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https://www.narviacademy.in/Topics/mathematics/mathematics-algebra-permutation-and-combination.php	# Permutation and Combination: #### Fundamental Counting Principle: If one work can be done by "a" different styles and a second work can be done by "b" different styles then the total syles of doing both works will be $$(a \times b)$$. #### Factorial: The factorial of an integer is the product of all less than or equal positive integers. It is denoted by $$n!$$, where n is any positive integer. The factorial of a negative integer is not possible.$$n! = n \ (n - 1) \ (n - 2)......3 \times 2 \times 1$$ $$OR$$ $$n! = 1 \times 2 \times 3.........(n - 1) \times n$$ $$n! = (n - 1)! \times n$$ Example: $$4! = 4 \times 3 \times 2 \times 1 = 24$$ Example: $$6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1$$ $$= 720$$ Note: Remember, $$0! = 1$$, $$1! = 1$$, $$nP_0 = 1$$, $$nP_n = n!$$. #### Permutation: The selection of objects in an ordered manner is called a permutation. Example: Three pens A, B, and C can be written in six different orders ABC, ACB, BAC, BCA, CAB, CBA Hence here the total number of permutation are 6. #### Notation of Permutation: If there are "n" distinct objects and we select "r" objects together then the number of permutations is denoted as $$nP_r$$ or P(n, r). $$nP_r = n \ (n - 1) \ (n - 2)......r$$ $$nP_r = \frac{n!}{(n - r)!}$$ Here $$(r \lt n)$$. Where, n = Total number of objects. P = Permutation. r = The number of selected objects at a time from the total number of distinct objects. #### Important Formulae: (i): n = total number of objects. r = Number of selected objects at a time from the total number of distict objects. $$nP_r = \frac{n!}{(n - r)!}$$ (ii): n = total number of objects. p, q, r = the number of different selected objects at a time from the total number of distinct objects. $$P(p, q, r) = \frac{n!}{p! q! r!}$$ Example: Find the value of $$10P_2$$? Solution: $$nP_r = \frac{n!}{(n - r)!}$$ $$10P_2 = \frac{10!}{(10 - 2)!}$$ $$= \frac{10!}{8!}$$ $$= \frac{10 \times 9 \times 8!}{8!}$$ $$10P_2 = 90$$	2022-09-30 05:32:55	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6868433356285095, "perplexity": 496.49126821170887}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335444.58/warc/CC-MAIN-20220930051717-20220930081717-00537.warc.gz"}
http://mathhelpforum.com/advanced-algebra/89214-graham-schmidt-orthogonalisation.html	# Math Help - Graham-Schmidt Orthogonalisation 1. ## Graham-Schmidt Orthogonalisation Write down a basis for the solution space of the equation x - y + 2z - w = 0. Use the Gram-Schmidt orthogonalisation procedure to nd an orthonormal basis of the solution space. (Use the standard Euclidean inner product, or dot product.) Firstly, to write down the a basis for the solution space, can I just choose any four vectors that satisfy the given equation? Secondly, when I do choose any vectors ie (1,1,1,2) and (5,8,3,3) I always get really messy fractions doing the orthogonalisation. Is there any way to know which vectors to choose to make it neat? Cheers, 2. Originally Posted by U-God Write down a basis for the solution space of the equation x - y + 2z - w = 0. Use the Gram-Schmidt orthogonalisation procedure to find an orthonormal basis of the solution space. (Use the standard Euclidean inner product, or dot product.) Firstly, to write down the a basis for the solution space, can I just choose any four vectors that satisfy the given equation? Secondly, when I do choose any vectors ie (1,1,1,2) and (5,8,3,3) I always get really messy fractions doing the orthogonalisation. Is there any way to know which vectors to choose to make it neat? Firstly, the solution space is three-dimensional, so you will only need three (linearly independent) vectors, not four, for a basis. Secondly, if you choose simple vectors (preferable with some coordinates zero) you are likely to minimise the arithmetic complexity. For example, you could choose (1,1,0,0), (0,0,1,2) and (1,0,0,1) as the basis. But the G–S procedure is inherently messy, and even if you start with simple-looking vectors you are still liable to end up with some complicated fractions.	2015-08-30 19:01:03	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.916620135307312, "perplexity": 392.57370516435486}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440644065330.34/warc/CC-MAIN-20150827025425-00283-ip-10-171-96-226.ec2.internal.warc.gz"}
https://motls.blogspot.com/2010/10/physics-nobel-prize-geim-novoselov.html?m=1	## Tuesday, October 05, 2010 ### Physics Nobel Prize: Geim, Novoselov The 2010 physics Nobel prize has been awarded to Andre Geim (UK), Konstantin Novoselov (UK) for their groundbreaking 2004 experimental discovery of graphene, the one-atom-thick planar hexagonal sheet of carbon atoms - or a two-dimensional material, if you wish. The distance between the adjacent carbon atoms (i.e. the side of the hexagon) is 0.142 nm. If you think that Geim looks very young, then notice that Novoselov was his graduate student when they did the key work. ;-) It's not a real surprise and in my opinion, it is a good choice, too. More precisely, it is an excellent choice, especially if you appreciate that e.g. Andrew Revkin proposed the name of James Hansen just a few hours ago. With a winner like Hansen, Alfred Nobel would instantly detonate the credibility of the physics prize with his own dynamite, by pressing Richard Curtis' red button. If you remember all TRF blog entries, they have been speculated as possible winners in 2008 and 2009. As soon as in 2006, I discussed non-relativistic chiral (left-right asymmetric) quantum field theories that could be realized with graphene. Note that in that article, you may also learn that Andre Geim had already won the Ig Nobel prize for a levitating frog. ;-) In an episode of The Big Bang Theory called The Einstein Approximation, Sheldon Cooper needed quite a lot of boosts to solve a rather simple problem about the electron dispersion relations in graphene, the best known conductor at room temperatures. Note that the two previous paragraphs are actually correlated: while the first one talks about a discovery of "a levitating frog", Sheldon Cooper coined the term "a toad of truth" in the episode described in the second paragraph. ;-) Just four days ago, graphene was also mentioned on TRF because it appeared in Andy Strominger's talk - as an example of a physical system for which the string-theoretical AdS/CFT correspondence has been useful. That's partly because graphene is a nearly perfect fluid - much like the other systems that are well covered by the holographic dual (and reinterpreted as a black hole). This fact is just another example of the tight relationships with string theory and its brand of quantum gravity that the most important state-of-the-art discoveries even in as faraway disciplines as atomic or condensed matter physics display. So far, three of the three 2010 Nobel prize winners were affiliated with British institutions (although I will surely refer to both physics Nobel prize winners as Russians and Geim is a Dutch citizen who was born to German parents in Sochi). That may be a coincidence. However, the Swedish committee could have also been motivated to fight against the proposed dramatic cuts in the funding for the British science.	2021-04-16 07:08:46	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.42998895049095154, "perplexity": 1535.672823730239}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038088731.42/warc/CC-MAIN-20210416065116-20210416095116-00072.warc.gz"}
https://stats.stackexchange.com/questions/101413/random-factor-nested-in-two-fixed-factors	# Random factor nested in two fixed factors I have read Random effect nested under fixed effect model in R, but I have a doubt: My data is on germling survivorship, I have Temperature as a fixed factor (2 levels), pH as a fixed factor (2 levels), and I have tank, which I included to check for tank effect (2 tanks per treatment combination, in a total of 8 tanks). How can I make a model which nests tank within the temp/pH fixed effect? From a previous post I read, we could do: Using aov like this: a0 <- aov(survivorship ~ pHtemp + Error(tank), data=d) summary(a0) or lme like this: library(nlme) m1 <- lme(survivorship ~ pHtemp, random=~1\|tank, data=d) anova(m1) I have tried these two models, but I got two different answers. Can anyone explain why? Is this correct, by using aov like this, is tank nested in pH:temp interaction? aov(survivorship ~ pHtemp + Error(tank) • Shouldn't you do ~1 + pHtemp \| tank and Error(tank/(pHtemp))? Jun 6, 2014 at 14:50 • How many observations do you have in each tank? Is the design balanced? (same number of observations in each tank?) Jun 6, 2014 at 15:24 • 9 observations per tank. Balanced design. Jun 8, 2014 at 8:08 • @"Lost in transcription" that formula would be correct if the treatments were nested inside the tanks - but it's the other way around. Jun 9, 2014 at 14:04 aov and lme are not the same functions. aov is a wrapper for lm, the general linear model function. For balanced designs and one or two random levels, aov can cope with a random term by fitting linear models to different error strata (according to the help files). Significance testing is done using appropriate F statistics. lme, on the other hand, fits a genuine mixed effects model using maximum likelihood (or REML) to obtain estimates of the parameters of the model. They are not required to give the same estimates. It is also possible that your formulae are miss-specified, but I can't tell from the information you have supplied in the question. I don't see where there are two levels in the model. You have a 2x2 factorial with two replicates (the tanks) at each treatment level. The "tank effect" is simply the residual error -- unless you are taking several measurements from each tank. Later I simulated some data based on the OP's problem: a 2x2 factorial with 2 replicates at each level (the tank) and 9 measurements from each tank. There are 3 ways to analyse these data 1. Use aov and the formula given by the OP 2. Use lme (resp lmer) and the formula given by the OP 3. Take the mean survivorship within each tank and use oav() on the means. All three methods lead to the same conclusions. The first and the third produce numerically identical F statistics (as they should, given the problem is balanced). aov and lme give different output. To see the coefficients for pH and temp you need to do coef() on the output of the aov() function. I got identical estimates. The p-values are slightly different, as one would expect given a different model, different estimation and different test statistic. Notice that you get 7 degrees of freedom in the aov() model. The treatments are randomized to the 8 tanks, so basically, the sample size is 8. Taking repeated measurements in each tank gives a more precise measurement of whatever is going on inside each tank -- which is good -- but in a sense, this is still an experiment in which n=8. • My experimental design is a 3-way anova, where we have Temperature and ph as fixed factors (2 levels each) and Tank as a random factor. Inside each tank I have 9 replicates where I measured germling survivorship. In this case Tank is nested in the interaction of Temperature and pH. I understand lme and aov are different functions, but then which will be the best one to use...As both of them can be used, I assumed that although different output occur, significant levels will remain...Maybe I have the model wrong... Jun 8, 2014 at 8:07 • @f_vazpinto I simulated some data with the structure you describe and I've added more specifics to my answer. Jun 9, 2014 at 13:54 • I have read a little bit more on the subject and because I have balanced design, I will go with aov. But I understand I might have my model wrong. When you said to use the means for each tank, I understood I got something wrong. Inside each tank I have 9 mesocoms, and I am using a mean from measurements from inside the mesocomos, so I have n = 9 within each tank. I think I can do aov(survivorship ~ Temperature pH + Error (Tank/mesocosm)). What do you think? Jun 10, 2014 at 10:14 • Also, with this model mesocosm is nested within Tank. My question will be if like this, Tank is nested within the fixed factors? Or because is a balanced design it is not necessary to specify tank nested within the fixed factors!!! Jun 10, 2014 at 10:30	2022-05-24 16:06:44	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6657343506813049, "perplexity": 1481.608719384734}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662573053.67/warc/CC-MAIN-20220524142617-20220524172617-00523.warc.gz"}
http://mathhelpforum.com/discrete-math/219420-solving-generating-function.html	## solving a generating function The problem is to solve fa(x)=(x-1)-2. The textbook told me to assume an = (c1n+c2)1n. So from (x-1)-2=c1x/(1-x)-2+c2x/(1-x) (using generating functions for $\sum nx^n$ and $\sum x^n$, I got the equation 1=c1x+c2x(1-x). But I'm stuck, since the right hand side involves no constant terms. The textbook says I'm supposed to get n+1. How can I proceed from the assumption an = (c1n+c2)1n?	2017-04-28 20:07:01	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9672248959541321, "perplexity": 912.0428613848383}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917123048.37/warc/CC-MAIN-20170423031203-00533-ip-10-145-167-34.ec2.internal.warc.gz"}
https://chemistry.stackexchange.com/questions/38968/are-organic-solvents-used-in-addition-reactions-catalysts	# Are Organic Solvents used in Addition Reactions catalysts? Say for example you are performing a halogenation reaction with dichloromethane (DCM) as the solvent: ethylene + chlorine $\stackrel{DCM}\longrightarrow$ 1,2-dichloroethane I have 2 questions: 1. Is the DCM acting as a catalyst to the reaction, or just a solvent? And if just a solvent, why do we have to use an organic solvent, why not water? 2. Are solvents like DCM necessary if the reactants are liquids already, or only for gaseous or solid reactions? Thank you • As for not using water, try dissolving some non-polar organics in water, then you'll see why. Also, water+chlorine would spark a whole bunch of side reactions we don't want to have. – Ivan Neretin Oct 13 '15 at 7:58 ## 2 Answers In the example you give, the dichloromethane is acting as a solvent. Solvents are usually chosen to be inert under the reaction conditions so that they do not react and produce unwanted products. There are examples of reactions in which no solvent is used, or in which the solvent is a reagent. An example could be forming an ester from a carboxylic acid, using an excess of the alcohol as both solvent and reagent, in the presence of an acid catalyst. That said, solvents are usually used as they severely effect the outcome of a reaction. Polar solvents (THF, diethyl ether) promote very different reactions to non polar ones (hexane) due to the stabilisation they provide for intermediates during the reaction, dilution can also play a role, deciding whether inter or intra-molecular reaction occurs. • Thank you very much, I was wondering though, are solvents like DCM necessary if the reactants are liquids already, or only for gaseous or solid reactions? – Jason Chami Oct 13 '15 at 7:35 To answer the second part of your question, solvents are also used as heat sinks. If no solvent is used, the heat given off from a particular reaction can lead to it being uncontrollable, potentially runaway. If engineering controls are used, no solvent is fine (usually in an industrial setting). However, in a laboratory setting, the heat evolution could cause flashing off (instant vaporisation) , in this instance of DCE, causing a large expansion of material changing from liquid to gas. DCM in itself may not be a great heat sink, but if the reaction is very dilute, the specific heat capacity is supplemented by the volume/mass present.	2019-09-17 06:41:14	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5151432156562805, "perplexity": 2233.823754723674}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514573053.13/warc/CC-MAIN-20190917061226-20190917083226-00060.warc.gz"}
https://www.thejournal.club/c/paper/754/	#### Online EM Algorithm for Latent Data Models ##### Olivier Cappé, Eric Moulines In this contribution, we propose a generic online (also sometimes called adaptive or recursive) version of the Expectation-Maximisation (EM) algorithm applicable to latent variable models of independent observations. Compared to the algorithm of Titterington (1984), this approach is more directly connected to the usual EM algorithm and does not rely on integration with respect to the complete data distribution. The resulting algorithm is usually simpler and is shown to achieve convergence to the stationary points of the Kullback-Leibler divergence between the marginal distribution of the observation and the model distribution at the optimal rate, i.e., that of the maximum likelihood estimator. In addition, the proposed approach is also suitable for conditional (or regression) models, as illustrated in the case of the mixture of linear regressions model. arrow_drop_up	2022-01-24 22:47:42	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.828183650970459, "perplexity": 307.65190437967175}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304686.15/warc/CC-MAIN-20220124220008-20220125010008-00000.warc.gz"}
https://upcommons.upc.edu/browse?value=Energy%20transfer&type=subject	Now showing items 1-20 of 25 • #### A communication-less control scheme for a variable air-gap wireless energy transfer system using current source resonant converter (Institute of Electrical and Electronics Engineers (IEEE), 2017) Conference report Restricted access - publisher's policy This paper presents a robust control method for wireless energy transfer systems using current source resonant converter without any communication network. The proposed control strategy is valid even for systems with ... • #### Anharmonicity in multifrequency atomic force microscopy (2014-07) External research report Open Access In multifrequency atomic force microscopy higher eigenmodes are externally excited to enhance resolution and contrast while simultaneously increasing the number of experimental observables with the use of gentle forces. ... • #### Control method for wireless inductive energy transfer systems with relatively large air gap (IEEE Press. Institute of Electrical and Electronics Engineers, 2013) Article Restricted access - publisher's policy Recent improvements in semiconductor technology make efficient switching possible at higher frequencies, which benefits the application of wireless inductive energy transfer. However, a higher frequency does not alter ... • #### Cubiertas verdes y rehabilitación: procesos de participación y cooperación universidad empresa (2018) Conference report Open Access Las cubiertas vegetales pueden aportar interesantes beneficios a la edificación existente: mejoras en el comportamiento térmico; propiedades acústicas; regulación de las aguas pluviales; y en clave ciudad, mejorar los ... • #### Development of a power flow model for the transmission network of the iberian peninsula (Universitat Politècnica de Catalunya / Technishe Universität Berlin, 2015) Master thesis (pre-Bologna period) Open Access Covenantee: Technische Universität Berlin Over the last years, due to the increasing use of renewable energy, the typical way of producing and transporting electricity in Iberian Peninsula has changed. The way to produce energy has evolved from thermal and hydraulic ... • #### Estació de càrrega de drons (Universitat Politècnica de Catalunya, 2020-06) Bachelor thesis Open Access El projecte consisteix en el disseny i simulació d’un ondulador, que genera un senyal amb freqüència suficient per a fer entrar en ressonància un tanc ressonantemissorcol·locat a laseva sortida.Gràcies a la part inductiva ... • #### Fertigstellung und Inbetriebnahme eines Versuchstands zur Vermessung experimenteller induktiver Batterieladesysteme (Universitat Politècnica de Catalunya, 2015) Master thesis Open Access Covenantee: Karlsruher Institut für Technologie Within the framework of inductive technology, this master’s thesis represents the conclusion of several previous projects that pursuit a common objective, to design and develop an inductive wireless power transfer system ... • #### Fluid dynamics and heat transfer in the wake of a sphere (2019-04) Article Restricted access - publisher's policy Direct numerical simulation and large-eddy simulation have been performed for a heated sphere at Reynolds numbers of $Re=1000$ and $Re=10^4$, respectively. The Prandtl number for both simulations has been $Pr=0.7$. ... • #### Heat and Mass Transfer Technological Center (Campus de Terrassa de la UPC, 2013-06-13) Conference report Open Access • #### Impact of mobile transmitter sources on radio frequency energy harvesting (Universitat Politècnica de Catalunya, 2012-09-05) Master thesis (pre-Bologna period) Open Access Covenantee: Northeastern University [ANGLÈS] Wireless energy harvesting sensors networks constitute a new paradigm, where the motes deployed in the field are no longer constrained by the limited battery resource, but are able to recharge themselves through ... • #### MEMS technologies for energy harvesting (Springer, 2016-11-11) Part of book or chapter of book Open Access The objective of this chapter is to introduce the technology of Microelectromechanical Systems, MEMS, and their application to emerging energy harvesting devices. The chapter begins with a general introduction to the most ... • #### On freezing resistance of borehole heat exchangers (Universitat Politècnica de Catalunya. Departament d'Enginyeria del Terreny, Cartogràfica i Geofísica, 2015-06-02) Conference report Open Access • #### Power reduction coordinated scheme for wind power plants connected with VSC-HVDC (2017-07-01) Article Open Access This article introduces a novel power coordination method for the operation under restricted conditions of offshore wind power plants connected with VSC-HVDC without the use of communications between converter stations. ... • #### Recuperated versus single-recuperator re-compressed supercritical CO2 Brayton power cycles for DEMO fusion reactor based on dual coolant lithium lead blanket (2017-12-01) Article Open Access The EUROfusion research program is currently exploring alternative solutions for a future fusion power plant with DEMO (DEMOnstration Power Plant) prototype. One of the most important issues arising from a dual coolant ... • #### Solvation dynamics in liquid water: 1: ultrafast energy fluxes (2015-01-30) Article Open Access Solvation dynamics in liquid water is addressed via nonequilibrium energy-transfer pathways activated after a neutral atomic solute acquires a unit charge, either positive or negative. It is shown that the well-known ... • #### Solvation dynamics in liquid water: III: energy fluxes and structural changes (2017-02-16) Article Open Access In previous installments it has been shown how a detailed analysis of energy fluxes induced by electronic excitation of a solute can provide a quantitative understanding of the dominant molecular energy flow channels ... • #### Solvation dynamics in water: 2. Energy fluxes on excited- and ground-state surfaces (2016-11-03) Article Open Access This series’ first installment introduced an approach to solvation dynamics focused on expressing the emission frequency shift (following electronic excitation of, and resulting charge change or redistribution in, a solute) ... • #### Spectroscopic characterization of Er3+, Yb3+ co-doped UC single crystals : the influence of host and sensitizer concentrations (Universitat Politècnica de Catalunya, 2018-10-24) Master thesis Open Access Covenantee: Bundesanstalt für Materialforschung und -prüfung The energy transfer upconversion (ETU) mechanism is known to be the most efficient route for the conversion of near infrared (NIR) light to visible emission in Ln3+-co-doped systems. In this work, we examined these energy ... • #### Study for the computational resolution of conservation equations of mass, momentum and energy. Possible application to different aeronautical and industrial engineering problems: Case 1A. (Universitat Politècnica de Catalunya, 2017-06-10) Bachelor thesis Restricted access - author's decision This project deals with the numerical simulation of the Navier-Stokes equations for different cases. By computing several benchmark cases, the code is tested and improved in order to compute more difficult cases such as ... • #### Study for the computational resolution of conservation equations of mass, momentum and energy. Possible application to different aeronautical and industrial engineering problems: Case 5A. (Universitat Politècnica de Catalunya, 2017-06-10) Bachelor thesis Restricted access - author's decision The numerical simulation of the RAE2822 aerofoil under transonic flow conditions (including shock-induced separation at the upper surface) has been performed using unsteady Reynolds-averaged numerical simulation (URANS), ...	2020-09-22 02:29:18	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.32551053166389465, "perplexity": 10043.84167068179}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400202686.56/warc/CC-MAIN-20200922000730-20200922030730-00474.warc.gz"}
http://legisquebec.gouv.qc.ca/en/showversion/cr/C-24.2,%20r.%2034?code=se:84_5&pointInTime=20190521	### C-24.2, r. 34 - Regulation respecting licences 84.5. The amount of the reimbursement applicable to a restricted licence issued, exclusively in class 8, in the cases referred to in sections 84.1 to 84.3, is obtained by applying the rules in those sections, with the reference to “\$17.80” replaced by “\$23.40”. O.C. 877-2010, s. 20; O.C. 1181-2011, s. 16. 84.5. The amount of the reimbursement applicable to a restricted licence issued, exclusively in class 8, in the cases referred to in sections 84.1 to 84.3, is obtained by applying the rules in those sections, with the reference to “\$17.70” replaced by “\$23.20”. O.C. 877-2010, s. 20; O.C. 1181-2011, s. 16. 84.5. The amount of the reimbursement applicable to a restricted licence issued, exclusively in class 8, in the cases referred to in sections 84.1 to 84.3, is obtained by applying the rules in those sections, with the reference to “\$17.60” replaced by “\$23”. O.C. 877-2010, s. 20; O.C. 1181-2011, s. 16. 84.5. The amount of the reimbursement applicable to a restricted licence issued, exclusively in class 8, in the cases referred to in sections 84.1 to 84.3, is obtained by applying the rules in those sections, with the reference to “\$17.40” replaced by “\$22.80”. O.C. 877-2010, s. 20; O.C. 1181-2011, s. 16. 84.5. The amount of the reimbursement applicable to a restricted licence issued, exclusively in class 8, in the cases referred to in sections 84.1 to 84.3, is obtained by applying the rules in those sections, with the reference to “\$17.20” replaced by “\$22.60”. O.C. 877-2010, s. 20; O.C. 1181-2011, s. 16. 84.5. The amount of the reimbursement applicable to a restricted licence issued, exclusively in class 8, in the cases referred to in sections 84.1 to 84.3, is obtained by applying the rules in those sections, with the reference to “\$17” replaced by “\$22.40”. O.C. 877-2010, s. 20; O.C. 1181-2011, s. 16. 84.5. The amount of the reimbursement applicable to a restricted licence issued, exclusively in class 8, in the cases referred to in sections 84.1 to 84.3, is obtained by applying the rules in those sections, with the reference to “\$16.60” replaced by “\$21.90”. O.C. 877-2010, s. 20; O.C. 1181-2011, s. 16.	2019-06-20 12:16:28	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8644345998764038, "perplexity": 3034.8243954491704}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627999210.22/warc/CC-MAIN-20190620105329-20190620131329-00347.warc.gz"}
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Parameters target specifies the framebuffer target. target must be gl_draw_framebuffer, gl_read_framebuffer, or gl_framebuffer.	2020-11-26 08:59:49	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.20601968467235565, "perplexity": 5842.947316021585}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141187753.32/warc/CC-MAIN-20201126084625-20201126114625-00574.warc.gz"}
https://math.stackexchange.com/questions/2796039/show-max-r-equiv-r-1-r-m-in-mathbbrm-sum-k-1m-mu-k-r-k-l	# Show $\max_{r\equiv (r_1,…, r_M) \in \mathbb{R}^M} \sum_{k=1}^M \mu_k r_k - \log\Big(\sum_{k=1}^M \exp(r_k) \Big)= \sum_{k=1}^M \mu_k \log(\mu_k)$ I am struggling with the following maximisation problem. Take a vector $\mu\equiv (\mu_1,..., \mu_M)\in \mathbb{R}^M$ such that $\mu_k\in [0,1]$ $\forall k=1,...,M$ and $\sum_{k=1}^M \mu_k=1$. I want to show that $$\max_{r\equiv (r_1,..., r_M) \in \mathbb{R}^M} \sum_{k=1}^M \mu_k r_k - \log\Big(\sum_{k=1}^M \exp(r_k) \Big)= \sum_{k=1}^M \mu_k \log(\mu_k)$$ I write first order conditions $$\begin{cases} \mu_1-\frac{\exp(r_1)}{\sum_{k=1}^M \exp(r_k)}=0\\ ...\\ \mu_M-\frac{\exp(r_M)}{\sum_{k=1}^M \exp(r_k)}=0\\ \end{cases}$$ $$\Updownarrow$$ $$\begin{cases} r_1=\log(\mu_1)+\log(\sum_{k=1}^M \exp(r_k))\\ ...\\ r_M=\log(\mu_M)+\log(\sum_{k=1}^M \exp(r_k)) \end{cases}$$ and assuming that this is the maximum, we can put it in the objective function and get the result. Now I need to ensure that we have a maximum and at this point I'm lost in the computation of the Hessian because I get many zeros. Could you help me with that part? You are done if you prove that the function is concave, that is the function log-sum-exp is convex. Two ways to do it is here and here. Another way is to use induction: prove first that $\ln(1+\exp{t})$ is convex and increasing. Then 1. $\ln(\exp{r_1}+\exp{r_2})=r_1+\ln(1+\exp(r_2-r_1))$ is convex. 2. Assume $\ln(\sum_{i=1}^M\exp{r_i})$ convex. Then $$\ln\Big(\sum_{i=1}^{M+1}\exp{r_i}\Big)=r_{M+1}+\ln\Big(1+\sum_{i=1}^M\exp(r_i-r_{M+1})\Big)=r_{M+1}+\ln\Big(1+\exp\underbrace{\ln\sum_{i=1}^Me^{r_i-r_{M+1}}}_{\text{convex}}\Big)$$ is convex. • Thanks. Can you remind me why if $\log(\sum_{y=1}^M \exp(r_k))$ is convex, then the objective function is concave? – TEX May 26 '18 at 11:22	2021-05-19 03:39:57	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9456011056900024, "perplexity": 130.88817175001614}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991562.85/warc/CC-MAIN-20210519012635-20210519042635-00474.warc.gz"}
https://deepai.org/publication/distributed-control-and-quality-of-service-in-multihop-wireless-networks	# Distributed Control and Quality-of-Service in Multihop Wireless Networks Control of wireless multihop networks, while simultaneously meeting end-to-end mean delay requirements of different flows is a challenging problem. Additionally, distributed computation of control parameters adds to the complexity. Using the notion of discrete review used in fluid control of networks, a distributed algorithm is proposed for control of multihop wireless networks with interference constraints. The algorithm meets end-to-end mean delay requirements by solving an optimization problem at review instants. The optimization incorporates delay requirements as weights in the function being maximized. The weights are dynamic and vary depending on queue length information. The optimization is done in a distributed manner using an incremental gradient ascent algorithm. The stability of the network under the proposed policy is analytically studied and the policy is shown to be throughput optimal. ## Authors • 4 publications • 7 publications • ### Quality-of-Service in Multihop Wireless Networks: Diffusion Approximation We consider a multihop wireless system. There are multiple source-destin... 10/29/2018 ∙ by Ashok Krishnan K. S., et al. ∙ 0 • ### Analytical Study of Incremental Approach for Information Dissemination in Wireless Networks In many scenarios, control information dissemination becomes a bottlenec... 08/05/2020 ∙ by Andrey Belogaev, et al. ∙ 0 • ### Recorp: Receiver-Oriented Policies for Industrial Wireless Networks Future Industrial Internet-of-Things (IIoT) systems will require wireles... 08/20/2020 ∙ by Ryan Brummet, et al. ∙ 0 • ### Tradeoff between Delay and Physical Layer Security in Wireless Networks Exchange of crucial and confidential information leads to the unpreceden... 02/01/2018 ∙ by Yi Zhong, et al. ∙ 0 • ### A Stochastic Resource-Sharing Network for Electric Vehicle Charging We consider a distribution grid used to charge electric vehicles subject... 11/15/2017 ∙ by Angelos Aveklouris, et al. ∙ 0 • ### PBE-CC: Congestion Control via Endpoint-Centric, Physical-Layer Bandwidth Measurements Wireless networks are becoming ever more sophisticated and overcrowded, ... 02/10/2020 ∙ by Yaxiong Xie, et al. ∙ 0 • ### Heat-Diffusion: Pareto Optimal Dynamic Routing for Time-Varying Wireless Networks A dynamic routing policy, referred to as Heat-Diffusion (HD), is develop... 02/15/2019 ∙ by Reza Banirazi, et al. ∙ 0 ##### This week in AI Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday. ## I Introduction and Literature Review A multihop wireless network consists of nodes transmitting and receiving information over the wireless medium, with data from a source node having to pass through multiple hops before it can reach its destination. The control of wireless networks, involving scheduling, routing and power control, is a complex and challenging problem. Applications often require distributed control as opposed to centralized control. Distributed control algorithms may not always match centralized algorithms in terms of performance. However, they offer ease of implementation from a practical perspective in scenarios where it may not be feasible to collect information from all over the network before arriving at a control decision. Different flows in a network, arising from different applications, may ask for Quality-of-Service (QoS). QoS may vary depending on the nature of the application. Some applications require an end-to-end mean delay guarantee on the packets being transmitted. Some others, such as a live streaming video, may require all packets to satisfy a hard delay requirement. In some cases, the QoS constraint is a bandwidth requirement for the user. Services involving VoIP (Voice over IP) are sensitive to delay and delay variability in the network, and require preferential treatment over other packets [1]. Another service that requires QoS is remote health-care, which involves collection of data about a patient from a remote location and transmitting it elsewhere to be analysed [2]. Such applications in the context of the Internet of Things (IoT) [3] will require the coming together of different kinds of traffic with various QoS requirements, and with different levels of sensitivity [4]. While directly solving problems that involve QoS requirements may not be straightforward, one can look for appropriate asymptotic solutions. One approach is to study the network in the large queue length regime, and translate mean delay requirements of flows into effective bandwidth and effective delay as given by large deviations theory, and formulate these as physical layer requirements [5]. In the case of multihop networks, however, owing to the complex coupling between queues, such a formulation is not easy to obtain [6]. Backpressure based methods are common in network control. These are connected to control based on Lyapunov Optimization [7]. Backpressure based algorithms may not provide good delay performance, especially in lightly loaded conditions [8], [9] . Techniques based on Markov Decision processes (MDPs) are also popular [10]. In [11], [12], the problem of minimizing power while providing mean and hard delay guarantees is studied. However the algorithm requires knowledge of system statistics and is not throughput optimal. Fluid limits [13] are an asymptotic technique used to study networks and obtain control solutions. The network parameters and variables, under a suitable scaling, are shown to converge to deterministic processes. This is called the fluid limit. The stability of the fluid limit has a direct bearing upon the stability of the original stochastic system [14], [15]. The technique of discrete review is used in [16]. Here, the network is reviewed at certain time instants, and control decisions are taken till the next time instant using the state information observed. In [17] the authors use fluid limit based techniques to establish the stability of a per-queue based scheduling algorithm. A robust fluid model, obtained by adding stochastic variability to the conventional fluid model, is discussed in [18]. Another algorithm using per hop queue length information, with a low complexity approximation that stabilizes a fraction of the capacity region is given in [19]. However, the algorithm does not address delay QoS. Our main contributions in this paper are summarised below. • [noitemsep,topsep=0pt] • We propose an algorithm that solves a weighted optimization in order to address mean delay requirements of different flows. The weights are time varying and state dependent, as opposed to fixed weight schemes. This assigns dynamic priorities to different flows. • Our policy uses the technique of discrete review, which involves taking decisions on the network control at certain time instants, thus reducing the overall control overhead as opposed to schemes which require computations in every slot, such as in [20]. Discrete review schemes have been used in queueing networks [16]; however, the implementation is centralized and they do not consider delay deadlines. The use of discrete review separates our policy from works such as [17] or [21] which involve decision making in each slot. The policies in [17], [19] are throughput optimal but do not provide other QoS. • Iterative gradient ascent is used to solve the optimization problem in a distributed manner, similar to what is done in [22]. This can be implemented easily in a cyclic manner, with message passing between the nodes after each step. The gradient calculation requires only local information, and the projection step requires knowledge of links with which a particular link interferes. • The algorithm works based on queue length information, which acts as a proxy for delay. Thus it differs from [22] which uses delay information to obtain delay guarantees, and thus has a different function being maximized. In addition, this algorithm is analysed extensively theoretically and is shown to be throughput optimal. Simultaneously, it also has provisions for mean delay QoS. The rest of this paper is organized as follows. In Section II, we describe the system model, and formulate an optimization problem to address our requirements. In Section III, we describe the algorithm and its distributed implementation in detail. In Section IV, we obtain the fluid limit of the system under our algorithm, and show its throughput optimality. In Section V we detail the simulation results, followed by conclusions in Section VI. ## Ii System Model and Problem Formulation We consider a multihop wireless network (Fig. 1). The network is a directed graph with being the set of vertices and , the set of links on . The system evolves in discrete time denoted by . We have directional links, with link from node to node having a time varying channel gain at time . At each node , denotes the cumulative process of exogenous arrival of packets destined to node , upto time . The packets arrive as an i.i.d sequence across slots,with mean arrival rate . All traffic in the network with the same destination is called flow ; the set of all flows is denoted by . Each flow has a fixed route to follow to its destination. At each node there are queues, with denoting the queue length at node corresponding to flow at time . The queues evolve as Qfi(t)=Qfi(0)+Afi(t)+∑k≠iSfki(t)−∑j≠iSfij(t), (1) where denotes the cumulative number of packets of flow that are transmitted from node to node till time . The vector of queues at time is denoted by . Similarly we have the arrival vector and the service vector . We will assume that the links are sorted into interference sets . At any time, only one link from an interference set can be active. A link may belong to multiple interference sets. In this work we will assume that any two links which share a common node will fall in the same interference set. We assume that each node transmits at unit power. Then, the rate of transmission between node and node can be written as where is some achievable rate function, and is the schedule at time . We want to develop scheduling policies such that the different flows obtain their end-to-end mean delay deadline guarantees. Our network control policy, Queue Weighted Discrete Review (QWDR), is as follows. We have a sequence of review times , chosen as Ti+1=Ti+max(1,log(1+k0\|\|Q(Ti)\|\|)), (2) where the are called review periods and . Define . At each , we solve the optimization problem, max∑i,j,fw(Qf(Ti),¯¯¯¯Qf)Qfij(Ti)ζfijμij, (3) s.t 0≤ζij:=∑f∈Fζfij≤1 ∀ij, (4) 0≤ζij+ζkl≤1, ∀(i,j),(k,l)∈Im,∀m, (5) assuming for at least one link flow pair . If all are zero, we define the solution to be for all . The first constraint corresponds to the fact that flows cannot simultaneously be scheduled on a link, and the second constraint corresponds to interference constraints. In (3), we optimize the sum of rates weighted by the function as well as the queue lengths. More weight may be given to flows with larger backlogs, while the function captures the delay requirement of the flow. These are chosen such that flows requiring a lower mean delay would have a higher weight compared to flows needing a higher mean delay. Also, flows whose mean delay requirements are not met should get priority over flows whose requirements have been met. The weights therefore are functions of the state, and denotes a desired value for the queue length of flow . We use the function w(x,¯¯¯x)=1+a11+exp(−a2(x−¯¯¯x)). (6) Thus is close to when is larger than , and reduces to as reduces. Thus, delays which are above certain thresholds obtain higher weights in the optimization function. We seek to regulate the queue lengths using with a careful selection of , and thereby control the delays. For any flow, the are chosen in the following manner. If the required end-to-end mean delay of the flow with arrival rate is , we choose . In some sense, we are taking the queue length equivalent to the required delay using Little’s Law and using it as a threshold that determines the scheduling process. The network control variables correspond to the fraction of time in one review period in which link will be transmitting flow . In a review period, we will assume that the channel gain is fixed (slow-fading), but drawn as an i.i.d sequence from a bounded distribution . Each node transmits at unit power. The rate over link is . Let be the number of time slots till time in which the channel was in state . Let be the number of slots till time , in which channel state was , the schedule was and flow was scheduled over . Clearly, for any , , , ∑ICmIijf(t)=Cm(t). (7) ## Iii Gradient Ascent and Distributed Implementation The optimization problem is separable into link-flow elements, with each link-flow element being a unique in the network. Let be the set of all link-flow elements. Any corresponds one-to-one with a link-flow element ; we call this mapping from all to as . Consider the optimization problem maxζ∈S∑k∈KGk(ζ) (8) with , and where and is the set of that satisfy constraints (4) and (5); however, we remove the assumption that the variables are positive. This is equivalent to the optimization problem (3) . This is a linear optimization problem with linear constraints. One can then define a sequential iteration ζj+1=ΠS[ζj+α∇Gkj(ζj)] (9) with being an arbitrary initial point, modulo , and denoting projection into the set . This is cyclic Incremental Gradient Ascent. Let . From Proposition 3.2 of [23], the following holds. ###### Lemma 1. The iterates given by equation (9) satisfy limj→∞sup∑k∈KGk(ζj)≥G∗−c, where , . Thus, given the optimization problem to be solved at a particular time, we can use the gradient ascent method (9) to arrive at an optimal point in a distributed sequential fashion. First, obtain , and then project onto . Since where , the first step is clear. The projection step is described below. ### Iii-a Distributed Projection Two links that share a node are assumed to interfere with each other. Therefore, an update of the optimization variables at a will affect only those links which have either or as end points. The set is defined by the intersection of half-spaces , where each is characterized by an equation , with being the unit normal vector. Due to the nature of our constraints, is non-negative. Each half-space corresponds to one interference constraint. During an update step, a point may break at most two interference constraints. This is because each link has two sets of constraints, one for each end. If one constraint is broken, one step of projection will suffice. If we break both constraints, we can iteratively project it, first to one hyperplane, then the next and so on repeatedly. It can be shown [24, Theorem 13.7] that this scheme converges to the projection onto the intersection of the hyperplanes. We will now obtain the analytical expressions for projecting a point onto a hyperplane. Let the hyperplane be defined by . Let the point lie outside , i.e., β∗≜⟨s,ν⟩>β. Define . It is easy to see that satisfies . Since , and is normal to the plane boundary of , it follows that is the perpendicular projection of onto . It can also be shown that satisfies all the other hyperplane constraints that does. Now we will describe the complete algorithm. ### Iii-B Algorithm Description At each , the problem (3)-(5) is solved in a distributed fashion. The nodes calculate for all , and , and use these till the end of the review cycle. We will now describe how are calculated at each node. We assume that there is some convenient ordering of the link-flow elements, and computation proceeds in that order. Let this order be , and assume that the elements of the vector are also arranged in the same order. At link-flow element , we update the first component of as s(1)=s(1)+α∇Gk1(s). (10) Here , where . The node then calculates the inner products β∗1≜⟨s,ν1⟩,β∗2≜⟨s,ν2⟩ where , correspond to the two interference constraints that the update step may break. These correspond to constraints at the two nodes at which link is incident. If exactly one constraint, say , gets broken, we can project the point back to the constraint set by calculating where is the number of links in that interference set. The element communicates to all elements in its interference set. All these elements do the update s(k)=s(k)−βex. If both constraints are violated, the above projection step has to be repeatedly done, first for elements corresponding to constraint , then for , again for and so on. After projection, the node passes to the node corresponding to the next component of , and the process is repeated cyclically, i.e, we repeat step (10) with 1 replaced by 2, and then by 3 and so on, across the nodes till a stopping time. At the stopping time, set any negative components of to zero. For each interference set , we check its constraint . If the constraint is not met, do an appropriate scaling. This ensures compliance with the constraints. The complete algorithm is given below, as Algorithm 1, QWDR (Queue Weighted Discrete Review), which uses in turn, Algorithms 2, 3 and 4. The last algorithm schedules flows on a link for a fraction of time equal to the corresponding . ## Iv Fluid Limit Define the system state to be , where the process with , representing the queue values at the last review instant, and representing the cumulative allocation vector from the last review instant to the current time. From the queue evolution (1) and the allocation, it is clear that the system evolves as a discrete time countable Markov chain, since at any time the next state may be computed by solving the optimization (3) with replaced by , and using the cumulative allocation process to determine how allocation must be done in the next slot to satisfy the solution of (3). The associated norm is . Positive recurrence of this Markov chain would imply stability. We will show positive recurrence of this Markov chain via its fluid limit. Consider a real valued process evolving over (discrete) time , with being its initial state. Consider a sequence of these processes as . Define the corresponding scaled (continuous time) process, h(n,t)=hn(n⌊t⌋)n. Define the scaled processes , , , and as above. For a scaled process , denote . For the vector processes , , , and , we define the corresponding scaled vector processes. The term fluid limit denotes the limits obtained as we scale for these processes. Consider . The process is a projection of . We assume that the rates satisfy . This will happen since the channel gains are assumed bounded and transmit power is fixed. Consider the scaled process . We use the following definition. ###### Definition 1. A sequence of functions is said to converge uniformly on compact sets (u.o.c) if uniformly on every compact subset of the domain. We obtain the following result for the components of . ###### Theorem 1. For almost every sample path , there exists a subsequence such that, Afi(nk,t)→afi(t), Sfij(nk,t)→sfij(t), (11) Cm(nk,t)→cm(t), CmIijf(nk,t)→cmIijf(t), (12) Qfi(nk,t)→qfi(t), ~Qfi(nk,t)→qfi(t), (13) ~Sfi(nk,t)→0, (14) uniformly on compact sets, for all , and . The limiting functions are also Lipschitz continuous, and hence almost everywhere differentiable. The points at which it is differentiable are called regular points. In addition, the limiting functions satisfy the following properties. afi(t)=λfit, cm(t)=πmt, (15) qfi(t) =qfi(0)+afi(t)+∑ksfki(t)−∑jsfij(t), (16) ˙qfi(t)=λfi+∑k˙sfki(t)−∑j˙sfij(t), (17) ∑IcmIijf(t)=cm(t), \|\|q(0)\|\|≤1, (18) sfij(t)=∫t0˙sfij(τ)dτ, (19) where satisfies ∑i,j,fw(qf(t))qfij(t)˙sfij(t)=max¯μ∑i,j,fw(qf(t))qfij(t)¯μij, (20) where the dot indicates derivative, at regular t and . ###### Proof. The Strong Law of Large Numbers implies Afi(nk,t)→afi(t), for any subsequence , with . Thus we obtain the first parts of (11) and (15). Since the rates are bounded, it follows that . Therefore, for , we have Sfij(nt2)−Sfij(nt1)≤n(t2−t1)μmax. Thus, the family of functions is uniformly bounded and equicontinuous. By the Arzela-Ascoli theorem [25], we can see that for any sequence with , there exists a subsequence along which Sfij(nk,t)→sfij(t), as wp 1, u.o.c. This implies the second part of (11). The resultant is Lipschitz, being the result of uniform convergence of a sequence of Lipschitz functions. The first part of (12), and second part of (15) follow from the Strong Law of Large Numbers applied to the channel process. From equation (1), we can see that the terms on the right hand side converge under this scaling. Consequently, Qfi(nk,t)→qfi(t), wp 1 u.o.c, as . Like , both and will be Lipschitz. Equation (16) follows by observing that the scaled queue process will satisfy the queueing equation (1), and applying the appropriate limit in that equation. Since the fluid variables and are Lipschitz, they are differentiable almost everywhere. At the points where they are differentiable, we obtain (17) by differentiating (16). The first part of (18) follows from (7). To see the second part of (12), observe that, by definition, 1nCmIijf(nt2)−CmIijf(nt1)≤t2−t1, (21) for . Applying Arzela-Ascoli theorem, we obtain the subsequence that satisfies the second part of (12). Since is almost everywhere differentiable, (19) follows. In obtaining the fluid limit of the allocation process , we will not distinguish between the actual and the ideal allocation, since they converge to the same limit. Let the actual allocation be . The actual allocation differs from the ideal allocation due to round-off errors. At a time , let . Bounding possible errors in each review period we get, \|^Sfij(nt)−Sfij(nt)\|≤μmax^Tm+mμmax. The last term follows by summing up round-off errors in review periods upto , and observing that in any review period , errors are of the form , where . Since , where , we get \|^Sfij(n,t)−Sfij(n,t)\|≤μmax{^Tmn+tT}. Since are and , we have and , and hence, the fluid limits of and are equal. To show (20), observe that Sfij(t)=∑m,ICmIijf(t)μij(I,m). Hence we have Sfij(nt2)−Sfij(nt1)=∑m,I(CmIijf(nt2)−CmIijf(nt1))μij(I,m). Multiplying LHS and RHS by , summing over i, j, f, and taking , the LHS becomes ∑i,j,fw(qf(t1))qfij(t1)[sfij(t2)−sfij(t1)], (22) where and . Since the allocation satisfies ∑w(Qf(n,t′))Qfij(n,t′)μij(I,m) =maxI∑w(Qf(n,t′))Qfij(n,t′)μij(I,m), where was the previous review point with . Since , we can write as limn→∞Qfi(n,t1)=limn→∞1nQfi(n(t′+Tn))=qfi(t′). (23) The RHS can therefore be written as ∑m,I,i,j,f[cmIijf(t2)−cmIijf(t1)]maxIμij(I,m)w(qf)qfij. Using (18) and (15), this becomes ∑m,i,j,f[cm(t2)−cm(t1)]maxIμij(I,m)w(qf)qfij, (24) = (t2−t1)∑m,i,j,fπmmaxIμij(I,m)w(qf)qfij. (25) Dividing (22) and (25) by , equating, and taking , ∑i,j,fw(qf(t1))qfij(t1)˙sfij(t1)=max¯μ∑i,j,fw(qf)qfij¯μij, where . Thus we obtain (20). The second part of (13)follows from (23). To obtain (14), observe that 0≤~Sfij(n,t)≤μmax^Tn, with being a review period. Taking , (14) follows. Since , the second part of (18) follows. ∎ Denote the vector of all by . We will use the following result to establish the stability of the network. ###### Theorem 2. (Theorem 4 of [15]) Let be a Markov Process with denoting its norm. If there exist and a time such that for a scaled sequence of processes , we have limn→∞supE[\|\|Y(n,T)\|\|]≤1−α, then the process is stable (positive recurrent). Using this result, we will establish stability of the network under our algorithm and show that it is throughput optimal. We first define the capacity region of the network. A schedule s is a mapping from , the set of all link-flow elements, to . Let the set of all feasible schedules be denoted by and is its convex hull. We define the capacity region as follows. ###### Definition 2. The capacity region is given by the set of all for which there exists an such that λfi≤∑mπm∑js(k)μmij−∑mπm∑rs(kr)μmri, (26) where , is the stationary probability that the channels are in state , and is the rate across link when the channels are in state . Now we establish the throughput optimality of our policy. ###### Theorem 3. The policy QWDR stabilizes the process for all arrivals in the interior of . ###### Proof. To prove this, we will first pick a suitable Lyapunov function, whose drift will be shown to be negative. Pick an arrival rate matrix . This implies that there are rates and that satisfy λfi+ϵ<∑nrfin−∑mrfmi, (27) for each . These rates correspond to the terms in (26). Consider the Lyapunov function L(q(t))=−∫∞texp(τ−t)∑i,fw(qf)qfi˙qfidτ, where the dot indicates the derivative. This is a continuous function of , with . We can write the derivative, ˙L(q(t)) =∑i,fw(qf)qfi˙qfi, =∑i,fw(qf)qfi(λfi+∑m˙sfmi(t)−∑n˙sfin(t)), <−ϵ∑i,fw(qf)qfi+∑i,fw(qf)qfi(∑nrfin, −∑mrfmi+∑m˙sfmi(t)−∑n˙sfin(t)), where the inequality followed from (27). Observing that ∑i,fw(qf)qfi(∑nrfin−∑mrfmi)=∑i,j,fw(qf)rfij(qfi−qfj), and that a similar equation holds for replaced by , it follows that if we show ∑i,j,fw(qf)rfij(qfi−qfj)≤∑i,j,fw(qf)˙sfij(qfi−qfj), (28) it will imply . We have ∑i,j,fw(qf)rfij(qfi−qfj)≤∑i,j,fw(qf)rfijqfij≤∑i,j,fw(qf)˙sfijqfij, where the second inequality follows from (20). Now, if we show that whenever , (28) will follow. To see this, assume that at some ,	2021-09-25 12:22:16	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8632224798202515, "perplexity": 661.3043709156275}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057622.15/warc/CC-MAIN-20210925112158-20210925142158-00487.warc.gz"}
http://stats.stackexchange.com/questions/24601/martingale-residuals-and-schoenfeld-residuals	# Martingale Residuals and Schoenfeld Residuals If the Martingale Residuals indicate that a predictor $X$ violates the proportional hazards assumption but the Schoenfeld Residuals indicate that it does not....which one should you trust? - In reference to @andrea answer, how do you know one violates the assumption and the other does not? – Glen Apr 13 '12 at 14:28	2013-12-07 16:44:24	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9739765524864197, "perplexity": 2472.4464633019784}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386163054976/warc/CC-MAIN-20131204131734-00087-ip-10-33-133-15.ec2.internal.warc.gz"}
https://physics.stackexchange.com/questions/504287/how-is-the-wave-function-viewed-as-the-quantum-state/504306	# How is the wave function viewed as the quantum state? I am not sure how the wave function can be viewed as quantum state. I begin with the eigen-equation $$A\|\psi\rangle = a\|\psi\rangle$$ If $$A$$ is a $$n$$ dimensional matrix with different eigenvalues $$a$$, then there will be $$n$$ eigenvectors. If I do orthonormalization to these eigenvectors, then there will be $$n$$ basis vectors. If the $$\|\psi\rangle$$ is vector in quantum state space, then this is the $$n$$ dimensional quantum state. Next, more specific consideration. The Schrodinger equation, $$H\|\psi\rangle=E_n\|\psi\rangle$$ with at the $$n$$ energy eigenvalue and $$H$$ is Hamiltonian (not in form of the matrix like above). Normally it is solved in the position state, that will be $$H\Psi_n(x) = E_n\Psi_n(x)$$ where $$\Psi_n(x) = \langle x\|\psi\rangle$$ is wave function of an $$n$$ energy eigenvalue. In this form, the wave function is just a continuous coefficient of $$\|x\rangle$$. How does this $$\Psi_n(x)$$ become quantum state ? Can I say that because there are $$n$$ wavefunctions on the same position space $$\|x\rangle$$ then they form the Hilbert space and can be viewed as quantum state? $$\int {\Psi_m}^*(x) \Psi_n(x) dx =<\Psi_m(x)\|\Psi_n(x)>= \delta_{m,n}$$ The wavefunctions themselves are simply the coefficients in the expansion of the quantum mechanical state vector in the position basis, as you already said: $$\Psi(x, \ t) \ = \ \langle x \| \Psi \rangle$$ I'm not sure if a Hilbert space is the right word to use, as the wavefunctions themselves are not vectors, however, any other wavefunction in our possible state space can be expressed as a linear combination of the stationary state wavefunctions of the Hamiltonian. I'm not totally sure what you mean when you ask how the wavefunction becomes the quantum state. The point of the set of stationary state wavefunctions in the position basis is that we can write the quantum mechanical state vector as a linear combination of them. For instance, consider the position basis $$\|x\rangle$$. We can write some state vector as a linear combination of position eigenstates. Remember that: $$\displaystyle\sum_{i} \ \|v_i\rangle \langle v_i\| \ = \ \mathbb{I}$$ For any orthonormal basis as: $$\Big( \displaystyle\sum_{i} \ \|v_i\rangle \langle v_i\| \Big) \|v\rangle \ = \ \displaystyle\sum_{i} v_i \|v_i\rangle \ = \ \|v\rangle$$ Now, this also holds for a continuous sum (an integral), so we have: $$\|\Psi\rangle \ = \ \mathbb{I} \|\Psi\rangle \ = \ \displaystyle\sum \|x\rangle \langle x \| \Psi \rangle \text{d}x \ = \ \displaystyle\sum \Psi(x, \ t) \|x\rangle \text{d}x$$ Cool, so we can expand the state vector in terms of a basis of eigenstates. But we can also expand the wavefunction in terms of another basis! For example, we can then expand the position wavefuntion in terms of the energy eigenstate basis. Thus, we have: $$\langle x \| \Psi \rangle \ = \ \langle x \| \mathbb{I} \| \Psi \rangle \ = \ \langle x \| \Big( \displaystyle\sum_{n} \ \|E_n\rangle \langle E_n \| \Big) \| \Psi \rangle \ \ = \ \displaystyle\sum_{n} \ \langle x \|E_n\rangle \langle E_n \| \Psi \rangle \ = \ \displaystyle\sum_{n} c_n \Psi_n(x, \ t)$$ So we can write the state vector as the wavefunction, and we can write the wavefunction as a linear combination of stationary states, with each of the $$c_n$$ coefficients corresponding to the probability amplitude of the specific energy eigenstates, thus telling us "how much" of each $$\Psi_n(x, \ t)$$ is in $$\langle x \| \Psi \rangle$$. So to answer your question, the wavefunctions are not quantum states, they are components of the quantum states that tells us certain information about the quantum state represented in a particular basis, but we can still expand/express each one as linear combinations of vector/functions in another basis. • Suppose $H\|\psi> = E\|\psi>$ with H is $n$ dimesion matrix. Solve it like normal eigen-equation, then there will be the $n$ dimesion of basis of energy correspond to eigen value $E_n$. The eigen vector $\|\psi>$ will be $\|\psi> = \Sigma_i^n c_i \|E_i>$. Next I express each of them in term of position basis, they will be $\|\psi> = \Sigma_i^n c_i \int <x\|E_i>\|x>dx = \Sigma_i^n c_i \Psi_i(x)\|x>$. right? – Kanokpon Arm Sep 25 '19 at 5:19 • Not quite, the energy eigenstates of $H\|\psi> = E\|\psi>$ are the set $\|E_n>. You seem to try to express the energy eigenvalues in terms of themselves in the first equation. – Jack Ceroni Sep 25 '19 at 11:12 • the correct way to do this would be to find the energy eigenvalues$H\|E_n\rangle \ = \ E_n\|E_n\rangle$. If we want to find the stationary position wavefunctions, we expand these eigenvectors in terms of the position basis:$\|E_n\rangle \ = \ \displaystyle\int \ \langle x \| E_n \rangle \|x\rangle dx \ = \ \displaystyle\int \ \psi_n(x) \ \|x\rangle dx\$. – Jack Ceroni Sep 25 '19 at 12:10 • In order to recover the full state vector from the wavefunction, we need to know the initial wavefunction for the system. To find the time-dependent wavefunction, we have to express the initial wavefunction as a linear combination of the energy stationary position wave functions, then add time-dependence, then integrate over this wavefunction with respect to all the position eigenstates. – Jack Ceroni Sep 25 '19 at 12:15 A wave function can be viewed as describing a quantum state in the same way that the components of a vector can be viewed as describing the vector itself. Yes, $$\psi(x_0)=\langle x_0\vert\psi\rangle$$ is the numerical value of $$\psi(x)$$ at $$x=x_0$$ but this numerical value is basically the component of the vector $$\vert\psi\rangle$$ along the basis vector $$\vert x_0\rangle$$ (see this question), just like $$\langle \hat k\vert \vec r\rangle=r_k$$. If you prefer to work in a momentum basis, then $$\psi(p)=\langle p\vert\psi\rangle$$ and the change of basis formula is contained in the overlap $$\langle p\vert x\rangle = \frac{e^{-i px/\hbar}}{\sqrt{2\pi \hbar}}$$ so that $$\langle p\vert\psi\rangle = \int dx \langle p\vert x\rangle \langle x\vert\psi\rangle$$ just like a change of basis is given by $$r_a =\langle \hat a\vert\vec r\rangle =\sum_k \langle \hat a\vert \hat k\rangle \langle \hat k\vert \vec r\rangle=\sum_k A_{ak}r_k\, .$$ Asher Peres in Peres, Asher. "What is a state vector?." American Journal of Physics 52.7 (1984): 644-650. quotes Ekstein as stating that "states are images of procedures by which a system is made to interact with a macroscopic apparatus". The reference to the original Ekstein paper is Ekstein, H. "Presymmetry." Physical Review 153.5 (1967): 1397.	2021-07-24 05:47:46	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 38, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8999027013778687, "perplexity": 169.50820415097309}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046150129.50/warc/CC-MAIN-20210724032221-20210724062221-00228.warc.gz"}
https://cmde.tabrizu.ac.ir/article_7148.html	# Approximate solution of the fuzzy fractional Bagley-Torvik equation by the RBF collocation method Document Type : Research Paper Authors 1 Department of Mathematics, Faculty of Mathematics Science and Statistics, Malayer University, Malayer 65719-95863, Iran 2 Department of Computer Engineering and Information Technology, Hamedan University of Technology, Hamedan 65155-579, Iran Abstract In this paper, we propose the spectral collocation method based on radial basis functions to solve the fractional Bagley-Torvik equation under uncertainty, in the fuzzy Caputo's H-differentiability sense with order ($1< \nu < 2$). We define the fuzzy Caputo's H-differentiability sense with order $\nu$ ($1< \nu < 2$), and employ the collocation RBF method for upper and lower approximate solutions. The main advantage of this approach is that the fuzzy fractional Bagley-Torvik equation is reduced to the problem of solving two systems of linear equations. Determining a good shape parameter is still an outstanding research topic. To eliminate the effects of the radial basis function shape parameter, we use thin plate spline radial basis functions which have no shape parameter. The numerical investigation is presented in this paper shows that excellent accuracy can be obtained even when few nodes are used in analysis. Efficiency and effectiveness of the proposed procedure is examined by solving two benchmark problems. Keywords ### History • Receive Date: 09 February 2017 • Revise Date: 15 August 2017 • Accept Date: 26 February 2018	2021-10-23 21:10:16	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4971678853034973, "perplexity": 913.222828212427}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585768.3/warc/CC-MAIN-20211023193319-20211023223319-00574.warc.gz"}
