsample(num_samples: Optional[int] = None, dtype=<class 'numpy.float32'>) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nDraw samples from the distribution.\n\nIf num_samples is given the first dimension of the output will be num_samples.\n\nParameters\n• num_samples – Number of samples to to be drawn.\n\n• dtype – Data-type of the samples.\n\nReturns\n\nA tensor containing samples. This has shape (batch_shape, eval_shape) if num_samples = None and (num_samples, batch_shape, eval_shape) otherwise.\n\nReturn type\n\nTensor\n\nproperty stddev\n\nTensor containing the standard deviation of the distribution.\n\nclass gluonts.mx.distribution.NegativeBinomialOutput[source]\nargs_dim: Dict[str, int] = {'alpha': 1, 'mu': 1}\ndistr_cls\n\nalias of NegativeBinomial\n\ndistribution(distr_args, loc: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol, None] = None, scale: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol, None] = None) → gluonts.mx.distribution.neg_binomial.NegativeBinomial[source]\n\nConstruct the associated distribution, given the collection of constructor arguments and, optionally, a scale tensor.\n\nParameters\n• distr_args – Constructor arguments for the underlying Distribution type.\n\n• loc – Optional tensor, of the same shape as the batch_shape+event_shape of the resulting distribution.\n\n• scale – Optional tensor, of the same shape as the batch_shape+event_shape of the resulting distribution.\n\nclassmethod domain_map(F, mu, alpha)[source]\n\nConverts arguments to the right shape and domain. The domain depends on the type of distribution, while the correct shape is obtained by reshaping the trailing axis in such a way that the returned tensors define a distribution of the right event_shape.\n\nproperty event_shape\n\nShape of each individual event contemplated by the distributions that this object constructs.\n\nclass gluonts.mx.distribution.NegativeBinomial(mu: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], alpha: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol])[source]\n\nNegative binomial distribution, i.e. the distribution of the number of successes in a sequence of independent Bernoulli trials.\n\nParameters\n• mu – Tensor containing the means, of shape (batch_shape, event_shape).\n\n• alpha – Tensor of the shape parameters, of shape (batch_shape, event_shape).\n\n• F\n\nproperty F\narg_names = None\nproperty args\nproperty batch_shape\n\nLayout of the set of events contemplated by the distribution.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape, and computing log_prob (or loss more in general) on such sample will yield a tensor of shape batch_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\nproperty event_dim\n\nNumber of event dimensions, i.e., length of the event_shape tuple.\n\nThis is 0 for distributions over scalars, 1 over vectors, 2 over matrices, and so on.\n\nproperty event_shape\n\nShape of each individual event contemplated by the distribution.\n\nFor example, distributions over scalars have event_shape = (), over vectors have event_shape = (d, ) where d is the length of the vectors, over matrices have event_shape = (d1, d2), and so on.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\nis_reparameterizable = False\nlog_prob(x: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nCompute the log-density of the distribution at x.\n\nParameters\n\nx – Tensor of shape (batch_shape, event_shape).\n\nReturns\n\nTensor of shape batch_shape containing the log-density of the distribution for each event in x.\n\nReturn type\n\nTensor\n\nproperty mean\n\nTensor containing the mean of the distribution.\n\nsample(num_samples: Optional[int] = None, dtype=<class 'numpy.float32'>) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nDraw samples from the distribution.\n\nIf num_samples is given the first dimension of the output will be num_samples.\n\nParameters\n• num_samples – Number of samples to to be drawn.\n\n• dtype – Data-type of the samples.\n\nReturns\n\nA tensor containing samples. This has shape (batch_shape, eval_shape) if num_samples = None and (num_samples, batch_shape, eval_shape) otherwise.\n\nReturn type\n\nTensor\n\nproperty stddev\n\nTensor containing the standard deviation of the distribution.\n\nclass gluonts.mx.distribution.UniformOutput[source]\nargs_dim: Dict[str, int] = {'low': 1, 'width': 1}\ndistr_cls\n\nalias of Uniform\n\nclassmethod domain_map(F, low, width)[source]\n\nConverts arguments to the right shape and domain. The domain depends on the type of distribution, while the correct shape is obtained by reshaping the trailing axis in such a way that the returned tensors define a distribution of the right event_shape.\n\nproperty event_shape\n\nShape of each individual event contemplated by the distributions that this object constructs.\n\nclass gluonts.mx.distribution.Uniform(low: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], high: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol])[source]\n\nUniform distribution.\n\nParameters\n• low – Tensor containing the lower bound of the distribution domain.\n\n• high – Tensor containing the higher bound of the distribution domain.\n\n• F\n\nproperty F\narg_names = None\nproperty args\nproperty batch_shape\n\nLayout of the set of events contemplated by the distribution.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape, and computing log_prob (or loss more in general) on such sample will yield a tensor of shape batch_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\ncdf(x: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nReturns the value of the cumulative distribution function evaluated at x\n\nproperty event_dim\n\nNumber of event dimensions, i.e., length of the event_shape tuple.\n\nThis is 0 for distributions over scalars, 1 over vectors, 2 over matrices, and so on.\n\nproperty event_shape\n\nShape of each individual event contemplated by the distribution.\n\nFor example, distributions over scalars have event_shape = (), over vectors have event_shape = (d, ) where d is the length of the vectors, over matrices have event_shape = (d1, d2), and so on.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\nis_reparameterizable = True\nlog_prob(x: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nCompute the log-density of the distribution at x.\n\nParameters\n\nx – Tensor of shape (batch_shape, event_shape).\n\nReturns\n\nTensor of shape batch_shape containing the log-density of the distribution for each event in x.\n\nReturn type\n\nTensor\n\nproperty mean\n\nTensor containing the mean of the distribution.\n\nquantile(level: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nCalculates quantiles for the given levels.\n\nParameters\n\nlevel – Level values to use for computing the quantiles. level should be a 1d tensor of level values between 0 and 1.\n\nReturns\n\nQuantile values corresponding to the levels passed. The return shape is\n\n(num_levels, …DISTRIBUTION_SHAPE…),\n\nwhere DISTRIBUTION_SHAPE is the shape of the underlying distribution.\n\nReturn type\n\nquantiles\n\nsample(num_samples: Optional[int] = None, dtype=<class 'numpy.float32'>) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nDraw samples from the distribution.\n\nIf num_samples is given the first dimension of the output will be num_samples.\n\nParameters\n• num_samples – Number of samples to to be drawn.\n\n• dtype – Data-type of the samples.\n\nReturns\n\nA tensor containing samples. This has shape (batch_shape, eval_shape) if num_samples = None and (num_samples, batch_shape, eval_shape) otherwise.\n\nReturn type\n\nTensor\n\nsample_rep(num_samples: Optional[int] = None, dtype=<class 'numpy.float32'>) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\nproperty stddev\n\nTensor containing the standard deviation of the distribution.\n\nclass gluonts.mx.distribution.Binned(bin_log_probs: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], bin_centers: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], label_smoothing: Optional[float] = None)[source]\n\nA binned distribution defined by a set of bins via bin centers and bin probabilities.\n\nParameters\n• bin_log_probs – Tensor containing log probabilities of the bins, of shape (batch_shape, num_bins).\n\n• bin_centers – Tensor containing the bin centers, of shape (batch_shape, num_bins).\n\n• F\n\n• label_smoothing – The label smoothing weight, real number in [0, 1). Default None. If not None, then the loss of the distribution will be “label smoothed” cross-entropy. For example, instead of computing cross-entropy loss between the estimated bin probabilities and a hard-label (one-hot encoding) [1, 0, 0], a soft label of [0.9, 0.05, 0.05] is taken as the ground truth (when label_smoothing=0.15). See (Muller et al., 2019) [MKH19], for further reference.\n\nproperty F\narg_names = None\nproperty args\nproperty batch_shape\n\nLayout of the set of events contemplated by the distribution.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape, and computing log_prob (or loss more in general) on such sample will yield a tensor of shape batch_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\nproperty bin_probs\ncdf(x: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nReturns the value of the cumulative distribution function evaluated at x\n\nproperty event_dim\n\nNumber of event dimensions, i.e., length of the event_shape tuple.\n\nThis is 0 for distributions over scalars, 1 over vectors, 2 over matrices, and so on.\n\nproperty event_shape\n\nShape of each individual event contemplated by the distribution.\n\nFor example, distributions over scalars have event_shape = (), over vectors have event_shape = (d, ) where d is the length of the vectors, over matrices have event_shape = (d1, d2), and so on.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\nis_reparameterizable = False\nlog_prob(x)[source]\n\nCompute the log-density of the distribution at x.\n\nParameters\n\nx – Tensor of shape (batch_shape, event_shape).\n\nReturns\n\nTensor of shape batch_shape containing the log-density of the distribution for each event in x.\n\nReturn type\n\nTensor\n\nloss(x: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nCompute the loss at x according to the distribution.\n\nBy default, this method returns the negative of log_prob. For some distributions, however, the log-density is not easily computable and therefore other loss functions are computed.\n\nParameters\n\nx – Tensor of shape (batch_shape, event_shape).\n\nReturns\n\nTensor of shape batch_shape containing the value of the loss for each event in x.\n\nReturn type\n\nTensor\n\nproperty mean\n\nTensor containing the mean of the distribution.\n\nquantile(level: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nCalculates quantiles for the given levels.\n\nParameters\n\nlevel – Level values to use for computing the quantiles. level should be a 1d tensor of level values between 0 and 1.\n\nReturns\n\nQuantile values corresponding to the levels passed. The return shape is\n\n(num_levels, …DISTRIBUTION_SHAPE…),\n\nwhere DISTRIBUTION_SHAPE is the shape of the underlying distribution.\n\nReturn type\n\nquantiles\n\nsample(num_samples=None, dtype=<class 'numpy.float32'>)[source]\n\nDraw samples from the distribution.\n\nIf num_samples is given the first dimension of the output will be num_samples.\n\nParameters\n• num_samples – Number of samples to to be drawn.\n\n• dtype – Data-type of the samples.\n\nReturns\n\nA tensor containing samples. This has shape (batch_shape, eval_shape) if num_samples = None and (num_samples, batch_shape, eval_shape) otherwise.\n\nReturn type\n\nTensor\n\nsmooth_ce_loss(x)[source]\n\nCross-entropy loss with a “smooth” label.\n\nproperty stddev\n\nTensor containing the standard deviation of the distribution.\n\nclass gluonts.mx.distribution.BinnedOutput(bin_centers: mxnet.ndarray.ndarray.NDArray, label_smoothing: Optional[float] = None)[source]\ndistr_cls\n\nalias of Binned\n\ndistribution(args, loc=None, scale=None) → gluonts.mx.distribution.binned.Binned[source]\n\nConstruct the associated distribution, given the collection of constructor arguments and, optionally, a scale tensor.\n\nParameters\n• distr_args – Constructor arguments for the underlying Distribution type.\n\n• loc – Optional tensor, of the same shape as the batch_shape+event_shape of the resulting distribution.\n\n• scale – Optional tensor, of the same shape as the batch_shape+event_shape of the resulting distribution.\n\nproperty event_shape\n\nShape of each individual event contemplated by the distributions that this object constructs.\n\nget_args_proj(args, *kwargs) → mxnet.gluon.block.HybridBlock[source]\nclass gluonts.mx.distribution.PiecewiseLinear(gamma: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], slopes: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], knot_spacings: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol])[source]\n\nPiecewise linear distribution.\n\nThis class represents the quantile function (i.e., the inverse CDF) associated with the a distribution, as a continuous, non-decreasing, piecewise linear function defined in the [0, 1] interval:\n\n$q(x; \\gamma, b, d) = \\gamma + \\sum_{l=0}^L b_l (x_l - d_l)_+$\n\nwhere the input $$x \\in [0,1]$$ and the parameters are\n\n• $$\\gamma$$: intercept at 0\n\n• $$b$$: differences of the slopes in consecutive pieces\n\n• $$d$$: knot positions\n\nParameters\n• gamma – Tensor containing the intercepts at zero\n\n• slopes – Tensor containing the slopes of each linear piece. All coefficients must be positive. Shape: (gamma.shape, num_pieces)\n\n• knot_spacings – Tensor containing the spacings between knots in the splines. All coefficients must be positive and sum to one on the last axis. Shape: (gamma.shape, num_pieces)\n\n• F\n\nproperty F\narg_names = None\nproperty args\nproperty batch_shape\n\nLayout of the set of events contemplated by the distribution.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape, and computing log_prob (or loss more in general) on such sample will yield a tensor of shape batch_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\ncdf(x: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nComputes the quantile level $$\\alpha$$ such that $$q(\\alpha) = x$$.\n\nParameters\n\nx – Tensor of shape gamma.shape\n\nReturns\n\nTensor of shape gamma.shape\n\nReturn type\n\nTensor\n\ncrps(x: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nCompute CRPS in analytical form.\n\nParameters\n\nx – Observation to evaluate. Shape equals to gamma.shape.\n\nReturns\n\nTensor containing the CRPS.\n\nReturn type\n\nTensor\n\nproperty event_dim\n\nNumber of event dimensions, i.e., length of the event_shape tuple.\n\nThis is 0 for distributions over scalars, 1 over vectors, 2 over matrices, and so on.\n\nproperty event_shape\n\nShape of each individual event contemplated by the distribution.\n\nFor example, distributions over scalars have event_shape = (), over vectors have event_shape = (d, ) where d is the length of the vectors, over matrices have event_shape = (d1, d2), and so on.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\nis_reparameterizable = False\nloss(x: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nCompute the loss at x according to the distribution.\n\nBy default, this method returns the negative of log_prob. For some distributions, however, the log-density is not easily computable and therefore other loss functions are computed.\n\nParameters\n\nx – Tensor of shape (batch_shape, event_shape).\n\nReturns\n\nTensor of shape batch_shape containing the value of the loss for each event in x.\n\nReturn type\n\nTensor\n\nquantile(level: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nCalculates quantiles for the given levels.\n\nParameters\n\nlevel – Level values to use for computing the quantiles. level should be a 1d tensor of level values between 0 and 1.\n\nReturns\n\nQuantile values corresponding to the levels passed. The return shape is\n\n(num_levels, …DISTRIBUTION_SHAPE…),\n\nwhere DISTRIBUTION_SHAPE is the shape of the underlying distribution.\n\nReturn type\n\nquantiles\n\nquantile_internal(x: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], axis: Optional[int] = None) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nEvaluates the quantile function at the quantile levels contained in x.\n\nParameters\n• x – Tensor of shape gamma.shape if axis=None, or containing an additional axis on the specified position, otherwise.\n\n• axis – Index of the axis containing the different quantile levels which are to be computed.\n\nReturns\n\nQuantiles tensor, of the same shape as x.\n\nReturn type\n\nTensor\n\nsample(num_samples: Optional[int] = None, dtype=<class 'numpy.float32'>) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nDraw samples from the distribution.\n\nIf num_samples is given the first dimension of the output will be num_samples.\n\nParameters\n• num_samples – Number of samples to to be drawn.\n\n• dtype – Data-type of the samples.\n\nReturns\n\nA tensor containing samples. This has shape (batch_shape, eval_shape) if num_samples = None and (num_samples, batch_shape, eval_shape) otherwise.\n\nReturn type\n\nTensor\n\nclass gluonts.mx.distribution.PiecewiseLinearOutput(num_pieces: int)[source]\ndistr_cls\n\nalias of PiecewiseLinear\n\ndistribution(distr_args, loc: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol, None] = None, scale: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol, None] = None) → gluonts.mx.distribution.piecewise_linear.PiecewiseLinear[source]\n\nConstruct the associated distribution, given the collection of constructor arguments and, optionally, a scale tensor.\n\nParameters\n• distr_args – Constructor arguments for the underlying Distribution type.\n\n• loc – Optional tensor, of the same shape as the batch_shape+event_shape of the resulting distribution.\n\n• scale – Optional tensor, of the same shape as the batch_shape+event_shape of the resulting distribution.\n\nclassmethod domain_map(F, gamma, slopes, knot_spacings)[source]\n\nConverts arguments to the right shape and domain. The domain depends on the type of distribution, while the correct shape is obtained by reshaping the trailing axis in such a way that the returned tensors define a distribution of the right event_shape.\n\nproperty event_shape\n\nShape of each individual event contemplated by the distributions that this object constructs.\n\nclass gluonts.mx.distribution.Poisson(rate: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol])[source]\n\nPoisson distribution, i.e. the distribution of the number of successes in a specified region.\n\nParameters\n• rate – Tensor containing the means, of shape (batch_shape, event_shape).\n\n• F\n\nproperty F\narg_names = None\nproperty args\nproperty batch_shape\n\nLayout of the set of events contemplated by the distribution.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape, and computing log_prob (or loss more in general) on such sample will yield a tensor of shape batch_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\nproperty event_dim\n\nNumber of event dimensions, i.e., length of the event_shape tuple.\n\nThis is 0 for distributions over scalars, 1 over vectors, 2 over matrices, and so on.\n\nproperty event_shape\n\nShape of each individual event contemplated by the distribution.\n\nFor example, distributions over scalars have event_shape = (), over vectors have event_shape = (d, ) where d is the length of the vectors, over matrices have event_shape = (d1, d2), and so on.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\nis_reparameterizable = False\nlog_prob(x: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nCompute the log-density of the distribution at x.\n\nParameters\n\nx – Tensor of shape (batch_shape, event_shape).\n\nReturns\n\nTensor of shape batch_shape containing the log-density of the distribution for each event in x.\n\nReturn type\n\nTensor\n\nproperty mean\n\nTensor containing the mean of the distribution.\n\nsample(num_samples: Optional[int] = None, dtype=<class 'numpy.float32'>) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nDraw samples from the distribution.\n\nIf num_samples is given the first dimension of the output will be num_samples.\n\nParameters\n• num_samples – Number of samples to to be drawn.\n\n• dtype – Data-type of the samples.\n\nReturns\n\nA tensor containing samples. This has shape (batch_shape, eval_shape) if num_samples = None and (num_samples, batch_shape, eval_shape) otherwise.\n\nReturn type\n\nTensor\n\nproperty stddev\n\nTensor containing the standard deviation of the distribution.\n\nclass gluonts.mx.distribution.PoissonOutput[source]\nargs_dim: Dict[str, int] = {'rate': 1}\ndistr_cls\n\nalias of Poisson\n\ndistribution(distr_args, loc: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol, None] = None, scale: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol, None] = None) → gluonts.mx.distribution.poisson.Poisson[source]\n\nConstruct the associated distribution, given the collection of constructor arguments and, optionally, a scale tensor.\n\nParameters\n• distr_args – Constructor arguments for the underlying Distribution type.\n\n• loc – Optional tensor, of the same shape as the batch_shape+event_shape of the resulting distribution.\n\n• scale – Optional tensor, of the same shape as the batch_shape+event_shape of the resulting distribution.\n\nclassmethod domain_map(F, rate)[source]\n\nConverts arguments to the right shape and domain. The domain depends on the type of distribution, while the correct shape is obtained by reshaping the trailing axis in such a way that the returned tensors define a distribution of the right event_shape.\n\nproperty event_shape\n\nShape of each individual event contemplated by the distributions that this object constructs.\n\nclass gluonts.mx.distribution.TransformedPiecewiseLinear(base_distribution: gluonts.mx.distribution.piecewise_linear.PiecewiseLinear, transforms: List[gluonts.mx.distribution.bijection.Bijection])[source]\narg_names = None\ncrps(y: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nCompute the continuous rank probability score (CRPS) of x according to the distribution.\n\nParameters\n\nx – Tensor of shape (batch_shape, event_shape).\n\nReturns\n\nTensor of shape batch_shape containing the CRPS score, according to the distribution, for each event in x.\n\nReturn type\n\nTensor\n\nclass gluonts.mx.distribution.TransformedDistribution(base_distribution: gluonts.mx.distribution.distribution.Distribution, transforms: List[gluonts.mx.distribution.bijection.Bijection])[source]\n\nA distribution obtained by applying a sequence of transformations on top of a base distribution.\n\narg_names = None\nproperty batch_shape\n\nLayout of the set of events contemplated by the distribution.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape, and computing log_prob (or loss more in general) on such sample will yield a tensor of shape batch_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\ncdf(y: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nReturns the value of the cumulative distribution function evaluated at x\n\nproperty event_dim\n\nNumber of event dimensions, i.e., length of the event_shape tuple.\n\nThis is 0 for distributions over scalars, 1 over vectors, 2 over matrices, and so on.\n\nproperty event_shape\n\nShape of each individual event contemplated by the distribution.\n\nFor example, distributions over scalars have event_shape = (), over vectors have event_shape = (d, ) where d is the length of the vectors, over matrices have event_shape = (d1, d2), and so on.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\nlog_prob(y: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nCompute the log-density of the distribution at x.\n\nParameters\n\nx – Tensor of shape (batch_shape, event_shape).\n\nReturns\n\nTensor of shape batch_shape containing the log-density of the distribution for each event in x.\n\nReturn type\n\nTensor\n\nquantile(level: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nCalculates quantiles for the given levels.\n\nParameters\n\nlevel – Level values to use for computing the quantiles. level should be a 1d tensor of level values between 0 and 1.\n\nReturns\n\nQuantile values corresponding to the levels passed. The return shape is\n\n(num_levels, …DISTRIBUTION_SHAPE…),\n\nwhere DISTRIBUTION_SHAPE is the shape of the underlying distribution.\n\nReturn type\n\nquantiles\n\nsample(num_samples: Optional[int] = None, dtype=<class 'numpy.float32'>) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nDraw samples from the distribution.\n\nIf num_samples is given the first dimension of the output will be num_samples.\n\nParameters\n• num_samples – Number of samples to to be drawn.\n\n• dtype – Data-type of the samples.\n\nReturns\n\nA tensor containing samples. This has shape (batch_shape, eval_shape) if num_samples = None and (num_samples, batch_shape, eval_shape) otherwise.\n\nReturn type\n\nTensor\n\nsample_rep(num_samples: Optional[int] = None, dtype=<class 'float'>) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\nclass gluonts.mx.distribution.TransformedDistributionOutput(base_distr_output: gluonts.mx.distribution.distribution_output.DistributionOutput, transforms_output: List[gluonts.mx.distribution.bijection_output.BijectionOutput])[source]\n\nClass to connect a network to a distribution that is transformed by a sequence of learnable bijections.\n\ndistr_cls = None\ndistribution(distr_args, loc: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol, None] = None, scale: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol, None] = None) → gluonts.mx.distribution.distribution.Distribution[source]\n\nConstruct the associated distribution, given the collection of constructor arguments and, optionally, a scale tensor.\n\nParameters\n• distr_args – Constructor arguments for the underlying Distribution type.\n\n• loc – Optional tensor, of the same shape as the batch_shape+event_shape of the resulting distribution.\n\n• scale – Optional tensor, of the same shape as the batch_shape+event_shape of the resulting distribution.\n\ndomain_map(F, args: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol])[source]\n\nConverts arguments to the right shape and domain. The domain depends on the type of distribution, while the correct shape is obtained by reshaping the trailing axis in such a way that the returned tensors define a distribution of the right event_shape.\n\nproperty event_shape\n\nShape of each individual event contemplated by the distributions that this object constructs.\n\nget_args_proj(prefix: Optional[str] = None) → gluonts.mx.distribution.distribution_output.ArgProj[source]\nclass gluonts.mx.distribution.InverseBoxCoxTransformOutput(lb_obs: float = 0.0, fix_lambda_2: bool = True)[source]\nargs_dim: Dict[str, int] = {'box_cox.lambda_1': 1, 'box_cox.lambda_2': 1}\nbij_cls\n\nalias of InverseBoxCoxTransform\n\nproperty event_shape\nclass gluonts.mx.distribution.BoxCoxTransformOutput(lb_obs: float = 0.0, fix_lambda_2: bool = True)[source]\nargs_dim: Dict[str, int] = {'box_cox.lambda_1': 1, 'box_cox.lambda_2': 1}\nbij_cls\n\nalias of BoxCoxTransform\n\ndomain_map(F, args: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Tuple[Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], ...][source]\nproperty event_shape\nclass gluonts.mx.distribution.Dirichlet(alpha: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], float_type: gluonts.core.component.DType = <class 'numpy.float32'>)[source]\n\nDirichlet distribution, specified by the concentration vector alpha of length d. https://en.wikipedia.org/wiki/Dirichlet_distribution\n\nThe Dirichlet distribution is defined on the open (d-1)-simplex, which means that a sample (or observation) x = (x_0,…, x_{d-1}) must satisfy:\n\nsum_k x_k = 1 and for all k, x_k > 0.\n\nParameters\n• alpha – concentration vector, of shape (…, d)\n\n• F – A module that can either refer to the Symbol API or the NDArray API in MXNet\n\nproperty F\narg_names = None\nproperty args\nproperty batch_shape\n\nLayout of the set of events contemplated by the distribution.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape, and computing log_prob (or loss more in general) on such sample will yield a tensor of shape batch_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\nproperty event_dim\n\nNumber of event dimensions, i.e., length of the event_shape tuple.\n\nThis is 0 for distributions over scalars, 1 over vectors, 2 over matrices, and so on.\n\nproperty event_shape\n\nShape of each individual event contemplated by the distribution.\n\nFor example, distributions over scalars have event_shape = (), over vectors have event_shape = (d, ) where d is the length of the vectors, over matrices have event_shape = (d1, d2), and so on.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\nis_reparameterizable = False\nlog_prob(x: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nCompute the log-density of the distribution at x.\n\nParameters\n\nx – Tensor of shape (batch_shape, event_shape).\n\nReturns\n\nTensor of shape batch_shape containing the log-density of the distribution for each event in x.\n\nReturn type\n\nTensor\n\nproperty mean\n\nTensor containing the mean of the distribution.\n\nsample(num_samples: Optional[int] = None, dtype=<class 'numpy.float32'>) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nDraw samples from the distribution.\n\nIf num_samples is given the first dimension of the output will be num_samples.\n\nParameters\n• num_samples – Number of samples to to be drawn.\n\n• dtype – Data-type of the samples.\n\nReturns\n\nA tensor containing samples. This has shape (batch_shape, eval_shape) if num_samples = None and (num_samples, batch_shape, eval_shape) otherwise.\n\nReturn type\n\nTensor\n\nproperty variance\n\nTensor containing the variance of the distribution.\n\nclass gluonts.mx.distribution.DirichletOutput(dim: int)[source]\ndistr_cls = None\ndistribution(distr_args, loc=None, scale=None) → gluonts.mx.distribution.distribution.Distribution[source]\n\nConstruct the associated distribution, given the collection of constructor arguments and, optionally, a scale tensor.\n\nParameters\n• distr_args – Constructor arguments for the underlying Distribution type.\n\n• loc – Optional tensor, of the same shape as the batch_shape+event_shape of the resulting distribution.\n\n• scale – Optional tensor, of the same shape as the batch_shape+event_shape of the resulting distribution.\n\ndomain_map(F, alpha_vector)[source]\n\nConverts arguments to the right shape and domain. The domain depends on the type of distribution, while the correct shape is obtained by reshaping the trailing axis in such a way that the returned tensors define a distribution of the right event_shape.\n\nproperty event_shape\n\nShape of each individual event contemplated by the distributions that this object constructs.\n\nclass gluonts.mx.distribution.DirichletMultinomial(dim: int, n_trials: int, alpha: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], float_type: gluonts.core.component.DType = <class 'numpy.float32'>)[source]\n\nDirichlet-Multinomial distribution, specified by the concentration vector alpha of length dim, and a number of trials n_trials. https://en.wikipedia.org/wiki/Dirichlet-multinomial_distribution\n\nThe Dirichlet-Multinomial distribution is a discrete multivariate probability distribution, a sample (or observation) x = (x_0,…, x_{dim-1}) must satisfy:\n\nsum_k x_k = n_trials and for all k, x_k is a non-negative integer.