http://accboise.com/g1nkto6u/855a78-lyman-series-formula	# lyman series formula His method was simple,although he carried out a very difficult task. n1 = 1. n2 = 2. since the electron is de-exited from 1(st) exited state (i.e n … Nobody could predict the wavelengths of the hydrogen lines until 1885 when the Balmer formula gave an Thus it is named after him. Asked on December 26, 2019 byavatar. The first line in the ultraviolet spectrum of the Lyman series was discovered in 1906 by Harvard physicist Theodore Lyman, who was studying the ultraviolet spectrum of electrically excited hydrogen gas. formula was first obtained by Johann Balmer (1885), as a special case for n = 2, and then generalised by Johannes Rydberg (1888). Lyman series of the hydrogen spectrum is 913.4\mathring {A}913.4 . So we have Rydberg's constant—1.097 times 10 to the 7 reciprocal meters— times 1 over the final energy level squared minus 1 over the initial energy level of 2 squared and then all that gets raised to the exponent negative 1 giving a maximum possible wavelength in the Lyman series of 121.5 nanometers. This basically means that you need #"13.6 eV"# to ionize a hydrogen atom. Paschen Series. ANSWER. You can use this formula for any transitions, … Using the Balmer – Rydberg formula, compute the location of the first four lines of the Lyman and Paschen series as well as their convergence limit. Historically, explaining the nature of the hydrogen spectrum was a considerable problem in physics. Make a similar graph showing all three series. Maximum wave length corresponds to minimum frequency i.e., n 1 = 1, n 2 = 2. Moreover, by assigning different values to n 1 and n 2 integers, we can get the wavelengths corresponding to the different line series such as Lyman series, Balmer series, Paschen series, etc. Your tool of choice here will be the Rydberg equation, transition, which is part of the Lyman series. where, R = Rydbergs constant (Also written is RH) Z = atomic number. Offset them vertically for clarity. Here is an illustration of the first series of hydrogen emission lines: The Lyman series. See all questions in Atoms and Electromagnetic Spectra. It is obtained in the ultraviolet region. mathematical reasoning behind them. The Lyman series concerns transitions to the ground state. could be viewed from analysis of the hydrogen spectra. In physics and chemistry, the Lyman series is a hydrogen spectral series of transitions and resulting ultraviolet emission lines of the hydrogen atom as an electron goes from n ≥ 2 to n = 1 (where n is the principal quantum number), the lowest energy level of the electron. The straight lines originating on the n =3, 4, and 5 orbits and terminating on the n = 2 orbit represent transitions in the Balmer series. (i) Using Bohr's postulates, derive the expression for the total energy of the electron in the stationary states of the hydrogen atom. To convert this to electronvolts, use the fact that, #"1 eV" = 1.6 * 10^(-19)color(white)(. Sign in\|Recent Site Activity\|Report Abuse\|Print Page\|Powered By Google Sites, Bohr Model of the Hydrogen Atom & Multi-Electron Atoms. The first thing to notice here is that when #n_i = oo#, which implies that the Rydberg equation can be simplified to this form, You can thus say that the wavelength of the emitted photon will be equal to, #lamda = 1/(1.097 * 10^7color(white)(. The Lyman series lies in the ultraviolet, whereas the Paschen, Brackett, and Pfund series lie in the infrared. E = hc/lambda, where lambda is the wavelength. Their formulas are similar to Balmer’s except that the constant term is the reciprocal of the square of 1, 3, 4, or 5, instead of 2, and the… This formula works for each of the visible lines, and was later shown to extend into the ultraviolet wavelengths, although Balmer himself did not realize this. )"m"^(-1)#, #lamda = 9.158 10^(-8)color(white)(. Since the question is asking for 1st line of Lyman series therefore. came up with his model, that these lines and Balmer’s formula would have any The same energy is needed for the transition #n = 1 -> n = oo#, which is the ionization potential for a hydrogen atom. unique formula for determining how the spectra of the hydrogen atom behaved. These observed spectral lines are due to the electron making transitions between two energy levels in an atom. Explanation: 1 λ = R( 1 (n1)2 − 1 (n2)2)⋅ Z2. This set of spectral lines is called the Lyman series. The longest wavelength line is associated with the lowest energy transition from the formula. Here is an illustration of the first series of hydrogen emission lines: Historically, explaining the nature of the hydrogen spectrum was a considerable problem in physi… Why are atomic spectra of an element discontinuous? His formula was based on the patterns of the four spectral lines that Why is the electromagnetic spectrum important? The number of lone pair and bond pair of electrons on the sulphur atom in sulphur dioxide molecule are respectively The classification of the series by the Rydberg formula was important in the development of quantum mechanics. If the transitions terminate instead on the n =1 orbit, the energy differences are greater and the radiations fall in the ultraviolet part of the spectrum. The spectrum of radiation emitted by hydrogen is non-continuous. Lyman series (n l =1) The series was discovered during the years 1906-1914, by Theodore Lyman. The Wave Number in Series: The wavenumber of a photon is the number of waves of the photon in a unit length. The λ symbol represents the wavelength, and RH is the Rydberg constant for hydrogen, with RH = 1.0968 × 107m−1. 656, 486, 434 and 410 nm corresponding to nf = 2 and ni = 3, 4, 5 and 6). The Lyman series limit corresponds to an ionization potential of 13.59 $$\text{volts}$$. A ˚.Calculate the short wavelength limit from Balmer series of the hydrogen spectrum. The Balmer series or Balmer lines in atomic physics, is the designation of one of a set of six different named series describing the spectral line emissions of the hydrogen atom.. General specification for all our ActiveX Control- Support Windows 2000/Windows XP/Windows Vista which must have the VB6 runtime environment- Support most development environment which supports ActiveX or OLE design (Visual Basic/Visual C++/C#/VB.NET/VBA/C++ Builder/Delphi and so on)- Support to read and write … You can use the Rydberg equation to calculate the series limit of the Lyman series as a check on this figure: n 1 = 1 for the Lyman series, and n 2 = infinity for the series limit. Wave length λ = 0.8227 × 10 7 = 8.227 × 10 6 m-1 The first six series have specific names: Lyman series with n 1 = 1 Balmer series with n 1 = 2 Paschen series (or Bohr series) with n 1 = 3 Brackett series with n 1 = 4 Pfund series with n 1 = 5 Humphreys series with n 1 = 6 However, Theodore Lyman analyzed the and discovered transitions that went down to the n=1 level. The Lyman Series and Others It is important to remember that the Balmer formula, and the Balmer series only focus on photons emitted from electrons that are transitioned to the n=2 level.The Lyman series deals with the same idea and principles of Balmer's work. If the transition of electron takes place from any higher orbit (principal quantum number = 2, 3, 4,…….) The wavelength (in cm) of second line in the Lyman series of hydrogen atomic spectrum is (Rydberg constant = R cm$^{-1}$) 10. For the Lyman series, nf = 1. Calculate the longest wavelength in Lyman Series. to the first orbit (principal quantum number = 1). The rest of the lines of the spectrum were discovered by Lyman from 1906-1914. Why is the electromagnetic spectrum a transverse wave? The physicist Theodore Lyman discovered the Lyman series while Johann Balmer discovered the Balmer series. It was not until Bohr Why is the electromagnetic spectrum continuous? Brackett Series Bristi Venkat. How can we calculate the Ephoton for the bandhead of the Lyman series (the transition n = ∞ → n = 1 for emission) in joules and in eV? The key difference between Lyman and Balmer series is that Lyman series forms when an excited electron reaches the n=1 energy level whereas Balmer series forms when an excited electron reaches the n=2 energy level.. Lyman series and Balmer series are named after the scientists who found them. He found a simple formula for the observed wavelengths: Further, for n=∞, you can get the limit of the series at a wavelength of 364.6 nm. According to Bohr’s model, Lyman series is displayed when electron transition takes place from higher energy states (nh=2,3,4,5,6,…) to nl=1 energy state. This is the ActiveX Control for MELSEC Q Series, Support Q Series CPUs. Balmer realized that the four visible lines from the spectra of Hydrogen must have different wavelengths, as shown in the table below. Setting n 1 to 1 and running n 2 from 2 to infinity yields the Lyman series. Also, you can’t see any lines beyond this; only a faint continuous spectrum.Furthermore, like the Balmer’s formula, here are the formulae for the other series: Lyman Series. ) the series by the Rydberg formula until a pattern was discovered, and then used this create! For MELSEC Q series, Support Q series, Support Q series CPUs astronomical! ) the series by the Rydberg formula may be applied to hydrogen obtain... 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Line is associated with the lowest energy transition is simply from the next level above the ground state n. Four visible lines from the spectra of hydrogen emission lines: the Lyman series the! Balmer discovered the Lyman series of hydrogen and calculating red shifts written is RH ) =... Photon is the ActiveX Control for MELSEC Q series, Support Q series CPUs # to a. First series of the series was discovered, and then used this to create his famous.! '' # R = Rydbergs constant ( Also written is RH ) Z atomic! To hydrogen to obtain its spectral lines are due to the n=1 level next level the., 486, 434 and 410 nm corresponding to nf = 2 and ni = 3, 4,.. Here will be the Rydberg formula may be applied to hydrogen to obtain its spectral lines rest... The formula λ = R ( 1 ( n1 ) 2 − (! The photon in a unit length unique formula for any transitions, … the Lyman series of hydrogen calculating! Series of the hydrogen spectrum is 913.4\mathring { a } 913.4 this basically that! Electron takes place from any higher orbit ( principal quantum number = 2 ni. 1885, Swiss physicist Johann Balmer developed a unique formula for any,. Calculating red shifts white ) ( series of the lines of the four lines... With the lowest energy transition is simply from the next level above the ground state figs... Of spectral lines is called the Lyman series ( n l =1 ) the was... Is simply from the formula from the next level above the ground state 2 to infinity yields Lyman... Transition of electron takes place from any higher orbit ( principal quantum number = 2, 3 4. ( n l =1 ) the series by the Rydberg formula was important in astronomical spectroscopy detecting... From any higher orbit ( principal quantum number = 2, 3, 4, 5 and 6.... Ev '' # to ionize a hydrogen atom eV '' # visible lines from the.! Wavelengths given by the Rydberg formula may be applied to hydrogen to obtain its spectral lines due!	2023-03-23 08:03:59	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8496023416519165, "perplexity": 1050.2072722038542}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945030.59/warc/CC-MAIN-20230323065609-20230323095609-00739.warc.gz"}
https://projecteuclid.org/euclid.ade/1495850457	## Advances in Differential Equations ### Local stabilization of compressible Navier-Stokes equations in one dimension around non-zero velocity #### Abstract In this paper, we study the local stabilization of one dimensional compressible Navier-Stokes equations around a constant steady solution $(\rho_s, u_s)$, where $\rho_s>0, u_s\neq 0$. In the case of periodic boundary conditions, we determine a distributed control acting only in the velocity equation, able to stabilize the system, locally around $(\rho_s, u_s)$, with an arbitrary exponential decay rate. In the case of Dirichlet boundary conditions, we determine boundary controls for the velocity and for the density at the inflow boundary, able to stabilize the system, locally around $(\rho_s, u_s)$, with an arbitrary exponential decay rate. #### Article information Source Adv. Differential Equations Volume 22, Number 9/10 (2017), 693-736. Dates First available in Project Euclid: 27 May 2017 Permanent link to this document	2018-04-23 11:29:05	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7656324505805969, "perplexity": 505.3308932762702}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125945942.19/warc/CC-MAIN-20180423110009-20180423130009-00141.warc.gz"}
http://www.cs.nyu.edu/pipermail/fom/2009-May/013666.html	# [FOM] P-point/notation T.Forster@dpmms.cam.ac.uk T.Forster at dpmms.cam.ac.uk Thu May 21 15:39:51 EDT 2009 I hope you will get a reply from someone better informed than i... My understanding is that the terminology comes from banach spaces: a p-point is a point such that a countable intersection of neighborhoods of it is also open. P-point ultrafilters have this property in the usual (stone) topology on ultrafilters. But, as i say, i hope you will get a fuller story from an expert. On May 21 2009, pax0 at seznam.cz wrote: > Hi, can someone please tell me, why certain ultrafilters on \omega are > called "P-points" : what "P" means here? And the associated property of > forcing notions, the "PP property": what "PP" stands for here? I would > just like to know what are these named after, not any definitions. Thank > you, Jan Pax _______________________________________________ FOM mailing > list FOM at cs.nyu.edu http://www.cs.nyu.edu/mailman/listinfo/fom	2015-11-29 17:42:57	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7767341732978821, "perplexity": 4981.206704733165}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398459214.39/warc/CC-MAIN-20151124205419-00238-ip-10-71-132-137.ec2.internal.warc.gz"}
http://en.wikipedia.org/wiki/Marconi's_law	# Marconi's law Marconi's law is the relation between height of antennas and maximum signaling distance of radio transmissions. Guglielmo Marconi enunciated at one time an empirical law that, for simple vertical sending and receiving antennas of equal height, the maximum working telegraphic distance varied as the square of the height of the antenna. It has been stated that the rule was tested in experiments made on Salisbury Plain in 1897, and also by experiments made by Italian naval officers on behalf of the Royal Italian Navy in 1900 and 1901. Captain Quintino Bonomo gave a report of these experiments in an official report.[citation needed] ## Description If H is the height of the antenna and D the maximum signalling distance in meters, then we have, according to Marconi's law $H = c \sqrt{D}$, where c is some constant. c D Apparatus 0.17–0.19 60 kilometres (37 mi) Marconi's original apparatus 0.15–0.16 60 kilometres (37 mi) Same, with longer sending spark 0.12–0.14 136 kilometres (85 mi) Marconi's improved apparatus, with jigger[1][2] in receiver 0.23–0.15 143 kilometres (89 mi) The same, but with Italian Navy telephonic receiver Marconi's law can be deduced theoretically as follows:[3] Hertz has shown that at large distances compared with their length, the magnetic force of a linear oscillator varies inversely to the distance. The maximum value of the current set up in any given receiving antenna varies as its length, also as the magnetic force of the waves incident on it, and as the maximum value of the current in the transmitting antenna. Hence, if the magnetic force of the waves incident on a receiving antenna of height and if the distance between the sending and receiving antenna, and if the maximum values of the currents in the sending and receiving antenna, we have various charging voltage of the current in the sending antenna which varies very nearly as its capacity — that is, as its height — and if the sending antenna has the same height as the receiving aerial, we have some constant. For any given receiving apparatus a certain constant minimum value of the maximum current in the receiving antenna is necessary to cause a signal. Therefore it follows that with given receiving and sending apparatus, we must have a constant. That is, the maximum signalling distance with given apparatus will vary as the square of the height of the antenna. The above law is, however, much interfered with by the nature of the surface over which the propagation takes place.	2014-09-23 01:10:42	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5720363259315491, "perplexity": 1014.3869842487685}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657137841.57/warc/CC-MAIN-20140914011217-00177-ip-10-234-18-248.ec2.internal.warc.gz"}
https://stats.stackexchange.com/questions/44929/probability-of-independent-events-given-the-history	Probability of independent events given the history I am having some trouble understanding something that feels very basic in probability theory concerning the past history of repeated independent events. Consider the tossing of a fair coin. $P(\text{head}) = P(\text{tail}) = 0.5$. Repeated tosses are independent events. Let's say that we already have four Heads in a row. Here's my dilemma: The probability of the next toss result being head = $0.5$, if I think of this as an independent event. But the probability of getting five heads in a row = $0.5^5$ given the history of the tossing. Aren't these statements conflicting? Does the probability of the next toss being a head really differ? So, if were to bet on the outcome, would it be any better to bet on tails? I can think of rationales for both cases but I can't wrap my mind around how both probabilities for a head can co-exist. An explanation would be deeply appreciated. • Your coin doesn't know anything about the previous flips. It's a 50% chance regardless of what has already happened. – bill_080 Dec 2 '12 at 22:36 The second statement is simply wrong. $P(HHHHH \| HHHH) = 0.5$, not $0.5^5$. (Here I mean the probability of $5$ heads in a row, given that the first $4$ are heads. Gung is using different notation.) The probability of $A$ given $B$ is $P(A\|B) = \frac{P(A \text{and} B)}{P(B)}$ which in this case would be $\frac{0.5^5}{0.5^4} = 0.5$. See conditional probability. Perhaps you have it confused with $P(A~\text{and}~B)$. Flawed human intuitions: This is a very common and pernicious confusion. You can read about this under the Wikipedia entry for the Gambler's Fallacy. Psychologists have also studied this phenomenon. Amos Tversky and Daniel Kahneman documenting it in their famous paper Belief in the law of small numbers (the title plays on the law of large numbers in statistics, discussed below). Theoretical work on cognitive mechanisms that help to produce this fallacy has been done by Ruma Falk and Clifford Konold (see, e.g., their paper, Making sense of randomness: Implicit encoding as a basis for judgment; more citations here). Runs: When you notice several heads in a row, you are perceiving a run. The (perfectly intuitive) belief is that runs are unlikely, thus, either the coin must not be fair, or it must revert to tails soon. Indeed, this intuition has been formalized by statisticians into a test for randomness / independence (i.e., the runs test). One thing to realize is that with lots of flips (a long series), runs of length 4 (for example) are actually quite common. Here is a quick simulation I ran to check how often I would see 4 or more of the same result in a row, given series of Bernoulli trials of lengths 20 and 50: isRun = function(x){ runL = 1 maxR = 1 # we iterate through the length of the series for(i in 2:lx){ # this increments the run length if the result is the same, # but restarts the counter otherwise runL = ifelse(x[i]-x[i-1]==0, runL+1, runL<-1) # if the current run length is longer than the previous max, # the new value is used maxR = ifelse(runL>maxR, runL, maxR) } return(maxR) } r4.20 = c() # these will store the results r4.50 = c() set.seed(1) # this makes the code reproducible for(i in 1:10000){ x20 = rbinom(20, size=1, prob=.5) # we generate series of length 20 & 50 x50 = rbinom(50, size=1, prob=.5) r4.20[i] = ifelse(isRun(x20)>3,1,0) # if the maximum run length is 4 or longer r4.50[i] = ifelse(isRun(x50)>3,1,0) } mean(r4.20) # [1] 0.7656 # ~77% of series mean(r4.50) # [1] 0.9796 # ~98% But what if you've only flipped your coin 4 times (thus far)? The probability of getting the same result 4 times is $$.5^4=.0625$$. Given that people flip coins commonly, this should happen quite often (more than one time in twenty). Convergence to long run probability: What about the fact that the number of heads in your series should converge to half the length of the series? This is true; it is guaranteed by the law of large numbers. The relative proportion is likely to converge fairly quickly (for example, there is a 95% probability that the percentage will be within 2 standard errors of the true probability, $$\pi$$, where $$S.E.(p) = \sqrt{\pi(1-\pi)/N}.$$ Thus, when the true probability is .5, and $$N=5$$, 95% of the time the proportion of heads should fall within $$.5\pm 2\times .5/\sqrt{5} = .5\pm 2\times .224 = (.052,.948)$$, and with $$N=100, (.4,.6)$$. (Actually, the normal approximation is imperfect the first case, because the N is small.) However, it will still fall outside of that interval 5% of the time. Importantly, although the series will converge to .5, there's no guarantee until you 'reach' infinity. In addition, the convergence is due as much to the growing denominator as it is to the numerator being $$.5\times N$$; that is, the number of heads can be very far from half in raw numbers, but close as a proportion of the total. Random variables vs. Realized values: While it is helpful to understand something about the intuitions that lead us astray and the true mathematical properties that govern these phenomena, the key concept is understanding the distinction between random variables and realized values. When you have a coin balanced on your thumb about to be flipped 5 times in a row, those outcomes are random variables, and the laws of probability apply to how they will behave in the long run. When the coin is laying on your forearm with one side facing up (whether you have yet seen which side or not), that outcome is a realized value. The laws of probability don't make impossible what has already happened (nor could they). Thus, $$Pr(H)=.5$$, and $$Pr(H\|HHHH)=.5$$ as well, because the four H's on the right side of the vertical bar (the given 4 prior outcomes) are realized values, not random variables, and are not related to the probability that the outcome of the next flip will be a head (at least under independence; with dependent data, the prior result must be a part of, or stored somehow within, the data generating process). Likewise, $$Pr(HHHHH)=.03125$$, and $$Pr(HHHHH\|HHHH)=.03125$$. I'll acknowledge that this still isn't necessarily very intuitive; you have millennia of evolution to overcome. Nonetheless, I have found that these considerations have helped me, and others, to think about randomness more clearly. Note that this discussion pertains to the Frequentist conception of probability. The notions of independence in the presence of information that is being accumulated over time can be adequately captured through sigma-algebras. If the name sigma algebra sounds daunting, consider it as an information set at an instant of time. For example, let $X_i$ denote 1 or 0 respectively based on whether the $i^{th}$ toss results in a head or tail. The sigma algebra $\mathcal{F}_0$ is a trivial sigma algebra as there is no information prior to the experiment. As time progresses, we perform the experiment and build information. For example, while $X_4$ is the random variable which is 1 or 0 depending on the outcome of the fourth toss, $X_4\|\mathcal{F}_4$ is a constant - 0 or 1 depending on what you got in your fourth toss. Similarly $X_5\|\mathcal{F}_4=X_5$ is a random variable as the outcome $X_5$ is independent of the information contained in $\mathcal{F}_4$. For your query, the outcome prior to the experiment, $P(X_1=1, X_2=1,\ldots X_5=1\|\mathcal{F}_0)=E(X_1X_2X_3X_4X_5\|\mathcal{F}_0)=E(X_1X_2X_3X_4X_5)=\frac{1}{2^5}$. After four tosses, we have to look at a different probability: $P(X_5=1\|\mathcal{F}_4)=E(X_5\|\mathcal{F}_4)=E(X_5)=0.5$. The penultimate equality comes about from the independence of $X_5$ from prior tosses. • While the response makes perfect sense to me mathematically, I am not sure I understand the difference between P(X1=1,...\|F0) and P(X5\|F4) from a real-world point of view.The fifth toss being a head is just a single event. It still sounds like the probability of the event is a constants 0.5 (due to independence) but it is also (.5)^5 when I see it as five heads occurring in a row. Can you explain the intuition in the difference there? – Aravind Dec 2 '12 at 18:56 • @Aravind: The main difference is the probability you are concerned with. It is 0.5^5 when you look at $P(X1=1,X2=1... X5=1)$ and 0.5 when you look at $P(X5=1)$. In the latter case you have summed over all other $X$s, i.e., $P(X5=1)=\sum_{x1,x2,x3,x4}P(X1=x1,X2=x2... X5=1)$. – Bravo Dec 2 '12 at 19:47 The question can be simplified by considering just two coin flips. The result of flips 1 and 2 are $$r_1$$ and $$r_2$$. There are perhaps three quantities which are lurking in the background of the question and need to be clearly distinguished. The marginal probability of the second toss coming up heads: $$$$\mathrm{prob}(r_2 = H \| \mathcal{I}) = 0.5$$$$ The conditional probability of the second toss coming up heads, given that the first comes up heads: $$$$\mathrm{prob}(r_2 = H \| r_1 = H, \mathcal{I}) = \mathrm{prob}(r_2 = H \| \mathcal{I}) = 0.5$$$$ The joint probability of the first and second toss coming up heads: \begin{align} \mathrm{prob}(r_2 = H, r_1 = H \| \mathcal{I}) &= \mathrm{prob}(r_2 = H \| r_1 = H, \mathcal{I}) \: \mathrm{prob}(r_1 = H \| \mathcal{I}) \\ &= \mathrm{prob}(r_2 = H \| \mathcal{I}) \: \mathrm{prob}(r_1 = H \| \mathcal{I}) \\ &= 0.5 \cdot 0.5 = 0.25 \end{align}	2020-01-21 09:22:21	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 16, "wp-katex-eq": 0, "align": 1, "equation": 2, "x-ck12": 0, "texerror": 0, "math_score": 0.918900191783905, "perplexity": 482.8660585867828}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250601628.36/warc/CC-MAIN-20200121074002-20200121103002-00404.warc.gz"}
https://socratic.org/questions/how-do-you-identify-all-vertical-asymptotes-for-f-x-3x-2-x-5-x-2-1	# How do you identify all vertical asymptotes for f(x)=(3x^2+x-5)/(x^2+1)? ##### 2 Answers Write your answer here... Start with a one sentence answer Then teach the underlying concepts Don't copy without citing sources preview ? #### Answer Write a one sentence answer... #### Explanation Explain in detail... #### Explanation: I want someone to double check my answer Describe your changes (optional) 200 1 Jan 10, 2017 #### Answer: None. See the graph and explanation. #### Explanation: By actual division, f = 3+(x-8)/(x^2+1) y = quotient = 3 and the factors of the denominator (x+i)(x-i) of the remainder = 0 give the asymptotes. The graph is asymptote-inclusive. So, the only real asymptote is the horizontal asymptote y = 3. graph{(y(x^2+1)-3x^2-x+5)(y-3)=0 [-20, 20, -10, 10]} Was this helpful? Let the contributor know! Write your answer here... Start with a one sentence answer Then teach the underlying concepts Don't copy without citing sources preview ? #### Answer Write a one sentence answer... #### Explanation Explain in detail... #### Explanation: I want someone to double check my answer Describe your changes (optional) 200 1 Gió Share Jan 10, 2017 #### Answer: Your function shouldn't have any vertical asymptote. #### Explanation: The vertical asymtote is found at values of $x$ that makes the denominator equal to zero (and so creating a discontinuity) but the denominator of your function will never be zero regardless of the real value of $x$ you may choose. You can also see this graphically: graph{(3x^2+x-5)/(x^2+1) [-9.12, 10.88, -13.76, -3.76]} Was this helpful? Let the contributor know! ##### Just asked! See more • 12 minutes ago • 14 minutes ago • 23 minutes ago • 25 minutes ago • 13 seconds ago • 3 minutes ago • 4 minutes ago • 5 minutes ago • 6 minutes ago • 11 minutes ago • 12 minutes ago • 14 minutes ago • 23 minutes ago • 25 minutes ago	2017-09-22 07:53:29	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 2, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9258209466934204, "perplexity": 10562.354566679862}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818688926.38/warc/CC-MAIN-20170922074554-20170922094554-00263.warc.gz"}
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(variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error 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(variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Liquid error (variable-products-thumbnail-product-loop line 98): include usage is not allowed in this context Blackbird from \$800.00 USD SD from \$765.00 USD Dwart from \$800.00 USD The Keg from \$765.00 USD 419Fish from \$765.00 USD Miso from \$800.00 USD What? from \$765.00 USD Twin Fin from \$800.00 USD New Traveler from \$810.00 USD Egg Not from \$855.00 USD Hatchet from \$800.00 USD Express from \$1,055.00 USD	2022-09-28 16:35:14	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, 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https://www.physicsforums.com/threads/mechanics-of-materials-simple-moment-question.290627/	# Mechanics of Materials: Simple moment question? 1. Feb 7, 2009 ### Seraph042 1. The problem statement, all variables and given/known data A long retaining wall is braced by wood shores set at an angle of 30 degrees and supported by concrete thrust blocks. The shores are evenly spaced, 3m apart. For analysis purposes, the wall and shored are idealized. Note that the base of the wall and both ends of the shored are assumed to be pinned. The pressure of the soil against the wall is assumed to be triangularly distributed, and the resultant force action on a 3m length of the wall is 190 kN. If each shore has a 150mm x 150mm square cross-section, what is the compressive stress on part C in the shores? 2. Relevant equations This is in part 1.2 of my book, labeled 'Normal Stress and Strain', and they give equations of moments as: Mx = P$$\overline{y}$$ My = -P$$\overline{x}$$ http://img101.imageshack.us/img101/9463/128mn6.th.png [Broken] 3. The attempt at a solution I honestly have no idea where to begin, the book has been no help with these problems, as there is almost no information or examples on how to solve this type of problem.	2017-08-23 17:13:41	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5035208463668823, "perplexity": 942.6311994929076}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886120573.75/warc/CC-MAIN-20170823152006-20170823172006-00608.warc.gz"}
https://msp.org/pjm/2018/296-2/pjm-v296-n2-p04-p.pdf	Vol. 296, No. 2, 2018 Recent Issues Vol. 305: 1 Vol. 304: 1 2 Vol. 303: 1 2 Vol. 302: 1 2 Vol. 301: 1 2 Vol. 300: 1 2 Vol. 299: 1 2 Vol. 298: 1 2 Online Archive Volume: Issue: The Journal Editorial Board Subscriptions Officers Special Issues Submission Guidelines Submission Form Contacts ISSN: 1945-5844 (e-only) ISSN: 0030-8730 (print) Author Index To Appear Other MSP Journals Length spectra of sub-Riemannian metrics on compact Lie groups András Domokos, Matthew Krauel, Vincent Pigno, Corey Shanbrom and Michael VanValkenburgh Vol. 296 (2018), No. 2, 321–340 Abstract Length spectra for Riemannian metrics have been well studied, while sub-Riemannian length spectra remain largely unexplored. Here we give the length spectrum for a canonical sub-Riemannian structure attached to any compact Lie group by restricting its Killing form to the sum of the root spaces. Surprisingly, the shortest loops are the same in both the Riemannian and sub-Riemannian cases. We provide specific calculations for $SU\left(2\right)$ and $SU\left(3\right)$. However, your active subscription may be available on Project Euclid at https://projecteuclid.org/pjm We have not been able to recognize your IP address 35.175.121.230 as that of a subscriber to this journal. Online access to the content of recent issues is by subscription, or purchase of single articles. or by using our contact form.	2020-04-02 19:42:15	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3158451020717621, "perplexity": 4310.119677954371}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370507738.45/warc/CC-MAIN-20200402173940-20200402203940-00194.warc.gz"}
https://math.stackexchange.com/questions/2304650/how-to-calculate-product-prod-k-0n-1-left-1-frac122k-right/2304966	# How to calculate product $\prod_{k=0}^{n-1}\left (1+\frac{1}{2^{2^k}}\right)$? How can I calculate the following product of series? $$\prod_{k=0}^{n-1}\left (1+\frac{1}{2^{2^k}}\right)$$....Can I take a geometric series and compare it with that? Multiply through by $\frac12=1-\frac1{2^{2^0}}$ to get \begin{align}\left(1-\frac1{2^{2^0}}\right)\prod_{k=0}^n\left(1+\frac1{2^{2^k}}\right)&=\left(1-\frac1{2^{2^0}}\right)\left(1+\frac1{2^{2^0}}\right)\prod_{k=1}^n\left(1+\frac1{2^{2^k}}\right)\\&=\left(1-\frac1{2^{2^1}}\right)\left(1+\frac1{2^{2^1}}\right)\prod_{k=2}^n\left(1+\frac1{2^{2^k}}\right)\\&=\left(1-\frac1{2^{2^2}}\right)\left(1+\frac1{2^{2^2}}\right)\prod_{k=3}^n\left(1+\frac1{2^{2^k}}\right)\\&=\left(1-\frac1{2^{2^3}}\right)\left(1+\frac1{2^{2^3}}\right)\prod_{k=4}^n\left(1+\frac1{2^{2^k}}\right)\\&=\quad\vdots\\&=\left(1-\frac1{2^{2^{n+1}}}\right)\end{align} $$\prod_{k=0}^n\left(1+\frac1{2^{2^k}}\right)=2-\frac1{2^{2^{n+1}-1}}$$ As a hint, consider $n = 3$: $\displaystyle\prod_{k = 0}^{2}\left(1+\dfrac{1}{2^{2^k}}\right) = \left(1+\dfrac{1}{2^1}\right)\left(1+\dfrac{1}{2^2}\right)\left(1+\dfrac{1}{2^4}\right)$ $= 1 + \dfrac{1}{2^1} + \dfrac{1}{2^2} + \dfrac{1}{2^1} \cdot \dfrac{1}{2^2} + \dfrac{1}{2^4} + \dfrac{1}{2^1} \cdot \dfrac{1}{2^4} + \dfrac{1}{2^2} \cdot \dfrac{1}{2^4} + \dfrac{1}{2^1} \cdot \dfrac{1}{2^2} \cdot \dfrac{1}{2^4}$ $= 1 + \dfrac{1}{2^1} + \dfrac{1}{2^2} + \dfrac{1}{2^3} + \dfrac{1}{2^4} + \dfrac{1}{2^5} + \dfrac{1}{2^6} + \dfrac{1}{2^7}$ $= 2-\dfrac{1}{2^7}$ Can you generalize this for larger values of $n$? • I'd love to see the full proof, as multiplying products out is quite a tedious thing. – Simply Beautiful Art May 31 '17 at 19:53 This is really the same as JimmyK4542's answer, but written in the general case. If you expand the product, you find that it is the sum of all possible terms of the form $$\frac{1}{2^{a_0 + a_1 2 + a_2 2^2 + \dots + a_{n-1}2^{n-1}}}$$ where each $a_i$ is either $0$ or $1$. Viewing the exponents as integers written in binary, they run though all integers $j = 0, 1, 2, \dots 2^n - 1$. We therefore find that the product is equal to $$\sum_{j = 0}^{2^n - 1} \frac{1}{2^j} = 2 - \frac{1}{2^{2^n - 1}}.$$ • why is this not getting many upvotes, that was genius – Oussama Boussif Jun 1 '17 at 2:20 If I were you, I would first simplify that to $$1+\frac{1}{2^{2^k}}=\frac{2^{2^k}+1}{2^{2^k}}$$ and so we have $$\prod_{k=1}^{n-1}\frac{2^{2^k}+1}{2^{2^k}}$$ By splitting this up, we get $$\prod_{k=1}^{n-1}\frac{1}{2^{2^k}}\prod_{k=1}^{n-1}\big(2^{2^k}+1\big)$$ Your insight about there being geometric series is correct, because look what happens when we evaluate the first product: $$\frac{1}{2^{2^1}}\frac{1}{2^{2^2}}...\frac{1}{2^{2^{n-1}}}$$ $$\frac{1}{2^{2^1+2^2+...+2^{n-1}}}$$ $$\frac{1}{2^{2^n-1}}$$ So we have $$\frac{1}{2^{2^n-1}}*\prod_{k=1}^{n-1}\big(2^{2^k}+1\big)$$ I'm afraid that's all I've got... I have no idea how to evaluate that last part. • 1) the sum of the geometric series would be $2^{2^n-1}$ if the product went from $0$ (not 1) to $n-1$; 2) to evaluate the last part, it should be followed Simply Beautiful Art's method: to multiply by $2^{2^0}-1$ and it will boil down to $2^{2^n}-1.$ – farruhota Jun 1 '17 at 10:52	2020-02-21 09:36:43	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6343631148338318, "perplexity": 218.94453235598397}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875145500.90/warc/CC-MAIN-20200221080411-20200221110411-00477.warc.gz"}
https://pendulumedu.com/qotd/quantitative-aptitude-mensuration-12-october-2020	Question of The Day12-10-2020 The ratio of volume and curved surface area of a cone is $$2\sqrt5 : 3$$. If the difference between radius and height of the cone is 5 cm, then what will be the curved surface area (in cm2) of the cone? Correct Answer : c ) $$50\sqrt5π$$ Explanation : Let us assume r, h, and L be the radius, height and slant height of the cone. According to the question, $${Volume \ of \ cone \over Curved \ surface \ area \ of \ cone}={{1\over3 }πr^2h \over πrL}$$ $${{1\over3 }πr^2h \over πrL}={2\sqrt5\over 3}$$ $${rh\over3L}={2\sqrt5\over3}$$ $$rh=2\sqrt5L$$ …. (1) Now, we know for a cone r2+h2=L2…….(2) According to the question, r – h = 5 …… (3) Squaring both sides, we get, r2 + h2 – 2rh = 25 …. (4) From equation 2 and 4 25 + 2rh = L2 Now, from equation 1 $$25+2×2\sqrt5L=L^2$$ $$L^2-4\sqrt5 L-25=0$$ $$L^2-5\sqrt5L+\sqrt5L-25=0$$ $$L(L-5\sqrt5)+\sqrt5(L-5\sqrt5)=0$$ $$L=5\sqrt5$$, and $$L=-\sqrt5\ (Not \ possible)$$ Thus, $$L=5\sqrt5$$ Putting value of L in equation 1 $$rh=2\sqrt5×5\sqrt5$$ ⇒ rh = 50 …. (5) From equation 3 and 5 Radius of cone = 10 cm and height of cone = 5 cm Therefore, Curved surface area of cone=$$πrL$$ $$π×10×5\sqrt5=50\sqrt5π$$ Hence, (c) is the correct answer. Such type of question is asked in various government exams like SSC CGL, SSC MTS, SSC CPO, SSC CHSL, RRB JE, RRB NTPC, RRB GROUP D, RRB OFFICER SCALE-I, IBPS PO, IBPS SO, RRB Office Assistant, IBPS Clerk, RBI Assistant, IBPS RRB OFFICER SCALE 2&3, UPSC CDS, UPSC NDA etc. Read Daily Current Affairs, Banking Awareness, Hindi Current Affairs, Word of the Day, and attempt free mock tests at PendulumEdu and boost your preparation for the actual exam. 0	2023-01-29 02:05:52	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6079705357551575, "perplexity": 9112.482462322296}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499697.75/warc/CC-MAIN-20230129012420-20230129042420-00129.warc.gz"}
https://math.stackexchange.com/questions/4257386/given-the-gcd-and-lcm-of-n-positive-integers-how-many-solutions-are-there	Given the GCD and LCM of n positive integers, how many solutions are there? Question: Suppose you know $$G:=\gcd$$ (greatest common divisor) and $$L:=\text{lcm}$$ (least common multiple) of $$n$$ positive integers; how many solution sets exist? In the case of $$n = 2$$, one finds that for the $$k$$ distinct primes dividing $$L/G$$, there are a total of $$2^{k-1}$$ unique solutions. I am happy to write out a proof of the $$n = 2$$ case if desirable, but my question here concerns the more general version. The $$n=3$$ case already proved thorny in my explorations, so I would be happy to see smaller cases worked out even if responders are unsure about the full generalization. Alternatively: If there is already an existing reference to this problem and its solution, then a pointer to such information would be most welcome, too! • @Yorch Your comment only links to the question in the case where $n=2$; for me, this case was no trouble! I am asking, specifically, about the general case: Where you have positive integers $\{a_1, \ldots, a_n\}$. Sep 22 '21 at 15:53 • do you require that the $n$ positive integers be distinct? Are you trying to count the multisets? I think that is the only version I haven't been able to solve. Sep 22 '21 at 16:04 • @Yorch No requirement that the integers be distinct and/but (ideally!) counting distinct solutions. If you think that you can make traction on a modified version (i.e. imposing additional constraints) then I'd still be pleased to see what you come up with. Sep 22 '21 at 16:08 If you are interested in counting tuples $$(a_1,a_2,\dots,a_n)$$ such that $$\gcd(a_1,\dots,a_n) = G$$ and $$\operatorname{lcm}(a_1,\dots,a_n) = L$$ then we can do it as follows. If $$L/G = \prod\limits_{i=1}^s p_i^{x_i}$$ then each $$a_i$$ must be of the form $$G \prod\limits_{j=1}^s p_i^{y_{i,j}}$$ with $$0 \leq y_{i,j} \leq x_i$$. Hence for each prime $$p_i$$ we require that the function from $$\{1,\dots, n\}$$ to $$\mathbb N$$ that sends $$j$$ to $$y_{i,j}$$ be a function that hits $$0$$ and $$x_i$$. The number of such functions is easy by inclusion-exclusion for $$x_i \geq 1$$, it is $$(x_i+1)^n - 2(x_i)^n + (x_i-1)^n$$. It follows the total number of tuples is $$\prod\limits_{i=1}^s ( (x_i+1)^n - 2x_i^n + (x_i-1)^n)$$. • Counting tuples as in, with repetition, right? E.g. $(1,2)$ and $(2,1)$ would each be counted in your computation? If so, isn't it the case that (using your notation) you could assign the $s$ distinct primes (to their various powers) as divisors of any of the $n$ integers or a subset of them (e.g. to $\{a_1, a_3, a_7\}$)? There are $2^n$ subsets of $\{a_1, \ldots, a_n\}$, but we exclude the full set (this is the $\gcd$) as well as the empty set for a total of $2^{n} - 2$ subsets. Assigning the aforementioned $s$ primes can now be done in in $s^{2^{n} - 2}$ ways. Or have I misunderstood? Sep 22 '21 at 17:17 • Yes, that is what it looks like when no prime appears more than once in $L/G$, you would get $(2^n-2)^s$@BenjaminDickman , when you have a prime with exponent greater than $1$ dividing $L/G$ it becomes more complex. Sep 22 '21 at 17:49 • lets consider $G=1$ and $L=8$ and $n = 3$. Here we must have that each $a_i$ is one of $1,2,4,8$, and we require that at least one of them is $1$ and at least one of them is $8$, there are $4^3$ total tuples, there are $3^3$ tuples that don't hit the value one, there are $3^3$ that don't hit the value $8$ and there are $2^3$ that don't hit etiher, so there are $4^3-2(3^3) + 2^3$ total triples that work. Sep 22 '21 at 18:08 • Ah, great! I have also been pointed to this same answer as Theorem 2.7 here: derby.openrepository.com/handle/10545/583372 (I may add an answer to this effect) Sep 22 '21 at 19:34 • The case $G,L$ is the same as the case $1,L/G$ Sep 23 '21 at 16:39 (Adding this community wiki answer to point out a relevant reference.) I was recently pointed to the following paper, in which this and related problems are proposed and solved: Bagdasar, O. (2014.) "On some functions involving the lcm and gcd of integer tuples." Scientific Publications of the State University of Novi Pazar Series A: Applied Mathematics, Informatics and mechanics, 6(2):91-100. PDF (no paywall). The result appears as Theorem 2.7 (cf. the comment of Yorch, too):	2022-01-23 03:00:56	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 26, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8209962248802185, "perplexity": 224.42383233340095}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320303956.14/warc/CC-MAIN-20220123015212-20220123045212-00715.warc.gz"}
https://meridian.allenpress.com/jiest/article-abstract/49/1/48/151015/Enveloping-the-Shock-Response-Spectrum-SRS-Does?redirectedFrom=fulltext	When the shock response spectrum (SRS) of a test envelops the SRS of the environment at all frequencies for a given mechanical system, typically the assumption is that a conservative test will result; that is, the peak response observed in the environment will be less than the peak response observed in the test. Other suggested measures characterizing a shock include the Fourier energy spectrum (with the assumption that the energy is larger in the test than in the environment), input duration (if the duration of the test is shorter than the duration of the environment), and peak velocity or pseudo velocity (if the peak velocity is greater in the test than in the environment). If these assumptions are met the test will be conservative. This paper shows that a test that complies with all of the suggested measures mentioned above could still produce a response that is smaller than the response from a hypothetical baseline environment. This content is only available as a PDF.	2021-05-12 08:13:31	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.814153790473938, "perplexity": 488.72087521361345}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991685.16/warc/CC-MAIN-20210512070028-20210512100028-00097.warc.gz"}
https://dsp.stackexchange.com/questions/65897/nyquist-shannon-sampling-theorem-implications-on-matching-data-records	# Nyquist-Shannon sampling theorem: implications on matching data records? I have two data records $$R_1$$ and $$R_2$$ with sampling periods $$T_1$$ and $$T_2$$, where $$T_1$$ < $$T_2$$. These records arise from sampling and filtering two signals to remove any noise (including aliasing noise) from signals with shorter periods. This implies that the data in $$R_1$$ and $$R_2$$ are not instantaneous observations but represent average states on time scales of $$T_1$$ and $$T_2$$, respectively. I want to fit a model $$R_2 = f(R_1)$$ and, thus, I want to match the two records as if they would've been sampled simultaneously, i.e., as if they would have the same sampling period. I tried this by • (A) Upsampling $$R_2$$ to $$T_1$$; • (B) Downsampling $$R_1$$ to $$T_2$$; • (C) Downsampling both, $$R_1$$ and $$R_2$$ to $$2 \cdot T_2$$. Afterwards I evaluated the performance of the model with cross-validation and found that the best match was obtained with (C). I believe this is a consequence of the Nyquist-Shannon theorem, which says that $$R_2$$ contains complete information only from signals with periods of $$2 \cdot T_2$$ or longer, while events with shorter periods (for instance, $$T_1$$) are not resolved by $$R_2$$. This means that I cannot determine accurately the relation $$R_2 = f(R_1)$$ at periods shorter than $$2 \cdot T_2$$. Therefore, the Nyquist-Shannon theorem seem to have obvious implications on how to match two records: For instance, to upsample $$R_2$$ as to match $$T_1$$ would not be correct, since we have inaccurate information about $$R_2$$ on the time scale $$T_1$$. On the contrary, observing the Nyquist-Shannon theorem implies matching the two signals by downsampling both of them to a period of $$2 \cdot T_2$$ (or longer), a time scale where both records would contain accurate information. My questions are: 1. Is this notion correct, i.e., is the downsampling of both records to $$2 \cdot T_2$$ the correct way of matching the sampling period of $$R_1$$ and $$R_2$$? 2. If yes, could somebody provide a quote for this from a text book or a paper, as well as some prominent examples in the literature where two records or signals are matched like this, for instance from signal analysis, acoustics, electronics, meteorology, etc? • Assuming both signals were properly anti-alias filtered prior to sampling, then they each accurately represent the signal at any point in continuous time for all signal content within the Nyquist bandwidth. The approach taken here is similar to what you could do to deriver your specific case: dsp.stackexchange.com/questions/63074/… Mar 28, 2020 at 19:10 • puh, this was quite a wall of text. I tried to structure it a bit with line breaks, nukimov, could you please check whether this looks like you want it to? Mar 29, 2020 at 11:23 • "...R2 contains complete information only from signals with periods of 2⋅T2 or longer, while events with shorter periods (for instance, T_1) are not resolved by R2.." If the information can be resolved by $2T_2$, why can't it be resolved by lesser time interval of $T_1$? I am feeling uneasy now thinking about it. Also, what is the ratio of $T_1/T_2$? Let us say if $T_1 = 2$, $T_2 = 3$, and Nyquist Interval is 2.5, then upsampling $R_2$ to $T_1$ wouldn't work because it is already aliased. (B) also wouldn't work. Only option is (C) here even though aliased. Mar 29, 2020 at 11:31 • @MarcusMüller: Alsmot perfect, thanks! I just corrected few things. Mar 29, 2020 at 15:34 • @jithin : "If the information can be resolved by 2∗T2, why can't it be resolved by lesser time interval of T1": I am probably expressing it wrong in the question. Surely if we could record the signal again with period T1 we would resolve it better than 2T2, but the record is already taken, it cannot be modified. So, what I am saying is that in that record we have only reliable information for time scales of 2*T2 or longer. We could interpolate between data points, for instance to get a period of T1, but interpolation does not create the missing information. Mar 29, 2020 at 15:37	2022-05-20 17:58:19	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 32, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6090630888938904, "perplexity": 723.0735985439967}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662533972.17/warc/CC-MAIN-20220520160139-20220520190139-00155.warc.gz"}
https://itprospt.com/num/16203427/1-2-s-kexs-33-1-25x4y2	5 1 2 s Kexs 33.) 1 25x4y2... Question 1 2 s Kexs 33.) 1 25x4y2 1 2 s Kexs 33.) 1 25x4y2 Similar Solved Questions 24, (11.7, #3-14) Find the critical points and any local maximum values, minimum values_ and saddle points of the function f (T,4) = S1 -Iv - IV? 24, (11.7, #3-14) Find the critical points and any local maximum values, minimum values_ and saddle points of the function f (T,4) = S1 -Iv - IV?... QUESTIONThese three questions go together.Evaluate the following improper integral if itis convergentSelect the correct integral,XnIdx 0+lin b_EKdxb_E(24 - Xdx z& 0_ xhuQUESTION 9To evaluatewhat methodyou will use?xhxsub with U=XIntegration by parts with U-Inx and dv=x dxsub with u-InxIntegration by parts with U=X and dv=Inx dxQUESTION 10converget to 1/2 Diverzenc convergentto 1/3 convergentto 1/5 QUESTION These three questions go together. Evaluate the following improper integral if itis convergent Select the correct integral, Xn Idx 0+ lin b_E Kdx b_E (24 - Xdx z& 0_ xhu QUESTION 9 To evaluate what methodyou will use? xhx sub with U=X Integration by parts with U-Inx and dv=x dx sub with... Fill in the blanks in each sentence with the suitable word.The worker is patting _____ the bumps on the floor sothat he can lay the marble properly.(A) Up (B) On(C) Down (D) Off Fill in the blanks in each sentence with the suitable word. The worker is patting _____ the bumps on the floor so that he can lay the marble properly. (A) Up (B) On (C) Down (D) Off... 4A 1 1 1 conducting rod ol radius R, 1 1 8 comulconp ) 1 1 1 1 200R3? 4 Weaei1 Wlat Untdnich 5.00R1 Dunauptuacuj W 2 which 4A 1 1 1 conducting rod ol radius R, 1 1 8 comulconp ) 1 1 1 1 200R3? 4 Weaei 1 Wlat Untdnich 5.00R1 Dunauptuacuj W 2 which... Consider tne frame shown in (Figure 1). Suppose that 440 N/mn_Part ADetermine the and components of force which the pin exert on the frame using scalar notationExpress your answers in kilonewtons to three significant figures_ Enter your answers separated by comma_View Available Hint(s)AEdvecSubmitProvlous AnsWorsIncorrect; Try AgainPart BFigureof 1Determine the and components of force which the pin B exert on the frame using scalar notation Express your answers in kilonewtons to three significan Consider tne frame shown in (Figure 1). Suppose that 440 N/mn_ Part A Determine the and components of force which the pin exert on the frame using scalar notation Express your answers in kilonewtons to three significant figures_ Enter your answers separated by comma_ View Available Hint(s) AEd vec S... In Neurospora, all mutants affecting the enzymes carbamyl phosphate synthetase and aspartate transcarbamylase map at the $p y r-3$ locus. If you induce $p y r \cdot 3$ mutations by ICR-170 (a chemical mutagen), you find that either both enzyme functions are lacking or only the transcarbamylase function is lacking; in no case is the synthetase activity lacking when the transcarbamylase activity is present. (ICR-170 is assumed to induce frameshifts.) Interpret these results in regard to a possible In Neurospora, all mutants affecting the enzymes carbamyl phosphate synthetase and aspartate transcarbamylase map at the $p y r-3$ locus. If you induce $p y r \cdot 3$ mutations by ICR-170 (a chemical mutagen), you find that either both enzyme functions are lacking or only the transcarbamylase funct... WFind and describe a physical situation that illustrates the Mean-Value Theorem. WFind and describe a physical situation that illustrates the Mean-Value Theorem.... The amount of a medicinal drug in a patient's bloodstream is modeled by (t) =4 (e 0.2t e2) where Q is measured in mg and t is time in hours since the initial dose: Enter exact value answers for all parts, and show your work:9a) (6 points) What was the initial amount in the patient's bloodstream?9b) (12 points) Find the time at which the concentration of the drug in the bloodstream is at its maximum; The amount of a medicinal drug in a patient's bloodstream is modeled by (t) =4 (e 0.2t e2) where Q is measured in mg and t is time in hours since the initial dose: Enter exact value answers for all parts, and show your work: 9a) (6 points) What was the initial amount in the patient's blood... Use a graphing calculator to estimate the solution to each equation to two decimal places. Then find the solution algebraically and compare it with your estimate.$$0.03 x-3497=0$$ Use a graphing calculator to estimate the solution to each equation to two decimal places. Then find the solution algebraically and compare it with your estimate. $$0.03 x-3497=0$$... College AlgebraWrite the following expression in factored form 3x^2+5x+2 College Algebra Write the following expression in factored form 3x^2+5x+2... A conducting rod moves with a constant velocity $\mathbf{v}$ in a direction perpendicular to a long, straight wire carrying a current $I$ as shown in Figure $\mathrm{P} 31.58$ . Show that the magnitude of the emf generated between the ends of the rod is $$\|\mathcal{E}\|=\frac{\mu_{0} v I \ell}{2 \pi r}$$ In this case, note that the emf decreases with increasing $r,$ as you might expect. A conducting rod moves with a constant velocity $\mathbf{v}$ in a direction perpendicular to a long, straight wire carrying a current $I$ as shown in Figure $\mathrm{P} 31.58$ . Show that the magnitude of the emf generated between the ends of the rod is \|\mathcal{E}\|=\frac{\mu_{0} v I \ell}{2 \... You are helicopter pilot for a hospital in a big city You get a call and need to help somebody that is 7.1 mi South of the hospital and 36.3 mi East of the hospital. What direction do you need to travel for what distance?* You are helicopter pilot for a hospital in a big city You get a call and need to help somebody that is 7.1 mi South of the hospital and 36.3 mi East of the hospital. What direction do you need to travel for what distance?*... 3. For the two autonomous differential equations below, do the following Find the equilibrium solution(s) b. Draw the phase portrait c.Label critical points as stable, unstable, or semi-stable_ #i, dy=y _3y #ii. d-y(4-y) dt dt~1 3. For the two autonomous differential equations below, do the following Find the equilibrium solution(s) b. Draw the phase portrait c.Label critical points as stable, unstable, or semi-stable_ #i, dy=y _3y #ii. d-y(4-y) dt dt ~ 1... Thc stcam reformation rcaction is an important sourcc of Hz (at 750 "C):CH-(g) HzO(g)CO(g)Usc the following information to calculate Kp (750 "C):Hz(g) Yz Oz(g)HzO(g)Ki1.56 x 10"}2 CH4(g) Oz(g)2 CO(g) 4 Hz(g)Kz5.90 x 1015Hz(g) Thc stcam reformation rcaction is an important sourcc of Hz (at 750 "C): CH-(g) HzO(g) CO(g) Usc the following information to calculate Kp (750 "C): Hz(g) Yz Oz(g) HzO(g) Ki 1.56 x 10"} 2 CH4(g) Oz(g) 2 CO(g) 4 Hz(g) Kz 5.90 x 1015 Hz(g)... Find the length of the curve: 23) X = cOS 2t,y sln 2t,0 =t<277 A) 7 B) 677C) 47D) 2724) x = 32,y-} (t+93/2,0sts1 A) 2 B) 7D) 2 Find the length of the curve: 23) X = cOS 2t,y sln 2t,0 =t<277 A) 7 B) 677 C) 47 D) 27 24) x = 32,y-} (t+93/2,0sts1 A) 2 B) 7 D) 2...	2022-09-28 15:18:45	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6120396256446838, "perplexity": 4248.93689568}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335257.60/warc/CC-MAIN-20220928145118-20220928175118-00640.warc.gz"}
https://lists.lyx.org/pipermail/lyx-users/2020-June/001089.html	# How to break long equations with LyX Paul A. Rubin parubin73 at gmail.com Sat Jun 20 18:13:10 UTC 2020 On 6/19/20 9:47 PM, list_email at icloud.com wrote: >> On Jun 19, 2020, at 5:14 PM, Paul A. Rubin <parubin73 at gmail.com> wrote: >> >> On 6/19/20 7:34 PM, list_email at icloud.com wrote: >>>> On Jun 19, 2020, at 8:15 AM, Paul A. Rubin <parubin73 at gmail.com> wrote: >>>> >>>> On 6/19/20 7:51 AM, list_email at icloud.com wrote: >>>>> I have tried mightily to get LyX to break long equations. I’ve studied multiple pages at stackexchange, both LaTeX and LyX, and can’t seem to get anything to work. >>>>> >>>>> I have had luck in the past with the second large block of code at this page: >>>>> >>>>> https://stackoverflow.com/questions/2904807/lyx-breaking-long-formula-lines >>>>> >>>>> but today I have some problems with it. >>>>> >>>>> First, it doesn’t work if the \text command appears inside my own LaTeX code that appears between \begin{dmath} and \end{dmath} or if I try to use the trick twice in the same document. (That’s a tentative analysis of the problem.) Specifically, LyX runs at 100% CPU eventually gives me a chance to abort and then follows up with this additional message: "The external program pdflatex finished with an error. It is recommended you fix the cause of the external program's error (check the logs)." >>>>> >>>>> Plus, I now want to to apply the line breaking to a line within an aligned environment (Insert -> Math -> Aligned Environment in the menu system.) This is causing things to look even worse, even though I added two “aligned” lines to the referenced code block. (If you look at the code you’ll see the obvious places to add the lines.) >>>>> >>>>> How do LyX-ers handle this? Is there “LyX” solution to breaking long equations? I’m OK with some ad hoc solution for now, or some ERT if it works. >>>>> >>>>> Thanks, >>>>> Jerry >>>>> >>>>> >>>> I've never used the breqn package, but with ordinary and AMS math environments, hitting Ctrl-Enter in the middle of a long formula will break it (inserting a line break, \\, in the LaTeX output). If that doesn't achieve what you want, perhaps you could post a minimal example and a specification of what the output should look like. >>>> >>>> Paul >>>> >>> Thanks, Paul. I’m on a Mac so of course Control-Enter has no meaning. Usually this translates to Mac-speak as Command-Enter. When I do Command-Enter in my equation, which is unfortunately inside a align environment, it instead adds a row to the matrix that represents the align environment. Ditto for Shift-Command-Enter. These two commands in LyX are mapped as Insert -> Formatting -> Ragged Line Break and Justified Line Break, respectively but invoking the menu commands with the cursor in my equation has exactly the same effect: adding a row to the align matrix (above the row where the cursor is.) When (Shift-)Command-Enter is done to a non-align display equation a similar thing happens except now the non-align equation is converted to an align equation with a blank new row _below_ the original equation. >>> >>> Right now I guess I would be pretty happy with merely a way to make Command-shift (Control-shift) do what is expected which is apparently break the equation instead of creating a new row. >>> >>> Jerry >>> >> Jerry, >> >> I just created an align environment with two equations, the left side of the first being ridiculously long. When I put the cursor somewhere toward the middle of the left side of the long equation and inserted a break (using Ctrl-Enter -- I'll get to the Mac part in a minute), it broke the equation and inserted a new row. So >> >> (x+x+x+x+...+x) =1 >> y =2 >> >> (where the right column contained the equal signs and integers) became >> >> (x+x+x+... >> +x+x+x+x) =1 >> y =2 >> >> where the right column is empty in the first row. See the attached minimal example. Is this not what you want? >> >> Regarding the key mapping, if you can find an unused key combo that you have a chance of remembering, you can map it to "newline-insert newline" using Tools > Preferences... > Editing > Shortcuts. That's what Ctrl+Enter binds to for me. >> >> Paul > Paul: > > Thanks. The effect appears to work by adding another row to the matrix and filling it with the partial equation. In your example the new row is on top. If the long equation is moved to the RHS the new row is below. > > I tried adding horizontal space to the second line of your broken equation but Latex seems to ignore it: when I click outside the math box and the equation is rendered, it is rendered without the horizontal space even though it was visible while in math editing mode. > > About Mac key mappings: According to the status line in the document window, when I hit Command-Shift, it displays “(newline-insert newline;) and then icons for “Command” and “new line” which is an arrow thingy. So I’m going to assume that the key mapping is correct but that there is another problem, meaning… > > …See my attached example. Attempting to break the line before the second exponential (1) doesn’t break the line, (2) adds a matrix row above, and (3) steals the = from the now-third row and puts it on the second row. > > The failure to break with Command-Enter does not seem to be a function of the align environment since it also fails in a stand-alone equation but adding a new row creates a new align environment. > > I notice that my long equation, as rendered by LyX in the LyX window, gets truncated on the right. I don’t know why—this does not happen in the document from which I am copying it. > > Summary: Control-(or Command-)Shift doesn’t work on my equation. > > Jerry > > > Jerry, I messed with your example file and attached the result. The good news is that your formula is breakable. The bad news is that there is a bit of a PITA component to doing so. The reason your attempt to break the formula failed was that it is enclosed in \left [ \right ], which apparently causes either LyX or LaTeX (I'm not sure which) to treat what is in between the brackets as unbreakable. The fix I came up with was to delete the bracketing, decide where I wanted to break the formula, then wrap the left half with just a left bracket and the right half with just a right bracket. You can do this using the "Insert delimiters" dialog (the "[ space ]" button on the tool bar), by unchecking the "Keep matched" box and then choosing the appropriate bracket on one side and "(None)" on the other. Once I'd done that, Ctrl+Return broke the line as expected. I also put in a second version with IMO better balance, in which I did the same thing but moved the = sign to the left column. Paul -------------- next part -------------- An HTML attachment was scrubbed... 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http://www.alecjacobson.com/weblog/?m=201004	Archive for April, 2010 Vi(m) tip #7: resize vertical split screen Monday, April 19th, 2010 You can resize vertical split screen windows in vim using the following commands. To make the current window shrink in width (you can precede these with numbers): <CTRL>+W < and similarly to grow in width <CTRL>+W > To make the current window full width: <CTRL>+W \| <CTRL>+W = Single image iphone apps now work offline Monday, April 19th, 2010 Using a nice little tutorial about cache manifests, I’ve made it possible for my single image apps (and yours) to run offline. Which means if you save them to your home screen on your iphone or ipod touch (or ipad) you can access them even in the deepest subway platform of the seven train in manhattan. marseille Sunday, April 18th, 2010 Saturday, April 17th, 2010 There is a new ad campaign in the New York City subways. The ads feature sad or serious looking models and dismal color schemes. The text reads something suggestively depressing like, “I thought I was doing my job” or “I though life would be the same”. Then the punch line is “Abortion changes you”. The ads expect you to complete the sentence “Abortion changes you for the worse.” But I thought, what would this ad look like if you completed the sentence the other way? So here’s my revision, taking the same words but implying a different meaning with the design. Normalize list of vectors in MATLAB Friday, April 16th, 2010 If a contains a list of row-vectors then you can normalize there lengths using the following: normalized_a = a./repmat(sqrt(sum(a.^2,2)),1,3); Erase item from list of pointers in C++ during iterator Thursday, April 15th, 2010 In a C++ program, I have a std::list (actually std::vector) of pointers to a class Foo: std::vector my_list; Maybe I have push a bunch of items onto this list and then selected one (using my UI or whatever). Anyway there is a certain item in the list that points to an instance of Foo that has the is_selected flag flipped to true. I want to implement a simple deleteSelected() function for this list. Here’s what I came up with (no guarantees, my C++ skills leave a lot to be desired): bool deleteSelected(){ bool deleted_some = false; std::vector<Foo>::iterator my_list_iterator = my_list.begin(); while(my_list_iterator != my_list.end();) { if(( my_list_iterator)->is_selected){ // clear the memory of this item delete (* my_list_iterator); // erase from list, returns next element in iterator my_list_iterator = my_list.erase(my_list_iterator); deleted_some = true; }else{ // otherwise, just increment the iterator my_list_iterator ++; } } return deleted_some; } Any reason why this isn’t correct? Note: Erasing this way could lead to an O(N2) running time if many items are selected. How can this be avoided with a std::vector? (Erasing all of the items is trivial, I mean how can I erase a dense general set of items in the list in linear time) Update: My friend told me that a better way to do this is with a decrementing index. Then when you erase using the index the items behind get moved but you’re already done processing them and since the index is going backwards it’s left in the right position. (This way is also arguably faster at least by a scale factor). Open .cpp and .h files in vim with split screens Thursday, April 15th, 2010 Here’s a little bash script I save in cvim.sh (apologies to chinese vim): #!/bin/bash base_name=echo $1 \| sed "s/\.$//g" vim -O2 $base_name.h$base_name.cpp So the if I type: ./cvim.sh foo vim opens foo.cpp and foo.h in split screen. skin sample Tuesday, April 13th, 2010 who’s got the crack Monday, April 12th, 2010 Simple MATLAB slerp Monday, April 12th, 2010 Interpolating between two vectors can catch you off guard. If you just linearly interpolate (x,y,z) values you could end up with a vanishing interpolated vector. Just imagine interpolating a 2-D vector from [-1,0] to [1,0]. Halfway you’ve got [0,0]. One way to do this a little better is to interpolate a rotation between the vectors. The natural path to take is the shortest one which happens to also be the shortest path (of two unit vectors) of their respect points along the unit sphere. This is called spherical linear interpolation or slerp. There’s more complicated ways to do this but in MATLAB I can simply do: function [c] = slerp(a,b,t) angle = acos( dot(a,b) ); % easy degenerate case if(0==angle) c = a; % hard case elseif(pi==angle) error('SLERP: angle between vectors cannot be exactly PI...'); else c = (sin((1.0-t)angle)/sin(angle))a + (sin(tangle)/sin(angle))b; end end Note: that slerping is not well defined for opposite parallel vectors. This makes sense geometrically because their respective points on the unit sphere have infinitely many, all equally minimal paths between them. E.g. the north pole has infinitely many shortest paths along the earth to the south pole. In the end, I lerp the magnitudes of the two vectors then use that to scale the slerp of their unit vectors: c = ( (1.0-t) * norm(a) + t* norm(b) ) * slerp( a./norm(a) , b./norm(b) , t); where t is your interpolation parameter. Slightly more efficiently: mag_a = norm(a); mag_b = norm(b); c = ((1.0-t)mag_a + tmag_b) * slerp(a./mag_a,b./mag_b,t); Note: Careful using norm it is not vectorized as you might think. I.e. it doesn’t return a row vector of scalars if you pass it a list of vectors (instead the matrix norm of that list treated as a matrix).	2017-03-28 23:30:38	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.24879594147205353, "perplexity": 3346.2184888918787}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218190134.25/warc/CC-MAIN-20170322212950-00011-ip-10-233-31-227.ec2.internal.warc.gz"}
https://igraph.org/r/html/1.2.3/topo_sort.html	# R igraph manual pages Use this if you are using igraph from R ## Topological sorting of vertices in a graph ### Description A topological sorting of a directed acyclic graph is a linear ordering of its nodes where each node comes before all nodes to which it has edges. ### Usage topo_sort(graph, mode = c("out", "all", "in")) ### Arguments graph The input graph, should be directed mode Specifies how to use the direction of the edges. For “out”, the sorting order ensures that each node comes before all nodes to which it has edges, so nodes with no incoming edges go first. For “in”, it is quite the opposite: each node comes before all nodes from which it receives edges. Nodes with no outgoing edges go first. ### Details Every DAG has at least one topological sort, and may have many. This function returns a possible topological sort among them. If the graph is not acyclic (it has at least one cycle), a partial topological sort is returned and a warning is issued. ### Value A vertex sequence (by default, but see the return.vs.es option of igraph_options) containing vertices in topologically sorted order. ### Author(s) Tamas Nepusz ntamas@gmail.com and Gabor Csardi csardi.gabor@gmail.com for the R interface ### Examples g <- barabasi.game(100) topo_sort(g) [Package igraph version 1.2.3 Index]	2023-02-06 22:40:44	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3591335415840149, "perplexity": 2418.1266992553183}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500365.52/warc/CC-MAIN-20230206212647-20230207002647-00334.warc.gz"}
https://icml.cc/Conferences/2021/ScheduleMultitrack?event=10409	Timezone: » Poster Is Pessimism Provably Efficient for Offline RL? Ying Jin · Zhuoran Yang · Zhaoran Wang Tue Jul 20 09:00 PM -- 11:00 PM (PDT) @ Virtual We study offline reinforcement learning (RL), which aims to learn an optimal policy based on a dataset collected a priori. Due to the lack of further interactions with the environment, offline RL suffers from the insufficient coverage of the dataset, which eludes most existing theoretical analysis. In this paper, we propose a pessimistic variant of the value iteration algorithm (PEVI), which incorporates an uncertainty quantifier as the penalty function. Such a penalty function simply flips the sign of the bonus function for promoting exploration in online RL, which makes it easily implementable and compatible with general function approximators. Without assuming the sufficient coverage of the dataset, we establish a data-dependent upper bound on the suboptimality of PEVI for general Markov decision processes (MDPs). When specialized to linear MDPs, it matches the information-theoretic lower bound up to multiplicative factors of the dimension and horizon. In other words, pessimism is not only provably efficient but also minimax optimal. In particular, given the dataset, the learned policy serves as the best effort'' among all policies, as no other policies can do better. Our theoretical analysis identifies the critical role of pessimism in eliminating a notion of spurious correlation, which emerges from theirrelevant'' trajectories that are less covered by the dataset and not informative for the optimal policy.	2022-12-08 02:57:41	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.674534022808075, "perplexity": 752.9312803742855}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711232.54/warc/CC-MAIN-20221208014204-20221208044204-00773.warc.gz"}