\n\nSuch a sample can be obtained by first drawing a vector p from a Dirichlet(alpha) distribution, then x is drawn from a Multinomial(p) with n trials\n\nParameters\n• dim – Dimension of any sample\n\n• n_trials – Number of trials\n\n• alpha – concentration vector, of shape (…, dim)\n\n• F – A module that can either refer to the Symbol API or the NDArray API in MXNet\n\nproperty F\narg_names = None\nproperty batch_shape\n\nLayout of the set of events contemplated by the distribution.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape, and computing log_prob (or loss more in general) on such sample will yield a tensor of shape batch_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\nproperty event_dim\n\nNumber of event dimensions, i.e., length of the event_shape tuple.\n\nThis is 0 for distributions over scalars, 1 over vectors, 2 over matrices, and so on.\n\nproperty event_shape\n\nShape of each individual event contemplated by the distribution.\n\nFor example, distributions over scalars have event_shape = (), over vectors have event_shape = (d, ) where d is the length of the vectors, over matrices have event_shape = (d1, d2), and so on.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\nis_reparameterizable = False\nlog_prob(x: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nCompute the log-density of the distribution at x.\n\nParameters\n\nx – Tensor of shape (batch_shape, event_shape).\n\nReturns\n\nTensor of shape batch_shape containing the log-density of the distribution for each event in x.\n\nReturn type\n\nTensor\n\nproperty mean\n\nTensor containing the mean of the distribution.\n\nsample(num_samples: Optional[int] = None, dtype=<class 'numpy.float32'>) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nDraw samples from the distribution.\n\nIf num_samples is given the first dimension of the output will be num_samples.\n\nParameters\n• num_samples – Number of samples to to be drawn.\n\n• dtype – Data-type of the samples.\n\nReturns\n\nA tensor containing samples. This has shape (batch_shape, eval_shape) if num_samples = None and (num_samples, batch_shape, eval_shape) otherwise.\n\nReturn type\n\nTensor\n\nproperty variance\n\nTensor containing the variance of the distribution.\n\nclass gluonts.mx.distribution.DirichletMultinomialOutput(dim: int, n_trials: int)[source]\ndistr_cls = None\ndistribution(distr_args, loc=None, scale=None) → gluonts.mx.distribution.distribution.Distribution[source]\n\nConstruct the associated distribution, given the collection of constructor arguments and, optionally, a scale tensor.\n\nParameters\n• distr_args – Constructor arguments for the underlying Distribution type.\n\n• loc – Optional tensor, of the same shape as the batch_shape+event_shape of the resulting distribution.\n\n• scale – Optional tensor, of the same shape as the batch_shape+event_shape of the resulting distribution.\n\ndomain_map(F, alpha_vector)[source]\n\nConverts arguments to the right shape and domain. The domain depends on the type of distribution, while the correct shape is obtained by reshaping the trailing axis in such a way that the returned tensors define a distribution of the right event_shape.\n\nproperty event_shape\n\nShape of each individual event contemplated by the distributions that this object constructs.\n\nclass gluonts.mx.distribution.Categorical(log_probs: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol])[source]\n\nA categorical distribution over num_cats-many categories.\n\nParameters\n• log_probs – Tensor containing log probabilities of the individual categories, of shape (batch_shape, num_cats).\n\n• F\n\nproperty F\narg_names = None\nproperty args\nproperty batch_shape\n\nLayout of the set of events contemplated by the distribution.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape, and computing log_prob (or loss more in general) on such sample will yield a tensor of shape batch_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\nproperty event_dim\n\nNumber of event dimensions, i.e., length of the event_shape tuple.\n\nThis is 0 for distributions over scalars, 1 over vectors, 2 over matrices, and so on.\n\nproperty event_shape\n\nShape of each individual event contemplated by the distribution.\n\nFor example, distributions over scalars have event_shape = (), over vectors have event_shape = (d, ) where d is the length of the vectors, over matrices have event_shape = (d1, d2), and so on.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\nlog_prob(x)[source]\n\nCompute the log-density of the distribution at x.\n\nParameters\n\nx – Tensor of shape (batch_shape, event_shape).\n\nReturns\n\nTensor of shape batch_shape containing the log-density of the distribution for each event in x.\n\nReturn type\n\nTensor\n\nproperty mean\n\nTensor containing the mean of the distribution.\n\nproperty probs\nsample(num_samples=None, dtype=<class 'numpy.int32'>)[source]\n\nDraw samples from the distribution.\n\nIf num_samples is given the first dimension of the output will be num_samples.\n\nParameters\n• num_samples – Number of samples to to be drawn.\n\n• dtype – Data-type of the samples.\n\nReturns\n\nA tensor containing samples. This has shape (batch_shape, eval_shape) if num_samples = None and (num_samples, batch_shape, eval_shape) otherwise.\n\nReturn type\n\nTensor\n\nproperty stddev\n\nTensor containing the standard deviation of the distribution.\n\nclass gluonts.mx.distribution.CategoricalOutput(num_cats: int, temperature: float = 1.0)[source]\ndistr_cls\n\nalias of Categorical\n\ndistribution(distr_args, loc=None, scale=None, kwargs) → gluonts.mx.distribution.distribution.Distribution[source]\n\nConstruct the associated distribution, given the collection of constructor arguments and, optionally, a scale tensor.\n\nParameters\n• distr_args – Constructor arguments for the underlying Distribution type.\n\n• loc – Optional tensor, of the same shape as the batch_shape+event_shape of the resulting distribution.\n\n• scale – Optional tensor, of the same shape as the batch_shape+event_shape of the resulting distribution.\n\ndomain_map(F, probs)[source]\n\nConverts arguments to the right shape and domain. The domain depends on the type of distribution, while the correct shape is obtained by reshaping the trailing axis in such a way that the returned tensors define a distribution of the right event_shape.\n\nproperty event_shape\n\nShape of each individual event contemplated by the distributions that this object constructs.\n\nclass gluonts.mx.distribution.LogitNormal(mu: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol], sigma: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol])[source]\n\nThe logit-normal distribution.\n\nParameters\n• mu – Tensor containing the location, of shape (batch_shape, event_shape).\n\n• sigma – Tensor indicating the scale, of shape (batch_shape, event_shape).\n\n• F\n\nproperty F\narg_names = None\nproperty args\nproperty batch_shape\n\nLayout of the set of events contemplated by the distribution.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape, and computing log_prob (or loss more in general) on such sample will yield a tensor of shape batch_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\nproperty event_dim\n\nNumber of event dimensions, i.e., length of the event_shape tuple.\n\nThis is 0 for distributions over scalars, 1 over vectors, 2 over matrices, and so on.\n\nproperty event_shape\n\nShape of each individual event contemplated by the distribution.\n\nFor example, distributions over scalars have event_shape = (), over vectors have event_shape = (d, ) where d is the length of the vectors, over matrices have event_shape = (d1, d2), and so on.\n\nInvoking sample() from a distribution yields a tensor of shape batch_shape + event_shape.\n\nThis property is available in general only in mx.ndarray mode, when the shape of the distribution arguments can be accessed.\n\nlog_prob(x: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nCompute the log-density of the distribution at x.\n\nParameters\n\nx – Tensor of shape (batch_shape, event_shape).\n\nReturns\n\nTensor of shape batch_shape containing the log-density of the distribution for each event in x.\n\nReturn type\n\nTensor\n\nquantile(level: Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol]) → Union[mxnet.ndarray.ndarray.NDArray, mxnet.symbol.symbol.Symbol][source]\n\nCalculates quantiles for the given levels.\n\nParameters\n\nlevel – Level values to use for computing the quantiles. level should be a 1d tensor of level values between 0 and 1.\n\nReturns\n\nQuantile values corresponding to the levels passed. The return shape is\n\n(num_levels, …DISTRIBUTION_SHAPE…),\n\nwhere DISTRIBUTION_SHAPE is the shape of the underlying distribution.\n\nReturn type\n\nquantiles\n\nsample(num_samples=None, dtype=<class 'numpy.float32'>)[source]\n\nDraw samples from the distribution.\n\nIf num_samples is given the first dimension of the output will be num_samples.\n\nParameters\n• num_samples – Number of samples to to be drawn.\n\n• dtype – Data-type of the samples.\n\nReturns\n\nA tensor containing samples. This has shape (batch_shape, eval_shape) if num_samples = None and (num_samples, batch_shape, eval_shape) otherwise.\n\nReturn type\n\nTensor\n\nclass gluonts.mx.distribution.LogitNormalOutput[source]\nargs_dim: Dict[str, int] = {'mu': 1, 'sigma': 1}\ndistr_cls\n\nalias of LogitNormal\n\ndistribution(distr_args, loc=None, scale=None, *kwargs) → gluonts.mx.distribution.distribution.Distribution[source]\n\nConstruct the associated distribution, given the collection of constructor arguments and, optionally, a scale tensor.\n\nParameters\n• distr_args – Constructor arguments for the underlying Distribution type.\n\n• loc – Optional tensor, of the same shape as the batch_shape+event_shape of the resulting distribution.\n\n• scale – Optional tensor, of the same shape as the batch_shape+event_shape of the resulting distribution.\n\nclassmethod domain_map(F, mu, sigma)[source]\n\nConverts arguments to the right shape and domain. The domain depends on the type of distribution, while the correct shape is obtained by reshaping the trailing axis in such a way that the returned tensors define a distribution of the right event_shape.\n\nproperty event_shape\n\nShape of each individual event contemplated by the distributions that this object constructs." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.647606,"math_prob":0.9454814,"size":85354,"snap":"2020-34-2020-40","text_gpt3_token_len":20118,"char_repetition_ratio":0.26672524,"word_repetition_ratio":0.83591026,"special_character_ratio":0.21812686,"punctuation_ratio":0.21338493,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9905491,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-08-05T22:31:55Z\",\"WARC-Record-ID\":\"<urn:uuid:89f70ac2-c131-4908-a770-894c779771a1>\",\"Content-Length\":\"332585\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:683e40db-eb4b-4c85-bda2-5d0fcd8606f2>\",\"WARC-Concurrent-To\":\"<urn:uuid:f85aab7d-20e1-4b49-9fa1-53a60b65df39>\",\"WARC-IP-Address\":\"13.32.202.59\",\"WARC-Target-URI\":\"http://gluon-ts.mxnet.io/master/api/gluonts/gluonts.mx.distribution.html\",\"WARC-Payload-Digest\":\"sha1:VTZKVY6NSM2UTFP4EDW363O7NHSKCWG2\",\"WARC-Block-Digest\":\"sha1:VMNHZKAKZHZJ25XIKBDVNBV3VEXALIGR\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-34/CC-MAIN-2020-34_segments_1596439735989.10_warc_CC-MAIN-20200805212258-20200806002258-00504.warc.gz\"}"}
https://tex.stackexchange.com/questions/346562/how-to-split-cell-text-into-multiline-in-table	[ "# How to split cell text into multiline in table?\n\nI'm writing a paper using the ACM double column template, and I have a table which I want to fit to just one column, and in order to do so, I want to split the text inside the cells to multiple lines. I have the following code segment:\n\n\\documentclass{paper}\n\\begin{document}\n\n\\begin{table}[thb]\n\\centering\n\\begin{tabular}{\|l\|c\|l\|} \\hline\n\\textbf{Col1} & \\textbf{Col2} & \\textbf{Col3} \\\\ \\hline\nThis is a \\\\very long line \\\\of text & Short text & Another long \\\\line of text \\\\ \\hline\n$\\pi$ & 1 in 5& Common in math\\\\\n\\hline\\end{tabular}\n\\end{table}\n\n\\end{document}\n\n\nBut, what it gives me an output which is not quite right, as can be seen below.", null, "First of all, the second part of the text of the last column is pushed into the first column. Then, also the last columns borders are not full. Any idea how to split a text to multiline in table cell?\n\nPackage tabularx is your friend:", null, "\\documentclass[twocolumn]{paper}\n\\usepackage{tabularx}\n\\newcolumntype{L}{>{\\raggedright\\arraybackslash}X}\n\n\\begin{document}\n\\begin{table}\n\\centering\n\\begin{tabularx}{\\linewidth}{\|L\|c\|L\|}\n\\hline\n\\textbf{Col1} & \\textbf{Col2} & \\textbf{Col3} \\\\\n\\hline\nThis is a very long line of text & Short text & Another long line of text \\\\\n\\hline\n$\\pi$ & 1 in 5& Common in math\\\\\n\\hline\n\\end{tabularx}\n\\end{table}\n\\end{document}\n\n• It is my understanding that the tabu package provides improvements with respect to tabularx, which may be interesting when typesetting long texts into tables, such as footnotes compatibility with hyperref and table use, etc. Maybe this is to be recommended as well. Sep 24, 2018 at 9:36\n• @SergeiPoulp, that was intention, but package is buggy and not maintained. with recent changes in the array (which is used in it) package it is not compatible with it anymopre, so it is not reliable. i would avoid it. Sep 24, 2018 at 9:39\n\nIf you want to control line breaks in cells, you can use the \\makecell command from the homonymous package. In addition, it has tools to add some vertical padding to cells:\n\n\\documentclass{paper}\n\n\\usepackage{array, makecell} %\n\n\\begin{document}\n\n\\begin{table}[thb]\n\\centering\\renewcommand\\cellalign{lc}\n\\setcellgapes{3pt}\\makegapedcells\n\\begin{tabular}{\|l\|c\|l\|} \\hline\n\\textbf{Col1} & \\textbf{Col2} & \\textbf{Col3} \\\\ \\hline\n\\makecell{This is a \\\\very long line \\\\of text} & Short text &\\makecell{ Another long \\\\line of text} \\\\ \\hline\n$\\pi$ & 1 in 5& Common in math\\\\\n\\hline\\end{tabular}\n\\end{table}\n\n\\end{document}", null, "Your wrong column alignment results from missing column delimiters (&) in your source code and can be fixed easily. This also fixes the broken vertical lines.\n\n\\begin{table}[thb]\n\\centering\n\\begin{tabular}{\|l\|c\|l\|}\n\\hline\n\\textbf{Col1} & \\textbf{Col2} & \\textbf{Col3} \\\\ \\hline\nThis is a & & \\\\ % <===== note the empty cells in this line\nvery long line & Short text & Another long \\\\\nof text & & line of text\\\\ \\hline % <===== and in this\n$\\pi$ & 1 in 5 & Common in math \\\\ \\hline\n\\end{tabular}\n\\end{table}", null, "A less manual way would be to use the p column type, but you have to specify the column width and LaTeX will do the linebreaks for you, but your last cell will probably also break:\n\n\\begin{table}[thb]\n\\centering\n\\begin{tabular}{\|p{1.8cm}\|c\|p{2cm}\|}\n\\hline\n\\textbf{Col1} & \\textbf{Col2} & \\textbf{Col3} \\\\ \\hline\nThis is a very long line of text & Short text & Another long line of text \\\\ \\hline\n$\\pi$ & 1 in 5 & Common in math \\\\ \\hline\n\\end{tabular}\n\\end{table}", null, "Or you can use the multirow package. Load \\usepackage{multirow} in your preamble {anywhere between \\documentclass{paper} and \\begin{document}, and then you can do:\n\n\\begin{table}[thb]\n\\centering\n\\begin{tabular}{\|l\|c\|l\|}\n\\hline\n\\textbf{Col1} & \\textbf{Col2} & \\textbf{Col3} \\\\ \\hline\n\\multirow{3}{}{\\parbox{1.8cm}{This is a very long line of text}} & & \\multirow{3}{}{\\parbox{2cm}{Another long line of text}} \\\\\n& Short text & \\\\\n& & \\\\ \\hline\n$\\pi$ & 1 in 5 & Common in math \\\\ \\hline\n\\end{tabular}\n\\end{table}\n\n\nNote that this aligns the columns vertically centered. The \\parbox{length} defines when your text should be broken.", null, "I found the answer in the link below: https://pt.overleaf.com/learn/latex/Tables I hope it helps!" ]	[ null, "https://i.stack.imgur.com/q45hT.png", null, "https://i.stack.imgur.com/bLgIO.png", null, "https://i.stack.imgur.com/kAhTm.png", null, "https://i.stack.imgur.com/ti3fe.png", null, "https://i.stack.imgur.com/uVeG9.png", null, "https://i.stack.imgur.com/TvTBB.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7931914,"math_prob":0.816031,"size":843,"snap":"2022-05-2022-21","text_gpt3_token_len":247,"char_repetition_ratio":0.115613826,"word_repetition_ratio":0.0,"special_character_ratio":0.2728351,"punctuation_ratio":0.07692308,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98261076,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12],"im_url_duplicate_count":[null,5,null,5,null,5,null,5,null,5,null,5,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-25T17:14:34Z\",\"WARC-Record-ID\":\"<urn:uuid:a41d455b-8b36-482c-9e08-bcb66d698335>\",\"Content-Length\":\"257407\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:5568d8be-92e4-44a5-8c81-dd7423725359>\",\"WARC-Concurrent-To\":\"<urn:uuid:203dfb25-8a71-49fc-a3b1-35ee802c0c7e>\",\"WARC-IP-Address\":\"151.101.193.69\",\"WARC-Target-URI\":\"https://tex.stackexchange.com/questions/346562/how-to-split-cell-text-into-multiline-in-table\",\"WARC-Payload-Digest\":\"sha1:FTVU7IUML75JYV6Z73EW5CS7BFXTKUQ5\",\"WARC-Block-Digest\":\"sha1:KGHNFMTRSN2NWIL5GJIHNFBIX3H7FCD4\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662588661.65_warc_CC-MAIN-20220525151311-20220525181311-00543.warc.gz\"}"}
http://sqa.fyicenter.com/1000155_Convert_JMeter_Test_Result_to_TestMan.html	[ "Convert JMeter Test Result to TestMan\n\nQ\n\nHow to Convert JMeter Test Result to TestMan Data Model?\n\n✍: FYIcenter.com\n\nA", null, "In order migrate JMeter test result to TestMan, we need to decide how to convert JMeter test result data to TestMan tables and fields.\n\nOne way to map JMeter test result to TestMan is described below:\n\n• 1. For each unique value of Test_Run_Case_Step.trid, create a record in Test_Run table.\n• 2. For each unique value of Test_Run_Case_Step.tcid within the same jmeter_test_result.trid, create a record in Test_Run_Case table.\n• 3. Each JMeter test result record represents a record in the Test_Run_Case_Step table.\n• 4. \"Duration\", \"Total\", and \"Failed\" in Test_Run and Test_Run_Case tables can be calculated from Test_Run_Case_Step table.\n\nHere is the SQL script ConvertJMeterData.sql to convert the JMeter Test Result to TestMan tables:\n\n-- ConvertJMeterData.sql\n\nuse TestMan;\n\ninsert into Test_Run (\nReference, -- jmeter_test_result.trid\nTimeStamp -- jmeter_test_result.timestamp\n) select\ntrid,\nmin(from_unixtime(timestamp/1000))\nfrom jmeter_test_result\ngroup by trid;\n\ninsert into Test_Run_Case (\nTest_Run_ID,\nReference, -- jmeter_test_result.tcid\nTimeStamp, -- jmeter_test_result.timestamp\nTarget, -- jmeter_test_result.target\nStation, -- jmeter_test_result.station\nTester, -- jmeter_test_result.tester\nName, -- jmeter_test_result.tcname\nComponent, -- jmeter_test_result.component\nFunction, -- jmeter_test_result.function\nTotal\n) select\nr.ID,\nj.tcid,\nmin(from_unixtime(j.timestamp/1000)),\nmin(j.target),\nmin(j.station),\nmin(j.tester),\nmin(j.tcname),\nmin(j.component),\nmin(j.function),\ncount(*)\nfrom jmeter_test_result j, Test_Run r\nwhere j.trid = r.reference\ngroup by r.ID, j.tcid;\n\ninsert into Test_Run_Case_Step (\nTest_Run_Case_ID,\nTimestamp, -- jmeter_test_result.timestamp\nDuration, -- jmeter_test_result.elapsed\nName, -- jmeter_test_result.label\nSuccess, -- jmeter_test_result.success\nOutput -- jmeter_test_result.output\n) select\nc.ID,\nfrom_unixtime(j.timestamp/1000),\nj.elapsed,\nj.label,\nif(j.success='true', 1, 0),\nj.output\nfrom jmeter_test_result j, Test_Run r, Test_Run_Case c\nwhere j.trid = r.Reference\nand r.ID = c.Test_Run_ID\nand j.tcid = c.Reference;\n\nSee the next tutorial on how to update Test_Run and Test_Run_Case tables from Test_Run_Case_Step table.\n\n2017-12-13, 516👍, 0💬" ]	[ null, "http://sqa.fyicenter.com/Test-Management/_icon_Test-Management.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.51931024,"math_prob":0.44581717,"size":2438,"snap":"2019-43-2019-47","text_gpt3_token_len":597,"char_repetition_ratio":0.2013147,"word_repetition_ratio":0.27027026,"special_character_ratio":0.24159147,"punctuation_ratio":0.2560175,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99596095,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-18T12:06:03Z\",\"WARC-Record-ID\":\"<urn:uuid:11adf24f-0f6c-4fe5-b410-63dbe8eed19a>\",\"Content-Length\":\"20563\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:84832d07-90b1-4265-911c-f8a799fca4af>\",\"WARC-Concurrent-To\":\"<urn:uuid:eca6c51a-12e0-415d-9e13-cb95756a3cc3>\",\"WARC-IP-Address\":\"74.208.236.35\",\"WARC-Target-URI\":\"http://sqa.fyicenter.com/1000155_Convert_JMeter_Test_Result_to_TestMan.html\",\"WARC-Payload-Digest\":\"sha1:RHT56A52FEDIQ76OKN4BB4HT3SWTILWX\",\"WARC-Block-Digest\":\"sha1:UB73JG2WGLNGOSYH43YGONHLAXREIVOH\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570986682037.37_warc_CC-MAIN-20191018104351-20191018131851-00262.warc.gz\"}"}
https://blog.csdn.net/sd4567855/article/details/80789163	[ "【数据结构与算法】第五章：散列\n\n# 第五章：散列\n\n• 散列表(hash table)：只支持二叉查找树所允许的一部分操作.\n• 散列(hashing)：一种用于以常数平均时间执行插入,删除和查找的级数.\n\n## 5.1 一般想法\n\n• 理想的散列表数据结构只不过是一个包含有关键字的具体固定大小的数组.一般而言,这个关键字就是带有一个相关之的字符串.\n• 我们把表的大小记作 TableSize T a b l e S i z e $TableSize$,并将其理解为散列数据结构的一部分而不仅仅是浮动于全局的某个变量.通常的习惯是让表从 0 0 $0$ TableSize1 T a b l e S i z e − 1 $TableSize - 1$ 变化.\n• 散列函数(hash function)：每个关键字映射到从 0 0 $0$ TableSize1 T a b l e S i z e − 1 $TableSize - 1$ 这个范围中的某个数,并且被放到适当额单元中.最理想的情况是,运算简单并且任何两个不同的关键字映射到不同的单元.但是这是不可能的,因为单元的数目是有限的,而关键字是用不完的.\n• 冲突(collision)：当两个关键字散列到同一个值的时候.\n\n## 5.2 散列函数\n\n• 当关键字是整数时,我们保证表的大小是一个素数,可以直接返回 KeymodTableSize K e y m o d T a b l e S i z e $Key mod TableSize$\n• 当关键字是字符串时,散列函数需要仔细选择.\n1. 一种选择方法是可以将字符串中的字符的 ASCII 码值相加起来.如下\n//将字符逐个相加来处理整个字符串\ntypedef unsigned int Index;\nIndex Hash( const char Key, int TableSize){\nunsigned int HashVal = 0;\nwhile( Key != '\\0')\nHashVal += Key++;\nreturn HashVal % TableSize;\n}\n\n2.另一种散列函数如下\n\nIndex Hash2( const char Key, int TableSize){\nreturn( Key + 27 * Key + 729 * Key) % TableSize;\n}\n\n3.第三种散列函数\n\nIndex Hash3( const char Key, int TableSize){\nunsigned int HashVal = 0;\nwhile( Key != '\\0')\nHashVal = ( HashVal<<5) + Key++;\nreturn HashVal % TableSize;\n}\n\n## 5.3 解决冲突的方法\n\n### 5.3.1 分离链接法\n\n• 分离链接法(separate chaining)：将散列到同一个值的所有元素保留到一个表中.为了方便,这些表都有表头.如下图.", null, "1. Find操作,我们使用散列函数来确定究竟是哪一个表.此时,我们通常的方式遍历该表并返回所找到的被查找项所在的位置.\n2. Insert操作,我们遍历整个表以检查该元素是否已经处在适当的位置.如果要插入重复元,那么通常要留出一个额外的域,这个域当重复元出现时候增加1.如果这个元素是个新元素,那么它或者被插入表的前端,或者被擦汗如到表的末尾.又是新元素插入到表的前端不仅是因为方便,而且新插入的元素可能最先被访问.\nstruct ListNode;\ntypedef struct ListNode Position;\nstruct HashTbl;\ntypedef struct HashTbl HashTable;\n\nstruct ListNode{\nElemeentType Element;\nPosition Next;\n};\n\nstruct HashTbl{\nint TableSize;\nList TheLists; //指向ListNode指针的指针\n};\n\nHashTable InitializeTable( int TableSize);\nvoid DestroyTable( HashTable H);\nPosition Find( ElementType Key, HashTable H);\nvoid Insert( ElementType Key, HashTable H);\nElementType Retrieve( Position P);\n//初始化过程\nHashTable InitializeTable( int TableSize){\nHashTable H;\nint i;\n\nif( TableSize < MinTableSize){\nError(\" Table is so small\");\nreturn NULL;\n}\n\nH = ( HashTable)malloc( sizeof( struct HashTbl));\nif( H == NULL)\nFatalError(\" Out of space\");\n\nH->TableSize = NextPrime( TableSize);\nH->TheLists = malloc( sizeof( List) * H->TableSize);\nif( H->TheLists == NULL)\nFatalError(\" Out of space\");\n\nfor( i=0; i<H->TableSize; i++){\nH->TheList[i] = ( Position)malloc( sizeof( struct ListNode));\nif( H->TheList[i] == NULL)\nFatalError(\" Out of space\");\nelse\nH->TheLists[i]->Next == NULL;\n}\n}\n\n//寻找并返回一个指针\nPosition Find( ElementType Key, HashTable H){\nPosition P;\nList L;\nL = H->TheLists[ Hash( key, H->TableSize)];\nP = L->Next;//L是头指针\nwhile( P!=NULL && P->Element !=Key)\nP = P->Next;\nreturn P;\n}\n\n//插入\nvoid Insert( ElementType Key, HashTable H){\nPosition Pos, NewCell;\nList L;\nPos = Find( Key, H);\nif( Pos == NULL){\nNewCell = ( Position)malloc( sizeof( struct ListNode));\nif( NewCell == NULL)\nFatalError(\" Out of space\");\nelse{\nL = H->TheLists[ Hash( Key, H->TableSize)];\nNewCell->Next = L->Next;\nNewCell->Element = Key; //当是整数时,Find同.\nL->Next = NewCell;\n}\n}\n}\n• 分离链接散列算法的缺点\n\n1. 需要指针.\n2. 给新单元分配地址需要时间,导致了算法时间缓慢.\n• 装填因子(load factor) λ λ $\\lambda$：散列表中元素的个数与散列表大小的比值.\n\n### 5.3.2 开放定址法\n\n• 开放定址散列法( Open addressing hashing)：如果有冲突发生,那么就要尝试选择另外的单元,直到找出空的单元为止.更一般地,单元 h0(X),h1(X),h2(X), h 0 ( X ) , h 1 ( X ) , h 2 ( X ) , $h_0(X), h_1(X), h_2(X),$ 等等相继被试选其中 hi(X)=(Hash(X)+F(i))modTableSize h i ( X ) = ( H a s h ( X ) + F ( i ) ) m o d T a b l e S i z e $h_i(X) = ( Hash(X) + F(i)) mod TableSize$, 且 F(0)=0 F ( 0 ) = 0 $F(0) = 0$ .\n考虑到所有的数据都要置入表内部,因此开放定址散列法需要的表比分离链接散列表的表要大.一般而言, 装填因子 λ λ $\\lambda$ 应该低于 0.5 .\n\n#### 5.3.2.1 线性探测法\n\n• 在线性探测法中,函数 F F $F$ i i $i$ 的线性函数,典型情形是 F(i)=i F ( i ) = i $F(i) = i$ .这相当于逐个探测每个单元以查找出一个空单元.\nfor example: 把关键字{ 89, 18, 49, 58, 69},插入到一个散列表中,此时的冲突解决办法选择 F(i)=i F ( i ) = i $F(i) = i$ .", null, "第一个冲突发生在插入关键字 49 时,它被放到下一个空闲地址,即 0 处.\n随后,关键字 58 依次与 18,89,49 发生冲突,试选三次后才找到空单元 2 .\n关键字 69 亦是如此.\n只要表足够大,我们总能找到一个自由单元,但是花费的时间是非常多的.\n\n• 一次聚集(primary clustering)：使用线性探测法时,即时表相对于比较空的时候,一些占据的单元也会形成一些区块.\n\n#### 5.3.2.2 平方探测法\n\n• 平方探测发时消除线性探测中狙击问题的冲突解决方法.本质上就是冲突函数为幂次函数的探测方法.流行的选择是 F(i)=i2 F ( i ) = i 2 $F(i) = i^2$ .\nfor example: 把关键字{ 89, 18, 49, 58, 69},插入到一个散列表中.", null, "当 49 与 89 冲突时,下一个位置为下一个单元,该单元是空的,因此 49 就放在此处.\n此后 58 在位置 8 处发生冲突,其后相邻的单元经过探测得知发生了另外的冲突.下一个探测的位置就在距离位置 8 为 2^2 = 4 远处,此时,这个单元也是空单元,因此关键字 58 就放在单元 2 的位置处.\n对于关键字 69 处理的过程也是一样.\n\n• 对于线性探测,让元素几乎填满散列表并不是个好主意,因为这时候表的性能将会降低.\n\n• 对于平方探测,一旦表被填写超过一半,当表的大小不是素数甚至在表被填满一半之前,就不能保证可以找到一个空单元了.这是因为最多有表的一般可以用作解决冲突的备选位置.\n\n• 定理\n如果使用平方探测,并且表的大小是素数,那么当表至少有一半是空的时候,总能够插入一个新的元素.\n\nh(X)+i2=h(X)+j2(modTableSize) h ( X ) + i 2 = h ( X ) + j 2 ( m o d T a b l e S i z e ) $h(X) + i^2 = h(X) + j^2 (mod TableSize)$\ni2=j2(modTableSize) i 2 = j 2 ( m o d T a b l e S i z e ) $i^2 = j^2 (mod TableSize)$\n(ij)(i+j)=0(modTableSize) ( i − j ) ( i + j ) = 0 ( m o d T a b l e S i z e ) $( i - j)( i + j) = 0 (mod TableSize)$\n\ntypedef unsigned int Index;\ntypedef Index Position;\n\nstruct HashTabl;\ntypedef struct HashTbl * HashTable;\n\nstruct HashEntry{\nElementType Element;\nEnum KindOfEntry Info;\n};\n\ntypedef struct HashEntry Cell;\n\nstruct HashTbl{\nint TableSize;\nCell TheCells;\n};\n\nHashTable InitializeTable( int TableSize);\nvoid DestroyTable( HashTable H);\nPosition Find( ElementType Key, HashTable H);\nvoid Insert( ElementType Key, HashTable H);\n//初始化开放定址散列表\nHashTable InitializeTable( int TableSize){\nHashTable H;\nint i;\nif( TableSize < MinTableSize){\nError(\" Table size is too small\");\nreturn NULL;\n}\n\nH = ( HashTable)malloc( sizeof( struct( HashTbl)));\nif( H == NULL)\nFatalError(\" Out of space\");\n\nH->TableSize = NextPrime( TableSize);\nH->TheCells = malloc( sizeof( Cell) H->TableSize);\nif( H->TheCells == NULL)\nFatalError(\" Out of space\");\n\nfor( i = 0; i < H->TableSize; i++)\nH->TheCells[i].Info = Empty;\n\nreturn H;\n}\n//Find\nPosition Find( ElementType Key, HashTable H){\nPosition CurrentPos;\nint CollisionNUm;\n\nCollisionNum = 0;\nCurrentPos = Hash( Key, H->TableSize);\nwhile( H->TheCells[ CurrentPos].Info != Empty &&\nH->TheCells[ CurrentPos].Element != Key){\nCurrentPos += 2 * ++CollisionNum - 1;\nif( CurrentPos >= H->TableSize )\nCurrentPos-= H>TableSize;\n}\nreturn CurrentPos;\n}\n//Insert\nvoid Insert( ElementType Key, HashTable H){\nPosition Pos;\nPos = Find( Key, H)\nif( H->TheCells[ Pos].Info != Legitimate){\nH->TheCells[ Pos].Info = Legitimate;\nH->TheCells[ Pos].Element = Key;\n}\n}\n• 二次聚集(secondary clustering)\n\n#### 5.3.2.3 双散列\n\n• 双散列(double hashing)：对于双散列,一种流行的选择是 F(i)=iHash2(X) F ( i ) = i ∗ H a s h 2 ( X ) $F(i) = i * Hash_2(X)$ 这个公式意味着,我们将第二个散列函数应用到 X X $X$ 并在距离 Hash2(X),2Hash2(X) H a s h 2 ( X ) , 2 H a s h 2 ( X ) $Hash_2(X) , 2Hash_2(X)$ 等处探测.但是要记住, Hash2(X) H a s h 2 ( X ) $Hash_2(X)$ 的选择不好将要导致灾难性的后果.\nfor example：把 99 插入到 { 89, 18, 49, 58, 69} 中.通常选择的是 Hash2(X)=Xmod9 H a s h 2 ( X ) = X m o d 9 $Hash_2(X) = X mod 9$ 将不再起作用.\n\n## 5.4 再散列\n\n• 对于使用平方探测的开放定址散列法,如果表的元素被填充的太满,那么操作的运行时间将会开始消耗的非常场,并且 Insert 操作可能失败.这种情况可能发生在有太多插入和移动的情形下.\n• 一种解决办法：建立另外一个大约两倍大的表(而且使用一个相关的新散列函数),扫描整个源是散列表,计算每个未删除的元素的新散列值并将它插入到新的散列表中.\nfor example：将元素 13, 15, 24, 6插入到大小为 7 的开放定制散列表中.其中散列函数是 h(X)=Xmod7 h ( X ) = X m o d 7 $h(X) = X mod 7$.假设使用线性探测法解决这个问题,那么插入结果如下图所示.\n06\n115\n2\n324\n4\n5\n613\n\n06\n115\n223\n324\n4\n5\n613\n\n0\n1\n2\n3\n4\n5\n66\n723\n824\n9\n10\n11\n12\n1313\n14\n1515\n16\n17\n\n- 以上这个过程就叫做再散列(rehashing).但我们可以观察到这是一个非常昂过的操作;其运行时间是 O(N) O ( N ) $O(N)$ 因为有 N N $N$ 个元素要再散列得到的表大小约为 2N 2 N $2N$.不过,由于不经常发生,因此实际效果根本没有这么差.特别地,在最后的再散列之前必然已经存在 N2 N 2 $\\frac{N}{2}$ 次 Insert 操作，当然添加到每一个插入上的花费基本是一个常数开销.\n- 再散列可以用平方探测以多种方法实现.\n1. 一种做法是只要表满到一半就再散列.\n2. 一种极端的方法是只有插入失败的时候再再散列.\n\n HashTable Rehash( HashTable H){\nint i,OldSize;\nCell OldCells;\n\nOldCells = H->TheCells;\nOldSize = H->TableSize;\n\nH = InitializeTable( 2 OldSize);\n\nfor( i = 0; i <= OldSize; i++){\nif( OldCells[i].Info == Legitimate)\nInsert( OldCells[i].Element, H);\n}\nfree(OldCells)\nreturn H;\n}\n\n## 5.5 可扩散列\n\n• 当数据量太大以至于装不进主存时,此时主要考虑的时检索数据所需要的硬盘存取次数.\n• 我们假设任意时刻都有 N N $N$ 个记录需要储存, N N $N$ 的值伴随时间变化而发生改变. 此外,最多可以把 M M $M$ 个记录放入一个磁盘区块.\n如果使用开放定址散列法或者分离链接散列法,主要问题在于一次 Find 操作期间冲突可能引起多个区块被考察,甚至对于理想分布的散列表亦是如此.不仅如此,当表过满的时候,必须执行代价巨大的再散列操作,它需要 O(N) O ( N ) $O(N)$ 次磁盘访问.\n• 可扩散列(extendible hashing)：它允许用两次磁盘访问执行一次 Find 操作.插入操作也需要很少的磁盘访问.\n• 现在我们假设数据由几个 6 比特的整数组成,参考下图,我们使用B-树的形式储存.", null, "“树”根含有 4 个指针,它们由这些数据的前两个比特来确定.每片树叶之多有 M=4 M = 4 $M = 4$ 个元素.碰巧的时,这里没一片树叶中的数据前两个比特都是相同的.为了更正,我们用 D D $D$ 表示根所使用的比特数,可称之为目录(directory).于是,目录中的项数为 2D 2 D $2^D$. dL d L $d_L$ 是树叶 L L $L$所有元素共有的最高位的位数, dLD d L ≤ D $d_L \\le D$.\n现在想要插入关键字 100100 ,它进入第三片树叶,但是第三片树叶已经满了,没有空间存放它,此时我们将这片树叶分裂成两片树叶,它们由前三个比特确定.这需要将目录的大小增加到 3.如下图.", null, "注意,所有未被分裂的树叶现在各由两个相邻的目录所指.因此,虽然整个目录被重写,但是其他树叶实际上并没有被访问.\n现在如果插入关键字 000000 ,那么第一片树叶就要被分裂,生成 dL=3 d L = 3 $d_L = 3$ 的两片树叶,由于 D=3 D = 3 $D = 3$ ,因此再目录中唯一的变化便是 000 和 001 指针的更新.如下图.", null, "• 这里我们还有一些重要的细节尚未考虑.\n首先,有可能当一片树叶的元素多余 D+1 D + 1 $D + 1$ 个前导位相同时需要多个目录分裂.例如,从原先的例子开始看起, D=2 D = 2 $D = 2$ ,如果插入 111010, 111011 并在最后插入 111100,那么目录的大小必须增加到 4 以区分这五个关键字.\n其次,存在重复关键字(duplicate key)的可能性,若存在多余 M M $M$ 个重复关键字,那么该算法根本无效,需要做出其他安排.\n\n• 可扩散列的性能：\n一个合理的假设：位模式(bit pattern)是均匀分布的.\n基于这个假设,我们得到树叶的期望个数为 NMlog2e N M l o g 2 e $\\frac{N}{M}log_2e$.因此,平均树叶满的程度为 ln2 l n 2 $ln2$.这个和B-树是一样的,这并不奇怪,因为对于这两个数据结构而言,当第 M+1 M + 1 $M + 1$ 被添加时,一些新的节点便会将建立起来.\n目录的期望大小为 O(N1+1/M/M) O ( N 1 + 1 / M / M ) $O(N^{1+1/M}/M)$ 因此,如果 M M $M$ 的值很小,那么目录可能过分地大.为了位置更小的目录,可以把第二个磁盘访问添加到每个 Find 操作中去.如果目录太大装不进主存,那么第二个磁盘访问怎么说还是需要的.\n\n## 我的微信公众号", null, "08-21", null, "219", null, "01-22", null, "1552\n02-26", null, "5550\n10-04", null, "1513\n08-24", null, "1万+\n10-31", null, "63\n12-24", null, "642\n08-05", null, "1万+\n06-12", null, "1260\n04-06", null, "73" ]	[ null, "http://static.zybuluo.com/vsym/w70ob8ppe72rzaxneb9fizmv/%E6%8D%95%E8%8E%B7.PNG", null, "http://static.zybuluo.com/vsym/erp8mrvzlubc905bzawi3u9s/image.png", null, "http://static.zybuluo.com/vsym/idns57sbgybhxyjvjo05p1vr/image.png", null, "http://static.zybuluo.com/vsym/eneltkrszre2rhqljka76dzv/image.png", null, "http://static.zybuluo.com/vsym/0gns9704ognbv3fxxmv1x0is/1.PNG", null, "http://static.zybuluo.com/vsym/4ojad5zu04pwf27bvitg8n89/image.png", null, "https://img-blog.csdn.net/20171029200801586", null, "https://csdnimg.cn/release/blogv2/dist/pc/img/readCountWhite.png", null, "https://csdnimg.cn/release/blogv2/dist/pc/img/[email protected]", null, "https://csdnimg.cn/release/blogv2/dist/pc/img/readCountWhite.png", null, "https://csdnimg.cn/release/blogv2/dist/pc/img/readCountWhite.png", null, "https://csdnimg.cn/release/blogv2/dist/pc/img/readCountWhite.png", null, "https://csdnimg.cn/release/blogv2/dist/pc/img/readCountWhite.png", null, "https://csdnimg.cn/release/blogv2/dist/pc/img/readCountWhite.png", null, "https://csdnimg.cn/release/blogv2/dist/pc/img/readCountWhite.png", null, "https://csdnimg.cn/release/blogv2/dist/pc/img/readCountWhite.png", null, "https://csdnimg.cn/release/blogv2/dist/pc/img/readCountWhite.png", null, "https://csdnimg.cn/release/blogv2/dist/pc/img/readCountWhite.png", null ]	{"ft_lang_label":"__label__zh","ft_lang_prob":0.71479046,"math_prob":0.9984704,"size":9860,"snap":"2020-45-2020-50","text_gpt3_token_len":6275,"char_repetition_ratio":0.13494319,"word_repetition_ratio":0.2554645,"special_character_ratio":0.32332656,"punctuation_ratio":0.21902439,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9938858,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36],"im_url_duplicate_count":[null,1,null,1,null,1,null,1,null,1,null,1,null,2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-10-30T02:39:28Z\",\"WARC-Record-ID\":\"<urn:uuid:ca32418b-4465-4089-ae47-2e5a594f2910>\",\"Content-Length\":\"300497\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:404ee126-0686-4602-85a4-d873d5757a56>\",\"WARC-Concurrent-To\":\"<urn:uuid:26bee881-fc1c-4464-81b0-2499a0b1fd98>\",\"WARC-IP-Address\":\"101.200.35.175\",\"WARC-Target-URI\":\"https://blog.csdn.net/sd4567855/article/details/80789163\",\"WARC-Payload-Digest\":\"sha1:SH7RQ54QGP4G2BA2NSLK3BFIX3E5V23P\",\"WARC-Block-Digest\":\"sha1:NOWQYY6BLOMCP3X4SWAF3KPNNBLAU65Y\",\"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-20201030003928-20201030033928-00696.warc.gz\"}"}
https://www.biostars.org/p/10454/	[ "How To Show The Name Of Genes On Manhattan Plot\n2\n5\nEntering edit mode\n12.4 years ago\nSara ▴ 130\n\nHi,\n\nI draw Manhattan plot in R but I like to show also the name of genes on it (http://www.genetics.org/content/187/2/367/F2.large.jpg) ? how can i do that ?\n\ngwas visualization r • 14k views\n8\nEntering edit mode\n12.4 years ago\nThomas ▴ 760\n\nIn relation to the above comments I just wanted to add a small example of a manhatten plot with addition of rs number (or genes) in R:\n\n### generation of a data set\n\npval<-runif(100000, 0, 1); logPval<--log(pval,base=10); pos=1:100000; chr<-paste(\"chr\",rep(1:20,ea=5000),sep=\"\"); rsID<-paste(\"rs\",1:100000,sep=\"\"); data<-as.data.frame(cbind(chr,pos,rsID,pval,logPval));\n\nvek<-as.numeric(gsub(data$chr,pattern=\"chr\",replacement=\"\"))%%2 ### vector that defines which dot should have a rs number (all with pval<0.0001) vek2<-ifelse(as.numeric(as.character(data[,\"pval\"]))<0.0001,T,F) ### plotting plot(x=as.numeric(data$pos),y=as.numeric(as.character(data$logPval)),col=c(\"red\",\"blue\")[as.factor(vek)]) ### adding the text text(labels=as.character(data$rsID[vek2]),x=as.numeric(data$pos)[vek2],y=as.numeric(as.character(data$logPval))[vek2],pos=4,cex=0.8)\n\n5\nEntering edit mode\n12.4 years ago\nSander Timmer ▴ 710\n\nIf I look at this plot I would almost think that these are placed there by hand.\n\nI'm not sure how your Manhattan plot looks like right now (did you use any package?) but Getting Genetics Done has quite some nice code examples about making a Manhattan plot and QQ plot in R using ggplot2\n\nIf you are willing to leave R you could also look at WGA viewer which can plot your Manhattan plot and add different data tracks next to it.\n\nIf you're just interested in showing the association later for a specific region I would recommend using LocusZoom, that tool can plot gene names + locations and adds LD information to a locus of interest.\n\n3\nEntering edit mode\n\n@Sander - Thanks for the link to my code. I've also used LocusZoom and found it useful. You can probably d/l a local copy and mod the code to add text to the plot.\n\n@Sarah - It shouldn't be hard to add the text in R using a text() command after creating the plot using the code in http://gettinggeneticsdone.blogspot.com/2011/04/annotated-manhattan-plots-and-qq-plots.html. You could even join your list of SNPs to a list of genes (as in http://gettinggeneticsdone.blogspot.com/2011/06/mapping-snps-to-genes-for-gwas.html ) and then automatically add gene labels if p is less than a threshold.\n\n0\nEntering edit mode\n\nI'd agree with Stephen that adding using text is probably the easiest way to do it. Unless you do this everyday and need a function to do it repeatedly, it's probably the best time investment." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.828798,"math_prob":0.72634554,"size":2570,"snap":"2023-40-2023-50","text_gpt3_token_len":696,"char_repetition_ratio":0.098597035,"word_repetition_ratio":0.1534091,"special_character_ratio":0.26692608,"punctuation_ratio":0.15156795,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96664506,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-08T03:09:17Z\",\"WARC-Record-ID\":\"<urn:uuid:5170b3e5-fa2b-4cf9-b583-af80cf444335>\",\"Content-Length\":\"27836\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7de4d831-f058-4d7c-af42-220a20d8a62f>\",\"WARC-Concurrent-To\":\"<urn:uuid:97cc2556-561c-43dd-870e-6df3be08113e>\",\"WARC-IP-Address\":\"45.79.169.51\",\"WARC-Target-URI\":\"https://www.biostars.org/p/10454/\",\"WARC-Payload-Digest\":\"sha1:WONHSEOLP6TF4E4EUKPHVI6YPWUK4V2B\",\"WARC-Block-Digest\":\"sha1:XEBBQHKBY23J6IQXR6D4YT2UASPFNNLX\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100710.22_warc_CC-MAIN-20231208013411-20231208043411-00547.warc.gz\"}"}
https://community.openhab.org/t/solved-calculate-duration-from-number-seconds/37445/11	[ "", null, "# [Solved]Calculate duration from number (seconds)\n\nTags: #<Tag:0x00007f5caa0c1710>\n\nI have an item which receives a number from an http request. that works as expected\nI want to calculate the hours and minutes (hh:mm) and send the new value to another item. Then I want to display that duration.\n\ne.g. 6060 = 01h 41min\n\nCan anyone help`?\n\nI tried several rules but non woked\n\n``````val totalSecs = SecondsNumber.state as Number\n\nval sec = totalSecs % 60\nval min = (totalSecs / 60) % 60\nval hrs = (totalSecs / (6060)) % 24\nval day = totalSecs / (606024)\n\n``````\n\nCould I ask to give a hint how to include your code to my Player-Item to show the min:sec instead of dezimal.\nHere my item (Squeezeboxplayer)\nI think I have to replace the %d, but how?\n\n``````Number SB_ARZ_Time \"Time [%d]\" { channel=\"squeezebox:squeezeboxplayer:LMS:SB_ARZ:currentPlayingTime\" }\n\n``````\n\nYou don’t. The code above is the body of a Rule. You must create Rules in text .rules files. See\n\nhttp://docs.openhab.org/tutorials/beginner/index.html\n\nhttp://docs.openhab.org/configuration/rules-dsl.html\n\nOK,\nI created a rule:\n\n``````rule \"Calculate decimal time counter\"\nwhen\nItem SB_ARZ_Time changed\nthen\nval totalSecs = SecondsNumber.state as Number\nval sec = totalSecs % 60\nval min = (totalSecs / 60) % 60\nval hrs = (totalSecs / (6060)) % 24\nval day = totalSecs / (606024)\nend\n``````\n\nBecause of my limited knowledge with object-orientated programming I don’t know how to handle the error which I see in the log.\n\n``````Rule 'Calculate decimal time counter': The name 'SecondsNumber' cannot be resolved to an item or type; line 5, column 18, length 13\n``````\n\nIt just says that you don‘t have an Item called „SecondsNumber“\n\nAlso, this is just a code fragment. You still need to do the work to take day, hrs, min, and sec into a String and postUpdate that to your appropriate Item.\n\nSB_ARZ_Time contains the number, so I changed to:\n\n``````rule \"Calculate decimal time counter\"\nwhen\nItem SB_ARZ_Time changed\nthen\nval totalSecs = SB_ARZ_Time.state as Number\nval sec = totalSecs % 60\nval min = (totalSecs / 60) % 60\nval hrs = (totalSecs / (6060)) % 24\nval day = totalSecs / (606024)\nend\n``````\n\nNow I get this error:\n\n``````Rule 'Calculate decimal time counter': Unknown variable or command '%'; line 6, column 12, length 14\n``````\n\nI really appreciate your help with some code.\n\nWell shoot. It looks like the Rules DSL can’t work with Numbers for the modulo operator.\n\n``val int totalSecs = (SB_ARZ_Time.state as Number).intValue``\n\nHi Rich,\n\nthank you for your quick reply! I will try it the next days. The follow up by Doxer is also very useful to me …\nOnce I have a working solution I will post it here … but it may take some days", null, "kind reagrds\nMarkus\n\nThis is the working rule:\n\n``````rule \"Calculate decimal time counter\"\nwhen\nItem SB_ARZ_Time changed\nthen\nval totalSecs = (SB_ARZ_Time.state as Number).intValue\nval sec = totalSecs % 60\nval min = (totalSecs / 60) % 60\nval hrs = (totalSecs / (6060)) % 24\nval day = totalSecs / (606024)\nlogInfo(\"default.rules\", min.toString + \":\" + sec.toString)\nend\n``````\n\nNow I have to investigate for the formating (ss:mm) and how to transfer this to the item.", null, "2 Likes\n\nSomething like this should work:\n\n``````TimeString.postUpdate(String::format(\"%02d:%02d:%02d:%02d\", day, hrs, min, sec))\n``````\n\nWhere TimeString is your String Item.\n\n1 Like\n\nGot my problem solved and it is running as expected.\n\nShort summary what I did:\n\nThos items are active:\n\n``````Number VU_Dauer \"Dauer [%s]\" \t\t( VUPLUS )\t{ http=\"<[http://192.168.1.6:80/web/getcurrent:3000:REGEX(.?<e2eventduration>(.?)</e2eventduration>.)]\" }\nString VU_Duration_converted \"Dauer1 [%s]\" \t\t( VUPLUS\n``````\n\nThis rule is set:\n\n``````rule \"Dauer\"\nwhen\nItem VU_Dauer changed\nthen\nval totalSecs = (VU_Dauer.state as Number).intValue\nval min = (totalSecs / 60) % 60\nval hrs = (totalSecs / (6060)) % 24\nval txt = (VU_Dauer)\nVU_Duration_converted.postUpdate(String::format(\"%02d:%02d\", hrs, min))\nlogWarn(\"hilfe\", \"\" +totalSecs)\nend\n``````\n\nLog tells me the correct received Number in seconds\n\n``````2017-12-21 11:37:49.498 [WARN ] [eclipse.smarthome.model.script.hilfe] - 21600\n``````\n\nRunning on OH 2 and OH 2.2 (release)\nThank your for the help provided, appreciate it very much!\n\nHi Markus,\nyour post helped me how to transfer the value from the rule to the item. Learning by doing", null, "1 Like" ]	[ null, "https://community-openhab-org.s3-eu-central-1.amazonaws.com/original/2X/0/0bf8618e720957d07d17407b2c0182b15ff28db9.png", null, "https://community.openhab.org/images/emoji/twitter/slight_smile.png", null, "https://community.openhab.org/images/emoji/twitter/frowning.png", null, "https://community.openhab.org/images/emoji/twitter/slight_smile.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6622596,"math_prob":0.89685553,"size":842,"snap":"2020-24-2020-29","text_gpt3_token_len":285,"char_repetition_ratio":0.10501193,"word_repetition_ratio":0.0,"special_character_ratio":0.347981,"punctuation_ratio":0.21472393,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97537977,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-05-31T19:51:53Z\",\"WARC-Record-ID\":\"<urn:uuid:3ef8fb8a-ff59-4757-a605-ac0b5493999c>\",\"Content-Length\":\"47560\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:efaf1b7b-2896-4594-bde8-65d82aabe4e1>\",\"WARC-Concurrent-To\":\"<urn:uuid:42c145c5-9cee-490f-9ef3-9d0a7f470f28>\",\"WARC-IP-Address\":\"46.101.248.207\",\"WARC-Target-URI\":\"https://community.openhab.org/t/solved-calculate-duration-from-number-seconds/37445/11\",\"WARC-Payload-Digest\":\"sha1:QM43P64QEVAEUQBUO77MJ3PY32EXZGSJ\",\"WARC-Block-Digest\":\"sha1:I2UOKSSSWBIQQRTYRYW5UQQM2OOTQUJO\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-24/CC-MAIN-2020-24_segments_1590347413624.48_warc_CC-MAIN-20200531182830-20200531212830-00531.warc.gz\"}"}
https://investingyrkwpjl.netlify.app/halbur65579qiqy/how-to-compute-rate-of-return-accounting-fa.html	[ "## How to compute rate of return accounting\n\n1 Feb 2017 Excel offers three functions for calculating the internal rate of return, and I recommend you use all three.\n\nFor the purpose of calculating net present value and internal rate of return, do companies use the accrual basis of accounting? Explain. Why might a firm choose 30 Oct 2019 The accounting rate of return is a method of calculating a projects return as a percentage of the investment in the project. It measures the 17 Mar 2016 But with IRR you calculate the actual return provided by the project's cash flows, then compare that rate of return with your company's hurdle rate ( It is an accounting technique to measure the profitability of the investment proposals. The Accounting Rate of Return (ARR) is calculated by dividing the Average IRR is harder to calculate than return on investment, but IRR has the advantage of automatically accounting for time differences between investments. This can 1 Feb 2017 Excel offers three functions for calculating the internal rate of return, and I recommend you use all three. five traditional criteria for determining whether a rate of return is appropriate (1). d = annual depreciation expense, which is the annual accounting charge for\n\n## 17 Mar 2016 But with IRR you calculate the actual return provided by the project's cash flows, then compare that rate of return with your company's hurdle rate (\n\nCalculate the IRR (Internal Rate of Return) of an investment with an unlimited number of cash flows. Depreciation should not be included in the economic analysis (nor should it have been included in the cash flow table). Depreciation is merely an accounting item Close enough to zero, Sam doesn't want to calculate any more. The Internal Rate of Return (IRR) is about 7%. So the key to the whole thing is calculating the Calculate the internal rate of return using Table 18.11 given the NPV for each Thirdly, IRR uses actual cash flows rather than accounting incomes like the ROR 18 Feb 2015 Accounting rate of return (ARR/ROI) = Average profit / Average book value * 100. The interpretation of the ARR / AAR rate. Abbreviated as ARR\n\n### Net income is the amount of total revenue that remains after accounting for all expenses for production, overhead, operations, administrations, debt service, taxes, amortization, and depreciation, as well as for one-time expenses for unusual events such as lawsuits or large purchases.\n\n24 Jul 2013 Estimate this by finding the cost of equity of projects or investments with similar risk. Like with the cost of debt, if the company has more than one 17 May 2018 a new approach to calculating an internal rate of return that illustrated the Congress, Rome 20-22 April, European Accounting Association. Since the deposits into the investment fund are irregular in their timing, there isn't really any single formula that will give the information you want. Your only hope 14 Aug 2012 This report shows how to calculate the Social. Internal Rate of Return of both technologies. We estimate the SIRR of FTTN at 15.2% and the SIRR 13 Mar 2017 This article will explain how to calculate the return on investment when The resulting number, expressed as a percentage, can be a good indicator of Your chief financial officer or accounting professional can help you\n\n### The average annual rate of return of your investment is the percentage change over several years, averaged out per year. A bank might guarantee a fixed rate per year, but the performance of many other investments varies from year to year. It helps to average the percentage change so you have a single number against which to compare other investments.\n\n24 Jul 2013 Estimate this by finding the cost of equity of projects or investments with similar risk. Like with the cost of debt, if the company has more than one 17 May 2018 a new approach to calculating an internal rate of return that illustrated the Congress, Rome 20-22 April, European Accounting Association. Since the deposits into the investment fund are irregular in their timing, there isn't really any single formula that will give the information you want. Your only hope 14 Aug 2012 This report shows how to calculate the Social. Internal Rate of Return of both technologies. We estimate the SIRR of FTTN at 15.2% and the SIRR 13 Mar 2017 This article will explain how to calculate the return on investment when The resulting number, expressed as a percentage, can be a good indicator of Your chief financial officer or accounting professional can help you\n\n## Accounting Rate of Return (ARR) is the percentage rate of return that is expected from an investment or asset compared to the initial cost of investment. Typically,\n\nAccounting Rate of Return (ARR) is the average net income an asset is expected to generate divided by its average capital cost, expressed as an annual percentage. The ARR is a formula used to make capital budgeting decisions, whether or not to proceed with a specific investment (a project, an acquisition, etc.) based on Making Capital Investment Decisions and How to Calculate Accounting Rate of Return – Formula & Example STEP 1. Before we start with calculating accounting rate of return we need to calculate an average STEP 2. The second step in our ARR calculation is to find the Annual depreciation charge. Determine the Annual Profit. This method of determining the Accounting Rate of Return uses the basic formula ARR = Average Annual Profit / Initial Investment. To begin, you'll need to find the Annual Profit. This number is based on accruals, not on cash, and it reflects the costs of amortization and depreciation. Simple Rate of Return Method: Learning Objectives: Compute the simple rate of return for an investment project. Definition and Explanation: The simple rate of return method is another capital budgeting technique that does not involve discounted cash flows. The method is also known as the accounting rate of return, the unadjusted rate of return, and the financial statement method.\n\nIRR is harder to calculate than return on investment, but IRR has the advantage of automatically accounting for time differences between investments. This can 1 Feb 2017 Excel offers three functions for calculating the internal rate of return, and I recommend you use all three." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.93678325,"math_prob":0.9141415,"size":6148,"snap":"2023-14-2023-23","text_gpt3_token_len":1243,"char_repetition_ratio":0.17138672,"word_repetition_ratio":0.41992188,"special_character_ratio":0.20624593,"punctuation_ratio":0.080789946,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9873741,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-03-29T15:22:19Z\",\"WARC-Record-ID\":\"<urn:uuid:b6d25bc6-44d9-45f8-a79d-e3818a871c7f>\",\"Content-Length\":\"32993\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:323144a3-6b67-408b-baf7-c65cacf8cf46>\",\"WARC-Concurrent-To\":\"<urn:uuid:1e34e399-3903-4601-af9f-c84cbcc2e8f3>\",\"WARC-IP-Address\":\"35.231.208.25\",\"WARC-Target-URI\":\"https://investingyrkwpjl.netlify.app/halbur65579qiqy/how-to-compute-rate-of-return-accounting-fa.html\",\"WARC-Payload-Digest\":\"sha1:OYFMSXGEVXC7QC2FGVSKUJK4ITTVIZEN\",\"WARC-Block-Digest\":\"sha1:LPLQ6HBOLUJ5A2X3SLITZO7DP6ENMZQB\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-14/CC-MAIN-2023-14_segments_1679296949009.11_warc_CC-MAIN-20230329151629-20230329181629-00159.warc.gz\"}"}
https://byjus.com/question-answer/a-number-from-1-to-11-is-chosen-at-random-what-is-the-probability-of-choosing-an-odd-number/	[ "", null, "", null, "", null, "", null, "Question\n\n# A number from $1$ to $11$ is chosen at random. What is the probability of choosing an odd number?\n\nOpen in App\nSolution\n\n## Given we can choose a number from $1$ to $11$.Total number of outcomes $=11$From $1$ to $11$, odd numbers are $1,3,5,7,9,11$The number of favorable outcomes $=6$We know that $\\mathrm{Probability}=\\frac{\\mathrm{number}\\mathrm{of}\\mathrm{favorable}\\mathrm{outcomes}}{\\mathrm{total}\\mathrm{number}\\mathrm{of}\\mathrm{outcomes}}$ $=\\frac{6}{11}$Therefore the probability of choosing an odd number from $1$ to $11$is $\\frac{6}{11}$.", null, "", null, "Suggest Corrections", null, "", null, "0", null, "", null, "", null, "", null, "", null, "", null, "Similar questions", null, "", null, "Explore more" ]	[ null, "data:image/svg+xml;base64,PHN2ZyB3aWR0aD0iNDQiIGhlaWdodD0iNDQiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgdmVyc2lvbj0iMS4xIi8+", null, "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7", null, "data:image/svg+xml;base64,PHN2ZyB3aWR0aD0iNDQiIGhlaWdodD0iNDQiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgdmVyc2lvbj0iMS4xIi8+", null, "https://byjus.com/question-answer/_next/image/", null, "data:image/svg+xml;base64,PHN2ZyB3aWR0aD0iMjAiIGhlaWdodD0iMjAiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgdmVyc2lvbj0iMS4xIi8+", null, "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7", null, "data:image/svg+xml;base64,PHN2ZyB3aWR0aD0iMjAiIGhlaWdodD0iMjAiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgdmVyc2lvbj0iMS4xIi8+", null, "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7", null, "data:image/svg+xml;base64,PHN2ZyB3aWR0aD0iNjAwIiBoZWlnaHQ9IjQwMCIgeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzIwMDAvc3ZnIiB2ZXJzaW9uPSIxLjEiLz4=", null, "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7", null, "data:image/svg+xml;base64,PHN2ZyB3aWR0aD0iNDAwIiBoZWlnaHQ9IjQwMCIgeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzIwMDAvc3ZnIiB2ZXJzaW9uPSIxLjEiLz4=", null, "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7", null, "data:image/svg+xml;base64,PHN2ZyB3aWR0aD0iNDQiIGhlaWdodD0iNDAiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgdmVyc2lvbj0iMS4xIi8+", null, "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7", null, "data:image/svg+xml;base64,PHN2ZyB3aWR0aD0iNDQiIGhlaWdodD0iNDAiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgdmVyc2lvbj0iMS4xIi8+", null, "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.91040605,"math_prob":1.0000046,"size":590,"snap":"2022-40-2023-06","text_gpt3_token_len":163,"char_repetition_ratio":0.19624573,"word_repetition_ratio":0.17475729,"special_character_ratio":0.2677966,"punctuation_ratio":0.11023622,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99997044,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32],"im_url_duplicate_count":[null,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\":\"2023-02-06T10:04:18Z\",\"WARC-Record-ID\":\"<urn:uuid:040a17e4-038d-402b-a691-3b2302bc1cf6>\",\"Content-Length\":\"160020\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d40a7d28-4dfe-48f4-a5b4-9f0c65242939>\",\"WARC-Concurrent-To\":\"<urn:uuid:9e255b37-d82b-4abb-9b3f-2ab9f9e488c7>\",\"WARC-IP-Address\":\"162.159.129.41\",\"WARC-Target-URI\":\"https://byjus.com/question-answer/a-number-from-1-to-11-is-chosen-at-random-what-is-the-probability-of-choosing-an-odd-number/\",\"WARC-Payload-Digest\":\"sha1:FLE4IYPIUO2LYQSULKCBDBHDY522DEZ2\",\"WARC-Block-Digest\":\"sha1:EZ6FDLFWFXVKOKSKPPU4EPNUUF7LXBZ4\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-06/CC-MAIN-2023-06_segments_1674764500334.35_warc_CC-MAIN-20230206082428-20230206112428-00584.warc.gz\"}"}
https://www.colorhexa.com/0083e0	[ "# #0083e0 Color Information\n\nIn a RGB color space, hex #0083e0 is composed of 0% red, 51.4% green and 87.8% blue. Whereas in a CMYK color space, it is composed of 100% cyan, 41.5% magenta, 0% yellow and 12.2% black. It has a hue angle of 204.9 degrees, a saturation of 100% and a lightness of 43.9%. #0083e0 color hex could be obtained by blending #00ffff with #0007c1. Closest websafe color is: #0099cc.\n\n• R 0\n• G 51\n• B 88\nRGB color chart\n• C 100\n• M 42\n• Y 0\n• K 12\nCMYK color chart\n\n#0083e0 color description : Pure (or mostly pure) blue.\n\n# #0083e0 Color Conversion\n\nThe hexadecimal color #0083e0 has RGB values of R:0, G:131, B:224 and CMYK values of C:1, M:0.42, Y:0, K:0.12. Its decimal value is 33760.\n\nHex triplet RGB Decimal 0083e0 `#0083e0` 0, 131, 224 `rgb(0,131,224)` 0, 51.4, 87.8 `rgb(0%,51.4%,87.8%)` 100, 42, 0, 12 204.9°, 100, 43.9 `hsl(204.9,100%,43.9%)` 204.9°, 100, 87.8 0099cc `#0099cc`\nCIE-LAB 53.613, 4.914, -55.462 21.568, 21.612, 73.552 0.185, 0.185, 21.612 53.613, 55.68, 275.063 53.613, -31.732, -87.069 46.489, 1.455, -61.262 00000000, 10000011, 11100000\n\n# Color Schemes with #0083e0\n\n• #0083e0\n``#0083e0` `rgb(0,131,224)``\n• #e05d00\n``#e05d00` `rgb(224,93,0)``\nComplementary Color\n• #00e0cd\n``#00e0cd` `rgb(0,224,205)``\n• #0083e0\n``#0083e0` `rgb(0,131,224)``\n• #0013e0\n``#0013e0` `rgb(0,19,224)``\nAnalogous Color\n• #e0cd00\n``#e0cd00` `rgb(224,205,0)``\n• #0083e0\n``#0083e0` `rgb(0,131,224)``\n• #e00013\n``#e00013` `rgb(224,0,19)``\nSplit Complementary Color\n• #83e000\n``#83e000` `rgb(131,224,0)``\n• #0083e0\n``#0083e0` `rgb(0,131,224)``\n• #e00083\n``#e00083` `rgb(224,0,131)``\n• #00e05d\n``#00e05d` `rgb(0,224,93)``\n• #0083e0\n``#0083e0` `rgb(0,131,224)``\n• #e00083\n``#e00083` `rgb(224,0,131)``\n• #e05d00\n``#e05d00` `rgb(224,93,0)``\n• #005694\n``#005694` `rgb(0,86,148)``\n``#0065ad` `rgb(0,101,173)``\n• #0074c7\n``#0074c7` `rgb(0,116,199)``\n• #0083e0\n``#0083e0` `rgb(0,131,224)``\n• #0092fa\n``#0092fa` `rgb(0,146,250)``\n• #149dff\n``#149dff` `rgb(20,157,255)``\n• #2ea8ff\n``#2ea8ff` `rgb(46,168,255)``\nMonochromatic Color\n\n# Alternatives to #0083e0\n\nBelow, you can see some colors close to #0083e0. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #00bbe0\n``#00bbe0` `rgb(0,187,224)``\n• #00a8e0\n``#00a8e0` `rgb(0,168,224)``\n• #0096e0\n``#0096e0` `rgb(0,150,224)``\n• #0083e0\n``#0083e0` `rgb(0,131,224)``\n• #0070e0\n``#0070e0` `rgb(0,112,224)``\n• #005ee0\n``#005ee0` `rgb(0,94,224)``\n• #004be0\n``#004be0` `rgb(0,75,224)``\nSimilar Colors\n\n# #0083e0 Preview\n\nText with hexadecimal color #0083e0\n\nThis text has a font color of #0083e0.\n\n``<span style=\"color:#0083e0;\">Text here</span>``\n#0083e0 background color\n\nThis paragraph has a background color of #0083e0.\n\n``<p style=\"background-color:#0083e0;\">Content here</p>``\n#0083e0 border color\n\nThis element has a border color of #0083e0.\n\n``<div style=\"border:1px solid #0083e0;\">Content here</div>``\nCSS codes\n``.text {color:#0083e0;}``\n``.background {background-color:#0083e0;}``\n``.border {border:1px solid #0083e0;}``\n\n# Shades and Tints of #0083e0\n\nA shade is achieved by adding black to any pure hue, while a tint is created by mixing white to any pure color. In this example, #000508 is the darkest color, while #f4faff is the lightest one.\n\n• #000508\n``#000508` `rgb(0,5,8)``\n• #00101c\n``#00101c` `rgb(0,16,28)``\n• #001c2f\n``#001c2f` `rgb(0,28,47)``\n• #002743\n``#002743` `rgb(0,39,67)``\n• #003357\n``#003357` `rgb(0,51,87)``\n• #003e6a\n``#003e6a` `rgb(0,62,106)``\n• #004a7e\n``#004a7e` `rgb(0,74,126)``\n• #005592\n``#005592` `rgb(0,85,146)``\n• #0061a5\n``#0061a5` `rgb(0,97,165)``\n• #006cb9\n``#006cb9` `rgb(0,108,185)``\n• #0078cc\n``#0078cc` `rgb(0,120,204)``\n• #0083e0\n``#0083e0` `rgb(0,131,224)``\n• #008ef4\n``#008ef4` `rgb(0,142,244)``\n• #0899ff\n``#0899ff` `rgb(8,153,255)``\n• #1ca1ff\n``#1ca1ff` `rgb(28,161,255)``\n• #2fa9ff\n``#2fa9ff` `rgb(47,169,255)``\n• #43b1ff\n``#43b1ff` `rgb(67,177,255)``\n• #57b9ff\n``#57b9ff` `rgb(87,185,255)``\n• #6ac1ff\n``#6ac1ff` `rgb(106,193,255)``\n• #7ec9ff\n``#7ec9ff` `rgb(126,201,255)``\n• #92d2ff\n``#92d2ff` `rgb(146,210,255)``\n• #a5daff\n``#a5daff` `rgb(165,218,255)``\n• #b9e2ff\n``#b9e2ff` `rgb(185,226,255)``\n• #cceaff\n``#cceaff` `rgb(204,234,255)``\n• #e0f2ff\n``#e0f2ff` `rgb(224,242,255)``\n• #f4faff\n``#f4faff` `rgb(244,250,255)``\nTint Color Variation\n\n# Tones of #0083e0\n\nA tone is produced by adding gray to any pure hue. In this case, #677179 is the less saturated color, while #0083e0 is the most saturated one.\n\n• #677179\n``#677179` `rgb(103,113,121)``\n• #5f7381\n``#5f7381` `rgb(95,115,129)``\n• #56748a\n``#56748a` `rgb(86,116,138)``\n• #4e7692\n``#4e7692` `rgb(78,118,146)``\n• #45779b\n``#45779b` `rgb(69,119,155)``\n• #3c79a4\n``#3c79a4` `rgb(60,121,164)``\n• #347aac\n``#347aac` `rgb(52,122,172)``\n• #2b7cb5\n``#2b7cb5` `rgb(43,124,181)``\n• #227dbe\n``#227dbe` `rgb(34,125,190)``\n• #1a7fc6\n``#1a7fc6` `rgb(26,127,198)``\n• #1180cf\n``#1180cf` `rgb(17,128,207)``\n• #0982d7\n``#0982d7` `rgb(9,130,215)``\n• #0083e0\n``#0083e0` `rgb(0,131,224)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #0083e0 is perceived by people affected by a color vision deficiency. This can be useful if you need to ensure your color combinations are accessible to color-blind users.\n\nMonochromacy\n• Achromatopsia 0.005% of the population\n• Atypical Achromatopsia 0.001% of the population\nDichromacy\n• Protanopia 1% of men\n• Deuteranopia 1% of men\n• Tritanopia 0.001% of the population\nTrichromacy\n• Protanomaly 1% of men, 0.01% of women\n• Deuteranomaly 6% of men, 0.4% of women\n• Tritanomaly 0.01% of the population" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.53023094,"math_prob":0.82887626,"size":3692,"snap":"2022-40-2023-06","text_gpt3_token_len":1671,"char_repetition_ratio":0.14669198,"word_repetition_ratio":0.0073664826,"special_character_ratio":0.55931747,"punctuation_ratio":0.23198198,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.992225,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-09-30T21:34:12Z\",\"WARC-Record-ID\":\"<urn:uuid:18cca348-49b8-477c-a0f7-5e628fae5994>\",\"Content-Length\":\"36148\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d1ca7ba2-6b8f-4fd1-94f5-ef935c0697cc>\",\"WARC-Concurrent-To\":\"<urn:uuid:ca68eff1-4f27-445f-8027-f6c99f19abea>\",\"WARC-IP-Address\":\"178.32.117.56\",\"WARC-Target-URI\":\"https://www.colorhexa.com/0083e0\",\"WARC-Payload-Digest\":\"sha1:ULDNFOFBOSDMWDMYC6B443IUABVQA37V\",\"WARC-Block-Digest\":\"sha1:VH67OZFOEO5ZSUSUHXGJSRG7HMUGJD54\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030335504.37_warc_CC-MAIN-20220930212504-20221001002504-00576.warc.gz\"}"}