http://mathhelpforum.com/calculus/139192-having-problems-numerical-methods-question-print.html	# Having problems with numerical methods question • April 14th 2010, 02:43 PM mistry88 Having problems with numerical methods question How would I do the following 2 questions below?? Thanks :) • April 14th 2010, 02:47 PM harish21 Quote: Originally Posted by mistry88 How would I do the following 2 questions below?? Thanks :) integrate by parts. let $u = tan^-1(x)$, and let $dv = x dx$. Then proceed. have you done integration by parts before? • April 14th 2010, 02:51 PM mistry88 Quote: Originally Posted by harish21 integrate by parts. let $u = tan^-1(x)$, and let $dv = x dx$. Then proceed. have you done integration by parts before? O ok thank you, yes I have done integration by parts before. I just proved it to equal the answer, but now don't know how to do the second part.. • April 15th 2010, 04:33 AM mr fantastic Quote: Originally Posted by mistry88 O ok thank you, yes I have done integration by parts before. I just proved it to equal the answer, but now don't know how to do the second part.. Where are you stuck? What have you tried? Have you reviewed your class notes and textbook for the formula? • April 15th 2010, 04:35 AM mistry88 Its ok now, I have figured out how to do it and have finished this question :D • April 15th 2010, 04:37 AM mr fantastic Quote: Originally Posted by mistry88 How would I do the following 2 questions below?? Thanks :) These questions look like they could be part of an assignment that counts towards your final grade. MHF policy is to not knowingly help with such questions as they are meant to be the work of the student not the work of others. Thread closed. Please feel free to pm me to discuss this further.	2013-12-21 23:21:59	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7746495008468628, "perplexity": 1257.0832575505442}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1387345776447/warc/CC-MAIN-20131218054936-00012-ip-10-33-133-15.ec2.internal.warc.gz"}
http://mathhelpforum.com/geometry/224187-area-triangle-coordinate-geometry-print.html	# Area of triangle in coordinate geometry • Nov 12th 2013, 04:44 AM AaPa Area of triangle in coordinate geometry Hello friends. There is a formula for area of a triangle in coordinate geometry which is as follows. $\frac{1}{2}\|x_1(y_2 - y_3)+x_2 (y_3 - y_1)+x_3 (y_1 - y_2)\|$ I do not understand some aspects of this formula. 1. mod sign 2. I know the proof for all points lying in the first quadrant. Is there a proof that the area won't change for points lying in other quadrants? I could check for all the possible sets but that will take too long. Are these two related? Thanks. • Nov 12th 2013, 05:20 AM emakarov Re: Area of triangle in coordinate geometry Quote: Originally Posted by AaPa I do not understand some aspects of this formula. 1. mod sign The argument of the absolute value function is twice the signed area of the triangle. It is positive if (x1, y1), (x2, y2) and (x3, y3) are vertices listed in one direction (clockwise or counterclockwise, I don't remember) and negative if they are listed in the opposite direction. Quote: Originally Posted by AaPa 2. I know the proof for all points lying in the first quadrant. Is there a proof that the area won't change for points lying in other quadrants? I could check for all the possible sets but that will take too long. Which proof do you know? One general way to derive this formula is to consider the signed area of the parallelogram built on vectors $(x_2 - x_1)e_1 + (y_2 - y_1)e_2$ and $(x_3 - x_1)e_1 + (y_3 - y_1)e_2$ () where $e_1$, $e_2$ are the vectors of an orthonormal positively oriented basis. The signed area function $\langle a,b\rangle$ takes two vectors $a$ and $b$ and returns a number. It has the following properties. $\langle a,b\rangle=-\langle b,a\rangle$ $\langle a,b+c\rangle=\langle a,b\rangle+\langle a,c\rangle$ $\langle a,xb\rangle=x\langle a,b\rangle$ (i.e., the function is linear in both arguments) $\langle a,a\rangle=0$ $\langle e_1,e_2\rangle=1$ If you expand () according to linearity, you should get the required formula. For more, see the shoelace formula in Wikipedia. • Nov 12th 2013, 06:52 AM AaPa Re: Area of triangle in coordinate geometry In my proof we drop perpendiculars from each of the vertices on x axis. We get 3 trapeziums. The area of triangle is the difference in areas of (sum of 2 trapeziums with a common parallel side) and (the other trapezium). And most of what you said I was not able to understand. I don't know that much mathematics. Thanks for answering though. • Nov 12th 2013, 01:16 PM emakarov Re: Area of triangle in coordinate geometry In fact, it is easy to see that the value the formula returns does not change with parallel shifts. This is obvious for vertical shifts: if y₁, y₂ and y₃ are all increased or decreased by the same amount, then the differences between them do not change. Consider now a horizontal shift, i.e., replace x₁, x₂ and x₃ by x₁ + Δ, x₂ + Δ and x₃ + Δ, respectively. Then the value of the formula changes by (1/2)Δ((y₂ - y₃) + (y₃ - y₁) + (y₁ - y₂)) = 0. So, it is enough to prove the formula for triangles in the first quadrant and then shift them to an arbitrary position. • Nov 13th 2013, 03:20 AM AaPa Re: Area of triangle in coordinate geometry Wow this is an elegant method. But how do we prove the formula for triangles whose points lie in different quadrants? • Nov 13th 2013, 04:03 AM emakarov Re: Area of triangle in coordinate geometry Hmm, a triangle with vertices in different quadrants can still be shifted so that all its vertices lie in the first quadrant, can it not? We don't have to use either horizontal or vertical shift; we can do both. • Nov 13th 2013, 07:18 AM AaPa Re: Area of triangle in coordinate geometry Quote: Originally Posted by emakarov It is positive if (x1, y1), (x2, y2) and (x3, y3) are vertices listed in one direction (clockwise or counterclockwise, I don't remember) and negative if they are listed in the opposite direction. That would mean x2(y3-y1) + x3(y1-y2) and x3(y3-y1) + x2(y1-y2) should have opposite signs but I am not able to find such a relation between them save x2= - x3 • Nov 13th 2013, 07:36 AM emakarov Re: Area of triangle in coordinate geometry Quote: Originally Posted by AaPa That would mean x2(y3-y1) + x3(y1-y2) and x3(y3-y1) + x2(y1-y2) should have opposite signs but I am not able to find such a relation between them. I assume you are considering the case when x1 = 0. You give two expressions: x2(y3-y1) + x3(y1-y2) and x3(y3-y1) + x2(y1-y2). If the second expression is the result of traversing the triangle in the opposite direction, then the second expression should be obtained from the first one by exchanging indices 2 and 3. Indeed, the first expression results from listing vertices as (x1, y1), (x2, y2), (x3, y3), and the second expression results from listing vertices as (x1, y1), (x3, y3), (x2, y2). Therefore, the second expression should be x3(y2 - y1) + x2(y1 - y3). It is indeed the opposite of x2(y3 - y1) + x3(y1 - y2). • Nov 13th 2013, 08:04 AM AaPa Re: Area of triangle in coordinate geometry i understood my mistake. thanks a lot.	2017-10-19 01:03:56	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 13, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8738912343978882, "perplexity": 531.6900541182769}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187823168.74/warc/CC-MAIN-20171018233539-20171019013539-00696.warc.gz"}
https://space.stackexchange.com/questions/13625/how-can-a-sounding-rocket-accurately-take-the-temperature-of-the-atmosphere-whil/13626	How can a sounding rocket accurately take the temperature of the atmosphere while flying through it at high speed? A sounding rocket is a rocket that ascends into the high atmosphere in order to take all sorts of measurements so we can learn more about the upper atmosphere. They don't go into orbit, so they can be smaller than what we normally think of space rockets. However, they can still go above 100km fairly easily, and they still go very fast. What I want to know is, how can it accurately measure the ambient temperature at whatever altitude it's at? The rocket will be flying very fast, incurring a lot of heat from air friction. • Note that the heat is not due to friction, but from compression of the air in front. – JDługosz Jan 22 '16 at 7:55 • @JDługosz I'm pretty sure it's from both. Solid surfaces suffer from skin friction across moving air, which produces heat just like any other friction. – DrZ214 Jan 22 '16 at 22:52 • @DrZ214 No, it's not. The influence of friction is negligible. – Rikki-Tikki-Tavi Sep 13 '16 at 16:29 According to the link here, In meteorological rockets, the temperature sensor is not measured as the rocket ascends but a payload containing the sensor is ejected from a high altitude and as it parachutes down measurements are beamed back. Here is an answer from over on aviation.stackexchange.com which addresses this issue. I've quoted a portion of it below, but see that link for more info. As you measure temperature moving at high velocities, your outside thermometer will measure a higher temp than what is actually outside (what a non-moving thermometer would get). That's because as the air rams into your thermometer it gets a little bit compressed, and that makes it heat up a little bit. Amazingly, some smart people have even calculated how much that "ram rise" is, and you can actually compensate (well, in theory) from the indicated temperature to calculate what the actual outside air temp is: $$Ram~Rise=SAT\times0.2\times{M}^2$$ According to Mathav Raj's answer, temperature isn't measure during ascent, but this explains how it could be done. • I think the document in Mathav Raj's answer might also contain this information - there is discussion in that document about a whole lot of other corrections that can be performed on the measured value, and that formula may also apply during ascent. The same ram rise issue is experienced on the way down. – Steve Jan 22 '16 at 12:49	2019-10-18 21:43:59	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6229389905929565, "perplexity": 884.9557476268984}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986684854.67/warc/CC-MAIN-20191018204336-20191018231836-00397.warc.gz"}
https://www.gradesaver.com/textbooks/math/precalculus/precalculus-6th-edition-blitzer/chapter-6-cumulative-review-exercises-page-801/1	## Precalculus (6th Edition) Blitzer The solutions of the equation are $x=\left( -1,2,i,-i \right)$. Use the rational root theorem from (1), ${{a}_{0}}=2$ and ${{a}_{n}}=1$. The dividers of ${{a}_{0}}=1,2$ and ${{a}_{n}}=1$. Now, as $\frac{{{a}_{0}}}{{{a}_{n}}}=\pm \frac{1,2}{1}$, we will check all the rational numbers. At first we will check if $-1$ is a root of the expression. Now, we will perform the synthetic division as below: $\begin{matrix} -1 & 1 & -1 & -1 & -1 & -2 \\ {} & {} & -1 & 2 & -1 & 2 \\ {} & 1 & -2 & 1 & -2 & 0 \\ \end{matrix}$ Since the remainder is zero, $x=-1$ is a root of the given equation and so the equation ${{x}^{4}}-{{x}^{3}}-{{x}^{2}}-x-2=0$ can be factored as below: \begin{align} & {{x}^{4}}-{{x}^{3}}-{{x}^{2}}-x-2=0 \\ & \left( x+1 \right)\left( {{x}^{3}}-2{{x}^{2}}+x-2 \right)=0 \\ & \left( x+1 \right)\left[ {{x}^{2}}\left( x-2 \right)+1\left( x-2 \right) \right]=0 \\ & \left( x+1 \right)\left( x-2 \right)\left( {{x}^{2}}+1 \right)=0 \end{align} Therefore, $x=-1,2,+i,-i$	2021-04-11 00:22:06	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 1.0000077486038208, "perplexity": 506.70157046454676}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038060603.10/warc/CC-MAIN-20210411000036-20210411030036-00368.warc.gz"}
http://conference.ippp.dur.ac.uk/event/616/	Oct 2016 - Sep 2017 # Combined threshold and transverse momentum resummation for inclusive observables ## by Giovanni Ridolfi Thursday, 18 May 2017 from to (Europe/London) at IPPP ( OC218 ) Description I present a combined resummation for the transverse momentum distribution of a colorless final state in perturbative QCD. Our result satisfies three requirements: it reduces to standard transverse momentum resummation to any desired logarithmic order in the small-p_T for fixed radiation energy; it reduces to threshold resummation to any desired logarithmic order in the threshold limit for fixed p_T; upon transverse momentum integration it reproduces the threshold resummation of the total cross section. I present some preliminary results and comparisons with standard resummation in the specific case of Higgs production in gluon fusion in the effective field theory limit.	2017-11-19 21:25:44	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8061389923095703, "perplexity": 2141.245036891933}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934805809.59/warc/CC-MAIN-20171119210640-20171119230640-00137.warc.gz"}
https://www.nature.com/articles/s42003-022-04144-8?utm_campaign=related_content&utm_source=ECOEVO&utm_medium=communities&error=cookies_not_supported&code=29ee6b5f-06f1-43ec-b875-de32cc541cd7	## Introduction A great number of hypotheses have been proposed to explain the diversity in patterns and colours in the animal kingdom, and biologists continue to debate the adaptive significance of pigmentation and markings. For example, the function of the black and white stripes of zebra has long been debated, with many popular hypotheses not withstanding analysis1. Some phenomena have received a lot of attention: it is well-established that camouflage plays an important role in disguising animals both from predator and prey2. Countershading, whereby the upperside of an organism is dark while the underside is pale, appears to allow animals to be concealed from both dorsal and ventral viewpoints: a pale underside blends in against a bright sky, while a dark upperside is less conspicuous against a backdrop of land or sea3. This colouration has evolved independently several times in various seabirds, suggesting an adaptive role4. While it is easy to understand the benefits of countershading, the function of other, similar, colour patterns is less clear. For instance, most species of the Larinae (gulls) are predominantly white, and the majority have a grey upperwing and back, which is often referred to as the mantle (in contrast to the typical definition, which refers solely to the part of the back below the nape)5. However, the nape, rump and tail are usually also white, making countershading an unsatisfactory explanation. Melanin, the pigment that produces grey, black or brown colours, is thought to be energetically costly to produce6,7, so it is likely that this pattern has arisen and been maintained through selection. In addition, the wingtips of gulls commonly comprise a fully black region. Melanin has many functions, including protection of feathers against damaging ultraviolet radiation8. Indeed, Dufour et al.9 recently found a positive effect of insolation (incident solar radiation) on Larinae mantle and wingtip pigmentation. Wing colouration may, however, be explained by additional factors. Hassanalian et al.10,11 showed that, because dark surfaces absorb heat, thus decreasing the density and increasing the viscosity of air flowing over them, the dark wing colour of many gliding birds may function to reduce drag by decreasing the amount of friction generated during flight. A recent analysis of seabirds4 found that wing darkness is associated with morphology optimized for flight efficiency. However, this analysis was conducted at a broad scale, and morphology differs within and among taxonomic groups. Furthermore, for most seabird groups, wing loading and aspect ratio appear to be positively correlated, whereas previous estimates indicate that it is negatively correlated for Larids such as gulls12. This may be because of differences in foraging behaviour, with gulls generally taking shorter foraging trips than other seabirds12. High aspect ratio wings, possessed by birds that have a long wingspan compared to wing breadth, are associated with flight efficiency because they create less induced drag, whereas low aspect ratio wings permit better maneuverability13. Additionally, high wing loading, a bird’s body mass per unit of wing area, results in a lower production of lift13. Birds must produce more lift than drag to remain in flight14, and there is likely to be a trade-off between adaptation for maneuverability and for long distance gliding. Gulls are an excellent system with which to test the hypothesis that wing darkness is related to flight efficiency. They share relatively similar morphology and ecology, but show striking variation in mantle darkness, the amount of black on wingtips and body size. For instance, one species, the Ivory Gull (Pagophila eburnea), is completely white, while others, notably large species such as the Great Black-backed Gull (Larus marinus) and Pacific Gull (L. pacificus), have almost black mantles and partially black wingtips. I hypothesized that the dark wing colouration of gulls functions to reduce drag, and that species with darker wings have evolved this pattern as a means of compensating for reduced flight efficiency derived from constraints on wing morphology. Therefore, I predicted that the variation in wing darkness could be explained, at least in part, by species’ wing loading, with relatively heavier species possessing darker mantles and wingtips. ## Results Wing loading ranged from 0.002 to 0.007 g mm−1 and was associated with an increase in mantle darkness across the four tested models. The OU model provided a significantly better fit of the data than either the NP or the BM model (Table 1). The lambda model did not fit the data significantly better than the NP model (Table 1). The phylogenetic half-life16,17 estimated by the OU model was 0.026 million years, which suggests a small but non-trivial influence of phylogeny on the measured traits, and selection towards an optimal value of mantle darkness over evolutionary history (Fig. 1). Both wing loading and absolute latitude had statistically significant effects on mantle darkness. The OU model estimated a positive increase on the Kodak Grey Scale (KGS) of 1.22 ± 0.51 SE for each standard deviation increase in wing loading (Table 1, Fig. 2a). Conversely, for each degree increase in distance from the equator, a reduction in mantle darkness equivalent to −0.07 ± 0.03 SE on the KGS was estimated (Table 1, Fig. 2b). ### Wing loading is positively related to the proportion of black on the wingtips Consistent with the findings on mantle darkness, wing loading was associated with an increase in the proportion of black pigmentation on the wingtips (Table 2). For each standard deviation increase in wing loading, the ratio of black to non-black regions on the wingtips was predicted to increase by a factor of 1.4. To illustrate, at the equator (latitude = 0°) and at mean wing loading, the proportion of black on the wingtips was estimated by the model to be 0.84. An increase in wing loading of one standard deviation predicts a proportion of 0.88, and two standard deviations 0.91. Additionally, the amount of black on the wingtips is predicted to change by a factor of 0.95 for each degree increase from the equator. Mantle darkness and wingtip darkness have a correlation coefficient of 0.79. ### Heavier species have less efficient wing morphology for gliding Wing loading was negatively correlated with aspect ratio (estimate: −0.39 ± 0.12 SE, R2 = 0.18, p = 0.002; Fig. 3), which is likely to reduce flight efficiency during gliding flight14. ## Discussion Variation in colouration among closely related species is not often easily explained, and there can be many competing hypotheses. One such hypothesis was proposed by Hassanalian et al.10, who found that a dark surface on the upper side of artificial wings reduces skin friction drag. Birds that spend a long time in flight, such as seabirds, could therefore be expected to benefit from dark wing pigmentation. Rogalla et al. corroborated this hypothesis and showed that darker birds’ wings do indeed create less drag when exposed to radiation4. However, because the production of melanin, the pigment responsible for dark feather colouration, is likely to be costly7,18, a trade-off can be expected. It is unlikely that species would produce dark feathers if the benefits they confer become superfluous. I proposed that species with a higher wing loading, which has a detrimental effect on flight efficiency, could be expected to have darker wings. Consistent with this expectation, wing darkness in the Larinae varies widely but tends to be darker in species with higher wing loading, regardless of ancestry. Furthermore, gull species with a higher wing loading have lower aspect ratio wings. High wing loading among birds is principally driven by a faster increase in mass than wing area as body size increases, a pattern observed across the avian class (excepting hummingbirds)19. As wing area reliably increases with increasing body mass19, a decrease in aspect ratio in gulls must occur as a result of wing breadth increasing faster than wing length. It therefore appears possible that darker mantles and wingtips have evolved in gull species that have become heavier as a means of compensating for the reduction in flight efficiency that results from possessing wings that are relatively short both in proportion to body mass and to wing breadth. Although the finding that higher wing loading is associated with darker wings may appear to contradict the findings of Rogalla et al.4, who found that wing darkness is related to more efficient flight morphology, in actuality both studies support the central hypothesis, which is that dark wing pigmentation increases flight efficiency. In some seabird taxa, such as albatrosses, species may use multiple means of optimizing flight efficiency, by decreasing wing loading and increasing both aspect ratio and melanin pigmentation. This may be because these species spend longer in flight than do gulls, and benefit from minimizing drag rather than optimizing maneuverability. While high aspect ratio wings cause a reduction in induced drag during flight, they are not optimal for take-off19. It is likely that gulls, which spend longer on land and at rest than most seabirds20, require wings optimized for rapid and regular take-off, which is a particular challenge for species with high wing loading. Other factors besides those examined in this analysis will explain some of the variation in wing darkness observed across the Larinae. Dufour et al. showed that mantle darkness is also negatively correlated with the average temperature in the non-breeding range9, suggesting that dark mantle colouration plays a thermoregulatory role, consistent with larger scale patterns in animal melanization21. The fact that relatively heavier (and thus larger) species, which can thermoregulate more effectively in cold temperatures, were more likely to have darker wings suggests that any effects of wing darkness on thermoregulation and flight efficiency are acting independently. It also seems unlikely that dark wing colouration evolved as a means of camouflage in gulls, since the larger species moult from cryptic brown juvenile plumage and have few predators as adults. Because thermal effects on efficiency should be more apparent during unpowered flight, where flight speed is low and the wing surface is continuously exposed to solar radiation, Rogalla et al. predicted that flight mode (i.e. flapping vs. gliding) would have influenced the evolution of dark wing pigmentation4. However, they did not find support for this prediction. All gull species were listed as employing flapping flight, despite gliding being a common flight strategy in this clade22. It may still be possible that flight mode has an effect on wing darkness, as the degree to which gliding flight is used varies among species, with larger species tending to glide more frequently than smaller ones22,23. Nevertheless, it is plausible that melanin could also increase efficiency during flapping flight4,24. The average length of foraging trips undertaken by each species could potentially influence wing darkness, as species that remain airborne for longer will have a greater need to optimize long distance flight rather than maneuverability during take-off. Migration distance may also be a key factor. For example, Herring Gull (L. argentatus) and Lesser Black-backed Gull (L. fuscus) have similar wing loading and breed at similar latitudes, but the latter has a far darker mantle. Lesser black-backed gulls migrate further, spending the winter near the equator5. Migration distance and absolute latitude are, however, likely to be correlated: species breeding nearer the poles are more likely to be migratory and have longer migration distances5. Lesser black-backed gulls and species with similar migration ecology may benefit from having darker plumage to protect their flight feathers from solar radiation, or from wind abrasion25, or perhaps because long distance migrants accrue greater benefits from reducing drag. These hypotheses are not mutually exclusive. Additionally, it is plausible that species nearer the equator gain more utility from dark pigmentation reducing drag owing to the greater insolation in these regions15. A method that can disentangle the effects of the potential protective and thermal benefits of melanism would greatly add to our understanding of the evolution of dark wing colouration in gulls and other birds. Differences in colouration between closely related species could also act as a means of species recognition, preventing or reducing potentially costly hybridization, or as a result of sexual selection for honest signals of mate condition26. Hybridization is relatively common in gulls, yet there remain distinct phenotypes27. Moreover, gulls are sexually monochromatic, indicating that the two sexes do not experience differential selection on plumage colouration. Experimental studies would need to be conducted to assess whether plumage colour is an important marker of species identity and condition in gulls. The present study suggests that, at least in part, variation in colour has evolved for reasons other than selection pressures imposed by conspecific or heterospecific visual systems, as is the case in mate recognition and camouflage. These results highlight the conditions under which colouration can function to increase fitness in ways that are unrelated to visual ecology. It is possible that colour may function in a similar, as yet undiscovered, way in other animal taxa. Furthermore, there may be potential for flight efficiency of aircraft to be improved by imitating the dark feather pigmentation that is widespread in seabirds. Full validation of the hypothesis that wing darkness is related to flight efficiency will require measuring the energetic costs incurred by living birds24. ## Methods ### Mantle and wingtip darkness I used the mantle and wingtip darkness values provided in the supplementary material of Dufour et al.9 in their analysis of the relationship between gull wing colouration and climactic conditions. They follow the Kodak grey scale (KGS) method of measuring gull mantle darkness, which has 20 units from 0 (white) to 19 (black), and calculated the mean values provided by Olsen5 and Howell and Dunn28. The mantle in the context of gulls refers to the back, scapulars, secondary feathers, secondary coverts and tertials. Wingtip darkness is calculated as the proportion of black on the upperside of each species’ hand region (primary feathers, primary coverts and alula) and was measured from colour photographs9. I only considered full species (N = 51) according to Jetz et al.’s BirdTree29 in my analysis so, where wing darkness measurements were provided for subspecies, I calculated the mean for the species. American Herring Gull (L. smithsonianus or L. argentatus smithsonianus) is treated as conspecific with European Herring Gull (L. argentatus). There was no wingtip measurement available for Glaucous-winged Gull, since this species has variable grey wingtips (i.e. no black component) and was excluded from Dufour et al.’s analysis of wingtips9. Wing loading requires an estimate of wing area, which is not widely available in the literature. I therefore used the information on hand length (H, known as wing length) and first secondary feather length (S) provided by the AVONET database30 and calculated wing area with the following equation: $$Wing\,area=(Wingspan-2\cdot H)\ast S+2(H\cdot S\cdot 0.5)$$ This method has been used in a study of common sandpipers (Actitis hypoleucos)31 and, while it underestimated wing area compared to planforms (drawings of the outline of a bird with the wings extended), the two measurements were significantly and highly correlated (R = 0.83, p < 0.01). I obtained wingspan measurements from Olson5. As only ranges were provided, I took the central value. These were highly correlated with both the minimum and maximum wingspan (both R > 0.98). There was no wingspan measurement available for Relict Gull (Ichthyaetus relictus), and therefore this species was not included in the analysis. The final sample size was therefore 50, apart from the wingtip analysis where the sample size was 49 due to the exclusion of Glaucous-winged Gull (see above)9. I divided the wing area calculation by the body mass (also from AVONET30) to obtain the final estimate of wing loading. To aid interpretation of the regression coefficient, I standardized this variable such that the mean takes a value of 0. ### Covariate: absolute latitude AVONET30 also provides the centroid latitudes (the geometric centre) of the breeding and resident ranges for each species. I converted these to absolute values, termed “absolute latitude”, to obtain a variable to include as a covariate in the analysis. This variable denotes the distance from the equator in degrees and is a proxy for the amount of insolation experienced by each species15. ### Statistics and reproducibility To control for shared ancestry, I downloaded the maximum clade credibility tree of Lari from the supplementary material of Jetz et al. (2012) and pruned the tree to include only the Larinae. I used the package phylolm32 in R v. 4.1.233 to run phylogenetic generalized least squares regressions of the relationship between wing loading and mantle darkness with absolute latitude as a covariate. As there is some contention in the literature about which type of phylogenetic model should be used34,35, I ran four different models for comparison (see Introduction). I compared the fit of the two models with fewer restrictions (NP and BM) with the two models with an extra parameter (OU and lambda) and selected the best supported model for inference while also reporting the results of the other models. In addition, to assess whether selection of the OU model over the BM model was not simply a result of bias in the tree, I simulated traits evolving along the tree through both a BM and an OU process 500 times and compared the difference in AIC in these simulations with the difference in AIC between the OU and BM model. The phylogenetic tree of the Larinae, with ancestral values of mantle darkness estimated along the branches, was produced using contMap in the package phytools36. As many gull species have discrete black regions on their wingtips, wingtip darkness was measured by Dufour et al. as the proportion of black on this section of the wing9. Proportion data is best modelled as a beta distribution37. There are few software packages that allow the analysis of phylogenetic data with a beta distribution, and I therefore used glmmTMB, which has an extension allowing incorporation of a phylogenetic covariance matrix for comparative analysis38. In beta regression, values must be greater than 0 and less than 1 and it is common practice to transform extreme values to lie within this range (there were too few extreme values to require a zero-one inflated beta regression)39. Species whose wingtips lack a black component (N = 5) were assigned the value 1 × 10−4 and those with fully black wingtips (N = 1) were assigned 9.999 × 10−1. Standardized wing loading and absolute latitude were entered as predictor variables. Model fit was assessed using the R package DHARMa, to check that there was no deviation of residuals from the expected distribution. To aid interpretation of the logit scale used by beta regression, I exponentiated the coefficients provided by the model output, which gives ratios; these are analogous to odds ratios in logistic regression. The intercept value is the ratio of black to non-black regions on the wingtip predicted for a species at the equator and with mean wing loading. The values for each predictor variable are the amount required to yield the ratio of black to non-black on the wingtips for each unit increase in x as predicted by the model. These ratios can then be converted back to proportions. ### Aspect ratio The aspect ratio of each species was calculated by dividing the square of the wingspan by the wing area. I conducted a linear regression with aspect ratio as the dependent variable and standardized wing loading as the independent variable. ### Reporting summary Further information on research design is available in the Nature Research Reporting Summary linked to this article.	2023-02-05 10:03:58	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5010800957679749, "perplexity": 2724.1171183618353}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500251.38/warc/CC-MAIN-20230205094841-20230205124841-00587.warc.gz"}
https://discuss.codechef.com/t/mobkun-editorial/104255	# MOBKUN - Editorial Author: Sai Panda Testers: Hriday, Utkarsh Gupta Editorialist: Nishank Suresh 1242 None # PROBLEM: A normal year contains N days, while a “Mob” year contains N+M days. Every K-th year is a “Mob” year. Given X, does the (X-1)-th day fall in a “Mob” year? # EXPLANATION: Let’s look at a consecutive set of K years, starting from the first. Years 1, 2, \ldots, K-1 are not “Mob” years, while year K is. In terms of days, this means the first (K-1)\times N days aren’t in a “Mob” year, while days (K-1)\times N + 1 to K \times N + M are in one. Notice that this already gives us the answer for when 1 \leq X \leq K\times N + M. What happens when X \gt K\times N + M? Well, by symmetry we can just ignore the first K\times N + M days! That is, the answer for X is the same as the answer for X - (K\times N + M). So, we keep subtracting K\times N + M from X till we reach a point where 1 \leq X \leq K\times N + M, then use the condition we derived above to answer for this X. However, this is too slow: for example, if K = N = M = 1, then we’d be subtracting 2 from X at each step, which is way too little when X is large. Instead, notice that the operation we are performing is exactly the modulo operation! That is, we are essentially computing X\pmod{K\times N + M}. So, simply compute this quantity, for example using the % operator in most languages. Notice that we want the result to be between 1 and K\times N + M, so if the result is zero then set it to K\times N + M. Finally, use the condition derived above to answer the query. This gives us a solution in \mathcal{O}(1) per test case. # TIME COMPLEXITY \mathcal{O}(1) per test case. # CODE: Editorialist's code (Python) for _ in range(int(input())): n, m, k, x = map(int, input().split()) x -= 1 print('No' if k > 1 and x % (kn + m) < (k-1)n else 'Yes') 1 Like Where am I going wrong? public static void main (String[] args) throws java.lang.Exception // your code goes here FastScanner fs = new FastScanner(); PrintWriter pw = new PrintWriter(System.out); int T = fs.nextInt(); while (T-- > 0) { int N = fs.nextInt(); int M = fs.nextInt(); int K = fs.nextInt(); int X = fs.nextInt(); if (X%(NK + M) <= N(K-1)) { pw.println("NO"); } else { pw.println("YES"); } } pw.close(); } if we take two more scanner to … Anime fan huh me tooo The problem says the day after (x -1) from day 1. That means xth day. Then why checking for (x -1)? 1 Like same doubt bro I assume you’re talking about the code linked at the bottom, because the editorial itself doesn’t use X-1 anywhere. I used X-1 in the code just to make implementation simpler. Notice that the editorial develops a logic where you check for whether X is less than or equal to (K-1)\cdot N, while the code checks whether X-1 is strictly less than (K-1)\cdot N. It should be obvious why these are equivalent. The only thing this avoids is the edge case when X\% (KN + M) = 0, where you need to treat this value as KN+M and not 0. I’ve also mentioned this in the editorial: This brings me to In relation to the discussion just above this: what does your code do when X\%(KN + M) = 0? Solution: 80937837 \| CodeChef check my solution u will understand i also wrote why things happende, and if it help don’t forget to drop a	2022-12-06 21:26:00	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7880982756614685, "perplexity": 2593.7403822155466}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711114.3/warc/CC-MAIN-20221206192947-20221206222947-00472.warc.gz"}
https://www.numerade.com/questions/evaluate-the-integral-displaystyle-int_0fracpi4-tan3-theta-sec2-theta-d-theta/	💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here! JH Evaluate the integral.$\displaystyle \int_0^{\frac{\pi}{4}} \tan^3 \theta \sec^2 \theta\ d \theta$ $\frac{1}{4}$ Discussion You must be signed in to discuss. Anna Marie V. Campbell University Heather Z. Oregon State University Caleb E. Baylor University Samuel H. University of Nottingham Lectures Join Bootcamp Video Transcript Let's do a U substitution here, take you to be tan of data, then do you equal sequence Where? Data. So let's go ahead and rewrite this. So watch out for those limits of integration. Here we have zero. It's a plug that in for data zero. So that's how new are lower Limit similarly for the upper limit plug that in U equals ten pyro for that's one. And then step back here. That's our one. And then we have Are you cubed right here? And this remaining term here in green, That's our deal. Seize the power rule here. You forthe over four zero one plugging that in point and then when you plug in zero, you get zero. So that's a final answer. JH Topics Integration Techniques Anna Marie V. Campbell University Heather Z. Oregon State University Caleb E. Baylor University Samuel H. University of Nottingham Lectures Join Bootcamp	2021-10-23 07:07:11	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8101414442062378, "perplexity": 5823.8616850989365}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585653.49/warc/CC-MAIN-20211023064718-20211023094718-00086.warc.gz"}
https://tutruong.expressions.syr.edu/?page_id=7	# Research My research lies in Complex and non-Archimedean Dynamics, Complex and Algebraic Geometry, Pluripotential Theory, and Several Complex Variables. The main objects of my research are complex varieties or projective varieties over a field other than complex numbers (e.g. the field of $p$-adic numbers), their geometric properties, and (meromorphic or rational) maps between them. I am also interested in applications of these fields to other fields, such as Mathematical Physics, Partial Differential Equations, and Statistics. A) SOME RESEARCH HIGHLIGHTS. In joint works with Fabrizio Catanese and Keiji Oguiso (see papers 1 and 3 below), I show the rationality and unirationality of some finite quotients of complex 3-tori. This solves a challenging question in Algebraic Geometry posed by Kenji Ueno in 1975. This also gives, for the first time, examples of unirational and rational 3-folds having primitive automorphisms of positive entropy. In joint works with Tien-Cuong Dinh and Viet-Anh Nguyen (see papers 6 and 8 below), I give criteria to check that a meromorphic selfmap does not preserve any non-trivial meromorphic fibration, and prove equidistribution and density results for isolated periodic points of a quite general class of meromorphic maps. I solve a question posed by Vincent Guedj in 2004 on the first dynamical degree of a meromorphic map. This result has applications to dynamics of complex 3-tori and more generally pseudo-automorphisms in dimension 3. See paper 7 below. I give an algebraic approach to define dynamical degrees for rational maps over an arbitrary algebraic closed field of characteristic zero. This has applications to dynamics over Berkovich analytic spaces. See paper 7 below. B) SELECTED WORKS IN PROGRESS. With Charles Favre, Topological entropy of endomorphisms over non-Archimedean fields. Preliminary report, July 2013. With Tien-Cuong Dinh and Viet-Anh Nguyen, Number of isolated periodic points of meromorphic maps. Preliminary report, June 2013. With Muhammed Alan, Monge-Ampere equations with singular right hand side. C) SELECTED PUBLICATIONS. Automorphisms of positive entropy + (Uni)rational varieties. 1) With Fabrizio Catanese and Keiji Oguiso, Unirationality of the Ueno-Campana’s threefold. Preprint: arXiv: 1310.3569. [pdf] 2) With Keiji Oguiso, Salem numbers in dynamics of K\”ahler $3$-folds and complex tori. Submitted for publication, preprint arXiv: 1309.4851. [pdf] 3) With Keiji Oguiso, Explicit examples of rational and Calabi-Yau threefolds with primitive automorphisms of positive entropy. Submitted for publication, preprint arXiv: 1306.1590. [pdf] 4) On automorphisms of blowups of projective manifolds. Submitted for publication, preprint arXiv: 1301.4957. [pdf] 5) On automorphisms of blowups of $\mathbb{P}^3$. Submitted for publication, preprint arXiv: 1202.4224. [pdf] Equidistribution of isolated periodic points. 6) With Tien-Cuong Dinh and Viet-Anh Nguyen, Equidistribution for meromorphic maps with dominant topological degree. Submitted for publication, preprint arXiv: 1303.5992. [pdf] Dynamical degrees. 7) The simplicity of the first spectral radius of a meromorphic map. This paper was divided into two parts. Part 1: accepted in Michigan Journal of Mathematics (pending minor revisions) [pdf]; Part 2: submitted for publication. Preprint arXiv: 1212.1019. [pdf] 8) With Tien-Cuong Dinh and Viet-Anh Nguyen, On the dynamical degrees of meromorphic maps preserving a fibration, Communications in Contemporary Mathematics 14, 1250042, 2012. [pdf] 9) Degree complexities of birational maps related to matrix inversions: Symmetric case, Mathematische Zeitschrift 270 (2012), no 3–4, 725–738. [pdf] 10) With Eric Bedford, Degree complexities of birational maps related to matrix inversion, Communications in Mathematical Physics 298 (2010), no. 2, 357–368. [pdf] 11) Degree complexity of a family of birational maps: II. Exceptional cases, Mathematical Physics, Analysis and Geometry 12 (2009), no 2, 157–180. [pdf] 12) With Eric Bedford, Kyounghee Kim, Nina Abarenkova, and Jean-Marie Maillard, Degree complexity of a family of birational maps, Mathematical Physics, Analysis and Geometry 11 (2008), no 1, 53–71. [pdf] Positive closed currents and Pullback by meromorphic maps. 13) With Dan Coman, Geometric properties of upper level sets of Lelong numbers on projective spaces. Submitted for publication, preprint arXiv: 1305.0864. [pdf] 14) Some dynamical properties of pseudo-automorphisms in dimension $3$. Transactions of the American Mathematical Society, accepted. Preprint arXiv: 1304.4100. [pdf] 15) Pullback of currents by meromorphic maps, Bulletin de la Soci\’et\’e Math\’ematique de France, accepted. Preprint arXiv: 1107.1743. [pdf] Analytic functions, Plurisubharmonic functions, and Applications. 16) With Dang Duc Trong, Cao Xuan Phuong, and Dinh Ngoc Thanh, Tikhonov’s regularization to deconvolution problem, Communications in Statistics: Theory and Methods, accepted. [pdf] 17) With Dang Duc Trong, Alain Pham Ngoc Dinh, and Phan Thanh Nam, Determination of the body force of a two dimensional isotropic elastic bodyJournal of Computational and Applied Mathematics 229 (2009), 192–207. [pdf] 18) Sets non-thin at $\infty$ in $\Bbb C ^m$, Journal of Mathematical Analysis and Applications 356 (2009), no 2, 517–524. [pdf] 19) With Dang Duc Trong, The growth at infinity of sequences of entire functions of bounded orders, Complex Variables and Elliptic Equations, Vol 53 (2008), No 8, 717–743. [pdf]	2017-11-18 02:32:05	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8398295640945435, "perplexity": 2508.988078855574}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934804518.38/warc/CC-MAIN-20171118021803-20171118041803-00416.warc.gz"}
https://gmatclub.com/forum/if-4-7-4-8-4-9-4-10-5-is-x-times-4-7-what-is-the-value-of-x-239161.html	GMAT Question of the Day - Daily to your Mailbox; hard ones only It is currently 25 Sep 2018, 12:30 ### GMAT Club Daily Prep #### Thank 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. Customized for You we will pick new questions that match your level based on your Timer History Track every week, we’ll send you an estimated GMAT score based on your performance Practice Pays we will pick new questions that match your level based on your Timer History # If 4^7 + 4^8 + 4^9 + 4^10/5 is x times 4^7, what is the value of x ? Author Message TAGS: ### Hide Tags SVP Status: Preparing for the GMAT Joined: 02 Nov 2016 Posts: 1677 Location: Pakistan GPA: 3.39 If 4^7 + 4^8 + 4^9 + 4^10/5 is x times 4^7, what is the value of x ? [#permalink] ### Show Tags Updated on: 27 Apr 2017, 21:48 00:00 Difficulty: 15% (low) Question Stats: 87% (01:20) correct 13% (01:04) wrong based on 44 sessions ### HideShow timer Statistics If $$\frac{4^7 + 4^8 + 4^9 + 4^{10}}{5}$$ is x times 4^7, what is the value of x ? A. 1/5 B. 4/5 C. 5 D. 13 E. 17 _________________ Official PS Practice Questions Press +1 Kudos if this post is helpful Last edited by stonecold on 27 Apr 2017, 21:48, edited 1 time in total. Edited the Question. BSchool Forum Moderator Joined: 26 Feb 2016 Posts: 3141 Location: India GPA: 3.12 Re: If 4^7 + 4^8 + 4^9 + 4^10/5 is x times 4^7, what is the value of x ? [#permalink] ### Show Tags 27 Apr 2017, 10:33 (4^7 + 4^8 + 4^9 + 4^10)/5 =(4^7(1 + 4 + 4^2 + 4^3))/5 =(4^7(1+4+16+64))/5 =4^7(85)/5 =4^7(17) which is 17 times 4^7(Option E) _________________ You've got what it takes, but it will take everything you've got Senior Manager Joined: 24 Apr 2016 Posts: 333 Re: If 4^7 + 4^8 + 4^9 + 4^10/5 is x times 4^7, what is the value of x ? [#permalink] ### Show Tags 27 Apr 2017, 10:50 (4^7 + 4^8 + 4^9 + 4^10)/5 = x * 4^7 => 4^7 * (1+4+4^2+4^3)/5 = x * 4^7 => (1+4+16+64)/5 = x => 85/5 = x = 17 Manager Joined: 05 Nov 2016 Posts: 88 Re: If 4^7 + 4^8 + 4^9 + 4^10/5 is x times 4^7, what is the value of x ? [#permalink] ### Show Tags 27 Apr 2017, 16:46 $$4^7$$(1+4+$$4^2$$+$$4^3$$)/5 $$4^7$$(1+4+16+64)/5 $$4^7$$(85)/5 $$4^7$$*17 Thus x=17 _________________ Kudos are always welcome ... as well your suggestions Manager Joined: 27 Jun 2015 Posts: 65 WE: Information Technology (Computer Software) Re: If 4^7 + 4^8 + 4^9 + 4^10/5 is x times 4^7, what is the value of x ? [#permalink] ### Show Tags 27 Apr 2017, 21:45 Thanks for the question. Its tagged to 700 level. But is it 700 level? Current Student Joined: 12 Aug 2015 Posts: 2647 Schools: Boston U '20 (M) GRE 1: Q169 V154 If 4^7 + 4^8 + 4^9 + 4^10/5 is x times 4^7, what is the value of x ? [#permalink] ### Show Tags 27 Apr 2017, 21:51 If 4^7 + 4^8 + 4^9 + 4^10/5 is x times 4^7, what is the value of x ? &nbs [#permalink] 27 Apr 2017, 21:51 Display posts from previous: Sort by # If 4^7 + 4^8 + 4^9 + 4^10/5 is x times 4^7, what is the value of x ? ## Events & Promotions Powered by phpBB © phpBB Group \| Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.	2018-09-25 19:30:22	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3291572630405426, "perplexity": 7630.479105602009}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267162385.83/warc/CC-MAIN-20180925182856-20180925203256-00236.warc.gz"}
http://tex.stackexchange.com/questions/48837/subcaption-package-incompatible-with-memoir-class	# subcaption package incompatible with memoir class? When I try to compile a document with the memoir class and the subcaption package I get the following error: ! Package subcaption Error: This package can't be used in cooperation with the subfig package. I presume this is because the memoir class loads the subfig package. Is that correct? Is there a way to make them work together? - Beyond what Harish says below, memoir also has built-in support for subfloats in general. See section 10.9 (Subcaptions) of the memoir manual -- no extra packages required, depending on your needs. – Mike Renfro Mar 21 '12 at 16:06 The subfig and subcaption packages can not be used in cooperation with each other. Instead, you can usecaption package with subfig to add some flavor to the captions and subcaptions (or you can use caption along with subcaption (which gives a subfigure command also). \documentclass{memoir} \usepackage[demo]{graphicx} % remove [demo] in your file \usepackage{subfig} % for subfigures \usepackage{caption} \usepackage{lipsum} \captionsetup[figure]{labelfont={bf,small},textfont={it,small}} \captionsetup[subfloat]{labelfont={bf,small},textfont={it,small}, subrefformat=parens} %<-----designing subcaption \newcommand{\myfigref}[2]{~\ref{#1}.\subref{#2}}% <---- a new macro for referring to a subfigure % \begin{document} %========================= \chapter{First chapter} \lipsum[1-4] %========================= \begin{figure}[ht] \includegraphics[width=1\textwidth]{my figure} \caption{My single picture}\label{fig:figures} \end{figure} %========================= \begin{figure}[ht] \centering \subfloat[My first picture]{\label{fig:mdleft}{\includegraphics[width=0.4\textwidth]{my figure}}}\hfill \subfloat[My second picture]{\label{fig:mdright}{\includegraphics[width=0.4\textwidth]{my figure}}} \caption{My two big pictures} \label{fig:subfigures} \end{figure} %=========================== From figure~\ref{fig:subfigures}.\subref{fig:mdleft}, we can see a small cat, in \myfigref{fig:subfigures}{fig:mdright} both can be used to refer figures. \end{document} - Thanks! How would you modify the example above to be able to "subref" to the subfigure captions? For example, in the text, I would like to say: In Figure 2.(a) we show ... . Also, why is it that your Figures start with the numbers 0.1 and 0.2? How would make that to go with the numbers 1, 2 etc.? – Amelio Vazquez-Reina Mar 21 '12 at 16:00 @roseck See my edited answer. – Harish Kumar Mar 21 '12 at 23:48 As Mike Renfro said in his comment, memoir already includes support for subfigures and subcaptions and there is no need to load packages subfig and caption. With next code you will reproduce Harish's result. \documentclass{memoir} \usepackage[demo]{graphicx} % remove [demo] in your file \usepackage{lipsum} % You need a newsubfloat element to use subcaption \newsubfloat{figure} % Command to set caption styles \captionnamefont{\bfseries\small} \captiontitlefont{\itshape\small} \subcaptionlabelfont{\bfseries\small} \subcaptionfont{\itshape\small} % \begin{document} %========================= \chapter{First chapter} \lipsum[1-4] %========================= \begin{figure}[ht] \includegraphics[width=1\textwidth]{my figure} \caption{My single picture}\label{fig:figures} \end{figure} %========================= \begin{figure}[ht] \centering \subbottom[My first picture\label{fig:mdleft}]% {\includegraphics[width=0.4\textwidth]{my figure}}\hfill \subbottom[My second picture\label{fig:mdright}]% {\includegraphics[width=0.4\textwidth]{my figure}} \caption{My two big pictures} \label{fig:subfigures} \end{figure} %=========================== %In next paragraph look at differences between \ref{subfigurelabel}, %\subcaptionref{subfigurelabel} and \subcaptionref{subfigurelabel} % In figure~\ref{fig:subfigures} we can see a small cat (\ref{fig:mdleft} or \subcaptionref{fig:mdleft}) and something else in \ref{fig:mdright} or \subcaptionref{fig:mdright}. \end{document} \newsubloat{figure} declares a new subfloat element which allows to use \subbottom commands. Now \ref{subfigurelabel} equals to '1.2(a)' while \subcaptionref{subfigurelabel} equals to '(a)' (with font attibutes) and the undocumented \subcaptionref* resets sublabel to normal font. - Thanks a lot!! Worked like a charm! :) – rmbianchi Aug 31 '12 at 14:05 Unfortunately the error message is misleading (), and the memoir document class is not working with my subcaption package yet. But you can give \let\subcaption\relax \let\subfloat\relax a try, just place this code before loading the subcaption package. () I have just changed that, so with future versions one will get the error message "Incompatible document class or package detected" instead. - I hope to be working on memoir soon again. Drop me an email, then er can see what can be done from the memoir side of things. – daleif Mar 22 '12 at 9:52 Finally I have found some time to take a closer look at this issue, and it seems that I was able to adapt the subcaption package for usage with the memoir document class. I'll release it with the upcoming version 3.3 of the caption package within the next weeks. – Axel Sommerfeldt Apr 10 '12 at 6:57 Thanks Axel for your work. Anyway I would like to let you know that while trying to compile memoir+subcaption with MacTex 2012 I still get the error from subcaption. – rmbianchi Aug 31 '12 at 13:06 Unfortunately the new version of the caption package bundle is not ready yet :-( See also: tex.stackexchange.com/a/27437/2574 – Axel Sommerfeldt Sep 1 '12 at 6:19	2016-02-13 09:01:19	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8885979652404785, "perplexity": 4815.472100718901}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701166261.11/warc/CC-MAIN-20160205193926-00172-ip-10-236-182-209.ec2.internal.warc.gz"}
http://thah.salernoeventicultura.it/scipy-extrapolate.html	# Scipy Extrapolate Extrapolator (interpolator=None, method=u'Linear', left=None, right=None) [source] ¶ Bases: object. Interpolate 2 D Or 3 D Scattered Data Matlab Griddata. interpolate. interp() accepts DataArray as similar to sel(), which enables us more advanced interpolation. Piecewise polynomial in the Bernstein basis. anderson_ksamp. An instance of this class is created by passing the 1-D vectors comprising the data. Yes, asking for numbers above 9 is stricto sensus extrapolation. A Demonstration Of The Improved Idw The Dots Are The Sample. Curve Fitting¶ One of the most important tasks in any experimental science is modeling data and determining how well some theoretical function describes experimental data. SciPy is a collection of mathematical algorithms and convenience functions built on the Numeric extension for Python. 0) does not > extrapolate data at the beginning and the end of a time series when using > the filtfilt function?. polyfit(x,y,1) f=interp1d(x,y. However, a general principal to numpy/scipy interpolators is that they interpolate and don't extrapolate. You can vote up the examples you like or vote down the ones you don't like. Curve fitting ¶ Demos a simple curve fitting. import numpy as np from scipy. interpolate)¶Sub-package for objects used in interpolation. Contribute to scipy/scipy development by creating an account on GitHub. Welcome to pyGAM's documentation!¶ pyGAM is a package for building Generalized Additive Models in Python, with an emphasis on modularity and performance. The ‘krogh’, ‘piecewise_polynomial’, ‘spline’, ‘pchip’ and ‘akima’ methods are wrappers around the respective SciPy implementations of similar names. Benchmarking Performance and Scaling of Python Clustering Algorithms If we're looking for scaling we can write off the scipy single linkage implementation Now we run that for each of our pre-existing datasets to extrapolate out predicted performance on the relevant dataset sizes. New in version 0. dblquad -- General purpose double integration. x and y are arrays of values used to approximate some function f, with y = f(x). fill_value can also be set to an array-like (or a two-element tuple of array-likes for separate below and above values) so long as it broadcasts properly to the non-interpolated dimensions of an array. cos (-x ** 2 / 8. u/magesing. Interpolate data with a piecewise cubic polynomial which is twice continuously differentiable [R0cc18619484f-1]. optimize)¶SciPy optimize provides functions for minimizing (or maximizing) objective functions, possibly subject to constraints. Algorithm to find the interpolating cubic spline. The goal of feature detection and matching is to identify a pairing between a point in one image and a corresponding point in another image. interp1d¶ class scipy. In curve fitting problems, the constraint that the interpolant has to go exactly through the data points is relaxed. Use a two-element tuple for the fill_value argument to specify separate fill values for input below and above the interpolation range. interpolate. PchipInterpolator¶ class scipy. In fact, using the same function, I can also extrapolate beyond my data, to get the estimates after 2010:. Linear spline: with two parameters and can only satisfy the following two equations required for to be continuous:. Unlike Scipy, the third argument is not a dense mgrid, but instead is just the ranges that would have been passed to mgrid. CubicSpline(). This article is republished with permission from the author from Medium's Towards Data Science blog. Data Structure : The basic data structure used by SciPy is a multidimensional array provided by the NumPy module. grid[1], self. python - Using fourier analysis for time series prediction fourier transform time series r (3) For data that is known to have seasonal, or daily patterns I'd like to use fourier analysis be used to make predictions. grid[2]), celldata, bounds_error=False, fill_value=None) return fn. Simply set fill_value='extrapolate' in the call. Piecewise polynomial in the Bernstein basis. Interpolation Python Interpolating A Gap In Scattered. PchipInterpolator(x, y, axis=0, extrapolate=None) [source] ¶ PCHIP 1-d monotonic cubic interpolation. Scipy library main repository. The first part of the word is "inter" as meaning "enter", which indicates us to look inside the data. 0) f = interpolate. The Scipy curve_fit function determines four unknown coefficients to minimize the difference between predicted and measured heart rate. The following are code examples for showing how to use scipy. polyfit( ) or numpy. meshgrid(x,y) def f. When used with the NumPy, SciPy, and matplotlib packages nmrglue provides a robust environment for rapidly developing new methods for processing, analyzing, and visualizing NMR data. 1/ reference/ generated/ scipy. Hope this is a relevant place to share. Extrapolate lines with numpy. log in sign up. nan, assume_sorted=False) [source] ¶ Interpolate a 1-D function. " is very debatable. Interpolation (scipy. from_derivatives. Yes, asking for numbers above 9 is stricto sensus extrapolation. linspace(0, 1, num=n, endpoint=False) # build the interpolator f_interp = scipy. interpolate. This is because the discrete Sibson approach requires the interpolated points to lie on an evenly spaced grid. grid[0], self. vq = interp1 (x,v,xq,method,extrapolation) specifies a strategy for evaluating points that lie outside the domain of x. brentq(f, a, b, args=(), xtol=2e-12, rtol=8. : You are free: to share - to copy, distribute and transmit the work; to remix - to adapt the work; Under the following conditions: attribution - You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but. By using the above data, let us create a interpolate function and draw a new interpolated graph. PchipInterpolator(x, y, axis=0, extrapolate=None) [source] ¶ PCHIP 1-d monotonic cubic interpolation. py; Optimized numdifftools. interpolate. linspace (0, 10, 80000) y = np. You can use interp function from scipy, it extrapolates left and right values as constant beyond the range: 2. linalg) • Sparse Eigenvalue Problems with ARPACK • Compressed Sparse Graph Routines scipy. interpolate is a convenient method to create a function based on fixed data points, which can be evaluated anywhere within the domain defined by the given data using linear interpolation. The algorithm given in w:Spline interpolation is also a method by solving the system of equations to obtain the cubic function in the symmetrical form. interp1d(x, y, kind=kind, axis=axis) # build the new sampling grid # exponentially spaced between t_min/n and 1 (exclusive) # we'll go one past where we need, and drop the last. Welcome to pyGAM's documentation!¶ pyGAM is a package for building Generalized Additive Models in Python, with an emphasis on modularity and performance. NearestNDInterpolator(). Modifying your code in this way gives: import numpy as np from scipy import interpolate x = np. pyplot as plt def extrapolate_nans(x, y, v): ''' Extrapolate the NaNs or masked values in a grid INPLACE using nearest value. The polynomial in the ith interval is x[i] <= xp < x[i+1]:. extrapolate='periodic', it will be set to False for the returned instance. The following are code examples for showing how to use scipy. interp1d has been improved. Sign up to join this community. Shape is determined by replacing the interpolation axis in the coefficient array with the shape of x. import numpy as np # Seed the random number generator for reproducibility np. "Learning SciPy for Numerical and Scientific Computing" unveils secrets to some of the most critical mathematical and scientific computing problems and will play an instrumental role in supporting your research. Brent's Method¶. linspace(-5, 5, num=50) y_data = 2. interpolate. Controls the extrapolation mode for elements not in the interval defined by the knot sequence. I have attempted to do that but it's not working. The LTE for the method is O(h 2), resulting in a first order numerical technique. By using the above data, let us create a interpolate function and draw a new interpolated graph. extrapolation (16) Python/Scipy 2D Interpolation(Non-uniform Data) This is a follow-up question to my previous post: Python/Scipy Interpolation(map_coordinates) Let's say I want to interpolate over a 2d rectangular area. py; Optimized numdifftools. ‘time’: Works on daily and higher resolution data to interpolate given length. nearest, zero, slinear, quadratic, cubic, spline, barycentric. Scipy Interpolate. The interpolant uses monotonic cubic splines to find the value of new points. py get_oribtal) azi azimuth viewing angle in degree (south is 0, counting clockwise) e. Further down in this post I'll share my code, but let's keep exploring. A Matplotlib. x and y are arrays of values used to approximate some function f, with y = f(x). Polynomial Interpolation And Extrapolation. You can vote up the examples you like or vote down the ones you don't like. Set extrapolation to 'extrap' when you want to use the method algorithm for extrapolation. For example, if you want to interpolate a two dimensional array along a particular dimension, as illustrated below, you can pass two 1-dimensional DataArray s with a. It is a pure Python package, and can easily be installed with pip install weave. The 'krogh', 'piecewise_polynomial', 'spline', 'pchip' and 'akima' methods are wrappers around the respective SciPy implementations of similar names. Piecewise polynomial in the Bernstein basis. Interpolation (scipy. interpolate - это удобный метод для создания функции на основе класса фиксированных точек данных - scipy. interpolate. Alternatively, you can specify a scalar value, in which case, interp1 returns that value for all points outside the domain of x. Data Structure : The basic data structure used by SciPy is a multidimensional array provided by the NumPy module. Curve Fitting¶ One of the most important tasks in any experimental science is modeling data and determining how well some theoretical function describes experimental data. If antiderivative is computed and self. 0 International license. One-dimensional smoothing spline fit to a given set of data points. pyplot as plt import numpy. Finally a statistical test (scipy. "Learning SciPy for Numerical and Scientific Computing" unveils secrets to some of the most critical mathematical and scientific computing problems and will play an instrumental role in supporting your research. Ill-conditioning First, the problem is ill-conditioned, but if you only provide a residual, Newton-Krylov is throwing away half your significant digits by finite differencing the residual to get the action of the Jacobian: $$J[x] y \approx \frac{F(x+\epsilon y) - F(x)}{\epsilon}$$ If you. interp1d support extrapolation via the fill_value="extrapolate" keyword. I had partial luck with scipy. The 'krogh', 'piecewise_polynomial', 'spline', 'pchip' and 'akima' methods are wrappers around the respective SciPy implementations of similar names. window_x], dtype=np. 0497870683679 0. if ext = 0 or 'extrapolate', returns the. extrapolate {bool, ‘periodic’, None}, optional If bool, determines whether to extrapolate to out-of-bounds points based on first and last intervals, or to return NaNs. PPoly¶ class scipy. interpolate. Extrapolation Interpolation What Are They Statistics. extrapolation. UnivariateSpline¶ class scipy. For interp2, the full grid is a pair of matrices whose elements represent a grid of points over a rectangular region. ndgriddata""" Convenience interface to N-D interpolation. If the requested windows and samples do not coincide with sampels in the original signal, spline interpolation is used to fill in intermediate values :param x: The discrete signal :param dim: The dimension of the sliding window embedding :param Tau: The increment between. must hold for some order. SciPy is both (1) a way to handle large arrays of numerical data in Python (a capability it gets from Numpy) and (2) a way to apply scientific, statistical, and mathematical operations to those arrays of data. This class returns a function whose call method uses interpolation. x must contain 2 complete cycles. solve_ivp (fun, t_span, but steps are taken using a 5th oder accurate formula (local extrapolation is done). Further down in this post I'll share my code, but let's keep exploring. Alternatively, you can specify a scalar value, in which case, interp1 returns that value for all points outside the domain of x. interp1d¶ class scipy. romb(y, dx=1. A simple way of doing extrapolations is to use interpolating polynomials or splines: there are many routines for this in scipy. 0) f = interpolate. Refer to: https:/ / docs. GitHub Gist: instantly share code, notes, and snippets. Interpolation (scipy. Linear spline: with two parameters and can only satisfy the following two equations required for to be continuous:. Matplotlib: gridding irregularly spaced data This requires Scipy 0. The SciPy (Scientific Python) package extends the functionality of NumPy with a substantial collection of useful algorithms, like minimization, Fourier transformation, regression, and other applied mathematical techniques. A third-order polynomial. interpolate. 1d example¶ This example compares the usage of the Rbf and UnivariateSpline classes from the scipy. Piecewise cubic polynomials (Akima interpolator). SciPy Reference Guide, Release 0. 1 Answers 1. Simply set fill_value='extrapolate' in the call. My former favourite, griddata, is a general workhorse for interpolation in arbitrary dimensions. Vq = interp2 (X,Y,V,Xq,Yq) returns interpolated values of a function of two variables at specific query points using linear interpolation. View license def _interpolated_template(self, templateid): """Return an interpolator for the given template""" phase, y = self. interpolate import griddata import matplotlib. "Learning SciPy for Numerical and Scientific Computing" unveils secrets to some of the most critical mathematical and scientific computing problems and will play an instrumental role in supporting your research. interpolate labels Sep 3, 2016. pyplot as plt def extrapolate_nans(x, y, v): ''' Extrapolate the NaNs or masked values in a grid INPLACE using nearest value. The following are code examples for showing how to use scipy. Interpolation refers to the process of generating data points between already existing data points. Extrapolation is the process of generating points outside a given set of known data points. UnivariateSpline (x, y, w = None, bbox = [None, None], k = 3, s). 