https://www.bettersizeinstruments.com/products/dynamic-light-scattering-dls/	[ " Dynamic Light Scattering DLS Particle Size Analyzer System Machine\n• Global", null, "# Dynamic Light Scattering (DLS)\n\nDynamic light scattering (DLS), also known as photon correlation spectroscopy (PCS), is a commonly used characterization method for nanoparticles. The DLS particle size analyzer has the advantages of accuracy, rapidity, and good repeatability for the measurement of Nano particles, emulsions or suspensions. BeNano 90 Zeta nano particle size analyser is a typical nanoparticle size measurement instrument based on dynamic light scattering.It can measure nanomaterial down to 1 nanometer which is an essential tool for nanoparticle size distribution measurement to understand and research nano powdered materials.\nInstruments\n\n## Theoretical background\n\nWhat is light scattering? When a monochromatic and coherent light source irradiates onto the particle, the electromagnetic wave will interact with the charges in atoms that compose the particle, and thus induce the formation of an oscillating dipole in the particle. Light scattering refers to the emission of light in all directions from oscillating dipole. During quasi-elastic light scattering, the frequency changes between scattered light and incident light are small, and the light scattered by the oscillating dipole has a spectrum that broadens around the incident light frequency.\nThe scattered light intensity depends on the particle's intrinsic physical properties such as size and molecular weight. The scattered light intensity is not a constant value; it fluctuates over time due to the random walk of particles that are undergoing Brownian motion which refers to the particle's continuous and spontaneous random walk when placed in the medium resulting from the collisions between the particles and the medium molecules. The fluctuations in scattered light intensity with time allows us to calculate the diffusion coefficient through the auto-correlation function analysis. To quantify the speed of Brownian motion, the translational diffusion coefficient is modelled by the Stokes-Einstein equation. Notice here the diffusion coefficient is specified by the word “translational”, indicating that only the translational, but not the rotational movement of the particle is taken into account. The translational diffusion coefficient has the unit of area per unit time, where the area is introduced to prevent the sign change convention when the particle is moving away from its origin. Then using the Stokes – Einstein equation, the particle size distribution can be calculated from the diffusion coefficient. This technique is called the dynamic light scattering, abbreviated as DLS.\n\nThe Stokes-Einstein equation is expressed as follows:", null, "Equation 1: The Stokes-Einstein equation", null, "Hydrodynamic radius refers to the effective radius of a particle that has identical diffusion to a perfectly spherical particle of that radius. For example, as seen in figure 1, the true radius of the particle refers to the distance between its center and its outer circumference, while the hydrodynamic radius includes the length of the attached segments since they diffuse as a whole. Hydrodynamic radius is inversely proportional to the translational diffusion coefficient.", null, "Figure 1: Illustration of hydrodynamic radius.\n\n## Applications\n\nBy analyzing the fluctuating scattered light intensity due to Brownian motion, DLS can obtain the particle size distribution of small particles suspended in a diluted solution. Typically, the measuring size limit of DLS falls in the nano and sub-micro range, with the magnitude of 1 nanometer to 10 micrometers. There are several advantages of using the DLS when sizing particles. First, DLS is non-invasive to the samples, meaning that the structure of the molecules would not be destroyed during sizing. A small amount of sample is sufficient for a diluted solution preparation. With the DLS method, results with great repeatability and accuracy can be obtained within a few minutes. The testing process is nearly all automatic, minimizing operation errors from different operators. With DLS, the particle size distribution can be measured at different temperatures, and thus a thermal analysis can be conducted on the test sample. DLS provides various industries the opportunity to control their products' quality and therefore maximizing product performance by controlling particle size. These industries include but are not limited to semi-conductors, renewable energy, pharmaceuticals, inks, pigments, batteries, et cetera.\n\n## Optical Setup\n\nThe whole setup of DLS instrument is shown in Figure 2.", null, "Figure 2: Dynamic light scattering optical set-up of BeNano 90, Bettersize Instruments.\n\n•Laser\nThe majority of the laser devices in DLS instruments are gas lasers and solid-state lasers. Typical example of gas laser in DLS setup is helium-neon laser which emits laser with a wavelength of 632.8 nm. A solid-state laser refers to a laser device where a solid act as the gain medium. In a solid-state laser, small amounts of solid impurities called “dopant\" are added to the gain medium to change its optical properties. These dopants are often rare-earth minerals such as neodymium, chromium, and ytterbium. The most commonly used solid-state laser is neodymium-doped yttrium aluminum garnet, abbreviated as Nd: YAG. Gas laser has the advantages of stable wavelength emission with relatively low cost. However, a gas laser usually has a relatively large volume that makes it very bulky. On the other hand, a solid-state laser is smaller in size and also less heavy, making it more flexible to handle.\n\n•Detector\nAfter the laser beam irradiates onto the sample cell, light is scattered by the particle, and this scattered light is fluctuated because of Brownian motion. A highly sensitive detector picks up these scattered light fluctuations signals at even low-intensity levels and converts them to electrical signals for further analysis in the correlator. Commonly used detectors in an optical setup of DLS include photomultiplier tube and avalanche photodiode. According to Lawrence W.G. et al., PMT and APD have similar noise to signal performance at most signal levels, while the APD outweighs the PMT at red and near-infrared spectral regions. APD also has higher absolute quantum efficiency than PMT. Because of these reasons, recently APD is being more frequently utilized in DLS devices.\n\n•Correlator\nAfter the optical setup, the process of scattering and collecting light intensity is completed. The signals detected by detectors are then analyzed in the correlator to eventually calculate the hydrodynamic radius distribution.\nWe can multiply the scattering intensity collected from the detector with itself after it has been shifted by some arbitrary interval tau (τ) in time. This τ can be anything between a few nanoseconds and microseconds, but the actual value of the time interval does not affect the test result.\nAfter applying mathematical algorithm, the auto-correlation function G1(q, τ) can be obtained. G1(q, τ) single-exponentially decays from 1 to 0, with 0 meaning there's no correlation at all between signals at time t and time t plus τ, and 1 meaning perfect correlation. Finally, with all the known information of the correlation function, the hydrodynamic radius can be computed using the Stokes-Einstein equation.\n\n## Monodisperse vs Polydisperse\n\nMonodisperse particles are all identical in size, shape, and mass, resulting in one narrow peak in the particle size distribution curve. On the other hand, polydisperse particles are not uniform in those parameters. It is important to realize the polydispersity of the samples because the algorithms of calculating hydrodynamic radius distribution in the correlator are different depending on whether the samples are monodisperse or polydisperse.\nTwo main mathematical algorithms are used to solve the auto-correlation function of polydisperse sample. The first and most common one is the Cumulants method, which involves solving the Taylor expansion of the auto-correlation function. However, the Cumulants method is only valid with samples that have small size polydispersity. Validation of the calculation can be done by computing and checking the polydispersity index, or PDI, and Cumulants analysis is only valid if the PDI value is relatively small. The CONTIN algorithm can directly compute the hydrodynamic radius distribution for samples that are widely dispersed. It is a relatively complicated mathematical method involving regularization.\n\n## Data Interpretation\n\nInterpreting results can aid us in evaluating the quality of the particle size test, and also obtain information about the particle size distribution.\nThe quality of the correlation function should be checked before proceeding to the particle size analysis since it directly relates to the accuracy of the particle size result. The overall shape of the correlation function could well indicate its quality. As shown in figure 6, if the correlation curve is a smooth curve exponentially decaying from 1 to 0 without presence of noise, it suggests that the correlation was well performed and it is good to proceed to particle size distribution analysis.", null, "Figure 6: Example of a good correlation function curve.\n\nHowever, if the curve is still overall smooth with some level of noise, as shown in the figure 7, it might be due to the presence of impurities in the samples that affect the repeatability of the results. Under this scenario, the operator can filter the sample solution with the appropriate syringe pore size again to remove the impurities such as big dust particles in the solution.", null, "Figure 7: Example of a correlation function curve with noise.\n\nWhen the scattering is insufficient in a test, its correlation function curve would look like the curve in figure 8.", null, "Figure 8: Example of a poor correlation function curve.\n\nIn this case, the maximum value of the function is much less than 1, and it does not exhibit exponentially decay behavior. The operator could increase the sample concentration or the number of sub-runs to increase the amount of scattering.\n\nDLS reports results in z-average particle size, which is a scattered intensity weighted size. It comes from the fact that when computing the correlation function integral using the Cumulants and CONTIN method, an average translational diffusion coefficient is obtained and thus resulting in the average hydrodynamic radius from the Stokes-Einstein equation. The z-average particle size’s validity should be checked with the polydispersity index or PDI. As shown in the table, a sample results report of particle size from DLS includes its z-average particle size with uncertainty, and the PDI value corresponding to that z-avg particle size.\nIf the value of PDI is large, indicating that the samples are possibly polydisperse, then the z-average particle size is not a fully representative description of the given sample.\nAccording to the ISO 22412:2017 Particle Size analysis of dynamic light scattering, the particle size results should be reported along with its uncertainties and repeatability. The measurement uncertainty is expressed by the standard deviation, while the repeatability is the relative standard deviation that describes how close the results obtained from multiple measurements are to each other within each run of the test. As regulated by ISO 22412:2017, monodisperse materials with diameters between 50nm and 200nm should have z-avg particle size with repeatability less than 2%.\n\n## Reference\n\nChu, B. Laser Light Scattering: Basic Principles and Practice, 2nd ed.; Academic Press: Boston, 1991.\n\nDian, L.; Yu, E.; Chen, X.; Wen, X.; Zhang, Z.; Qin, L.; Wang, Q.; Li, G.; Wu, C. Enhancing Oral Bioavailability of Quercetin Using Novel Soluplus Polymeric Micelles. Nanoscale Res Lett 2014, 9 (1), 684. https://doi.org/10.1186/1556-276X-9-684.\n\nDhont, J. K. G. An Introduction to Dynamics of Colloids; Studies in interface science; Elsevier: Amsterdam, Netherlands ; New York, 1996.\n\nFalke, S.; Betzel, C. Dynamic Light Scattering (DLS): Principles, Perspectives, Applications to Biological Samples. In Radiation in Bioanalysis; Pereira, A. S., Tavares, P., Limão-Vieira, P., Eds.; Bioanalysis; Springer International Publishing: Cham, 2019; Vol. 8, pp 173–193. https://doi.org/10.1007/978-3-030-28247-9_6.\n\nISO 22412:2017. Particle Size Analysis – Dynamic Light Scattering (DLS). International Organization for Standardization.\n\nLawrence, W. G., Varadi, G., Entine, G., Podniesinski, E., & Wallace, P. K. (2008). A comparison of avalanche photodiode and photomultiplier tube detectors for flow cytometry. Imaging, Manipulation, and Analysis of Biomolecules, Cells, and Tissues VI. doi:10.1117/12.758958\n\nLight Scattering from Polymer Solutions and Nanoparticle Dispersions; Springer Laboratory; Springer Berlin Heidelberg: Berlin, Heidelberg, 2007. https://doi.org/10.1007/978-3-540-71951-9.\n\nNanoscale Informal Science Education Network, NISE Network, Scientific Image – Gold Nanoparticles. Retrieved from https://www.nisenet.org/catalog/scientific-image-gold-nanoparticles.\n\n•", null, "•", null, "[email protected]\n•", null, "•", null, "" ]	[ null, "https://www.bettersizeinstruments.com/uploads/image/20210120/16/nano-banner.jpg", null, "https://www.bettersizeinstruments.com/uploads/image/20210301/15/the-stokes-einstein-equation.jpg", null, "https://www.bettersizeinstruments.com/uploads/image/20210301/15/equation-1.jpg", null, "https://www.bettersizeinstruments.com/uploads/image/20210301/15/illustration-of-hydrodynamic-radius.jpg", null, "https://www.bettersizeinstruments.com/uploads/image/20210301/15/dynamic-light-scattering-optical-set-up-of-benano-90-bettersize-instruments.jpg", null, "https://www.bettersizeinstruments.com/uploads/image/20210301/15/example-of-a-good-correlation-function-curve.jpg", null, "https://www.bettersizeinstruments.com/uploads/image/20210301/15/example-of-a-correlation-function-curve-with-noise.jpg", null, "https://www.bettersizeinstruments.com/uploads/image/20210301/15/example-of-a-poor-correlation-function-curve.jpg", null, "https://www.bettersizeinstruments.com/themes/simple/img/add.png", null, "https://www.bettersizeinstruments.com/themes/simple/img/email.png", null, "https://www.bettersizeinstruments.com/themes/simple/img/phone.png", null, "https://www.bettersizeinstruments.com/uploads/image/20190613/13/bettersize-wechat.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.88801944,"math_prob":0.84033173,"size":16860,"snap":"2021-43-2021-49","text_gpt3_token_len":3419,"char_repetition_ratio":0.15697674,"word_repetition_ratio":0.020145044,"special_character_ratio":0.19270463,"punctuation_ratio":0.14787799,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9509763,"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],"im_url_duplicate_count":[null,null,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,5,null,5,null,5,null,5,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-12-05T11:17:00Z\",\"WARC-Record-ID\":\"<urn:uuid:3a10f1c0-5f82-4ef7-be99-d45d1ad35257>\",\"Content-Length\":\"155939\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e9869b39-8e2e-4e8f-8c6f-192d539f7f4e>\",\"WARC-Concurrent-To\":\"<urn:uuid:9ce38251-9df6-4bd8-b677-e22c508b7f61>\",\"WARC-IP-Address\":\"47.246.23.146\",\"WARC-Target-URI\":\"https://www.bettersizeinstruments.com/products/dynamic-light-scattering-dls/\",\"WARC-Payload-Digest\":\"sha1:5W2QMUSF5KOI6G5LMN6ZAMCEFFJIOS6I\",\"WARC-Block-Digest\":\"sha1:S6JU4RT6VNNOVDHVJ4RUFEABJFS2QYDJ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964363157.32_warc_CC-MAIN-20211205100135-20211205130135-00069.warc.gz\"}"}
https://jhmtr.semnan.ac.ir/article_149.html	[ "# Effect of magnetic field on the boundary layer flow, heat, and mass transfer of nanofluids over a stretching cylinder\n\nDocument Type : Full Lenght Research Article\n\nAuthors\n\nDepartment of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran\n\nAbstract\n\nThe effect of a transverse magnetic field on the boundary layer flow and heat transfer of an\nisothermal stretching cylinder is analyzed. The governing partial differential equations for the\nmagnetohydrodynamic, temperature, and concentration boundary layers are transformed into a set\nof ordinary differential equations using similarity transformations. The obtained ordinary\ndifferential equations are numerically solved for a range of non-dimensional parameters. Results\nshow that the presence of a magnetic field would significantly affects the boundary layer profiles.\nAn increase in magnetic parameter would decrease the reduced Nusselt and Sherwood numbers.\n\nKeywords\n\n#### Full Text\n\n1.\n\n Effect of magnetic field on the boundary layer flow, heat, and mass transfer of nanofluids over a stretching cylinder Aminreza Noghrehabadi*, Mohammad Ghalambaz, Ehsan Izadpanahi, Rashid Pourrajab Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran\n\n PAPER INFO\n\nHistory:\n\nReceived in revised form 22 November 2013\n\nAccepted 14 December 2013\n\nKeywords:\n\nNanofluid\n\nStretching cylinder\n\nMagnetic field\n\nBrownian motion\n\nThermophoresis\n\n A B S T R A C T The effect of a transverse magnetic field on the boundary layer flow and heat transfer of an isothermal stretching cylinder is analyzed. The governing partial differential equations for the magnetohydrodynamic, temperature, and concentration boundary layers are transformed into a set of ordinary differential equations using similarity transformations. The obtained ordinary differential equations are numerically solved for a range of non-dimensional parameters. Results show that the presence of a magnetic field would significantly affects the boundary layer profiles. An increase in magnetic parameter would decrease the reduced Nusselt and Sherwood numbers. © 2014 Published by Semnan University Press. All rights reserved.\n Journal of Heat and Mass Transfer Research Journal homepage: http://jhmtr.journals.semnan.ac.ir\n Journal of Heat and Mass Transfer Research 1 (2014) 9-15\n\nIntroduction\n\nRecently, a number of studies have been carried out on the effects of electrically conducting fluids on the flow and heat transfer of a viscous fluid passing a moving surface in the presence of a magnetic field. Liquid metals and water mixed with a little acid are the two common examples of electrically conducting liquids. There are some examples about technological applications of magnetohydrodynamic (MHD) viscous flow which include hot rolling, wire drawing, annealing, thinning of copper wires, glass-fiber and paper production, drawing of plastic films, metal and polymer extrusion, and metal spinning. In all these cases, the properties of the final product depend on the rate of cooling by drawing such strips in electrically conducting fluids subject to a magnetic field. Therefore, the heating or cooling characteristics during such processes have a significant influence on the quality of the final products. The heating or cooling characteristics mostly depend on the skin friction and the surface heat transfer rate.\n\nCommon heat transfer fluids such as water, ethylene glycol, and engine oil have limited heat transfer capabilities owing to their low thermal conductivity, whereas metals have much higher thermal conductivities than these fluids. Therefore, dispersing high thermal conductive solid particles in a conventional heat transfer fluid may enhance the thermal conductivity of the resulting fluid.\n\nNanofluid is a fluid containing nanometer-sized particles, called nanoparticles. The term \"Nanofluid\" has been first proposed by Choi to indicate engineered colloids consist of nanoparticles dispersed in a base fluid. The base fluid is usually a conductive fluid, such as water or ethylene glycol. Other base fluids include bio-fluids, polymer solutions, oils, and other lubricants. One of the outstanding characteristic of nanofluids is their enhanced thermal conductivity . The nanoparticles used in synthesis of nanofluids are typically metallic (Al, Cu), metallic oxides (Al2O3, TiO2), carbides (SiC), nitrides (AlN, SiN) or carbon nanotubes with the diameter which ranges between 1 and 100 nm. The thermophoresis and Brownian motion effects are also important in heat transfer of nanofluids. The migration of nanoparticles because of these effects would influence the local heat transfer rate.\n\nRecently, the flow and heat transfer over stretching surfaces have attracted the attention of many researchers [3-6].\n\nIshak et al. investigated the magnetohydrodaynamic flow and heat transfer over a stretching cylinder. They reduced the governing equations to a system of ordinary differential equations. Later, the system of equations was numerically solved using Keller box method. The effect of magnetic parameter, Prandtl number, and Reynolds number on the velocity and temperature fields were thoroughly examined. Wang investigated the steady flow of a viscous fluid outside a stretching hollow cylinder. Ishak et al. studied the effect of suction/blowing on the flow and heat transfer past a stretching cylinder. They found that the magnitude of the skin friction coefficient increases with Reynolds number while the variation of Prandtl number does not show a significant effect on the skin friction coefficient.\n\nRecently, Rasekh et al. have analyzed the flow and heat transfer of nanofluids over a stretching cylinder. They reduced the governing equations to a set of ordinary differential equations. They have reported that the slip of nanoparticles because of thermophoresis and Brownian motion forces affects the heat transfer rate of nanofluids in the boundary layer. Gorla et al. have considered a melting boundary condition on the surface of the stretching cylinder and analyzed the flow and heat transfer of nanofluids.\n\nTo the best of author’s knowledge, the effect of a magnetic field on the boundary layer flow and heat transfer of nanofluids over a stretching cylinder has not been analyzed yet. The present study aims to analyze the development of the steady boundary layer flow and heat transfer of a magnetohydrodynamic nanofluid over a stretching cylinder. The governing partial differential boundary layer equations in the cylindrical form are presented and then transformed into a set of ordinary differential equations. The obtained equations are a function of magnetic parameter M, suction/injection parameter γ, Reynolds number Re, Prandtl number Pr, Lewis number Le, Brownian motion parameter Nb, and thermophoresis parameter Nt. The equations are solved numerically for a range of non-dimensional parameters.\n\n2. Formulation of the problem\n\nConsider the laminar steady flow of an incompressible electrically conducting nanofluid (with electrical conductivity σ) over a linear stretching cylinder. The movement of flow is because of the stretch of the cylinder. The flow outside the boundary layer is quiescent. A uniform magnetic field of intensity B0 acts in the radial direction. It is assumed that the effect of the induced magnetic field is negligible, which is valid when the magnetic Reynolds number is small. The viscous dissipation, Ohmic heating, and Hall effects are neglected as they are also assumed to be small. Fig. 1 depicts a schematic view of the physical model and the coordinate system. z-axis is measured along the axis of the cylinder and the r-axis is measured in the radial direction. The axial velocity of the stretching cylinder was assumed to be linear. Hence, it can be represented as ww=2c.z where c is a positive constant. The surface of the stretching cylinder is permeable; therefore, the surface of the cylinder is subject to mass transfer, which can be represented as uw=-c.a.γ. The positive and negative values of γ show mass absorption and mass injection, respectively. The temperature and concentration of nanofluid outside the boundary layer are constant values of Tw and φw. The thermo-physical properties are assumed to be constant. Under such assumptions, the governing equation for conservation of mass, momentum, thermal energy, and nanoparticles’ concentration are as following:\n\n (1) (2) (3) (4) (5)\n\nhere u and w are the velocity components along the r and z axes, respectively. p is the fluid pressure, ρ is the density of nanofluid, ν is the kinematic viscosity of nanofluid, σ is the electrical conductivity of nanofluid and B0 is the strength of the uniform magnetic field, α is the thermal diffusivity of nanofluid, DB is the Brownian diffusion coefficient, DT is the thermophoresis diffusion coefficient. τ is the ratio between the effective heat capacity of the nanoparticles ((ρc)p) and heat capacity of the nanofluid ((ρc)nf), i.e. τ = (ρc)p /(ρc)nf.\n\nThe boundary conditions on the surface of the cylinder are:\n\n (6) Fig. 1. Physical model and coordinate system.\n\nwhere c is a constant and z is the axial direction. The appropriate boundary conditions at the far field (i.e. r→∞) are:\n\n (7)\n\nIntroducing the following similarity variables reduces the governing and boundary conditions to the set of ordinary differential equations (Eqs. 9-11) subjected to boundary conditions 12 and 13:\n\n , , , (8-a) (8-b) (9) (10) (11) (12) (13) The parameters in Eqs. (9)-(11) are defined as: (14) (15)\n\nhere Pr, Re, Le, M, Nb and Nt denote the Prandtl number, Reynolds number, Lewis number, the magnetic parameter, the Brownian motion parameter, and the thermophoresis parameter, respectively. The pressure P also can be determined from Eq. (3) as following:\n\n (16)\n\nPhysical quantities of interest are the skin friction coefficient Cf, Nusselt number Nu, and Sherwood number Sh, which can be defined as:\n\n (17)\n\nwhere τw is the wall shear stress, qw is the wall heat flux, and mw is the nanoparticle mass flux from the surface of the tube, given as:\n\n (18)\n\nUsing similarity variables the non-dimensional skin friction coefficient, Nusselt number, and Sherwood number are obtained as:\n\n (19)\n\nTo estimate the accuracy of the present results, an error analysis should be considered. For this purpose the error percentage is introduced as:\n\n (20)\n\nhere, X could be any quantity such as f\"(1), θ'(1), or etc.\n\n3. Results and discussion\n\nThe ordinary differential equations, Eqs. (9)-(11), subject to the boundary conditions, Eqs. (12) and (13), are numerically solved using the forth-order Rung-Kutta and Newton-Raphson method with a systematic guessing of f ''(1), θ'(1), and Φ'(1) using the shooting technique. The step size Δη= 0.001 is used for calculations. The computations were done using Fortran 90.\n\nBy neglecting the effects of thermophoresis and Brownian motion, the present study reduces to the case of a pure fluid, which was studied by Ishak . Therefore, the results reported by Ishak are used to evaluate the accuracy of the present solution. Table 1 shows a comparison between the present results and those reported by Ishak for different values of magnetic parameter when Re=10 and Pr=7.0. Table 1 shows excellent agreement between the results of present study and the results reported by Ishak .\n\nIn the present study, the values of magnetic parameter (M) are chosen 0 < M < 5 to clearly show the effect of this parameter on the dimensionless velocity, temperature and concentration profiles as well as the Nusselt number. Most nanofluids reported in the literatures have large values of Lewis number, i.e., Le > 1 [13-15]. Hence, the values of Lewis number are chosen 2<Le<10. The same values of Nb, and Nt as those adopted by Rasekh et al. and Gorla et al. are used in the present study. The latter values ,compared to the previous studies, allow us to evaluate the effect of magnetic fields.\n\nFig. 2 exhibits the effect of magnetic parameter (M) on the velocity profiles. The maximum value of velocity is at the surface of the cylinder, and then the velocity decreases asymptotically to zero far from the stretching surface.\n\nThe velocity profiles decrease as the magnetic parameter increases. The increase of magnetic parameter increases the induced Lorentz force in the boundary layer, and hence, it decreases the velocity profiles in the boundary layer. This indicates the fact that an increase in the magnetic parameter would increases the Lorentz force, and consequently, an augmentation of the Lorenz force opposes the flow and reduces the fluid motion. However, variation of magnetic parameter does not show significant effect on the thickness of hydraulic boundary layer.\n\nFig. 3 depicts the effect of magnetic parameter on temperature profiles. This figure shows that the temperature profiles increase as the magnetic parameter\n\n Fig. 2. Effect of magnetic parameter on the velocity profiles.\n\nTable 1: Comparison of results for the skin friction coefficient f ''(1) and the reduced Nusselt number –θ'(1) for several values of M for Re = 10, Pr=7 and Nt = Nb = 0.\n\n -f ''(1) -θ'(1) M Current result Ishak et al. Error percent Current result Ishak et al. Error percent 0.00 3.44448 3.4444 2.3E-03 6.1579 6.1592 2.1E-02 0.01 3.34617 3.3461 2.1E-03 6.1575 6.1588 2.1E-02 0.05 3.35291 3.3528 3.3E-03 6.1560 6.1583 3.7E-02 0.10 3.36131 3.3612 3.2E-03 6.1541 6.1554 2.1E-02 0.50 3.42743 3.4274 8.8E-04 6.1390 6.1402 2.0E-02 1.00 3.50769 3.5076 2.6E-03 6.1207 6.1219 2.0E-02 2.00 3.66154 3.6615 1.1E-03 6.0857 6.0864 1.1E-02 5.00 4.08263 4.0825 3.2E-03 5.9899 5.9895 6.7E-03\n\nincreases. Indeed, the increase of magnetic parameter reduces the magnitude of velocity profiles in the boundary layer, and hence, the temperature in the boundary layer would rise. The variation of magnetic parameter does not show significant effect on the thickness of thermal boundary layer past the stretching cylinder. Fig. 4 illustrates the effect of magnetic parameter on the concentration profiles. As it can be seen, the increase of magnetic parameter increases the magnitude of concentration profiles. As mentioned, increase of magnetic parameter reduces the magnitude of velocity profiles in the boundary layer. Therefore, the decrease of velocity in the boundary layer induces the diffusion of nanoparticles in the boundary layer. However, on the other hand, increase of magnetic parameter tends to decrease the temperature gradients in the boundary layer (as what was seen in Fig. 3). In nanofluids, the thermophoresis force acts opposite to the temperature gradient and tends to move nanoparticles from hot to cold. The magnitude of thermophoresis is proportional to the temperature gradient . Therefore, a decrease in the temperature gradient decreases the effect of thermophoresis in the boundary layer, and consequently tends to decrease the diffusion of nanoparticles. Fig. 4 demonstrates that as the magnetic parameter increases, the effect of variation of velocity on the concentration profiles is the dominant effect.\n\nIncreasing the magnetic parameter increases the Lorentz force which creates the force opposed to the fluid motion. Increasing the Lorentz force decreases the velocity in the boundary layer. Based on the momentum equations, it is clear that the magnetic force corresponds to multiplex of velocity and the magnetic field magnitude. In the present study, the magnetic field was assumed to be comparatively high and uniform in the boundary layer.\n\nThus, the magnetic force is solely a function of velocity of the fluid in the boundary layer. It should be noticed that the velocity in the boundary layer is because of the stretching of the cylinder. Consequently, the\n\n Fig. 3. Effect of magnetic parameter on the temperature profiles. Fig. 4. Effect of magnetic parameter on concentration profiles.\n\nmaximum velocity can be observed on the surface of the cylinder while the minimum velocity is zero which is the quiescent part of the fluid far from the surface (near the edge of the boundary layer). As a result, the maximum magnitude of induced Lorentz force can be seen in the vicinity of the cylinder (this is where the magnetic field strongly affects the velocity and consequently temperature profiles). Far from the surface of the cylinder, the velocities are very low, and consequently, the induced Lorentz force is also very low. Hence, as it can be seen in the figures, the effect of magnetic field is negligible on the thickness of the boundary layer.\n\nFigs. 5 and 6 depict the effect of magnetic parameter on the Nusselt number for selected values of thermophoresis and Brownian motion parameters. These figures show that the Nusselt number is a decreasing function of the magnetic parameter. This observation is in good agreement with Fig. 3. As it was mentioned, the increase in magnetic parameter tends to decrease temperature gradients in the boundary layer and hence decreases the Nusselt number. Figs. 5 and 6 also show that the Nusselt number is a decreasing function of the thermophoresis and Brownian motion parameters. The Brownian motion effect tends to move the nanoparticles from high concentration areas to low ones. Therefore, in the present study, both of the Brownian motion and thermophoresis effects tend to move the nanoparticles away from the stretching cylinder. Indeed, the augmentation of Brownian motion or thermophoresis parameters intensifies the diffusion of nanoparticles into the boundary layer and consequently decreases the Nusselt number.\n\nFig. 7 shows the effect of suction/injection parameter on the Nusselt number for various values of magnetic parameter. This figure shows that the reduced Nusselt number is an increasing function of suction/injection parameter. However, it is a decreasing function of the magnetic parameter. It is noticed from Fig. 7 that the Nusselt number is significantly affected by suction/injection parameter. The positive and negative values of γ indicate mass suction and mass injection, respectively.\n\n Fig. 5. Effects of Nt and M on the Nusselt number. Fig. 6. Effects of Nb and M on Nusselt number.\n\nBy increasing the suction, i.e. increase in the magnitude of γ>0, the thickness of termal boundary layer decreases, and hence, the temperature gradient at the surface of the cylinder (Nusselt number) increases. This is due to the fact that increasing the suction would bring a large amount of ambient fluid into the surface of the cylinder. In contrast, increasing the mass injection would percolate the fluid through the boundary layer which can\n\n Fig. 7. Effects of M and γ on Nusselt number.\n\nincrease the thickness of temperature boundary layer, and hence, the temperature gradient at the surface of the cylinder decreases.\n\nThe Nusselt number includes the ratio between convective heat transfer coefficient and conduction heat transfer coefficient (i.e. Nu=hnfa/knf). The experiments demonstrate that dispersing nanoparticles would significantly augment the thermal conductivity of the resulting fluid. Therefore, there is an initial significant potential of increasing heat transfer because of the increase in the thermal conductivity of the mixture as hnf ~knf in using nanoparticles. Now, the results of the present study indicate that presence of Brownian motion, thermophoresis, and magnetic field would decrease the reduced Nusselt number. If the increase in the thermal conductivity of the mixture because of the presence of nanoparticles be very significant, then an overall convective enhancement can be seen. However, if the increase in the thermal conductivity of the mixture because of the presence of nanoparticles does not be significant, then the overall convective coefficient may be deteriorated.\n\n4. Conclusion\n\nA combined similarity and numerical approaches was utilized to study the effect of magnetic field on the flow, temperature, and concentration profiles in the boundary layer. The effect of non-dimensional parameters on the Nusselt number is analyzed. The results reveal that:\n\n• An increase in the magnetic parameter would decrease the magnitude of velocity profiles, but it would increase the magnitude of temperature and concentration profiles in the boundary layer.\n• The variation of magnetic parameter does not show significant effects on the thickness of the boundary layer profiles (i.e. velocity, temperature, and concentration profiles).\n• The Nusselt number is a decreasing function of magnetic parameter, Brownian motion, and thermophoresis parameter, but it is an increasing function of the suction/injection parameter.\n\nBased on the results of the present study, it can be concluded that the effect of Brownian motion and thermophoresis on the reduced Nusselt number is significant. As the reduced Nusselt number is a decreasing function of both Brownian motion and thermophoresis parameters, the heat transfer, associated with using nanofluids, may not be as much as the observed enhancement in the thermal conductivity of nanofluids. Therefore, the single phase models, which neglected the Brownian motion and thermophoresis effects, would overestimate the heat transfer rate induced by using nanofluids.\n\nAcknowledgements\n\nThe authors are grateful to Shahid Chamran University of Ahvaz for its crucial support.\n\n Nomenclature a radius of the cylinder B0 uniform magnetic field c constant C nanoparticle volume fraction C∞ ambient nanoparticle volume fraction Cw nanoparticle volume fraction at the stretching cylinder Cf skin friction coefficient DB the Brownian diffusion coefficient DT the thermophoresis diffusion coefficient k thermal conductivity of nanofluid Le Lewis number M magnetic parameter mw wall mass flux Nb Brownian motion parameter Nt thermophoresis parameter Nu Nusselt number p pressure p∞ ambient pressur Pr Prandtl number qw wall Heat flux Re Reynolds number Sh Sherwood number T nanofluid temperature T∞ ambient nanofluid temperature Tw nanofluid temperature at the stretching cylinder u,w velocity components along r- and z-axes uw velocity of the stretching cylinder r,z Cartesian coordinates (z-axis is aligned along the stretching cylinder and r-axis is normal to it) Greek α thermal diffusivity of nanofluid (ρc)nf heat capacity of the nanofluid (ρc)p effective heat capacity of the nanoparticle material σ electrical conductivity of nanofluid η similarity variable φ(η) dimensionless nanoparticle volume fraction θ(η) dimensionless temperature ρ nanofluid density ρp nanoparticle mass density ν kinematic viscosity τ parameter defined by ratio between the effective heat capacity of the nanoparticle material and heat capacity of the nanofluid τw wall shear stress\n\nReferences\n\n. S.U.S. Choi, Enhancing thermal conductivity of fluids with nanoparticles, in: The Proceedings of the 1995 ASME International Mechanical Engineering Congress and Exposition, San Francisco, USA, ASME, FED 231/MD 66, 99-105 (1995).\n\n. H. Masuda and A. Ebata and K. Teramea and N. Hishinuma, Altering the thermal conductivity and viscosity of liquid by dispersing ultra-fine particles, Netsu Bussei, 4, 227-233 (1993).\n\n. T. Fang, and A. Aziz, Viscous Flow with Second-Order Slip Velocity over a Stretching Sheet, Z. Naturforsch., 65a,1087 –1092 (2010).\n\n. T. Hayat, M. Nawaz, Effect of Heat Transfer on Magnetohydrodynamic Axisymmetric Flow Between Two Stretching Sheets, Z. Naturforsch., 65a, 961 –968 (2010).\n\n. A. S. Butt, S. Munawar, A. Ali, and A. Mehmood, Entropy Analysis of Mixed Convective Magnetohydrodynamic Flow of a Viscoelastic Fluid over a Stretching Sheet, Z. Naturforsch., 67a, 451–459 (2012).\n\n. S. Mukhopadhyay, Upper-Convected Maxwell Fluid Flow over an Unsteady Stretching Surface Embedded in Porous Medium Subjected to Suction/Blowing, Z. Naturforsch., 67a, 641–646 (2012).\n\n. A. Ishak and R. Nazar and I. Pop, Magnetohydrodynamic (MHD) flow and heat transfer due to a stretching cylinder, Energy Conv. Manag., 49, 3265-3269 (2008).\n\n. C.Y. Wang, Fluid flow due to a stretching cylinder, Phys. Fluids, 31, 466-468 (1988).\n\n. A. Ishak and R. Nazar and I. Pop, Uniform suction/blowing effect on flow and heat transfer due to a stretching cylinder, Appl. Math. Model, 32, 2059-2066 (2008).\n\n. A. Rasekh and D.D. Ganji and S. Tavakoli, numerical solution for a nanofluid past over a stretching circular cylinder with non-unifom heat source, Frontiers Heat. Mass. Transf. (FHMT), 3, 043003 (2012).\n\n. R. Subba and R. Gorla and A. Chamkha and E. Al-Meshaiei, melting heat transfer in a nanofluid boundary layer on a stretching circular cylinder, J. Naval Arch. Marin. Eng., 9, 1-10 (2012).\n\n. M. Subhas Abel and P.G. Siddheshwar and N. Mahesha, Numerical solution of the momentum and heat transfer equations for a hydromagnetic flow due to a stretching sheet of a non-uniform property micropolar liquid, Appl. Math. Comp., 217, 5895–5909 (2011).\n\n. W.A. Khan and I. Pop, Boundary-layer flow of a nanofluid past a stretching sheet, Int. J. Heat. Mass. Transf., 53, 2477–2483 (2010).\n\n. R. Kandasamy and P. Loganathan and P. Puvi Arasu, Scaling group transformation for MHD boundary-layer flow of a nanofluid past a vertical stretching surface in the presence of suction/injection, Nuclear Eng. Design, 241, 2053-2059 (2011).\n\n. N. Bachok and A. Ishak and I. Pop, Unsteady boundary-layer flow and heat transfer of a nanofluid over a permeable stretching/shrinking sheet, Int. J. Heat. Mass. Transf., 55, 2102-2109 (2012).\n\n. J. Buongiorno, Convective Transport in Nanofluids, J. Heat. Transf., 128, 240-245 (2006).\n\n#### References\n\n. S.U.S. Choi, Enhancing thermal conductivity of fluids with nanoparticles, in: The Proceedings of the 1995 ASME International Mechanical Engineering Congress and Exposition, San Francisco, USA, ASME, FED 231/MD 66, 99-105 (1995).\n. H. Masuda and A. Ebata and K. Teramea and N. Hishinuma, Altering the thermal conductivity and viscosity of liquid by dispersing ultra-fine particles, Netsu Bussei, 4, 227-233 (1993).\n. T. Fang, and A. Aziz, Viscous Flow with Second-Order Slip Velocity over a Stretching Sheet, Z. Naturforsch., 65a,1087 –1092 (2010).\n. T. Hayat, M. Nawaz, Effect of Heat Transfer on Magnetohydrodynamic Axisymmetric Flow Between Two Stretching Sheets, Z. Naturforsch., 65a, 961 –968 (2010).\n. A. S. Butt, S. Munawar, A. Ali, and A. Mehmood, Entropy Analysis of Mixed Convective Magnetohydrodynamic Flow of a Viscoelastic Fluid over a Stretching Sheet, Z. Naturforsch., 67a, 451–459 (2012).\n. S. Mukhopadhyay, Upper-Convected Maxwell Fluid Flow over an Unsteady Stretching Surface Embedded in Porous Medium Subjected to Suction/Blowing, Z. Naturforsch., 67a, 641–646 (2012).\n. A. Ishak and R. Nazar and I. Pop, Magnetohydrodynamic (MHD) flow and heat transfer due to a stretching cylinder, Energy Conv. Manag., 49, 3265-3269 (2008).\n. C.Y. Wang, Fluid flow due to a stretching cylinder, Phys. Fluids, 31, 466-468 (1988).\n. A. Ishak and R. Nazar and I. Pop, Uniform suction/blowing effect on flow and heat transfer due to a stretching cylinder, Appl. Math. Model, 32, 2059-2066 (2008).\n. A. Rasekh and D.D. Ganji and S. Tavakoli, numerical solution for a nanofluid past over a stretching circular cylinder with non-unifom heat source, Frontiers Heat. Mass. Transf. (FHMT), 3, 043003 (2012).\n. R. Subba and R. Gorla and A. Chamkha and E. Al-Meshaiei, melting heat transfer in a nanofluid boundary layer on a stretching circular cylinder, J. Naval Arch. Marin. Eng., 9, 1-10 (2012).\n. M. Subhas Abel and P.G. Siddheshwar and N. Mahesha, Numerical solution of the momentum and heat transfer equations for a hydromagnetic flow due to a stretching sheet of a non-uniform property micropolar liquid, Appl. Math. Comp., 217, 5895–5909 (2011).\n. W.A. Khan and I. Pop, Boundary-layer flow of a nanofluid past a stretching sheet, Int. J. Heat. Mass. Transf., 53, 2477–2483 (2010).\n. R. Kandasamy and P. Loganathan and P. Puvi Arasu, Scaling group transformation for MHD boundary-layer flow of a nanofluid past a vertical stretching surface in the presence of suction/injection, Nuclear Eng. Design, 241, 2053-2059 (2011).\n. N. Bachok and A. Ishak and I. Pop, Unsteady boundary-layer flow and heat transfer of a nanofluid over a permeable stretching/shrinking sheet, Int. J. Heat. Mass. Transf., 55, 2102-2109 (2012).\n. J. Buongiorno, Convective Transport in Nanofluids, J. Heat. Transf., 128, 240-245 (2006).\n\n### History\n\n• Receive Date: 10 August 2013\n• Revise Date: 22 November 2013\n• Accept Date: 14 December 2013\n• First Publish Date: 01 May 2014" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.83733994,"math_prob":0.9032093,"size":23726,"snap":"2023-14-2023-23","text_gpt3_token_len":5402,"char_repetition_ratio":0.17245595,"word_repetition_ratio":0.09516129,"special_character_ratio":0.21592346,"punctuation_ratio":0.13411489,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9741288,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-06-02T19:20:35Z\",\"WARC-Record-ID\":\"<urn:uuid:43ba7a8c-b920-470a-b55c-97eaaf62a8d4>\",\"Content-Length\":\"98481\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4ac1fd19-bcc3-45db-805b-684f0ceb9505>\",\"WARC-Concurrent-To\":\"<urn:uuid:dd2df357-f521-4816-81fd-622be75bde69>\",\"WARC-IP-Address\":\"94.182.28.25\",\"WARC-Target-URI\":\"https://jhmtr.semnan.ac.ir/article_149.html\",\"WARC-Payload-Digest\":\"sha1:7S4ITDUFVJQ72H4EN5GYAQ5H6UDW5CIN\",\"WARC-Block-Digest\":\"sha1:UWXFGB7O3SIZSABILJJTYW5UNPQJWQTF\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224648850.88_warc_CC-MAIN-20230602172755-20230602202755-00227.warc.gz\"}"}
http://www.spss123.com.tw/2017/08/blog-post_9.html	[ "## 2017年8月11日星期五\n\n### 用表快速決定樣本\n\nEditor’s note: Paul C. Boyd is a principal of the Research Advisors, Franklin, Mass.\nThere are various formulas for calculating the required sample size for a study. These formulas\nrequire knowledge of the variance or proportion in the population and a determination as to the\nmaximum desirable error, as well as the acceptable Type I error risk. For example, sample size\nformulas were addressed in a July 1999 Quirk’s article by Gang Xu (“Estimating sample size\nfor a descriptive study in quantitative research .”)\nSuch formulas are typically presented in such a way as to avoid the issue of population size\n- they assume that the sample is to be drawn from an infinitely large population. Still, these\nformulas may appear unnecessarily complex to researchers who have to deal with these\nissues on only an occasional basis. The question they ask is simple: Isn’t there an easier way?\nThe answer is yes. After all, why bother with formulas when you don’t have to? Many researchers\nprefer a simple table to assist them with the determination of the appropriate sample size(s)\nfor their studies.\nIt is possible to use one of these formulas to construct a table that suggests the optimal sample\nsize - given a population size, a specific margin of error and a desired confidence interval. This\ncan help researchers avoid the formulas altogether and simplify the process of determining\nappropriate sample sizes. The accompanying table presents the results of one set of these calculations. This table may easily be used to determine the appropriate sample size for almost any study.\nFor business and social science research the first column within the table is usually considered acceptable (confidence level = 95 percent, margin of error = ±5 percent). To use the table, simply determine the size of the population from which the sample is to be drawn down the left-most column (use the next highest value if the exact population size is not listed) and then identify the value in the next column. The value in this column is the sample size that is required to generate a margin of error of ± 5 percent for any population proportion with a 95 percent confidence level. Should more precision be required (i.e., a smaller margin of error) or greater confidence desired (0.99), the other columns of the table should be employed.\nThus, if you have 5,000 customers and you want to sample a sufficient number to generate a 95 percent confidence interval that predicted the proportion who, say, would be repeat customers within ±2-1/2 percent, you would need responses from a (random) sample of 1,176 of all your customers.\nAs you can see, using the table is much simpler than employing a formula. (A dynamic version of the table is available for download as an Excel spreadsheet that allows the user to change the margin of error, confidence level and/or the population size. Visit http://research-advisors.com/documents/SampleSize-web.xls .)\nSuppose these customers were divided into two subgroups - Group A, consisting of 1,500 customers and Group B consisting of 3,500 - and you wanted to determine the proportions of each. In order to maintain the same levels of confidence and precision (95 percent and ±2-1/2 percent) you would need random samples of 759 from Group A and 1,068 from Group B.\nCaution is urged to avoid lower levels of confidence (e.g., 95 percent) or larger margins of error (5 percent) solely for the purpose of minimizing the required sample size. As with all statistical procedures, the confidence level should be determined by the consequences of drawing the wrong conclusion due to sampling error. Likewise, the margin of error should be determined based upon the usefulness of the interval constructed (and remember that the interval width is twice the margin of error).\nThe formula used for these calculations is shown here (this is the formula used by Krejcie and Morgan in their article “Determining Sample Size for Research Activities”):\n\nAll of the sample estimates discussed present figures for the largest possible sample size for the desired level of confidence. Should the proportion of the sample with the desired characteristic be substantially different than 50 percent, then the desired level of accuracy can be established with a smaller sample. However, since you typically can’t know what this percentage is until you actually ask a sample, it is wisest to assume that it will be 50 percent and use the listed larger sample size.\nReferences\nKrejcie, Robert V. and Morgan, Daryle W. “Determining Sample Size for Research Activities.” Educational and Psychological Measurement 30 (1970): 607-610.\nXu, Gang. “Estimating Sample Size for a Descriptive Study in Quantitative Research .” Quirk’s Marketing Research Review, June 1999.\n\nAll of the sample estimates discussed present figures for the largest possible sample size for the desired level of confidence. Should the proportion of the sample with the desired characteristic be substantially different than 50 percent, then the desired level of accuracy can be established with a smaller sample. However, since you typically can’t know what this percentage is until you actually ask a sample, it is wisest to assume that it will be 50 percent and use the listed larger sample size.\nReferences\nKrejcie, Robert V. and Morgan, Daryle W. “Determining Sample Size for Research Activities.” Educational and Psychological Measurement 30 (1970): 607-610.\nXu, Gang. “Estimating Sample Size for a Descriptive Study in Quantitative Research .” Quirk’s Marketing Research Review, June 1999." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.89400953,"math_prob":0.8375073,"size":5639,"snap":"2019-51-2020-05","text_gpt3_token_len":1172,"char_repetition_ratio":0.13895297,"word_repetition_ratio":0.27030033,"special_character_ratio":0.21298103,"punctuation_ratio":0.10182517,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97579265,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-12T01:07:34Z\",\"WARC-Record-ID\":\"<urn:uuid:5a07a483-fe20-4a61-9f14-17b73535b687>\",\"Content-Length\":\"62581\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:415b7de1-efb9-4346-aedd-e783e345f1a1>\",\"WARC-Concurrent-To\":\"<urn:uuid:40cded1b-a55c-402f-acdd-c86afba7d1ae>\",\"WARC-IP-Address\":\"172.217.13.83\",\"WARC-Target-URI\":\"http://www.spss123.com.tw/2017/08/blog-post_9.html\",\"WARC-Payload-Digest\":\"sha1:3J76WQYYXZIEOQ4TOKVFJVM42TSNBHOF\",\"WARC-Block-Digest\":\"sha1:IW7HWQGFBLO4OEE7O25UCH27HY7HKPUQ\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575540534443.68_warc_CC-MAIN-20191212000437-20191212024437-00350.warc.gz\"}"}
https://wow-essay.com/free-essay-samples/essay-sample-on-basic-principles-of-the-algorithms/	[ "# Essay Sample on Basic Principles of the Algorithms\n\n## Introduction to Algorithms\n\nThe most basic techniques in developing an algorithm are as follows:\n\n• Divide and conquer\n• Dynamic programming\n• Backtracking\n• Hill-climbing\n• Greedy algorithms\n\nA solvable problem can be solved using one type of algorithm of each type: the methodical way, the obvious way, the clever way, and the miraculous way.\n\n85k+ topics\n700K+ happy students\n91K+ free samples\n\nSample Details:\n\nPages: 3\n\nWords: 571\n\nTo understand algorithms, the user must know at least one programming language at a level where they can translate the codes into solutions to a problem. It is also necessary that the user has a working knowledge of data structures: stacks, arrays, linked lists, queues, trees, disjoint sets, heaps, and graphs (Wikibooks, 2004). The user must also know basic algorithms such as sorting, binary search, depth-first search, or breadth-first search. If the user is unfamiliar with these things, it would be helpful to consult further references about data structures before studying algorithms.\n\n## The Importance of Efficiency\n\nEfficiency is not required in every problem there is. To understand algorithmic efficiency, however, efficiency is concerned with the space and the time needed to execute the task (Wikibooks, 2004). When space or time is inexpensive or abundant, the programmer can focus on the solution without worrying about compiling the code and running faster.\n\nThere are particular cases where efficiency matters:\n\n• Limited resources\n• A large set of data\n• Real-time applications (where latency matters most)\n• Computationally costly jobs\n• Subroutines that require frequent use in the program run\n\n## Brief Discussion of Common Algorithmic TechniquesDivide and Conquer\n\nIn certain problems where the program input is already in the array, the solution can be made by cutting the problem into smaller chunks (divide), recursively tackling these small parts, then combining the tiny individual solutions into one result. Some good examples of divide-and-conquer algorithms are quick-to-sort and merge-sort algorithms.\n\n## Backtracking\n\nThis technique is not the most efficient because it is a brute-force strategy. However, optimizations can be made to the program to reduce the number of branches. When one leaf is visited, the algorithm will go back up the stack to undo the program choices that failed, then proceed to other branches of the tree. Backtracking is a technique that works best with problems where there is already a self-similarity. This means that smaller problem instances resemble the entirety of the problem.\n\n## Randomization\n\nFor countless applications, randomization is becoming increasingly important. This technique generates and uses random numbers that fit a tailored solution to one instance of a problem.\n\n## Hill Climbing\n\nThe fundamental concept with hill climbing is, to begin with, an inefficient solution to the problem, then apply repeated optimization techniques to this poor solution until it becomes more optimal or when a specific criterion is met. Hill climbing works best in network flow. It is useful in many problems that depict different relationships, making it applicable outside computing networks. As a hill climbing technique, network flows can solve matching problems outside of computer networks.\n\n## Dynamic Programming\n\nThis technique works best with backtracking algorithms because dynamic programming is an optimization technique. When there is a need to solve subproblems repeatedly, precious time can be saved by dealing with the small subproblems (or leaves) first (smallest to largest, bottom-up strategy) and storing each subproblem solution in a table.\n\n## References\n\nWikibooks. (2004, September 28). Algorithms/Introduction. Retrieved August 16, 2022, from https://en.wikibooks.org/wiki/Algorithms/Introduction\n\nLost writing steam? Not sure your paper will be awesome?\n\nOrder a WOW custom essay from a pro writer!" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.90871763,"math_prob":0.812906,"size":3813,"snap":"2023-40-2023-50","text_gpt3_token_len":750,"char_repetition_ratio":0.12785508,"word_repetition_ratio":0.0,"special_character_ratio":0.18804091,"punctuation_ratio":0.114503816,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9706924,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-24T10:59:20Z\",\"WARC-Record-ID\":\"<urn:uuid:8a95c6cc-f41d-4248-9d8c-542e23663823>\",\"Content-Length\":\"43206\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7a44a43d-0b23-4dc4-b083-0c8267079970>\",\"WARC-Concurrent-To\":\"<urn:uuid:397816a9-4e3d-4c50-ae75-4b958bfc71be>\",\"WARC-IP-Address\":\"152.160.232.195\",\"WARC-Target-URI\":\"https://wow-essay.com/free-essay-samples/essay-sample-on-basic-principles-of-the-algorithms/\",\"WARC-Payload-Digest\":\"sha1:XKD7EQIDS5PN7EAQOYSBV2YRTM5ZZ457\",\"WARC-Block-Digest\":\"sha1:6IP3A2BTYFRR526IR47KHKMF5DH2LGAL\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233506632.31_warc_CC-MAIN-20230924091344-20230924121344-00603.warc.gz\"}"}
https://physics.stackexchange.com/questions/501145/validity-of-the-derivation-of-time-energy-uncertainty-principle	[ "# Validity of the derivation of time-energy uncertainty principle?\n\n## Background\n\nThe top voted answer to this question seems to make some assumptions I'm uncertain about (to say the least): What is $\\Delta t$ in the time-energy uncertainty principle?\n\n## Assumptions\n\n• The uncertainty principle is usually a statement about the measurement (while it is true they are applicable during the unitary process as well. They usually are not used in that context).\n• Since they usually the measurement is considered a discontinuous process is he considering an interpretation where there is no measurement such as many worlds?\n\n## Question\n\nIs there a version of this derivation (compatible with the discontinuous measurement interpretations of quantum mechanics) where one is allowed to use the calculus in the way he does (both integration and differentiation)?\n\nP.S: I have already commented on this.\n\n• I don't understand the question. Is there a version of this derivation where one is allowed to use the calculus in the way he does (both integration and differentiation)? Yes there is, it is the one you are referring to. – Aaron Stevens Sep 10 at 16:26\n• @AaronStevens I also mention the measurement is discontinuous (at least in some interpretations). In that case I want a version of this derivation where one can do those manipulation there too. – More Anonymous Sep 10 at 16:28\n• Since, I'm getting a down vote despite explaining my objection (in the comment). Can someone clarify why the objection is wrong? – More Anonymous Sep 10 at 16:31\n• Baez's summary is based on the resolution of an optimal clock, Δt, the approximate amount of time it takes for the expectation value of an observable to change by a standard deviation provided the system is in a pure state. What is your question?? – Cosmas Zachos Sep 10 at 16:48\n• @CosmasZachos I'm discussing this in the chat at the moment ... (I can't do both simultaneously) – More Anonymous Sep 10 at 16:57\n\nThe WP summary of the Mandeshtam-Tamm relation is, for an observable $$\\hat B$$, $$\\sigma_E ~~~\\frac{\\sigma_B}{\\left\| \\frac{\\mathrm{d}\\langle \\hat B \\rangle}{\\mathrm{d}t}\\right \|} \\ge \\frac{\\hbar}{2} ~~,$$ where the second factor on the l.h.s., with dimensions of time, is a lifetime of the state ψ with respect to the hermitean observable $$\\hat B$$. Roughly, the time interval (Δt) after which the expectation value ⟨$$\\hat B$$⟩ changes appreciably. For a stationary state, the drift rate of ⟨$$\\hat B$$⟩ goes to zero, and the variance of energy goes to 0 as well, as it should.\n\nThis is all in standard QM, unitarily evolving, with or without measurements. You may do any and all measurements discontinuous, delirious, expialidocious, whatever, and plot your results, but you must be talking about the same state ψ all the time. The distribution in B will have a variance, which is what is under discussion.\n\n(Heuristically, a state ψ that only exists for a short time cannot have a definite energy. To have a definite energy, the frequency of the state must be defined accurately, and this requires the state to persist for many cycles, the reciprocal of the required accuracy. In spectroscopy, excited states have a finite lifetime. By above, they do not have a definite energy, and, each time they decay, the energy they release is slightly different. The average energy of the outgoing photon has a peak at the theoretical energy of the state, but the distribution has a finite width called the natural linewidth. Fast-decaying states have a broad linewidth, while slow-decaying states have a narrow linewidth.)\n\nI have not fully appreciated your misgivings, but they seem to me to also apply to the standard Δx Δp uncertainty principle: A pure state will have corresponding distributions for x and p with nontrivial variances, computable through standard continuous QM, which your measurements will probe.\n\n• I feel my I came to the conclusion that my question was based on legimate doubts but if you have the patience to understand what they were here is the link: chat.stackexchange.com/transcript/message/51655733#51655733 Also mentioning $\\Delta x \\Delta p$ uncertainty makes me think you suspect the derivation in question enables you to make the claim that $2$ measurements cannot be arbitrarily close together (in time) ... But in the chat we have users comparable to your points (and one even more) who agree this derivation cannot warrant that. – More Anonymous Sep 10 at 21:30\n• I'm sorry, I must then not understand your question. The relation, and my answer have little to do with measurement. They provide probabilities of outcomes when/if you make a measurement. Once you have made a measurement, you have altered the state, and you are not talking about that state anymore. Probabilities are estimated experimentally by repeatedly measuring the \"same\" state, no? – Cosmas Zachos Sep 10 at 21:37\n• Yes, see assumption $1$. And I asked the chatroom what was the experimental context of this derivation and the (accepted) answer seemed to be of very limited scope (which I suspect most upvoters of the original answer probably do not know). – More Anonymous Sep 10 at 21:40\n• Oh... If you are thinking about measurements, I have nothing to say. All derivations of this ilk use standard QM and leave it to measurements to experimentally probe the answers. They really, really, deal with the same state ψ... – Cosmas Zachos Sep 10 at 21:43\n• Of course. We might agree there. This is (highly abstractly) what spectroscopists do to extract lifetimes out of linewidths. – Cosmas Zachos Sep 10 at 21:48\n\nTime is dissipation of energy. Delta t in that context is the ratio of original to current energy density. Delta E is the remaining original energy. As energy dissipates, Delta t increases, and Delta E goes to zero.\n\nFor an analogy consider meausring a wave in water. Early in the wave the amplitude is high and similar to when the wave was created. Delta T is low and Delta E is high. Over time, the wave peters out. Delta T is high because little amplitude is left and Delta E is low." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.91996676,"math_prob":0.9128332,"size":1904,"snap":"2019-35-2019-39","text_gpt3_token_len":452,"char_repetition_ratio":0.123157896,"word_repetition_ratio":0.0,"special_character_ratio":0.21953781,"punctuation_ratio":0.13079019,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.973029,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-09-20T11:45:36Z\",\"WARC-Record-ID\":\"<urn:uuid:d6805f2b-3e26-4f59-a24c-47880f7398de>\",\"Content-Length\":\"157803\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b561df0d-2ac7-4780-a0b9-fafacba0d59b>\",\"WARC-Concurrent-To\":\"<urn:uuid:333dabad-f1b9-467d-b2b3-6d9ad93b8943>\",\"WARC-IP-Address\":\"151.101.193.69\",\"WARC-Target-URI\":\"https://physics.stackexchange.com/questions/501145/validity-of-the-derivation-of-time-energy-uncertainty-principle\",\"WARC-Payload-Digest\":\"sha1:UQL2X3KP625RVV4LH5ZN63LK6FBQUP2O\",\"WARC-Block-Digest\":\"sha1:44EA7E5ISCSONEFD6O4F73ZC2HBK3ZPG\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-39/CC-MAIN-2019-39_segments_1568514574018.53_warc_CC-MAIN-20190920113425-20190920135425-00056.warc.gz\"}"}