8817841970012523e-16, maxiter=100, full_output=False, disp=True) [source] ¶ Find root of f in [a,b]. 5 * x_data) + np. 1d example¶ This example compares the usage of the Rbf and UnivariateSpline classes from the scipy. Although, since your data has a nice quadratic behavior, a better solution would be to fit it with a global polynomial, which is simpler and would yield more predictable results, poly = np. Scipy library main repository. 0) does not > extrapolate data at the beginning and the end of a time series when using > the filtfilt function?. I would like to use Snowmelt Runoff Model (SRM) for my research, I need to interpolate MODIS 8-Day snow cover data in to daily. Runge-Kutta methods are a class of methods which judiciously uses the information. from_derivatives. Numerical integration in Python with unknown constant. NearestNDInterpolator(). Controls the extrapolation mode for elements not in the interval defined by the knot sequence. If you have a max value of 1. interpolate, and there are quite easy to use (just give the (x, y) points, and you get a function [a callable, precisely]). py get_oribtal) azi azimuth viewing angle in degree (south is 0, counting clockwise) e. ; In the following we consider approximating between any two consecutive points and by a linear, quadratic, and cubic polynomial (of first, second, and third degree). interpolate) • Fourier Transforms (scipy. Contribute to scipy/scipy development by creating an account on GitHub. Example of the use of Spline(), Interp(), and Interpolate() functions. 1/ reference/ generated/ scipy. One-dimensional smoothing spline fit to a given set of data points. I have used Univariate splines from scipy, it silently extrapolates and the results can be quite "off" – Dhara Jun 26 '12 at 19:37. If antiderivative is computed and self. X and Y contain the coordinates of the sample points. max() values of x at which the residuals are less than a tolerance = 100 meters. Alternatively, you can specify a scalar value, in which case, interp1 returns that value for all points outside the domain of x. where(abs(data. This can only be achieved if polynomials of degree 5 or higher are used. Runge-Kutta Methods In the forward Euler method, we used the information on the slope or the derivative of y at the given time step to extrapolate the solution to the next time-step. updated doctest in nd_scipy. interp1d(x, y, kind='linear', axis=-1, copy=True, bounds_error=True, fill_value=np. if ext=1 or ‘zeros’, return 0 if ext=2 or ‘raise’, raise a ValueError. interpolate. import numpy as np # Seed the random number generator for reproducibility np. Piecewise polynomial in the Bernstein basis. Currently only supports maintaining the same number of dimensions. interp1d (x, y, kind='linear', axis=-1, copy=True, bounds_error=None, fill_value=nan, assume_sorted=False) [source] ¶. The other method used quite often is w:Cubic Hermite spline, this gives us the spline in w:Hermite form. My son was assigned the following simple math worksheet. You can vote up the examples you like or vote down the ones you don't like. Hey! sorry but the title is not clear enough because I didn't know how to describe it with few words. The Extrapolator class acts as a wrapper around a given Colour or scipy interpolator class instance with compatible signature. interpolate and kriging from scikit-learn. 00 and a value to interpolate of 1. window_x], dtype=np. Note: this page is part of the plotly. py Apache License 2. It is intended to be exhaustive. interp1dの新しいオプションがあり、外挿が可能です。コールでfill_value = 'extrapolate'を設定するだけです。この方法でコードを変更すると、次のようになります。. abs() to compute the residuals as the differences y_data - y_model; Find the. grid[0], self. signal) • Linear Algebra (scipy. #4697 anntzer wants to merge 1 commit into scipy : master from anntzer : anderson-darling-extrapolation Conversation 11 Commits 1 Checks 0 Files changed. My variable 'z' contains the data as shown b…. Modifying your code in this way gives: import numpy as np from scipy import interpolate x = np. The result is represented as a PPoly instance with breakpoints matching the given data. Let's say you have a bunch of lines and you would like to extrapolate (guess data points beyond the range of the data set) them. Let me discuss each method briefly, Method: Scipy. Python, NumPy and SciPy Interpolation of a Single Point and a Series of Points - Duration: 16:38. interpolate. interpolate - это удобный метод для создания функции на основе класса фиксированных точек данных - scipy. 1-d Example This example compares the usage of the Rbf and UnivariateSpline classes from the scipy. If antiderivative is computed and self. linspace(0, 1, num=n, endpoint=False) # build the interpolator f_interp = scipy. interp1d support extrapolation via the fill_value="extrapolate" keyword. seed(0) x_data = np. interp1d that allows extrapolation. 0, there is a new option for scipy. fill_value='extrapolate'とするとデータの外を補完できますが、もちろん離れれば離れるほど当てはまりは悪くなります。'cubic'の補完では11すら当てはまりません。. interpolate)¶ Sub-package for objects used in interpolation. brenth¶ scipy. GitHub Gist: instantly share code, notes, and snippets. 0000001, you're gonna get nans. Interpolation and Extrapolation in 2D in Python/v3 Learn how to interpolation and extrapolate data in two dimensions Note: this page is part of the documentation for version 3 of Plotly. Depending on the frequency of observations, a time series may typically be hourly, daily, weekly, monthly, quarterly and annual. def field_interpolator(self, celldata): from scipy. Curve fitting ¶ Demos a simple curve fitting. " This is an array object that is convenient for scientific computing. The values of s are determined by cubic spline interpolation of x and y. For more information on their behavior, see the SciPy documentation and SciPy tutorial. Sometimes, you might have seconds and minute-wise time series as well, like, number of clicks and user visits every minute etc. Also, are you sure you want to extrapolate? sometimes, getting out NaNs and knowing you are going out of range is a much better choice. Scipy library main repository. arange(0,10) y = np. figure(figsize=(6, 4. interpolate import griddata import matplotlib. interpolate module. # The final sample is positioned at (n-1)/n, so we omit the endpoint x = np. Its argument 'kind' specifies the interpolation type used. interpolate import interp1d import matplotlib. 1d example¶ This example compares the usage of the Rbf and UnivariateSpline classes from the scipy. interp1d(x, y, fill_value='extrapolate. The algorithm given in w:Spline interpolation is also a method by solving the system of equations to obtain the cubic function in the symmetrical form. " This is an array object that is convenient for scientific computing. You can use interp function from scipy, it extrapolates left and right values as constant beyond the range: 2. Interpolation Scipy Interpolate Scipy V0 14 0 Reference. Data Structure : The basic data structure used by SciPy is a multidimensional array provided by the NumPy module. axis - the axis along which to integrate show - When y is a single 1-d array, then if this argument is True. where(abs(data. Interpolation and Extrapolation in 2D in Python/v3 Learn how to interpolation and extrapolate data in two dimensions Note: this page is part of the documentation for version 3 of Plotly. Algorithm to find the interpolating cubic spline. Interpolation (scipy. PPoly(c, x, extrapolate=None) [source] ¶ Piecewise polynomial in terms of coefficients and breakpoints. X and Y contain the coordinates of the sample points. seasonal_decompose¶ statsmodels. interp1d has been improved. The interpolant uses monotonic cubic splines to find the value of new points. There have been a number of deprecations and API changes in this release, which are documented below. Let's say you have a bunch of lines and you would like to extrapolate (guess data points beyond the range of the data set. interpolate module. __call__ whether to extrapolate based on the first and last intervals or return nans. Radial basis functions can be used for smoothing/interpolating scattered data in n-dimensions, but should be used with caution for extrapolation outside of the observed data range. interpolate. Interpolation Python Interpolating A Gap In Scattered. I have used Univariate splines from scipy, it silently extrapolates and the results can be quite "off" – Dhara Jun 26 '12 at 19:37. The following are code examples for showing how to use scipy. interpn(points, values, xi, method='linear', bounds_error=True, fill_value=nan) [source] ¶ Multidimensional interpolation on regular grids. Hello, I have a data which represents aerosol size distribution in between 0. As listed below, this sub-package contains spline functions and classes, 1-D and multidimensional (univariate and multivariate) interpolation classes, Lagrange and Taylor polynomial interpolators, and wrappers for FITPACK and DFITPACK functions. (inter and extra are derived from Latin words meaning 'between' and 'outside' respectively) Interpolation and Extrapolation ¶. status : array The status: 0 is success, 1 is extrapolation within close_limit, 2 is extrapolation outside close_limit, 3 is failure, 4 is failure due to non-convergence of the Newton iteration in tensor product cells. 只需在通话中设置fill_value ='extrapolate'。用这种方式修改你的代码给出： import numpy as np from scipy import interpolate x = np. interp1d¶ class scipy. I have two lists of data that I have done a linear fit on, and I would like to extrapolate this linearly but I don't really know how. interpolate - это удобный метод для создания функции на основе класса фиксированных точек данных - scipy. romb(y, dx=1. Sign up to join this community. Default is self. So I'm working on a function that will read data out of a file and place it into a numpy array. The higher the order is, the more smooth the spline becomes. NumPy arrays can be of arbitrary integer dimension, and these principles extrapolate to 3D, 4D, etc. This class returns a function whose call method uses spline interpolation to find the. interpolation. You may do so in any reasonable manner, but. min() andnp. Contribute to scipy/scipy development by creating an account on GitHub. 9 """ from __future__ import division, print_function. vq = interp1 (x,v,xq,method,extrapolation) specifies a strategy for evaluating points that lie outside the domain of x. Akima1DInterpolator. array ([[1, 2],[3, 4]]) #Passing the values to the eig function l, v = linalg. interpolate)¶ Sub-package for objects used in interpolation. interp1d¶ class scipy. 0) f = interpolate. #4697 anntzer wants to merge 1 commit into scipy : master from anntzer : anderson-darling-extrapolation Conversation 11 Commits 1 Checks 0 Files changed. It is a pure Python package, and can easily be installed with pip install weave. New in version 0. They are from open source Python projects. figure(figsize=(6, 4. Modifying your code in this way gives: import numpy as np from scipy import interpolate x = np. 558931 500 NaN N… How to extrapolate a raster using in R. CubicSpline(). bounds_error:. The interpolant uses monotonic cubic splines to find the value of new points. Piecewise cubic polynomials (Akima interpolator). interpolate import griddata import matplotlib. 0 micrometer ranges. although based on the basin characteristics I have extracted 9. pp = spline (x,y) returns a piecewise polynomial structure for use by ppval and the spline utility unmkpp. def draw_graph(self, data_vector, color): #interpolate the data vector to fill in gaps d_interpld = interp1d(self. The results always pass through the original sampling of the function. It generates a function of points, based on our data. Returns the integral of function (a function of one variable) over the interval (a, b). grid[1], self. 0 International license. Scipy library main repository. interpolate. Interpolate values according to different methods. I am using the griddata interpolation package in scipy, and an extrapolation function pulled from fatiando: import numpy as np import scipy from scipy. Interpolation (scipy. 8817841970012523e-16, maxiter=100, full_output=False, disp=True) [source] ¶ Find a root of a function in a bracketing interval using Brent's method. However, a general principal to numpy/scipy interpolators is that they interpolate and don't extrapolate. as given by self. quad -- General purpose integration. Examples----->>> from scipy import stats >>> import matplotlib. interp1d (x, y, kind='linear', axis=-1, copy=True, bounds_error=None, fill_value=nan, assume_sorted=False) [source] ¶. The interpolant uses monotonic cubic splines to find the value of new points. Interpolation and Extrapolation in 2D in Python/v3 Learn how to interpolation and extrapolate data in two dimensions. fftpack) • Signal Processing (scipy. My son was assigned the following simple math worksheet. 0 International license. from_derivatives. interp1d support extrapolation via the fill_value="extrapolate" keyword. The following are code examples for showing how to use scipy. polyfit( ) or numpy. Extrapolate values in Pandas DataFrame It's very easy to interpolate NaN cells in a Pandas DataFrame: In[98]: df Out[98]: neg neu pos avg 250 0. This class returns a function whose call method uses spline interpolation to find the. brenth¶ scipy. The results always pass through the original sampling of the function. interpolate. Linear 1-d interpolation (interp1d) ¶ The interp1d class in scipy. Cubic spline data interpolator. A third-order polynomial. The other method used quite often is w:Cubic Hermite spline, this gives us the spline in w:Hermite form. I have attempted to do that but it's not working. brenth(f, a, b, args=(), xtol=2e-12, rtol=8. For more information on their behavior, see the SciPy documentation and SciPy tutorial. (Thus, it is fast and reliable. CubicSpline¶ class scipy. eig (A) #printing the result for eigen values print l #printing the result for eigen vectors print v. Ask Question I was hoping to use one of the SciPy's numerical integration functions such as integrate. PchipInterpolator¶ class scipy. Radial basis functions can be used for smoothing/interpolating scattered data in n-dimensions, but should be used with caution for extrapolation outside of the observed data range. signal vs Matlab: filtfilt and reflection On 4/15/14, John Krasting - NOAA Federal < [hidden email] > wrote: > Hi Scipy Users - > > Am I correct in reading that filtfilt in scipy. interp1d for 1-dimensional interpolation and scipy. 0 has been released. This class returns a function whose call method uses interpolation to find the value of new points. X and Y contain the coordinates of the sample points. interpolate. It provides a unique opportunity to interact with the "Who's who" of the Python for Scientific Computing fraternity and learn, understand, participate and contribute what is happening in the realms of Scientific Computing using Python. If your data is out of order, your also gonna screw things up. Fits a spline y = spl(x) of degree k to the provided x, y data. • Optimization (scipy. io) is a free Python distribution for SciPy stack. The API will be immediately familiar to anyone with experience of scikit-learn or scipy. interpolate is a convenient method to create a function based on fixed data points, which can be evaluated anywhere within the domain defined by the given data using linear interpolation. A variation on the classic Brent routine to find a zero of the function f between the arguments a and b that uses hyperbolic extrapolation instead of inverse quadratic extrapolation. Scipy Interpolate Interp2d Scipy V0 16 1 Reference Guide. UnivariateSpline as illustrated in this answer. interpolate import interp1d x = np. quad adaptive quadrature using QUADPACK romberg adaptive Romberg quadrature quadrature adaptive Gaussian. If you have a max value of 1. Returns the same object type as the caller, interpolated at some or all NaN values. polyfit( ) or numpy. x and y are arrays of values used to approximate some function f: y = f(x). Vq = interp2 (X,Y,V,Xq,Yq) returns interpolated values of a function of two variables at specific query points using linear interpolation. PCHIP 1-d monotonic cubic interpolation. interpolate. x, y and z are arrays of values used to approximate some function f: z = f(x, y). Modifying your code in this way gives: import numpy as np from scipy import interpolate x = np. You can vote up the examples you like or vote down the ones you don't like. 只需在通话中设置fill_value ='extrapolate'。用这种方式修改你的代码给出： import numpy as np from scipy import interpolate x = np. The code below illustrates the different kinds of interpolation method available for scipy. Yes, asking for numbers above 9 is stricto sensus extrapolation. 0497870683679 0. interp1d If the longitude dimension is not circular then extrapolation is allowed to make sure all end regular grid points get a value. 00 and a value to interpolate of 1. This class returns a function whose call method uses interpolation to find the value of new points. Python, NumPy and SciPy Interpolation of a Single Point and a Series of Points - Duration: 16:38. View MATLAB Command. Interpolation Scipy Interpolate Scipy V0 14 0 Reference. Interpolation and Extrapolation in 2D in Python/v3 Learn how to interpolation and extrapolate data in two dimensions Note: this page is part of the documentation for version 3 of Plotly. Interpolation and Extrapolation in 1D in Python/v3 Learn how to interpolation and extrapolate data in one dimension. Please note that only method='linear' is supported for DataFrame/Series with a MultiIndex. It contains many new features, numerous bug-fixes, improved test coverage and better documentation. interpolate. python - Using fourier analysis for time series prediction fourier transform time series r (3) For data that is known to have seasonal, or daily patterns I'd like to use fourier analysis be used to make predictions. The values of s are determined by cubic spline interpolation of x and y. arange(0,10) y = np. x and y are arrays of values used to approximate some function f, with y = f(x). interpolate is a convenient method to create a function based on fixed data points which can be evaluated anywhere within the domain defined by the given data using linear interpolation. vq = interp1 (x,v,xq,method,extrapolation) specifies a strategy for evaluating points that lie outside the domain of x. import numpy as n import scipy. If bc_type is a string, then the specified condition will be applied at both ends of a spline. window_x], dtype=np. Extrapolate lines with numpy. 4 Using radial basis functions for smoothing/interpolation Radial basis functions can be used for smoothing/interpolating scattered data in n-dimensions, but should be used with caution for extrapolation outside of the observed data range. 1-d Example This example compares the usage of the Rbf and UnivariateSpline classes from the scipy. However, the data I get is in the form of lists of different variables (x,y,z, temp, etc. Hey! sorry but the title is not clear enough because I didn't know how to describe it with few words. interpolate import griddata import matplotlib. When given a task to find a spline fit to a set of data, you have the choice of giving the routine the knots or by asking the routine to find an 'optimal. As of SciPy version 0. Let's say you have a bunch of lines and you would like to extrapolate (guess data points beyond the range of the data set. If 'periodic', periodic extrapolation is used. meshgrid(x,y) def f. Project: graph_distillation Author: google File: imgproc. Lesson 26: Introduction to Numpy and Scipy The central object for NumPy and SciPy is the ndarray, commonly referred to as a "NumPy array. PPoly¶ class scipy. The interp1d class in the scipy. state_x, data_vector) #convert data vector to a data array the size of the window's x dimension data_bar = np. interpolate is a convenient method to create a function based on fixed data points, which can be evaluated anywhere within the domain defined by the given data using linear interpolation. The values along its columns are constant. seed(0) x_data = np. Please note that only method='linear' is supported for DataFrame/Series with a MultiIndex. View MATLAB Command. Last updated on January 23, 2017. nan, assume_sorted=False) [source] ¶ Interpolate a 1-D function. arange(0,10) y = np. Extrapolate lines with numpy. Contribute to scipy/scipy development by creating an account on GitHub. Spline Interpolation of Sine Data. 0 micrometer ranges. solve_ivp (fun, t_span, but steps are taken using a 5th oder accurate formula (local extrapolation is done). One matrix contains the x-coordinates, and the other matrix contains the y-coordinates. 0) f = interpolate. The following are code examples for showing how to use scipy. In the following example, we calculate the function $$z(x,y) = \sin\left(\frac{\pi x}{2}\right)e^{y/2}$$ on a grid of points $(x,y)$ which is not evenly-spaced in. Topical software¶ This page indexes add-on software and other resources relevant to SciPy, categorized by scientific discipline or computational topic. I did not try splines, Chebyshev polynomials, etc. An instance of this class is created by passing the 1-D vectors comprising the data. This class returns a function whose call method uses spline interpolation to find the. They are from open source Python projects. interpolate. Unlike Scipy, the third argument is not a dense mgrid, but instead is just the ranges that would have been passed to mgrid. operating system. ) and the xyz-grid is generally irregular, but the math that we need to do on these arrays is matrix based so I need to find a way to convert the lists to a nice rectangular (if 2D) or retangular prismatic (3D) set. Hey! sorry but the title is not clear enough because I didn't know how to describe it with few words. Here are some of the interpolation methods which uses scipy backend. interp1d has been improved. As listed below, this sub-package contains spline functions and classes, 1-D and multidimensional (univariate and multivariate) interpolation classes, Lagrange and Taylor polynomial interpolators, and wrappers for FITPACK and DFITPACK functions. Refer to: https:/ / docs. Time series is a sequence of observations recorded at regular time intervals. An instance of this class is created by passing the 1-d vectors comprising the data. #importing the scipy and numpy packages from scipy import linalg import numpy as np #Declaring the numpy array A = np. Assigned: Feb. interpolate. Fourier Extrapolation in Python. 1-d Example This example compares the usage of the Rbf and UnivariateSpline classes from the scipy. It contains many new features, numerous bug-fixes, improved test coverage and better documentation. graph_objs as go from plotly. # The final sample is positioned at (n-1)/n, so we omit the endpoint x = np. • Optimization (scipy. To do the interpolation, I used the Scipy function interpolate. Last updated on January 23, 2017. Hope this is a relevant place to share. UnivariateSpline as illustrated in this answer. x and y are arrays of values used to approximate some function f, with y = f(x). NumPy arrays can be of arbitrary integer dimension, and these principles extrapolate to 3D, 4D, etc. SciPy guarantees fast, accurate, and easy-to-code solutions to your numerical and scientific computing applications. py and profiletools. Two extrapolation methods are available: - Linear: Linearly extrapolates given points using the slope defined by the interpolator boundaries (xi[0], xi[1]) if x < xi[0] and (xi[-1], xi[-2]) if x. interpolate)¶Sub-package for objects used in interpolation. brentq(f, a, b, args=(), xtol=2e-12, rtol=8. The interpolant uses monotonic cubic splines to find the value of new points. 1d example¶ This example compares the usage of the Rbf and UnivariateSpline classes from the scipy. You can vote up the examples you like or vote down the ones you don't like. It is intended to be exhaustive. PchipInterpolator¶ class scipy. So I guess my first claim "but last two [nan] don't [make sense] since a previous value is available. cth must have the same size and projection as the channel orbital an orbital object define by the tle file (see pyorbital. This can only be achieved if polynomials of degree 5 or higher are used. interp2d(x, y, z, kind='linear', copy=True, bounds_error=False, fill_value=nan) [source] ¶ Interpolate over a 2-D grid. interpolate. Interpolation (scipy. CubicSpline. 1/ reference/ generated/ scipy. In this exercise, we consider the perils of extrapolation. Note: this page is part of the documentation for version 3 of Plotly. The valid arguments are 'linear', 'nearest', 'zero', 'slinear', 'quadratic', 'cubic'. Runge-Kutta methods are a class of methods which judiciously uses the information. py, which is not the most recent from scipy import interpolate x = np. def draw_graph(self, data_vector, color): #interpolate the data vector to fill in gaps d_interpld = interp1d(self. interpolate)¶ Sub-package for objects used in interpolation. This class returns a function whose call method uses interpolation to find the value of new points. If you have a max value of 1. This is done because the antiderivative is no longer periodic and its correct evaluation outside of the initially given x interval is difficult. Extrapolate Anderson-Darling p-values linearly. Controls the extrapolation mode for elements not in the interval defined by the knot sequence. Linear spline: with two parameters and can only satisfy the following two equations required for to be continuous:. interpolate. Default is self. The algorithm given in w:Spline interpolation is also a method by solving the system of equations to obtain the cubic function in the symmetrical form. 只需在通话中设置fill_value ='extrapolate'。用这种方式修改你的代码给出： import numpy as np from scipy import interpolate x = np. interpolate is a convenient method to create a function based on fixed data points, which can be evaluated anywhere within the domain defined by the given data using linear interpolation. Piecewise polynomial in the Bernstein basis. This class returns a function whose call method uses interpolation. SciPy guarantees fast, accurate, and easy-to-code solutions to your numerical and scientific computing applications. seed(0) x_data = np. It includes solvers for nonlinear problems (with support for both local and global optimization algorithms), linear programing, constrained and nonlinear least-squares, root finding, and curve fitting. Spline functions and spline curves in SciPy. Brent's method is a combination of bisection, secant and inverse quadratic interpolation. vq = interp1(x,v,xq,method,extrapolation) specifies a strategy for evaluating points that lie outside the domain of x. def draw_graph(self, data_vector, color): #interpolate the data vector to fill in gaps d_interpld = interp1d(self. Linear 1-d interpolation (interp1d) ¶ The interp1d class in scipy. 0000001, you're gonna get nans. Although the data is evenly spaced in this example, it need not be so to use this routine. pyplot as plt import numpy as np x=[1,2,3,4,5,6] y=[2,4,6,8,10,12] p2=np. Last updated on January 23, 2017. SciPy guarantees fast, accurate, and easy-to-code solutions to your numerical and scientific computing applications. The interp1d class in the scipy. Examples----->>> from scipy import stats >>> import matplotlib. Returns the integral of function (a function of one variable) over the interval (a, b). interpolate. py; Optimized numdifftools. if ext=1 or ‘zeros’, return 0 if ext=2 or ‘raise’, raise a ValueError. I have attempted to do that but it's not working. Fill missing values using different methods. 0, there is a new option for scipy. Advanced Interpolation¶. Set extrapolation to 'extrap' when you want to use the method algorithm for extrapolation. I would like to use Snowmelt Runoff Model (SRM) for my research, I need to interpolate MODIS 8-Day snow cover data in to daily. Parameters x array_like. Returns: romb: ndarray. linspace(-1,1,100) y = np. interpolate. Linear 1-d interpolation (interp1d) ¶ The interp1d class in scipy. cth must have the same size and projection as the channel orbital an orbital object define by the tle file (see pyorbital. OF THE 10th PYTHON IN SCIENCE CONF. py install line_profiler on travis; Made python 3 compatible; Updated tests; Added test_profiletools. interpolate)¶Sub-package for objects used in interpolation. fill_value can also be set to an array-like (or a two-element tuple of array-likes for separate below and above values) so long as it broadcasts properly to the non-interpolated dimensions of an array. interpolation. However the second claim (which really is the crux of my post) is hard to argue against: you can't extrapolate to previous value if there in no previous value. "Learning SciPy for Numerical and Scientific Computing" unveils secrets to some of the most critical mathematical and scientific computing problems and will play an instrumental role in supporting your research. py Apache License 2. interp1d support extrapolation via the fill_value="extrapolate" keyword. array ([[1, 2],[3, 4]]) #Passing the values to the eig function l, v = linalg. The interp1d class in the scipy. It contains many new features, numerous bug-fixes, improved test coverage and better documentation. interpn() for multi-dimensional interpolation. Brent's Method¶. import numpy as np from scipy. (SCIPY 2011) Improving efﬁciency and repeatability of lake volume estimates using Python Tyler McEwen‡, Dharhas Pothina‡, Solomon Negusse‡ F Abstract—With increasing population and water use demands in Texas, ac-curate estimates of lake volumes is a critical part of planning for future water. This file is licensed under the Creative Commons Attribution-Share Alike 4. from scipy. SciPy is both (1) a way to handle large arrays of numerical data in Python (a capability it gets from Numpy) and (2) a way to apply scientific, statistical, and mathematical operations to those arrays of data. An overview of the module is provided by the help command: >>> help (integrate) Methods for Integrating Functions given function object. Interpolation Scipy Interpolate Scipy V0 14 0 Reference. interpolate improvements ¶. Welcome to pyGAM's documentation!¶ pyGAM is a package for building Generalized Additive Models in Python, with an emphasis on modularity and performance. get_viewing_geometry ele elevation viewing angle in degree (zenith is 90. interpolate)¶Sub-package for objects used in interpolation. Класс UnivariateSpline в scipy. (SCIPY 2011) Improving efﬁciency and repeatability of lake volume estimates using Python Tyler McEwen‡, Dharhas Pothina‡, Solomon Negusse‡ F Abstract—With increasing population and water use demands in Texas, ac-curate estimates of lake volumes is a critical part of planning for future water. s = spline (x,y,xq) returns a vector of interpolated values s corresponding to the query points in xq. Its argument 'kind' specifies the interpolation type used. quad -- General purpose integration. To gain access to the interpolation functions, import the module: import scipy. Yes, asking for numbers above 9 is stricto sensus extrapolation. Intermediate Python: Using NumPy, SciPy and Matplotlib Lesson 19 - Odds and Ends 1. interpolate. As you can see in the image I have used interp1d to graphically 'predict' the value of y when x=7. Extrapolate Anderson-Darling p-values linearly. BPoly(c, x[, extrapolate, axis]) Piecewise polynomial in terms of coefficients and breakpoints. def draw_graph(self, data_vector, color): #interpolate the data vector to fill in gaps d_interpld = interp1d(self. Please note that only method='linear' is supported for DataFrame/Series with a MultiIndex. Let me discuss each method briefly, Method: Scipy. fill_value='extrapolate'とするとデータの外を補完できますが、もちろん離れれば離れるほど当てはまりは悪くなります。'cubic'の補完では11すら当てはまりません。. Learn how to use python api scipy. extrapolate='periodic', it will be set to False for the returned instance. interpolate. A simple way of doing extrapolations is to use interpolating polynomials or splines: there are many routines for this in scipy. Let's say you have a bunch of lines and you would like to extrapolate (guess data points beyond the range of the data set) them. PchipInterpolator¶ class scipy. brentq(f, a, b, args=(), xtol=2e-12, rtol=8. def draw_graph(self, data_vector, color): #interpolate the data vector to fill in gaps d_interpld = interp1d(self. It is a private function, and therefore will be removed from the public API in a following release. x and y are arrays of values used to approximate some function f, with y = f(x). #6814: ENH: Different extrapolation modes for different dimensions in. versionadded:: 0. r/scipy: Press J to jump to the feed. 0) f = interpolate. interpolate import RectBivariateSpline import matplotlib. View MATLAB Command. Interpolation of an N-D curve¶ The scipy. where(abs(data. if ext=1 or 'zeros', return 0; if ext=2 or 'raise', raise a ValueError; if ext=3 or 'const', return the boundary value. The interp1d class in the scipy. 010394302658. Alternatively, you can specify a scalar value, in which case, interp1 returns that value for all points outside the domain of x. 61v88he7z6ht j6ez86v8q7yha 8xuglai8jj nwesa1yaxtq0pt9 9lfx88q053 55sv2g4nc9cw f0pr0bjyhr tf0nn00k1vu5d c81p52ax88 cobuev2m6ad3kk wl2ajf5685it 70fstmfzg763 9nd2s0l1dyi6t1 69jfh1ixzcvh 4jffoul0is etgbng5dhex5pas xnttvhmy35 bgxl0456ibq y07vrmp8cevadis 5z0zqq9u7jln dvoreahnyo f13jyz7nnfvc l1ysh3h0dt rwx2i0h2j93d7 90rklu01vfib w0h60ovvh1 7vfrfyrosk jgjnx7qsy96	2020-06-07 06:03:12	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2727993428707123, "perplexity": 2947.609499822162}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590348523564.99/warc/CC-MAIN-20200607044626-20200607074626-00030.warc.gz"}
http://mathhelpforum.com/latex-help/40417-arctan-x.html	1. ## arctan(x) Why doesnt math]\arctan(x)[/tex] yield a version that is not italicized, is it not a function, it says it is on LaTeX websites The same goes for any inverse trigonometric or hyperbolic functions 2. Originally Posted by Mathstud28 Why doesnt math]\arctan(x)[/tex] yield a version that is not italicized, is it not a function, it says it is on LaTeX websites The same goes for any inverse trigonometric or hyperbolic functions i guess the syntax is off. \arctan x works ...$\displaystyle \arctan x$ see? it is just the way the codes are set up. no parentheses 3. Originally Posted by Mathstud28 Why doesnt math]\arctan(x)[/tex] yield a version that is not italicized, is it not a function, it says it is on LaTeX websites The same goes for any inverse trigonometric or hyperbolic functions $$\arctan(x)$$ produces: $\displaystyle \arctan(x)$ RonL 4. Originally Posted by CaptainBlack $$\arctan(x)$$ produces: $\displaystyle \arctan(x)$ RonL Hmm...I think you are magic CaptainBlack, for it did not work before...well anyways $\displaystyle \arctan(x)!$....and thats happiness..not factorials xD $\displaystyle \arctanh(x)$ $\displaystyle \leftarrow$ what about arctanh? 5. Originally Posted by Mathstud28 Hmm...I think you are magic CaptainBlack, for it did not work before...well anyways $\displaystyle \arctan(x)!$....and thats happiness..not factorials xD what were you doing?! you probably had a typo in the arctan itself 6. Originally Posted by Jhevon what were you doing?! you probably had a typo in the arctan itself shut up... 7. Originally Posted by Mathstud28 Hmm...I think you are magic CaptainBlack, for it did not work before...well anyways $\displaystyle \arctan(x)!$....and thats happiness..not factorials xD $\displaystyle \arctanh(x)$ $\displaystyle \leftarrow$ what about arctanh? arctanh is not on the standard list of functions so you have to do it the hardway: $${\rm{arctanh}}(x)$$ $\displaystyle {\rm{arctanh}}(x)$ RonL 8. ## Re: arctan(x) Originally Posted by CaptainBlack arctanh is not on the standard list of functions so you have to do it the hardway: $${\rm{arctanh}}(x)$$ $\displaystyle {\rm{arctanh}}(x)$ RonL What is that "\rm" for? 9. ## Re: arctan(x) Originally Posted by Monoxdifly What is that "\rm" for? According to the "Bible" for TeX it is an out-of-date font declaration. i.e. no longer used.	2019-05-27 03:40:33	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9395067095756531, "perplexity": 4295.295651647645}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232260658.98/warc/CC-MAIN-20190527025527-20190527051527-00130.warc.gz"}
https://math.stackexchange.com/questions/3186522/evaluate-conditional-probability-in-brownian-motion	# evaluate conditional probability in brownian motion Let $$W_t$$ be a standard brownian motion, and let $$0 < x < y$$. We want to calculate: $$\mathbb{P}(W_y > 0 \vert W_x > 0)$$. I am pretty stuck on how to do this. The only insight I have is that we would probably want to take advantage of the fact that increments are independent in a Brownian motion to rewrite $$W_x, W_y$$ to evaluate this conditional probability, but I don't know how to do that or set up the integral that would probably result. I am new to this topic, so I apologize if this is a dumb question. • One way to get started is to note that the pair $(W_x,W_y)$ is jointly normal, with zero means, and covariance matrix $\left[\matrix{x&x\cr x&y\cr}\right]$. – John Dawkins Apr 15 at 15:42 • @JohnDawkins hmm, that makes sense! Then I can find out what $P(W_x, W_y) > 0$ is. But I would also need to calculate what $P(W_x > 0)$ is to find the full expression, do you have a suggestion for that? Thank you very much! – 0k33 Apr 15 at 21:00 • But $W_X$ is mean zero normal, so $P(W_x>0)=1/2$. – John Dawkins Apr 15 at 21:55 • @JohnDawkins oh man. I was sleeping on that one. Thank you so much, I know what to do now! If you want to put your comments as an answer, I will accept it, but if not that's also ok :) – 0k33 Apr 15 at 22:27	2019-05-25 23:08:21	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 4, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7326536178588867, "perplexity": 167.1143049111947}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232258453.85/warc/CC-MAIN-20190525224929-20190526010929-00079.warc.gz"}
https://mirror.niser.ac.in/cran/web/packages/PINSPlus/vignettes/PINSPlus.html	\tableofcontents \newpage \section{Introduction} In recent articles published in Genome Research [@nguyen2017novel] and Bioinformatics [@nguyen2019pinsplus], Nguyen et al. proposed a perturbation clustering approach for multi-omics data integration and disease subtyping called PINS. The framework was tested upon many datasets obtained from The Cancer Genome Atlas (TCGA), the European Genome-Phenome Archive and simulation study. Please consult Nguyen et al. [@nguyen2019pinsplus;@nguyen2017novel; @nguyen2017horizontal] for the mathematical description. PINS+ offers many improvements of PINS from practical perspectives. One outstanding feature is that the package is extremely fast and highly scalable. For example, it takes PINS+ only two minutes using a single core to analyze the Breast invasive carcinoma (BRCA) dataset (622 patients with three data types, mRNA, miRNA, and methylation) while it takes PINS 236 minutes (almost four hours) to analyze the same dataset. For more details on big data analysis, please consult Nguyen et al. [@nguyen2021smrt]. This document provides a tutorial on how to use the PINS+ package. PINS+ is designed to be convenient for users and uses two main functions: PerturbationClustering and SubtypingOmicsData. PerturbationClustering allows users to cluster a single data type while SubtypingOmicsData allows users to cluster multiple types of data. \section{PerturbationClustering} The PerturbationClustering function automatically determines the optimal number of clusters and the membership of each item (patient or sample) from a single data type in an \textbf{unsupervised analysis}. #### Preparing data The input of the function PerturbationClustering is a numerical matrix or data frame in which the rows represent items while the columns represent features. Load example data AML2004 library(PINSPlus) data(AML2004) data <- as.matrix(AML2004$Gene) #### Run PerturbationClustering Run PerturbationClustering with default parameters system.time(result <- PerturbationClustering(data = data, verbose = FALSE)) ## user system elapsed ## 4.264 6.072 0.789 PerturbationClustering supports parallel computing using the ncore parameter (default ncore = 1): result <- PerturbationClustering(data = data) Print out the number of clusters: result$k ## [1] 4 Print out the cluster membership: result$cluster ## ALL_Bcell_1 ALL_Bcell_2 ALL_Bcell_3 ALL_Bcell_4 ALL_Bcell_5 ## 2 2 3 2 2 ## ALL_Bcell_6 ALL_Bcell_7 ALL_Bcell_8 ALL_Bcell_9 ALL_Bcell_10 ## 2 3 3 3 3 ## ALL_Bcell_11 ALL_Bcell_12 ALL_Bcell_13 ALL_Bcell_14 ALL_Bcell_15 ## 2 2 3 2 2 ## ALL_Bcell_16 ALL_Bcell_17 ALL_Bcell_18 ALL_Bcell_19 ALL_Tcell_1 ## 3 2 2 2 1 ## ALL_Tcell_2 ALL_Tcell_3 ALL_Tcell_4 ALL_Tcell_5 ALL_Tcell_6 ## 1 1 1 1 1 ## ALL_Tcell_7 ALL_Tcell_8 AML_1 AML_2 AML_3 ## 1 1 4 2 4 ## AML_4 AML_5 AML_6 AML_7 AML_8 ## 4 4 4 4 4 ## AML_9 AML_10 AML_11 ## 4 4 4 Compare the result with the known sutypes [@Brunet:2004]: condition <- seq(unique(AML2004$Group[, 2])) names(condition) = unique(AML2004$Group[, 2]) plot(prcomp(AML2004$Gene)$x, col = result$cluster, pch = condition[AML2004$Group[, 2]], main = "AML2004") legend("bottomright", legend = paste("Cluster ", sort(unique(result$cluster)), sep = ""), fill = sort(unique(result$cluster))) legend("bottomleft", legend = names(condition), pch = condition) By default, PerturbationClustering runs with kMax = 5 and kmeans as the basic algorithm. PerturbationClustering performs kmeans clustering to partition the input data with $$k\in[2,10]$$ and then computes the optimal value of $$k$$. result <- PerturbationClustering(data = data, kMax = 5, clusteringMethod = "kmeans") To switch to other basic algorithms, use the clusteringMethod argument: result <- PerturbationClustering(data = data, kMax = 5, clusteringMethod = "pam") or result <- PerturbationClustering(data = data, kMax = 5, clusteringMethod = "hclust") By default, kmeans clustering runs with parameters nstart = 20 and iter.max = 1000. Users can pass new values to clusteringOptions to change these values: result <- PerturbationClustering( data = data, clusteringMethod = "kmeans", clusteringOptions = list(nstart = 100, iter.max = 500), verbose = FALSE ) Instead of using the built-in clustering algorithms such as kmeans, pam, and hclust, users can also pass their own clustering algorithm via the clusteringFunction argument. result <- PerturbationClustering(data = data, clusteringFunction = function(data, k){ # this function must return a vector of cluster kmeans(x = data, centers = k, nstart = k10, iter.max = 2000)$cluster }) In the above example, we use our version of kmeans instead of the built-in kmeans where the value of nstart parameter is dependent on the number of clusters k. Note that the implementation of clusteringFunction must accept two arguments: (1) data - the input matrix, and (2) k - the number of clusters. It must return a vector indicating the cluster to which each item is allocated. By default, PerturbationClustering adds noise to perturbate the data before clustering. The noise perturbation method by default accepts two arguments: noise = NULL and noisePercent = "median". To change these parameters, users can pass new values to perturbOptions: result <- PerturbationClustering(data = data, perturbMethod = "noise", perturbOptions = list(noise = 1.23)) or result <- PerturbationClustering(data = data, perturbMethod = "noise", perturbOptions = list(noisePercent = 10)) If the noise parameter is specified, the noisePercent parameter will be skipped. PerturbationClustering provides another built-in perturbation method called subsampling with a percent parameter: result <- PerturbationClustering(data = data, perturbMethod = "subsampling", perturbOptions = list(percent = 80)) If users wish to use their own perturbation method, they can pass it to the perturbFunction parameter: result <- PerturbationClustering(data = data, perturbFunction = function(data){ rowNum <- nrow(data) colNum <- ncol(data) epsilon <- matrix( data = rnorm(rowNum colNum, mean = 0, sd = 1.23456), nrow = rowNum, ncol = colNum ) list( data = data + epsilon, ConnectivityMatrixHandler = function(connectivityMatrix, iter, k) { connectivityMatrix } ) }) The one argument perturbFunction takes is data - the original input matrix. The perturbFunction must return a list object which contains the following entities: • data: a matrix after perturbating from input data and is ready for clustering. • ConnectivityMatrixHandler: a function that takes three arguments: i) connectivityMatrix - the connectivity matrix generated after clustering, ii) iter - the current iteration, and iii) k - the number of clusters. This function must return a compatible connectivity matrix with the original connectivity matrix. It aims to correct the connectivityMatrix if needed and returns its corrected version. PerturbationClustering provides several arguments to control stopping criterias: • iterMax: the maximum number of iterations. • iterMin: the minimum number of iterations that allows PerturbationClustering to calculate the stability of the perturbed connectivity matrix based on its AUC (Area Under the Curve) with the original one. If the perturbed connectivity matrix for current processing k is stable (based on madMin and msdMin), the iteration for this k will be stopped. • madMin: the minimum of Mean Absolute Deviation of AUC of Connectivity matrices. • msdMin: the minimum of Mean Square Deviation of AUC of Connectivity matrices. \section{Clustering big data using simulation} #### Preparing data We will create a simulation dataset that contains 50,000 samples and 5,000 genes. The dataset is represented in a matrix where rows are samples and columns are genes. The dataset has three distinct subtypes. Prepare data: sampleNum <- 50000 # Number of samples geneNum <- 5000 # Number of genes subtypeNum <- 3 # Number of subtypes # Generate expression matrix exprs <- matrix(rnorm(sampleNumgeneNum, 0, 1), nrow = sampleNum, ncol = geneNum) rownames(exprs) <- paste0("S", 1:sampleNum) # Assign unique names for samples # Generate subtypes group <- sort(rep(1:subtypeNum, sampleNum/subtypeNum + 1)[1:sampleNum]) names(group) <- rownames(exprs) # Make subtypes separate for (i in 1:subtypeNum) { exprs[group == i, 1:100 + 100(i-1)] <- exprs[group == i, 1:100 + 100*(i-1)] + 2 } # Plot the data library(irlba) exprs.pca <- irlba::prcomp_irlba(exprs, n = 2)$x plot(exprs.pca, main = "PCA") Run PINSPlus clustering: set.seed(1) t1 <- Sys.time() result <- PerturbationClustering(data = exprs.pca, ncore = 1) t2 <- Sys.time() Print out the running time: t2-t1 Print out the number of clusters: result$k Get the clusters assignment subtype <- result$cluster Here we assess the clustering accurracy using Adjusted Rand Index (ARI) [@steinley2004properties]. ARI takes values from -1 to 1 where 0 stands for a random clustering and 1 stands for a perfect partition result. if (!require("mclust")) install.packages("mclust") library(mclust) ari <- mclust::adjustedRandIndex(subtype, group) Plot the cluster assginments colors <- as.numeric(as.character(factor(subtype))) plot(exprs.pca, col = colors, main = "Cluster assigments for simulation data") legend("topright", legend = paste("ARI:", ari)) legend("bottomright", fill = unique(colors), legend = paste("Group ", levels(factor(subtype)), ": ", table(subtype)[levels(factor(subtype))], sep = "" ) ) \section{SubtypingOmicsData} SubtypingOmicsData automatically finds the optimum number of subtypes and its membership from multi-omics data through two processing stages: • Stage I: The algorithm first partitions each data type using the function PerturbationClustering and then merges the connectivities across data types into similarity matrices. Similarity-based clustering algorithms such as partitioning around medoids (pam) and hierarchical clustering (hclust) are used to partition the built similarity. The algorithm returns the partitioning that agrees the most with individual data types. • Stage II: The algorithm attempts to split each discovered group if there is a strong agreement between data types, or if the subtyping in Stage I is very unbalanced. #### Preparing data # Load the kidney cancer carcinoma data data(KIRC) # SubtypingOmicsData's input data must be a list of # numeric matrices that have the same number of rows: dataList <- list (as.matrix(KIRC$GE), as.matrix(KIRC$ME), as.matrix(KIRC$MI)) names(dataList) <- c("GE", "ME", "MI") # Run SubtypingOmicsData: result <- SubtypingOmicsData(dataList = dataList) By default, SubtypingOmicsData runs with parameters agreementCutoff = 0.5 and kMax = 10. SubtypingOmicsData uses the PerturbationClustering function to cluster each data type. The parameters for PerturbationClustering are described above in the previous part of this document. If users wish to change the parameters for PerturbationClustering, they can pass it directly to the function: result <- SubtypingOmicsData( dataList = dataList, clusteringMethod = "kmeans", clusteringOptions = list(nstart = 50) ) Plot the Kaplan-Meier curves and calculate Cox p-value: library(survival) cluster1=result$cluster1;cluster2=result$cluster2 a <- intersect(unique(cluster2), unique(cluster1)) names(a) <- intersect(unique(cluster2), unique(cluster1)) a[setdiff(unique(cluster2), unique(cluster1))] <- seq(setdiff(unique(cluster2), unique(cluster1))) + max(cluster1) colors <- a[levels(factor(cluster2))] coxFit <- coxph( Surv(time = Survival, event = Death) ~ as.factor(cluster2), data = KIRC$survival, ties = "exact" ) mfit <- survfit(Surv(Survival, Death == 1) ~ as.factor(cluster2), data = KIRC$survival) plot( mfit, col = colors, main = "Survival curves for KIRC, level 2", xlab = "Days", ylab = "Survival",lwd = 2 ) legend("bottomright", legend = paste( "Cox p-value:", round(summary(coxFit)\$sctest[3], digits = 5), sep = "" ) ) legend( "bottomleft", fill = colors, legend = paste("Group ", levels(factor(cluster2)), ": ", table(cluster2)[levels(factor(cluster2))], sep ="" ) ) ` \newpage # References \setlength{\parindent}{-0.2in} \setlength{\leftskip}{0.2in} \setlength{\parskip}{8pt} \noindent	2022-12-03 12:23:39	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.25843173265457153, "perplexity": 7143.965541836154}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710931.81/warc/CC-MAIN-20221203111902-20221203141902-00478.warc.gz"}
https://nforum.ncatlab.org/discussion/8156/string-diagrams-for-linearly-distributive-categories-with-unit-counit/	## Not signed in Want to take part in these discussions? Sign in if you have an account, or apply for one below ## Site Tag Cloud Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support. • CommentRowNumber1. • CommentAuthorMike Shulman • CommentTimeNov 13th 2017 Blute-Cockett-Seely-Trimble describes a string diagram / circuit diagram / proof net calculus for linearly distributive categories, which is significantly complicated by the presence of units; as discussed in section 2.3 of the paper, some of the unit and counit links have to be “attached” to other strings to prevent diagrams that should be distinct from getting identified. However, the example given there depends on the fact that the units $\top$ and $\bot$ for the tensor and cotensor products are different; as noted therein, if $\top$ in the example were replaced by $\bot$ then the two problematic diagrams would represent the same morphism. This makes me wonder, if we have a linearly distributive category that happens to satisfy $\top=\bot$, then does the whole string diagram calculus work without these extra attachments? This would be especially convenient because any closed monoidal category $(C,\otimes,\top)$ can be embedded by a closed functor into a linearly distributive (indeed $\ast$-autonomous) category in which $\top=\bot$, namely $Chu(C,\top)$. So we could soundly use linearly distributive string diagrams to reason about closed monoidal categories, without the need for the clunky “boxes” that are sometimes used to deal with internal-homs. • CommentRowNumber2. • CommentAuthorMike Shulman • CommentTimeNov 13th 2017 Oops, I’m not sure why I thought the embedding of $C$ in $Chu(C,d)$ is closed; it’s strong monoidal but doesn’t preserve internal-homs. So that’s not as interesting as I thought it was. • CommentRowNumber3. • CommentAuthorTodd_Trimble • CommentTimeNov 25th 2017 Sorry, I’ve been away from the nForum for a while. I’m pretty certain that the usual string diagram calculus (or the calculus of ordinary proof nets or Kelly-Mac Lane graphs) suffices for the case $\top = \bot$. I think this equation is sometimes referred to as the “mix” rule, and that a reference for the claim might be Blute’s thesis. • CommentRowNumber4. • CommentAuthorMike Shulman • CommentTimeNov 25th 2017 Ah, interesting; I hadn’t made the connection, but now I can see that that’s similar to the mix rule. I’ve usually seen the mix rule as $\frac{\Gamma \vdash \Delta \qquad \Phi \vdash \Psi}{\Gamma,\Phi\vdash\Delta,\Psi}$ which I can see follows from $\top=\bot$ and a cut. I guess there should be a 0-ary mix rule $\frac{\quad}{\quad\vdash\quad}$ as well? Do these two rules suffice to prove $\top=\bot$? • CommentRowNumber5. • CommentAuthorSam Staton • CommentTimeNov 26th 2017 Hi, one reference is Cockett and Seely, Proof theory for full intuitionistic linear logic, bilinear logic, and mix categories. An “isomix” category is one where ⊤≅⊥ — Lemma 6.6. • CommentRowNumber6. • CommentAuthorTodd_Trimble • CommentTimeNov 26th 2017 Thanks, Sam; that is also, I imagine, a better reference than Blute’s thesis for the claim about coherence. • CommentRowNumber7. • CommentAuthorMike Shulman • CommentTimeNov 28th 2017 Ah, thanks! I’ve read other parts of that paper, but always skipped the bit about mix. (-: I created mix rule to record this. • CommentRowNumber8. • CommentAuthorTodd_Trimble • CommentTimeNov 29th 2017 Thanks, Mike! • CommentRowNumber9. • CommentAuthorSam Staton • CommentTimeDec 1st 2017 • (edited Dec 3rd 2017) I think mix gives a different perspective on composition and perhaps hypergraphs are the right place to consider mix. Say a “hypergraph” on a set of vertices $V$ is a species coloured by $V$, ie a presheaf on the free symmetric monoidal category generated by $V$. Then we can say a “mix hypergraph” is a monoid for the Day convolution structure. It’s a model of linear logic without any connectives, without cut, but with mix. If we consider hypergraphs with an involution $$ on $V$, then we can also define “traced $$-hypergraph” as one where every edge on $(\Gamma,A,A)$ has an associated trace edge on $\Gamma$, satisfying some conditions. And then I think we can define “traced mix $$-hypergraph”, by putting on some more coherence conditions. Polycategory-like composition can then be defined by first using mix and then tracing. So traced mix $$-hypergraphs can be thought of as polycategories, and hopefully the representable ones are precisely the compact closed categories. • CommentRowNumber10. • CommentAuthorMike Shulman • CommentTimeDec 3rd 2017 Shouldn’t you consider directed hypergraphs, maybe as presheaves on $F(V\times V)$? • CommentRowNumber11. • CommentAuthorSam Staton • CommentTimeDec 3rd 2017 • (edited Dec 3rd 2017) I was thinking of one sided sequents. So for each list $\Gamma$ of vertices, there is a set of edges. And mix associates to each edge $p$ on $\Gamma$, and each edge $q$ on $\Delta$, an edge $(p\|q)$ on $(\Gamma,\Delta)$. But for the 2-sided formulation, I agree, a directed hypergraph should have, for each pair of lists of edges, a set of vertices. I suppose you meant $F(V+V)$? • CommentRowNumber12. • CommentAuthorMike Shulman • CommentTimeDec 3rd 2017 Yes, $F(V+V)$. It seems to me like if you want something with “no connectives” your sequents should be 2-sided; making things 1-sided generally presupposes a negation connective. • CommentRowNumber13. • CommentAuthorMike Shulman • CommentTimeDec 3rd 2017 Is there a standard notion of “mix polycategory”? It seems like kind of the “dual” of a properad: a polycategory composes only simply connected graphs, a properad composes connected ones, a prop composes arbitrary ones, while a “mix polycategory” would I guess compose disjoint unions of simply connected ones. • CommentRowNumber14. • CommentAuthorSam Staton • CommentTimeDec 12th 2017 Hi Mike, I have been meaning to come back to this because the literature on these things seems sparse and perhaps you or others understand it better than me. Regarding the role of negation, • When you form $F(V+V)$, it seems that you are freely adding a strict negation, in a similar way to the way that a multicategory is a coloured PRO, is that right? • In many presentations of classical linear logic, it seems that negation is not a “connective” but something more primitive. e.g. wikipedia • Do you know examples of naturally occurring linear distributive categories that are not -autonomous, but that still feel like models of classical linear logic? (so other than distributive lattices and when the two monoidal structures coincide?) • CommentRowNumber15. • CommentAuthorMike Shulman • CommentTimeDec 12th 2017 Good questions. • I don’t think so; if $X$ is a presheaf on $F(V+V)$ then $X(inl(x),inr(y),inl(z))$ means a morphism $(x,z) \to (y)$, and there’s no operation that mixes the $inl$’s and the $inr$’s. • Right, it took me a long time to really understand this. The key phrase that helped me is negation normal form, which means a way of expressing a formula in which all the negations are “pushed all the way inside”. The provable laws of ordinary classical (linear) logic, in which negation is a connective, imply that every formula is equivalent to one in negation normal form. This suggests that we could set up a system in which only formulas in negation normal form are permitted, where “negation” is an operation on formulas (i.e. on syntax) rather than a connective (an inductive constructor of syntax). It’s actually the same sort of thing as cut-elimination: every derivation is equivalent to one in “normal form” that doesn’t use cut, so we can set up a system in which only cut-free derivations exist, with cut as an operation on cut-free derivations (i.e. given cut-free derivations of $\Gamma\vdash A,\Delta$ and $\Phi,A\vdash \Psi$ we can construct a cut-free derivation of $\Gamma,\Phi\vdash \Delta,\Psi$). • No. (-: • CommentRowNumber16. • CommentAuthorMike Shulman • CommentTimeDec 13th 2017 Re: the third question, I don’t know whether to consider Dialectica-like models as “naturally occurring”, but they do give examples. E.g. if you apply a Dialectica construction to the fibration of subobjects in a cartesian closed coherent (but not Boolean) category, I think you get a linearly distributive category that is not $\ast$-autonomous, not a distributive lattice, and whose two monoidal structures don’t coincide. • CommentRowNumber17. • CommentAuthorSam Staton • CommentTimeDec 13th 2017 • (edited Dec 13th 2017) Hi, Thanks for the Dialectica idea, I’ll have a look. Regarding 1 in #16. I’ll say that a “strict -polycategory” is a polycategory with involution where $A^{\bot\bot}=A$ and $C(\Gamma,A^\bot;\Delta)=C(\Gamma;A,\Delta)$. And I’ll assume all polycategories are symmetric. So a strict -polycategory might as well be one-sided. We could even define it this way, with a one-sided composition $C(;\Gamma,A^\bot)\times C(;A,\Delta)\to C(;\Gamma,\Delta)$. I think many naturally occurring models of CLL are of this form. Now what I meant was that if $C$ is a polycategory with objects $V$ then it seems we can define a strict -polycategory $C$ with objects $(V+V)$ by saying that $C(inl(\Gamma);inl(\Delta))=C(\Gamma;\Delta)$, and that $(inl(v))^\bot=inr(v)$, and something about the permutation action. (This might well be a free construction.) And now I think we can regard a polycategory over $V$ as the same thing as a strict -polycategory over $(V+V)$ that satisfies the last two conditions. This seems to be in line with how you were defining directed hypergraphs. The point I was trying to make is that just as sometimes coloured PROs seem more basic than multicategories (and vice versa), so the same might be true for 1- versus 2-sided sequent calculi. • CommentRowNumber18. • CommentAuthorMike Shulman • CommentTimeDec 13th 2017 I agree that you can freely generate a $\ast$-polycategory from any polycategory in that way, and that you should be able to recover the original polycategory in sort of the same way that you can recover a multicategory from the monoidal category that it freely generates. But in such an $\ast$-polycategory a morphism has both a source and a target, each of which can contain both objects and their duals, so there is a formal distinction between “$A$ in the domain” and “$A^\perp$ in the codomain” that isn’t present in $F(V+V)$. This may be what you’re trying to get at with a “strict” $\ast$-polycategory, if by “$C(\Gamma,A^\bot;\Delta)=C(\Gamma;A,\Delta)$” you mean a literal equality of ZFC-style sets. But that sort of definition is fraught with problems, so if that’s what you want I think it’s better to actually define it one-sidedly. (In the literature on cyclic operads, the one-sided versions are called “entries-only”.) So we’re not “freely adding” a strict negation, we’re just representing domains and codomains in a different equivalent way. By the way, although one of the early definitions of “PRO” included the assumption that it was generated by a multicategory (i.e. every morphism with target $x_1\otimes\cdots\otimes x_n$ is a tensor product of morphisms with target $x_i$), nowadays people don’t usually include that. So not every PRO is generated by a multicategory. • CommentRowNumber19. • CommentAuthorSam Staton • CommentTimeDec 13th 2017 • (edited Dec 13th 2017) Thanks Mike. Yes, that’s what I meant. (I also prefer the one-sided version than the strict thing I wrote, but I got the impression that you didn’t like one-sided things, perhaps mistakenly.) I’d still like to put $a^{\perp\perp}=a$, if you don’t mind. So can I put it like this?: To give a polycategory with object set $V$ is to give an entries-only -polycategory with object set $(V+V)$ where $inl(v)^{\perp}=inr(v)$ such that a permutation condition holds. (I think the permutation condition is that the presheaf on $F(V+V)$ comes from a presheaf on $F(V)\times F(V)$.) I did think this would be a free construction, left adjoint to a forgetful functor (EntriesOnly-Poly) $\to$(Poly), but I haven’t checked. • CommentRowNumber20. • CommentAuthorMike Shulman • CommentTimeDec 14th 2017 In general I prefer two-sided things, but I prefer honestly one-sided things over one-sided things that are pretending to be two-sided. (-: Would you like to make star-polycategory?	2018-07-21 09:10:08	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 74, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9210952520370483, "perplexity": 1204.0955394336363}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676592475.84/warc/CC-MAIN-20180721090529-20180721110529-00588.warc.gz"}