https://sources.debian.org/src/openems/0.0.35+dfsg.1-3/openEMS/matlab/AddMRStub.m/	[ "`12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667686970717273` ``````function CSX = AddMRStub( CSX, materialname, prio, MSL_width, len, alpha, resolution, orientation, normVector, position ) % CSX = AddMRStub( CSX, materialname, prio, MSL_width, len, alpha, % resolution, orientation, normVector, position ) % % Microstrip Radial Stub % % CSX: CSX-object created by InitCSX() % materialname: property for the MSL (created by AddMetal() or AddMaterial()) % prio: priority % MSL_width: width of the MSL to connect the stub to % len: length of the radial stub % alpha: angle subtended by the radial stub (degrees) % resolution: discrete angle spacing (degrees) % orientation: angle of main direction of the radial stub (degrees) % normVector: normal vector of the stub % position: position of the end of the MSL % % This radial stub definition is equivalent to the one Agilent ADS uses. % % example: % CSX = AddMRStub( CSX, 'PEC', 10, 1000, 5900, 30, 1, -90, [0 0 1], [0 -10000 254] ); % % % Sebastian Held % Jun 1 2010 % % See also InitCSX AddMetal AddMaterial % check normVector if ~(normVector(1) == normVector(2) == 0) && ... ~(normVector(1) == normVector(3) == 0) && ... ~(normVector(2) == normVector(3) == 0) \|\| (sum(normVector) == 0) error 'normVector must have exactly one component ~= 0' end normVector = normVector ./ sum(normVector); % normVector is now a unit vector % convert angles to radians alpha_rad = alpha/180pi; orientation_rad = orientation/180pi; resolution_rad = resolution/180pi; % % build stub at origin (0,0,0) and translate/rotate it later % D = 0.5 MSL_width / sin(alpha_rad/2); R = cos(alpha_rad/2) * D; % point at the center of the MSL p(1,1) = 0; p(2,1) = -MSL_width/2; p(1,2) = 0; p(2,2) = MSL_width/2; for a = alpha_rad/2 : -resolution_rad : -alpha_rad/2 p(1,end+1) = cos(a) * (D+len) - R; p(2,end) = sin(a) * (D+len); end % rotate rot = [cos(-orientation_rad), -sin(-orientation_rad); sin(-orientation_rad), cos(-orientation_rad)]; p = (p.' * rot).'; % translate idx_elevation = [1 2 3]; idx_elevation = idx_elevation(normVector>0); dim1 = mod( idx_elevation, 3 ) + 1; dim2 = mod( idx_elevation+1, 3 ) + 1; p(1,:) = p(1,:) + position(dim1); p(2,:) = p(2,:) + position(dim2); elevation = position(idx_elevation); CSX = AddPolygon( CSX, materialname, prio, normVector, elevation, p ); ``````" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.50759554,"math_prob":0.9968139,"size":2487,"snap":"2020-24-2020-29","text_gpt3_token_len":894,"char_repetition_ratio":0.15304068,"word_repetition_ratio":0.041763343,"special_character_ratio":0.41737032,"punctuation_ratio":0.20238096,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99835086,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-07-10T14:01:03Z\",\"WARC-Record-ID\":\"<urn:uuid:d4fc86a1-567b-4e7c-960b-1fbca37874f1>\",\"Content-Length\":\"16866\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:8db9a673-be4b-4881-b6b1-afdcbd73677f>\",\"WARC-Concurrent-To\":\"<urn:uuid:650265f8-fc80-4c30-80ab-17ed1bb003df>\",\"WARC-IP-Address\":\"209.87.16.74\",\"WARC-Target-URI\":\"https://sources.debian.org/src/openems/0.0.35+dfsg.1-3/openEMS/matlab/AddMRStub.m/\",\"WARC-Payload-Digest\":\"sha1:HYTKE7SLDFHRA3Y5FW4TR2R3OMJG37PS\",\"WARC-Block-Digest\":\"sha1:NSJ3VTMRIB2HDJ27LTARDUZNVHPR4ZBG\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-29/CC-MAIN-2020-29_segments_1593655908294.32_warc_CC-MAIN-20200710113143-20200710143143-00246.warc.gz\"}"}
https://testbook.com/question-answer/the-number-of-3-digits-even-number-is-_____--608a63a2c1cd3eae38b22686	[ "# The number of 3 digits even number is _____.\n\nThis question was previously asked in\nMP Patwari Previous Paper 17 (Held On: 16 Dec 2017 Shift 1)\nView all MP Patwari Papers >\n1. 500\n2. 499\n3. 450\n4. 449\n\nOption 3 : 450\n\n## Detailed Solution\n\nConcept used :\n\nL = a + (n - 1)d (where, L = last term, a = first term, n = number of terms and d is the common difference)\n\nCalculations :\n\nFirst 3 digit even number = 100\n\nLast 3 digit number = 998\n\n3 digit even numbers will be 100, 102, 104,......998.\n\nNow,\n\n998 = 100 + (n -1)2 (as per given formula)\n\n⇒ (n - 1)2 = 898\n\n⇒ n - 1 = 449\n\n⇒ n = 450\n\n∴ The number of 3 digits even number is 450" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7655867,"math_prob":0.9992898,"size":382,"snap":"2021-43-2021-49","text_gpt3_token_len":143,"char_repetition_ratio":0.17195767,"word_repetition_ratio":0.0,"special_character_ratio":0.46596858,"punctuation_ratio":0.17777778,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9980981,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-12-03T20:02:15Z\",\"WARC-Record-ID\":\"<urn:uuid:858f7e51-8c4c-44cd-95bb-f45c4115328b>\",\"Content-Length\":\"119191\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b381017b-bb04-48f8-8fd4-be473975603b>\",\"WARC-Concurrent-To\":\"<urn:uuid:878958ad-f8f5-45ea-a5e8-c2be4c2b3e8a>\",\"WARC-IP-Address\":\"104.22.44.238\",\"WARC-Target-URI\":\"https://testbook.com/question-answer/the-number-of-3-digits-even-number-is-_____--608a63a2c1cd3eae38b22686\",\"WARC-Payload-Digest\":\"sha1:JNXEJO37JXB2RAGVEHY4YHBN6TBPQB5Y\",\"WARC-Block-Digest\":\"sha1:C5NK5XRJI6ZMR6YUIYGM7LEJJQKB6JVO\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964362918.89_warc_CC-MAIN-20211203182358-20211203212358-00478.warc.gz\"}"}
https://www.positioniseverything.net/javascript-const	[ "# JavaScript Const Variable: The Ultimate Guide on The Const Keyword", null, "JavaScript const variable, along with keywords such as let, package, and others, plays an important role while writing a script. It is also used in C++ to declare the constant variables.\n\nIn simple words, constants are variables that cannot change values and they do not have to be primitive variables. In this article, we will review JavaScript constants with examples, so let’s get right on that!\n\n## What Is Const in JavaScript: Basics\n\nTo define a JavaScript constant variable using the const keyword in JavaScript, we should know that the keyword would create a read-only reference when it comes to the value. Let’s look at an example:\n\n const CONSTANT_NAME = value;\n\nWhen using constant identifiers, do note that they will be in uppercase. The const in JavaScript declares the block-scoped variables just like the let keyword. The only difference with the JavaScript constant variable is the const keyword would not reassign like it would using the let keyword.\n\n### – The Let Keyword in an Example\n\nThe let keyword declares variables that are mutable as you can change them anytime. The constants in JavaScript are immutable. Once assigned a value, they cannot be reassigned. Let’s see that in an example for better understanding:\n\n let a = 5; a = 10; a = a + 5; console.log(a); // 15\n\n### – The Const Keyword in an Example\n\nIn the example shown above, we can see the usage of the let keyword. Now, let’s see the effect a JavaScript const function has in a similar scenario:\n\n const RATE = 0.3; RATE = 0.5; // TypeError\n\nLooking at the example above, we can see that reassigning the variable declared by the const keyword results in a TypeError. So, what do we do now?\n\n#### What If the Variable Declared by Const Keyword Results in TypeError?\n\nWell, if the variable declared by the const keyword results in a TypeError we need to initialize the value to the variable that is declared by the const in JavaScript. Let’s see what is the result if we miss the initializer during the declaration of the JavaScript constant variable.\n\n const RED; // SyntaxError\n\nAs you can see, we have a syntax error in this case. Now, let’s see the relation of the JavaScript constants and objects.\n\n## What Is Const in JavaScript: Objects\n\nAs mentioned earlier, the const in JavaScript makes sure its variables created are read-only. Does that mean the value for the JavaScript constant variable reference is immutable? No. Let’s look at this example for clarity:\n\n const individual = { weight: 90 }; individual.weight = 78; // OK console.log(person.age); // 78\n\nIf you look at the example shown above, you cannot reassign a different value to the individual constant. However, you can change the individual variable’s value even though it’s a constant. Let’s look at an example:\n\n individual = { weight: 78 }; // TypeError\n\n### – How to Make Individual Objects Immutable\n\nAs we would want to make the individual object immutable, we will need to freeze it. How? By using the object.freeze(). Let’s use this method in the following example:\n\n const individual = Object.freeze({weight: 90}); individual.weight = 78; // TypeError\n\nNow, if you meticulously take a look, you will see the Object.freeze() method as shallow. What does that mean? Well, it can freeze the object properties but not of the objects that are referenced by those properties.\n\n### – Example of Constant Variable and Freeze Object Relation\n\nLet’s look at this with another example by using a small business. Supposing the small business name is XYZ Store, let’s see the relation of constant and frozen in the following example:\n\n const small business = Object.freeze({ name: ‘XYZ Store’, address: { street: ‘XYZ Street, 123’, city: ‘New York’, state: ‘NY’, zipcode: 12345 } });\n\nThe example above shows the Object.freeze that has frozen the properties of the objects. However, the address object is still mutable (can be changed). Hence, we can add a new property to this part if needed. Let’s see this in an example:\n\n### – Notes on Information So Far\n\nSo far, we have learned the assignment of variables and reassignment, reference properties, and how Object.freeze works with const in JavaScript. Now, let’s move on to JavaScript constants and arrays.\n\n## What Is Const in JavaScript: Arrays\n\nBefore we dive into the relation of JavaScript constant variable and array, let’s briefly describe arrays. Arrays are single variables used to store different kinds of elements. The array is normally used as a reference to multiple variables in most languages but in JavaScript, it is a single variable.\n\n### – Arrays and Const in JavaScript\n\nAs arrays are single variables in JavaScript, we can declare them as a color with one element by using the const keyword. Once done, we can change them by adding another color. However, since arrays are single variables, reassigning will not be possible. Let’s look at this situation with an example:\n\n const colors = [‘blue’]; colors.push(‘orange’); console.log(colors); // [“blue”, “orange”] colors.pop(); colors.pop(); console.log(colors); // [] colors = []; // TypeError\n\nIf you look at the example above, trying to use the orange color array over the blue brings us a type error.\n\nLet’s go ahead and see the effect of const in JavaScript with loops.\n\n## Understanding Loops With JavaScript Const\n\nThe ECMAScript6 or ES6 has a construct that is fairly new, mainly referred to as for…of. This construct allows a loop creation over the iterable objects that can be arrays, maps, and even sets. Let’s look at some examples to understand JavaScript const function in the for…of loop.\n\n let scores = [25, 40, 60]; for (let score of scores) { console.log(score); }\n\n### – Using Const Variable in a Loop\n\nLet’s suppose you don’t intend to modify the score variable within the loop. What do you do? You can use const in JavaScript to solve this issue. Let’s see it in an example:\n\n let scores = [25, 40, 60]; for (const score of scores) { console.log(score); }\n\nAs you can see in the example above, the for…of loop binds the JavaScript const function within the loop iterations. In simple words, for each iteration, a new score constant is created.\n\n#### Using Const Variable in a Loope: Example Returning Type Error\n\nSo, in an imperative for loop, a JavaScript constant variable will not work. Still, using const keyword to declare a variable in such a loop will only return a type error. Let’s take a look at such a scenario:\n\n for (const i = 0; i < scores.length; i++) { // TypeError console.log(scores[i]); }\n\nWondering why this happens? Well, the declaration is evaluated for a single time before the loop starts.\n\nLet’s try to understand more about syntax in JavaScript constant variable.\n\n## Understanding Syntax With JavaScript Const\n\nLet’s understand syntax by using constants in JavaScript as names and values, also known as identifiers and expressions. The constant name is nameN and is a legal identifier whereas valueN is a constant value and is also a legal expression. The following example shows this in detail:\n\n const name1 = value1 [, name2 = value2 [, … [, nameN = valueN]]];\n\nBesides this syntax, we can also use a destructuring assignment syntax to declare variables. Let’s look at an example:\n\n const { bar } = xyz; // where xyz = { lot: 5, loz: 8 };\n\nThe example shown above will create a const in Javascript with the name “lot” and will provide a value of “5”.\n\nWe used the terms scope and block-scope earlier. Let’s see some examples to understand them better.\n\n## Understanding Scope With JavaScript Const\n\nThe block scope in JavaScript defines the location of a variable within a program. Block scopes, also known as loop variables, are declared in a for loop. After the loop, they are not accessible unless they are defined before the loop.\n\nNow, let’s see an example to understand this concept further:\n\n if (X === 1) {\n\nIf we use the example above, it will create a block scope of the X variable. It will declare a block scope using the let keyword.\n\n let X = 5;\n\nIn the example above, we made X=5 so X is 5. Now, let’s try it with a JavaScript constant variable:\n\n console.log(‘my input is’ + X);\n\nThe example shown above will be hoisted as a global context and will show an error.\n\n### – JavaScript Const: Some Things to Consider\n\nWe must know that the JavaScript constant function creates a scope that can be global or local depending on the block on which it is declared. One thing to remember is that, unlike the var variables, JavaScript constants do not become a property for the window object.\n\nFor a const in JavaScript, an initializer is required. However, all the temporal dead zones are applicable for both let and const in JavaScript. For a constant, name sharing with a function or a variable in the same scope block is not possible.\n\n## Must-Knows for JavaScript Const\n\nConstants in JavaScript were introduced in ES6 (2015) where the variables once defined with const keyword were not redeclared or reassigned, and the variables defined with JavaScript constant variable were scope-blocked. These are some quick tips you should remember about const in JavaScript:\n\n• Since the variables cannot be reassigned, they must be assigned when declared\n• If the value will not change, a const keyword should be used\n• Use const in JavaScript when working with array, function, object, regExp\n• The const keyword defines a constant reference, not a constant value\n• You can change the elements of constant array and properties of constant object\n\n## Final Thoughts\n\nWe covered all there was to JavaScript const. The topics we covered are:\n\n•", null, "Objects with JavaScript constants\n• Arrays with const in JavaScript\n• Loops with constants in JavaScript\n• Syntax with JavaScript constant Variable\n• Scope with Javascript const function\n\nWe are certain that this guide has helped you to learn the complexities and the quick fixes to know what is const in JavaScript. The more you practice on the things that we discussed, the more proficient you will end up becoming when you use the JavaScript constant variable." ]	[ null, "data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASwAAADIAQAAAAB6pOH4AAAAAnRSTlMAAHaTzTgAAAAeSURBVFjD7cExAQAAAMKg9U9tB2+gAAAAAAAAAOA3HngAARco3ZkAAAAASUVORK5CYII=", null, "data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASwAAADIAQAAAAB6pOH4AAAAAnRSTlMAAHaTzTgAAAAeSURBVFjD7cExAQAAAMKg9U9tB2+gAAAAAAAAAOA3HngAARco3ZkAAAAASUVORK5CYII=", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8280542,"math_prob":0.8692589,"size":10515,"snap":"2023-40-2023-50","text_gpt3_token_len":2293,"char_repetition_ratio":0.193131,"word_repetition_ratio":0.03607666,"special_character_ratio":0.22672373,"punctuation_ratio":0.13105837,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.965822,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-25T00:02:55Z\",\"WARC-Record-ID\":\"<urn:uuid:f5bbd714-a29a-4664-b560-dec765487593>\",\"Content-Length\":\"210178\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2bfadcdf-5307-4fb4-b0ae-6ad96538a2d5>\",\"WARC-Concurrent-To\":\"<urn:uuid:08a67ede-df25-4e63-ac5b-4696e87fd051>\",\"WARC-IP-Address\":\"35.214.136.217\",\"WARC-Target-URI\":\"https://www.positioniseverything.net/javascript-const\",\"WARC-Payload-Digest\":\"sha1:T4IILCA3NGKVL7JRJFVW4NCLVDY5KUE3\",\"WARC-Block-Digest\":\"sha1:UJLGZOSR5CJUKNM4GW3RICAYSMAPUKPQ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233506669.96_warc_CC-MAIN-20230924223409-20230925013409-00162.warc.gz\"}"}
https://ukm.pure.elsevier.com/en/publications/hata-based-propagation-loss-formula-using-terrain-criterion-for-1	[ "# Hata based propagation loss formula using terrain criterion for 1800 MHz\n\nMahdi A. Nisirat, Salim Alkhawaldeh, Mahamod Ismail, Liyth Nissirat\n\nResearch output: Contribution to journalArticle\n\n6 Citations (Scopus)\n\n### Abstract\n\nMany mobile propagation models are going under intensive corrections; recently, to suit other new criteria's such as rough terrain areas. This proposed model modifies Hata main urban equation by adding a formula representing a logarithmic linear regression estimator of the standard deviation (σ) of the measuring campaign path in Amman city, Madaba city, and Jiza town, Jordan. High correlation factor of -96.7% is calculated between excess measured path loss compared to Hata urban path loss and log(σ). Root mean square error (RMSE) difference between this model and the measured raw data path loss has overcome RMSE calculated for Hata model, by an average of 21 dB, for open areas. The correction of suburban areas is calculated, on average, as 20 dB, and for urban areas as 17 dB.\n\nOriginal language English 855-859 5 AEU - International Journal of Electronics and Communications 66 10 https://doi.org/10.1016/j.aeue.2012.03.001 Published - Oct 2012\n\n### Fingerprint\n\nMean square error\nLinear regression\n\n### Keywords\n\n• Micro-cells\n• Mobile communications\n• Path loss\n• Terrain roughness\n\n### ASJC Scopus subject areas\n\n• Electrical and Electronic Engineering\n\n### Cite this\n\nHata based propagation loss formula using terrain criterion for 1800 MHz. / Nisirat, Mahdi A.; Alkhawaldeh, Salim; Ismail, Mahamod; Nissirat, Liyth.\n\nIn: AEU - International Journal of Electronics and Communications, Vol. 66, No. 10, 10.2012, p. 855-859.\n\nResearch output: Contribution to journalArticle\n\nNisirat, Mahdi A. ; Alkhawaldeh, Salim ; Ismail, Mahamod ; Nissirat, Liyth. / Hata based propagation loss formula using terrain criterion for 1800 MHz. In: AEU - International Journal of Electronics and Communications. 2012 ; Vol. 66, No. 10. pp. 855-859.\n@article{bdbd6fd9181d42ba86e3f48a151b05fe,\ntitle = \"Hata based propagation loss formula using terrain criterion for 1800 MHz\",\nabstract = \"Many mobile propagation models are going under intensive corrections; recently, to suit other new criteria's such as rough terrain areas. This proposed model modifies Hata main urban equation by adding a formula representing a logarithmic linear regression estimator of the standard deviation (σ) of the measuring campaign path in Amman city, Madaba city, and Jiza town, Jordan. High correlation factor of -96.7{\\%} is calculated between excess measured path loss compared to Hata urban path loss and log(σ). Root mean square error (RMSE) difference between this model and the measured raw data path loss has overcome RMSE calculated for Hata model, by an average of 21 dB, for open areas. The correction of suburban areas is calculated, on average, as 20 dB, and for urban areas as 17 dB.\",\nkeywords = \"Micro-cells, Mobile communications, Path loss, Terrain roughness\",\nauthor = \"Nisirat, {Mahdi A.} and Salim Alkhawaldeh and Mahamod Ismail and Liyth Nissirat\",\nyear = \"2012\",\nmonth = \"10\",\ndoi = \"10.1016/j.aeue.2012.03.001\",\nlanguage = \"English\",\nvolume = \"66\",\npages = \"855--859\",\njournal = \"AEU - International Journal of Electronics and Communications\",\nissn = \"1434-8411\",\npublisher = \"Urban und Fischer Verlag Jena\",\nnumber = \"10\",\n\n}\n\nTY - JOUR\n\nT1 - Hata based propagation loss formula using terrain criterion for 1800 MHz\n\nAU - Nisirat, Mahdi A.\n\nAU - Alkhawaldeh, Salim\n\nAU - Ismail, Mahamod\n\nAU - Nissirat, Liyth\n\nPY - 2012/10\n\nY1 - 2012/10\n\nN2 - Many mobile propagation models are going under intensive corrections; recently, to suit other new criteria's such as rough terrain areas. This proposed model modifies Hata main urban equation by adding a formula representing a logarithmic linear regression estimator of the standard deviation (σ) of the measuring campaign path in Amman city, Madaba city, and Jiza town, Jordan. High correlation factor of -96.7% is calculated between excess measured path loss compared to Hata urban path loss and log(σ). Root mean square error (RMSE) difference between this model and the measured raw data path loss has overcome RMSE calculated for Hata model, by an average of 21 dB, for open areas. The correction of suburban areas is calculated, on average, as 20 dB, and for urban areas as 17 dB.\n\nAB - Many mobile propagation models are going under intensive corrections; recently, to suit other new criteria's such as rough terrain areas. This proposed model modifies Hata main urban equation by adding a formula representing a logarithmic linear regression estimator of the standard deviation (σ) of the measuring campaign path in Amman city, Madaba city, and Jiza town, Jordan. High correlation factor of -96.7% is calculated between excess measured path loss compared to Hata urban path loss and log(σ). Root mean square error (RMSE) difference between this model and the measured raw data path loss has overcome RMSE calculated for Hata model, by an average of 21 dB, for open areas. The correction of suburban areas is calculated, on average, as 20 dB, and for urban areas as 17 dB.\n\nKW - Micro-cells\n\nKW - Mobile communications\n\nKW - Path loss\n\nKW - Terrain roughness\n\nUR - http://www.scopus.com/inward/record.url?scp=84863727199&partnerID=8YFLogxK\n\nUR - http://www.scopus.com/inward/citedby.url?scp=84863727199&partnerID=8YFLogxK\n\nU2 - 10.1016/j.aeue.2012.03.001\n\nDO - 10.1016/j.aeue.2012.03.001\n\nM3 - Article\n\nAN - SCOPUS:84863727199\n\nVL - 66\n\nSP - 855\n\nEP - 859\n\nJO - AEU - International Journal of Electronics and Communications\n\nJF - AEU - International Journal of Electronics and Communications\n\nSN - 1434-8411\n\nIS - 10\n\nER -" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.85719126,"math_prob":0.71570593,"size":3811,"snap":"2019-51-2020-05","text_gpt3_token_len":974,"char_repetition_ratio":0.11137378,"word_repetition_ratio":0.67790896,"special_character_ratio":0.25347677,"punctuation_ratio":0.13571429,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9627782,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-01-21T10:40:58Z\",\"WARC-Record-ID\":\"<urn:uuid:5c7d03fe-299d-4199-92b5-982c4f276815>\",\"Content-Length\":\"32267\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:3d177141-6927-4a08-9b8c-76b3ce01b70f>\",\"WARC-Concurrent-To\":\"<urn:uuid:9c8a974c-8ac9-4a5d-9a65-81bf84a3943b>\",\"WARC-IP-Address\":\"52.220.215.79\",\"WARC-Target-URI\":\"https://ukm.pure.elsevier.com/en/publications/hata-based-propagation-loss-formula-using-terrain-criterion-for-1\",\"WARC-Payload-Digest\":\"sha1:5C6657B7SNOW54Z7VD7RZBANV7NNZRVY\",\"WARC-Block-Digest\":\"sha1:F43SJ6TV5YHATX2Q4IGVHUG4EI23WLFH\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-05/CC-MAIN-2020-05_segments_1579250603761.28_warc_CC-MAIN-20200121103642-20200121132642-00507.warc.gz\"}"}
https://risk.asmedigitalcollection.asme.org/dynamicsystems/article-abstract/139/6/061001/473557/Direct-Integration-Method-for-Time-Delayed-Control	[ "A direct integration method (DIM) for time-delayed control (TDC) is proposed in this research. For a second-order dynamic system with time-delayed controllers, a Volterra integral equation of the second kind is used instead of a state derivative equation. With the proposed DIM where matrix exponentials are avoided, semi-analytical representation of the Floquet transition matrix for stability analysis can be derived, the stability region on the parametric space comprising control variables can also be plotted. Within this stability region, optimal control variables are subsequently obtained using a multilevel conjugate gradient optimization method. Further simulation examples demonstrated the superiority of the proposed DIM in terms of computational efficiency and accuracy, as well as the effectiveness of the optimization-based controller design approach.\n\n## References\n\n1.\nUlsoy\n,\nA. G.\n,\n2015\n, “\nTime-Delayed Control of Siso Systems for Improved Stability Margins\n,”\nASME J. Dyn. Syst., Meas., Control\n,\n137\n(\n4\n), p.\n041014\n.\n2.\nStépán\n,\nG.\n,\n1989\n, “\nRetarded Dynamical Systems: Stability and Characteristic Functions\n,”\nPitman Research Notes\n(Mathematics Series),\nLongman Scientific & Technical\n,\nNew York\n.\n3.\nGu\n,\nK.\n,\nChen\n,\nJ.\n, and\nKharitonov\n,\nV.\n,\n2003\n, “\nStability of Time-Delay Systems\n,”\nControl Engineering\n,\nBirkhäuser Boston\n,\nCambridge, MA\n.\n4.\nMarshall\n,\nJ.\n,\n1992\n, “\nTime-Delay Systems: Stability and Performance Criteria With Applications\n,”\nMathematics and Its Applications\n(Ellis Horwood Series),\nEllis Horwood\n,\n.\n5.\nPyragas\n,\nK.\n,\n1992\n, “\nContinuous Control of Chaos by Self-Controlling Feedback\n,”\nPhys. Lett. A\n,\n170\n(\n6\n), pp.\n421\n428\n.\n6.\nGu\n,\nK.\n, and\nNiculescu\n,\nS.-I.\n,\n2003\n, “\nSurvey on Recent Results in the Stability and Control of Time-Delay Systems\n,”\nASME J. Dyn. Syst., Meas., Control\n,\n125\n(\n2\n), pp.\n158\n165\n.\n7.\n,\nF. E.\n,\nvon Bremen\n,\nH. F.\n,\nKumar\n,\nR.\n, and\nHosseini\n,\nM.\n,\n2003\n, “\nTime Delayed Control of Structural Systems\n,”\nEarthquake Eng. Struct. Dyn.\n,\n32\n(\n4\n), pp.\n495\n535\n.\n8.\n,\nF. E.\n,\nVon Bremen\n,\nH.\n, and\nPhohomsiri\n,\nP.\n,\n2007\n, “\nTime-Delayed Control Design for Active Control of Structures: Principles and Applications\n,”\nStruct. Control Health Monit.\n,\n14\n(\n1\n), pp.\n27\n61\n.\n9.\nChung\n,\nL.\n,\nLin\n,\nC.\n, and\nLu\n,\nK.\n,\n1995\n, “\nTime-Delay Control of Structures\n,”\nEarthquake Eng. Struct. Dyn.\n,\n24\n(\n5\n), pp.\n687\n701\n.\n10.\nYang\n,\nB.\n, and\nMote\n,\nC.\n, Jr.\n,\n1990\n, “\nVibration Control of Band Saws: Theory and Experiment\n,”\nWood Sci. Technol.\n,\n24\n(\n4\n), pp.\n355\n373\n.\n11.\nYang\n,\nB.\n, and\nMote\n,\nC.\n,\n1992\n, “\nOn Time Delay in Noncolocated Control of Flexible Mechanical Systems\n,”\nASME J. Dyn. Syst., Meas., Control\n,\n114\n(\n3\n), pp.\n409\n415\n.\n12.\nSan-Millan\n,\nA.\n,\nRussell\n,\nD.\n,\nFeliu\n,\nV.\n, and\nAphale\n,\nS. S.\n,\n2015\n, “\nA Modified Positive Velocity and Position Feedback Scheme With Delay Compensation for Improved Nanopositioning Performance\n,”\nSmart Mater. Struct.\n,\n24\n(\n7\n), p.\n075021\n.\n13.\nSuh\n,\nI.\n, and\nBien\n,\nZ.\n,\n1979\n, “\nProportional Minus Delay Controller\n,”\nIEEE Trans. Autom. Control\n,\n24\n(\n2\n), pp.\n370\n372\n.\n14.\nVillafuerte\n,\nR.\n,\nMondie\n,\nS.\n, and\nGarrido\n,\nR.\n,\n2013\n, “\nTuning of Proportional Retarded Controllers: Theory and Experiments\n,”\nIEEE Trans. Control Syst. Technol.\n,\n21\n(\n3\n), pp.\n983\n990\n.\n15.\nHövel\n,\nP.\n,\n2010\n,\nControl of Complex Nonlinear Systems With Delay\n,\nSpringer-Verlag, Berlin/Heidelberg\n.\n16.\nRamírez\n,\nA.\n,\nGarrido\n,\nR.\n, and\nMondié\n,\nS.\n,\n2015\n, “\nVelocity Control of Servo Systems Using an Integral Retarded Algorithm\n,”\nISA Trans.\n,\n58\n, pp.\n357\n366\n.\n17.\nGoyal\n,\nV.\n,\nDeolia\n,\nV. K.\n, and\nSharma\n,\nT. N.\n,\n2015\n, “\nRobust Sliding Mode Control for Nonlinear Discrete-Time Delayed Systems Based on Neural Network\n,”\nIntell. Control Autom.\n,\n6\n(\n1\n), p.\n75\n.\n18.\nNiculescu\n,\nS.-I.\n, and\nGu\n,\nK.\n,\n2012\n,\n, Vol.\n38\n,\nSpringer-Verlag, Berlin/Heidelberg\n.\n19.\nNiculescu\n,\nS.-I.\n,\nDion\n,\nJ.-M.\n,\nDugard\n,\nL.\n, and\nLI\n,\nH.\n,\n1997\n, “\nStability of Linear Systems With Delayed State: An LMI Approach\n,”\nJ. Eur. Syst. Autom.\n,\n31\n(\n6\n), pp.\n955\n969\n.\n20.\nFridman\n,\nE.\n, and\nShaked\n,\nU.\n,\n2003\n, “\nDelay-Dependent Stability and h∞ Control: Constant and Time-Varying Delays\n,”\nInt. J. Control\n,\n76\n(\n1\n), pp.\n48\n60\n.\n21.\nFridman\n,\nE.\n, and\nShaked\n,\nU.\n,\n2002\n, “\nAn Improved Stabilization Method for Linear Time-Delay Systems\n,”\nIEEE Trans. Autom. Control\n,\n47\n(\n11\n), pp.\n1931\n1937\n.\n22.\nWu\n,\nM.\n,\nHe\n,\nY.\n, and\nShe\n,\nJ.-H.\n,\n2004\n, “\nNew Delay-Dependent Stability Criteria and Stabilizing Method for Neutral Systems\n,”\nIEEE Trans. Autom. Control\n,\n49\n(\n12\n), pp.\n2266\n2271\n.\n23.\nFeng\n,\nZ.\n,\nLam\n,\nJ.\n, and\nGao\n,\nH.\n,\n2011\n, “\nα-Dissipativity Analysis of Singular Time-Delay Systems\n,”\nAutomatica\n,\n47\n(\n11\n), pp.\n2548\n2552\n.\n24.\nDorf\n,\nR. C.\n, and\nBishop\n,\nR. H.\n,\n2001\n,\nModern Control Systems\n, 9th ed.,\nPrentice-Hall\n,\n.\n25.\nWang\n,\nD.\n,\n2013\n,\nDesign of Lower-Order Controllers for Time-Delay Systems: A Parametric Space Approach\n,\nScience Press\n,\nBeijing\n.\n26.\nOlgac\n,\nN.\n,\nErgenc\n,\nA. F.\n, and\nSipahi\n,\nR.\n,\n2005\n, “\nDelay Scheduling: A New Concept for Stabilization in Multiple Delay Systems\n,”\nJ. Vib. Control\n,\n11\n(\n9\n), pp.\n1159\n1172\n.\n27.\nYi\n,\nS.\n,\n2009\n, “\nTime-Delay Systems: Analysis and Control Using the Lambert w Function\n,” Ph.D. thesis,\nThe University of Michigan\n,\nAnn Arbor, MI\n.\n28.\nDuan\n,\nS.\n,\nNi\n,\nJ.\n, and\nUlsoy\n,\nA. G.\n,\n2011\n, “\nDecay Function Estimation for Linear Time Delay Systems Via the Lambert W Function\n,”\nJ. Vib. Control\n,\n18\n(\n10\n), pp.\n1462\n1473\n.\n29.\nFarkas\n,\nM.\n,\n2013\n,\nPeriodic Motions\n, Vol.\n104\n,\n,\nNew York\n.\n30.\nInsperger\n,\nT.\n, and\nStépán\n,\nG.\n,\n2002\n, “\nSemi-Discretization Method for Delayed Systems\n,”\nInt. J. Numer. Methods Eng.\n,\n55\n(\n5\n), pp.\n503\n518\n.\n31.\nInsperger\n,\nT.\n, and\nStépán\n,\nG.\n,\n2004\n, “\nUpdated Semi-Discretization Method for Periodic Delay-Differential Equations With Discrete Delay\n,”\nInt. J. Numer. Methods Eng.\n,\n61\n(\n1\n), pp.\n117\n141\n.\n32.\nInsperger\n,\nT.\n, and\nStépán\n,\nG.\n,\n2011\n,\nSemi-Discretization for Time-Delay Systems: Stability and Engineering Applications\n, Vol.\n178\n,\n,\nNew York\n.\n33.\nDing\n,\nY.\n,\nZhu\n,\nL.\n,\nZhang\n,\nX.\n, and\nDing\n,\nH.\n,\n2011\n, “\nNumerical Integration Method for Prediction of Milling Stability\n,”\nASME J. Manuf. Sci. Eng.\n,\n133\n(\n3\n), p.\n031005\n.\n34.\nDong\n,\nW.\n,\nDing\n,\nY.\n,\nZhu\n,\nX.\n, and\nDing\n,\nH.\n,\n2015\n, “\nOptimal Proportional–Integral–Derivative Control of Time-Delay Systems Using the Differential Quadrature Method\n,”\nASME J. Dyn. Syst., Meas., Control\n,\n137\n(\n10\n), p.\n101005\n.\n35.\nDelves\n,\nL.\n, and\nMohamed\n,\nJ.\n,\n1988\n,\nComputational Methods for Integral Equations\n,\nCambridge University Press\n,\nCambridge, UK\n.\n36.\nLi\n,\nX.\n,\n2008\n,\nIntegral Equations\n,\nScience Press\n,\nBeijing, China\n.\n37.\nYang\n,\nW. Y.\n,\nCao\n,\nW.\n,\nChung\n,\nT.-S.\n, and\nMorris\n,\nJ.\n,\n2005\n,\nApplied Numerical Methods Using MATLAB\n,\nWiley\n,\nNew York\n.\n38.\nBellman\n,\nR. E.\n, and\nCooke\n,\nK. L.\n,\n1963\n,\nDifferential-Difference Equations\n,\nRand Corporation\n,\n.\n39.\nGraham\n,\nD.\n, and\nLathrop\n,\nR. C.\n,\n1953\n, “\nThe Synthesis of Optimum Transient Response: Criteria and Standard Forms\n,”\nTrans. Am. Inst. Electr. Eng., Part II: Appl. Ind.\n,\n72\n(\n5\n), pp.\n273\n288\n.\n40.\nLax\n,\nP.\n,\n2007\n, “\nLinear Algebra and Its Applications\n,”\nNo. 10 in Linear Algebra and Its Applications\n,\nWiley\n,\nNew York\n.\n41.\nRao\n,\nS. S.\n, and\nRao\n,\nS.\n,\n2009\n,\nEngineering Optimization: Theory and Practice\n,\nWiley\n,\nNew York\n.\n42.\nLi\n,\nX.\n, and\nDe Souza\n,\nC. E.\n,\n1997\n, “\nCriteria for Robust Stability and Stabilization of Uncertain Linear Systems With State Delay\n,”\nAutomatica\n,\n33\n(\n9\n), pp.\n1657\n1662\n.\n43.\nPark\n,\nP.\n,\n1999\n, “\nA Delay-Dependent Stability Criterion for Systems With Uncertain Time-Invariant Delays\n,”\nIEEE Trans. Autom. Control\n,\n44\n(\n4\n), pp.\n876\n877\n.\n44.\nSheng\n,\nJ.\n, and\nSun\n,\nJ.\n,\n2005\n, “\nFeedback Controls and Optimal Gain Design of Delayed Periodic Linear Systems\n,”\nJ. Vib. Control\n,\n11\n(\n2\n), pp.\n277\n294\n." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.75331795,"math_prob":0.8182351,"size":5303,"snap":"2023-14-2023-23","text_gpt3_token_len":1362,"char_repetition_ratio":0.17758067,"word_repetition_ratio":0.3202329,"special_character_ratio":0.23100132,"punctuation_ratio":0.21499014,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95381945,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-06-11T00:59:03Z\",\"WARC-Record-ID\":\"<urn:uuid:fb904e41-fdca-49dc-9715-4e4b0e7af345>\",\"Content-Length\":\"188293\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:66370fca-28ea-4bc1-ba7e-e332f4789c0d>\",\"WARC-Concurrent-To\":\"<urn:uuid:aeaa5dfd-f52d-4589-b563-ab3e56d370cb>\",\"WARC-IP-Address\":\"52.179.114.94\",\"WARC-Target-URI\":\"https://risk.asmedigitalcollection.asme.org/dynamicsystems/article-abstract/139/6/061001/473557/Direct-Integration-Method-for-Time-Delayed-Control\",\"WARC-Payload-Digest\":\"sha1:YF6S5H52YG3AGPK7LSHO7SNMIIQGXJAO\",\"WARC-Block-Digest\":\"sha1:QGQGERTBSEYAYYYPVJFEI6QILC65DL55\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224646652.16_warc_CC-MAIN-20230610233020-20230611023020-00639.warc.gz\"}"}
https://blog.codekiller.top/2021/02/03/%E6%9D%8E%E5%AE%8F%E6%AF%85%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0/19_Unsupervised%20Learning%20PCA%20part1/	[ "绿色健康小清新\n\nUnsupervised Learning: PCA(Ⅰ)\n\nPCA for 1-D\n\n$z_1=w^1\\cdot x$，其中$w^1$表示$w$的第一个row vector，假设$w^1$的长度为1，即$\|\|w^1\|\|_2=1$，此时$z_1$就是$x$$w^1$方向上的投影\n\n• 我们希望找一个projection的方向，它可以让projection后的variance越大越好\n\n• 我们不希望projection使这些data point通通挤在一起，导致点与点之间的奇异度消失\n\n• 其中，variance的计算公式：$Var(z_1)=\\frac{1}{N}\\sum\\limits_{z_1}(z_1-\\bar{z_1})^2, \|\|w^1\|\|_2=1$$\\bar {z_1}$$z_1$的平均值\n\nPCA for n-D\n\n$z=Wx$来说：\n\n• $z_1=w^1\\cdot x$，表示$x$$w^1$方向上的投影\n• $z_2=w^2\\cdot x$，表示$x$$w^2$方向上的投影\n\n$z_1,z_2,...$串起来就得到$z$，而$w^1,w^2,...$分别是$W$的第1,2,…个row，需要注意的是，这里的$w^i$必须相互正交，此时$W$是正交矩阵(orthogonal matrix)，如果不加以约束，则找到的$w^1,w^2,...$实际上是相同的值\n\nLagrange multiplier\n\ncalculate $w^1$\n\n• 首先计算出$\\bar{z_1}$\n\n\\begin{aligned} &z_1=w^1\\cdot x\\\\ &\\bar{z_1}=\\frac{1}{N}\\sum z_1=\\frac{1}{N}\\sum w^1\\cdot x=w^1\\cdot \\frac{1}{N}\\sum x=w^1\\cdot \\bar x \\end{aligned}\n\n• 然后计算maximize的对象$Var(z-1)$\n\n其中$Cov(x)=\\frac{1}{N}\\sum(x-\\bar x)(x-\\bar x)^T$\n\n\\begin{aligned} Var(z_1)&=\\frac{1}{N}\\sum\\limits_{z_1} (z_1-\\bar{z_1})^2\\\\ &=\\frac{1}{N}\\sum\\limits_{x} (w^1\\cdot x-w^1\\cdot \\bar x)^2\\\\ &=\\frac{1}{N}\\sum (w^1\\cdot (x-\\bar x))^2\\\\ &=\\frac{1}{N}\\sum(w^1)^T(x-\\bar x)(x-\\bar x)^T w^1\\\\ &=(w^1)^T\\frac{1}{N}\\sum(x-\\bar x)(x-\\bar x)^T w^1\\\\ &=(w^1)^T Cov(x)w^1 \\end{aligned}\n\n• 当然这里想要求$Var(z_1)=(w^1)^TCov(x)w^1$的最大值，还要加上$\|\|w^1\|\|_2=(w^1)^Tw^1=1$的约束条件，否则$w^1$可以取无穷大\n\n• $S=Cov(x)$，它是：\n\n• 对称的(symmetric)\n• 半正定的(positive-semidefine)\n• 所有特征值(eigenvalues)非负的(non-negative)\n• 使用拉格朗日乘数法，利用目标和约束条件构造函数：\n\n$g(w^1)=(w^1)^TSw^1-\\alpha((w^1)^Tw^1-1)$\n\n• $w^1$这个vector里的每一个element做偏微分：\n\n$\\partial g(w^1)/\\partial w_1^1=0\\\\ \\partial g(w^1)/\\partial w_2^1=0\\\\ \\partial g(w^1)/\\partial w_3^1=0\\\\ ...$\n\n• 整理上述推导式，可以得到：\n\n其中，$w^1$是S的特征向量(eigenvector)\n\n$Sw^1=\\alpha w^1$\n\n• 注意到满足$(w^1)^Tw^1=1$的特征向量$w^1$有很多，我们要找的是可以maximize $(w^1)^TSw^1$的那一个，于是利用上一个式子：\n\n$(w^1)^TSw^1=(w^1)^T \\alpha w^1=\\alpha (w^1)^T w^1=\\alpha$\n\n• 此时maximize $(w^1)^TSw^1$就变成了maximize $\\alpha$，也就是当$S$的特征值$\\alpha$最大时对应的那个特征向量$w^1$就是我们要找的目标\n\n• 结论：$w^1$$S=Cov(x)$这个matrix中的特征向量，对应最大的特征值$\\lambda_1$\n\ncalculate $w^2$\n\n• 同样是用拉格朗日乘数法求解，先写一个关于$w^2$的function，包含要maximize的对象，以及两个约束条件\n\n$g(w^2)=(w^2)^TSw^2-\\alpha((w^2)^Tw^2-1)-\\beta((w^2)^Tw^1-0)$\n\n• $w^2$的每个element做偏微分：\n\n$\\partial g(w^2)/\\partial w_1^2=0\\\\ \\partial g(w^2)/\\partial w_2^2=0\\\\ \\partial g(w^2)/\\partial w_3^2=0\\\\ ...$\n\n• 整理后得到：\n\n$Sw^2-\\alpha w^2-\\beta w^1=0$\n\n• 上式两侧同乘$(w^1)^T$，得到：\n\n$(w^1)^TSw^2-\\alpha (w^1)^Tw^2-\\beta (w^1)^Tw^1=0$\n\n• 其中$\\alpha (w^1)^Tw^2=0,\\beta (w^1)^Tw^1=\\beta$\n\n而由于$(w^1)^TSw^2$是vector×matrix×vector=scalar，因此在外面套一个transpose不会改变其值，因此该部分可以转化为：\n\n注：S是symmetric的，因此$S^T=S$\n\n\\begin{aligned} (w^1)^TSw^2&=((w^1)^TSw^2)^T\\\\ &=(w^2)^TS^Tw^1\\\\ &=(w^2)^TSw^1 \\end{aligned}\n\n我们已经知道$w^1$满足$Sw^1=\\lambda_1 w^1$，代入上式：\n\n\\begin{aligned} (w^1)^TSw^2&=(w^2)^TSw^1\\\\ &=\\lambda_1(w^2)^Tw^1\\\\ &=0 \\end{aligned}\n\n• 因此有$(w^1)^TSw^2=0$$\\alpha (w^1)^Tw^2=0$$\\beta (w^1)^Tw^1=\\beta$，又根据\n\n$(w^1)^TSw^2-\\alpha (w^1)^Tw^2-\\beta (w^1)^Tw^1=0$\n\n可以推得$\\beta=0$\n\n• 此时$Sw^2-\\alpha w^2-\\beta w^1=0$就转变成了$Sw^2-\\alpha w^2=0$，即\n\n$Sw^2=\\alpha w^2$\n\n• 由于$S$是symmetric的，因此在不与$w_1$冲突的情况下，这里$\\alpha$选取第二大的特征值$\\lambda_2$时，可以使$(w^2)^TSw^2$最大\n\n• 结论：$w^2$也是$S=Cov(x)$这个matrix中的特征向量，对应第二大的特征值$\\lambda_2$\n\nPCA-decorrelation\n\n$z=W\\cdot x$\n\nPCA可以让不同dimension之间的covariance变为0，即不同new feature之间是没有correlation的，这样做的好处是，减少feature之间的联系从而减少model所需的参数量\n\n-------------本文结束感谢您的阅读-------------" ]	[ null ]	{"ft_lang_label":"__label__zh","ft_lang_prob":0.86745906,"math_prob":1.0000094,"size":3069,"snap":"2022-05-2022-21","text_gpt3_token_len":2420,"char_repetition_ratio":0.10603589,"word_repetition_ratio":0.0,"special_character_ratio":0.27109808,"punctuation_ratio":0.06477733,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.0000098,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-25T17:38:42Z\",\"WARC-Record-ID\":\"<urn:uuid:b0f2a363-f446-431a-a684-72aae0439acc>\",\"Content-Length\":\"270898\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b5312c9b-a57c-49aa-9b16-ce10e839cf66>\",\"WARC-Concurrent-To\":\"<urn:uuid:16367bb1-8578-4b36-a281-8855cf48328f>\",\"WARC-IP-Address\":\"47.116.134.123\",\"WARC-Target-URI\":\"https://blog.codekiller.top/2021/02/03/%E6%9D%8E%E5%AE%8F%E6%AF%85%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0/19_Unsupervised%20Learning%20PCA%20part1/\",\"WARC-Payload-Digest\":\"sha1:CW3OVYM6H7THYZZMFXLYQSFWE4YNVV6O\",\"WARC-Block-Digest\":\"sha1:GNBCY432N4SFQKXNM6EGFFQIKPAPLSI7\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320304859.70_warc_CC-MAIN-20220125160159-20220125190159-00045.warc.gz\"}"}
http://blog.jesseseay.com/improving-arduino-sensor-range	[ "## Improving Arduino sensor range\n\nAdding a fixed resistor ½ the value of a variable resistance sensor improves Arduino performance.\n\nWhenever you connect a 2-lead variable resistor (VR) sensor (like a photo cell or bend sensor) to an Arduino, you add a resistor to it. I did this with my knitted stretch sensor. It creates a circuit known as a voltage divider, which controls the voltage level, based on the relative resistance of the resistor to the sensor. This is important because the voltage level is what AnalogRead \"reads\" in Arduino.\n\nI wondered what value would give the best performance for my knitted sensors. So I used the equation below to calculate the output range of voltage dividers, based on the ratio between R1 and R2, given that R2 is my knitted sensor and R1 is the (unchanging) resistor. I graphed the outputs for each VR value at 0%, 25%, 50%, 75%, and 100% of its maximum range.\n\nI found as I widened the ratio, the range widens; the bottom part gets steeper but the top flattens out.\n\nI liked the results of a 1:2 ratio (light blue line) so I used that with my knitted sensors.\n\nLater, I looked online and found Adafruit’s tutorial on photocells, which suggests using the Axel-Benz formula (choose a resistor the square root of the min + max resistance of your resistive sensor). This is useful if your minimum resistance isn’t zero. For my examples, it suggested a value slightly higher than the ½ value I’d settled on.\n\nOn a final note, none of this can match the range of a single potentiometer: when R2 decreases as R1 increases, we get a nice linear sweep with a full range from 0V to V+." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9024453,"math_prob":0.8694602,"size":1657,"snap":"2023-40-2023-50","text_gpt3_token_len":394,"char_repetition_ratio":0.1306715,"word_repetition_ratio":0.0,"special_character_ratio":0.23415811,"punctuation_ratio":0.09763314,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9826638,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-24T07:49:22Z\",\"WARC-Record-ID\":\"<urn:uuid:7f82003a-762c-4dcd-9563-71177e81e34a>\",\"Content-Length\":\"20428\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:bac9df68-4739-45b3-b523-8948490547a3>\",\"WARC-Concurrent-To\":\"<urn:uuid:400ea3ed-37e3-41a8-a393-a4fe35d07506>\",\"WARC-IP-Address\":\"188.93.148.37\",\"WARC-Target-URI\":\"http://blog.jesseseay.com/improving-arduino-sensor-range\",\"WARC-Payload-Digest\":\"sha1:QUBNBWETEBTY7RJSBKMRYYXNWRSCGMT5\",\"WARC-Block-Digest\":\"sha1:KCQ6M6D2VU3LBWPMAC3EQ53MZBKBFUQI\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233506623.27_warc_CC-MAIN-20230924055210-20230924085210-00794.warc.gz\"}"}
https://fr.mathworks.com/matlabcentral/cody/problems/43065	[ "Cody\n\n# Problem 43065. Energy of an object\n\nCalculate the total mechanical energy of an object.\n\nTotal Energy= Potential energy + Kinetic energy\n\nP.E.=mgh\n\nK.E.=1/2mv^2\n\ng=9.8m/s^2\n\n### Solution Stats\n\n66.67% Correct \| 33.33% Incorrect\nLast Solution submitted on Nov 07, 2019" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7284295,"math_prob":0.93953407,"size":337,"snap":"2019-51-2020-05","text_gpt3_token_len":100,"char_repetition_ratio":0.15615615,"word_repetition_ratio":0.0,"special_character_ratio":0.29376855,"punctuation_ratio":0.08974359,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99007446,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-15T07:22:30Z\",\"WARC-Record-ID\":\"<urn:uuid:7dd31a8c-c0a1-4054-b406-543ef171ff0b>\",\"Content-Length\":\"87737\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:96eb2fe9-95f7-47f8-9590-4cea07db132e>\",\"WARC-Concurrent-To\":\"<urn:uuid:28e6f3aa-4375-41ce-8185-f0817f71a4d8>\",\"WARC-IP-Address\":\"104.91.36.45\",\"WARC-Target-URI\":\"https://fr.mathworks.com/matlabcentral/cody/problems/43065\",\"WARC-Payload-Digest\":\"sha1:R2WIMBKADAKE2NUPBNLPY5ZATJTJUU6H\",\"WARC-Block-Digest\":\"sha1:32R5QLAU2NRGOQKK2IMU33ONQXBQQGUA\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575541307797.77_warc_CC-MAIN-20191215070636-20191215094636-00392.warc.gz\"}"}
https://www.koobits.com/2013/01/14/the-1-key-to-solving-problem-sums-most-parents-ignore	[ "", null, "# The #1 Key to Solving Problem Sums…that Most Parents Ignore\n\nProblem sums, or math word problems, are one of the most challenging learning tasks for primary school students. Parents often worry about their children’s ability to handle these complex math questions, which require advanced thinking and special methods to solve. As such, kids are frequently drilled on problem sums by parents or even sent for special math tuition classes and workshops to learn various special problem sums solving techniques. Unfortunately, all of these fail to address the number one key to solving problem sums, which is to understand the question.", null, "## The #1 Key to Solving Problem Sums: Comprehension\n\nMathematical inability is usually the last reason why children are unable to solve problem sums and math word problems. In fact, problem sums require only basic arithmetic skills like addition, subtraction, multiplication, division, fractions, and ratios. These questions are designed, rather, to test students’ understanding and application of mathematical concepts. If your child does not comprehend the question and merely uses a certain technique to solve a problem sum, he or she will have even more trouble with Math and other subjects later on in their learning journey. Before trying various heuristics to solve a problem sum, ensure that your child comprehends the question first:\n1. Read through the entire question\n2. Break the question down into parts\n3. Determine the order of steps to get to the solution\nOnce the order of steps has been determined, your child can then apply methods such as model drawing or supposition to solve the problem sum.\n\n#### Example Question (Primary 3)\n\nA kettle has 420ml more water than a jug. When 150ml of water is poured from the jug into the kettle, there is 4 times as much water in the kettle as the jug. How much water was there in the jug at first?\nHere is how the problem can be broken down into parts:\n• The kettle has 420ml more water than the jug.", null, "• When 150ml of water is poured from the jug into the kettle,", null, "• There is 4 times as much water in the kettle as the jug.", null, "With the problem sum broken down into parts and visualized using models, your child can then solve the problem using basic arithmetic.\n\n## How to Practise Problem Sums Comprehension\n\nInstead of drilling your child on various techniques to solve different types of problem sums, focus on reading the question.\n1. Get your child to go through various questions in his/her math workbook or assessment books without solving them.\n2. Then, ask him/her to identify the questions which seem similar.\n3. Determine the steps needed to get the solution, but don’t do the math. See if the steps can be applied to similar questions.\nIncreased reading is the key to improving your child’s English language comprehension skills. With better comprehension, you’ll find that your child can solve problem sums more easily and quickly. Do you have any practical tips of your own (not “secret” techniques) for solving problem sums?" ]	[ null, "https://www.facebook.com/tr", null, "https://www.koobits.com/wp-content/plugins/a3-lazy-load/assets/images/lazy_placeholder.gif", null, "https://www.koobits.com/wp-content/plugins/a3-lazy-load/assets/images/lazy_placeholder.gif", null, "https://www.koobits.com/wp-content/plugins/a3-lazy-load/assets/images/lazy_placeholder.gif", null, "https://www.koobits.com/wp-content/plugins/a3-lazy-load/assets/images/lazy_placeholder.gif", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.94031894,"math_prob":0.82726216,"size":1861,"snap":"2020-24-2020-29","text_gpt3_token_len":399,"char_repetition_ratio":0.13301024,"word_repetition_ratio":0.12101911,"special_character_ratio":0.21332617,"punctuation_ratio":0.09943182,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9830103,"pos_list":[0,1,2,3,4,5,6,7,8,9,10],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-06-01T01:26:54Z\",\"WARC-Record-ID\":\"<urn:uuid:64bec268-ed01-4d5f-a3fd-196752754d40>\",\"Content-Length\":\"91198\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:efcf4c1f-0056-4df7-8fde-4631ab8211cb>\",\"WARC-Concurrent-To\":\"<urn:uuid:53552408-e9fc-4053-841e-ed344e8f6b90>\",\"WARC-IP-Address\":\"104.22.64.135\",\"WARC-Target-URI\":\"https://www.koobits.com/2013/01/14/the-1-key-to-solving-problem-sums-most-parents-ignore\",\"WARC-Payload-Digest\":\"sha1:F7F25JB7ZVQGBRACLFFT74J7SAADVMHK\",\"WARC-Block-Digest\":\"sha1:TQHLGL2P3YTHNESKZAYEGOHB66HPQCEM\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-24/CC-MAIN-2020-24_segments_1590347413901.34_warc_CC-MAIN-20200601005011-20200601035011-00115.warc.gz\"}"}
https://uniquejankari.in/nptel-introduction-to-machine-learning-assignment-2-answers-2022/	[ "# NPTEL Introduction to Machine Learning Assignment 2 Answers July 2023\n\nNPTEL Introduction to Machine Learning Assignment 2 Answers 2023:- In this post, We have provided answers of NPTEL Introduction to Machine Learning Assignment 2. We provided answers here only for reference. Plz, do your assignment at your own knowledge.\n\n## NPTEL Introduction To Machine Learning Week 2 Assignment Answer 2023\n\n1. The parameters obtained in linear regression\n\n• can take any value in the real space\n• are strictly integers\n• always lie in the range [0,1]\n• can take only non-zero values\n`Answer :- a. can take any value in the real space`\n\n2. Suppose that we have N independent variables (X1,X2,…Xn) and the dependent variable is Y . Now imagine that you are applying linear regression by fitting the best fit line using the least square error on this data. You found that the correlation coefficient for one of its variables (Say X1) with Y is -0.005.\n\n• Regressing Yon X1 mostly does not explain away Y .\n• Regressing Y on X1 explains away Y .\n• The given data is insufficient to determine if regressing Yon X1 explains away Y or not.\n`Answer :- b. Regressing Yon X1 mostly does not explain away Y .`\n\n3. Which of the following is a limitation of subset selection methods in regression?\n\n• They tend to produce biased estimates of the regression coefficients.\n• They cannot handle datasets with missing values.\n• They are computationally expensive for large datasets.\n• They assume a linear relationship between the independent and dependent variables.\n• They are not suitable for datasets with categorical predictors.\n`Answer :- c. They are computationally expensive for large datasets.`\n\n4. The relation between studying time (in hours) and grade on the final examination (0-100) in a random sample of students in the Introduction to Machine Learning Class was found to be:Grade = 30.5 + 15.2 (h)\n\nHow will a student’s grade be affected if she studies for four hours?\n\n• It will go down by 30.4 points.\n• It will go down by 30.4 points.\n• It will go up by 60.8 points.\n• The grade will remain unchanged.\n• It cannot be determined from the information given\n`Answer :- c. It will go up by 60.8 points.`\n\n5. Which of the statements is/are True?\n\n• Ridge has sparsity constraint, and it will drive coefficients with low values to 0.\n• Lasso has a closed form solution for the optimization problem, but this is not the case for Ridge.\n• Ridge regression does not reduce the number of variables since it never leads a coefficient to zero but only minimizes it.\n• If there are two or more highly collinear variables, Lasso will select one of them randomly\n```Answer :- c. Ridge regression does not reduce the number of variables since it never leads a coefficient to zero but only minimizes it.\n\nd. If there are two or more highly collinear variables, Lasso will select one of them randomly```\n\n6. Find the mean of squared error for the given predictions:", null, "Hint: Find the squared error for each prediction and take the mean of that.\n\n• 1\n• 2\n• 1.5\n• 0\n`Answer :- a. 1`\n\n7. Consider the following statements:\n\nStatement A: In Forward stepwise selection, in each step, that variable is chosen which has the maximum correlation with the residual, then the residual is regressed on that variable, and it is added to the predictor.\nStatement B: In Forward stagewise selection, the variables are added one by one to the previously selected variables to produce the best fit till then\n\n• Both the statements are True.\n• Statement A is True, and Statement B is False\n• Statement A is False and Statement B is True\n• Both the statements are False.\n`Answer :- a. Both the statements are True.`\n\n8. The linear regression model y=a0+a1x1+a2x2+…….+apxp is to be fitted to a set of N training data points having p attributes each. Let X be N×(p+1) vectors of input values (augmented by 1‘s), Y be N×1 vector of target values, and θθ be (p+1)×1 vector of parameter values (a0,a1,a2,…,ap. If the sum squared error is minimized for obtaining the optimal regression model, which of the following equation holds?\n\n• XTX=XY\n• Xθ=XT\n• XTXθ =Y\n• XTXθ=XTY\n`Answer :- d. XTXθ=XTY`\n\n9. Which of the following statements is true regarding Partial Least Squares (PLS) regression?\n\n• PLS is a dimensionality reduction technique that maximizes the covariance between the predictors and the dependent variable.\n• PLS is only applicable when there is no multicollinearity among the independent variables.\n• PLS can handle situations where the number of predictors is larger than the number of observations.\n• PLS estimates the regression coefficients by minimizing the residual sum of squares.\n• PLS is based on the assumption of normally distributed residuals.\n• All of the above.\n• None of the above.\n`Answer :- a`\n\n10. Which of the following statements about principal components in Principal Component Regression (PCR) is true?\n\n• Principal components are calculated based on the correlation matrix of the original predictors.\n• The first principal component explains the largest proportion of the variation in the dependent variable.\n• Principal components are linear combinations of the original predictors that are uncorrelated with each other.\n• PCR selects the principal components with the highest p-values for inclusion in the regression model.\n• PCR always results in a lower model complexity compared to ordinary least squares regression.\n`Answer :- c. Principal components are linear combinations of the original predictors that are uncorrelated with each other.`\n\n## NPTEL Introduction To Machine Learning Week 2 Assignment Answer 2023\n\n1. The parameters obtained in linear regression\n\n• can take any value in the real space\n• are strictly integers\n• always lie in the range [0,1]\n• can take only non-zero values\n`Answer :- Click Here`\n\n2. Suppose that we have N independent variables (X1,X2,…Xn) and the dependent variable is Y . Now imagine that you are applying linear regression by fitting the best fit line using the least square error on this data. You found that the correlation coefficient for one of its variables (Say X1) with Y is -0.005.\n\n• Regressing Yon X1 mostly does not explain away Y .\n• Regressing Y on X1 explains away Y .\n• The given data is insufficient to determine if regressing Yon X1 explains away Y or not.\n`Answer :- Click Here`\n\n3. Which of the following is a limitation of subset selection methods in regression?\n\n• They tend to produce biased estimates of the regression coefficients.\n• They cannot handle datasets with missing values.\n• They are computationally expensive for large datasets.\n• They assume a linear relationship between the independent and dependent variables.\n• They are not suitable for datasets with categorical predictors.\n`Answer :- Click Here`\n\n4. The relation between studying time (in hours) and grade on the final examination (0-100) in a random sample of students in the Introduction to Machine Learning Class was found to be:Grade = 30.5 + 15.2 (h)\n\nHow will a student’s grade be affected if she studies for four hours?\n\n• It will go down by 30.4 points.\n• It will go down by 30.4 points.\n• It will go up by 60.8 points.\n• The grade will remain unchanged.\n• It cannot be determined from the information given\n`Answer :- Click Here`\n\n5. Which of the statements is/are True?\n\n• Ridge has sparsity constraint, and it will drive coefficients with low values to 0.\n• Lasso has a closed form solution for the optimization problem, but this is not the case for Ridge.\n• Ridge regression does not reduce the number of variables since it never leads a coefficient to zero but only minimizes it.\n• If there are two or more highly collinear variables, Lasso will select one of them randomly\n`Answer :- Click Here`\n\n6. Find the mean of squared error for the given predictions:", null, "Hint: Find the squared error for each prediction and take the mean of that.\n\n• 1\n• 2\n• 1.5\n• 0\n`Answer :- `\n\n7. Consider the following statements:\n\nStatement A: In Forward stepwise selection, in each step, that variable is chosen which has the maximum correlation with the residual, then the residual is regressed on that variable, and it is added to the predictor.\nStatement B: In Forward stagewise selection, the variables are added one by one to the previously selected variables to produce the best fit till then\n\n• Both the statements are True.\n• Statement A is True, and Statement B is False\n• Statement A is False and Statement B is True\n• Both the statements are False.\n`Answer :- Click Here`\n\n8. The linear regression model y=a0+a1x1+a2x2+…….+apxp is to be fitted to a set of N training data points having p attributes each. Let X be N×(p+1) vectors of input values (augmented by 1‘s), Y be N×1 vector of target values, and θθ be (p+1)×1 vector of parameter values (a0,a1,a2,…,ap. If the sum squared error is minimized for obtaining the optimal regression model, which of the following equation holds?\n\n• XTX=XY\n• Xθ=XT\n• XTXθ =Y\n• XTXθ=XTY\n`Answer :- Click Here`\n\n9. Which of the following statements is true regarding Partial Least Squares (PLS) regression?\n\n• PLS is a dimensionality reduction technique that maximizes the covariance between the predictors and the dependent variable.\n• PLS is only applicable when there is no multicollinearity among the independent variables.\n• PLS can handle situations where the number of predictors is larger than the number of observations.\n• PLS estimates the regression coefficients by minimizing the residual sum of squares.\n• PLS is based on the assumption of normally distributed residuals.\n• All of the above.\n• None of the above.\n`Answer :- `\n\n10. Which of the following statements about principal components in Principal Component Regression (PCR) is true?\n\n• Principal components are calculated based on the correlation matrix of the original predictors.\n• The first principal component explains the largest proportion of the variation in the dependent variable.\n• Principal components are linear combinations of the original predictors that are uncorrelated with each other.\n• PCR selects the principal components with the highest p-values for inclusion in the regression model.\n• PCR always results in a lower model complexity compared to ordinary least squares regression.\n`Answer :- Click Here`\n\n## NPTEL Introduction to Machine Learning Assignment 2 Answers 2022 [July-Dec]\n\nQ1. The parameters obtained in linear regression\n\na. can take any value in the real space\nb. are strictly integers\nc. always lie in the range [0,1]\nd. can take only non-zero values\n\n`Answer:- a`\n\n2. Suppose that we have NN independent variables (X1,X2,…XnX1,X2,…Xn) and the dependent variable is YY . Now imagine that you are applying linear regression by fitting the best fit line using the least square error on this data. You found that the correlation coefficient for one of its variables (Say X1X1) with YY is -0.005.\n\na. Regressing Y on X1 mostly does not explain away Y.\nb. Regressing Y on X1 explains away Y.\nc. The given data is insufficient to determine if regressing Y on X1 explains away Y or not.\n\n`Answer:- a`\n\n3. Consider the following five training examples\n\n``We want to learn a function f(x) of the form f(x)=ax+b which is parameterised by (a,b).Using mean squared error as the loss function, which of the following parameters would you use to model this function to get a solution with the minimum loss?``\n• (4, 3)\n• (1, 4)\n• (4, 1)\n• (3, 4)\n`Answer:- b`\n\n4. The relation between studying time (in hours) and grade on the final examination (0-100) in a random sample of students in the Introduction to Machine Learning Class was found to be:\nGrade = 30.5 + 15.2 (h)\nHow will a student’s grade be affected if she studies for four hours?\n\na. It will go down by 30.4 points.\nb. It will go down by 30.4 points.\nc. It will go up by 60.8 points.\nd. The grade will remain unchanged.\ne. It cannot be determined from the information given\n\n`Answer:- c`\n\n5. Which of the statements is/are True?\n\na. Ridge has sparsity constraint, and it will drive coefficients with low values to 0.\nb. Lasso has a closed form solution for the optimization problem, but this is not the case for Ridge.\nc. Ridge regression does not reduce the number of variables since it never leads a coefficient to zero but only minimizes it.\nd. If there are two or more highly collinear variables, Lasso will select one of them randomly.\n\n`Answer:- c, d`\n\n6. Consider the following statements:\n\nAssertion(A): Orthogonalization is applied to the dimensions in linear regression.\nReason(R): Orthogonalization makes univariate regression possible in each orthogonal dimension separately to produce the coefficients.\n\na. Both A and R are true, and R is the correct explanation of A.\nb. Both A and R are true, but R is not the correct explanation of A.\nc. A is true, but R is false.\nd. A is false, but R is true.\ne. Both A and R are false.\n\n`Answer:- a`\n\n7. Consider the following statements:\n\nStatement A: In Forward stepwise selection, in each step, that variable is chosen which has the maximum correlation with the residual, then the residual is regressed on that variable, and it is added to the predictor.\n\nStatement B: In Forward stagewise selection, the variables are added one by one to the previously selected variables to produce the best fit till then\n\na. Both the statements are True.\nb. Statement A is True, and Statement B is False\nc. Statement A if False and Statement B is True\nd. Both the statements are False.\n\n`Answer:- d`\n\n8. The linear regression model y=a0+a1x1+a2x2+…+apxp is to be fitted to a set of N training data points having p attributes each. Let X be N×(p+1) vectors of input values (augmented by 1‘s), Y be N×1 vector of target values, and θ be (p+1)×1 vector of parameter values (a0,a1,a2,…,ap). If the sum squared error is minimized for obtaining the optimal regression model, which of the following equation holds?\n\n`Answer:- d`\n\n## About Introduction to Machine Learning\n\nWith the increased availability of data from varied sources there has been increasing attention paid to the various data driven disciplines such as analytics and machine learning. In this course we intend to introduce some of the basic concepts of machine learning from a mathematically well motivated perspective. We will cover the different learning paradigms and some of the more popular algorithms and architectures used in each of these paradigms.\n\n### COURSE LAYOUT\n\n• Week 0: Probability Theory, Linear Algebra, Convex Optimization – (Recap)\n• Week 1: Introduction: Statistical Decision Theory – Regression, Classification, Bias Variance\n• Week 2: Linear Regression, Multivariate Regression, Subset Selection, Shrinkage Methods, Principal Component Regression, Partial Least squares\n• Week 3: Linear Classification, Logistic Regression, Linear Discriminant Analysis\n• Week 4: Perceptron, Support Vector Machines\n• Week 5: Neural Networks – Introduction, Early Models, Perceptron Learning, Backpropagation, Initialization, Training & Validation, Parameter Estimation – MLE, MAP, Bayesian Estimation\n• Week 6: Decision Trees, Regression Trees, Stopping Criterion & Pruning loss functions, Categorical Attributes, Multiway Splits, Missing Values, Decision Trees – Instability Evaluation Measures\n• Week 7: Bootstrapping & Cross Validation, Class Evaluation Measures, ROC curve, MDL, Ensemble Methods – Bagging, Committee Machines and Stacking, Boosting\n• Week 8: Gradient Boosting, Random Forests, Multi-class Classification, Naive Bayes, Bayesian Networks\n• Week 9: Undirected Graphical Models, HMM, Variable Elimination, Belief Propagation\n• Week 10: Partitional Clustering, Hierarchical Clustering, Birch Algorithm, CURE Algorithm, Density-based Clustering\n• Week 11: Gaussian Mixture Models, Expectation Maximization\n• Week 12: Learning Theory, Introduction to Reinforcement Learning, Optional videos (RL framework, TD learning, Solution Methods, Applications)\n\n### CRITERIA TO GET A CERTIFICATE\n\nAverage assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.\nExam score = 75% of the proctored certification exam score out of 100\n\nFinal score = Average assignment score + Exam score\n\nYOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100." ]	[ null, "data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%200%200'%3E%3C/svg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%200%200'%3E%3C/svg%3E", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8603735,"math_prob":0.95806164,"size":16965,"snap":"2023-40-2023-50","text_gpt3_token_len":3906,"char_repetition_ratio":0.13548729,"word_repetition_ratio":0.6661957,"special_character_ratio":0.22841144,"punctuation_ratio":0.12652677,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99838996,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-10-01T15:14:35Z\",\"WARC-Record-ID\":\"<urn:uuid:186c87bc-fb70-4fe7-8074-837090f2023e>\",\"Content-Length\":\"117201\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:5cb449e8-1d71-476f-a233-b0a8ecc4d81a>\",\"WARC-Concurrent-To\":\"<urn:uuid:7e4e6b6e-7a8c-47e4-b897-6c8d29838f72>\",\"WARC-IP-Address\":\"217.21.88.153\",\"WARC-Target-URI\":\"https://uniquejankari.in/nptel-introduction-to-machine-learning-assignment-2-answers-2022/\",\"WARC-Payload-Digest\":\"sha1:L7LHU7PZLOSLTIUBOV5TQVBCJY43BO25\",\"WARC-Block-Digest\":\"sha1:UKDYI2BQCMJFPCJZWBOXM6NDP6C5GG7Z\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510903.85_warc_CC-MAIN-20231001141548-20231001171548-00653.warc.gz\"}"}