https://www.studysmarter.us/explanations/math/pure-maths/multiplicative-relationship/	Suggested languages for you: \| \| ## All-in-one learning app • Flashcards • NotesNotes • ExplanationsExplanations • Study Planner • Textbook solutions # Multiplicative Relationship Relationship refers to the connection between things and the way they interact with each other. There are different types of relationships: platonic, romantic, business, family, etc. Relationships are not restricted to humans and animals alone. In mathematics, some relationships exist between numbers and quantities. In this article, we will be looking at the multiplicative relationship between quantities. ## Multiplicative relationship definition A multiplicative relationship between quantities is the relationship that exists when the quantities are directly proportional to each other or they are multiples of each other. In a multiplicative relationship, there is a constant number that is used to multiply another number to get a corresponding value. ## Multiplicative relationship equation A multiplicative relationship between two quantities is in the form, where is the output or dependent quantity, is the input or independent quantity, is the constant, or the constant of multiplication. The constant is what determines if the relationship is multiplicative or not. Hence if the product of constant and will not give , for every input and output, then it is not a multiplicative relationship. If you have a set of inputs and outputs and you want to determine if their relationship is multiplicative, you take note of the constant and make sure it is the same all through. We note that multiplication and division operations are related. Hence, if you have the values of and , you can get by dividing into while making sure that we are not dividing by zero. ## Multiplicative relationship examples Let's take some examples to understand what a multiplicative relationship is. Find the constants of the multiplicative relationships below. 1. 4 and 16 2. 2 and 6 Solution a. 4 and 16 4 is the input and 16 is the output. You can write this in the form of the multiplicative relationship equation. Dividing both sides of the equation by 4 to isolate we get, The constant is 4. b. 2 and 6 2 is the input and 6 is the output. You can write this in form of the multiplicative relationship equation to get the constant. Dividing both sides of the equation by 2 to isolate we get, The constant is 3. Let's take another example. Determine which set in the table below has a multiplicative relationship. Set A Set B Input (x) Output (y) Input (x) Output (y) 6 12 3 12 8 13 5 20 11 16 7 28 2 7 15 60 SolutionThe table above shows two sets A and B that contains pairs of numbers to compare. We want to know which set has a multiplicative relationship and which one does not.Recall the equation for a multiplicative relationship, Let's see what we will have if the numbers in set A are substituted in our equation. The first pair of numbers are 6 and 12. Our equation suggests that 6 multiplied by a number will give 12. Substituting in the equation gives Let's simplify further to get the constant , We can't conclude now that set A has a multiplicative relationship because there are still other pairs of numbers to consider and the constant has to be the same for all of them. The next pair of numbers are 8 and 13. 13 is the output and 8 is the input . Let's substitute in the formula to see what constant would be. Divide both sides by 8 to isolate , we get The constant we got here is different from the one we got before which means that the numbers in Set A do not have a multiplicative relationship. Let's consider now Set B.The first pair of numbers are 3 and 12. Let's substitute in our equation to see what our constant would be. Divide both sides by 3 to isolate to get, The constant is 4. Let's see if it will be the same for the other numbers in the set. The next pair of numbers are 5 and 20. Substituting in the equation will give, Dividing both sides of the equation by 5, to isolate , we get The constant here is 4. The third pair is 7 and 28. Substituting in the equation will give,Dividing both sides by 7, to isolate , we getAgain, we have 4 as the constant.The last pair of numbers are 15 and 60. Substituting in the equation will give,Dividing both sides by 15, to isolate , we getYou can see that the constant is 4 all through. This means that Set B has a multiplicative relationship. The multiplicative relationship is not restricted to a particular pair of numbers. All numbers when paired together have a multiplicative relationship. Consider the numbers 12 and 13, where 12 is the input and 13 is the output. If you are asked to find the multiplicative relationship between these numbers, you might be tempted to say that there is none, because there is no whole number that you can use to multiply 12 to give 13. This is where ratios and fractions come in. The constant in a multiplicative relationship can be expressed in form of a ratio or fraction. So, yes! 12 and 13 have a multiplicative relationship. If you multiply 12 by , you will get 13. When you come across these kinds of situations, you make sure that the denominator of the fraction you want to use to multiply has the same value as the input and the numerator must be the result you desire to get. Hence, the denominator in the fraction above is 12 and the numerator is 13. Let's take some examples. Show the multiplicative relationship between the pairs below. 1. 15 and 17 2. 35 and 27 Solution a. 15 and 17 Here, 15 is the input, and 17 is the output. To show the multiplicative relationship between 15 and 17, we have to multiply 15 by a fraction. The numerator of the fraction must be 17 and the denominator must be 15 so we can cancel out to get 17 as the answer. Let's recall the multiplicative relationship equation. where is 17 is 15 is the constant, is 17 as desired and is . b. 35 and 27 Here, 35 is the input, and 27 is the output. To show the multiplicative relationship between 25 and 27, we have to multiply 35 by a fraction. The numerator of the fraction must be 27 and the denominator must be 35 so we can cancel out to get 27 as the answer. Recall, the multiplicative relationship equation. where is 27 is 35 is the constant as desired and . Let's take another example. Determine which set in the table has a multiplicative relationship. Set A Set B Input (x) Output (y) Input (x) Output (y) 3 7 5 2 4 5 10 4 10 2 20 8 7 9 15 6 Solution We want to know which set of numbers have a multiplicative relationship. Let's start with Set A. The first pair of numbers in set A are 3 and 7 where 3 is the input and 7 is the output. Recall the multiplicative relationship equation, We will substitute in the equation to get the constant, The constant is . Let's find out if the next pair will give the same constant. The next pair is 4 and 5 where 4 is the input and 5 is the output. Let's substitute in the multiplicative relationship formula. The constant here is different from the first. This means that the numbers in set A do not have a multiplicative relationship. Let's take a look at set B. The first pair of numbers are 5 and 2 where 5 is the input and 2 is the output. Let's substitute in the multiplicative relationship formula. The constant is . If the rest of the pair have as their constant, then there is a multiplicative relationship. The next pair is 10 and 4 where 10 is the input and 4 is the output. Let's substitute in the multiplicative relationship formula. We have a constant of which is the same as the first. Let's try the last two pair. The third pair is 20 and 8 where 20 is the input and 8 is the output. Substituting in the formula will give, The constant is again. The last pair is 15 and 6 where 15 is the input and 6 is the output. Let's substitute in the multiplicative relationship formula. Again, we have the constant to be . This means that the numbers in set B have a multiplicative relationship. ## Multiplicative relationship graph Multiplicative relationships can also be represented in a graph. You can use the multiplicative relationship equation to derive pairs of numbers that can be plotted on a graph. A graph representing multiplicative relationships is a straight line and it always starts from the origin, because anything multiplied by zero is zero. Let's see some examples. If complete the table below and plot the graph. x y 0 1 2 3 Solution The equation given is and you will notice that it is in the form of the multiplicative relationship equation What we need to do is substitute the values of in the equation given to get . When , When , When , When , Now let's put the results we've gotten in the table. x y 0 0 1 4 2 8 3 12 Now that we've completed the table, let's plot the graph. We can see that the graph has the characteristics of a multiplicative relationship graph which is that it is linear and it starts from the origin (0, 0). So far, we've shown what multiplicative relationships are and how to solve them using numbers. Although, the numbers represent values of quantities, let's now look at a real-world situation concerning multiplicative relationships. Let's take some examples. A company pays its workers £13 per hour. Show the multiplicative relationship here, create a table and plot a graph from the information on the table. Solution The question says a company pays £13 per hour. Believe it or not, there are two quantities to consider here. You have to consider the money earned and the hours worked. Now, we have to figure out what x and y are. Recall that x is the input or independent quantity and y is the output or dependent quantity. The independent quantity here is the hours worked. This is because the worker has control over it. The worker decides how many hours they can work. The dependent quantity is the money earned because it depends on how many hours are worked. Recall the multiplicative relationship equation A worker will earn £13 per hour meaning that: and . We can substitute this in the equation to get the constant, For a question like this, you may not need to go through this step to find the constant because it is quite clear that you will have to multiply 13 by the number of hours worked to get the total money earned. Now let's move on to creating a table. The table will contain the number of hours worked and the money earned. The number of hours will be multiplied by the constant 13 to get the money earned. We have when , when , when , when So, we will use the values we've got to fill the table. Number of hours worked (x) Money earned (y) 1 13 2 26 5 65 6 78 With this information, we can now plot a graph. We know that the graph is correct because it is linear. ## Multiplicative Relationship - Key takeaways • Multiplicative relationships between quantities are the relationships that exist when the quantities are directly proportional to each other or they are multiples of each other. • If you have a set of inputs and outputs and you want to determine if their relationship is multiplicative, you take note of the constant and make sure it is the same all through. • If the constant is not the same, then it is not a multiplicative relationship. • The constant of multiplication in a multiplicative relationship is not necessarily an integer, it can be a real number. • The graph of a multiplicative relationship between quantities is a straight line passing through the origin. Multiplicative relationship between quantities is the relationship that exists when the quantities are multiples of each other. If a relationship is additive, you will be able to add a constant number to one value to get a corresponding value all through. If a relationship is multiplicative, you will be able to multiply a constant number to one value to get a corresponding value all through. Two pairs of quantities whose values are 2 and 4 and 1 and 2 respectively have a multiplicative relationship because 2 can be multiplied by 2 to get 4 and 2 can also be multiplied by 1 to get 2. A multiplicative pattern is when a constant number is multiplied by an input to get a corresponding value. The aspects of multiplicative relations are the input, output and the constant. The multiplicative relation is y = ax where y is the output x is the input a is the constant ## Final Multiplicative Relationship Quiz Question What is a multiplicative relationship? A multiplicative relationship between quantities is the relationship that exists when the quantities are directly proportional to each other or they are multiples of each other. Show question Question How do you identify a multiplicative relationship? If you have a set of inputs and outputs and you want to determine if their relationship is multiplicative, you take note of the constant and make sure it is the same all through. If the constant is not the same, then it is not a multiplicative relationship. Show question 60% of the users don't pass the Multiplicative Relationship quiz! Will you pass the quiz? Start Quiz ## Study Plan Be perfectly prepared on time with an individual plan. ## Quizzes Test your knowledge with gamified quizzes. ## Flashcards Create and find flashcards in record time. ## Notes Create beautiful notes faster than ever before. ## Study Sets Have all your study materials in one place. ## Documents Upload unlimited documents and save them online. ## Study Analytics Identify your study strength and weaknesses. ## Weekly Goals Set individual study goals and earn points reaching them. ## Smart Reminders Stop procrastinating with our study reminders. ## Rewards Earn points, unlock badges and level up while studying. ## Magic Marker Create flashcards in notes completely automatically. ## Smart Formatting Create the most beautiful study materials using our templates.	2022-11-30 17:30:47	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8496304154396057, "perplexity": 458.8391100401313}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710765.76/warc/CC-MAIN-20221130160457-20221130190457-00272.warc.gz"}
https://indico.cern.ch/event/181055/contributions/308880/	# Quark Matter 2012 12-18 August 2012 US/Eastern timezone ## Event anisotropy v_2 in Au+Au collisions at 7.7 - 62.4 GeV with STAR 17 Aug 2012, 15:20 20m Regency 2/3 () ### Regency 2/3 Oral Presentation Exploring the QCD phase diagram Shusu Shi (CCNU) ### Description The exploration of the QCD phase diagram in the region of a possible phase transition between the Quark Gluon Plasma (QGP) and the hadron gas phase is one of the main goals of the RHIC Beam Energy Scan(BES). One of the most important observables from high-energy nuclear collisions to study the early evolution of the expanding system is the elliptic flow $v_{2}$. At the top RHIC energy, $\sqrt{s_{NN}}$ = 200 GeV, the number-of-constituent quark (NCQ) scaling of $v_{2}(p_{T})$ is interpreted as a signature of deconfinement and the formation of the QGP phase. A disappearance of the NCQ scaling is expected for a pure hadronic system at low beam energies. Hence it is a necessary signature to identify the phase transition. We present the $v_2$ measurement at midrapidity from Au+Au collisions at $\sqrt{s_{NN}}=$ 7.7, 11.5, 19.6, 27, 39 and 62.4 GeV for inclusive charged hadrons, light nuclei ($d$, $\bar{d}$) and identified hadrons ($\pi^{\pm}$, $K^{\pm}$, $K_{S}^{0}$, $p$, $\bar{p}$, $\phi$, $\Lambda$, $\bar{\Lambda}$, $\Xi^{-}$, $\bar{\Xi}^{+}$, $\Omega^{-}$, $\bar{\Omega}^{+}$) up to 4 GeV/$c$ in $p_{T}$. The beam energy and centrality dependence of charged hadron $v_2$ are presented with comparison to higher energies at RHIC and LHC. The identified hadron $v_{2}$ are used to discuss the NCQ scaling for different beam energies. Significant difference in $v_{2}(p_{T})$ is observed between particles and corresponding anti-particles for $\sqrt{s_{NN}} <$ 39 GeV. These differences are more pronounced for baryons compared to mesons and they increase with decreasing energy and increasing centrality. The $v_{2}$ difference between particles and anti-particles shows an almost linear dependency with the baryon chemical potential $\mu_{B}$. The transport model calculations of UrQMD and AMPT models are compared with the experimental data. Slides	2020-08-08 01:12:49	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8027840852737427, "perplexity": 1295.50485271707}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439737233.51/warc/CC-MAIN-20200807231820-20200808021820-00308.warc.gz"}
https://www.lmfdb.org/ModularForm/GL2/Q/holomorphic/1200/3/l/f/	# Properties Label 1200.3.l.f Level $1200$ Weight $3$ Character orbit 1200.l Analytic conductor $32.698$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$ # Related objects ## Newspace parameters Level: $$N$$ $$=$$ $$1200 = 2^{4} \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 1200.l (of order $$2$$, degree $$1$$, not minimal) ## Newform invariants Self dual: no Analytic conductor: $$32.6976317232$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{-11})$$ Defining polynomial: $$x^{2} - x + 3$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 75) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$ ## $q$-expansion Coefficients of the $$q$$-expansion are expressed in terms of $$\beta = \frac{1}{2}(1 + \sqrt{-11})$$. We also show the integral $$q$$-expansion of the trace form. $$f(q)$$ $$=$$ $$q + ( -3 + \beta ) q^{3} + ( 6 - 5 \beta ) q^{9} +O(q^{10})$$ $$q + ( -3 + \beta ) q^{3} + ( 6 - 5 \beta ) q^{9} + ( 5 - 10 \beta ) q^{11} + 10 q^{13} + ( 1 - 2 \beta ) q^{17} -7 q^{19} + ( -6 + 12 \beta ) q^{23} + ( -3 + 16 \beta ) q^{27} + ( -10 + 20 \beta ) q^{29} -42 q^{31} + ( 15 + 25 \beta ) q^{33} -40 q^{37} + ( -30 + 10 \beta ) q^{39} + ( 5 - 10 \beta ) q^{41} + 50 q^{43} + ( 14 - 28 \beta ) q^{47} -49 q^{49} + ( 3 + 5 \beta ) q^{51} + ( -14 + 28 \beta ) q^{53} + ( 21 - 7 \beta ) q^{57} + ( 20 - 40 \beta ) q^{59} -8 q^{61} -45 q^{67} + ( -18 - 30 \beta ) q^{69} + ( 10 - 20 \beta ) q^{71} -35 q^{73} -12 q^{79} + ( -39 - 35 \beta ) q^{81} + ( -21 + 42 \beta ) q^{83} + ( -30 - 50 \beta ) q^{87} + ( 45 - 90 \beta ) q^{89} + ( 126 - 42 \beta ) q^{93} -70 q^{97} + ( -120 - 35 \beta ) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - 5q^{3} + 7q^{9} + O(q^{10})$$ $$2q - 5q^{3} + 7q^{9} + 20q^{13} - 14q^{19} + 10q^{27} - 84q^{31} + 55q^{33} - 80q^{37} - 50q^{39} + 100q^{43} - 98q^{49} + 11q^{51} + 35q^{57} - 16q^{61} - 90q^{67} - 66q^{69} - 70q^{73} - 24q^{79} - 113q^{81} - 110q^{87} + 210q^{93} - 140q^{97} - 275q^{99} + O(q^{100})$$ ## Character values We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times$$. $$n$$ $$401$$ $$577$$ $$751$$ $$901$$ $$\chi(n)$$ $$-1$$ $$1$$ $$1$$ $$1$$ ## Embeddings For each embedding $$\iota_m$$ of the coefficient field, the values $$\iota_m(a_n)$$ are shown below. For more information on an embedded modular form you can click on its label. Label $$\iota_m(\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$ 401.1 0.5 − 1.65831i 0.5 + 1.65831i 0 −2.50000 1.65831i 0 0 0 0 0 3.50000 + 8.29156i 0 401.2 0 −2.50000 + 1.65831i 0 0 0 0 0 3.50000 8.29156i 0 $$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles ## Inner twists Char Parity Ord Mult Type 1.a even 1 1 trivial 3.b odd 2 1 inner ## Twists By twisting character orbit Char Parity Ord Mult Type Twist Min Dim 1.a even 1 1 trivial 1200.3.l.f 2 3.b odd 2 1 inner 1200.3.l.f 2 4.b odd 2 1 75.3.c.f yes 2 5.b even 2 1 1200.3.l.s 2 5.c odd 4 2 1200.3.c.d 4 12.b even 2 1 75.3.c.f yes 2 15.d odd 2 1 1200.3.l.s 2 15.e even 4 2 1200.3.c.d 4 20.d odd 2 1 75.3.c.c 2 20.e even 4 2 75.3.d.c 4 60.h even 2 1 75.3.c.c 2 60.l odd 4 2 75.3.d.c 4 By twisted newform orbit Twist Min Dim Char Parity Ord Mult Type 75.3.c.c 2 20.d odd 2 1 75.3.c.c 2 60.h even 2 1 75.3.c.f yes 2 4.b odd 2 1 75.3.c.f yes 2 12.b even 2 1 75.3.d.c 4 20.e even 4 2 75.3.d.c 4 60.l odd 4 2 1200.3.c.d 4 5.c odd 4 2 1200.3.c.d 4 15.e even 4 2 1200.3.l.f 2 1.a even 1 1 trivial 1200.3.l.f 2 3.b odd 2 1 inner 1200.3.l.s 2 5.b even 2 1 1200.3.l.s 2 15.d odd 2 1 ## Hecke kernels This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{3}^{\mathrm{new}}(1200, [\chi])$$: $$T_{7}$$ $$T_{11}^{2} + 275$$ $$T_{13} - 10$$ ## Hecke characteristic polynomials $p$ $F_p(T)$ $2$ $$T^{2}$$ $3$ $$9 + 5 T + T^{2}$$ $5$ $$T^{2}$$ $7$ $$T^{2}$$ $11$ $$275 + T^{2}$$ $13$ $$( -10 + T )^{2}$$ $17$ $$11 + T^{2}$$ $19$ $$( 7 + T )^{2}$$ $23$ $$396 + T^{2}$$ $29$ $$1100 + T^{2}$$ $31$ $$( 42 + T )^{2}$$ $37$ $$( 40 + T )^{2}$$ $41$ $$275 + T^{2}$$ $43$ $$( -50 + T )^{2}$$ $47$ $$2156 + T^{2}$$ $53$ $$2156 + T^{2}$$ $59$ $$4400 + T^{2}$$ $61$ $$( 8 + T )^{2}$$ $67$ $$( 45 + T )^{2}$$ $71$ $$1100 + T^{2}$$ $73$ $$( 35 + T )^{2}$$ $79$ $$( 12 + T )^{2}$$ $83$ $$4851 + T^{2}$$ $89$ $$22275 + T^{2}$$ $97$ $$( 70 + T )^{2}$$	2021-08-02 06:01:59	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9721582531929016, "perplexity": 6079.537697401762}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154304.34/warc/CC-MAIN-20210802043814-20210802073814-00097.warc.gz"}
http://jinyeongpark.com/?cat=16	# Seminar on PDE and related topics in October 2018 1 Time: 12th October (Friday) 14:30 - 15:30 Speaker: Prof. Woocheol Choi (Incheon National University) Place: #702, Natural Science Building, Hanyang University Title: Introduction to the control theory with applications in mechanical engineerings. Abstract: 제어이론은 수학과 공학의 접점에 있는 분야로 20세기를 거치며 광범위하게 발전해 왔다. 특히 기계공학에서의 필수적인 역할을 하고 있으며, 현대에는 에너지, 반도체 등의 기술 발전으로 드론과 다양한 로봇들이 상용화 되고 있고, 관련된 제어기술의 수요도 증가하고 있다. 이번 발표에서는 제어 이론의 몇가지 기본적인 아이디어들과 예들을 소개하고, 최근 몇가지 발전 동향을 살펴본다. 2 Time: 17th October (Wednesday) 16:00 - 17:00 Speaker: Seungyeon Cho (Sungkyunkwan University) Place: #702, Natural Science Building, Hanyang University Title: High order conservative semi-Lagrangian scheme for the BGK model of the Boltzmann equation Abstract: In this work, we present a conservative semi-Lagrangian finite-difference scheme for the BGK model. The classical semi-Lagrangian finite difference scheme for the BGK model performs stably for all the range of Knudsen number, but are not conservative. There are two source of such loss of the conservation property. First, the accuracy of the cancellation of the relaxation operator in the zeroth, first and second velocity moments depends heavily on the number of velocity grids and non-negligible errors may arise if the number of velocity grids is not sufficient. Secondly, since the scheme is not of the conservative form, the error may accumulate in the numerical computation of the transport term. To treat the first problem and ensure the machine precision conservation of mass, momentum and energy with a relatively small number of velocity grid points, we replace the continuous Maxwellian with the discrete Maxwellian introduced by Mieussens. The second difficulty is treated by implementing a conservative correction procedure based on the flux difference form. The effectiveness of the proposed scheme is demonstrated by extensive numerical tests. 3 Time: 30th October (Tuesday) 14:30 - 16:00 Speaker: Prof. Kyung Hoon Han (University of Suwon) Place: #208, Natural Science Building, Hanyang University Title: 인공신경망의 기초 Abstract: 인공신경망 기법은 안면인식, 기계번역, 자율주행등에 응용되며 머신러닝의 핵심기법으로 부각되고 있다. 인공신경망은 그레디언트, 연쇄법칙과 같은 다변수 미분이론이 그 기초를 이루고 있다. 본 발표에서는 인공신경망의 원리와 수학적 기초를 설명하고 파이썬을 통해 시연해본다. # PDE seminar in September 2018 1 Time: 14th September (Friday) 16:00 - 17:00 Speaker: Prof. Younghun Hong (Chung-Ang University) Place: #701, Natural Science Building, Hanyang University Title: Dynamics in the semi-classical limit Abstract: Quantum mechanics describes nature at the atomic/subatomic scale, while classical mechanics does at macroscopic scale. These two theories are connected via the (semi-)classical limit h→0. In this talk, we discuss the semi-classical limit focusing on analysis of orthogonal families of functions (by Lieb-Thirring, Frank-Lewin-Lieb-Seiringer and Frank-Sabin). This is a survey talk. 2 Time: 18th September (Tuesday) 14:30 - 15:30 Speaker: Prof. Hantaek Bae (UNIST) Place: #208, Natural Science Building, Hanyang University Title: Incompressible Navier-Stokes equations: regularity of the velocity field and the flow map Abstract: In this talk, I will introduce the notion of mild solution and its analyticity. After that, I will show Holder regularity of the associated flow map. # Seminar on particle and kinetic models describing collective behaviors. Time: 18 June 2018, 14:30 - 16:45 Place: Department of Mathematics, Hanyang University Organizer: Prof. Jinyeong Park (Hanyang University) 1. Large-time dynamics of the particle and kinetic Kuramoto models with frustration Speaker: Dr. Dongnam Ko (Seoul National University) 14:30 - 15:10 Abstract: The synchronous collective motion is widely studied for the practical reasons. The Kuramoto model is one of the simplified models which describes individuals and their interactions. In many real cases, the interaction has some phase shift error, which is called frustration. We look over the synchronization results of this model in the particle (ODE) and kinetic (PDE) descriptions. The main concern is to present a sufficient condition which leads to the synchronization phenomena. We will see how phase shift destroys the gradient structure and keeps the particle-path analysis. 2. Remarks on the Fokker-Planck type equations derived from the synchronization particle models Speaker: Jaeseung Lee (Seoul National University) 15:10 - 15:30 Abstract: In kinetic theory of many-body systems, it is well known that mean-field kinetic equations can effectively describe the large ODE systems. In this talk, we present two types of viscous kinetic mean-field equations: the Kuramoto-Sakaguchi-Fokker-Planck(KS-FP) equation and the swarming model on a unit sphere. For the KS-FP equation, we study the stability and instability of the incoherent state where the all oscillators are uniformly distributed on the phase space. The similar results are also sought with the swarming model on the unit sphere. These phenomena depend on the interplay between the diffusion and coupling strength between the oscillators. 3. Asymptotic behavior and stability problem for the Schrödinger-Lohe model Speaker: Dohyun Kim (Seoul National University) 15:45 - 16:05 Abstract: We present asymptotic behavior and stability problem for the Schrödinger-Lohe(S-L) system which was first introduced as a possible phenomenological model exhibiting quantum synchronization. We present several sufficient frameworks leading to the emergent behavior of the S-L system. Moreover, we show that there are only two possible asymptotic states: completely synchronized state or bi-polar state. On the other hand, we provide the standing wave solutions for the S-L model with the harmonic potential and discuss the stability for standing wave solutions. 4. Emergent behaviors of continuous and discrete thermomechanical Cucker-Smale models on general digraphs Speaker: Do Heon Kim (Seoul National University) 16:05 - 16:25 Abstract: We present emergent dynamics of continuous and discrete thermomechanical Cucker-Smale(TCS) models equipped with temperature as an extra observable on general digraph. In previous literature, the emergent behaviors of the TCS models were mainly studied on a complete graph or symmetric connected graphs. Under this symmetric setting, the total momentum is a conserved quantity. This determines the asymptotic velocity and temperature a priori using the initial data only. Moreover, this conservation law plays a crucial role in the flocking analysis based on the elementary $\ell_2$ energy estimates. In this paper, we consider a more general connection topology which is registered by a general digraph, and the weights between particles are given to be inversely proportional to the metric distance between them. Due to this possible symmetry breaking in communication, the total momentum is not a conserved quantity, and this lack of conservation law makes the asymptotic velocity and temperature depend on the whole history of solutions. To circumvent this lack of conservation laws, we instead employ some tools from matrix theory on the scrambling matrices and some detailed analysis on the state-transition matrices. We present two sufficient frameworks for the emergence of mono-cluster flockings on a digraph for the continuous and discrete models. Our sufficient frameworks are given in terms of system parameters and initial data. 5. Large-time behavior of Thermo-mechanical Cucker-Smale ensemble immersed in various fluids Speaker: Jeongho Kim (Seoul National University) 16:25 - 16:45 Abstract: In this presentation, we consider the kinetic Thermo-mechanical Cucker-Smale (TCS) equation coupled with compressible/incompressible fluid. In our model, particle ensemble and fluid are coupled via mechanical drag force. We first provide the well-posedness theory for a weak or strong solution using a standard technique. Then, we discuss the large-time behavior for TCS ensemble coupled with both types of fluids.	2019-03-23 11:33:21	{"extraction_info": {"found_math": true, "script_math_tex": 1, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5456150770187378, "perplexity": 2717.5756381584115}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202781.83/warc/CC-MAIN-20190323101107-20190323123107-00167.warc.gz"}
https://mathhothouse.me/2014/12/04/part-3-of-3-solutions-to-pre-rmo-oct-2014/	## part 3 of 3 — Solutions to Pre RMO Oct 2014 Question Set A. Question 20. What is the number of ordered pairs $(A,B)$ where A and B are subsets of ${1,2,3,4,5}$ such that neither $A \subseteq B$ nor $B \subseteq A$? Solution. Just list down A and B explicitly. Note that A and B are disjoint and that $(A,B)$ is an ordered pair. Question 13. For how many natural numbers n between 1 and 2014 (both inclusive) is $\frac {8n}{9999-n}$ an integer? Solution. Firstly, note that $9999-n$ is even. Hence, n is odd. Also, $8n \geq 9999-n$ to yield an exact integer, so $n \geq 1111$. Now, do the one of the core tricks for problem solving in number theory. Plug and play with numbers 🙂 Put $n=1111$. This works. Next, note that $(9999-n)k=8n$ for some positive integer k. Hence, we get $9999k=(k+8)n$ From this we observe that $n=1111$ is the only possible solution. Hence, the answer is 1. Note : Question 16: HW to be posted on the blog 🙂 More later, Nalin Pithwa This site uses Akismet to reduce spam. Learn how your comment data is processed.	2019-10-17 21:16:58	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 13, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7254722714424133, "perplexity": 396.58046123691486}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986676227.57/warc/CC-MAIN-20191017200101-20191017223601-00114.warc.gz"}
https://blender.stackexchange.com/questions/156843/create-an-adaptive-description-for-an-operator-that-take-an-attribute?noredirect=1	# Create an adaptive description for an Operator that take an attribute? [duplicate] Sometimes the attributes of an operator can change quite dratically the output for the end user. is there a way to make the description of this operator adaptive to the attribute ? exemple in the script below: class SCATTER_OT_print(bpy.types.Operator): bl_idname = "scatter.print" bl_label = "" pref : bpy.props.StringProperty() bl_description = "print: " + pref #Adaptive desctiption ? def execute(self, context): print(self.pref) • Can you give an example of how the operator will change it's functionality in such a way that the original description will no longer be informative? – Ray Mairlot Oct 31 '19 at 18:24 • Albeit the dupe listed is attempting to change label rather than description, the same answer applies. Somewhat related blender.stackexchange.com/questions/56727/… – batFINGER Nov 4 '19 at 9:59	2020-08-10 11:51:16	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4580625891685486, "perplexity": 2420.7984463159064}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738674.42/warc/CC-MAIN-20200810102345-20200810132345-00589.warc.gz"}
https://www.learnnext.com/CBSE/Class-6/Science/Physics/Electricity-And-Circuits/Electric-Circuit/L-2822.htm	]]> LearnNext ##### Get a free home demo of LearnNext Available for CBSE, ICSE and State Board syllabus. Call our LearnNext Expert on 1800 419 1234 (tollfree) OR submit details below for a call back clear # Electric Circuit 61,780 Views Have a doubt? Clear it now. live_help Have a doubt, Ask our Expert #### Electric Circuit - Lesson Summary Electricity needs a path to flow from the positive terminal to the negative terminal of an electric cell. A connection that provides a path outside an electric cell, for the electricity to flow from the positive terminal to the negative terminal of the cell, is called an electrical circuit. For example, a bulb glows only when the positive terminal and the negative terminal of an electric cell are connected to the two terminals of the bulb. If the wires from the bulb are connected to the same terminal (either positive or negative), then the bulb does not glow. Sometimes, the bulb may not glow even though the connections are properly made. This may be because the flow of electricity is incomplete as the filament in the bulb is broken. A bulb with broken filament is said to be fused. A device that is used to stop the flow of electricity by breaking the circuit is called a switch. Switches have wide range of applications. Some common types of switches are: • Toggle switches, which are used in our houses. • Pushbutton switches, which are used in the starter of a water pump. • Joystick switches, which are used in the remote control unit of a toy car. Electric circuit including a switch Activity 1: To connect a bulb to an electric cell, we will need: • Four pieces of wire and • An adhesive tape First, remove the plastic insulation from the ends of all the four wires, such that a small length of the metal wire is exposed. Fix the exposed end of one wire to the positive terminal of the cell. Fix the exposed end of another wire to the negative terminal of the cell. Now, fix the exposed ends of the other two pieces of the wires to the two terminals of a bulb with the adhesive tape. This is what the bulb and the electric cell will look like with the wires attached to them. We now connect one of the wires of the bulb to a wire from the electric cell. Then we connect the second wire from the bulb to the remaining wire from the electric cell. The bulb now starts glowing. Activity 2: Let’s connect all the wires to the positive terminal of the cell now. The bulb still doesn’t glow. It is because the connection should be made in a specific way for the bulb to glow. Now let’s reconnect it, the way we connected the first time. The bulb glows again. Electricity needs a path to pass from the positive terminal to the negative terminal of the cell. When the positive and the negative terminals of an electric cell are connected to the two terminals of a bulb, the path is completed and the bulb glows. A connection that provides a complete path for the electricity to pass from the positive terminal of the cell to its negative terminal, outside an electric cell, is called an electrical circuit. At times a bulb in the circuit will not glow even though the connections are correct. The reason could be a fused bulb. A bulb is said to have fused when its filament breaks. When the filament is broken, there is a break in the flow of electricity through the terminals of the bulb. That is, the path required by electricity to flow is broken. Hence, the bulb does not glow. We need to disconnect one of the wires to switch off the bulb in the circuit that we just made. But then we’ll need to reconnect the wire manually to get the bulb to glow again. A switch in the circuit will make it easy to switch the bulb on and off. A switch is a device that is used to stop the flow of electricity by breaking the circuit. A switch enables us to break or complete a circuit on the click of a button. Making a switch: We need the followingt to construct an electric switch thermocol piece, • A pair of thumbtacks, • A metal paper clip, • Four pieces of insulated wire, • An electric cell and • A torch bulb. We start by creating the circuit. There will be one difference, though. We will leave one of the wires of the electric cell and the bulb unconnected. • We connect one end of the loose wire from the cell to a thumbtack, which is fixed on the thermocol. Now we connect one end of the loose wire from the bulb to another thumbtack fixed to the thermocol close to the thumbtack fixed earlier. The distance between the two thumbtacks should be less than the length of the paper clip. The switch is ready. When we want to switch the bulb on, just bring the paper clip in contact with the thumbtack. This completes the circuit and the bulb starts glowing. To click it off, take the clip away from the thumbtack. Switches can be found in a variety of applications. A few common types of switches are: • Toggle switch • Used in our houses. • Pushbutton switch • Used in the starter of a water pump. • Joystick switch • Used in the remote control unit of a toy car.	2019-06-19 03:17:14	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.582021176815033, "perplexity": 670.8198462845678}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627998882.88/warc/CC-MAIN-20190619023613-20190619045613-00192.warc.gz"}
http://kleine.mat.uniroma3.it/mp_arc-bin/mpa?yn=08-113	08-113 Victor Dinu, Arne Jensen, and Gheorghe Nenciu Non-exponential decay laws in perturbation theory of near threshold eigenvalues (380K, pdf) Jun 17, 08 Abstract , Paper (src), View paper (auto. generated pdf), Index of related papers Abstract. We consider a two channel model of the form $$H_{\varepsilon}=\begin{bmatrix} H_{\rm op} & 0\\ 0 & E_0 \end{bmatrix} +\varepsilon\begin{bmatrix} 0 & W_{12}\\ W_{21}&0 \end{bmatrix} \quad \text{on} \quad \mathcal{H}=\mathcal{H}_{\rm op}\oplus \mathbf{C}.$$ The operator $H_{\rm op}$ is assumed to have the properties of a Schr\"{o}dinger operator in odd dimensions, with a threshold at zero. As the energy parameter $E_0$ is tuned past the threshold, we consider the survival probability $\lvert{\langle{\Psi_0},{e^{-itH_{\varepsilon}}\Psi_0}\rangle}\rvert^2,$ where $\Psi_0$ is the eigenfunction corresponding to eigenvalue $E_0$ for $\varepsilon=0$. We find non-exponential decay laws for $\varepsilon$ small and $E_0$ close to zero, provided that the resolvent of $H_{\rm op}$ is not at least Lipschitz continuous at the threshold zero. Files: 08-113.src( 08-113.keywords , DJN.pdf.mm )	2017-11-21 08:05:24	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9599363207817078, "perplexity": 1017.9405160352976}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934806327.92/warc/CC-MAIN-20171121074123-20171121094123-00045.warc.gz"}
https://ask.sagemath.org/question/54611/very-different-matrix-inverse-result-in-complex-ring-cc-and-in-real-ring-rr-while-entry-only-contain-real-elements/?answer=54628	# Very different matrix inverse result in complex ring CC and in real ring RR while entry only contain real elements I would use an dramatized example here but it was encountered during a project as well. Suppose two matrix consisted of the same entry of only real elements. However, one was in the real domain RR, and one was in the complex domain CC. The inverse of the complex matrix and the real matrix different significantly. Example: test_S=matrix(RR,5) for ix in range(0,5): for iy in range(0,5): test_S[ix,iy]=sin(ix+iy)sin(iy+1); and test_S_CC=matrix(CC,5) for ix in range(0,5): for iy in range(0,5): test_S_CC[ix,iy]=sin(ix+iy)sin(iy+1); which returned test_S [ 0.000000000000000 0.765147401234293 0.128320060202457 -0.106799974237582 0.725716283876408] [ 0.708073418273571 0.826821810431806 0.0199148566748170 0.572750016904307 0.919535764538226] [ 0.765147401234293 0.128320060202457 -0.106799974237582 0.725716283876408 0.267938303940044] [ 0.118748392158235 -0.688158561598754 -0.135323401369264 0.211462346264655 -0.630000397639817] [ -0.636827341031836 -0.871947375471875 -0.0394311173578842 -0.497209097294248 -0.948719639025321] test_S_CC [ 0.000000000000000 0.765147401234293 0.128320060202457 -0.106799974237582 0.725716283876408] [ 0.708073418273571 0.826821810431806 0.0199148566748170 0.572750016904307 0.919535764538226] [ 0.765147401234293 0.128320060202457 -0.106799974237582 0.725716283876408 0.267938303940044] [ 0.118748392158235 -0.688158561598754 -0.135323401369264 0.211462346264655 -0.630000397639817] [ -0.636827341031836 -0.871947375471875 -0.0394311173578842 -0.497209097294248 -0.948719639025321] However, their inverse (test_S)^-1 [ 2.87043424444896e15 -9.36229301025494e15 1.13569572695379e16 -8.12065238284797e15 1.72141024999095e15] [-1.10320559226948e15 3.19497062929143e15 5.27553667803348e15 -7.22878751888619e15 8.54302211670640e15] [ 1.94664421070014e16 -3.02112860544102e15 0.000000000000000 1.80143985094820e16 0.000000000000000] [ 8.29739198582516e14 9.39732200089164e15 -1.02939420054183e16 1.02939420054183e16 0.000000000000000] [-2.15677123538261e15 -1.45141888820365e15 -7.07708512872506e15 5.95118522188244e15 -9.00719925474099e15] (test_S_CC)^-1 [-1.00798918109020e16 1.87532050063097e15 1.07471168476593e16 -2.09935440833922e16 1.10831351979113e16] [ 2.64758058163658e15 7.44366790239271e15 -8.04492396917722e15 9.82621377301499e15 4.42753908914828e14] [ 2.35701470124050e16 -4.71646526274252e15 1.02939420054183e16 1.08658276723860e16 9.15017067148291e15] [ 1.53627372015977e16 -1.32579194813951e15 -1.02939420054183e16 2.51629693465780e16 -9.15017067148291e15] [-4.69821640166124e15 -7.20926442861200e15 5.14697100270914e15 -8.57828500451523e15 -3.43131400180609e15] where (test_S)^(-1)-test_S_CC^(-1) [ 1.29503260553510e16 -1.12376135108859e16 6.09840421878568e14 1.28728917005442e16 -9.36172494792037e15] [-3.75078617390606e15 -4.24869727310128e15 1.33204606472107e16 -1.70550012919012e16 8.10026820779157e15] [-4.10370490540364e15 1.69533665730150e15 -1.02939420054183e16 7.14857083709603e15 -9.15017067148291e15] [-1.45329980030152e16 1.07231139490312e16 0.000000000000000 -1.48690273411597e16 9.15017067148291e15] [ 2.54144516627863e15 5.75784554040835e15 -1.22240561314342e16 1.45294702263977e16 -5.57588525293490e15] Is this a bug? How to fix the issue? edit retag close merge delete Sort by » oldest newest most voted That's not a bug, your matrix is simply not invertible. You can see it by switching the ring to SR to perform exact computations: test_S_SR = matrix(SR, 5) for ix in range(0, 5): for iy in range(0, 5): test_S_SR[ix, iy] = sin(ix+iy)sin(iy+1) sage: test_S_SR [ 0 sin(2)sin(1) sin(3)sin(2) sin(4)sin(3) sin(5)sin(4)] [ sin(1)^2 sin(2)^2 sin(3)^2 sin(4)^2 sin(5)^2] [sin(2)sin(1) sin(3)sin(2) sin(4)sin(3) sin(5)sin(4) sin(6)sin(5)] [sin(3)sin(1) sin(4)sin(2) sin(5)sin(3) sin(6)sin(4) sin(7)sin(5)] [sin(4)sin(1) sin(5)sin(2) sin(6)sin(3) sin(7)sin(4) sin(8)sin(5)] sage: test_S_SR.determinant().trig_reduce() # can take a few seconds 0 The float version looks invertible but that's only due to machine precision. Since the internal mechanism are probably different for RR and CC, it's normal that you get different answers. more But this happened to invertible matrix as well. The above result was only for demonstration, since it was calculated with float precision. I encountered this in a project where an invertible matrix calculated in CC had a very different inverse than the one calculated with RR. And a final result ought to be 0 but returned 0.0354399342695375 - 0.109072902259946I. One observation was that the invertible matrix calculated in CC was almost 1e2 times less preciece than the standard numpy matrix. After I used RR and complete the matrix inverse by directly calling the inverse function in numpy package, the result then returned correctly. There was something very wrong with the precision control of matrix inverse in CC. ( 2020-12-10 04:27:07 +0200 )edit In CC from numpy.linalg import inv as np_inv matrix(np_inv(rho_num_S))rho_num_S returned 0.9999999999999999 and 0.9999999999999999 for one of the entry where rho_num_S^-1rho_num_S returned 1.07087986853908 and 0.723606797749979 for two of the entry. where in RR both expression returned 1.00000... I don't have enough space to copy the function but you can try couple of square matrix of higher order. For the interest in our project, default matrix inverse operation in CC worked for square matrix of 3 by 3, but failed for square matrix of 6 by 6, and default matrix inverse operation in RR worked for square matrix 6 by 6 but failed for square matrix of 10 by 10. But so far, the inverse function provided by numpy package had been working for all those cases. ( 2020-12-10 04:34:57 +0200 )edit WorksForMe (on 9.3.beta3) : sage: MR=MatrixSpace(RR,3).random_element() sage: MR [-0.0413379232879041 -0.383726107921675 0.402484964228335] [ 0.0264553329794861 0.345098500636929 0.264737280303141] [ -0.141479831307881 -0.998284842827106 0.178457190865074] sage: MR.det() 0.0117348614307324 sage: MR^-1 [ 27.7692689578674 -28.4039106845136 -20.4930893556867] [ -3.59408846998909 4.22386369616762 1.83995041270540] [ 1.91007962570815 1.10972616436864 -0.350583891628722] sage: MRMR^-1 [ 1.00000000000000 -4.99600361081320e-16 1.11022302462516e-16] [-2.22044604925031e-16 1.00000000000000 -8.32667268468867e-17] [-2.77555756156289e-16 -2.77555756156289e-17 1.00000000000000] sage: MC=MR.change_ring(CC) sage: MC [-0.0413379232879041 -0.383726107921675 0.402484964228335] [ 0.0264553329794861 0.345098500636929 0.264737280303141] [ -0.141479831307881 -0.998284842827106 0.178457190865074] sage: MC.det() 0.0117348614307324 sage: MC^-1 [ 27.7692689578674 -28.4039106845136 -20.4930893556867] [ -3.59408846998909 4.22386369616762 1.83995041270540] [ 1.91007962570815 1.10972616436864 -0.350583891628722] sage: (MC^-1)-(MR^-1) [0.000000000000000 0.000000000000000 0.000000000000000] [0.000000000000000 0.000000000000000 0.000000000000000] [0.000000000000000 0.000000000000000 0.000000000000000] Of course, that's not a proof, just an example. If you have a counter-example, I'd be glad to see it... IMHO, Florentin is right : any deviation has probably to be attributed to imprecisions in floating point approximate computations. HTH, more It would be nice to be able to use Calcium for that. Calcium has matrix operations in arbitrary precision. more	2021-07-31 18:56:54	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.616029679775238, "perplexity": 10798.63582100657}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154099.21/warc/CC-MAIN-20210731172305-20210731202305-00130.warc.gz"}
https://publications.mfo.de/handle/mfo/3914/browse?type=author&value=Curbera%2C+Guillermo+P.	Now showing items 1-1 of 1 • #### Convolution in Dual Cesàro Sequence Spaces [OWP-2022-20] (Mathematisches Forschungsinstitut Oberwolfach, 2022-12-16) We investigate convolution operators in the sequence spaces $d_p$, for 1 $\leqslant p<\infty$. These spaces, for $p$ > 1, arise as dual spaces of the Cesàro sequence spaces $ces_p$ thoroughly investigated by G. Bennett. A ...	2023-03-24 13:18:43	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.884149432182312, "perplexity": 3518.3868053334077}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945282.33/warc/CC-MAIN-20230324113500-20230324143500-00402.warc.gz"}
https://gamedev.stackexchange.com/questions/142846/why-does-my-2d-top-down-joystick-code-occasionally-stop-working?noredirect=1	# Why does my 2D top-down joystick code occasionally stop working? I'm working on a 2D top-down game, and am working on the player controls. I have the following code currently controlling a player sprite: void Update () { float moveHorizontal = Input.GetAxis("Horizontal"); float moveVertical = Input.GetAxis("Vertical"); float headingAngle = Mathf.Atan2(moveHorizontal, moveVertical); Debug.Log("Heading angle: " + (headingAngle * Mathf.Rad2Deg).ToString() + " degrees."); if (transform.rotation != newHeading && (moveHorizontal != 0f \|\| moveVertical != 0f)) { Debug.Log("Turning. Rotation: " + transform.rotation + " \| New Heading: " + newHeading); transform.rotation = Quaternion.Slerp(transform.rotation, newHeading, turnSpeed * Time.deltaTime); } else { Debug.Log("Heading in the right direction, moving..."); transform.position += new Vector3(moveHorizontal * moveSpeed * Time.deltaTime, moveVertical * moveSpeed * Time.deltaTime, 0); } } This code sort of works, but occasionally the player will stop moving, even though it's rotated in the direction that the joystick is pointing. When that happens, the transform.rotation quaternion will be something like '(0, 0, -7, -7)', but the newHeading quaternion will be '(0, 0, 7, 7)', like they've flipped around. When that happens, the transform.rotation != newHeading in the if condition is always true, so the else condition is never reached. If I keep moving the joystick to different locations, eventually the player will start moving again. By the way, I have a sprite attached as a child to a game object, and the sprite is rotated 90 degrees in the z-axis, if that makes any difference. Any help would be appreciated! • Atan2 takes arguments in the y,x order, so vertical first – Bálint Jun 23 '17 at 14:28 • I've changed the order of the atan2 args to no effect. – Nikolas Adair Jun 23 '17 at 22:41 Remember, the basic == / != operators, unless explicitly overridden to check for something else, are looking for bitwise equality. They answer the question "are these two items literally the same, down to the very last decimal place?" This is important to keep in mind, because very often we don't want bitwise equality. Instead, we want to ask "are these two items effectively the same for gameplay purposes?" The 20th binary digit after the decimal is rarely visible to players, so checking for a match bit-for-bit is usually much more exacting than we want, finding mismatches when as players and designers we expect to see a match. This is why you'll often see advice to never compare two floating point numbers for exact equality - use range based comparisons (< <= >= >) or epsilons like Unity's Mathf.Approximately() method instead, to match floats that have a meaningful value rather than an exact bit pattern. This gets compounded in the case of quaternions by the fact that quaternions form a double cover over the set of 3D rotations. That means any single rotation in 3D can be expressed equivalently as two different quaternions, q and -1q, like your example of (0, 0, 0.707, 0.707) and (0, 0, -0.707, -0.707). You can verify that assigning your transform's rotation to either of these quaternions yields the same result, but we can see at a glance that comparing them for numeric equality won't find them to be the same, or even similar. Instead of checking if two quaternions are bit-for-bit identical, what we really want to ask is "do these two rotations face the same way?" To do that, we can measure the similarity between the two quaternions using Quaternion.Angle() to determine the angle of rotation between them. If the angle is very very small, then you can be confident they're sufficiently equivalent. (You can also use a dot product for this, to get the cosine of the angle instead, but using the Angle convenience methods gives us a nice, linear, easy-to-interpret result that's often worth the extra trig) One last thing before I finish this answer: your rotation update contains some common errors. transform.rotation = Quaternion.Slerp(transform.rotation, newHeading, turnSpeed Time.deltaTime); When you interpolate between your current value and a target using a small step, the result is not a linear approach at a consistent speed, but an exponential ease-out. (Fast at the start, and slowing down as your value gets closer and closer to its target, approaching it asymptotically) • This is fine and desirable at times, but because it's a non-linear rate of change, multiplying by deltaTime does not correctly adjust it for a variable framerate. You need to use an exponential weight, as described in this answer. You also probably don't need to use the more expensive Slerp, which ensures a more even rate of change. Since you're already using a non-linear easing, you probably wouldn't notice a change from switching to the simpler Lerp. • Alternatively, if you want a constant rate of change, use the RotateTowards() helper method - this handles the necessary math to rotate at a constant speed without overshooting. • This is extremely helpful! It really baffled me that the condition didn't appear to be functioning, so knowing how the Quaternions are best compared is invaluable. The information about the interpolation methods is apropos as well, because the exponential ease-out that you've described is the next issue I needed to tackle! Thanks a ton for the help! – Nikolas Adair Jun 24 '17 at 19:34	2020-10-21 02:32:58	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5048185586929321, "perplexity": 1400.683256837443}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107874637.23/warc/CC-MAIN-20201021010156-20201021040156-00523.warc.gz"}
https://socratic.org/questions/how-do-you-use-the-trapezoidal-rule-and-the-simpson-s-rule-when-n-4-when-approxi	# How do you use the Trapezoidal Rule and the Simpson's Rule when n=4 when approximating the integral (5t + 6) dt from [3,6]? Sep 23, 2015 ${\int}_{3}^{6} \left(5 t + 6\right) \mathrm{dt} \approx 85.5$ #### Explanation: ${\int}_{a}^{b} f \left(t\right) \mathrm{dt} \approx \frac{\Delta x}{2} \left(f \left({t}_{0}\right) + 2 f \left({t}_{1}\right) + 2 f \left({t}_{2}\right) + \ldots + 2 f \left({t}_{n - 1}\right) + f \left({t}_{n}\right)\right)$ Where $\Delta t = \frac{b - a}{2}$ We have $a = 3 , b = 6 , n = 4$ Therefore, $\Delta t = \frac{6 - 3}{4} = \frac{3}{4}$ Next, we divide [3,6] into four equal intervals with the length $\frac{3}{4}$ This will give us the following endpoints: $3 , \frac{15}{4} , \frac{9}{2} , \frac{21}{4} , 6$ Now we simply evaluate the function at these endpoints; $f \left({t}_{0}\right) = f \left(a\right) = f \left(3\right) = 21$ $2 f \left({t}_{1}\right) = 2 f \left(\frac{15}{4}\right) = \frac{99}{2} = 49.5$ $2 f \left({t}_{2}\right) = 2 f \left(\frac{9}{2}\right) = 57$ $2 f \left({t}_{3}\right) = 2 f \left(\frac{21}{4}\right) = \frac{129}{2} = 64.5$ $f \left({t}_{4}\right) = f \left(b\right) = f \left(6\right) = 36$ Now, we just sum up the values and multiply by $\frac{\Delta t}{2} = \frac{3}{8}$ $= \frac{3}{8} \left(21 + 49.5 + 57 + 64.5 + 36\right) = 85.5$ Hope this helps :)	2019-03-18 13:35:34	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 14, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.914305567741394, "perplexity": 547.8318020791503}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912201329.40/warc/CC-MAIN-20190318132220-20190318154220-00139.warc.gz"}
http://forestbpms.co/hd99v/1195d3-domain-and-range-of-logarithmic-functions-worksheet	Free Printables Worksheet Domain And Range Of Logarithmic Functions Worksheet We found some Images about Domain And Range Of Logarithmic Functions Worksheet: To flip the card, click on the card. 1) y = log 6 (x − 1) − 5 x y −8 −6 −4 −2 2 4 6 8 −8 −6 −4 −2 2 4 6 8 2) y = log 5 (x − 1) + 3 x y ... 4 3 mAIl XlM QrQiRgah StMsO 0rfe TsAepr evNekd9.D Z nMXapdFeP 7w mi at0h0 iI EnLfViCnbi it PeP 3A8lZgse Wb5r7aw N24. https://www.facebook.com/NumberSenseTV/videos/1137160513395869 How do you write the domain and range? 21. log 4 + log 25 22. ln(ln ee200) 23. ln √z You may remove cards as you learn them and randomize the list for better practice. Remember that since “d” comes before “r”, the domain of functions have to do with the “$$x$$”’s and the range of functions have to do with the “$$y$$”’s. Exponential and Logarithmic Graph Worksheet. Displaying top 8 worksheets found for - Domain And Range For Logarithmic Functions. Domain, Range And Functions - Lessons - Tes Teach Math Plane - Domain & Range - Functions & Relations Exponential and Logarithm Functions - ppt video online download Example 1 Domain: Range: Horizontal Asymptote: x -2 -1 1 2 State the domain, range, and asymptote. Domain and Range Worksheet Answer Key Also Graphing Transformations Of Logarithmic Functions Worksheet December 08, 2018 We tried to locate some good of Domain and Range Worksheet Answer Key Also Graphing Transformations Of Logarithmic Functions image to suit your needs. Properties of an exponential function: For all positive real numbers , the 1. has the set of real numbers as its domain. Improve your math knowledge with free questions in "Domain and range of exponential and logarithmic functions" and thousands of other math skills. Hence the condition on the argument x - 1 > 0 Free printable Function worksheets (pdf) with answer keys on the domain/range, evaluating functions, composition of functions ,1 to 1 , and more. The range of $$y={\log}_b(x)$$ is the domain of $$y=b^x$$: $$(−\infty,\infty)$$. Example 3: Find the domain and range of the function y = log ( x ) − 3 . Videos, worksheets, solutions and activities to help PreCalculus students learn how to graph logarithmic functions. Worksheet will open in a new window. Your analysis of each function must include: Domain. Flashcards: Domain and Range of Exponential Functions. 1. Find the derivative of each function, given that a is a constant (a) yx= a (b) ya= x (c) yx= x (d) ya= a 2. Domains can be found algebraically; ranges are often found algebraically and graphically. Projektanci CAD tworzą takie modele od podstaw, ale równie często spotykamy się z sytuacją, gdy trójwymiarowe modele… Yes, if we know the function is a general logarithmic function. Proces pozyskiwania trójwymiarowych modeli może odbywać się dwojako. State the Domain and Range of each of the given relations in the space provided. Find the derivative of each. The example below shows two different ways that a function can be represented: as a function table, and as a set of coordinates. Let us come to the names of those three parts with an example. Range (y) = Domain (y-1) Therefore, the range of y is . Be it worksheets, online classes, doubt sessions, or any other form of relation, it’s the logical thinking and smart learning approach that we, at Cuemath, believe in. Students will be able to graph the logarithmic function by graphing the inverse of the exponential function. R - {0} Another Way to Find Range of Rational Functions. That is, the argument of the logarithmic function must be greater than zero. Logarithmic Functions The function ex is the unique exponential function whose tangent at (0;1) has slope 1. Function Review Worksheet Math Tutorial Lab Special Topic Example Problems Evaluate the following functions: 1.If f(x) = x2 2x+ 1, nd (a) f(2) (b) f(p 5) (c) f( 1 + p 2) (d) f(2w + 1) 2.If f(x) = p x+ 4, nd (a) f( 1) (b) f(a) (c) f(x+ h) (d) f(,) Determine which of the curves are graphs of functions. This is a whole lesson looking at the Range and Domain in functions and inverse functions. We can form another set of ordered pairs from F by interchanging the x- and y-values of each pair in F.We call this set G. The graph is nothing but the graph y = log ( x ) translated 3 units down. The domain and range of a function is all the possible values of the independent variable, x, for which y is defined. Explain the meanings of function, domain and range. Exponential Functions typically resemble this model: f(x) = b^x Ex: f(x) = 6^x To graph this particular equation, substitute values for the exponent (x) and plot the points. Domain and Range Worksheet Answer Key together with Graphing Transformations Of Logarithmic Functions Worksheet December 08, 2018 We tried to locate some good of Domain and Range Worksheet Answer Key together with Graphing Transformations Of Logarithmic Functions image to suit your needs. Then sketch the graph. To apply the domain and range in real-world settings, we take a function that represents a real-world situation and then analyze what the domain and range represent in the function. 3. To download/print, click on pop-out icon or print icon to worksheet to print or download. Diff Show all work in question 8 cards as you learn them randomize! Function and then the range is y > 0 functions giving their domain and range ) y. Of functions ( and relations ) sound really difficult and scary, but they not! A function and inverse function x, for which y is ) x y... the. Parts with an example use parentheses where necessary early and often ( a ) and! 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Not y2 = x3 d. y = log3 ( x-1 ) -2 graphs!	2021-09-24 22:10:05	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.38063323497772217, "perplexity": 1582.9512838124483}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057580.39/warc/CC-MAIN-20210924201616-20210924231616-00113.warc.gz"}
https://zbmath.org/authors/?q=ai%3Ahe.lingbing	zbMATH — the first resource for mathematics He, Lingbing Compute Distance To: Author ID: he.lingbing Published as: He, L.; He, Ling-Bing; He, Lingbing Documents Indexed: 33 Publications since 1996 all top 5 Co-Authors 5 single-authored 3 Chen, Yemin 2 Danchin, Raphaël 2 Desvillettes, Laurent 2 Le Bris, Claude 2 Lelièvre, Tony 2 Xu, Li 2 Zhang, Ping 1 Alexandre, Radjesvarane 1 Benoit, David 1 Carrapatoso, Kleber 1 Goudon, Thierry 1 Jiang, Jin-Cheng 1 Moussa, Ayman 1 Yang, Xiongfeng 1 Yu, Pin 1 Zhang, Zhifei 1 Zhou, Yulong all top 5 Serials 4 Archive for Rational Mechanics and Analysis 4 SIAM Journal on Mathematical Analysis 3 Kinetic and Related Models 2 Journal of Statistical Physics 1 Communications in Mathematical Physics 1 Journal of Mathematical Analysis and Applications 1 Journal of Differential Equations 1 Journal of Functional Analysis 1 Mathematische Annalen 1 Asymptotic Analysis 1 M$^3$AS. Mathematical Models \& Methods in Applied Sciences 1 Discrete and Continuous Dynamical Systems 1 Annals of PDE all top 5 Fields 20 Partial differential equations (35-XX) 16 Fluid mechanics (76-XX) 6 Statistical mechanics, structure of matter (82-XX) 2 Integral equations (45-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Mechanics of deformable solids (74-XX)	2019-05-26 16:20:16	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5074975490570068, "perplexity": 11708.814526252861}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232259316.74/warc/CC-MAIN-20190526145334-20190526171334-00519.warc.gz"}
http://gasturbinespower.asmedigitalcollection.asme.org/article.aspx?articleid=1426335	0 Research Papers: Gas Turbines: Cycle Innovations # Chemical Looping Combustion Using the Direct Combustion of Liquid Metal in a Gas Turbine Based Cycle [+] Author and Article Information Niall R. McGlashan Department of Mechanical Engineering, Imperial College London, South Kensington, London, SW7 2BX, UKn.mcglashan@ic.ac.uk Peter R. N. Childs, Andrew L. Heyes Department of Mechanical Engineering, Imperial College London, South Kensington, London, SW7 2BX, UK Pure Na, in either vapor or liquid state, is unlikely to be present at noticeable levels in molten salt gasifiers due the higher oxygen activity. J. Eng. Gas Turbines Power 133(3), 031701 (Nov 10, 2010) (13 pages) doi:10.1115/1.4001984 History: Received April 08, 2010; Revised April 26, 2010; Published November 10, 2010; Online November 10, 2010 ## Abstract A combined cycle gas-turbine generating power and hydrogen is proposed and evaluated. The cycle embodies chemical looping combustion (CLC) and uses a Na based oxygen carrier. In operation, a stoichiometric excess of liquid Na is injected directly into the combustion chamber of a gas-turbine cycle, where it is burnt in compressed $O2$ produced in an external air separation unit (ASU). The resulting combustion chamber exit stream consists of hot Na vapor and this is expanded in a turbine. Liquid $Na2O$ oxide is also generated in the combustion process but this can be separated, readily, from the Na vapor and collects in a pool at the bottom of the reactor. To regenerate liquid Na from $Na2O$, and hence complete the chemical loop, a reduction reactor (the reducer) is fed with three streams: the hot $Na2O$ from the oxidizer, the Na vapor (plus some entrained wetness) exiting a Na-turbine, and a stream of solid fuel, which is assumed to be pure carbon for simplicity. The sensible heat content of the liquid $Na2O$ and latent and sensible heat of the Na vapor provide the heat necessary to drive the endothermic reduction reaction and ensure the reducer is externally adiabatic. The exit gas from the reducer consists of almost pure CO, which can be used to generate byproduct $H2$ using the water-gas shift reaction. A mass and energy balance of the system is conducted assuming reactions reach equilibrium. The analysis allows for losses associated with turbomachinery; heat exchangers are assumed to operate with a finite approach temperature. However, pressure losses in equipment and pipework are assumed negligible—a reasonable assumption for this type of analysis that will still yield meaningful data. The analysis confirms that the combustion chamber exit temperature is limited by both first and second law considerations to a value suitable for a practical gas-turbine. The analysis also shows that the overall efficiency of the cycle, under optimum conditions and taking into account the work necessary to drive the ASU, can exceed 75%. <> ## Figures Figure 1 Graph showing the first law efficiency and work output of a process enacting reaction (1) versus the processes’ total internal and external entropy production Figure 2 Schematic diagram of a Na burning: CLC system with auxiliary air separation unit and water-gas shift reactor. The CO2/H2 separation and CO2 compression systems are not shown. (The station numbering is consistent with Appendix ). Figure 3 Cross section showing internal details of oxidation reactor. The proposed reactor is of the entrained flow type and uses a blast of oxygen fed through tuyeres at the base to oxidize a spray of metal droplets falling from the top. The reactor’s walls are protected by a layer of metal oxide frozen to an inner membrane wall, which is gas cooled. Figure 4 Cross section showing internal details of reduction reactor. The proposed reactor is of the molten bath type and uses a blast of metal vapor to transport solid fuel into a melt of oxides and carbonates. Heat released by condensation of the metal vapor drives the endothermic reduction reaction between the fuel and the bath’s constituents. Figure 5 Graph showing the two possible operating regimes of the reduction reaction at equilibrium, separated by the vapor pressure line for Na—at pressures higher than Pvap, no C(s) can exist; at pressures below Pvap, no Na(l) can exist. Figure 6 Cross section through proposed reactor/pipe wall design, showing frozen Na2O layer and gas cooling arrangement Figure 7 Graph showing: the overall efficiency ηov and second law efficiency ηH2 of the CLC/H2 system with and without a bottoming Rankine cycle and the optimum reducer pressure Predu versus the oxidizer pressure Poxi ## Discussions Some tools below are only available to our subscribers or users with an online account. ### Related Content Customize your page view by dragging and repositioning the boxes below. Related Journal Articles Related Proceedings Articles Related eBook Content Topic Collections • TELEPHONE: 1-800-843-2763 (Toll-free in the USA) • EMAIL: asmedigitalcollection@asme.org	2017-10-23 09:39:19	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 6, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.25031960010528564, "perplexity": 4047.83172590647}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187825889.47/warc/CC-MAIN-20171023092524-20171023112524-00705.warc.gz"}
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https://zbmath.org/?q=an:0718.18008	# zbMATH — the first resource for mathematics Local cyclic homology. (English) Zbl 0718.18008 This paper deals with cyclic homology in the spirit of the algebraic de Rham cohomology of a formal neighborhood. Local (cyclic) homology of filtered associative algebras is defined and discussed. In the commutative case, it is shown that the canonical homomorphism of filtered algebraic $$S^ 1$$-chain complexes C(A)$$\to \lim_{\leftarrow k}C(A/I_ k)$$ induces an isomorphism $$\hat C(A)=\lim_{\leftarrow p}C(A)/F_ pC(A)\to \lim_{\leftarrow k}C(A/I_ k)$$. This result enables the author to obtain a sort of generalization of a result of Feigin and Tsygan on periodic homology. It is also shown that for a filtered k-algebra A with filtration HC-cofinite, the F-filtration on $${}_ B\hat C*(A)$$ is strongly convergent. ##### MSC: 18G60 Other (co)homology theories (MSC2010) Full Text: ##### References: [1] Boardman, J. M.: Conditionally convergent spectral sequences, preprint, 1981. · Zbl 0947.55020 [2] Burghelea, D.: Cyclic homology and the K-theory of spaces I. Proc. Summer Inst. on Algebraic K-theory, Boulder, Colorado, 1983, Contemp. Math. vol. 55, part I. (1986), pp. 89-115. [3] Cartan, H. and Eilenberg, S.: Homological Algebra, Princeton Univ. Press, Princeton (1956). [4] Connes, A. and Cuntz, J.: Quasi homomorphismes, cohomologie cyclique et positivité, Comm. Math. Phys. 114 (1988), 515-526. · Zbl 0664.46067 · doi:10.1007/BF01242141 [5] Cuntz, J.: A new look at KK-theoty, K-Theory 1 (1988), 31-51. · Zbl 0636.55001 · doi:10.1007/BF00533986 [6] Feigin, B. L. and Tsygan, B. L.: Additive K-theory, in K-Theory, Arithmetic and Geometry, Lecture Notes in Math. 1289, Springer-Verlag, New York, Heidelberg, Berlin (1987), pp. 97-209. · Zbl 0635.18008 [7] Goodwillie, T. G.: Cyclic homology, derivations and the free loop space, Topology 24(2) (1985), 187-215. · Zbl 0569.16021 · doi:10.1016/0040-9383(85)90055-2 [8] Hartshorne, R.: On the De Rham cohomology of algebraic varieties, Publ. Math. IHES 45 (1976), 5-99. · Zbl 0326.14004 [9] Hood, C. E. and Jones, J. D. S.: Some algebraic properties of cyclic homology groups, K-Theory 1 (1987), 361-384. · Zbl 0636.18005 · doi:10.1007/BF00539623 [10] Kassel, C.: Cyclic homology, comodules and mixed complexes, J. Algebra 107(1), (1987), 195-216. · Zbl 0617.16015 · doi:10.1016/0021-8693(87)90086-X [11] Loday, J. L. and Quillen, D.: Cyclic homology and the Lie algebra homology of matrices, Comment. Math. Helv. 59 (1984), 565-591. · Zbl 0565.17006 · doi:10.1007/BF02566367 [12] MacLane, S.: Homology, Springer Verlag, Berlin, Göttingen, Heidelberg (1963). [13] Northcott, D. G.: Lessons on Rings, Modules and Multiplicities, Cambridge Univ. Press, Cambridge (1968). · Zbl 0159.33001 [14] Seibt, P.: Cyclic Homology of Algebras, World Scientific, Singapore, N. Jersey, Hong Kong (1987). · Zbl 0743.16009 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.	2021-04-17 15:08:37	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7934377789497375, "perplexity": 3369.1036885929634}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038460648.48/warc/CC-MAIN-20210417132441-20210417162441-00396.warc.gz"}
https://www.fx141.com/936/	# scalping forex profit magic When all indicators turn blue we BUY.. when any of the four indicators change color we exit the trade When all indicators turn Red we SELL.. When any of the four indicators change color we exit the trade.  Entry signals is marked by Arrow (Red/Blue)  Exit Signal is achieved either by take profit levels or a change in color of any of the four indicators contrary to the colors of the entry signals. I’ll repeat When all indicators turn blue we BUY.. when any of the four indicators change color we exit the trade When all indicators turn Red we SELL.. When any of the four indicators change color we exit the trade.  Entry signals is marked by Arrow (Red/Blue)  Exit Signal is achieved either by take profit levels or a change in color of any of the four indicators contrary to the colors of the entry signals. IMPORTANT: If you master the instructions on this particular page then using Forex Profit Magic trade Alert Software will be as easy as Child play and it will generate profitable signals for you like clockwork!	2020-04-03 11:07:31	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8359485268592834, "perplexity": 3564.3314663993124}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370510846.12/warc/CC-MAIN-20200403092656-20200403122656-00010.warc.gz"}
https://www.deepdyve.com/lp/ou_press/effects-of-mantle-rheologies-on-viscous-heating-induced-by-glacial-HKSbjt1w9K	# Effects of mantle rheologies on viscous heating induced by Glacial Isostatic Adjustment Effects of mantle rheologies on viscous heating induced by Glacial Isostatic Adjustment Summary It has been argued that viscous dissipation from mantle flow in response to surface loading during glacial cycles can result in short-term heating and thus trigger transient volcanism or changes in mantle properties, which may in turn affect mantle dynamics. Furthermore, heating near the Earth's surface can also affect the stability of ice sheets. We have studied the magnitude and spatial-temporal distribution of viscous heating induced in the mantle by the realistic ice model ICE-6G and gravitationally consistent ocean loads. Three types of mantle rheologies, including linear, non-linear and composite rheologies are considered to see if non-linear creep can induce larger viscous heating than linear rheology. We used the Coupled-Laplace-Finite-Element model of Glacial Isostatic Adjustment (GIA) to compute the strain, stress and shear heating during a glacial cycle. We also investigated the upper bound of temperature change and surface heat flux change due to viscous heating. We found that maximum viscous heating occurs near the end of deglaciation near the edge of the ice sheet with amplitude as high as 120 times larger than that of the chondritic radioactive heating. The maximum heat flux due to viscous heating can reach 30 mW m−2, but the area with large heat flux is small and the timescale of heating is short. As a result, the upper bound of temperature change due to viscous heating is small. Even if 30 glacial cycles are included, the largest temperature change can be of the order of 0.3 °C. Thus, viscous heating induced by GIA cannot induce volcanism and cannot significantly affect mantle material properties, mantle dynamics nor ice-sheet stability. Loading of the Earth, Europe, North America, Heat generation and transport, Rheology: mantle 1 INTRODUCTION In a fluid, the presence of viscosity, which represents the frictional interaction between neighbouring fluid elements, transforms some kinetic energy of the fluid into heat energy for dissipation (e.g. Landau & Lifshitz 1966). This so-called ‘viscous heating’ can potentially change the temperature and therefore material properties of mantle rocks. If viscous heating is large, then it can be very important because it can induce melting and therefore volcanism. It can also alter seismic properties and thus our interpretation of internal structure of the Earth, or alter mantle viscosity, which may in turn affect mantle dynamics. For example, viscous heating generated by tidal deformation induced by Jupiter may have caused volcanism on the Jovian moon Io (Ross & Schubert 1987; Segatz et al.1988). There is speculation that glacial cycles may have triggered volcanism during the Quaternary (e.g. Nakada & Yokose 1992; Sigvaldason et al.1992; Huybers & Langmuir 2009, Uenzelmann-Neben et al.2012). The link between them is generally attributed to decompression (Jull & McKenzie 1996; Slater et al.1998), but volcanism can also be triggered by viscous heating induced by Glacial Isostatic Adjustment (GIA) of the Earth in response to cycles of ice and ocean loading. Hanyk et al. (2005) modeled viscous heating due to GIA using simple ice load histories on a spherical Earth with linear rheology. They found that viscous heating can generate observable transient heat flux on the surface of the Earth. They also suggested that some degree of volcanism may be associated with viscous heating if the deglaciation period is short, and speculated that higher values of viscous heating can be generated if mantle rheology is non-linear. Indeed, if viscous heating is large enough at the base of the ice sheet, then glacial loading can also affect the stability of ice sheets by basal heating (e.g. Pattyn 2010). On the other hand, if viscous heating leads to lower mantle viscosity near the surface, then this would lead to faster land uplift and that may help to stabilize marine ice sheets (Gomez et al.2015). In this paper, we improve on Hanyk's work by using a realistic ice history model ICE-6G (Peltier et al.2015) together with realistic, self-gravitating oceans. As we shall see, the interaction among ice sheets and the loading of the ocean floor by meltwater affects the spatial distribution of viscous heating. A realistic loading history is also important, as it will eliminate the unrealistic results due to unreasonably fast or slow deglaciation histories. In addition, we consider three types of mantle rheologies in our Earth models: linear, non-linear and composite rheologies to see how large non-linear creep can affect the magnitude of viscous dissipation. Besides studying the effect of viscous heating on surface heat flux, we also study the following questions: what temperature changes inside the Earth are produced by viscous heating induced by glacial cycles? Do these temperature changes significantly affect present-day seismic velocities and thus the interpretation of seismic tomography? Can they affect viscosity and thus mantle flow induced during GIA? In the following sections, we will start with a brief review of the three different types of mantle rheologies, and provide a brief discussion of our model. Then, we will present the results, focusing on the magnitude and spatial and temporal distribution of viscous heating for some simple and other more sophisticated Earth models. After that, we will estimate the effects of viscous heating on the upper bound of heat flux change and see if the upper bound of temperature increase can trigger volcanism and affect ice stability or material properties inside the Earth. 2 THE MODEL 2.1 Mantle rheologies and rate of viscous dissipation Creep experiments on mantle rocks show that both linear and non-linear creep laws operate in the mantle (e.g. Karato & Wu 1993). If both creep laws operate simultaneously, then we have composite rheology. For this case, the creep mechanism with the highest creep rate becomes the dominant creep mechanism. The constitutive relation for these rheologies relates the deviatoric stress σD and the deviatoric strain rate $${{\boldsymbol{\dot{\varepsilon\! }}}_{\boldsymbol{D}}}$$, which are defined as $${{\boldsymbol{\sigma\! }}_{\boldsymbol{D}}} = {\boldsymbol{\sigma }} - \frac{1}{3}{\sigma _{ii}}{{\bf I}}$$ (1) $${{\boldsymbol{\dot{\varepsilon\! }}}_{\boldsymbol{D}}} = {\boldsymbol{\dot{\varepsilon }}} - \frac{1}{3}{\dot{\varepsilon }_{ii}}{{\bf I}}$$ (2)where σ and $${\boldsymbol{\dot{\varepsilon }}}$$ are the stress tensor and the strain rate tensor, respectively, I is the identity tensor, σii is the sum of diagonal components of σ and $${\dot{\varepsilon }_{ii}}$$ is the sum of diagonal components of $${\boldsymbol{\dot{\varepsilon }}}$$. In the following, we refer to σDij and $${\dot{\varepsilon }_{Dij}}$$ as the components of σD and $${{\boldsymbol{\dot{\varepsilon\! }}}_{\boldsymbol{D}}}$$, respectively. The relation between σD and $${{\boldsymbol{\dot{\varepsilon\! }}}_{\boldsymbol{D}}}$$ for composite, linear and non-linear rheologies can be expressed as (e.g. van der Wal et al.2010): $${{\boldsymbol{\sigma\! }}_{\boldsymbol{D}}} = \frac{1}{{\frac{1}{{2\eta }} + A{\sigma _E}^{n - 1}}}{{\boldsymbol{\dot{\varepsilon\! }}}_{\boldsymbol{D}}}$$ (3a) Here, η is the dynamic viscosity for linear creep, A is the non-linear creep parameter determined from shear experiments, and its value depends on temperature, pressure and material properties. σE is the effective deviatoric stress defined by $${\sigma _E} = \sqrt {\frac{1}{2}{\sigma _{Dij}}{\sigma _{Dij}}}$$ and n is the stress exponent with experimental value between 2 and 6. Here, we will take n = 3, as that is a typical value for mantle rocks (Karato & Wu 1993, Ranalli 1995). If A = 0, then eq. (3a) reduces to the relation for linear rheology. If A ≠ 0 and η = ∞, then it becomes the relation for non-linear rheology. It is useful to define the effective viscosity $${\eta _{{\rm{eff}}}} = \frac{1}{2}{( {\frac{1}{{2\eta }} + A{\sigma _E}^{n - 1}} )^{ - 1}}$$, so that eq. (3a) becomes $${{\boldsymbol{\sigma\! }}_{\boldsymbol{D}}} = 2{\eta _{{\rm{eff}}}}{{\boldsymbol{\dot{\varepsilon\! }}}_{\boldsymbol{D}}}$$ (3b) For non-linear or composite rheology, the effective viscosity changes with stress level and thus with space and time. For non-linear rheology or composite rheology with a fixed η, a decrease in σE will result in an increase in effective viscosity. The viscous dissipation rate ϕ (hereafter called ‘viscous heating’) is given by (e.g. eq. 7 in Hanyk et al.2005): $$\phi = {{\boldsymbol{\sigma\! }}_{\boldsymbol{D}}}{:}\, {{\boldsymbol{\dot{\varepsilon\! }}}_{\boldsymbol{D}}} = \frac{1}{{2{{\boldsymbol{\eta }}_{{{\bf eff}}}}}}{{\boldsymbol{\sigma\! }}_{\boldsymbol{D}}}{:}\,{{\boldsymbol{\sigma\! }}_{\boldsymbol{D}}}$$ (4a) This shows that shear heating decreases if the effective viscosity increases provided that σD does not change rapidly. For surface loading problems like GIA, σD is determined by the changing surface loads, although σD is also affected by stress relaxation where the decay time constant is proportional to the effective viscosity. In terms of von Mises stress $$\tau = \sqrt 3 {\sigma _E}$$, the creep parameter A and viscosity η, eq. (4a) can be written as: $$\phi = \frac{2}{3} \left( {\frac{1}{{2\eta }} + \frac{1}{3}A{\tau ^2}} \right){\tau ^2}$$ (4b)which clearly shows the strong dependence of ϕ on von Mises stress τ. Eq. (4a) can also be written as: $$\phi = 2{{\boldsymbol{\eta }}_{{{\bf eff}}}}{{\boldsymbol{\dot{\varepsilon\! }}}_{\boldsymbol{D}}}{:}\,{{\boldsymbol{\dot{\varepsilon\! }}}_{\boldsymbol{D}}}$$ which shows that viscous heating would increase with larger effective viscosity provided that the strain rate $${{\boldsymbol{\dot{\varepsilon\! }}}_{\boldsymbol{D}}}$$ is constant. For our problem, $${{\boldsymbol{\dot{\varepsilon\! }}}_{\boldsymbol{D}}}$$ is not constant, but $${{\boldsymbol{\dot{\varepsilon\! }}}_{\boldsymbol{D}}}{:}\,{{\boldsymbol{\dot{\varepsilon\! }}}_{\boldsymbol{D}}}$$ is determined by (σD/ηeff)2. Thus, eqs (4a) or (4b) will be used for our discussion below. 2.2 The GIA model The Coupled Laplace-Finite-Element (CLFE) GIA model of Wu (2004), later modified by van der Wal et al. (2010), is used in this study. Finite-element grids with different (0.5° and 2°) spatial resolution have been used for the computations. It is found that 2° resolution is adequate for our purpose. The inputs of the GIA model are elastic and creep parameters for the Earth model, and ice loading history. Unlike the simple ice sheet model used in Hanyk et al. (2005), the ice model used here is the realistic global ICE6G model of Peltier et al. (2015). Since ICE6G provides ice thickness history from 26 kBP to the present, we assume that the ice thickness increased linearly from zero at 108 kBP to the ice thickness at 26 kBP. Also, the ice was taken from the water in the oceans and meltwater returned to the oceans. The self-consistent sea level equation is solved for realistic oceans (Wu 2004). Since the effects of time-dependent coastline and rotational feedback are small on the von Mises stress τ and shear heating, they have not been included. As we shall see below, the localization of viscous heating in time makes the consideration of previous glacial cycles unnecessary. For the Earth models, the elastic parameters for models M1–M3 are the same as those in van der Wal et al. (2010), and for M4, they are the same as that in model VM5a of Peltier et al. (2015). The rheological parameters are described in Table 1. Here, parameter A* is the creep parameter determined from uniaxial experiments and is related to A, the creep parameter from shear experiments by $${A^} = 2A/\sqrt {{3^{n + 1}}}$$ (van der Wal et al.2010). In Table 1, M1 and M4 are linear rheological models. M1 has a uniform viscosity of 3 × 1021 Pa s, while in M4, the viscosities in the upper mantle (100–670 km depth), shallow lower mantle (670–1271 km depth) and deep lower mantle (1271–2891 km depth) are 5 × 1020, 1.6 × 1021 and 3 × 1021 Pa s respectively. M4 is considered because model VM5a is used for the construction of ICE6G (Peltier et al.2015), and so these should be used together. The rheological parameters in models M2 and M3 are uniform in the mantle. M2 has a non-linear rheology, while model M3 has a composite rheology. In other models, the effects of compressibility and a low viscosity (LV) zone below the lithosphere are also studied (see Tables 2–4) as they can also affect the magnitude of viscous heating. Table 1. Rheological parameters of four Earth models. M1 M2 M3 M4 A(Pa − 3 · s − 1) 0 1.11 × 10−34 1.11 × 10−34 0 η (Pa s) 3 × 1021 0 3 × 1021 VM5a n 1 3 3 1 M1 M2 M3 M4 A(Pa − 3 · s − 1) 0 1.11 × 10−34 1.11 × 10−34 0 η (Pa s) 3 × 1021 0 3 × 1021 VM5a n 1 3 3 1 View Large Table 2. The maximum local viscous heating of all time for uniform mantle models with various rheology (A and η). ϕMax η(Pa · s) 3.00 × 1020 3.00 × 1021 3.00 × 1022 Non-linear A* (Pa − 3 · s − 1) Linear 11.64 3.95 0.54 1.11 × 10−36 11.64 6.14 2.73 2.23 1.11 × 10−35 11.45 11.45 10.24 9.99 1.11 × 10−34 9.58 10.04 10.12 10.14 1.11 × 10−33 6.73 6.55 6.54 6.53 ϕMax η(Pa · s) 3.00 × 1020 3.00 × 1021 3.00 × 1022 Non-linear A* (Pa − 3 · s − 1) Linear 11.64 3.95 0.54 1.11 × 10−36 11.64 6.14 2.73 2.23 1.11 × 10−35 11.45 11.45 10.24 9.99 1.11 × 10−34 9.58 10.04 10.12 10.14 1.11 × 10−33 6.73 6.55 6.54 6.53 View Large Table 3. The maximum local viscous heating of all epochs for two values of Poisson's ratio (i.e. compressibility) with various rheology (A* [Pa−3 s−1] and η [Pa s]). ϕMax A* = 0 η = 3 × 1021 A* = 1.11 × 10−34 (non − linear) A* = 1.11 × 10−34η = 3 × 1021 Poisson's ratio 0.4900 3.95 10.14 10.04 0.2877 6.18 10.59 10.40 ϕMax A* = 0 η = 3 × 1021 A* = 1.11 × 10−34 (non − linear) A* = 1.11 × 10−34η = 3 × 1021 Poisson's ratio 0.4900 3.95 10.14 10.04 0.2877 6.18 10.59 10.40 View Large Table 4. The maximum local viscous heat of all time in models with an LV zone below the lithosphere. Units: A∗ in [Pa−3 s−1] and η in [Pa s]. ϕMax A=0 η = 3 × 1018 A = 1.11 × 10−34 (non − linear) A* = 1.11 × 10−36η = 3 × 1018 LV zone thickness (km) 40 102.18 26.01 102.19 100 118.80 30.52 118.81 ϕMax A=0 η = 3 × 1018 A = 1.11 × 10−34 (non − linear) A* = 1.11 × 10−36η = 3 × 1018 LV zone thickness (km) 40 102.18 26.01 102.19 100 118.80 30.52 118.81 View Large The outputs of the CLFE model contain spatial temporal evolution of the displacements and state of stress throughout the mantle. From the stress output at any time step, the local viscous heating for each element can be computed using eqs (4a) or (4b). In this paper, viscous heating is normalized by the chondritic radiogenic heating of 3 × 10−9 W m−3 (Hanyk et al.2005). 3 RESULTS 3.1 Spatial-temporal distribution of viscous heating for M1–M4 In Fig. 1, the spatial distribution of normalized viscous heating for models M1–M4 is shown at 13 kBP, the time when the viscous heating peaked (see Figs 2–5 below). It can be noted that viscous dissipation mainly occurs around past ice margins in Laurentia, the North American Cordillera, Fennoscandia and the Barents Sea area where the shear stresses are largest. Due to the constructive interference between the thick Laurentide ice sheets and the thinner Cordilleran ice sheet at 13 kBP, the peak amplitude occurs between their ice margins. However, in the ocean area between the northeast coasts of Canada and Greenland, the destructive interference between ice and water loading results in very low viscous heating. Similarly, constructive interference between the thinner ice sheets in Fennoscandia and the Barents Sea at 13 kBP, results in a smaller local peak between them. Fig. 1 also shows that the magnitude of viscous dissipation for M2 and M3 is more than two times higher than that for M1. The similarity between the results of M2 and M3 at this and all other times indicates that non-linear creep dominates in the composite rheology. However, the presence of an LV upper mantle in M4 results in much higher viscous heating than for M1–M3. The maxima in M1, M2, M3 and M4 are 3.95, 10.14, 10.04 and 22.36 times that of chondritic radiogenic heating, respectively. Figure 1. View largeDownload slide Spatial distribution of the normalized viscous heating for M1–M4, at 13 kBP and depth at 337.5 km. In the subplot for M2, the location of vertical cross-sections in Laurentia and Fennoscandia are indicated by white lines with black dots. Figure 1. View largeDownload slide Spatial distribution of the normalized viscous heating for M1–M4, at 13 kBP and depth at 337.5 km. In the subplot for M2, the location of vertical cross-sections in Laurentia and Fennoscandia are indicated by white lines with black dots. Figure 2. View largeDownload slide Cross-sectional view of viscous heating in Laurentia at different times for M1 and M2. Plots for M3 are not shown because its results are very similar to those of M2. Figure 2. View largeDownload slide Cross-sectional view of viscous heating in Laurentia at different times for M1 and M2. Plots for M3 are not shown because its results are very similar to those of M2. Figure 3. View largeDownload slide Same as in Fig. 2, except for cross-section in Fennoscandia. Figure 3. View largeDownload slide Same as in Fig. 2, except for cross-section in Fennoscandia. Figure 4. View largeDownload slide Cross-sectional view of viscous heating in Laurentia (left-hand panel) and Fennoscandia (right-hand panel) at different times for M4. Figure 4. View largeDownload slide Cross-sectional view of viscous heating in Laurentia (left-hand panel) and Fennoscandia (right-hand panel) at different times for M4. Figure 5. View largeDownload slide (a) The local ice history of the site with maximum viscous heating from 26 thousand years before present time (kBP) to the present. M2 and M3 share the same site which is different from that of M1; (b) the viscous heating dependence on time for that site and (c) the maximum local viscous heating at different times in M1–M3 (see the main text). Figure 5. View largeDownload slide (a) The local ice history of the site with maximum viscous heating from 26 thousand years before present time (kBP) to the present. M2 and M3 share the same site which is different from that of M1; (b) the viscous heating dependence on time for that site and (c) the maximum local viscous heating at different times in M1–M3 (see the main text). To visualize how viscous heating varies with depth, vertical cross-sections in Laurentia and Fennoscandia are shown in Figs 2–4. The locations of these vertical cross-sections are indicated by the two dashed lines in the subplot for M2 in Fig. 1. Figs 2–4 also show how viscous heating varies with time from 15 kBP to 13 and 10 kBP. The spatial-temporal variation in Laurentia for M1 and M2 (similarly for M3) are shown in Fig. 2, while those in Fennoscandia are shown in Fig. 3. Fig. 4 shows the variation in both Laurentia and Fennoscandia for M4. In general, Figs 2–4 show that the location and magnitude of high viscous heat changes with time and in space and the magnitude of viscous heating peaks at 13 kBP. As we shall see in Fig. 5, this is mainly due to the changes of ice thickness and location of the ice centre in time. From Figs 2–4, we see that the peak of viscous heating in M1 generally occurs between 400 and 670 km depth, but in M2 (similarly for M3), the peak under Laurentia is at a shallower depth (Fig. 2). Under Fennoscandia, the locations of the peaks in M1 and M2 are at comparable depth until 13 kBP, after that the peak in M2 is again at a shallower depth than in M1 (Fig. 3). In M4, the presence of the LV upper mantle above a higher viscosity lower mantle pushes the peak to a shallower depth than M1 (Fig. 4). All these are due to the spatial distribution of the von Mises (equivalent) stress τ which is affected by the viscosity structure of the Earth model. Thus, we see that the magnitude of maximum local viscous heating depends on mantle rheology. Fig. 5(a) shows the local ice history at the Earth's surface above the sites with maximum viscous heating for the Earth model under consideration. The time evolution of viscous heating at the sites with maximum heating is shown in Fig. 5(b). At other locations in the Earth, the viscous heating may have a smaller magnitude than the maximum value, but, the value may peak at different times. When all the sites in the mantle are considered, the maximum viscous heating for the whole mantle is shown in Fig. 5(c). Inspection of Figs 5(a) and (b) shows that maximum viscous dissipation occurs near the end of deglaciation at 13 kBP when the rate of melting is fastest. This confirms the finding of the simple ice deglaciation models of Hanyk et al. (2005). In addition, the sharp decline of viscous heating after 13 kBP means that the effect is localized in time, thus the effects of previous glacial cycles are small and can be neglected in our computation. 3.2 Effect of A* and η on the magnitude of viscous heating in uniform mantles In the last subsection, the spatial-temporal variation of viscous heating is shown for a fixed value of A* and η. In this section, we study how the values of A* and η affect the peak value of viscous heating at all times in uniform mantles like M1–M3. We study the range of values for A* from 1 × 10−36 to 1 × 10−33 Pa −3 s−1 and, for η, from 3 × 1020 to 3 × 1022 Pa s as these represent typical values found in uniform mantles. The results are summarized in Table 2. For linear rheology (top row below the labels), it can be seen that the lower the mantle viscosity, the larger is the viscous heating (see discussion of eqs 4a or 4b above). For non-linear rheology (the column on the far right), the largest viscous heating is achieved around A* = 1.11 × 10−34 Pa−3 s−1. This is due to the trade-off between the parameter A* (or A) and τ: for small values of A* (below 1.11 × 10−34 Pa−3 s−1), the relaxation time is long and the magnitude of von Mises stress τ does not change rapidly in time. According to eq. (4a), viscous heating increases with larger value of A* when rheology is non-linear because the effect of stress relaxation is small. However, when A* is above 1.11 × 10−34 Pa−3 s−1, the relaxation time is fast and thus τ decreases rapidly, causing viscous heating to decrease with further increasing of A. For composite rheology, the trade-off between A and τ also exist, but the relaxation time of τ is further modified by the value of η. Thus viscous heating no longer peaks at A* around 1.11 × 10−34 Pa−3 s−1 (see Table 2), but at smaller value of A* when the value of η decreases. Table 2 shows that the largest viscous heating within the studied range of parameters is at A* = 1.11 × 10−36 Pa−3 s−1 and when η has the lowest value of 3 × 1020 Pa s (see eq. 4b). 3.3 Effect of mantle compressibility Next, we investigate the effect of material compressibility for linear, non-linear and composite rheology by changing the Poisson's ratio from around 0.5 (incompressible material) to 0.2877 (compressible). The results for models with uniform mantle are summarized in Table 3 which show that compressibility almost doubles the peak viscous heating when the rheology is linear. This is in line with the finding of Hanyk et al. (2005). The reason is that the von Mises stress τ in the upper mantle increases with compressibility. However, from the perspective of strain rate, the reason is less clear: intuitively, with compressibility, volumetric strain rate $${\dot{\varepsilon }_{rr}}^t$$ is greater than zero. However, it is well known (e.g. Chandrasekhar 1981, p. 14, eq. 29) that $$\phi = 2\eta ({\boldsymbol{\dot{\varepsilon }}}_{ij}^2 - \frac{1}{3}\dot{\varepsilon }_{rr}^2)$$ so that ϕ might decrease unless $$\dot{\varepsilon }_{ij}^2$$ increases faster than $$\frac{1}{3}\dot{\varepsilon }_{rr}^2$$, which is apparently the case. Table 3 shows that the effect of compressibility is not as large when the rheology is non-linear or composite because the increase in von Mises stress is smaller. 3.4 Effect of a low viscosity zone From model M4, we saw that an LV upper mantle is able to give a peak value of viscous heating of 22.36 times that of chondritic radiogenic heating. Here, we want to explore the effect of even lower viscosity in the LV zone below the lithosphere for all three types of rheology. The models are modified from VM5a with the addition of an LV zone. The thickness and rheology (A* and η) of the LV zone are listed in Table 4. The linear viscosity in both linear and composite rheology is 3 × 1018 Pa s, that is, two orders of magnitude smaller than that in the upper mantle. The parameter A* is set to 1.11 × 10−34 Pa−3 s−1 in non-linear rheology because this value gives the largest of the peak viscous heating for uniform non-linear rheology models as shown in Table 1. For the same reason, the parameters for composite rheology are taken to be A* = 1.11 × 10−36 Pa−3 s−1 and η = 3 × 1018 Pa s. Results in Table 4 show that the existence of the LV zone can increase the peak value of viscous heating to be over 100 times that of the chondritic radiogenic heating in linear rheology and composite rheology, compared with about 20–30 times in non-linear rheology. This result is also consistent with the predictions of eq. (5). In the following section, we shall investigate whether viscous heating produces significant changes in temperature or surface heat flow. 4 UPPER BOUND ON HEAT FLOW AND TEMPERATURE CHANGE The spatial-temporal evolution of viscous dissipation inside the Earth can be treated as an extra heat source which we denoted as $$H( {\vec{r},t} )$$ and has units of energy generated per unit volume and per unit time. This heat source can raise the local temperature and result in net heat flow according to the heat flow equation (e.g. Turcotte & Schubert 2014), $$H\left( {\vec{r},t} \right) = \vec{\nabla } \cdot \vec{q}\left( {\vec{r},t} \right) + \rho C\frac{\partial }{{\partial t}}T\left( {\vec{r},t} \right)$$ (5) Here, $$\frac{\partial }{{\partial t}}T( {\vec{r},t} )$$ denotes the rate of temperature change of a volume element with density ρ and specific heat C; $$\vec{q}( {\vec{r},t} )$$ is the heat flux and $$\vec{\nabla } \cdot \vec{q}( {\vec{r},t} )$$ denotes the net heat flow out of the volume element. To complete the computation, note that the heat flux is related to the temperature gradient by Fourier's law of conduction: $$\vec{q}\left( {\vec{r},t} \right) = - \kappa \vec{\nabla }T\left( {\vec{r},t} \right)$$ (6)where κ is the coefficient of thermal conductivity. In this paper, we are only interested in estimating (i) the upper bound of the induced heat flux (or heat flow) and (ii) the upper bound of the temperature increase due to viscous heating. To estimate the upper bound of the change in heat flux, we take $$\frac{\partial }{{\partial t}}T ( {\vec{r},t} ) = 0$$ in eq. (5) and assume that the heat flow is outwards in the radial direction only. After integrating with respect to the radius, one obtains $$\delta q \left( {r,\theta ,\varphi ,t} \right) = \mathop \smallint \nolimits_{{\rm{CMB}}}^r H\left( {r',\theta ,\varphi ,t} \right){r^{'2}}dr'/{r^2}$$ (7)where CMB is the core–mantle boundary, and θ and φ are latitude and longitude respectively. To estimate the upper bound of the temperature change, we assume that there is no heat flux in eq. (5) and do the time integration from 26 kBP to the time under consideration (since the heat generated before 26 kBP is very small) to get $$\delta T \left( {r, \theta, \varphi ,t} \right) = \mathop \smallint \nolimits_{26{\rm{kBP}}}^t H ( {r, theta ,\varphi ,t'} )/( {\rho C} )dt'$$ (8)where C is taken to be 1 kJ kg − 1 °C and uniform in the mantle (e.g. Turcotte & Schubert 2014). Fig. 6 shows the effect of viscous heating on the upper bound of the change in transient heat flux at the surface of the Earth for models M1–M4. The yellow dotted line on M4 indicates the location of the ice margin. Fig. 6 shows that the upper bound of the heat flux at 13 kBP peaks between the edge of the Laurentide and the Cordilleran ice sheets just like in Fig. 1 and the peak magnitude is of the order of 10–30 mW m−2. To put these numbers in perspective, the mean continental heat flux is around 65 mW m−2 (Jaupart & Mareschal 2007) and the mantle heat flux in Canada is about 15 mW m−2 (Jaupart & Mareschal 2007). Thus, the transient heat flux from viscous dissipation due to GIA is not negligible at 13 kBP. An interesting question is whether this extra heat flux near the boundary between the Laurentide and the Cordilleran ice sheets can affect ice stability there. However, since the area of high heat flux is small and the period of high heating is relatively short, the effects on the upper bound of the total heat flow or temperature change are small. This will be demonstrated below. Figure 6. View largeDownload slide Upper bound of perturbed surface heat flux (in mW m−2) at 13 kBP for M1–M4. The yellow dotted line on M4 indicates the location of the ice margin. Figure 6. View largeDownload slide Upper bound of perturbed surface heat flux (in mW m−2) at 13 kBP for M1–M4. The yellow dotted line on M4 indicates the location of the ice margin. How does viscous heating affect the total heat flow out of the Earth? Fig. 7 shows the time evolution of the total heat flow for models M1–M4. This is obtained by integrating the surface heat flux over the surface area of the whole Earth. For M2 and M3, the maximum total heat flow due to viscous heating is at 14 kBP, while for models with linear rheology (i.e. M1 and M4), it is around 10 kBP. The reason why they are at different times is due to the difference in the ηeff and the growth and decay of von Mises stress τ in different models. For M2 and M3, the von Mises stress in the Earth is larger at 14 kBP, while for M1 and M4 it is larger around 10 kBP. For models M1–M4, the total heat flow attained a peak value of around 0.15–0.20 TW, but today the values are less than 0.02 TW. For the models with an LV zone, the peak value of total heat flow is similar to that in M4 although the maximum viscous heating is about five times larger. Since the total heat loss of the Earth today is around 44 TW (Stein 1995), 0.2 TW is less than 0.5 per cent of the current heat loss. Figure 7. View largeDownload slide The time evolution of the upper bound of total perturbed heat flow at the Earth's surface for models M1–M4. Figure 7. View largeDownload slide The time evolution of the upper bound of total perturbed heat flow at the Earth's surface for models M1–M4. Finally, we wish to estimate the upper bound of the temperature change induced by viscous heating for model M4, which has the largest viscous heating in models without LV zone. Fig. 8 shows the upper bound of the temperature change at different depths accumulated up to 13 and 0 kBP (see eq. 8). We can see that the upper bound of the temperature change due to viscous heating is only of the order of 2 × 10−3 °C. However, we can see in Table 4 that the maximum viscous heating for linear and composite rheology models with an LV zone is about five times larger than that for M4, which makes the temperature change almost one order of magnitude larger, that is, 1 × 10−2 °C. Even if there are 30 glacial cycles, then the largest temperature change can only be about 0.3 °C. Thus, the upper bound of the temperature change due to viscous heating is still too small to affect the mantle temperature field, to induce any widespread melting or volcanism or to significantly affect mantle rock properties (including seismic velocities today or mantle viscosity which can potentially affect mantle flow) or affect ice sheet stability. Figure 8. View largeDownload slide The spatial distribution of the upper bound of temperature anomalies (in 10−4 °C) for M4 at depths of 325 and 602.5 km and at 13 and 0 kBP. Figure 8. View largeDownload slide The spatial distribution of the upper bound of temperature anomalies (in 10−4 °C) for M4 at depths of 325 and 602.5 km and at 13 and 0 kBP. 5 CONCLUSIONS We modeled viscous heating in linear, non-linear and composite rheologies using realistic oceans and realistic ice history model ICE-6G. We found that viscous heating is determined by both mantle rheology and ice history. In particular, the magnitude peaks near the end of deglaciation and near the edge of ice sheets. The spatial distribution of viscous heating is also affected by the presence of ocean loading. In general, a small value of η gives the largest viscous heating and for a fixed value of η, larger heating is found in composite rheology than in linear rheology. The viscous heating induced is of the order of 10−9–10−7 W m−3 for a range of reasonable rheology parameters. The upper bound of the transient heat flux due to viscous heating can be as high as about 30 mW m−2 which is not negligible, and is consistent with the finding of Hanyk et al. (2005). However, since the area with heat production is small and the time period of heat production is short, the upper bound of the temperature change due to viscous heating over 30 glacial cycles is of the order of 0.3 °C only. Contrary to the suggestion of Hanyk et al. (2005), we show that even when taking into account non-Newtonian or composite rheology, the upper bound of temperature change due to viscous heating is not large enough to trigger volcanism, affect ice stability or mantle material properties such as seismic velocity and viscosity. ACKNOWLEDGEMENTS We are grateful to Jerry Mitrovica and an anonymous reviewer for their useful comments and suggestions. This work is supported by General Research Fund project17305314 from the Hong Kong Research Grants Council to Patrick Wu. The FE calculation was performed with the ABAQUS package from Hibbitt, Karlsson and Sorensen Inc. This research is conducted in part using the research computing facilities and/or advisory services offered by Information Technology Services, the University of Hong Kong. REFERENCES Chandrasekhar S., 1981. Hydrodynamic and Hydromagnetic Stability , pp. 704, Dover. Gomez N., Pollard D., Holland D., 2015. Sea-level feedback lowers projections of future Antarctic Ice-Sheet mass loss, Nat. Commun. , 6, 8798, doi:10.1038/ncomms9798. https://doi.org/10.1038/ncomms9798 Google Scholar CrossRef Search ADS PubMed Huybers P., Langmuir C., 2009. Feedback between deglaciation, volcanism, and atmospheric CO2, Earth planet. Sci. Lett. , 286( 3–4), 479– 491. https://doi.org/10.1016/j.epsl.2009.07.014 Google Scholar CrossRef Search ADS Hanyk L., Matyska C., Yuen D.A., 2005. 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Published by Oxford University Press on behalf of The Royal Astronomical Society. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Geophysical Journal International Oxford University Press # Effects of mantle rheologies on viscous heating induced by Glacial Isostatic Adjustment , Volume 213 (1) – Apr 1, 2018 12 pages /lp/ou_press/effects-of-mantle-rheologies-on-viscous-heating-induced-by-glacial-HKSbjt1w9K Publisher The Royal Astronomical Society ISSN 0956-540X eISSN 1365-246X D.O.I. 10.1093/gji/ggx535 Publisher site See Article on Publisher Site ### Abstract Summary It has been argued that viscous dissipation from mantle flow in response to surface loading during glacial cycles can result in short-term heating and thus trigger transient volcanism or changes in mantle properties, which may in turn affect mantle dynamics. Furthermore, heating near the Earth's surface can also affect the stability of ice sheets. We have studied the magnitude and spatial-temporal distribution of viscous heating induced in the mantle by the realistic ice model ICE-6G and gravitationally consistent ocean loads. Three types of mantle rheologies, including linear, non-linear and composite rheologies are considered to see if non-linear creep can induce larger viscous heating than linear rheology. We used the Coupled-Laplace-Finite-Element model of Glacial Isostatic Adjustment (GIA) to compute the strain, stress and shear heating during a glacial cycle. We also investigated the upper bound of temperature change and surface heat flux change due to viscous heating. We found that maximum viscous heating occurs near the end of deglaciation near the edge of the ice sheet with amplitude as high as 120 times larger than that of the chondritic radioactive heating. The maximum heat flux due to viscous heating can reach 30 mW m−2, but the area with large heat flux is small and the timescale of heating is short. As a result, the upper bound of temperature change due to viscous heating is small. Even if 30 glacial cycles are included, the largest temperature change can be of the order of 0.3 °C. Thus, viscous heating induced by GIA cannot induce volcanism and cannot significantly affect mantle material properties, mantle dynamics nor ice-sheet stability. Loading of the Earth, Europe, North America, Heat generation and transport, Rheology: mantle 1 INTRODUCTION In a fluid, the presence of viscosity, which represents the frictional interaction between neighbouring fluid elements, transforms some kinetic energy of the fluid into heat energy for dissipation (e.g. Landau & Lifshitz 1966). This so-called ‘viscous heating’ can potentially change the temperature and therefore material properties of mantle rocks. If viscous heating is large, then it can be very important because it can induce melting and therefore volcanism. It can also alter seismic properties and thus our interpretation of internal structure of the Earth, or alter mantle viscosity, which may in turn affect mantle dynamics. For example, viscous heating generated by tidal deformation induced by Jupiter may have caused volcanism on the Jovian moon Io (Ross & Schubert 1987; Segatz et al.1988). There is speculation that glacial cycles may have triggered volcanism during the Quaternary (e.g. Nakada & Yokose 1992; Sigvaldason et al.1992; Huybers & Langmuir 2009, Uenzelmann-Neben et al.2012). The link between them is generally attributed to decompression (Jull & McKenzie 1996; Slater et al.1998), but volcanism can also be triggered by viscous heating induced by Glacial Isostatic Adjustment (GIA) of the Earth in response to cycles of ice and ocean loading. Hanyk et al. (2005) modeled viscous heating due to GIA using simple ice load histories on a spherical Earth with linear rheology. They found that viscous heating can generate observable transient heat flux on the surface of the Earth. They also suggested that some degree of volcanism may be associated with viscous heating if the deglaciation period is short, and speculated that higher values of viscous heating can be generated if mantle rheology is non-linear. Indeed, if viscous heating is large enough at the base of the ice sheet, then glacial loading can also affect the stability of ice sheets by basal heating (e.g. Pattyn 2010). On the other hand, if viscous heating leads to lower mantle viscosity near the surface, then this would lead to faster land uplift and that may help to stabilize marine ice sheets (Gomez et al.2015). In this paper, we improve on Hanyk's work by using a realistic ice history model ICE-6G (Peltier et al.2015) together with realistic, self-gravitating oceans. As we shall see, the interaction among ice sheets and the loading of the ocean floor by meltwater affects the spatial distribution of viscous heating. A realistic loading history is also important, as it will eliminate the unrealistic results due to unreasonably fast or slow deglaciation histories. In addition, we consider three types of mantle rheologies in our Earth models: linear, non-linear and composite rheologies to see how large non-linear creep can affect the magnitude of viscous dissipation. Besides studying the effect of viscous heating on surface heat flux, we also study the following questions: what temperature changes inside the Earth are produced by viscous heating induced by glacial cycles? Do these temperature changes significantly affect present-day seismic velocities and thus the interpretation of seismic tomography? Can they affect viscosity and thus mantle flow induced during GIA? In the following sections, we will start with a brief review of the three different types of mantle rheologies, and provide a brief discussion of our model. Then, we will present the results, focusing on the magnitude and spatial and temporal distribution of viscous heating for some simple and other more sophisticated Earth models. After that, we will estimate the effects of viscous heating on the upper bound of heat flux change and see if the upper bound of temperature increase can trigger volcanism and affect ice stability or material properties inside the Earth. 2 THE MODEL 2.1 Mantle rheologies and rate of viscous dissipation Creep experiments on mantle rocks show that both linear and non-linear creep laws operate in the mantle (e.g. Karato & Wu 1993). If both creep laws operate simultaneously, then we have composite rheology. For this case, the creep mechanism with the highest creep rate becomes the dominant creep mechanism. The constitutive relation for these rheologies relates the deviatoric stress σD and the deviatoric strain rate $${{\boldsymbol{\dot{\varepsilon\! }}}_{\boldsymbol{D}}}$$, which are defined as $${{\boldsymbol{\sigma\! }}_{\boldsymbol{D}}} = {\boldsymbol{\sigma }} - \frac{1}{3}{\sigma _{ii}}{{\bf I}}$$ (1) $${{\boldsymbol{\dot{\varepsilon\! }}}_{\boldsymbol{D}}} = {\boldsymbol{\dot{\varepsilon }}} - \frac{1}{3}{\dot{\varepsilon }_{ii}}{{\bf I}}$$ (2)where σ and $${\boldsymbol{\dot{\varepsilon }}}$$ are the stress tensor and the strain rate tensor, respectively, I is the identity tensor, σii is the sum of diagonal components of σ and $${\dot{\varepsilon }_{ii}}$$ is the sum of diagonal components of $${\boldsymbol{\dot{\varepsilon }}}$$. In the following, we refer to σDij and $${\dot{\varepsilon }_{Dij}}$$ as the components of σD and $${{\boldsymbol{\dot{\varepsilon\! }}}_{\boldsymbol{D}}}$$, respectively. The relation between σD and $${{\boldsymbol{\dot{\varepsilon\! }}}_{\boldsymbol{D}}}$$ for composite, linear and non-linear rheologies can be expressed as (e.g. van der Wal et al.2010): $${{\boldsymbol{\sigma\! }}_{\boldsymbol{D}}} = \frac{1}{{\frac{1}{{2\eta }} + A{\sigma _E}^{n - 1}}}{{\boldsymbol{\dot{\varepsilon\! }}}_{\boldsymbol{D}}}$$ (3a) Here, η is the dynamic viscosity for linear creep, A is the non-linear creep parameter determined from shear experiments, and its value depends on temperature, pressure and material properties. σE is the effective deviatoric stress defined by $${\sigma _E} = \sqrt {\frac{1}{2}{\sigma _{Dij}}{\sigma _{Dij}}}$$ and n is the stress exponent with experimental value between 2 and 6. Here, we will take n = 3, as that is a typical value for mantle rocks (Karato & Wu 1993, Ranalli 1995). If A = 0, then eq. (3a) reduces to the relation for linear rheology. If A ≠ 0 and η = ∞, then it becomes the relation for non-linear rheology. It is useful to define the effective viscosity $${\eta _{{\rm{eff}}}} = \frac{1}{2}{( {\frac{1}{{2\eta }} + A{\sigma _E}^{n - 1}} )^{ - 1}}$$, so that eq. (3a) becomes $${{\boldsymbol{\sigma\! }}_{\boldsymbol{D}}} = 2{\eta _{{\rm{eff}}}}{{\boldsymbol{\dot{\varepsilon\! }}}_{\boldsymbol{D}}}$$ (3b) For non-linear or composite rheology, the effective viscosity changes with stress level and thus with space and time. For non-linear rheology or composite rheology with a fixed η, a decrease in σE will result in an increase in effective viscosity. The viscous dissipation rate ϕ (hereafter called ‘viscous heating’) is given by (e.g. eq. 7 in Hanyk et al.2005): $$\phi = {{\boldsymbol{\sigma\! }}_{\boldsymbol{D}}}{:}\, {{\boldsymbol{\dot{\varepsilon\! }}}_{\boldsymbol{D}}} = \frac{1}{{2{{\boldsymbol{\eta }}_{{{\bf eff}}}}}}{{\boldsymbol{\sigma\! }}_{\boldsymbol{D}}}{:}\,{{\boldsymbol{\sigma\! }}_{\boldsymbol{D}}}$$ (4a) This shows that shear heating decreases if the effective viscosity increases provided that σD does not change rapidly. For surface loading problems like GIA, σD is determined by the changing surface loads, although σD is also affected by stress relaxation where the decay time constant is proportional to the effective viscosity. In terms of von Mises stress $$\tau = \sqrt 3 {\sigma _E}$$, the creep parameter A and viscosity η, eq. (4a) can be written as: $$\phi = \frac{2}{3} \left( {\frac{1}{{2\eta }} + \frac{1}{3}A{\tau ^2}} \right){\tau ^2}$$ (4b)which clearly shows the strong dependence of ϕ on von Mises stress τ. Eq. (4a) can also be written as: $$\phi = 2{{\boldsymbol{\eta }}_{{{\bf eff}}}}{{\boldsymbol{\dot{\varepsilon\! }}}_{\boldsymbol{D}}}{:}\,{{\boldsymbol{\dot{\varepsilon\! }}}_{\boldsymbol{D}}}$$ which shows that viscous heating would increase with larger effective viscosity provided that the strain rate $${{\boldsymbol{\dot{\varepsilon\! }}}_{\boldsymbol{D}}}$$ is constant. For our problem, $${{\boldsymbol{\dot{\varepsilon\! }}}_{\boldsymbol{D}}}$$ is not constant, but $${{\boldsymbol{\dot{\varepsilon\! }}}_{\boldsymbol{D}}}{:}\,{{\boldsymbol{\dot{\varepsilon\! }}}_{\boldsymbol{D}}}$$ is determined by (σD/ηeff)2. Thus, eqs (4a) or (4b) will be used for our discussion below. 2.2 The GIA model The Coupled Laplace-Finite-Element (CLFE) GIA model of Wu (2004), later modified by van der Wal et al. (2010), is used in this study. Finite-element grids with different (0.5° and 2°) spatial resolution have been used for the computations. It is found that 2° resolution is adequate for our purpose. The inputs of the GIA model are elastic and creep parameters for the Earth model, and ice loading history. Unlike the simple ice sheet model used in Hanyk et al. (2005), the ice model used here is the realistic global ICE6G model of Peltier et al. (2015). Since ICE6G provides ice thickness history from 26 kBP to the present, we assume that the ice thickness increased linearly from zero at 108 kBP to the ice thickness at 26 kBP. Also, the ice was taken from the water in the oceans and meltwater returned to the oceans. The self-consistent sea level equation is solved for realistic oceans (Wu 2004). Since the effects of time-dependent coastline and rotational feedback are small on the von Mises stress τ and shear heating, they have not been included. As we shall see below, the localization of viscous heating in time makes the consideration of previous glacial cycles unnecessary. For the Earth models, the elastic parameters for models M1–M3 are the same as those in van der Wal et al. (2010), and for M4, they are the same as that in model VM5a of Peltier et al. (2015). The rheological parameters are described in Table 1. Here, parameter A* is the creep parameter determined from uniaxial experiments and is related to A, the creep parameter from shear experiments by $${A^} = 2A/\sqrt {{3^{n + 1}}}$$ (van der Wal et al.2010). In Table 1, M1 and M4 are linear rheological models. M1 has a uniform viscosity of 3 × 1021 Pa s, while in M4, the viscosities in the upper mantle (100–670 km depth), shallow lower mantle (670–1271 km depth) and deep lower mantle (1271–2891 km depth) are 5 × 1020, 1.6 × 1021 and 3 × 1021 Pa s respectively. M4 is considered because model VM5a is used for the construction of ICE6G (Peltier et al.2015), and so these should be used together. The rheological parameters in models M2 and M3 are uniform in the mantle. M2 has a non-linear rheology, while model M3 has a composite rheology. In other models, the effects of compressibility and a low viscosity (LV) zone below the lithosphere are also studied (see Tables 2–4) as they can also affect the magnitude of viscous heating. Table 1. Rheological parameters of four Earth models. M1 M2 M3 M4 A(Pa − 3 · s − 1) 0 1.11 × 10−34 1.11 × 10−34 0 η (Pa s) 3 × 1021 0 3 × 1021 VM5a n 1 3 3 1 M1 M2 M3 M4 A(Pa − 3 · s − 1) 0 1.11 × 10−34 1.11 × 10−34 0 η (Pa s) 3 × 1021 0 3 × 1021 VM5a n 1 3 3 1 View Large Table 2. The maximum local viscous heating of all time for uniform mantle models with various rheology (A and η). ϕMax η(Pa · s) 3.00 × 1020 3.00 × 1021 3.00 × 1022 Non-linear A* (Pa − 3 · s − 1) Linear 11.64 3.95 0.54 1.11 × 10−36 11.64 6.14 2.73 2.23 1.11 × 10−35 11.45 11.45 10.24 9.99 1.11 × 10−34 9.58 10.04 10.12 10.14 1.11 × 10−33 6.73 6.55 6.54 6.53 ϕMax η(Pa · s) 3.00 × 1020 3.00 × 1021 3.00 × 1022 Non-linear A* (Pa − 3 · s − 1) Linear 11.64 3.95 0.54 1.11 × 10−36 11.64 6.14 2.73 2.23 1.11 × 10−35 11.45 11.45 10.24 9.99 1.11 × 10−34 9.58 10.04 10.12 10.14 1.11 × 10−33 6.73 6.55 6.54 6.53 View Large Table 3. The maximum local viscous heating of all epochs for two values of Poisson's ratio (i.e. compressibility) with various rheology (A* [Pa−3 s−1] and η [Pa s]). ϕMax A* = 0 η = 3 × 1021 A* = 1.11 × 10−34 (non − linear) A* = 1.11 × 10−34η = 3 × 1021 Poisson's ratio 0.4900 3.95 10.14 10.04 0.2877 6.18 10.59 10.40 ϕMax A* = 0 η = 3 × 1021 A* = 1.11 × 10−34 (non − linear) A* = 1.11 × 10−34η = 3 × 1021 Poisson's ratio 0.4900 3.95 10.14 10.04 0.2877 6.18 10.59 10.40 View Large Table 4. The maximum local viscous heat of all time in models with an LV zone below the lithosphere. Units: A∗ in [Pa−3 s−1] and η in [Pa s]. ϕMax A=0 η = 3 × 1018 A = 1.11 × 10−34 (non − linear) A* = 1.11 × 10−36η = 3 × 1018 LV zone thickness (km) 40 102.18 26.01 102.19 100 118.80 30.52 118.81 ϕMax A=0 η = 3 × 1018 A = 1.11 × 10−34 (non − linear) A* = 1.11 × 10−36η = 3 × 1018 LV zone thickness (km) 40 102.18 26.01 102.19 100 118.80 30.52 118.81 View Large The outputs of the CLFE model contain spatial temporal evolution of the displacements and state of stress throughout the mantle. From the stress output at any time step, the local viscous heating for each element can be computed using eqs (4a) or (4b). In this paper, viscous heating is normalized by the chondritic radiogenic heating of 3 × 10−9 W m−3 (Hanyk et al.2005). 3 RESULTS 3.1 Spatial-temporal distribution of viscous heating for M1–M4 In Fig. 1, the spatial distribution of normalized viscous heating for models M1–M4 is shown at 13 kBP, the time when the viscous heating peaked (see Figs 2–5 below). It can be noted that viscous dissipation mainly occurs around past ice margins in Laurentia, the North American Cordillera, Fennoscandia and the Barents Sea area where the shear stresses are largest. Due to the constructive interference between the thick Laurentide ice sheets and the thinner Cordilleran ice sheet at 13 kBP, the peak amplitude occurs between their ice margins. However, in the ocean area between the northeast coasts of Canada and Greenland, the destructive interference between ice and water loading results in very low viscous heating. Similarly, constructive interference between the thinner ice sheets in Fennoscandia and the Barents Sea at 13 kBP, results in a smaller local peak between them. Fig. 1 also shows that the magnitude of viscous dissipation for M2 and M3 is more than two times higher than that for M1. The similarity between the results of M2 and M3 at this and all other times indicates that non-linear creep dominates in the composite rheology. However, the presence of an LV upper mantle in M4 results in much higher viscous heating than for M1–M3. The maxima in M1, M2, M3 and M4 are 3.95, 10.14, 10.04 and 22.36 times that of chondritic radiogenic heating, respectively. Figure 1. View largeDownload slide Spatial distribution of the normalized viscous heating for M1–M4, at 13 kBP and depth at 337.5 km. In the subplot for M2, the location of vertical cross-sections in Laurentia and Fennoscandia are indicated by white lines with black dots. Figure 1. View largeDownload slide Spatial distribution of the normalized viscous heating for M1–M4, at 13 kBP and depth at 337.5 km. In the subplot for M2, the location of vertical cross-sections in Laurentia and Fennoscandia are indicated by white lines with black dots. Figure 2. View largeDownload slide Cross-sectional view of viscous heating in Laurentia at different times for M1 and M2. Plots for M3 are not shown because its results are very similar to those of M2. Figure 2. View largeDownload slide Cross-sectional view of viscous heating in Laurentia at different times for M1 and M2. Plots for M3 are not shown because its results are very similar to those of M2. Figure 3. View largeDownload slide Same as in Fig. 2, except for cross-section in Fennoscandia. Figure 3. View largeDownload slide Same as in Fig. 2, except for cross-section in Fennoscandia. Figure 4. View largeDownload slide Cross-sectional view of viscous heating in Laurentia (left-hand panel) and Fennoscandia (right-hand panel) at different times for M4. Figure 4. View largeDownload slide Cross-sectional view of viscous heating in Laurentia (left-hand panel) and Fennoscandia (right-hand panel) at different times for M4. Figure 5. View largeDownload slide (a) The local ice history of the site with maximum viscous heating from 26 thousand years before present time (kBP) to the present. M2 and M3 share the same site which is different from that of M1; (b) the viscous heating dependence on time for that site and (c) the maximum local viscous heating at different times in M1–M3 (see the main text). Figure 5. View largeDownload slide (a) The local ice history of the site with maximum viscous heating from 26 thousand years before present time (kBP) to the present. M2 and M3 share the same site which is different from that of M1; (b) the viscous heating dependence on time for that site and (c) the maximum local viscous heating at different times in M1–M3 (see the main text). To visualize how viscous heating varies with depth, vertical cross-sections in Laurentia and Fennoscandia are shown in Figs 2–4. The locations of these vertical cross-sections are indicated by the two dashed lines in the subplot for M2 in Fig. 1. Figs 2–4 also show how viscous heating varies with time from 15 kBP to 13 and 10 kBP. The spatial-temporal variation in Laurentia for M1 and M2 (similarly for M3) are shown in Fig. 2, while those in Fennoscandia are shown in Fig. 3. Fig. 4 shows the variation in both Laurentia and Fennoscandia for M4. In general, Figs 2–4 show that the location and magnitude of high viscous heat changes with time and in space and the magnitude of viscous heating peaks at 13 kBP. As we shall see in Fig. 5, this is mainly due to the changes of ice thickness and location of the ice centre in time. From Figs 2–4, we see that the peak of viscous heating in M1 generally occurs between 400 and 670 km depth, but in M2 (similarly for M3), the peak under Laurentia is at a shallower depth (Fig. 2). Under Fennoscandia, the locations of the peaks in M1 and M2 are at comparable depth until 13 kBP, after that the peak in M2 is again at a shallower depth than in M1 (Fig. 3). In M4, the presence of the LV upper mantle above a higher viscosity lower mantle pushes the peak to a shallower depth than M1 (Fig. 4). All these are due to the spatial distribution of the von Mises (equivalent) stress τ which is affected by the viscosity structure of the Earth model. Thus, we see that the magnitude of maximum local viscous heating depends on mantle rheology. Fig. 5(a) shows the local ice history at the Earth's surface above the sites with maximum viscous heating for the Earth model under consideration. The time evolution of viscous heating at the sites with maximum heating is shown in Fig. 5(b). At other locations in the Earth, the viscous heating may have a smaller magnitude than the maximum value, but, the value may peak at different times. When all the sites in the mantle are considered, the maximum viscous heating for the whole mantle is shown in Fig. 5(c). Inspection of Figs 5(a) and (b) shows that maximum viscous dissipation occurs near the end of deglaciation at 13 kBP when the rate of melting is fastest. This confirms the finding of the simple ice deglaciation models of Hanyk et al. (2005). In addition, the sharp decline of viscous heating after 13 kBP means that the effect is localized in time, thus the effects of previous glacial cycles are small and can be neglected in our computation. 3.2 Effect of A* and η on the magnitude of viscous heating in uniform mantles In the last subsection, the spatial-temporal variation of viscous heating is shown for a fixed value of A* and η. In this section, we study how the values of A* and η affect the peak value of viscous heating at all times in uniform mantles like M1–M3. We study the range of values for A* from 1 × 10−36 to 1 × 10−33 Pa −3 s−1 and, for η, from 3 × 1020 to 3 × 1022 Pa s as these represent typical values found in uniform mantles. The results are summarized in Table 2. For linear rheology (top row below the labels), it can be seen that the lower the mantle viscosity, the larger is the viscous heating (see discussion of eqs 4a or 4b above). For non-linear rheology (the column on the far right), the largest viscous heating is achieved around A* = 1.11 × 10−34 Pa−3 s−1. This is due to the trade-off between the parameter A* (or A) and τ: for small values of A* (below 1.11 × 10−34 Pa−3 s−1), the relaxation time is long and the magnitude of von Mises stress τ does not change rapidly in time. According to eq. (4a), viscous heating increases with larger value of A* when rheology is non-linear because the effect of stress relaxation is small. However, when A* is above 1.11 × 10−34 Pa−3 s−1, the relaxation time is fast and thus τ decreases rapidly, causing viscous heating to decrease with further increasing of A. For composite rheology, the trade-off between A and τ also exist, but the relaxation time of τ is further modified by the value of η. Thus viscous heating no longer peaks at A* around 1.11 × 10−34 Pa−3 s−1 (see Table 2), but at smaller value of A* when the value of η decreases. Table 2 shows that the largest viscous heating within the studied range of parameters is at A* = 1.11 × 10−36 Pa−3 s−1 and when η has the lowest value of 3 × 1020 Pa s (see eq. 4b). 3.3 Effect of mantle compressibility Next, we investigate the effect of material compressibility for linear, non-linear and composite rheology by changing the Poisson's ratio from around 0.5 (incompressible material) to 0.2877 (compressible). The results for models with uniform mantle are summarized in Table 3 which show that compressibility almost doubles the peak viscous heating when the rheology is linear. This is in line with the finding of Hanyk et al. (2005). The reason is that the von Mises stress τ in the upper mantle increases with compressibility. However, from the perspective of strain rate, the reason is less clear: intuitively, with compressibility, volumetric strain rate $${\dot{\varepsilon }_{rr}}^t$$ is greater than zero. However, it is well known (e.g. Chandrasekhar 1981, p. 14, eq. 29) that $$\phi = 2\eta ({\boldsymbol{\dot{\varepsilon }}}_{ij}^2 - \frac{1}{3}\dot{\varepsilon }_{rr}^2)$$ so that ϕ might decrease unless $$\dot{\varepsilon }_{ij}^2$$ increases faster than $$\frac{1}{3}\dot{\varepsilon }_{rr}^2$$, which is apparently the case. Table 3 shows that the effect of compressibility is not as large when the rheology is non-linear or composite because the increase in von Mises stress is smaller. 3.4 Effect of a low viscosity zone From model M4, we saw that an LV upper mantle is able to give a peak value of viscous heating of 22.36 times that of chondritic radiogenic heating. Here, we want to explore the effect of even lower viscosity in the LV zone below the lithosphere for all three types of rheology. The models are modified from VM5a with the addition of an LV zone. The thickness and rheology (A* and η) of the LV zone are listed in Table 4. The linear viscosity in both linear and composite rheology is 3 × 1018 Pa s, that is, two orders of magnitude smaller than that in the upper mantle. The parameter A* is set to 1.11 × 10−34 Pa−3 s−1 in non-linear rheology because this value gives the largest of the peak viscous heating for uniform non-linear rheology models as shown in Table 1. For the same reason, the parameters for composite rheology are taken to be A* = 1.11 × 10−36 Pa−3 s−1 and η = 3 × 1018 Pa s. Results in Table 4 show that the existence of the LV zone can increase the peak value of viscous heating to be over 100 times that of the chondritic radiogenic heating in linear rheology and composite rheology, compared with about 20–30 times in non-linear rheology. This result is also consistent with the predictions of eq. (5). In the following section, we shall investigate whether viscous heating produces significant changes in temperature or surface heat flow. 4 UPPER BOUND ON HEAT FLOW AND TEMPERATURE CHANGE The spatial-temporal evolution of viscous dissipation inside the Earth can be treated as an extra heat source which we denoted as $$H( {\vec{r},t} )$$ and has units of energy generated per unit volume and per unit time. This heat source can raise the local temperature and result in net heat flow according to the heat flow equation (e.g. Turcotte & Schubert 2014), $$H\left( {\vec{r},t} \right) = \vec{\nabla } \cdot \vec{q}\left( {\vec{r},t} \right) + \rho C\frac{\partial }{{\partial t}}T\left( {\vec{r},t} \right)$$ (5) Here, $$\frac{\partial }{{\partial t}}T( {\vec{r},t} )$$ denotes the rate of temperature change of a volume element with density ρ and specific heat C; $$\vec{q}( {\vec{r},t} )$$ is the heat flux and $$\vec{\nabla } \cdot \vec{q}( {\vec{r},t} )$$ denotes the net heat flow out of the volume element. To complete the computation, note that the heat flux is related to the temperature gradient by Fourier's law of conduction: $$\vec{q}\left( {\vec{r},t} \right) = - \kappa \vec{\nabla }T\left( {\vec{r},t} \right)$$ (6)where κ is the coefficient of thermal conductivity. In this paper, we are only interested in estimating (i) the upper bound of the induced heat flux (or heat flow) and (ii) the upper bound of the temperature increase due to viscous heating. To estimate the upper bound of the change in heat flux, we take $$\frac{\partial }{{\partial t}}T ( {\vec{r},t} ) = 0$$ in eq. (5) and assume that the heat flow is outwards in the radial direction only. After integrating with respect to the radius, one obtains $$\delta q \left( {r,\theta ,\varphi ,t} \right) = \mathop \smallint \nolimits_{{\rm{CMB}}}^r H\left( {r',\theta ,\varphi ,t} \right){r^{'2}}dr'/{r^2}$$ (7)where CMB is the core–mantle boundary, and θ and φ are latitude and longitude respectively. To estimate the upper bound of the temperature change, we assume that there is no heat flux in eq. (5) and do the time integration from 26 kBP to the time under consideration (since the heat generated before 26 kBP is very small) to get $$\delta T \left( {r, \theta, \varphi ,t} \right) = \mathop \smallint \nolimits_{26{\rm{kBP}}}^t H ( {r, theta ,\varphi ,t'} )/( {\rho C} )dt'$$ (8)where C is taken to be 1 kJ kg − 1 °C and uniform in the mantle (e.g. Turcotte & Schubert 2014). Fig. 6 shows the effect of viscous heating on the upper bound of the change in transient heat flux at the surface of the Earth for models M1–M4. The yellow dotted line on M4 indicates the location of the ice margin. Fig. 6 shows that the upper bound of the heat flux at 13 kBP peaks between the edge of the Laurentide and the Cordilleran ice sheets just like in Fig. 1 and the peak magnitude is of the order of 10–30 mW m−2. To put these numbers in perspective, the mean continental heat flux is around 65 mW m−2 (Jaupart & Mareschal 2007) and the mantle heat flux in Canada is about 15 mW m−2 (Jaupart & Mareschal 2007). Thus, the transient heat flux from viscous dissipation due to GIA is not negligible at 13 kBP. An interesting question is whether this extra heat flux near the boundary between the Laurentide and the Cordilleran ice sheets can affect ice stability there. However, since the area of high heat flux is small and the period of high heating is relatively short, the effects on the upper bound of the total heat flow or temperature change are small. This will be demonstrated below. Figure 6. View largeDownload slide Upper bound of perturbed surface heat flux (in mW m−2) at 13 kBP for M1–M4. The yellow dotted line on M4 indicates the location of the ice margin. Figure 6. View largeDownload slide Upper bound of perturbed surface heat flux (in mW m−2) at 13 kBP for M1–M4. The yellow dotted line on M4 indicates the location of the ice margin. How does viscous heating affect the total heat flow out of the Earth? Fig. 7 shows the time evolution of the total heat flow for models M1–M4. This is obtained by integrating the surface heat flux over the surface area of the whole Earth. For M2 and M3, the maximum total heat flow due to viscous heating is at 14 kBP, while for models with linear rheology (i.e. M1 and M4), it is around 10 kBP. The reason why they are at different times is due to the difference in the ηeff and the growth and decay of von Mises stress τ in different models. For M2 and M3, the von Mises stress in the Earth is larger at 14 kBP, while for M1 and M4 it is larger around 10 kBP. For models M1–M4, the total heat flow attained a peak value of around 0.15–0.20 TW, but today the values are less than 0.02 TW. For the models with an LV zone, the peak value of total heat flow is similar to that in M4 although the maximum viscous heating is about five times larger. Since the total heat loss of the Earth today is around 44 TW (Stein 1995), 0.2 TW is less than 0.5 per cent of the current heat loss. Figure 7. View largeDownload slide The time evolution of the upper bound of total perturbed heat flow at the Earth's surface for models M1–M4. Figure 7. View largeDownload slide The time evolution of the upper bound of total perturbed heat flow at the Earth's surface for models M1–M4. Finally, we wish to estimate the upper bound of the temperature change induced by viscous heating for model M4, which has the largest viscous heating in models without LV zone. Fig. 8 shows the upper bound of the temperature change at different depths accumulated up to 13 and 0 kBP (see eq. 8). We can see that the upper bound of the temperature change due to viscous heating is only of the order of 2 × 10−3 °C. However, we can see in Table 4 that the maximum viscous heating for linear and composite rheology models with an LV zone is about five times larger than that for M4, which makes the temperature change almost one order of magnitude larger, that is, 1 × 10−2 °C. Even if there are 30 glacial cycles, then the largest temperature change can only be about 0.3 °C. Thus, the upper bound of the temperature change due to viscous heating is still too small to affect the mantle temperature field, to induce any widespread melting or volcanism or to significantly affect mantle rock properties (including seismic velocities today or mantle viscosity which can potentially affect mantle flow) or affect ice sheet stability. Figure 8. View largeDownload slide The spatial distribution of the upper bound of temperature anomalies (in 10−4 °C) for M4 at depths of 325 and 602.5 km and at 13 and 0 kBP. Figure 8. View largeDownload slide The spatial distribution of the upper bound of temperature anomalies (in 10−4 °C) for M4 at depths of 325 and 602.5 km and at 13 and 0 kBP. 5 CONCLUSIONS We modeled viscous heating in linear, non-linear and composite rheologies using realistic oceans and realistic ice history model ICE-6G. We found that viscous heating is determined by both mantle rheology and ice history. In particular, the magnitude peaks near the end of deglaciation and near the edge of ice sheets. The spatial distribution of viscous heating is also affected by the presence of ocean loading. In general, a small value of η gives the largest viscous heating and for a fixed value of η, larger heating is found in composite rheology than in linear rheology. The viscous heating induced is of the order of 10−9–10−7 W m−3 for a range of reasonable rheology parameters. The upper bound of the transient heat flux due to viscous heating can be as high as about 30 mW m−2 which is not negligible, and is consistent with the finding of Hanyk et al. (2005). However, since the area with heat production is small and the time period of heat production is short, the upper bound of the temperature change due to viscous heating over 30 glacial cycles is of the order of 0.3 °C only. Contrary to the suggestion of Hanyk et al. (2005), we show that even when taking into account non-Newtonian or composite rheology, the upper bound of temperature change due to viscous heating is not large enough to trigger volcanism, affect ice stability or mantle material properties such as seismic velocity and viscosity. ACKNOWLEDGEMENTS We are grateful to Jerry Mitrovica and an anonymous reviewer for their useful comments and suggestions. This work is supported by General Research Fund project17305314 from the Hong Kong Research Grants Council to Patrick Wu. The FE calculation was performed with the ABAQUS package from Hibbitt, Karlsson and Sorensen Inc. This research is conducted in part using the research computing facilities and/or advisory services offered by Information Technology Services, the University of Hong Kong. REFERENCES Chandrasekhar S., 1981. Hydrodynamic and Hydromagnetic Stability , pp. 704, Dover. Gomez N., Pollard D., Holland D., 2015. Sea-level feedback lowers projections of future Antarctic Ice-Sheet mass loss, Nat. Commun. , 6, 8798, doi:10.1038/ncomms9798. https://doi.org/10.1038/ncomms9798 Google Scholar CrossRef Search ADS PubMed Huybers P., Langmuir C., 2009. Feedback between deglaciation, volcanism, and atmospheric CO2, Earth planet. Sci. Lett. , 286( 3–4), 479– 491. https://doi.org/10.1016/j.epsl.2009.07.014 Google Scholar CrossRef Search ADS Hanyk L., Matyska C., Yuen D.A., 2005. 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DeepDyve ### Freelancer DeepDyve ### Pro Price FREE$49/month \$360/year Save searches from PubMed Create lists to Export lists, citations	2018-09-24 23:25:36	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 30, "x-ck12": 0, "texerror": 0, "math_score": 0.7602772116661072, "perplexity": 2034.0646640251607}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267160842.79/warc/CC-MAIN-20180924224739-20180925005139-00265.warc.gz"}