https://www.buffalobrewingstl.com/raphson-method/info-dto.html	[ "# Info\n\nT0 = 2.9°F, Ts+ ! = 0°F, N = 8, and P = 800 lb/in2 abs. Initial temperature profile to be constant at Tj = 25°F for all j (j = 1, 2, ..., N). The initial vapor rate profile is to be constant at Vj = 90.88 0 = 1, 2, ...,8), and the liquid rates are L} = 6.3092 0 =1, 2, ...,7), and L8 = 15.42 Use the K values and enthalpies given in Tables B-5 and B-6\n\nc3h(\n\nc3h(" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7912168,"math_prob":0.9998722,"size":402,"snap":"2020-24-2020-29","text_gpt3_token_len":156,"char_repetition_ratio":0.11557789,"word_repetition_ratio":0.0,"special_character_ratio":0.45771143,"punctuation_ratio":0.26050422,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9975316,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-05-28T19:17:17Z\",\"WARC-Record-ID\":\"<urn:uuid:5dca43ac-5aa9-4d56-8f63-ff97bff2f540>\",\"Content-Length\":\"10180\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:40a3928b-4d9f-4cd8-a727-814ff7dbf420>\",\"WARC-Concurrent-To\":\"<urn:uuid:fa8742b9-c1ae-489f-911b-834f8d5de670>\",\"WARC-IP-Address\":\"104.18.56.106\",\"WARC-Target-URI\":\"https://www.buffalobrewingstl.com/raphson-method/info-dto.html\",\"WARC-Payload-Digest\":\"sha1:DCPSG4JECNT2VKBAPSBS7ILTNMGL5ATC\",\"WARC-Block-Digest\":\"sha1:4ZSHX2FC7JYBL57HTLUXULMJ6E2TCC6Q\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-24/CC-MAIN-2020-24_segments_1590347399830.24_warc_CC-MAIN-20200528170840-20200528200840-00260.warc.gz\"}"}
https://zbmath.org/?q=an:06434322	[ "# zbMATH — the first resource for mathematics\n\nOn the three-dimensional Vahlen theorem. (English. Russian original) Zbl 1369.11048\nMath. Notes 95, No. 1, 136-138 (2014); translation from Mat. Zametki 95, No. 1, 154-156 (2014).\nFrom the text: Let $$\\gamma^{(1)}, \\ldots, \\gamma^{(s)}$$ be the basis nodes of a full-rank lattice\n$\\Gamma = \\left\\{ m_1 \\gamma^{(1)} + \\cdots + m_s \\gamma^{(s)}: m_1,\\ldots, m_s \\in \\mathbb Z \\right\\} \\subset \\mathbb R^s.$\nVahlen’s theorem concerning the approximation of numbers by convergents has the following interpretation in terms of lattices: for every Voronoi basis $$\\{\\gamma^{(1)}, \\gamma^{(2)}\\}$$,\n$\\min\\left\\{\\left\|\\gamma_1^{(1)}, \\gamma_2^{(1)}\\right\|, \\left\|\\gamma_1^{(2)}, \\gamma_2^{(2)}\\right\|\\right\\} \\leq \\tfrac{1}{2} \\det \\Gamma.$\n\n##### MSC:\n 11H06 Lattices and convex bodies (number-theoretic aspects)\nFull Text:\n##### References:\n A. V. Ustinov, in Mathematics and Informatics, 1, Sovr. Probl. Matem., To the 75th Birthday of Anatolii Alekseevich Karatsuba (MIAN, Moscow, 2012), Vol. 16, pp. 103–128 [Proc. Steklov Inst. Math., 280, suppl. 2 (2013), S91–S116]. G. F. Voronoi, Collected Works in Three Volumes, Vol. 1 (Izdatel’stvo Akademii Nauk Ukrainskoi SSR, Kiev, 1952) [in Russian]. M. O. Avdeeva and V. A. Bykovskii, Mat. Zametki 79(2), 163 (2006) [Math. Notes 79 (1–2), 151–156 (2006)]. K. Th. Vahlen, J. fürMath. 115(3), 221 (1895). A. Ya. Khinchin, Continued Fractions (Nauka, Moscow, 1978; Dover Publications, Inc., Mineola, NY, 1997). H. Minkowski, Ann. Sci. École Norm. Sup. (3) 13, 41 (1896). · JFM 27.0170.01 H. Hancock, Development of the Minkowski Geometry of Numbers, Vol. 1,2 (Dover Publ., 1964). · Zbl 0123.25603 O. A. Gorkusha, Mat. Zametki 69(3), 353 (2001) [Math. Notes 69 (3–4), 320 (2001)]. V. A. Bykovskii and O. A. Gorkusha, Mat. Sb. 192(2), 57 (2001) [Sb. Math. 192 (1–2), 215–223 (2001)]. M. O. Avdeeva and V. A. Bykovskii, Mat. Sb. 194(7), 3 (2003) [Sb. Math. 194 (7–8), 955 (2003)]. V. A. Bykovskii, Mat. Zametki 66(1), 30 (1999) [Math. Notes 66 (1–2), 24 (1999) (2000)]. S. V. Gassan, Chebyshevskii Sb. 6(3), 51 (2005) [in Russian].\nThis reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.62368286,"math_prob":0.96225274,"size":2762,"snap":"2021-43-2021-49","text_gpt3_token_len":1059,"char_repetition_ratio":0.09390863,"word_repetition_ratio":0.04411765,"special_character_ratio":0.4250543,"punctuation_ratio":0.27925116,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98814756,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-12-05T10:05:14Z\",\"WARC-Record-ID\":\"<urn:uuid:aee45a32-1d32-4310-bcaf-ee04c3c41b7e>\",\"Content-Length\":\"50376\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c05d682f-88ae-4560-ab77-37c9674f3867>\",\"WARC-Concurrent-To\":\"<urn:uuid:c9f62240-2530-4483-9a5b-b74757ed1de8>\",\"WARC-IP-Address\":\"141.66.194.2\",\"WARC-Target-URI\":\"https://zbmath.org/?q=an:06434322\",\"WARC-Payload-Digest\":\"sha1:OXIHXHH2NDT2KRWE3P5BLVPLJTG7B7YO\",\"WARC-Block-Digest\":\"sha1:75HWMBAACCTPCT54DA253CXAW77ODESM\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964363157.32_warc_CC-MAIN-20211205100135-20211205130135-00415.warc.gz\"}"}
https://www.stata.com/statalist/archive/2006-03/msg00164.html	[ "", null, "", null, "", null, "", null, "# Re: Re: st: Total Least Squares Regression, anyone\n\n From \"Anders Alexandersson\" To [email protected] Subject Re: Re: st: Total Least Squares Regression, anyone Date Mon, 6 Mar 2006 13:32:21 -0500\n\n```For a graphical approach to total least squares regression, Tero might\nfind my program -ellip- helpful. At least it will give the orthogonal\nregression slope and can handle different error variance ratios. I'm\nnot aware of a Stata command for estimating total least squares\nregression models.\n\nTero Kivel wrote:\n\"The data [...] should be analysed using the method of Total Least\nSquares Regression, and the slope of the regression, the offset of the\nregression and the standard deviation\nof the regression should be made available.\"\n\n\n For searches and help try:\n* http://www.stata.com/support/faqs/res/findit.html\n* http://www.stata.com/support/statalist/faq\n* http://www.ats.ucla.edu/stat/stata/\n```" ]	[ null, "https://www.stata.com/includes/images/statalist_front.gif", null, "https://www.stata.com/includes/images/statalist_middle.gif", null, "https://www.stata.com/includes/images/statalist_end.gif", null, "https://www.stata.com/includes/contimages/spacer.gif", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6828732,"math_prob":0.57612216,"size":844,"snap":"2020-45-2020-50","text_gpt3_token_len":201,"char_repetition_ratio":0.13809524,"word_repetition_ratio":0.0,"special_character_ratio":0.21445498,"punctuation_ratio":0.16770187,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98034155,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-11-25T00:31:18Z\",\"WARC-Record-ID\":\"<urn:uuid:0036cd01-0e32-4561-b78f-5b13e765ccec>\",\"Content-Length\":\"7138\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:60525093-4747-490f-abc1-8e4a28435913>\",\"WARC-Concurrent-To\":\"<urn:uuid:d5b8f72c-9532-4b96-ae26-f2ee6d5e2359>\",\"WARC-IP-Address\":\"66.76.6.5\",\"WARC-Target-URI\":\"https://www.stata.com/statalist/archive/2006-03/msg00164.html\",\"WARC-Payload-Digest\":\"sha1:7X2UNQ23RGNNARZ4MB54WNZHYVQE2TZF\",\"WARC-Block-Digest\":\"sha1:VIGOE3QAOR7R4QIIYYHZLPUP6SRGHSMX\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141177607.13_warc_CC-MAIN-20201124224124-20201125014124-00081.warc.gz\"}"}
https://www.colorhexa.com/4e4e40	[ "# #4e4e40 Color Information\n\nIn a RGB color space, hex #4e4e40 is composed of 30.6% red, 30.6% green and 25.1% blue. Whereas in a CMYK color space, it is composed of 0% cyan, 0% magenta, 17.9% yellow and 69.4% black. It has a hue angle of 60 degrees, a saturation of 9.9% and a lightness of 27.8%. #4e4e40 color hex could be obtained by blending #9c9c80 with #000000. Closest websafe color is: #666633.\n\n• R 31\n• G 31\n• B 25\nRGB color chart\n• C 0\n• M 0\n• Y 18\n• K 69\nCMYK color chart\n\n#4e4e40 color description : Very dark grayish yellow.\n\n# #4e4e40 Color Conversion\n\nThe hexadecimal color #4e4e40 has RGB values of R:78, G:78, B:64 and CMYK values of C:0, M:0, Y:0.18, K:0.69. Its decimal value is 5131840.\n\nHex triplet RGB Decimal 4e4e40 `#4e4e40` 78, 78, 64 `rgb(78,78,64)` 30.6, 30.6, 25.1 `rgb(30.6%,30.6%,25.1%)` 0, 0, 18, 69 60°, 9.9, 27.8 `hsl(60,9.9%,27.8%)` 60°, 17.9, 30.6 666633 `#666633`\nCIE-LAB 32.785, -2.8, 8.31 6.792, 7.439, 5.928 0.337, 0.369, 7.439 32.785, 8.769, 108.623 32.785, 0.717, 9.958 27.274, -3.281, 6.205 01001110, 01001110, 01000000\n\n# Color Schemes with #4e4e40\n\n• #4e4e40\n``#4e4e40` `rgb(78,78,64)``\n• #40404e\n``#40404e` `rgb(64,64,78)``\nComplementary Color\n• #4e4740\n``#4e4740` `rgb(78,71,64)``\n• #4e4e40\n``#4e4e40` `rgb(78,78,64)``\n• #474e40\n``#474e40` `rgb(71,78,64)``\nAnalogous Color\n• #47404e\n``#47404e` `rgb(71,64,78)``\n• #4e4e40\n``#4e4e40` `rgb(78,78,64)``\n• #40474e\n``#40474e` `rgb(64,71,78)``\nSplit Complementary Color\n• #4e404e\n``#4e404e` `rgb(78,64,78)``\n• #4e4e40\n``#4e4e40` `rgb(78,78,64)``\n• #404e4e\n``#404e4e` `rgb(64,78,78)``\n• #4e4040\n``#4e4040` `rgb(78,64,64)``\n• #4e4e40\n``#4e4e40` `rgb(78,78,64)``\n• #404e4e\n``#404e4e` `rgb(64,78,78)``\n• #40404e\n``#40404e` `rgb(64,64,78)``\n• #24241e\n``#24241e` `rgb(36,36,30)``\n• #323229\n``#323229` `rgb(50,50,41)``\n• #404035\n``#404035` `rgb(64,64,53)``\n• #4e4e40\n``#4e4e40` `rgb(78,78,64)``\n• #5c5c4b\n``#5c5c4b` `rgb(92,92,75)``\n• #6a6a57\n``#6a6a57` `rgb(106,106,87)``\n• #787862\n``#787862` `rgb(120,120,98)``\nMonochromatic Color\n\n# Alternatives to #4e4e40\n\nBelow, you can see some colors close to #4e4e40. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #4e4b40\n``#4e4b40` `rgb(78,75,64)``\n• #4e4c40\n``#4e4c40` `rgb(78,76,64)``\n• #4e4d40\n``#4e4d40` `rgb(78,77,64)``\n• #4e4e40\n``#4e4e40` `rgb(78,78,64)``\n• #4d4e40\n``#4d4e40` `rgb(77,78,64)``\n• #4c4e40\n``#4c4e40` `rgb(76,78,64)``\n• #4b4e40\n``#4b4e40` `rgb(75,78,64)``\nSimilar Colors\n\n# #4e4e40 Preview\n\nThis text has a font color of #4e4e40.\n\n``<span style=\"color:#4e4e40;\">Text here</span>``\n#4e4e40 background color\n\nThis paragraph has a background color of #4e4e40.\n\n``<p style=\"background-color:#4e4e40;\">Content here</p>``\n#4e4e40 border color\n\nThis element has a border color of #4e4e40.\n\n``<div style=\"border:1px solid #4e4e40;\">Content here</div>``\nCSS codes\n``.text {color:#4e4e40;}``\n``.background {background-color:#4e4e40;}``\n``.border {border:1px solid #4e4e40;}``\n\n# Shades and Tints of #4e4e40\n\nA shade is achieved by adding black to any pure hue, while a tint is created by mixing white to any pure color. In this example, #030302 is the darkest color, while #f8f8f7 is the lightest one.\n\n• #030302\n``#030302` `rgb(3,3,2)``\n• #0d0d0b\n``#0d0d0b` `rgb(13,13,11)``\n• #181814\n``#181814` `rgb(24,24,20)``\n• #23231d\n``#23231d` `rgb(35,35,29)``\n• #2e2e25\n``#2e2e25` `rgb(46,46,37)``\n• #38382e\n``#38382e` `rgb(56,56,46)``\n• #434337\n``#434337` `rgb(67,67,55)``\n• #4e4e40\n``#4e4e40` `rgb(78,78,64)``\n• #595949\n``#595949` `rgb(89,89,73)``\n• #646452\n``#646452` `rgb(100,100,82)``\n• #6e6e5b\n``#6e6e5b` `rgb(110,110,91)``\n• #797963\n``#797963` `rgb(121,121,99)``\n• #84846c\n``#84846c` `rgb(132,132,108)``\n• #8e8e76\n``#8e8e76` `rgb(142,142,118)``\n• #979780\n``#979780` `rgb(151,151,128)``\n• #a0a08b\n``#a0a08b` `rgb(160,160,139)``\n• #a9a996\n``#a9a996` `rgb(169,169,150)``\n• #b2b2a1\n``#b2b2a1` `rgb(178,178,161)``\n• #babaab\n``#babaab` `rgb(186,186,171)``\n• #c3c3b6\n``#c3c3b6` `rgb(195,195,182)``\n• #ccccc1\n``#ccccc1` `rgb(204,204,193)``\n• #d5d5cc\n``#d5d5cc` `rgb(213,213,204)``\n• #deded6\n``#deded6` `rgb(222,222,214)``\n• #e7e7e1\n``#e7e7e1` `rgb(231,231,225)``\n• #efefec\n``#efefec` `rgb(239,239,236)``\n• #f8f8f7\n``#f8f8f7` `rgb(248,248,247)``\nTint Color Variation\n\n# Tones of #4e4e40\n\nA tone is produced by adding gray to any pure hue. In this case, #494945 is the less saturated color, while #8a8a04 is the most saturated one.\n\n• #494945\n``#494945` `rgb(73,73,69)``\n• #4e4e40\n``#4e4e40` `rgb(78,78,64)``\n• #53533b\n``#53533b` `rgb(83,83,59)``\n• #595935\n``#595935` `rgb(89,89,53)``\n• #5e5e30\n``#5e5e30` `rgb(94,94,48)``\n• #64642a\n``#64642a` `rgb(100,100,42)``\n• #696925\n``#696925` `rgb(105,105,37)``\n• #6f6f1f\n``#6f6f1f` `rgb(111,111,31)``\n• #74741a\n``#74741a` `rgb(116,116,26)``\n• #7a7a14\n``#7a7a14` `rgb(122,122,20)``\n• #7f7f0f\n``#7f7f0f` `rgb(127,127,15)``\n• #858509\n``#858509` `rgb(133,133,9)``\n• #8a8a04\n``#8a8a04` `rgb(138,138,4)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #4e4e40 is perceived by people affected by a color vision deficiency. This can be useful if you need to ensure your color combinations are accessible to color-blind users.\n\nMonochromacy\n• Achromatopsia 0.005% of the population\n• Atypical Achromatopsia 0.001% of the population\nDichromacy\n• Protanopia 1% of men\n• Deuteranopia 1% of men\n• Tritanopia 0.001% of the population\nTrichromacy\n• Protanomaly 1% of men, 0.01% of women\n• Deuteranomaly 6% of men, 0.4% of women\n• Tritanomaly 0.01% of the population" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.52051187,"math_prob":0.48372132,"size":3673,"snap":"2021-21-2021-25","text_gpt3_token_len":1694,"char_repetition_ratio":0.12128645,"word_repetition_ratio":0.011070111,"special_character_ratio":0.56003267,"punctuation_ratio":0.23404256,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99119705,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-05-15T21:00:52Z\",\"WARC-Record-ID\":\"<urn:uuid:fb7eb1fb-89d9-4c12-90d6-21520d8c86eb>\",\"Content-Length\":\"36224\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b77b1c44-7bd4-4ee1-92f6-a82656faf5f1>\",\"WARC-Concurrent-To\":\"<urn:uuid:bb8927bd-b5d3-433b-b33b-35bb1a22dee3>\",\"WARC-IP-Address\":\"178.32.117.56\",\"WARC-Target-URI\":\"https://www.colorhexa.com/4e4e40\",\"WARC-Payload-Digest\":\"sha1:D7ILAZCV4KR5MWSNEAJDGSEF7LIYR2QO\",\"WARC-Block-Digest\":\"sha1:PV2B7264EAR6HNP4HJ3N3U3ZN436Z5LB\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-21/CC-MAIN-2021-21_segments_1620243991378.52_warc_CC-MAIN-20210515192444-20210515222444-00440.warc.gz\"}"}
http://cc1.ifj.edu.pl/docs/doxygen/classsrc_1_1wi_1_1forms_1_1user_1_1_change_quota_form.html	[ "", null, "cc1 v2.1 CC1 source code docs\nsrc.wi.forms.user.ChangeQuotaForm Class Reference\n\nClass for quota's change form. More...\n\n## Static Public Attributes\n\ntuple cpu = forms.IntegerField(label=_(\"Cpu Total\"))\ntuple memory = forms.IntegerField(label=_(\"Memory Total [MB]\"))\ntuple points = forms.IntegerField(min_value=0, label=_(\"Points\"))\ntuple public_ip = forms.IntegerField(min_value=0, label=_(\"Public IPs Total\"))\ntuple storage = forms.IntegerField(label=_(\"Storage Total [MB]\"))\n\n## Detailed Description\n\nClass for quota's change form.\n\nDefinition at line 387 of file user.py.\n\n## Member Data Documentation\n\n tuple src.wi.forms.user.ChangeQuotaForm.cpu = forms.IntegerField(label=_(\"Cpu Total\"))\nstatic\n\nDefinition at line 388 of file user.py.\n\n tuple src.wi.forms.user.ChangeQuotaForm.memory = forms.IntegerField(label=_(\"Memory Total [MB]\"))\nstatic\n\nDefinition at line 389 of file user.py.\n\n tuple src.wi.forms.user.ChangeQuotaForm.points = forms.IntegerField(min_value=0, label=_(\"Points\"))\nstatic\n\nDefinition at line 392 of file user.py.\n\n tuple src.wi.forms.user.ChangeQuotaForm.public_ip = forms.IntegerField(min_value=0, label=_(\"Public IPs Total\"))\nstatic\n\nDefinition at line 391 of file user.py.\n\n tuple src.wi.forms.user.ChangeQuotaForm.storage = forms.IntegerField(label=_(\"Storage Total [MB]\"))\nstatic\n\nDefinition at line 390 of file user.py.\n\nThe documentation for this class was generated from the following file:" ]	[ null, "http://cc1.ifj.edu.pl/docs/doxygen/cc1.svg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.5022122,"math_prob":0.611996,"size":1149,"snap":"2023-14-2023-23","text_gpt3_token_len":270,"char_repetition_ratio":0.18515284,"word_repetition_ratio":0.056603774,"special_character_ratio":0.25935596,"punctuation_ratio":0.22705314,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97050494,"pos_list":[0,1,2],"im_url_duplicate_count":[null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-03-28T08:38:32Z\",\"WARC-Record-ID\":\"<urn:uuid:acae7d74-6ecb-4be8-becd-991c8d58312e>\",\"Content-Length\":\"13040\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:63e6c652-3f7e-4ccc-9ebf-9ccd715c10ae>\",\"WARC-Concurrent-To\":\"<urn:uuid:271f793f-dcd8-4840-bd17-18566d1b0584>\",\"WARC-IP-Address\":\"192.245.169.10\",\"WARC-Target-URI\":\"http://cc1.ifj.edu.pl/docs/doxygen/classsrc_1_1wi_1_1forms_1_1user_1_1_change_quota_form.html\",\"WARC-Payload-Digest\":\"sha1:U4OFMGKPIVBNXYGOVZH6HLGE7E5HM45Q\",\"WARC-Block-Digest\":\"sha1:OF4BIDFLJ6Q4BDN5WRYHSQCFITM55KZR\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-14/CC-MAIN-2023-14_segments_1679296948817.15_warc_CC-MAIN-20230328073515-20230328103515-00757.warc.gz\"}"}
http://forums.wolfram.com/mathgroup/archive/2001/Jan/msg00476.html	[ "", null, "", null, "", null, "", null, "", null, "", null, "", null, "Re: Queries: notebook, matrices\n\n• To: mathgroup at smc.vnet.net\n• Subject: [mg27019] Re: [mg26975] Queries: notebook, matrices\n• From: Tomas Garza <tgarza01 at prodigy.net.mx>\n• Date: Tue, 30 Jan 2001 23:22:35 -0500 (EST)\n• References: <[email protected]>\n• Sender: owner-wri-mathgroup at wolfram.com\n\n```1. You can Select the input cells you would like to recalculate and then\nCell \| Cell Properties \| Initialization Cell. Then, when you reopen your\nnotebook and activate the first cell you will be asked whether you want to\ninitialize all cells. Say Yes and that's it. By the way if there is a lot of\ntime-consuming calculation which doesn't change from one session to the\nnext, you'd do well to save the results with >> and read them back with <<\n\n2. My guess is you'll have to specify each time that you want your matrix\ndisplayed in matrix form. Of course you may define a function for that\npurpose, which will save you the trouble of typing the whole thing, such as,\ne.g.\n\nIn:=\na = {{1, 2, 3, 4}, {4, 5, 6, 7}}\nOut=\n{{1, 2, 3, 4}, {4, 5, 6, 7}}\nIn:=\nd[a_] := MatrixForm[a]\nIn:=\nd[a]\nOut//MatrixForm=\n\\!\\(\\*\nTagBox[\nRowBox[{\"(\", \"\\[NoBreak]\", GridBox[{\n{\"1\", \"2\", \"3\", \"4\"},\n{\"4\", \"5\", \"6\", \"7\"}\n}], \"\\[NoBreak]\", \")\"}],\n(MatrixForm[ #]&)]\\)\n\n3. OK, there is a standard program which I got years ago from Wolfram\nsupport, I guess, which takes data from Mathematica and stores them as\nAscii text files which can then be read by Excel or some other such\nprogram (I presume you want to use your data outside Mathematica;\notherwise there is no point in saving it with a specified format). The\ncode is as follows:\n\nWriteMatrix[filename_String, data_List] :=\nWith[{myfile = OpenWrite[filename]},\nScan[(WriteString[myfile, First[#]];\nScan[WriteString[myfile, \"\\t\", #] &, Rest[#]];\nWriteString[myfile, \"\\n\"]) &, data];\nClose[myfile]]\n\nOnce you define this function WriteMatrix, you may use it as follows:\n\nIn:=\na = {{1, 2, 3}, {1, 4, 5}, {1, 6, 7}};\n\nIn:=\nWriteMatrix[\"b\", a]\nOut=\n\"b\"\n\nThis says: take list a and store it in Ascii form under the name \"b\".\nOnce you execute this, you will find b in the directory you're working.\nThen you may read b from Excel.\n\nTomas Garza\nMexico City\n\n----- Original Message -----\nFrom: \"M. Damerell\" <uhah208 at rhbnc.ac.uk>\nTo: mathgroup at smc.vnet.net\nSubject: [mg27019] [mg26975] Queries: notebook, matrices\n\n>\n>\n> Sorry if these are answered in a FAQ file, I could not\n> find any FAq file for this group. Math. 4.0, windows95.\n>\n> 1. I do a lot of calculation in a notebook, save it,\n> then when I restart Math & open the file I have to\n> recalculate each item before I can resume where I\n> left off. Is there any way to tell Math to recalculate\n> everything when the file is reopened?\n>\n> 2. I enter a matrix as (say) A={{1,2,3},{4,5,6} etc\n> and it displays in that form. Is there any way to make\n> Math display matrices as matrices? I know you can do\n>\n> B=A.A//MatrixForm\n>\n> this looks right but Math doesnt know this is a matrix.\n> So I would like matrices to be held internally in list\n> form but displayed in matrix form.\n>\n> 3. and finally, is there any way to export the matrix\n> into Excel?\n>\n>\n\n```\n\n• Prev by Date: Re: 1. Input of screen coordinates; 2. Fast graphics\n• Next by Date: RE: RE: 1. Input of screen coordinates; 2. Fast graphics\n• Previous by thread: Queries: notebook, matrices\n• Next by thread: Re: Queries: notebook, matrices" ]	[ null, "http://forums.wolfram.com/mathgroup/images/head_mathgroup.gif", null, "http://forums.wolfram.com/mathgroup/images/head_archive.gif", null, "http://forums.wolfram.com/mathgroup/images/numbers/2.gif", null, "http://forums.wolfram.com/mathgroup/images/numbers/0.gif", null, "http://forums.wolfram.com/mathgroup/images/numbers/0.gif", null, "http://forums.wolfram.com/mathgroup/images/numbers/1.gif", null, "http://forums.wolfram.com/mathgroup/images/search_archive.gif", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8586208,"math_prob":0.6812727,"size":3322,"snap":"2019-35-2019-39","text_gpt3_token_len":976,"char_repetition_ratio":0.09795057,"word_repetition_ratio":0.01754386,"special_character_ratio":0.33503914,"punctuation_ratio":0.20718232,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9720622,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-09-16T05:11:02Z\",\"WARC-Record-ID\":\"<urn:uuid:85ac5762-bcae-45e0-a286-9b2ef60da378>\",\"Content-Length\":\"45553\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6dbefb35-12d9-46d2-a022-ff61e771f317>\",\"WARC-Concurrent-To\":\"<urn:uuid:41e9e135-8079-49da-854b-843a82b11719>\",\"WARC-IP-Address\":\"140.177.205.73\",\"WARC-Target-URI\":\"http://forums.wolfram.com/mathgroup/archive/2001/Jan/msg00476.html\",\"WARC-Payload-Digest\":\"sha1:T7KOA6GVWNP76OAYJ2N4ECQ45RPEVMKC\",\"WARC-Block-Digest\":\"sha1:PYXA5ZXR6A7NFPA55QDEWSPL4VXJIIY6\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-39/CC-MAIN-2019-39_segments_1568514572484.20_warc_CC-MAIN-20190916035549-20190916061549-00111.warc.gz\"}"}
https://www.assignmentexpert.com/homework-answers/physics/mechanics-relativity/question-4320	[ "# Answer to Question #4320 in Mechanics \| Relativity for Sara\n\nQuestion #4320\nhi i have a question for you, To set a speed record in measured straight line distance d, a race car must be driven first in one direction in time t1 and then in the opposite direction time t2. a) to eliminate the effects of the wind and obtain the ca's speed Vc in a windless situation, should we find the average of d/t1 and d/t2 (method 1) or should we devidee d by the average of t1 and t2. b) what is the fractional difference in the two methods when a steady wind belows along the car's route and the ratio of the wind speed Vw to the car's speed Vc is 0.0180\n1\n2012-04-03T10:57:02-0400\nv = speed of car with no wind\nu = speed of the wind along the path of the car\nv - u = speed when going against the wind\nv + u = when going in the same direction as the wind\n\nv - u = d/t1\nv + u = d/t2\n2v = [d/t1 + d/t2]\nv = (1/2)[d/t1 + d/t2]\n\nOf course the meanings of t1 and t2 are not important since they appear in the equation in exactly the same way. So the method to use is method 1.\n\nu/v = 0.018 so u = 0.018v\n\nOther method v = d/[(t1 + t2)/2] = (2){1/[t1/d + t2/d]}\n\ndiff = (1/2)[d/t1 + d/t2] - (2){1/[t1/d + t2/d]}\ndiff = (1/2){d/t1 + d/t2 - 4/[t1/d + t2/d]}\ndiff = (1/2){2v - 4/[1/(v - u) + 1/v + u)]}\ndiff = (1/2){2v - 4(v + u)(v - u)/2v}\ndiff = [1/(4v)][4v^2 - 4(v^2 - u^2)]\ndiff = (u)(u/v) = u^2/v\nfractional diff = diff/v = (u/v)^2 = (0.018)^2 = 0,00032\n\nNeed a fast expert's response?\n\nSubmit order\n\nand get a quick answer at the best price\n\nfor any assignment or question with DETAILED EXPLANATIONS!" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9332023,"math_prob":0.9981581,"size":1178,"snap":"2019-51-2020-05","text_gpt3_token_len":359,"char_repetition_ratio":0.14139694,"word_repetition_ratio":0.0,"special_character_ratio":0.32852292,"punctuation_ratio":0.04597701,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9919033,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-01-23T20:56:37Z\",\"WARC-Record-ID\":\"<urn:uuid:9e354869-e339-44af-a24b-33f3f3c0ce30>\",\"Content-Length\":\"47196\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:086ece1c-2424-4200-b298-52962a951c06>\",\"WARC-Concurrent-To\":\"<urn:uuid:48336cc3-2cfc-4b33-b536-9bad84bf885d>\",\"WARC-IP-Address\":\"52.24.16.199\",\"WARC-Target-URI\":\"https://www.assignmentexpert.com/homework-answers/physics/mechanics-relativity/question-4320\",\"WARC-Payload-Digest\":\"sha1:K4SNKRQWNDRO2CLMWXNY76FC4LHVEDYA\",\"WARC-Block-Digest\":\"sha1:5327FQU5NBKPA7HGRLRUAA4XCEQJMFP5\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-05/CC-MAIN-2020-05_segments_1579250613416.54_warc_CC-MAIN-20200123191130-20200123220130-00249.warc.gz\"}"}
https://lists.defectivebydesign.org/archive/html/help-octave/1995-09/msg00014.html	[ "help-octave\n[Top][All Lists]\n\n## Re: Arrays of strings\n\n From: John Eaton Subject: Re: Arrays of strings Date: Wed, 6 Sep 1995 17:37:54 -0500\n\n```address@hidden <address@hidden> showed how\nto simulate vectors of strings using numeric matrices and\ntoascii/setstr:\n\n: Here's what I did I wrote a tiny function stostr:\n:\n: function var = stostr(var, loc, string)\n: var(loc,1:max(size(toascii(string)))) = toascii(string);\n\nYes, this is about the best you can do with 1.1.1. For 1.2, Octave\nwill support vectors of strings. Indexing will work as will\nconversion to numeric matrices using toascii (or abs, if\nimplicit_str_to_num_ok is set is set to true).\n\nAlso, the internal representation will be 1-byte characters, not be a\nmatrix of doubles, so strings should be more space-efficient in Octave\ncompared to Matlab, and Octave will not force to to pad strings to\nthe same length in order to put them in an array. For example,\n\nfoo = [\"this\"; \"is\"; \"an\"; \"array\"; \"of\"; \"strings\"]\n\nwill be perfectly acceptable.\n\nThanks,\n\njwe\n\n```" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.72960633,"math_prob":0.6766531,"size":1062,"snap":"2023-14-2023-23","text_gpt3_token_len":290,"char_repetition_ratio":0.11247637,"word_repetition_ratio":0.011976048,"special_character_ratio":0.2777778,"punctuation_ratio":0.18468468,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96358544,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-06-08T11:18:44Z\",\"WARC-Record-ID\":\"<urn:uuid:a14fd141-7443-42fa-b3c3-5047305adcbb>\",\"Content-Length\":\"5453\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d45ad738-50cf-4352-bd88-9f9200633976>\",\"WARC-Concurrent-To\":\"<urn:uuid:1b561c5a-b700-45dd-a1a2-8fa316fd6497>\",\"WARC-IP-Address\":\"209.51.188.17\",\"WARC-Target-URI\":\"https://lists.defectivebydesign.org/archive/html/help-octave/1995-09/msg00014.html\",\"WARC-Payload-Digest\":\"sha1:EDAMCLXZ6RBM23HN2TDW2HZZM4OVZJA5\",\"WARC-Block-Digest\":\"sha1:QQC4DPMMNRZLAHJHSZ7Z2I34BKUFHYVN\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224654871.97_warc_CC-MAIN-20230608103815-20230608133815-00742.warc.gz\"}"}
https://wikidev.in/wiki/assembly/8086/CWD	[ "You are here : assembly8086CWD\n\n# CWD - 8086\n\n`Converts word to double word.If High bit of AX=1 then : DX = 65535 (0FFFFh)else : DX = 0`\n\n`CWD`\n\n### Example\n\n```MOV DX, 0 ; DX = 0\nMOV AX, 0 ; AX = 0\nMOV AX, -5 ; DX AX = 00000h:0FFFBh\nCWD ; DX AX = 0FFFFh:0FFFBh\nRET```" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6222649,"math_prob":0.99390656,"size":288,"snap":"2022-40-2023-06","text_gpt3_token_len":126,"char_repetition_ratio":0.16549295,"word_repetition_ratio":0.15151516,"special_character_ratio":0.44444445,"punctuation_ratio":0.2,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9650975,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-02-08T15:55:40Z\",\"WARC-Record-ID\":\"<urn:uuid:82a88fa6-428b-4328-ac6d-b2837f73a93a>\",\"Content-Length\":\"6635\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e2715189-36b0-4844-8f79-43c218fc0595>\",\"WARC-Concurrent-To\":\"<urn:uuid:303cdeab-b8a7-434c-8b5b-55be075e6607>\",\"WARC-IP-Address\":\"104.21.60.239\",\"WARC-Target-URI\":\"https://wikidev.in/wiki/assembly/8086/CWD\",\"WARC-Payload-Digest\":\"sha1:2YRZMMZRZHC6D7ZUXRBSMG6AO3CTLBUF\",\"WARC-Block-Digest\":\"sha1:ATDCXKEHQE7ICZHX67U3E63OVS6ZRL67\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-06/CC-MAIN-2023-06_segments_1674764500837.65_warc_CC-MAIN-20230208155417-20230208185417-00258.warc.gz\"}"}