http://mathhelpforum.com/advanced-applied-math/27426-simplex-method-maximize-objective-function.html	Math Help - simplex method maximize objective function 1. simplex method maximize objective function A farmer has 100 acres to plant in corn and beans. Let c represent the # of acres planted in corn and b = # of acres planted in beans. It costs $72 / acre to plant corn and$40 / acre to plant beans. If the farmer has $12,000 to spend planting crops, how many acres should he plant in each crop if corn has a profit of$24 / acre and beans $32 / acre? Write the objective function and the system of constraints. Show the initial tableau and solve. My thoughts... I guess we are trying to get maximum revenue. It seems to me since beans are cheaper to plant and have higher profit, that we are going to plant all beans. Objective function: z = 32b + 24c (this seems like the amount of revenue?) Constraints ? b + c <= 100 40b + 72c <= 12000 Intial Tableau Can anyone give me any feedback as to whether I am on the right track? 2. Originally Posted by BenDunn A farmer has 100 acres to plant in corn and beans. Let c represent the # of acres planted in corn and b = # of acres planted in beans. It costs$72 / acre to plant corn and $40 / acre to plant beans. If the farmer has$12,000 to spend planting crops, how many acres should he plant in each crop if corn has a profit of $24 / acre and beans$32 / acre? Write the objective function and the system of constraints. Show the initial tableau and solve. My thoughts... I guess we are trying to get maximum revenue. It seems to me since beans are cheaper to plant and have higher profit, that we are going to plant all beans. Objective function: z = 32b + 24c (this seems like the amount of revenue?) Constraints ? b + c <= 100 40b + 72c <= 12000 Intial Tableau Can anyone give me any feedback as to whether I am on the right track? What you have is correct. To get the initial tableau you introduce initial slack variables e, f so we have: z - 32b - 24c = 0 b + c +e = 100 40b + 72c + f= 12000 Then the initial tableau in matrix form is: $\left[ \begin{array}{ccccc} 1&-32&-24&0&0\\ 0&1&1&1&0\\ 0&40&72&0&1 \end{array} \right]$ $ \left[ \begin{array}{c} z\\b\\c\\e\\f \end{array} \right] = \left[ \begin{array}{c} 0\\100\\1200 \end{array} \right] $ RonL	2015-05-29 19:47:34	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6090210676193237, "perplexity": 2234.0270485585847}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207930259.97/warc/CC-MAIN-20150521113210-00279-ip-10-180-206-219.ec2.internal.warc.gz"}
https://socratic.org/questions/how-do-you-find-the-slope-intercept-form-of-the-equation-of-the-line-that-passes	# How do you find the slope-intercept form of the equation of the line that passes through the given point (-2,-7) and has the slope 1? Apr 2, 2015 The answer is: $y = x - 5$ The slope-intercept form is: $y = m x + n$ The slope $m$ is already given as $1$ Lets plug the given point in the equation: $- 7 = 1 \cdot \left(- 2\right) + n$ $n = - 5$ So the line equation is: $y = x - 5$	2022-09-28 12:42:47	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 7, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8438431620597839, "perplexity": 289.6564818646485}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335254.72/warc/CC-MAIN-20220928113848-20220928143848-00579.warc.gz"}
https://chemistry.stackexchange.com/questions/45034/is-this-asking-for-the-equivalence-point/45037	# Is this asking for the equivalence point? Is this question asking for the equivalence point of the titration curve? At what point does the concentration of acetic acid equal the concentration of the acetate ion? What is the pH of the equimolar, ideal buffer solution at this point. At first, I thought this question was asking about the point right before the titration curve shoots up. However, I don't recall ever learning about such a point. • Welcome to Chemistry.SE! Take the tour to get familiar with this site. Mathematical expressions and equations can be formatted using $\LaTeX$ syntax. This appears to be a homework question, please share your thoughts and attempts towards the solution - although I am not sure if it is just a very basic question. Have a look at the wikipedia page of buffer solutions, I am certain it will address this issue. – Martin - マーチン Feb 10 '16 at 6:16 • The equivalence point is would not be what you are looking for. You are trying to find the half-equivalence point, where instead of all the acid being neutralized and converted to acetate, only half is. If you have a titration curve, this occurs at half the equivalence volume. Based on MaxW's formula below, what would the pH be when the concentrations of acetic acid and acetate are equal? – Tyberius Mar 15 '17 at 15:19 In general the "pKa" is the term used to define the point at which the protonated and unprotonated forms are equal. The pKa is from the negative log of the acid dissociation constant as given by the reaction: $$\ce{HA <=> H+ + A-}$$ and the equation: $$K_\mathrm{a} = \dfrac{\ce{[H+] [A- ]}}{\ce{[HA]}}$$ where $\ce{[H+] = [A- ]}$ then: $$K_\mathrm{a} = \dfrac{\ce{[H+]^2}}{\ce{[HA]}}$$ and $$\ce{pKa} = -\log \ce{Ka} = -\log \dfrac{\ce{[H+]^2}}{\ce{[HA]}}$$	2020-05-30 08:02:56	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6418242454528809, "perplexity": 680.8367782649599}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347407667.28/warc/CC-MAIN-20200530071741-20200530101741-00223.warc.gz"}
https://math.stackexchange.com/questions/117702/orthogonal-projections-with-sum-p-i-i-proving-that-i-ne-j-rightarrow-p	# Orthogonal projections with $\sum P_i =I$, proving that $i\ne j \Rightarrow P_{j}P_{i}=0$ I am reading Introduction to Quantum Computing by Kaye, Laflamme, and Mosca. As an exercise, they write "Prove that if the operators $P_{i}$ satisfy $P_{i}^{}=P_{i}$ and $P_{i}^{2}=P_{i}$ , then $P_{i}P_{j}=0$ for $i\ne j$.'' In the context of this problem, it has been assumed that $I=\sum_{i=1}^{n} P_{i}$, where I suppose that $n$ could be infinite. I have shown that this is true in the trivial case $n=2$, but the general case has been eluding me. How should I attack this? For each $j$, $$P_j=P_jIP_j=P_j\left(\sum_{k=1}^n P_k\right)P_j=\sum_{k=1}^nP_jP_kP_j=P_j+\sum_{k\neq j}P_jP_kP_j,$$ so $\sum\limits_{k\neq j}P_jP_kP_j=0$. For each $i\neq j$, $P_jP_iP_j=(P_iP_j)^P_iP_j$ is a positive operator, and a sum of positive operators is positive, so $-P_jP_iP_j=\sum\limits_{k\neq i,j}P_jP_kP_j$ is also positive. This is only possible if $P_jP_iP_j=0$. Since $\\|P_iP_j\\|^2=\\|(P_iP_j)^P_iP_j\\|=\\|P_jP_iP_j\\|$, it follows that $P_iP_j=0$. Because of the properties you state, $\\|P_{j}x\\|^{2}=(x,P_{j}x)=(P_{j}x,x)$. Therefore, $$\\|x\\|^{2} = (\sum_{j}P_{j}x,x)= \sum_{j}\\|P_{j}x\\|^{2}.$$ Apply this identity to $x=P_{k}y$, and use the fact that $P_{k}^{2}=P_{k}$: $$\\|P_{k}y\\|^{2} = \sum_{j\ne k}\\|P_{j}P_{k}y\\|^{2}+\\|P_{k}y\\|^{2}.$$ The only way this can happen is $P_{j}P_{k}y=0$ for all $j \ne k$. For all $$i,j$$ you have $$P_i+P_j\le\sum_k P_k\le I$$, hence $$P_i\le I-P_j$$. Multiplying by $$P_j$$ on left and right on LHS and RHS you then get $$P_j P_i P_j\le P_j(I-P_j)P_j=0,$$ hence $$P_j P_i P_j=0$$, which implies $$P_j P_i P_j=(P_j P_i)(P_j P_i)^\dagger=0$$ and thus $$P_i P_j=P_j P_i=0$$. You can also prove the other direction: if $$P_i P_j=0$$ for all $$i\neq j$$ then $$\sum_k P_k$$ is a projector, as $$\left(\sum_k P_k\right)^2=\sum_k P_k + \sum_{i Here is a slight variant of Jonas’ argument. Assume that $p_{1},\ldots,p_{n}$ are projection elements of a unital $C^{}$-algebra $A$, where $n \in \Bbb{N}_{\geq 2}$, such that $$\sum_{k = 1}^{n} p_{k} = 1_{A}.$$ Choose distinct $i,j \in [n]$, where $[n] \stackrel{\text{df}}{=} \Bbb{N}_{\leq n}$. Then \begin{align} p_{i} & = p_{i} 1_{A} \\ & = p_{i} \sum_{k \in [n]} p_{k} \\ & = \sum_{k \in [n]} p_{i} p_{k} \\ & = p_{i}^{2} + p_{i} p_{j} + \sum_{k \in [n] \setminus \{ i,j \}} p_{i} p_{k} \\ & = p_{i} + p_{i} p_{j} + \sum_{k \in [n] \setminus \{ i,j \}} p_{i} p_{k}. \end{align} It follows that $$p_{i} p_{j} p_{j}^{} = p_{i} p_{j} = - \sum_{k \in [n] \setminus \{ i,j \}} p_{i} p_{k} = - \sum_{k \in [n] \setminus \{ i,j \}} p_{i} p_{k} p_{k}^{},$$ and consequently, $$(\spadesuit) \qquad (p_{i} p_{j}) (p_{i} p_{j})^{} = p_{i} p_{j} p_{j}^{} p_{i}^{} = - \sum_{k \in [n] \setminus \{ i,j \}} p_{i} p_{k} p_{k}^{} p_{i}^{} = - \sum_{k \in [n] \setminus \{ i,j \}} (p_{i} p_{k}) (p_{i} p_{k})^{}.$$ On the extreme left of $(\spadesuit)$, we have a positive element, while on the extreme right of $(\spadesuit)$, we have a negative element. This can only mean that both extremes are zero, so $(p_{i} p_{j}) (p_{i} p_{j})^{} = 0_{A}$. Hence, $$\\| p_{i} p_{j} \\|_{A}^{2} = \\| (p_{i} p_{j}) (p_{i} p_{j})^{} \\|_{A} = \\| 0_{A} \\|_{A} = 0,$$ or equivalently, $p_{i} p_{j} = 0_{A}$.	2022-01-26 01:02:19	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 12, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9991888403892517, "perplexity": 705.3641317503806}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304876.16/warc/CC-MAIN-20220125220353-20220126010353-00152.warc.gz"}
https://scicomp.stackexchange.com/questions/27454/why-does-multiplying-two-first-derivative-finite-difference-matrices-not-give-th	Why does multiplying two first derivative finite difference matrices not give the matrix for the second derivative? The finite difference matrix for the first derivative is $\begin{bmatrix} -1 & 1 & 0 \\ 0 & -1 & 1 \\ 0 & 0 & -1 \end{bmatrix}$. The finite difference matrix for the second derivative is $\begin{bmatrix} -2 & 1 & 0 \\ 1 & -2 & 1 \\ 0 & 1 & -2 \end{bmatrix}$. $\begin{bmatrix} -1 & 1 & 0 \\ 0 & -1 & 1 \\ 0 & 0 & -1 \end{bmatrix} \begin{bmatrix} -1 & 1 & 0 \\ 0 & -1 & 1 \\ 0 & 0 & -1 \end{bmatrix} = \begin{bmatrix} 1 & -2 & 1 \\ 0 & 1 & -2 \\ 0 & 0 & 1 \end{bmatrix}$. Why does multiplying together two first derivative matrices not give the second derivative matrix? • This is simply because $D_+ D_+ \neq D^2$ you need the information before and behind (to get the same stencil). Try multiplying $D_+ D_-$ (the forward diff operator and backward). – Gregory Jul 20 '17 at 18:29 • Thanks, however, I am wondering something like the following: $\frac{d}{dx} \frac{df}{dx} = \frac{d^2f}{dx^2}$, so why does $D(Df) \neq D^2f$? You are taking the derivative of the derivative of $f$, so why do you not get the second derivative of $f$? – islanss Jul 20 '17 at 18:37 • You do get D^2, just not the approximation you're thinking of. Try expanding these operators in a taylor series to see. – Gregory Jul 20 '17 at 18:43 • It would probably be better if you didn't think of your second matrix in the question as the FD matrix, but rather a FD matrix. – Gregory Jul 20 '17 at 18:48 • That's exactly the point. Just like there is a forward and a backward first derivative matrix, there are multiple choices to compute second derivatives. $D_+D_+$ happens to be one of them, just not the one you've seen before. – Wolfgang Bangerth Jul 20 '17 at 20:29 Look at the operators $$D_+^2 u = \frac{u_{n+2} - 2 u_{n+1} + u_n}{\Delta x^2}.$$ If you taylor expand this for small $\Delta x$ you arrive at $$D_+^2 u = u_{xx} - \Delta x u_{xxx} + O(\Delta x^2)$$. Thus $D_+^2 = D^2$ in the limit as $\Delta x \to 0$ (as it should), but note the error is first order in $\Delta x$ and so it is not a great approximation. Consider instead, the one you are thinking of $$D_- D_+ u = \frac{u_{n+1} - 2 u_n + u_{n-1}}{\Delta x^2}.$$ Again taking a taylor expansion we have $$D_- D_+ u = u_{xx} + \frac{\Delta x^2}{12} u_{xxxx} + O(\Delta x^4).$$ Thus this approximation is actually better since the error goes down quadratically rather than linearly.	2021-03-01 14:09:08	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9249378442764282, "perplexity": 294.49703601277514}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178362513.50/warc/CC-MAIN-20210301121225-20210301151225-00489.warc.gz"}
http://mathematica.stackexchange.com/questions/20641/why-cant-mathematica-solve-these-non-linear-equations	# Why can't Mathematica solve these non-linear equations? [closed] $l_{2}$ and $\theta$ are the variables. All other parameters are constants. I need to find $l_{2}$ and $\theta$ in terms of these constants. $\frac{\mu_{0}\sin(\theta-\theta_{0})}{\sqrt{l_{2}^2 +\beta_{0}l_{2}+\mu_{0}l_{2}\cos(\theta-\theta_{0}) +\lambda_{0}}} + \frac{\mu_{1}\sin(\theta-\theta_{1})}{\sqrt{l_{2}^2 +\beta_{1}l_{2}+\mu_{1}l_{2}\cos(\theta-\theta_{1}) +\lambda_{1}}} =0$ and $\frac{2l_{2}+\beta_{0}+\mu_{0}\cos(\theta-\theta_{0})}{\sqrt{l_{2}^2 +\beta_{0}l_{2}+\mu_{0}l_{2}\cos(\theta-\theta_{0}) +\lambda_{0}}}+ \frac{2l_{2}+\beta_{1}+\mu_{1}\cos(\theta-\theta_{1})}{\sqrt{l_{2}^2 +\beta_{1}l_{2}+\mu_{1}l_{2}\cos(\theta-\theta_{1}) +\lambda_{1}}} =\frac{-2}{1+Vr^{l_{2}/D}}$ Here's the Mathematica code I used: Solve[{(μ0 Sin[t - t0])/Sqrt[ l2^2 + β0 l2 +μ0 l2 Cos[t - t0] + λ0] + (μ1 Sin[t - t1])/ Sqrt[l2^2 + β1 l2 + μ1 l2 Cos[t - t1] + λ1] == 0, (2 l2 + β0 + μ0 Cos[t - t0])/Sqrt[ l2^2 + β0 l2 + μ0 l2 Cos[t - t0] + λ0] + ( 2 l2 + β1 + μ1 Cos[t - t1])/Sqrt[ l2^2 + β1 l2 + μ1 l2 Cos[t - t1] + λ1] + 2/( 1 + V r^(l2/D0)) == 0}, {t, l2}] This didn't work. How can I use Mathematica techniques to solve this equation? - ## closed as too localized by m_goldberg, whuber, Yves Klett, Szabolcs, rcollyerMar 7 '13 at 2:54 This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question. As posed this is not a question -- it's just a complaint. What kind of answer are you look for? – m_goldberg Mar 5 '13 at 3:19 @m_goldberg how do I solve that? – Norman Mar 5 '13 at 4:02 In spirit this is the same question as mathematica.stackexchange.com/questions/20606/…. It suffers from exactly the same problem: you cannot hope to find a closed symbolic solution to an equation in which the unknown(s) appear as exponents (as $l_2$ does on the rhs) unless there is some magical cancellation (which there is not here). – whuber Mar 5 '13 at 4:28 when susbtitue values still doesn't work. [Mu]0 = 0; [Mu]1 = -9418; t0 = 0; t1 = 0; [Lambda]0 = 250000; [Lambda]1 = 22629049; [Beta]0 = 0; [Beta]1 = 0; V = 148; r = 1.1; D0 = 3640; – Norman Mar 5 '13 at 5:33 Solve cannot unravel the transcendental dependencies (use of both l2 and r^(l2/D0) will likely cause trouble here). Per documentation "Solve deals primarily with linear and polynomial equations." Use the method Simon Woods shows, or similar, for solving in presence of explicitly numeric parameters. – Daniel Lichtblau Mar 5 '13 at 14:54 Since you have provided numerical values for the constants, you can 1. Use plotting functions to approximately locate the solutions 2. Use FindRoot to refine the approximations First define the numerical constants and the equations: μ0 = 0; μ1 = -9418; t0 = 0; t1 = 0; λ0 = 250000; \ λ1 = 22629049; β0 = 0; β1 = 0; V = 148; r = 1.1; \ D0 = 3640; eq = {(μ0 Sin[t - t0])/ Sqrt[l2^2 + β0 l2 + μ0 l2 Cos[ t - t0] + λ0] + (μ1 Sin[t - t1])/ Sqrt[l2^2 + β1 l2 + μ1 l2 Cos[t - t1] + λ1] == 0, (2 l2 + β0 + μ0 Cos[t - t0])/ Sqrt[l2^2 + β0 l2 + μ0 l2 Cos[ t - t0] + λ0] + (2 l2 + β1 + μ1 Cos[ t - t1])/ Sqrt[l2^2 + β1 l2 + μ1 l2 Cos[t - t1] + λ1] + 2/(1 + V r^(l2/D0)) == 0}; Using ContourPlot you can visualise the solutions: With[{eq = eq}, ContourPlot[eq, {t, -7, 7}, {l2, -3000, 3000}]] It looks like the first equation is satisfied by $t = n \pi$. Let's check: eq[[1]] /. Sin[t] -> 0 (* True ) The solutions of the second equation occur around $l2 = 2000$ for $cos \theta = 1$ and $l2 = -2000$ for $cos \theta = -1$. We can use FindRoot to refine these estimates: FindRoot[eq[[2]] /. Cos[t] -> 1, {l2, 2000}] ( {l2 -> 1879.45} ) FindRoot[eq[[2]] /. Cos[t] -> -1, {l2, -2000}] ( {l2 -> -2152.18} *) So the solutions are $t=n\pi$ and $l2=1879.45 \text{ for even } n$, $l2=-2152.18\text{ for odd } n$ - if we have another two constraints like below how could I use mathematica to solve the problem l2^2 + [Beta]0 l2 + [Mu]0 l2 Cos[t - t0] + [Lambda]0 >[Mu]4 and l2^2 + [Beta]1 l2 + [Mu]1 l2 Cos[t - t1] + [Lambda]0 >[Mu]5 – Norman Mar 7 '13 at 10:24	2014-10-30 14:56:27	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4123338460922241, "perplexity": 7249.288580677921}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1414637898141.14/warc/CC-MAIN-20141030025818-00238-ip-10-16-133-185.ec2.internal.warc.gz"}
https://www.proc-iahs.net/382/409/2020/	Journal topic Proc. IAHS, 382, 409–414, 2020 https://doi.org/10.5194/piahs-382-409-2020 Proc. IAHS, 382, 409–414, 2020 https://doi.org/10.5194/piahs-382-409-2020 Pre-conference publication 22 Apr 2020 Pre-conference publication \| 22 Apr 2020 # Understanding the dynamic behaviour for the Madrid aquifer (Spain): insights from the integration of A-DInSAR and 3-D groundwater flow and geomechanical models Understanding the dynamic behaviour for the Madrid aquifer (Spain): insights from the integration of A-DInSAR and 3-D groundwater flow and geomechanical models Roberta Bonì1, Claudia Meisina1, Pietro Teatini2, Francesco Zucca1, Claudia Zoccarato2, Andrea Franceschini2, Pablo Ezquerro3, Marta Béjar-Pizarro3, José A. Fernández-Merodo3, Carolina Guardiola-Albert3, José L. Pastor4, Roberto Tomás4, and Gerardo Herrera3 Roberta Bonì et al. • 1Department of Earth and Environmental Sciences, University of Pavia, Pavia, 27100, Italy • 2Department of Civil, Environmental and Architectural Engineering, University of Padua, Padua, 35131, Italy • 3Geohazards InSAR Laboratory and Modeling Group, Instituto Geológico y Minero de España, Madrid, 28003, Spain • 4Geohazards InSAR Laboratory and Modeling Group, Instituto Geológico y Minero de España, Madrid, 28003, Spain Abstract Advanced Differential Interferometric Synthetic Aperture Radar (A-DInSAR) techniques and 3-D groundwater flow and geomechanical models are integrated to improve our knowledge about the Tertiary detritic aquifer of Madrid (TDAM). In particular, the attention is focused on the Manzanares-Jarama well field, located to the northwest of Madrid, which experienced five cycles of extensive groundwater withdrawal followed by natural recovery, to cope with the droughts occurred in summer 1995, 1999, 2002, 2006, and 2009. Piezometric records and A-DInSAR data acquired by ERS-1/2 and ENVISAT satellites during the periods 1992–2000 and 2002–2010, respectively, have been used to calibrate the groundwater flow and the geomechanical models. A time-lag of about one month between the hydraulic head changes and the displacements of the land surface has been detected by a joint wavelet analysis of A-DInSAR and piezometer head time series. Overall, the results show the effectiveness of the proposed integrated approach composed of A-DInSAR and 3-D geomechanical model to characterize the aquifer-system response during and after the groundwater withdrawal. 1 Introduction Groundwater numerical models provide a quantitative framework to understand the hydrogeological processes and represent a practical tool to comprehend how an aquifer system works (Anderson et al., 2015). Groundwater models integrate numerically the Partial differential equations governing the physical process of the water movement within a defined portion of a porous medium. Modelling design requires to set-up the model boundaries and geometry, provide the aquifer parameters and choose the code able to simulate the physical processes of interest (Anderson et al., 2015). Therefore, the groundwater model conceptualization needs extensive datasets that often lack due to the high costs required to collect. Figure 1Geographical location from Google Earth, Data SIO, NOAA, U.S., Navy, NGA, GEBCO, US Dept of State Geographer, ©2019 Google, Image Landsat/Copernicus (a) and geological map (b) of the study area. The piezometers and the well locations are also depicted. The geological map is derived from IGME (1995) and the water bodies and the rivers from https://servicio.mapama.gob.es/sia/visualizacion/descargas/mapas.jsp (last access: 2 March 2020). To remediate, at least in part, this paucity of measurements, in this work a novel methodology using A-DInSAR data as supporting tool for groundwater modelling purposes is presented. The methodology has been developed and tested to understand the dynamic behaviour of the Madrid aquifer. It represents a strategic groundwater resource in Spain, exploited in the past to cope with an increased groundwater demand during drought periods. The achieved results give insight about a fast response of the aquifer-system during and after the extraction periods. 2 Study area The study area is the Manzanares-Jarama wellfield, that is located northwest of Madrid, in Spain (Fig. 1). The analysed wellfield includes 32 wells, which withdraw groundwater from the “Manzanares-Jarama aquifer”, and 17 observation wells. The analysed aquifer extends for about 540 km2 and represents only a portion of the 2500 km2 Tertiary detritic aquifer (TDAM) located in the tectonic depression of the Madrid basin. The aquifer is a heterogeneous multi-layer system characterized by sand lenses embedded in a clay and clay-sand matrix (Ezquerro et al., 2014). The aquifer includes Tertiary detritical deposits and a Quaternary coverage (Martínez-Santos et al., 2010). The northern and southern boundaries of the aquifer are the Paleozoic relief of the Sierra of Guadarrama and evaporitic materials, respectively (Hernández-García and Custodio, 2004). Conversely, in the western and eastern boundaries areas, the alluvial deposits of the Manzanares and Jarama rivers are found, respectively. Figure 2Line-of-sight (LOS) velocity maps measured usingERS-1/2 (1992–2000) (a) and ENVISAT (2003–2010) images (b). World imagery Source: Esri, DigitalGlobe, GeoEye, Earthstar Geographics, CNES/Airbus DS, USDA, USGS, AeroGRID, IGN, and the GIS User Community. 3 Data and methodology ## 3.1 Satellite and piezometric data analysis The analysed satellite data are Synthetic Aperture Radar (SAR) images acquired by ERS-1/2 and ENVISAT in descending and ascending mode, respectively. The ERS-1/2 images cover the period from April 1992 to November 2000, and the ENVISAT dataset between August 2003 and September 2010. The ERS-1/2 and ENVISAT scenes were processed using the PSP-IFSAR technique (Costantini et al., 2008) to obtain the A-DInSAR dataset including line-of-sight (LOS) displacement time series and average velocity for each target in the periods 1992–2000 and 2003–2010 (Fig. 2). Available observation well measurements recorded the hydraulic head changes from 1998 to 2012 (Fig. 3) and show three major extraction phases causing a groundwater drawdown of about 100–150 m, corresponding with major drought periods followed by recovery periods (Yélamos and Villarroya, 1991; Canal de Isabel II Gestión, 2014). Figure 3Piezometric head time series acquired in the period 1998–2010. The location of the observation wells is reported in Fig. 1b. The methodology implemented by Tomás et al. (2016), based on a wavelet approach, was used for the joint analysis of the A-DInSAR and piezometric level time series to understand cause-and-effect relationships and to identify intermittent periodicity. On the other hand, Continuous Wavelet Transform (CWT), was applied to identify nonstationary intermittent oscillations in time series data. Cross Wavelet Transform (XWT) and Wavelet Coherence (WTC) were applied to find the common power and relative phase in time-frequency space of two-time series (Grinsted et al., 2004). The result is a 2-D plot of complex numbers. A high absolute value suggests a common time patterns between both time series. Furthermore, the phase (i.e. the angle of the vectors) of the XWT provides a quantification of the time shift (delay time) between the two time-series. It is worth nothing that both the A-DInSAR and piezometric head time series have been preliminary equalized in the time sampling interval using a 35 d interval that corresponds to the revisit time of ERS and ENVISAT. Then, a linear regression of the time series records was used to distinguish linear and non-linear component. The wavelet approach has been applied using the non-linear component resulting from the difference between the original time-series and the fitted linear component. Figure 4Schematic overview of the integrated approach used to reconstruct the 3-D model with the support of A-DInSAR data. ## 3.2 Integration of the A-DInSAR into numerical models In this work, the A-DInSAR data are used as supporting tool for different phases of the numerical model reconstruction (Fig. 4). In particular, the A-DInSAR data are exploited to (i) define the lateral boundaries of the static model, (ii) estimate the model parametrization, (iii) choose an appropriate code to simulate the physical processes, and (iv) to calibrate of the model. The joint use of the wellfield location and the average velocities measured by the A-DInSAR technique allows to identifying the influence area of the wellfield. Furthermore, the piezometric head time series and the displacement time series have been jointly used to estimate the aquifer storage (Ss) using a methodology applied by several authors on A-DInSAR-based and extensometers-based displacement measurements (Sneed and Galloway, 2000; Burbey, 2003; Tomás et al., 2010; Bonì et al., 2016). More precisely, the specific storage is computed dividing the bulk storage (Sk) by the aquifer thickness. The bulk storage is estimated using the following equation Eq. (1): $\begin{array}{}\text{(1)}& {S}_{k}=\frac{\mathrm{\Delta }d}{\mathrm{\Delta }h},\end{array}$ where Δd is the displacement, estimated by the satellite data, and related to the aquifer compaction as a result of the hydraulic head decrease Δh. The joint analysis of A-DInSAR displacements and piezometric head time series, as described in Sect. 3.1, supports the choice of the simulator in the geomechanical model. Finally, A-DInSAR displacement time series are used for cross-comparison with the simulated displacement to verify the model results. ## 3.3 Numerical model approaches The numerical approaches implemented in this work aims simulating groundwater flow and pumping induced land displacements. First of all, a static model is build up to reconstruct the three dimensional geometry including the main hydrogeological layers of the study area. Then, the 3-D static model is used for the hydrogeological and the geomechanical simulations. More precisely, the 3-D finite element (FE) grid of the selected domain is constructed using GEN3-D (Teatini et al., 2006). The groundwater flow model is simulated through the SAT3-D (SATurated Three-Dimensional) code (Teatini et al., 2011) that solves the following equation Eq. (2) (Bear 1972): $\begin{array}{}\text{(2)}& \mathrm{\nabla }\left(k\cdot \mathrm{\nabla }h\right)={S}_{\mathrm{s}}\cdot \frac{\partial h}{\partial t}+q\end{array}$ where k and h are the hydraulic permeability tensor and the hydraulic head, respectively, t is time, and q is the source/sink term. Ss is the specific storage, which is related to oedometric bulk compressibility cb through the relationship ${S}_{\mathrm{s}}=\mathit{\gamma }\left({c}_{\mathrm{b}}+\mathit{\varphi }\mathit{\beta }\right)$ with ϕ the medium porosity and β the volumetric water compressibility. The output of the groundwater flow model is the incremental pore pressure variation (p) due to groundwater pumping that is used as input in the geomechanical model. By assuming an elastic isotropic medium, the SUB3-D code (Teatini et al., 2006) is used to estimate the incremental displacement field u along the x, y, and z directions. SUB3-D solves the following equations Eq. (3) (Verruijt, 1969): $\begin{array}{}\text{(3)}& G{\mathrm{\nabla }}^{\mathrm{2}}{u}_{i}+\left(\mathit{\lambda }\phantom{\rule{0.125em}{0ex}}+\phantom{\rule{0.125em}{0ex}}G\right)\frac{\partial \mathit{\epsilon }}{\partial i}=\frac{\partial p}{\partial i}\phantom{\rule{1em}{0ex}}i=x,y\end{array}$ where λ and G are the Lamé constant and shear modulus of porous medium, respectively, $\mathit{\epsilon }=\frac{\partial {u}_{x}}{\partial x}+\frac{\partial {u}_{y}}{\partial y}+\frac{\partial {u}_{z}}{\partial z}$ is the volumetric strain, and ui is the displacement component along the ith coordinate direction. It is worth noting that: $\begin{array}{}\text{(4)}& G=\frac{E}{\mathrm{2}\left(\mathrm{1}+\mathit{\nu }\right)}\end{array}$ and $\begin{array}{}\text{(5)}& E=\frac{\left(\mathrm{1}+\mathit{\nu }\right)\left(\mathrm{1}-\mathrm{2}\mathit{\nu }\right)}{{c}_{\mathrm{b}}\left(\mathrm{1}-\mathit{\nu }\right)}\end{array}$ where E and ν stand for the Young modulus and the Poisson ratio, respectively. The groundwater flow and geomechanical models are calibrated using a trial and error approach. The hydraulic conductivity was calibrated the records at the piezometric wells starting from values reported by Hernández Torrego (2012) and from values obtained via pumping test for pilot points (e.g. CB5 piezometer, see the location in Fig. 1). The Young modulus and Lamè constants were calibrated using InSAR outcome. Consequently, the solution of Eq. (1) must takes the elastic storage obtained using Eqs. (4) and (5) starting from literature values (Ezquerro et al., 2014). Furthermore, for the geomechanical model the Poisson's ratio ν was set to 0.3, representing a common value used in the case of sedimentary deposits (Teatini et al., 2006). 4 Results and discussion ## 4.1 Remote assessment of aquifer-system response during and after pumping The analysis of the A-DInSAR displacement and the piezometric head time series has been performed for 17 piezometers of the Manzanares-Jarama wellfield using the wavelet approach as described in Sect. 3.1. The results provide insight about a mean time lag of 1.0±0.6 months, with minimum and maximum values equal to 0.0 and 3.3 months, respectively. The spatial pattern of the aquifer-system response is slightly larger in the northern sector of the study area. The aquifer-system response during and after pumping is fast, showing land subsidence during the extraction phase coinciding with the drought periods, and uplift in the recovery phase, providing fundamental information about the governing parameters controlling the hydro-geomechanical response. Figure 53-D model of the Manzanares-Jarama wellfield (a) and simulated and observed displacement at piezometer FE-1. (b) See the location in Fig. 1. The observed displacements are an average value of the values measured on the PS located within a buffer zone of 1000 m from the well, therefore also the standard deviation is reported. ## 4.2 Numerical simulation of aquifer-system response during and after pumping The join analysis of the satellite and piezometric data has provided fundamental information to design and calibrate the 3-D model of the Manzanares-Jarama well field. In particular, the model has been built including three main hydrogeological units; i.e. the upper phreatic aquifer, the intermediate aquitard and the lower confined aquifer (Fig. 5a). The model domain extends for the upper 700 m of the sedimentary sequence, whose top and bottom maps have been extracted by the ground surface elevation using the high resolution 5 m cell digital elevation model from Instituto Geográfico Nacional (IGN) and geological information (IGME, 1989). Since the piezometric drawdown caused by the wellfield did not reach a distance larger than 10 km from the wells, (Ezquerro et al., 2014; Béjar-Pizarro et al., 2017), the horizontally domain extends in order to account a buffer ring of 10 km around the wellfield. The aquifer's dynamic has been simulated during the period from 1994 to 2010, that includes four 1–1.5 year long periods of groundwater withdrawal. The modelling results show that the periods of groundwater extraction caused a land subsidence higher than 20 mm over an area of about 190 km2 and a maximum horizontal movement up to 6 mm. The simulated displacement generally agrees with the A-DInSAR measurements, capturing the minimum and maximum peak values (Fig. 5b). Furthermore, the calibrated model has allowed quantifying the land surface movements in the central zone of the study areas where A-DInSAR displacements are unavailable due to the presence of vegetation coverage. 5 Conclusions In this work, the potential of the integrated use of A-DInSAR data and 3-D groundwater flow and geomechanical models to capture and assess aquifer dynamics is shown. The approach has been applied to investigate the response during and after pumping of a portion of the Madrid aquifer. The aquifer-system has been characterized by a time-lag of about one month only between the hydraulic head changes and the land displacements, suggesting that the clayey units within the aquifer-system play a minor role. Data availability Data availability. All data generated or analysed during this study are included in this published article. Author contributions Author contributions. RB built the three-dimensional numerical modeling for the Manzanares-Jarama wellfield and prepared the manuscript. CM provided support and guidance throughout the research process for the geological interpretation of the data. PT provided a guidance to build the groundwater flow and geomechanical models and he contributed to the analysis of the results. CZ and AF from UniPD supported the development of the groundwater flow and geomechanical models. FZ supported the numerical modeling and the interpretation of the results. GH provided the geological, the hydrogeological and A-DInSAR data and supported their analysis. PE and MBP from IGME supply the geological and hydrogeological interpretation of the study area. JAFM supported the interpretation of the geomechanical model. CGA provided a guidance for the interpretation of the groundwater flow model. RT and JLP performed the wavelet analysis. All authors co-wrote and reviewed the manuscript. Competing interests Competing interests. The authors declare that they have no conflict of interest. Special issue statement Special issue statement. This article is part of the special issue “TISOLS: the Tenth International Symposium On Land Subsidence – living with subsidence”. It is a result of the Tenth International Symposium on Land Subsidence, Delft, the Netherlands, 17–21 May 2021. Acknowledgements Acknowledgements. The research was funded by University of Pavia in the framework of a research grant award “assegno di tipo A premiale” for research activities at the Dept. of Earth and Environmental Sciences, within the research project entitled “Sustainable groundwater resources management by integrating A-DInSAR derived monitoring and flow modeling results” assigned to Roberta Bonì in March 2019 (supv. Claudia Meisina). The activity has been developed within the scientific collaboration established in the framework of the UNESCO Land Subsidence International Initiative (LaSII, https://www.landsubsidence-unesco.org/, last access: 2 March 2020). Financial support Financial support. This research has been supported by the Università degli Studi di Pavia (Assegno di tipo A premiale: “Sustainable groundwater resources management by integrating A-DInSAR derived monitoring and flow modeling results” assigned to Roberta Bonì in March 2019) and the Spanish Ministry of Economy, Industry and Competitiveness (MINECO), the State Agency of Research (AEI), and the European Funds for Regional Development (FEDER) (grant no. TEC2017-85244-C2-1-P). References Anderson, M. P., Woessner, W. W., and Hunt, R. J.: Applied groundwater modeling: simulation of flow and advective transport, Academic press, 2015. Bear, J.: Dynamics of fluids in porous materials, Society of Petroleum Engineers: Dallas, TX, USA, 1972. Béjar-Pizarro, M., Ezquerro, P., Herrera, G., Tomás, R., Guardiola-Albert, C., Hernández, J. M. R., Fernández Merodo, J. A., Marchamalo, M., and Martínez, R.: Mapping groundwater level and aquifer storage variations from InSAR measurements in the Madrid aquifer, Central Spain, J. Hydrol., 547, 678–689, 2017. Bonì, R., Cigna, F., Bricker, S., Meisina, C., and McCormack, H.: Characterisation of hydraulic head changes and aquifer properties in the London Basin using Persistent Scatterer Interferometry ground motion data, J. Hydrol., 540, 835–849, 2016. Burbey, T. J.: Use of time-subsidence data during pumping to characterize specific storage and hydraulic conductivity of semiconfining units, J. Hydrol., 281, 3–22, 2003. Canal de Isabel II Gestión: Captación de aguas de superficie y subterraneas, Technical report, 2014 (in Spanish). Costantini, M., Falco, S., Malvarosa, F., and Minati, F.: A new method for identification and analysis of persistent scatterers in series of SAR images, in: Geoscience and Remote Sensing Symposium, IGARSS 2008, IEEE International 2008, 6–11 July 2008, 2, II-449, 2008. Ezquerro, P., Herrera, G., Marchamalo, M., Tomás, R., Béjar-Pizarro, M., and Martínez, R.: A quasi-elastic aquifer deformational behavior: Madrid aquifer case study, J. Hydrol., 519, 1192–1204, 2014. Grinsted, A., Moore, J. C., and Jevrejeva, S.: Application of the cross wavelet transform and wavelet coherence to geophysical time series, Nonlin. Processes Geophys., 11, 561–566, https://doi.org/10.5194/npg-11-561-2004, 2004. Hernández-García, M. E. and Custodio, E.: Natural baseline quality of Madrid Tertiary Detrital Aquifer groundwater (Spain): a basis for aquifer management, Environ. Geol., 46, 173–188, 2004. Hernández Torrego, E.: La recarga profunda de agua en las masas 003-010 y 003-011 del acuífero detrítico terciario de la fosa del Tajo (Madrid), PhD thesis, 2012. IGME: Geological Map of Spain, region 559, Technical report, available at: http://info.igme.es/cartografiadigital/geologica/Magna (last access: 21 May 2019), 1989 (in Spanish). IGME: Mapa Geológico de la Península Ibérica, Baleares y Canarias a escala 1:1.000.000, edición, 1995. Martínez-Santos, P., Pedretti, D., Martínez-Alfaro, P. E., Conde, M., and Casado, M.: Modelling the effects of groundwater-based urban supply in Low-permeability aquifers: application to the Madrid Aquifer, Spain, Water Resour. Manag., 24, 4613–4638, 2010. Sneed, M. and Galloway, D. L.: Aquifer-system compaction and land subsidence: measurements, analyses, and simulations: the Holly site, Edwards Air Force Base, Antelope Valley, California, US Geol Surv Water-Resour Invest Rep, 00-4015, 65 pp., 2000. Teatini, P., Ferronato, M., Gambolati, G., and Gonella, M.: Groundwater pumping and land subsidence in the Emilia-Romagna coastland, Italy: Modeling the past occurrence and the future trend, Water Resour. Res., 42, https://doi.org/10.1029/2005WR004242, 2006. Teatini, P., Ferronato, M., Gambolati, G., Baù, D., and Putti, M.: Anthropogenic Venice uplift by seawater pumping into a heterogeneous aquifer system, Water Resour. Res., 46, W11547, https://doi.org/10.1029/2010WR009161, 2011. Tomás, R., Herrera, G., Delgado, J., Lopez-Sanchez, J. M., Mallorquí, J. J., and Mulas, J.: A ground subsidence study based on DInSAR data: calibration of soil parameters and subsidence prediction in Murcia City (Spain), Eng. Geol., 111, 19–30, 2010. Tomás, R., Li, Z., Lopez-Sanchez, J. M., Liu, P., and Singleton, A.: Using wavelet tools to analyse seasonal variations from InSAR time-series data: a case study of the Huangtupo landslide, Landslides, 13, 437–450, https://doi.org/10.1007/s10346-015-0589-y, 2016. Verruijt, A.: Elastic storage of aquifers, in: Flow Through Porous Media, edited by: De Wiest, R., Elsevier, NY, 331–376, 1969. Yélamos, J. G. and Villarroya, F. I.: Variación de la piezometría y el caudal en cuatro explotaciones de aguas subterráneas en el acuífero del Terciario detrítico de Madrid, Bol. Geol. Min, 102, 857–874, 1991.	2020-05-25 14:41:00	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 7, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5081090331077576, "perplexity": 6338.313788907289}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347388758.12/warc/CC-MAIN-20200525130036-20200525160036-00314.warc.gz"}
http://www.math.utoronto.ca/cms/dynamics-learning-semianr/2011-10-14?CalendarStart=2011-10-14	## Dynamics Learning Seminar These seminars are for learning interesting and exciting topics in Dynamical Systems. ### Yoccoz renormalization by Artem Dudko \| University of Toronto Time: 14:00 (Friday, Oct. 14, 2011) Location: BA6180, Bahen Center, 40 St. George St. Abstract: In this talk I will describe the Yoccoz's renormalization construction for germs with irrationally indifferent fixed point at the origin. Siegel and Brjuno proved that any germ f(z)=a_1z+a_2z^2+... with a_1 a Brjuno number is linearizable at the origin. Using the renormalization idea I will sketch a proof of the Yoccoz's lower bound for the radius of the corresponding Siegel disk. #### Dates in this series · Monday, Sep. 26, 2011: On linearization of holomorphic maps with an irrationally indifferent fixed point (Liudmyla Kadets) · Monday, Oct. 03, 2011: On Siegel's linearization theorem. (Liudmyla Kadets) · Friday, Oct. 14, 2011: Yoccoz renormalization (Artem Dudko)	2013-05-23 05:14:24	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8579623103141785, "perplexity": 6003.465215565095}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368702849682/warc/CC-MAIN-20130516111409-00047-ip-10-60-113-184.ec2.internal.warc.gz"}
http://mathhelpforum.com/advanced-algebra/73530-examining-transformation-print.html	# Examining a transformation • February 13th 2009, 06:11 PM arbolis Examining a transformation I couldn't think a lot on this problem and I'd like to know whether my way of thinking is not wrong. Determine whether the following transformation is invertible and in case of being invertible, give its inverse. Let $T:\mathbb{R}^3 \to \mathbb{R}^3$ be defined by $T(v)=2v-(1,1,1)$. My attempt : Well I think that it has an inverse and that it's $\frac{v}{2}+\left( \frac{1}{2},\frac{1}{2},\frac{1}{2} \right)$. But I'd love to know how I could find a general way to determine if a transformation has an inverse. I guess by writing its matrix with respect to the canonical basis (or any other basis) and check out if the matrix is invertible... But I'm not sure. Nor I'm sure how to write such a matrix in this example. • February 13th 2009, 09:03 PM ThePerfectHacker Quote: Originally Posted by arbolis I couldn't think a lot on this problem and I'd like to know whether my way of thinking is not wrong. Determine whether the following transformation is invertible and in case of being invertible, give its inverse. Let $T:\mathbb{R}^3 \to \mathbb{R}^3$ be defined by $T(v)=2v-(1,1,1)$. My attempt : Well I think that it has an inverse and that it's $\frac{v}{2}+\left( \frac{1}{2},\frac{1}{2},\frac{1}{2} \right)$. But I'd love to know how I could find a general way to determine if a transformation has an inverse. I guess by writing its matrix with respect to the canonical basis (or any other basis) and check out if the matrix is invertible... But I'm not sure. Nor I'm sure how to write such a matrix in this example. Let $B = \{ \b{i},\b{j},\b{k}\}$ and now compute $T\b{i},T\b{j},T\b{k}$. Can you find the matrix now? • February 13th 2009, 10:37 PM math2009 $T(\vec{v})=2\vec{v}-\begin{bmatrix} 1\\1\\1 \end{bmatrix} . \ \vec{v},\vec{v}_1,\vec{v}_1 \in R^3, k\in R$ At first, we need verify if T is linear transformation. $T(\vec{v}_1+\vec{v}_2)=2(\vec{v}_1+\vec{v}_2)-\begin{bmatrix} 1\\1\\1 \end{bmatrix}$, but $T(\vec{v}_1)+T(\vec{v}_2)=2(\vec{v}_1+\vec{v}_2)-2\begin{bmatrix} 1\\1\\1 \end{bmatrix}$, $T(\vec{v}_1+\vec{v}_2)\neq T(\vec{v}_1)+T(\vec{v}_2)$ $T(k\vec{v})=2k\vec{v}-\begin{bmatrix} 1\\1\\1 \end{bmatrix},\ kT(\vec{v})=2k\vec{v}-k\begin{bmatrix} 1\\1\\1 \end{bmatrix}$ , $T(k\vec{v})\neq kT(\vec{v})$ T is NOT a linear transformation. Your defination is mistake. So you couldn't get inverse matrix. Your solution is inverse function. Generally, $A\in R^{n\times n},T(\vec{x})=A\vec{x}$ , get rank(A) by rref(A). If rank(A)=n and A is square matrix, then A is invertible. • February 14th 2009, 04:12 AM HallsofIvy math2009, arbolis never said linear transformation, just "transformation". Of course, in this case, it cannot be written as a matrix so ThePerfectHackers's idea doesn't help. In general a function is invertible if it is one-to-one and onto. "One-to-one" means that two different values in the domain cannot be mapped into the same value in the range. "Onto" means that every member of the range has some value of the domain mapped to it. For this transformation, in component notation, T(x,y,z)= (2x-1, 2y-1, 2z-1). Is it one-to-one? Suppose T(x',y',z')= T(x,y,z). Then 2x'- 1= 2x- 1, 2y- 1= 2y-1, and 2z'-= 2z-1. Add 1 to both sides of each equation, divide both sides of each equation by 2 and we get x'= x, y'= y, and z'= z. Yes, this transformation is one-to-one. Is it onto? Suppose (u, v, w) is any member of $R^3$. Is there an (x, y, z) so that T(x, y, z)= (u, v, w), we must have 2x- 1= u, 2y- 1= v, 2z- 1= w. Solving for x, y, z, we have x= (u+1)/2, y= (v+1)/2, z= (w+1)/2. Since those are perfectly good numbers, ((u+1)/2, (v+1)/2, (w+1)/2) is a member of $R^3$ that is mapped into (u, v, w). Since (u, v, w) could be any member of $R^3$ so T is onto $R^3$. Being both one-to-one and onto, T has an inverse. And, we have already found its inverse by going backward from (u, v, w) to ((u+1)/2, (v+1)/2, (w+1)/2). $T^{-1}\left[\begin{array}{c} u \\ v \\ w\end{array}\right]=\left[\begin{array}{c}\frac{u+1}{2} \\ \frac{v+1}{2} \\ \frac{w+1}{2}\end{array}\right]$ or, for V a member of $R^3$, $T^{-1}v= \frac{1}{2}\left(V+ \left[\begin{array}{c} 1 \\ 1 \\ 1\end{array}\right]\right)$, exactly what arbolis said. (I said that since this transformation is not linear it cannot be written as a matrix. It can be written as a matrix and a difference: $T\left(\left[\begin{array}{c} x \\ y \\ z \end{array}\right]\right)= \left[\begin{array}{ccc} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2\end{array}\right]\left[\begin{array}{c} x \\ y \\ z \end{array}\right]- \left[\begin{array}{c}1 \\ 1 \\ 1\end{array}\right]$: multiply by the matrix and then subtract. Since finding an inverse basically involved "doing everything backwards", its inverse can be expressed as "first add, then multiply by the inverse matrix". Since the matrix is diagonal, its inverse is trivial and we have $T^{-1}\left[\begin{array}{c} x \\ y \\ z \end{array}\right]=\left[\begin{array}{ccc} \frac{1}{2} & 0 & 0 \\ 0 & \frac{1}{2} & 0 \\ 0 & 0 & \frac{1}{2}\end{array}\right]\left(\left[\begin{array}{c} x \\ y \\ z \end{array}\right]+ \left[\begin{array}{c}1 \\ 1 \\ 1\end{array}\right]\right)$) • February 14th 2009, 04:29 AM math2009 HallsofIvy,function is not usually discussed with tranformation He may have implicit linear tranformation especially in this branch of forum. arbolis, how do you think ?	2016-06-29 01:38:46	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 24, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8269427418708801, "perplexity": 578.1250776608715}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783397428.37/warc/CC-MAIN-20160624154957-00123-ip-10-164-35-72.ec2.internal.warc.gz"}
https://dealii.org/developer/doxygen/deal.II/classSparseDirectUMFPACK.html	Reference documentation for deal.II version Git 4c0e8c9979 2020-03-28 07:38:34 +0100 #include <deal.II/lac/sparse_direct.h> Inheritance diagram for SparseDirectUMFPACK: [legend] ## Public Types using size_type = types::global_dof_index ## Public Member Functions SparseDirectUMFPACK () ~SparseDirectUMFPACK () override Setting up a sparse factorization void initialize (const SparsityPattern &sparsity_pattern) template<class Matrix > void factorize (const Matrix &matrix) template<class Matrix > Functions that represent the inverse of a matrix void vmult (Vector< double > &dst, const Vector< double > &src) const void vmult (BlockVector< double > &dst, const BlockVector< double > &src) const void Tvmult (Vector< double > &dst, const Vector< double > &src) const void Tvmult (BlockVector< double > &dst, const BlockVector< double > &src) const size_type m () const size_type n () const Functions that solve linear systems void solve (Vector< double > &rhs_and_solution, const bool transpose=false) const void solve (Vector< std::complex< double >> &rhs_and_solution, const bool transpose=false) const void solve (BlockVector< double > &rhs_and_solution, const bool transpose=false) const void solve (BlockVector< std::complex< double >> &rhs_and_solution, const bool transpose=false) const template<class Matrix > void solve (const Matrix &matrix, Vector< double > &rhs_and_solution, const bool transpose=false) template<class Matrix > void solve (const Matrix &matrix, Vector< std::complex< double >> &rhs_and_solution, const bool transpose=false) template<class Matrix > void solve (const Matrix &matrix, BlockVector< double > &rhs_and_solution, const bool transpose=false) template<class Matrix > void solve (const Matrix &matrix, BlockVector< std::complex< double >> &rhs_and_solution, const bool transpose=false) Public Member Functions inherited from Subscriptor Subscriptor () Subscriptor (const Subscriptor &) Subscriptor (Subscriptor &&) noexcept virtual ~Subscriptor () Subscriptoroperator= (const Subscriptor &) Subscriptoroperator= (Subscriptor &&) noexcept void subscribe (std::atomic< bool > const validity, const std::string &identifier="") const void unsubscribe (std::atomic< bool > const validity, const std::string &identifier="") const unsigned int n_subscriptions () const template<typename StreamType > void list_subscribers (StreamType &stream) const void list_subscribers () const template<class Archive > void serialize (Archive &ar, const unsigned int version) ## Static Public Member Functions static ::ExceptionBaseExcUMFPACKError (std::string arg1, int arg2) Static Public Member Functions inherited from Subscriptor static ::ExceptionBaseExcInUse (int arg1, std::string arg2, std::string arg3) static ::ExceptionBaseExcNoSubscriber (std::string arg1, std::string arg2) ## Private Member Functions void clear () template<typename number > void sort_arrays (const SparseMatrixEZ< number > &) ## Private Attributes size_type n_rows size_type n_cols void * symbolic_decomposition std::vector< types::suitesparse_indexAp std::vector< double > control ## Detailed Description This class provides an interface to the sparse direct solver UMFPACK, which is part of the SuiteSparse library (see this link). UMFPACK is a set of routines for solving non-symmetric sparse linear systems, Ax=b, using the Unsymmetric-pattern MultiFrontal method and direct sparse LU factorization. Matrices may have symmetric or unsymmetric sparsity patterns, and may have unsymmetric entries. The use of this class is explained in the step-22 and step-29 tutorial programs. This matrix class implements the usual interface of preconditioners, that is a function initialize(const SparseMatrix<double>&matrix,const AdditionalData) for initializing and the whole set of vmult() functions common to all matrices. Implemented here are only vmult() and vmult_add(), which perform multiplication with the inverse matrix. Furthermore, this class provides an older interface, consisting of the functions factorize() and solve(). Both interfaces are interchangeable. Note This class exists if the UMFPACK interface was not explicitly disabled during configuration. UMFPACK has its own license, independent of that of deal.II. If you want to use the UMFPACK you have to accept that license. It is linked to from the deal.II ReadMe file. UMFPACK is included courtesy of its author, Timothy A. Davis. #### Instantiations There are instantiations of this class for SparseMatrix<double>, SparseMatrix<float>, SparseMatrixEZ<float>, SparseMatrixEZ<double>, BlockSparseMatrix<double>, and BlockSparseMatrix<float>. Definition at line 90 of file sparse_direct.h. ## ◆ size_type Declare type for container size. Definition at line 96 of file sparse_direct.h. ## ◆ SparseDirectUMFPACK() SparseDirectUMFPACK::SparseDirectUMFPACK ( ) Constructor. See the documentation of this class for the meaning of the parameters to this function. Definition at line 55 of file sparse_direct.cc. ## ◆ ~SparseDirectUMFPACK() SparseDirectUMFPACK::~SparseDirectUMFPACK ( ) override Destructor. Definition at line 42 of file sparse_direct.cc. ## ◆ initialize() [1/2] void SparseDirectUMFPACK::initialize ( const SparsityPattern & sparsity_pattern ) This function does nothing. It is only here to provide a interface consistent with other sparse direct solvers. Definition at line 49 of file sparse_direct.cc. ## ◆ factorize() template<class Matrix > void SparseDirectUMFPACK::factorize ( const Matrix & matrix ) Factorize the matrix. This function may be called multiple times for different matrices, after the object of this class has been initialized for a certain sparsity pattern. You may therefore save some computing time if you want to invert several matrices with the same sparsity pattern. However, note that the bulk of the computing time is actually spent in the factorization, so this functionality may not always be of large benefit. In contrast to the other direct solver classes, the initialization method does nothing. Therefore initialize is not automatically called by this method, when the initialization step has not been performed yet. This function copies the contents of the matrix into its own storage; the matrix can therefore be deleted after this operation, even if subsequent solves are required. Definition at line 214 of file sparse_direct.cc. ## ◆ initialize() [2/2] template<class Matrix > void SparseDirectUMFPACK::initialize ( const Matrix & matrix, const AdditionalData additional_data = AdditionalData() ) Initialize memory and call SparseDirectUMFPACK::factorize. Definition at line 755 of file sparse_direct.cc. ## ◆ vmult() [1/2] void SparseDirectUMFPACK::vmult ( Vector< double > & dst, const Vector< double > & src ) const Preconditioner interface function. Usually, given the source vector, this method returns an approximate solution of Ax = b. As this class provides a wrapper to a direct solver, here it is actually the exact solution (exact within the range of numerical accuracy of course). In other words, this function actually multiplies with the exact inverse of the matrix, $$A^{-1}$$. Definition at line 762 of file sparse_direct.cc. ## ◆ vmult() [2/2] void SparseDirectUMFPACK::vmult ( BlockVector< double > & dst, const BlockVector< double > & src ) const Same as before, but for block vectors. Definition at line 771 of file sparse_direct.cc. ## ◆ Tvmult() [1/2] void SparseDirectUMFPACK::Tvmult ( Vector< double > & dst, const Vector< double > & src ) const Same as before, but uses the transpose of the matrix, i.e. this function multiplies with $$A^{-T}$$. Definition at line 780 of file sparse_direct.cc. ## ◆ Tvmult() [2/2] void SparseDirectUMFPACK::Tvmult ( BlockVector< double > & dst, const BlockVector< double > & src ) const Same as before, but for block vectors Definition at line 790 of file sparse_direct.cc. ## ◆ m() SparseDirectUMFPACK::size_type SparseDirectUMFPACK::m ( ) const Return the dimension of the codomain (or range) space. Note that the matrix is of dimension $$m \times n$$. Definition at line 798 of file sparse_direct.cc. ## ◆ n() SparseDirectUMFPACK::size_type SparseDirectUMFPACK::n ( ) const Return the dimension of the domain space. Note that the matrix is of dimension $$m \times n$$. Definition at line 805 of file sparse_direct.cc. ## ◆ solve() [1/8] void SparseDirectUMFPACK::solve ( Vector< double > & rhs_and_solution, const bool transpose = false ) const Solve for a certain right hand side vector. This function may be called multiple times for different right hand side vectors after the matrix has been factorized. This yields substantial savings in computing time, since the actual solution is fast, compared to the factorization of the matrix. The solution will be returned in place of the right hand side vector. Parameters [in,out] rhs_and_solution A vector that contains the right hand side $$b$$ of a linear system $$Ax=b$$ upon calling this function, and that contains the solution $$x$$ of the linear system after calling this function. [in] transpose If set to true, this function solves the linear $$A^T x = b$$ instead of $$Ax=b$$. Precondition You need to call factorize() before this function can be called. Definition at line 344 of file sparse_direct.cc. ## ◆ solve() [2/8] void SparseDirectUMFPACK::solve ( Vector< std::complex< double >> & rhs_and_solution, const bool transpose = false ) const Like the previous function, but for a complex-valued right hand side and solution vector. If the matrix that was previously factorized had complex-valued entries, then the rhs_and_solution vector will, upon return from this function, simply contain the solution of the linear system $$Ax=b$$. If the matrix was real-valued, then this is also true, but the solution will simply be computed by applying the factorized $$A^{-1}$$ to both the real and imaginary parts of the right hand side vector. Definition at line 384 of file sparse_direct.cc. ## ◆ solve() [3/8] void SparseDirectUMFPACK::solve ( BlockVector< double > & rhs_and_solution, const bool transpose = false ) const Same as before, but for block vectors. Definition at line 499 of file sparse_direct.cc. ## ◆ solve() [4/8] void SparseDirectUMFPACK::solve ( BlockVector< std::complex< double >> & rhs_and_solution, const bool transpose = false ) const Same as before, but for complex-valued block vectors. Definition at line 514 of file sparse_direct.cc. ## ◆ solve() [5/8] template<class Matrix > void SparseDirectUMFPACK::solve ( const Matrix & matrix, Vector< double > & rhs_and_solution, const bool transpose = false ) Call the two functions factorize() and solve() in that order, i.e. perform the whole solution process for the given right hand side vector. The solution will be returned in place of the right hand side vector. Definition at line 540 of file sparse_direct.cc. ## ◆ solve() [6/8] template<class Matrix > void SparseDirectUMFPACK::solve ( const Matrix & matrix, Vector< std::complex< double >> & rhs_and_solution, const bool transpose = false ) Same as before, but for complex-valued solution vectors. Definition at line 552 of file sparse_direct.cc. ## ◆ solve() [7/8] template<class Matrix > void SparseDirectUMFPACK::solve ( const Matrix & matrix, BlockVector< double > & rhs_and_solution, const bool transpose = false ) Same as before, but for block vectors. Definition at line 576 of file sparse_direct.cc. ## ◆ solve() [8/8] template<class Matrix > void SparseDirectUMFPACK::solve ( const Matrix & matrix, BlockVector< std::complex< double >> & rhs_and_solution, const bool transpose = false ) Same as before, but for complex-valued block vectors. Definition at line 588 of file sparse_direct.cc. ## ◆ clear() void SparseDirectUMFPACK::clear ( ) private Free all memory that hasn't been freed yet. Definition at line 68 of file sparse_direct.cc. ## ◆ sort_arrays() template<typename number > void SparseDirectUMFPACK::sort_arrays ( const SparseMatrixEZ< number > & matrix ) private Make sure that the arrays Ai and Ap are sorted in each row. UMFPACK wants it this way. We need to have three versions of this function, one for the usual SparseMatrix, one for the SparseMatrixEZ, and one for the BlockSparseMatrix classes Definition at line 150 of file sparse_direct.cc. ## ◆ n_rows size_type SparseDirectUMFPACK::n_rows private The dimension of the range space, i.e., the number of rows of the matrix. Definition at line 367 of file sparse_direct.h. ## ◆ n_cols size_type SparseDirectUMFPACK::n_cols private The dimension of the domain space, i.e., the number of columns of the matrix. Definition at line 373 of file sparse_direct.h. ## ◆ symbolic_decomposition void* SparseDirectUMFPACK::symbolic_decomposition private The UMFPACK routines allocate objects in which they store information about symbolic and numeric values of the decomposition. The actual data type of these objects is opaque, and only passed around as void pointers. Definition at line 380 of file sparse_direct.h. ## ◆ Ap std::vector SparseDirectUMFPACK::Ap private The arrays in which we store the data for the solver. These are documented in the descriptions of the umfpack__symbolic() and umfpack__numeric() functions, but in short: • Ap is the array saying which row starts where in Ai • Ai is the array that stores the column indices of nonzero entries • Ax is the array that stores the values of nonzero entries; if the matrix is complex-valued, then it stores the real parts • Az is the array that stores the imaginary parts of nonzero entries, and is used only if the matrix is complex-valued. Definition at line 418 of file sparse_direct.h. ## ◆ control std::vector SparseDirectUMFPACK::control private Control and work arrays for the solver routines. Definition at line 426 of file sparse_direct.h. The documentation for this class was generated from the following files:	2020-03-28 16:52:32	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3061874210834503, "perplexity": 7393.30178801688}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370492125.18/warc/CC-MAIN-20200328164156-20200328194156-00009.warc.gz"}
http://www.ck12.org/book/CK-12-Middle-School-Math-Concepts-Grade-7/r4/section/9.4/	<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" /> # 9.4: Equations with Square Roots Difficulty Level: At Grade Created by: CK-12 Estimated3 minsto complete % Progress Practice Equations with Square Roots MEMORY METER This indicates how strong in your memory this concept is Progress Estimated3 minsto complete % Estimated3 minsto complete % MEMORY METER This indicates how strong in your memory this concept is Have you ever thought about the square footage of the infield in baseball? The infield is the area of the baseball field that has the base lines as boundaries. It is the area contained within the base lines. The area outside of the base lines is called the outfield. We know that the distance from one base to another is \begin{align}90 \ ft\end{align}. The shape of the infield is a square. It makes sense to say that the distance from first base to second base times the distance from second base to third base will provide us with the measurement for the area of the infield. We can write the following equation. \begin{align}y = x^2\end{align} What is \begin{align}x\end{align}? What is \begin{align}y\end{align}? Solving this equation requires that you understand how to solve equations by using square roots. Pay attention and we will return to this equation at the end of the Concept. ### Guidance If we know that the square of a number is equal to a product, then we can write this equation. \begin{align}y = x^2\end{align} This is an equation that expresses that if we multiply the value of \begin{align}x\end{align} by itself, we will end up with the value of \begin{align}y\end{align}. We can say that \begin{align}x\end{align} is the square root of \begin{align}y\end{align}. We can use this information to solve equations involving square roots. \begin{align}x^2=81\end{align} To solve this equation, we want to figure out the value of \begin{align}x\end{align}. To do this, we can take the square root of both sides of the equation. Why would we do this? Think about it. The \begin{align}x\end{align} is being squared. We want to get the variable alone. To do this, we need to perform the inverse operation. The opposite of squaring a number is finding the square root of the number. Therefore, if we take the square root of both sides of the equation, then we will get \begin{align}x\end{align} alone. \begin{align}\sqrt{x^2} = \sqrt{81}\end{align} Next, we can cancel the square and the square root. They are inverses of each other and they cancel each other out. \begin{align}\bcancel{\sqrt{x^2}} = x\end{align} Now we find the square root of 81. 81 is a perfect square, so the square root of 81 is 9. \begin{align}x=9\end{align} Sometimes, you will have a problem that is a little more complicated. Take a look. \begin{align}x^2+3=12\end{align} We want to find the value of \begin{align}x\end{align}. First, notice that we have a two step equation. One of the operations is multiplication with the square and the other is addition. Let’s start by subtracting three from both sides. \begin{align}x^2+3-3&=12-3\\ x^2&=9\end{align} Now we want to get \begin{align}x\end{align} alone. To do this, we take the square root of both sides of the equation. \begin{align}\bcancel{\sqrt{x^2}} &= \sqrt{9}\\ x&=3\end{align} Sometimes, the equation with have a square root in it and we have to work with that. \begin{align}\sqrt{x-1} = 8\end{align} Wow! Here we have a variable and a number in a radical. Let’s get rid of the radical first. To get cancel out the square root of a number, we use the inverse operation. We square both sides of the equation. \begin{align}\left ( \sqrt{x-1} \right )^2 = 8^2\end{align} The square and the square root cancel each other out. \begin{align}(\bcancel{\sqrt{x-1})^2} &= 8^2\\ x-1 &= 64\end{align} Now we can solve for \begin{align}x\end{align} quite easily. Begin by adding 1 to both sides of the equation. \begin{align}x-1+1&=64+1\\ x&=65\end{align} Now it's time for you to try a few on your own. #### Example A \begin{align}x^2=49\end{align} Solution:\begin{align}x = 7\end{align} #### Example B \begin{align}x^2=64\end{align} Solution:\begin{align}x = 8\end{align} #### Example C \begin{align}x^2 + 2=38\end{align} Solution:\begin{align}x = 6\end{align} Here is the original problem once again. The infield is the area of the baseball field that has the base lines as boundaries. It is the area contained within the base lines. The area outside of the base lines is called the outfield. We know that the distance from one base to another is \begin{align}90 \ ft\end{align}. The shape of the infield is a square. It makes sense to say that the distance from first base to second base times the distance from second base to third base will provide us with the measurement for the area of the infield. We can write the following equation. \begin{align}y = x^2\end{align} What is \begin{align}x\end{align}? What is \begin{align}y\end{align}? Let's begin by looking at the given information. In the original problem, it is presented that the distance from first base to second base times the distance from second base to third base would give the area of the infield. The distance from first to second base is the same as the distance from second to third. This is our \begin{align}x\end{align} measurement. \begin{align}x = 90 \ ft\end{align} Now we can substitute this value for \begin{align}x\end{align}. \begin{align}y = 90^2\end{align} \begin{align}y = 8100 \ sq. ft.\end{align} ### Vocabulary Here are the vocabulary words that are found in this Concept. Square root a number that when multiplied by itself equals the square of the number. Perfect Square square roots that are whole numbers. the symbol that lets us know that we are looking for a square root. an expression with numbers, operations and radicals in it. ### Guided Practice Here is one for you to try on your own. Evaluate. \begin{align}x^2+5=174\end{align} To start, let's subtract five from both sides. \begin{align}x^2+5-5=174-5\end{align} \begin{align}x^2 = 169\end{align} Now we take the square root of both sides. \begin{align}\sqrt{x^2} = \sqrt{169}\end{align} \begin{align}x = 13\end{align} ### Video Review Here is a video for review. ### Practice Directions: Solve each equation. 1. \begin{align}x^2=9\end{align} 2. \begin{align}x^2=49\end{align} 3. \begin{align}x^2=100\end{align} 4. \begin{align}x^2=64\end{align} 5. \begin{align}x^2=90\end{align} 6. \begin{align}x^2=256\end{align} 7. \begin{align}x^2+3=12\end{align} 8. \begin{align}x^2-5=20\end{align} 9. \begin{align}x^2+3=39\end{align} 10. \begin{align}x^2-4=60\end{align} 11. \begin{align}x^2+11=92\end{align} 12. \begin{align}\sqrt{x+1} = 10\end{align} 13. \begin{align}x^2+5=41\end{align} 14. \begin{align}x^3=8\end{align} 15. \begin{align}x^3+4=31\end{align} ### Notes/Highlights Having trouble? Report an issue. Color Highlighted Text Notes Show Hide Details Description Difficulty Level: Authors: Tags: Subjects:	2017-03-25 21:01:26	{"extraction_info": {"found_math": true, "script_math_tex": 61, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8648138642311096, "perplexity": 859.221458320505}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218189032.76/warc/CC-MAIN-20170322212949-00491-ip-10-233-31-227.ec2.internal.warc.gz"}
https://www.gradesaver.com/textbooks/math/precalculus/precalculus-mathematics-for-calculus-7th-edition/chapter-1-section-1-5-equations-1-5-exercises-page-56/29	## Precalculus: Mathematics for Calculus, 7th Edition Published by Brooks Cole # Chapter 1 - Section 1.5 - Equations - 1.5 Exercises - Page 56: 29 #### Answer $t=-2$ #### Work Step by Step $(t-4)^{2}=(t+4)^2+32$ Let's remember the following properties: $(a+b)^{2}=a^{2}+2ab+b^{2}$ $(a-b)^{2}=a^{2}-2ab+b^{2}$ Evaluate the powers present in the equations using said properties: $t^{2}-2(t)(4)+4^{2}=t^{2}+2(t)(4)+4^{2}+32$ We can get rid of the terms present in both sides of the equation. This means $t^{2}$ and $4^{2}$ will disappear from the equation. We get: $-2(t)(4)=2(t)(4)+32$ Simplify and solve for $t$: $-8t=8t+32$ $-8t-8t=32$ $-16t=32$ $t=\dfrac{32}{-16}=-2$ After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.	2018-09-21 14:36:50	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9184447526931763, "perplexity": 633.8810654158177}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267157203.39/warc/CC-MAIN-20180921131727-20180921152127-00102.warc.gz"}
https://nrich.maths.org/public/topic.php?code=72&cl=3&cldcmpid=475	# Resources tagged with: Generalising Filter by: Content type: Age range: Challenge level: ### Loopy ##### Age 14 to 16 Challenge Level: Investigate sequences given by $a_n = \frac{1+a_{n-1}}{a_{n-2}}$ for different choices of the first two terms. Make a conjecture about the behaviour of these sequences. Can you prove your conjecture? ### Converging Means ##### Age 14 to 16 Challenge Level: Take any two positive numbers. Calculate the arithmetic and geometric means. Repeat the calculations to generate a sequence of arithmetic means and geometric means. Make a note of what happens to the. . . . ### Gnomon Dimensions ##### Age 14 to 16 Challenge Level: These gnomons appear to have more than a passing connection with the Fibonacci sequence. This problem ask you to investigate some of these connections. ### Harmonic Triangle ##### Age 14 to 16 Challenge Level: Can you see how to build a harmonic triangle? 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Find a relationship between p, i and the area of the polygons. ### Winning Lines ##### Age 7 to 16 An article for teachers and pupils that encourages you to look at the mathematical properties of similar games. ### AMGM ##### Age 14 to 16 Challenge Level: Can you use the diagram to prove the AM-GM inequality? ### Go Forth and Generalise ##### Age 11 to 14 Spotting patterns can be an important first step - explaining why it is appropriate to generalise is the next step, and often the most interesting and important. ### Painted Cube ##### Age 14 to 16 Challenge Level: Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces? ### Shear Magic ##### Age 11 to 14 Challenge Level: What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles? ### Games Related to Nim ##### Age 5 to 16 This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning. ### Polycircles ##### Age 14 to 16 Challenge Level: Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon? ### For Richer for Poorer ##### Age 14 to 16 Challenge Level: Charlie has moved between countries and the average income of both has increased. How can this be so? ### Triangle Numbers ##### Age 11 to 14 Challenge Level: Take a look at the multiplication square. The first eleven triangle numbers have been identified. Can you see a pattern? Does the pattern continue? ### Handshakes ##### Age 11 to 14 Challenge Level: Can you find an efficient method to work out how many handshakes there would be if hundreds of people met? ### Problem Solving, Using and Applying and Functional Mathematics ##### Age 5 to 18 Challenge Level: Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information. ### Square Pizza ##### Age 14 to 16 Challenge Level: Can you show that you can share a square pizza equally between two people by cutting it four times using vertical, horizontal and diagonal cuts through any point inside the square? ### Steel Cables ##### Age 14 to 16 Challenge Level: Some students have been working out the number of strands needed for different sizes of cable. 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Can you describe your reasoning?	2020-01-23 22:39:47	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5160209536552429, "perplexity": 1289.7312620526368}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250614086.44/warc/CC-MAIN-20200123221108-20200124010108-00077.warc.gz"}
https://pykeen.readthedocs.io/en/latest/byo/interaction.html	This is a tutorial about how to implement your own interaction modules (also known as scoring functions) as subclasses of pykeen.nn.modules.Interaction for use in PyKEEN. ## Implementing your first Interaction Module¶ Imagine you’ve taken a time machine back to 2013 and you have just invented TransE, defined as: $f(h, r, t) = -\\| \mathbf{e}_h + \mathbf{r}_r - \mathbf{e}_t \\|_2$ where $$\mathbf{e}_i$$ is the $$d$$-dimensional representation for entity $$i$$, $$\mathbf{r}_j$$ is the $$d$$-dimensional representation for relation $$j$$, and $$\\|...\\|_2$$ is the $$L_2$$ norm. To implement TransE in PyKEEN, you need to subclass the pykeen.nn.modules.Interaction. This class it itself a subclass of torch.nn.Module, which means that you need to provide an implementation of torch.nn.Module.forward(). However, the arguments are predefined as h, r, and t, which correspond to the representations of the head, relation, and tail, respectively. from pykeen.nn.modules import Interaction class TransEInteraction(Interaction): def forward(self, h, r, t): return -(h + r - t).norm(p=2, dim=-1) Note the dim=-1 because this operation is actually defined over an entire batch of head, relation, and tail representations. A reference implementation is provided in pykeen.nn.modules.TransEInteraction As a researcher who just invented TransE, you might wonder what would happen if you replaced the addition + with multiplication . You might then end up with a new interaction like this (which just happens to be DistMult, which was published just a year after TransE): $f(h, r, t) = \mathbf{e}_h^T diag(\mathbf{r}_r) \mathbf{e}_t$ where $$\mathbf{e}_i$$ is the $$d$$-dimensional representation for entity $$i$$, $$\mathbf{r}_j$$ is the $$d$$-dimensional representation for relation $$j$$. from pykeen.nn.modules import Interaction class DistMultInteraction(Interaction): def forward(self, h, r, t): return (h r * t).sum(dim=-1) A reference implementation is provided in pykeen.nn.modules.DistMultInteraction ## Interactions with Hyper-Parameters¶ While we previously defined TransE with the $$L_2$$ norm, it could be calculated with a different value for $$p$$: $f(h, r, t) = -\\| \mathbf{e}_h + \mathbf{r}_r - \mathbf{e}_t \\|_p$ This could be incorporated into the interaction definition by using the __init__(), storing the value for $$p$$ in the instance, then accessing it in forward(). from pykeen.nn.modules import Interaction class TransEInteraction(Interaction): def __init__(self, p: int): super().__init__() self.p = p def forward(self, h, r, t): return -(h + r - t).norm(p=self.p, dim=-1) In general, you can put whatever you want in __init__() to support the calculation of scores. ## Interactions with Trainable Parameters¶ In ER-MLP, the multi-layer perceptron consists of an input layer with $$3 \times d$$ neurons, a hidden layer with $$d$$ neurons and output layer with one neuron. The input is represented by the concatenation embeddings of the heads, relations and tail embeddings. It is defined as: $f(h, r, t) = W_2 ReLU(W_1 cat(h, r, t) + b_1) + b_2$ with hidden dimension $$y$$, $$W_1 \in \mathcal{R}^{3d \times y}$$, $$W_2\ \in \mathcal{R}^y$$, and biases $$b_1 \in \mathcal{R}^y$$ and $$b_2 \in \mathcal{R}$$. $$W_1$$, $$W_1$$, $$b_1$$, and $$b_2$$ are global parameters, meaning that they are trainable, but are neither attached to the entities nor relations. Unlike the $$p$$ in TransE, these global trainable parameters are not considered hyper-parameters. However, like hyper-parameters, they can also be defined in the __init__ function of your pykeen.nn.modules.Interaction class. They are trained jointly with the entity and relation embeddings during training. import torch.nn from pykeen.nn.modules import Interaction class ERMLPInteraction(Interaction): def __init__(self, embedding_dim: int, hidden_dim: int): super().__init__() # The weights of this MLP will be learned. self.mlp = torch.nn.Sequential( torch.nn.Linear(in_features=3 * embedding_dim, out_features=hidden_dim, bias=True), torch.nn.ReLU(), torch.nn.Linear(in_features=hidden_dim, out_features=1, bias=True), ) def forward(self, h, r, t): x = broadcast_cat([h, r, t], dim=-1) return self.mlp(x) Note that pykeen.utils.broadcast_cat() was used instead of the standard torch.cat() because of the standardization of shapes of head, relation, and tail vectors. A reference implementation is provided in pykeen.nn.modules.ERMLPInteraction ## Interactions with Different Shaped Vectors¶ The Structured Embedding uses a 2-tensor for representing each relation, with an interaction defined as: $f(h, r, t) = - \\|\textbf{M}_{r}^{head} \textbf{e}_h - \textbf{M}_{r}^{tail} \textbf{e}_t\\|_p$ where $$\mathbf{e}_i$$ is the $$d$$-dimensional representation for entity $$i$$, $$\mathbf{M}^{head}_j$$ is the $$d \times d$$-dimensional representation for relation $$j$$ for head entities, $$\mathbf{M}^{tail}_j$$ is the $$d \times d$$-dimensional representation for relation $$j$$ for tail entities, and $$\\|...\\|_2$$ is the $$L_p$$ norm. For the purposes of this tutorial, we will propose a simplification to Strucuterd Embedding (also similar to TransR) where the same relation 2-tensor is used to project both the head and tail entities as in: $f(h, r, t) = - \\|\textbf{M}_{r} \textbf{e}_h - \textbf{M}_{r} \textbf{e}_t\\|_2$ where $$\mathbf{e}_i$$ is the $$d$$-dimensional representation for entity $$i$$, $$\mathbf{M}_j$$ is the $$d \times d$$-dimensional representation for relation $$j$$, and $$\\|...\\|_2$$ is the $$L_2$$ norm. from pykeen.nn.modules import Interaction class SimplifiedStructuredEmbeddingInteraction(Interaction): relation_shape = ('dd',) def forward(self, h, r, t): h_proj = r @ h.unsqueeze(dim=-1) t_proj = r @ t.unsqueeze(dim=-1) return -(h_proj - t_proj).squeeze(dim=-1).norm(p=2, dim=-1) Note the definition of the relation_shape. By default, the entity_shape and relation_shape are both equal to ('d', ), which uses eigen-notation to show that they both are 1-tensors with the same shape. In this simplified version of Structured Embedding, we need to denote that the shape of the relation is $$d \times d$$, so it’s written as dd. ## Interactions with Multiple Representations¶ Sometimes, like in the canonical version of Structured Embedding, you need more than one representation for entities and/or relations. To specify this, you just need to extend the tuple for relation_shape with more entries, each corresponding to the sequence of representations. from pykeen.nn.modules import Interaction class StructuredEmbeddingInteraction(Interaction): relation_shape = ( 'dd', # Corresponds to $\mathbf{M}^{head}_j$ 'dd', # Corresponds to $\mathbf{M}^{tail}_j$ ) def forward(self, h, r, t): # Since the relation_shape is more than length 1, the r value is given as a sequence # of the representations defined there. You can use tuple unpacking to get them out r_h, r_t = r h_proj = r_h @ h.unsqueeze(dim=-1) t_proj = r_t @ t.unsqueeze(dim=-1) return -(h_proj - t_proj).squeeze(dim=-1).norm(p=2, dim=-1) ## Interactions with Different Dimension Vectors¶ TransD is an example of an interaction module that not only uses two different representations for each entity and two representations for each relation, but they are of different dimensions. It can be implemented by choosing a different letter for use in the entity_shape and/or relation_shape dictionary. Ultimately, the letters used are arbitrary, but you need to remember what they are when using the pykeen.models.make_model(), pykeen.models.make_model_cls(), or pykeen.pipeline.interaction_pipeline() functions to instantiate a model, make a model class, or run the pipeline using your custom interaction module (respectively). from pykeen.nn.modules import Interaction from pykeen.utils import project_entity class TransDInteraction(Interaction): entity_shape = ("d", "d") relation_shape = ("e", "e") def forward(self, h, r, t): h, h_proj = h r, r_proj = r t, t_proj = t h_bot = project_entity( e=h, e_p=h_p, r_p=r_p, ) t_bot = project_entity( e=t, e_p=t_p, r_p=r_p, ) return -(h_bot + r - t_bot).norm(p=2, dim=-1) Note The pykeen.utils.project_entity() function was used in this implementation to reduce the complexity. So far, it’s the case that all of the models using multiple different representation dimensions are quite complicated and don’t fall into the paradigm of presenting simple examples. A reference implementation is provided in pykeen.nn.modules.TransDInteraction ## Differences between pykeen.nn.modules.Interaction and pykeen.models.Model¶ The high-level pipeline() function allows you to pass pre-defined subclasses of pykeen.models.Model such as pykeen.models.TransE or pykeen.models.DistMult. These classes are high-level wrappers around the interaction functions pykeen.nn.modules.TransEInteraction and nn.modules.DistMultInteraction that are more suited for running benchmarking experiments or practical applications of knowledge graph embeddings that include lots of information about default hyper-parameters, recommended hyper-parameter optimization strategies, and more complex applications of regularization schemas. As a researcher, the pykeen.nn.modules.Interaction is a way to quickly translate ideas into new models that can be used without all of the overhead of defining a pykeen.models.Model. These components are also completely reusable throughout PyKEEN (e.g., in self-rolled training loops) and can be used as standalone components outside of PyKEEN. If you are happy with your interaction module and would like to go the next step to making it generally reusable, check the “Extending the Models” tutorial. ## Ad hoc Models from Interactions¶ A pykeen.models.ERModel can be constructed from pykeen.nn.modules.Interaction. The new style-class, pykeen.models.ERModel abstracts the interaction away from the representations such that different interactions can be used interchangably. A new model can be constructed directly from the interaction module, given a dimensions mapping. In each pykeen.nn.modules.Interaction, there is a field called entity_shape and relation_shape that allows for using eigen-notation for defining the different dimensions of the model. Most models share the d dimensionality for both the entity and relation vectors. Some (but not all) exceptions are: With this in mind, you’ll have to investigate the dimensions of the vectors through the PyKEEN documentation. If you’re implementing your own, you have control over this and will know which dimensions to specify (though the d for both entities and relations is standard). As a shorthand for {'d': value}, you can directly pass value for the dimension and it will be automatically interpreted as the {'d': value}. Make a model class from lookup of an interaction module class: >>> from pykeen.nn.modules import TransEInteraction >>> from pykeen.models import make_model_cls >>> embedding_dim = 3 >>> model_cls = make_model_cls( ... dimensions={"d": embedding_dim}, ... interaction='TransE', ... interaction_kwargs={'p': 2}, ... ) If there’s only one dimension in the entity_shapes and relation_shapes, it can be directly given as an integer as a shortcut. >>> # Implicitly can also be written as: >>> model_cls_alt = make_model_cls( ... dimensions=embedding_dim, ... interaciton='TransE', ... interaction_kwargs={'p': 2}, ... ) Make a model class from an interaction module class: >>> from pykeen.nn.modules import TransEInteraction >>> from pykeen.models import make_model_cls >>> embedding_dim = 3 >>> model_cls = make_model_cls({"d": embedding_dim}, TransEInteraction, {'p': 2}) Make a model class from an instantiated interaction module: >>> from pykeen.nn.modules import TransEInteraction >>> from pykeen.models import make_model_cls >>> embedding_dim = 3 >>> model_cls = make_model_cls({"d": embedding_dim}, TransEInteraction(p=2)) All of these model classes can be passed directly into the model argument of pykeen.pipeline.pipeline(). ## Interaction Pipeline¶ The pykeen.pipeline.pipeline() also allows passing of an interaction such that the following code block can be compressed: from pykeen.pipeline import pipeline from pykeen.nn.modules import TransEInteraction model = make_model_cls( interaction=TransEInteraction, interaction_kwargs={'p': 2}, dimensions={'d': 100}, ) results = pipeline( dataset='Nations', model=model, ... ) into: from pykeen.pipeline import pipeline from pykeen.nn.modules import TransEInteraction results = pipeline( dataset='Nations', interaction=TransEInteraction, interaction_kwargs={'p': 2}, dimensions={'d': 100}, ... ) This can be used with any subclass of the pykeen.nn.modules.Interaction, not only ones that are implemented in the PyKEEN package.	2021-08-04 22:43:01	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6274387240409851, "perplexity": 3239.0920437875307}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046155188.79/warc/CC-MAIN-20210804205700-20210804235700-00239.warc.gz"}
https://de.zxc.wiki/wiki/Spontane_Emission	# Spontaneous emission The spontaneous emission , also called quantum emission in older literature , is a quantum mechanical phenomenon. It describes the emission of photons when transitioning between states of atoms or molecules with different energies . In contrast to the stimulated emission , the spontaneous emission takes place without external influence, so it belongs to the decay processes and the random processes . ## description The exact point in time at which an energetically excited system emits a photon cannot be predicted. Instead, quantum physics only allows the specification of a probability that an emission will take place within a certain period of time. It can be characterized, for example, via the half-life after which just half of the particles in an ensemble of excited atoms or molecules have each emitted a photon, or over the life of the excited state. In the context of quantum mechanics, which among other things describes the structure of atoms and molecules, the absorption of a photon and its stimulated emission can be well understood; Both are triggered by the radiation of an electromagnetic wave and only differ in their mathematical description by one sign . The spontaneous emission, on the other hand, is initially not to be understood; Contrary to intuition , according to the rules of quantum mechanics, in the absence of external disturbances, a state of higher energy is also stable. The mechanism of spontaneous emission was therefore only understood in the context of quantum electrodynamics , which can also describe the generation and annihilation of photons. After that, the vacuum is filled with certain vacuum fluctuations of the electromagnetic field . These vibrations correspond to its basic energetic state and therefore cannot be destroyed by absorption in principle. The phenomenon of spontaneous emission can now be qualitatively and quantitatively traced back to a stimulated emission that is triggered by these vacuum fluctuations. ## Mathematical description The number of spontaneous emissions or the excited particles per volume and time is proportional to the particle number density in the excited state : ${\ displaystyle N}$${\ displaystyle V}$${\ displaystyle t}$ ${\ displaystyle n}$ ${\ displaystyle {\ frac {\ partial N} {\ partial t}} \ propto n \ cdot V}$ However, if there is a sufficient amount of particles, emitted photons will be absorbed by non-excited particles; H. Emission and absorption are in balance. This means that the intensity (including the stimulated emission) is not exceeded according to the Planck formula and the total intensity is therefore independent of the number of particles. ## Individual evidence 1. Albert Einstein: On the quantum theory of radiation . In: Physical Society Zurich. Notifications . tape 16 , 1916, pp. 47-62 . 2. Albert Einstein: On the quantum theory of radiation . In: Physikalische Zeitschrift . tape 18 , 1917, pp. 121-128 . 3. D. Meschede: Gerthsen Physik . 23rd edition. S. 577 .	2022-08-11 08:18:20	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 5, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8456180691719055, "perplexity": 503.17985863025666}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571246.56/warc/CC-MAIN-20220811073058-20220811103058-00672.warc.gz"}
http://clay6.com/qa/19694/the-bond-energy-in-kcal-mol-of-c-c-single-bond-is-approximately	Browse Questions # The bond energy (in kcal/mol) of C-C single bond is approximately $\begin{array}{1 1}(a)\;1\\(b)\;10\\(c)\;100\\(d)\;1000\end{array}$ Can you answer this question? The C-C single bond dissociation energy is 100 kcal/mol Hence (c) is the correct answer. answered Dec 6, 2013	2017-03-23 04:28:58	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8880993723869324, "perplexity": 11440.94688946648}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218186774.43/warc/CC-MAIN-20170322212946-00349-ip-10-233-31-227.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/local-conformal-transformation-coordinate-or-metrical-transformation.767483/	# Local conformal transformation:Coordinate or metrical transformation? 1. Aug 25, 2014 ### Johanna222 Hello, I was wondering what the exact definition of conformal transformations is. This is a question in the context of Shape Dynamics. In Shape dynamics, time is viewed as a global parameter of the universe, and as such is invariant under spatial coordinate transformation. Part of the diffeomorphism invariance of General Relativity (the diffeomorphisms that mix space and time), is thus not present in the theory, but instead traded for invariance under local spatial conformal transformations (LSCT's). Interpreting these LCTS's as coordinate transformation ($\vec{x} \mapsto C(x^{\mu})\vec{x}$) leads to a problem: They should already be part of the diffeomorphism symmetry (of space), giving empty trading. Are these LCTS's to be interpreted as transformations of the metric, leaving coordinates invariant? I assume $C(x^{\mu})$ to be positive and differentiable. 2. Aug 28, 2014 ### Greg Bernhardt I'm sorry you are not finding help at the moment. Is there any additional information you can share with us? 3. Aug 29, 2014 ### haushofer I'm confused by the word " local" ; usually the generators are defined by the conformal Killing eqn. Making the generators local again would just give gct's, but I guess you already know that. I do know that one can obtain GR by gauging the conformal algebra. The " extra" generators (wrt Poincare), generating special conformal transfos and dilatations, give gauge fields which can be solved and gauged away (Stuckelberg) respectively. The action of a conformal scalar then gives the Hilbert action after gaugefixing this scalar field. In the superconformal case this is used to construct matter couplings in supergravity. Do you have a reference? I'm not so familar with shape dynamics, but am curious :)	2018-01-20 17:07:20	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9133521318435669, "perplexity": 1408.9243100002848}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084889677.76/warc/CC-MAIN-20180120162254-20180120182254-00122.warc.gz"}
https://tldr.dendron.so/notes/common.grip.html	# grip • Start the server and serve the rendered README file of a current directory: grip • Start the server and serve a specific Markdown file: grip {{path/to/file.md}} • Start the server and open the README file of the current directory in the browser: grip --browser • Start the server in the specified port and serve the rendered README file of the current directory: grip {{port}}	2022-12-08 15:41:06	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.32254675030708313, "perplexity": 5588.690465779922}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711344.13/warc/CC-MAIN-20221208150643-20221208180643-00697.warc.gz"}
http://rationalwiki.org/wiki/Conservapedia_talk:What_is_going_on_at_CP%3F/Archive153	# Conservapedia talk:What is going on at CP?/Archive153 This is an archive page, last updated 31 March 2012. Please do not make edits to this page. ## Chicago Michelle lied wigo Are those two identical? They look it on the surface. Should we comment out the later one and leave the +73 one? ħuman 02:20, 6 October 2009 (UTC) They actually are different. One is about their trumpetalism on the main page; the other is their argument the day before where through their skills of debate they showed it to be The TruthTM. - π 02:35, 6 October 2009 (UTC) Maybe my English isn't that great, but I read the quote from her as saying she saw all of those athletes as she sat on her father's lap. "Some of my best memories are sitting on my dad’s lap, cheering on Olga and Nadia, Carl Lewis, and others for their brilliance and perfection", Oxford comma or not, looks like she saw all of them whilst in the lap. I'm not insane, though, so I suspect she was misremembering rather than conspiring with her husband to be a socialcommunazifemiblacksupremacist. Coarb 03:28, 6 October 2009 (UTC) It was a pretty poorly constructed sentence, and her delivery, which could have saved it with a little pause, didn't. But to call it deliberate obfuscation is just hilarious. The best bit though was Jinx running his mouth about Barack just out of the blue. I'll bet you could walk into his bedroom at night, whisper "Obama" into his ear, and he'd jerk upright babbling "NAMBLA Communist Tax Destroy America Mommy". DogPMarmite Patrol 15:48, 6 October 2009 (UTC) I should find a clip and listen to it sometime. It reads to me like she started with the homey Dad's lap thing, and of course was remembering Olga and Nadia. Then perhaps she realized mid-sentence that those were two Russian gymnasts, and tacked on an American runner (?) she remembered for balance, losing the "Dad's lap" part along the way. Anywys, too bad she lost the Olympics for Chicago! ħuman 19:05, 6 October 2009 (UTC) ## Jinx's rights WTF is "Fireproof Your Marriage Bible Study"? ГенгисYou have the right to be offended; and I have the right to offend you. 06:36, 6 October 2009 (UTC) It's a whole world of crazy StarFish 07:32, 6 October 2009 (UTC) I was imagining asbestos bed sheets! ## CP borked again? OpenDNS is reporting: Nameserver trace for www.conservapedia.com: Looking for who is responsible for root zone and followed l.root-servers.net. Looking for who is responsible for com and followed f.gtld-servers.net. Looking for who is responsible for conservapedia.com and followed ns2.m264.sgded.com. Nameservers for www.conservapedia.com: ns1.m264.sgded.com returned (SERVFAIL) ns2.m264.sgded.com returned (SERVFAIL) Or is it just me? Steve 07:15, 6 October 2009 (UTC) Working ok for me right now, but I was having DNS-ish problems last night. These kinds of issues can affect different people differently depnding on your ISP etc. It should work through in 24 hours at the most. StarFish 07:31, 6 October 2009 (UTC) It isn't working for me either. If I may venture a guess: Conservapedia is right now on the ten at digg!Maybe it couldn't cope with the traffic. Also, I can't wait to see what Andy will make of that. The article dugg is the one about the 'conservative bible', it's sure to attract all sorts of fundies, not all of those will be on his sides. Now that's it has hit the fan, times are gonna become interesting!--Ireon 09:34, 6 October 2009 (UTC) I would say that almost definitely it is a blogrush phenomenon. Of course Andy will claim it as people rejecting liberal bias and wanting to learn about conservative Christian values. Everyone else, of course, will know that every visit is purely to mock and laugh at his pathetic efforts. I usually record the page views stats on a daily basis, so it will be interesting to see what affect the inrush has had. It would be amusing if Andy is forced to cough up more cash for an increased bandwidth. ГенгисYou have the right to be offended; and I have the right to offend you. 10:41, 6 October 2009 (UTC) Maybe their DNS is b0rked. I can't resolve the host at the office (getting SERVFAIL like earlier), and am getting a fail from http://isthisdown.com/conservapedia.com.aspx too. Is there such a word as "digg-dotted"? Steve 11:23, 6 October 2009 (UTC) It's back up now. Maybe Andy had to press the reset button. ГенгисYou have the right to be offended; and I have the right to offend you. 13:37, 6 October 2009 (UTC) Hurray! Now it brings us news that changing the colour of the Bible's ink is just the same as changing the words - [1]. <facepalm> Steve 13:45, 6 October 2009 (UTC) MO - [2] the source of the new headline. "Nasty big meanies criticising our academically-unsound unqualified Bible-censoring club." Steve 13:53, 6 October 2009 (UTC) Hehe, I like "Bible-censoring club". I also like "...most people are liberals..." - Andy S. [3] ħuman 03:11, 7 October 2009 (UTC) timestamp wrong, forgot to sign! (UD) It looks like they're having capacity problems again. I get "Service Temporarily Unavailable". Come on Andy ask your mom for more money to increase your bandwidth. ГенгисYou have the right to be offended; and I have the right to offend you. 20:54, 6 October 2009 (UTC) Looks to me, right now based on their recent changes, like it is being assaulted by shitloads of vandals. Where's TK's banhammer when you need it?Lord Goonie Hooray! I'm helping! 03:15, 7 October 2009 (UTC) I am amazed they have left account registration open to be honest. - π 03:23, 7 October 2009 (UTC) ## Jinx He's jerking Andy off particularly hard today, what with this and his policing of the page. Steady on there Jinx, Andy's only human! EddyP 16:52, 6 October 2009 (UTC) No one is having more fun than Karajou today. I wouldn't be surprised if he's cranked one out over this. — Sincerely, Neveruse513 / Talk / Block 17:03, 6 October 2009 (UTC) ## Ah, sunlight Looks like Andy's getting the attention he feels he deserves again with this Conservabible. I always wondered how he'd top the Lenski Affair. This seems to be going past even the blogosphere. HumanisticJones 21:14, 6 October 2009 (UTC) It's a shame registration is closed. I wish more and more conservatives could find out directly from the crack team at CP that they are in fact not real conservatives. — Sincerely, Neveruse513 / Talk / Block 21:18, 6 October 2009 (UTC) I am fuckign pissed because my IP is blocked and can't view CP from my work PC. AceMcWicked 21:20, 6 October 2009 (UTC) Well at the very basic level without involving soemthing like Tor, you could use an anon proxy like Hidemyass.com. However, if you want to follow RW links you'll also have to read RationalWiki through them. Seempul. ГенгисYou have the right to be offended; and I have the right to offend you. 21:52, 6 October 2009 (UTC) If you knew the nature of my work and my employer you'd understand why they block and take a dim view of anon proxies from work computers. AceMcWicked 23:14, 6 October 2009 (UTC) Are you New Zealand's first intelligence agent Ace? Nice to see you Kiwi's are boosting your security. Any plan soon for an air force? - π 23:29, 6 October 2009 (UTC) If NZ didn't have an intelligence agency who would remind you Aussies that its pants first, then shoes. AceMcWicked 23:32, 6 October 2009 (UTC) Touché. - π 23:34, 6 October 2009 (UTC) If Tor doesn't work you can always use the websites... If the company uses Websense, a google search for unblocked proxy avoidance pages usually works...OpalHonors 23:39, 6 October 2009 (UTC) Na, if they caught me the shit would hit that fan. AceMcWicked 23:44, 6 October 2009 (UTC) I was only suggesting the anon proxy for your home IP which I thought you meant was blocked. ГенгисYou have the right to be offended; and I have the right to offend you. 06:42, 7 October 2009 (UTC) ## Genesis 1 Not WIGO worthy, but I found this edit humorous. Web 23:36, 6 October 2009 (UTC) Yeah, Taj really cracked me up with that delete tag. - π 23:38, 6 October 2009 (UTC) I know right? The situational irony and social implications of that tag were deep. Web 23:40, 6 October 2009 (UTC) I mean if you delete Genesis, do you cause the universe to stop existing? - π 23:43, 6 October 2009 (UTC) Exactly! Taj is such a genius! Web 23:46, 6 October 2009 (UTC) ## I'm fucking famous! Mike Malloy read my email on the air! "Don't forget to mention that the "Project" on Conservapedia was initiated by its founder, none other than Andrew Schlafly - son of Phyllis Schlafly, and co-editor of the Harvard Law Review with Barack Obama [(check their article on BHO for a laugh or three...) skipped over] - of course, Barack was elected President of the HLR, and a few more things later in life. Andrew, however, is now censoring the Bible with a handful of homeschoolers and wing nuts. [Mike chuckled] We watch and track many of the goings-on at CP at RationalWiki.org, among other more worthy pastimes." I screwed up our url, but RW.org goes straight to RW.com. He even said my name and mentioned my humanthoughts.org website. Also, one thing I am seeing with this "Conservative Bible Project" blogrush is that no one is linking to the CP site - they're just quoting each other, and Andy's ten (or whatever) theses. ħuman 01:50, 7 October 2009 (UTC) (EC)Most bloggers never bother checking original sources, they just crib from one another - like real journalists. - π 01:53, 7 October 2009 (UTC) Fuckin' right, man. COngrats on the Malloy mention!Lord Goonie Hooray! I'm helping! 01:52, 7 October 2009 (UTC) I wonder if it'll be on-line somewhere archived. Good for you Human. Sterile gas tank 02:25, 7 October 2009 (UTC) If someone should find it online, post it here! Please!The Goonie Punk Can't sleep, clowns will eat me! 02:26, 7 October 2009 (UTC) It looks like it will eventually be up here! Sterile gas tank 02:45, 7 October 2009 (UTC) You know, if a few of us tried, we might be able to get Andy on FOX News. I say FOX because Andy would not appear on any other station. We just have to make sure Andy ends up on the right show. If he lands on Beck, we have a wasted opportunity. But if he were grilled by Bill, who actually denounces some of the more bat-shit crazy protesters, Andy would look like an idiot cult leader to one of America's biggest audiences. Just a thought. Anyway, kudos Hu. Its kinda funny he gave the site a promo like that despite the article on him.--Thanatos 03:56, 7 October 2009 (UTC) He was on MSNBC or CNN once debating the use of HPV vaccine. He is smiling at the end all happy because he thinks he won because he got the last word. - π 04:25, 7 October 2009 (UTC) I remember seeing it. Andy is an attention whore. I have some theories about it relating to his mother, but that is beside the point. If we can get Andy talking, he will destroy himself. And considering this is a matter of faith, if Bill really goes at him, Andy might snap. Imagine, in front of millions, Andy calling O'Reilly an (insert comment from the ALS quote generator).--Thanatos 04:32, 7 October 2009 (UTC) Apparently Andy's on Colmes' radio show. Not sure if it's aired yet, but it's been recorded. There's a reference to the project on his website, but no audio of the interview yet. Maybe tomorrow? DickTurpis 04:50, 7 October 2009 (UTC) Beck may be costing Fox ad revenues even in the UK. ГенгисYou have the right to be offended; and I have the right to offend you. 06:34, 7 October 2009 (UTC) ## Still moar Ed I'm not sure it's even worth mentioning this. I should just say "Ed Poor" and everybody will nod in understanding at yet another "masterpiece" by the "greatest thing ever to happen to Wikipedia". This time it's Kevin Jenningsimg getting the "throw down an obscure quote, followed by a request for somebody who isn't a fucking lazy retard to complete the article". And of course, Mr WP doesn't add a category or even the handy {{reflist}} tag. Smeg Ed - you're a fucking moron and you need to remember that with authority comes responsibility, not just mindless delegation. --Psy - C20H25N3OYou know you want to 11:57, 3 October 2009 (UTC) • This is not an article. This is facepalm. (Don't know why I am saying this. It just felt appropriate.) --wwwwolf (barks/growls) 12:04, 3 October 2009 (UTC) I get a Chuck-like flash whenever I see the name "Ed Poor". But all the images are of Ed's trademark less-than-stubs. --Sid He doesn't even get NAMBLA's name right - North American Association for Man-Boy Love Association. As for the article it is typical of Ed's "high standards". The problem is that his idea of a wiki is more akin to an eight-year old's scrapbook than even the rest of CP let alone something like Wikipedia. Lily Inspirate me. 13:11, 3 October 2009 (UTC) Yeah, that struck me as particularly brilliant. ħuman 19:22, 3 October 2009 (UTC) I also love how he forgot to mention why Kevin Jennings' opinions would matter to anyone... ħuman 19:25, 3 October 2009 (UTC) NAMBLA - I saw this on South Park a few years ago and thought it was hilarious. I saw that episode again recently and looked up nambla.com, after the North American Marlon Brando Look-a-likes complained about the domain name being stolen from them. As I expected, a South Park fan had bought to domain name and set up a site - and very funny - if a little bit disturbing it was - too. However I then googled NAMBLA and discovered that it is a fucking real association! I still cannot believe it. Please PLEASE tell me I've fallen for a parody. Fucking motherfuck me. NAMBLA....... DeltaStar 20:05, 3 October 2009 (UTC) Sorry to say they're a real organization. And I'm sure the FBI and Chris Hansen are watching their every move. --Gulik 18:40, 5 October 2009 (UTC) NAMBLA is a real group; however, the group only barely exists at this point. Its widely beliebed that the web site it only maintained by a few enthusiasts, and that a lot of the subscribers to its mailings are undercover law enforcement officers. To be fair, it was once larger, but it practically dead at this point (and good riddance.) MDB 14:45, 7 October 2009 (UTC) ## This should be fun... Incoming! Sterile gas tank 15:34, 5 October 2009 (UTC) A while back, we had some serious problems with spamming by the Conservapædia cretins, and I had to put the word "conservapedia" into the filter file. - That would be Ken, of course. ГенгисYou have the right to be offended; and I have the right to offend you. 19:08, 5 October 2009 (UTC) ### Conservative Bible Project Anyone care to ask his opinion of this critique of the CP Bible Project by conservative journalist & blogger Rod Dreher? €₳$£ΘĪÐMethinks it is a Weasel 19:10, 5 October 2009 (UTC) Dude, Andy has this on the mainpage! Ace McWickedThe Liquid Room 19:13, 5 October 2009 (UTC) Ah, I didn't notice that. I see he's totally missing the point of the criticism as per always. €₳$£ΘĪÐMethinks it is a Weasel 19:18, 5 October 2009 (UTC) No less than Harper's has picked up the story.--Tom Moorefiat justitia 19:27, 5 October 2009 (UTC) Sadly, No! is also on the case. They're finally getting the press coverage that Andy so craves! --Gulik 19:29, 5 October 2009 (UTC) This Catholic blogger was evidently on the case before Crunchycon. ГенгисYou have the right to be offended; and I have the right to offend you. 19:40, 5 October 2009 (UTC) I'm thrilled with the press coverage. I can't wait until this gets under the skin of some concerned fundies. — Sincerely, Neveruse513 / Talk / Block 20:14, 5 October 2009 (UTC) We can only hope Andy attempts to take the media to task, and we end up with a new Lenski. Z3rotalk 20:22, 5 October 2009 (UTC) I want to write Catholic priests for their reaction. "Ohai, preest. I'm a Catholic Conservative. Is this the Bible for me?" — Sincerely, Neveruse513 / Talk / Block 20:28, 5 October 2009 (UTC) No. Please to use this bible. Z3rotalk 21:04, 5 October 2009 (UTC) It's made the Huffington Post!!! Near the top of the main page!!! Gauss 20:29, 5 October 2009 (UTC) Odd that HuffPo doesn't seem to actually link to it, or am I mistaken? ħuman 00:52, 6 October 2009 (UTC) a blog at Time magazine. Viral, basically. Sterile gas tank 21:25, 5 October 2009 (UTC) Anyone else having trouble accessing Conservapedia? It's taking a few attempts to load pages. I wonder if this horde of lulz seekers are causing the Slashdot effect? Ask me about your mother 21:29, 5 October 2009 (UTC) I hope this get Lenski-esque. Its been too long since last time. Remember to use capture tags people! AceMcWicked 21:37, 5 October 2009 (UTC) This add-on for Firefox might also be useful, if you don't have it already. --Arcan ¡ollǝɥ 22:08, 5 October 2009 (UTC) I don't remember this many articles on Lenski, especially high ones as high profile as the Huffington Post, although he might have gotten a mention in the Guardian, he usual dose for shit like this. - π 21:58, 5 October 2009 (UTC) The single best line from the comments on the various articles is one point. When its pointed out that the lead of the project is Phyllis Schlafly's spawn, the Conservapedians are referred to as "Phyllistines." Priceless. MDB 22:06, 5 October 2009 (UTC) It's getting a modicum of notice on Twitter as well ;) Worm(t \| c) 22:07, 5 October 2009 (UTC) Do we have a page on the thing? It'd be good to ride this.--Tom Moorefiat justitia 22:08, 5 October 2009 (UTC) :::::::Created Conservapedia Bible Project.--Tom Moorefiat justitia 22:12, 5 October 2009 (UTC) Conservapedia:The Conservative Bible Project--Tom Moorefiat justitia 22:26, 5 October 2009 (UTC) NewsBusters actually likes the project! "consider some of more legitimate theologically conservative concerns that the project managers point to, such as . . . language in other translations that glosses over the stark biblical teachings on Hell and eternal punishment." Heehee. €₳$£ΘĪÐMethinks it is a Weasel 22:14, 5 October 2009 (UTC) I did a quick google search for "Conservative bible project" and yup, its all over the web now. Andy, you have done it again! AceMcWicked 22:16, 5 October 2009 (UTC) Google got 1.69 million hits a couple of hours ago, 1.73 million now. This lulz is growing rapidly! Gauss 05:42, 6 October 2009 (UTC) I suck at wiki forensics, but does it look like there's been some nuking of the history for the talk page at Conservapedia? I find it odd that Talk:Bible_Retranslation_Project hasn't changed since the 7th of August, and I'm sure I saw an earlier conversation in which an editor was asking for Andy's approval to reply to those nasty bloggers? Ask me about your mother 22:30, 5 October 2009 (UTC) cp:Bible Retranslation Project != cp:Conservative Bible Project, that might've tripped you up. I also brought this up on the RW article talk page... --Sid 22:33, 5 October 2009 (UTC) Are you using a different Google than I am? SoldierInGodsArmy 22:56, 5 October 2009 (UTC) Right Wing Watch picked it up, too. --Crazyswordsman 22:31, 5 October 2009 (UTC) even the Islamic blogs are picking it up. AceMcWicked 22:38, 5 October 2009 (UTC) It is now on the front page of digg. YorickIs Joe Biden Eva Braun? 22:59, 5 October 2009 (UTC) I've started a new section in the RW article, trying to keep track of blog reactions to the project. Obviously there's too damn many to count now, but if you find a blog that has a good quote about the project, or is by somebody notable, add it to the list. €₳$£ΘĪÐMethinks it is a Weasel 23:06, 5 October 2009 (UTC) "98th 57th most popular search in the past hour" Something Conservapedia-related becomes a Google trend - a first? --Sid 23:05, 5 October 2009 (UTC) I just got through to CP's recent changes after a dozen tries--it's a mess. A sea of redlinked new user names, blanked and reverted pages, lots of blocks. I know, that's no different, but it looks like JPatt is going nuts trying to stem the damage.. RaoulDuke 23:11, 5 October 2009 (UTC) Oh, yeah--the Conservative Bible Project has been protected (no linky as it kept timing out)--so much for helping to contribute. Thanks for coming. RaoulDuke 23:19, 5 October 2009 (UTC) Google blog searching "Conservative Bible Project" gives 120 blog entries (and went up by one while I reloaded....) Sterile gas tank 00:08, 6 October 2009 (UTC) I hope this doesn't fizzle, it would be awesome if it made Colbert or teh Daily Show. ħuman 01:01, 6 October 2009 (UTC) God damn...The #conservativebible hashtag is on fire. ~15 tweets a minute at the moment. none of them make any fucking sense. — Sincerely, Neveruse513 / Talk / Block 01:35, 6 October 2009 (UTC) I think the best thing about Andy's project is that he wants to remove one of Jesus's really famous quotes: "forgive them, Father, they know not what they do" (or whatever). That would also mean deleting a movement from one of Haydn's famous works. DickTurpis 01:51, 6 October 2009 (UTC) I saw that and assumed it was parody; but, as Poe teaches us, you never can tell.--Simple 02:25, 6 October 2009 (UTC) Oh, and now Assfly is pulling more statistics out of his ass. Can people this stupid really exist? It's positively mindboggling. DickTurpis 01:59, 6 October 2009 (UTC) Shelly the Republican also: STR--218.215.157.182 07:27, 6 October 2009 (UTC) And to kill CP's servers completely: Boing Boing --Sid 08:42, 6 October 2009 (UTC) Check the influx of new users! It's gonna be banhammer time!--Ireon 14:25, 6 October 2009 (UTC) BANHAMMER!! --Ireon 15:34, 6 October 2009 (UTC) Thus speaketh Karajouimg: "Liberal hypocrisy anyone? In their condemnation of the Conservative Bible Translation Project, the critics have forgotten their praise for last year's "Green Bible", an eco-friendly edition made from recycled paper, processed soy ink, and the words of nature - not Christ - in green." And I suppose that Conservapedia Bible Translation Project is nothing more, nothing less, than verbatim copy of the King James Bible, with Andy's Conservative Words highlighted in gold and green, the colours of Capitalism? --wwwwolf (barks/growls) 08:21, 7 October 2009 (UTC) The Conservative Bible Project now has a (brief) page on Wikipedia [4] and has been added to the WP entry. Was it us, or one of the bloggers? Broccoli 19:43, 7 October 2009 (UTC) Us? Creating articles with the Article Wizard? My my! RW is a highly intellectual wiki, for highly Internet-savvy people! =) Anyway, since someone slapped the article a CSD A7 tag, I merged the thing to Conservapedia's WP article. --wwwwolf (barks/growls) 20:23, 7 October 2009 (UTC) ### Sleazy edit button "Once someone buys into evolution, he typically refuses to learns anything about the Bible again" - ALS. ORLY? I did most - or all - of my Bible-learnin' after I not only was an eviliutionist, but also an atheist. Fuckwad. PS, the typo is sic, please to add to quote generator. ħuman 02:09, 6 October 2009 (UTC) now that andypants knows people are watching, the insights will flow... — Sincerely, Neveruse513 / Talk / Block 02:15, 6 October 2009 (UTC) @That quote that Hooman brought up. Mehbeh that's because people realise that evilution makes much more sense than everyone being inbred descendants of two people who were created by a magical man in teh sky. I gotta say, I'm loving today, CP has finally (nearly) reached the mainstream and it's to their disadvantage because now everyone can see how... special they are. -RedbackOMG, someone get the Raid! 03:16, 6 October 2009 (UTC) "Special", indeed. To the embarrassment of those we call "special" due to their difficulties in life. Andy ain't one of them. To abuse a word I swore off in the early days of RW as "not funny", Andy is retarded. In so many ways. ħuman 06:21, 6 October 2009 (UTC) It is so telling that none of the other sysops have gone near this project. Shades of the Lenski imbroglio I think.-- Kriss AkabusiAAAWOOOGAAAR!!1 09:32, 6 October 2009 (UTC) I don't see it like that at all. I don't think any of the sysops have ever shown interest in any of Andy's projects, they don't show interest in each other's projects, and apart from Ken they seem to get bored with their own projects. Karajou has sometimes added stuff on war and copy/pastes from the CIA World Factbook but really their aim is denigrate liberals, evolutionsist and atheists not construct an online encyclopedia even if it does have a conservative Christian "bias" (Bias is really too mild a word for what Andy's doing.) ГенгисYou have the right to be offended; and I have the right to offend you. 11:13, 6 October 2009 (UTC) I wonder what aSK thinks of this? Ajkgordon 10:28, 6 October 2009 (UTC) I assume that Philip thinks it's stupid.-- Kriss AkabusiAAAWOOOGAAAR!!1 10:36, 6 October 2009 (UTC) They made it onto the Mike Malloy Show... ħuman 01:15, 7 October 2009 (UTC) ## Liberal style bot Whoever posted this WIGO (and whoever is MarkGall) needs to come over here and help me wash the beer off my screen. That's fucking classic.--EcheNegraMente You are everything you are nothing at all 05:17, 6 October 2009 (UTC) "I can recognize a liberal simply by his style, such as his high word-to-substance ratio." Andy is in true form. Awesome wigo. Awesome stupidity, Andy. ħuman 05:34, 6 October 2009 (UTC) That is brilliant! One of the best WIGOs I've ever seen. I also give my congratulations to MarkGall, whoever you are. Regarding Andy and his super-skills, I seem to recall him sysoping a vandal or two, I guess he must've been drunk; or maybe this was before he developed his superhuman talent. As for Andy himself, it's easy to see if he's been around with a quick E. Coli test - you know, from all that shit that comes out his mouth. -RedbackOMG, someone get the Raid! 05:47, 6 October 2009 (UTC) Ok who else thinks we should start a betting pool on the first sysop that the bot will identify as a liberal? I have 2 goats on Andy himself :)--BoredCPer 06:11, 6 October 2009 (UTC) I place five internet goats on Joaquin Martinez. ħuman 06:18, 6 October 2009 (UTC) Π goats on everyone who is not a sysop, and a gerbil each way on Andy. ГенгисYou have the right to be offended; and I have the right to offend you. 06:30, 6 October 2009 (UTC) THEORY: Are MarkGall and JacobB the same person? They both seem to be math buffs, they both get into the same debates, they both translate the bible... this is fishy! Zelmerszoetrop 07:12, 6 October 2009 (UTC) I guessed the same. In any case, this is the most fantastic parody in ages. 07:33, 6 October 2009 (UTC) This reminds me of the "cylon detector" from BSG. I hope Andy puts too much trust into it and it becomes a shitstorm of bannings and suspicion. 194.6.79.200 11:03, 6 October 2009 (UTC) This will probably go the way of the Guard Dog, it won't work when Andy "tests" it, so he will lose interest and the contributors work will go to nothing. - π 11:06, 6 October 2009 (UTC) Andy is literally one of the biggest prats alive... this is gold. SJ Debaser 13:56, 6 October 2009 (UTC) Indeed. I can't wait for Andy to rape statistics all over again for this one. — Sincerely, Neveruse513 / Talk / Block 14:01, 6 October 2009 (UTC) Bit late to this party, but please find here [[5]] the final design for the casing. Steve 14:52, 6 October 2009 (UTC) I can't wait for him to block someone for running afoul of the liberal style bot. (It'll probably be something like "The bot called you a liberal therefore you are one therefore the bot works.) Then, when it declares Andy a liberal, he will deep-burn anything related to it. BTW nice pic Steve. Tetronian 20:47, 6 October 2009 (UTC) I'm guessing that the bot will turn to a real-life version of the Star Trek computer/god Vaal? Let's just check back in a few hundred years to see who's running the show at Conservapedia? Ask me about your mother 20:53, 6 October 2009 (UTC) ### The formula This can only get funnier from here really. - π 01:06, 7 October 2009 (UTC) I am willing to bet $C_4$ ends up negative because of the number of times Andy has fought to ensure he has the last word. - π 01:15, 7 October 2009 (UTC) Or else it will just be that only sysops decide what qualifies as "last wordism" in a case-by-case basis. Overall, though, I'm actually really impressed by the amount of the thought that went into that formula. Watch out, Bugler, this guy is pretty damn good. Tetronian 01:19, 7 October 2009 (UTC) That one is what makes it look like parody to me - all the others can be determined by a bot, they are simple wiki data requests. Last wordism requires human intervention to determine it. ħuman 01:25, 7 October 2009 (UTC) That may be the only reason that this wacky plan will ever be implemented: when Andy gathers the data on everyone, he will realize that all the sysops (especially him) are "liberal" according to the equation. But a case-by-case variable will allow them to manipulate the data so that they do not qualify as "liberal." I suspect that subjectiveness is the only reason that 90/10 is still around, I'm hoping this will be no different. Tetronian 01:32, 7 October 2009 (UTC) How are they going to fit the constants with out definite values for liberality, or are everyone going to be appraised as relative to Andy? - π 01:35, 7 October 2009 (UTC) 90/10's not subjective. Look, it's measured by the first term! --Lesjohn 01:37, 7 October 2009 (UTC) I'm guessing the constants are going to be based on the same "liberal style" article, which Andy wrote. So it effectively will be relative to him. But 90/10 is subjective, because of the quality of edits, a factor which Andy always brings up ("your edits are lacking substance"). On the other hand, Ken's edit-gasms count for as many edits as he makes despite the fact that they are miniscule. Tetronian 01:44, 7 October 2009 (UTC) The bot is suppose to detect parodist right? But isn't the point of parody is that you imitate the object of parody's speech? A good parodist, I am think Bugler here would be almost statistically identical to Andy. I never remember him formulating long replies, it was always "shut up and open your mind" much the same as Andy's response. - π 02:20, 7 October 2009 (UTC) ...which is why this whole thing is so funny - Andy just doesn't get it. Also you're welcome Mark.img Tetronian 02:26, 7 October 2009 (UTC) I dislike the round up to zero thing. If he had written it as $\sqrt{1/2-\mathrm{LastWdProp}}$ then liberals who like last wordism, would end up with a complex number - a sure sign they are liberals. - π 02:31, 7 October 2009 (UTC) This is great. Just when CP was becoming boring. If Markgall is a parodist then this is great work. Otherwise he is an idiot. According to his formula any user who makes only one edit and that edit is to a talk page is infinitely liberal. On the other hand any user who makes no talk page edits cannot have his level of liberalness defined. Also you can now ignore the 90/10 rule since the formula is so massively weighted towards the difference between the number of liberal terms and the number of conservative terms. These nonsense equations are usually spat out by PR companies. Ben Goldacre is pretty good at keeping track of them(see for example [6]). JoeDuffy 09:47, 7 October 2009 (UTC) Conservastan take on the event: Ayyy, Robot! --72.229.223.87 02:09, 7 October 2009 (UTC) LOL, love the forks sticking out of it. Tetronian 02:16, 7 October 2009 (UTC) Someone has to suggest a regression analysis to determine the coefficients. There must be graphs as well! Sterile gas tank 02:34, 7 October 2009 (UTC) What are you talking about? Schlafly Statistics has the best regression technique. - π 02:36, 7 October 2009 (UTC) I love the use of the square root and the power to the square, designed to arbitrarily penalize without any reason! But hey, this whole formula is crazy. What it does, basically, is establish a list of forbidden words and phrases. And also, prevent posting. I can't wait to see the first victim to this mad scheme "User, you are mathematically a liberal. Godspeed." It kinda reminds me of the pin-in-the-flesh approach to find witches.--Ireon 12:05, 7 October 2009 (UTC) Oh dear - it rates talk-page posts over main-page - looks like Terry's fucked then. --PsygremlinHable! 17:46, 7 October 2009 (UTC) ## Good neologism Pretty run-of-the-mill parthian, this, but I did enjoy its description of Conservapedia as a "crap-site". In general, it's nice to see a few fresh, wide-eyed dissenters, no doubt brought by the blog attention to the Bible project. A few of them will probably turn up here soon.-- Kriss AkabusiAAAWOOOGAAAR!!1 15:58, 6 October 2009 (UTC) call that a neologism? I made up "coprochiropteran" yesterday, pi deep-fried jerboas to whoever can work out what it means. Totnesmartin 17:16, 6 October 2009 (UTC) Something about crap and bones? No idea what Teran is, but it reminds me of StarCraft. Ask me about your mother 17:23, 6 October 2009 (UTC) Shit (copro) and bat (chiropteran). Thus batshit. 17:45, 6 October 2009 (UTC) Publius Wins! Enjoy your jerboas! Totnesmartin 18:06, 6 October 2009 (UTC) The whole dialogue is hilarious. Conservapedia editors may be allowed to hold the opinion that Finnish public schools tell lies. But they cannot deny the fact that the Finnish public schools tell those alleged lies in Finnish, not Russian. And that, my friends, is what ultimately weighs more in this debate. </patriot> --wwwwolf (barks/growls) 21:15, 7 October 2009 (UTC) ## Long live the parodists Andy has promoted his illustrious biblical scholars for their contributions to his grand endeavour. [7] Meritocracy indeed! 23:07, 6 October 2009 (UTC) More direct link. - π 23:23, 6 October 2009 (UTC) So now they can work day and night on writing Andy's Bible? --Sid 00:19, 7 October 2009 (UTC) That recent changes log is awful. I actual feel sorry for them with all these new people showing up and trashing the place because they are bored unfunny idiots. I was hoping for some new blood to liven the place up, but all there is are annoying idiots who hang around aggregate sites looking for what they think passes for laughs. - π 01:49, 7 October 2009 (UTC) I agree. Parody = good, deleting pages and posting shit = bad. DeltaStar 06:47, 7 October 2009 (UTC) But we are the sole source of vandalism for Conservapedia, remember? tmtoulouse 17:42, 7 October 2009 (UTC) ## We should show this to Andy... Enough said. ĴαʊΆʃÇä₰ I like pyrrhic lavas 04:59, 7 October 2009 (UTC) Or at least this one. ĵ₳¥ášÇ♠ʘ current location: in-between the spine-chilling idiot 05:07, 7 October 2009 (UTC) We all know that Google was bribed by Wikipedia to put their articles on the top of every search. Also people don't yet realize that Wikipedia never says anything true about any subject. Also Mainstream Media censorship. Also Ken's Google links meant something. Also let's throw in Obama somehow. ~ Kupochama[1][2], on behalf of Andy, 16:29, 7 October 2009 (UTC) ## TK The TK police OK, so he's back, but doesn't seem to be doing much. Still recovering or getting bored with CP? CrundyTalk nerdy to me 13:45, 7 October 2009 (UTC) Who knows. It must take a lot to keep living and breathing excreta like Terry away from a shitheap like CP, but since I don't believe a single word I've ever seen him utter I can't fully credit that he was actually out sick for all of September. He's such an odious and sickening shell of a human that I can imagine other reasons he'd be out of circulation for nearly exactly 30 days. Can you? 17:59, 7 October 2009 (UTC) I didn't want to be the one to say that first. When everyone was wishing a speedy recovery to TK, I was thinking to myself, "Really? Am I the only one who doubts that he's actually sick?"--EcheNegraMente You are everything you are nothing at all 18:53, 7 October 2009 (UTC) ## Oh, the lies Apparently the bible translators are continually referencing the Greek originals and biblical linguistic scholarship! Props to Jacob for defending the project with a claim which can never be disproven. [8] 19:42, 7 October 2009 (UTC) bragging about you're own work much? Zelmerszoetrop 00:18, 8 October 2009 (UTC) I wish. 00:24, 8 October 2009 (UTC) The new block+edit guys are really cranking out the crap now. I'd say between them they're averaging at least 1200 liberal points (1.2 kMarx?). --Lesjohn 03:25, 8 October 2009 (UTC) ## AndyPandy on Dave Ross Can be found here (October 7, 2009 11:00 am-12:00 pm)--AndyPandy - because paranoia and abject failure doesn't hold you back, although it should. 21:15, 7 October 2009 (UTC) And Andy gets shafted at 6:33.--AndyPandy - because paranoia and abject failure doesn't hold you back, although it should. 21:16, 7 October 2009 (UTC) You the man...I couldn't find it. — Sincerely, Neveruse513 / Talk / Block 21:20, 7 October 2009 (UTC) And at 12:10.--AndyPandy - because paranoia and abject failure doesn't hold you back, although it should. 21:22, 7 October 2009 (UTC) And I finally get to found out how to pronounce AndyPandy's last name. How come I can look at porn all day, but it's only when I here how his name is pronounced that I feel the need to scrub myself down with lye?--AndyPandy - because paranoia and abject failure doesn't hold you back, although it should. 21:27, 7 October 2009 (UTC) Because hes just that full of it....OpalHonors 21:28, 7 October 2009 (UTC) His points about interpolation are valid. — Sincerely, Neveruse513 / Talk / Block 21:37, 7 October 2009 (UTC) First those liberal vandals are behind every failing at his site, now liberal vandals are behind the bible. Soon Andy will be blaming liberal vandals when his bottle of scotch is empty. YorickIs Joe Biden Eva Braun? 21:52, 7 October 2009 (UTC) "Why isn't the mail here? LIBERALS!!!!" Tetronian 21:54, 7 October 2009 (UTC) I love how Andy projects his experiences at his "weekie" to the cannonization of the bible. Me!Sheesh!Mine! 22:36, 7 October 2009 (UTC) Direct link. Very nice find... ħuman 22:47, 7 October 2009 (UTC) Thankyou. Didn't want to put a direct link in myself, can't remember what the fracking law is in the UK regarding direct linking, let alone what the law is for someone using a UK IP address to link from one non-UK site to another.--AndyPandy - because paranoia and abject failure doesn't hold you back, although it should. 22:53, 7 October 2009 (UTC) Oh, and while I remember, that point when AndyPandy tries to pretend that James Dobson is involved somewhere in the project? Complete bollocks. If it was true it would be splashed all over the AFA website. Bah, Andy really missed a trick. The answer to "So that was added hundreds of years ago by vandals?" is "No, Dave, actually it was the Huns." --JeevesMkII The gentleman's gentleman at the other site 04:28, 8 October 2009 (UTC) Andy has pointed out that the Bible has been re-written on several occasions in recent years in order to have God's word (such as it is) fit a particular ideology or world-view: feminist Bibles, environmentalist ones, queer-friendly takes. Are these projects any less (or more) silly? Is what Andy's doing singularly stupid (well, anything he does is, in its own way, of course) or is it part of a larger trend in which people try to get the central ideas of their faith (which are comparatively easy to change) with a world-view tied to broader material/political/social factors (which may be harder to change). If we're to have a scornful article on the Conservative Bible Project, should we have an equally scornful article on this? Just throwing it out there...RaoulDuke 02:42, 7 October 2009 (UTC) Usual they are re-translating from the original Greek or Aramaic so as to ensure the changes they are making are textual relevant. They don't pick an English translation and start mincing it. - π 02:46, 7 October 2009 (UTC) There's that, I'll give you that--but that's far from the only criticism that the blog-o-sphere has re: Andy's project: it seems like a lot of the stuff that's come out in the past 36 hours is targeting the "making the Bible for a particular ideology" aspect and not the "original languages" thing. RaoulDuke 03:20, 7 October 2009 (UTC) And none of them link to the damn source. ħuman 03:25, 7 October 2009 (UTC) (EC)It does sort of put me in mind of the idea of picking the news channel you watch based on ideology. I guess until 15 or 20 years ago you use to rely on the news being independent and just serving up the truth as they could best find it, but is all gone now and we have hyper-partisan news service feeding their viewers what they want. Maybe Andy's bible is the final step in this trend. For years you have been able to choose whether you wanted a liberal or fundamentalist church depending on you preferred prejudice. Maybe the bible really has become that unsanctified now you can choose that as well. - π 03:30, 7 October 2009 (UTC) The primary difference between this and the examples that Schlafly has pointed out (that are mentioned above) is that those groups are traditionally suppressed by the Religious-Right and certainly have something to gain by re-interpreting the Bible in a way more friendly to their thinking (environmentalism, feminism, gay community etc.). Indeed the part of the Venn Diagram where "gay" and "Christian" overlap is catered for by special interest groups who need to say "look, the Bible really doesn't condemn homosexuality like this, it's Jesus that's important and he said nothing about it being immoral!". On the other hand, the ultra-conservatives and religious-right do indeed like to harp on about the "inerrant word of God" and Biblical absolute morality. So the Conservapedia project also generates a feeling that these people are being very hypocritical in doing this - that they claim that their views are directly sourced from the authority of the Bible, but they still have to alter this authority to back themselves up. moral 08:59, 7 October 2009 (UTC) Also I am not convinced that "liberals" (as if every liberal thinks the same) are likely to have a particularly favourable view of any changes to the bible. I for instance am only now hearing about the "green bible" and I think it is just as batshit crazy as the conservapedia one. I am no hypocrit - I think all attempts to politicise sacred religious texts are as bad as each other. --DamoHi 09:20, 7 October 2009 (UTC) Most of those politically motivated ones just highlight certain passage in another colour just to emphasis a point. The green bible has green text for pro-environmental passage. There are also bibles with red text for Jesus' actual words so you can see what he said versus what others said he said. Most try to prove their point without changing the words themselves. - π 09:32, 7 October 2009 (UTC) I think Pi is right. The Green Bible, for instance, is just the New Revised Standard edition, with certain text highlighted in green, and written on recycled paper or something. I think it also has a study guide centered on environmental issues. If Andy had decided to write a conservative bible based on something like that, perhaps with passages relevant to modern conservatism highlighted and with some analysis based on some of his batshit crazy ideas, I don't think there'd be much of an issue, except with his qualifications to undertake such a project. Retranslating, removing passages you don't like (turning the Seven Last Words of Christ into the Six Last Words of Christ), and deciding certain words are too "liberal", all without any knowledge of the original languages, is just crazy. I'm looking forward to hearing him defend himself against Colmes, though I'd prefer Jon Stewart. DickTurpis 11:44, 7 October 2009 (UTC) (redent) Yup, Pi is right. The Green Bible does contain additional works, and it's fine so long as there's a clear line between scripture and commentary. Even Andy wouldn't be stupid enough to believe that an essay by Desmond Tutu was part of the material considered by the Council of Trent (16th century), and the Green Bible does not appear to be trying to give that impression. What the Green Bible is doing is no different to a students edition of Hamlet, in which interesting verses are highlighted and commentary added. What Andy is doing is more akin to relocating the setting to Chicago, and turning Ophelia in to sex-crazed hooker robot with a thing for laissez-faire economics. Ask me about your mother 12:30, 7 October 2009 (UTC) I do hear what ya'll are saying but I do think that drawing the readers attention to one part of the bible or another as more important than another is equally as stupid as rewriting the whole thing. If the bible is the unaltered word of god then surely it should not need humans to emphasize some parts of it and hence de-emphasize others. --DamoHi 01:18, 8 October 2009 (UTC) Council of Trent? That's us, isn't it? Totnesmartin 12:39, 7 October 2009 (UTC) That's an odd coincidence. Didn't think of that. Anyway, it's the 16th century, so I'd better stop editing. I've some wenching to do, and my organiser tells me that I'm due to contract bubonic plague at 4:30pm today. Ask me about your mother 12:49, 7 October 2009 (UTC) ### I don't get CP's criticism on the criticism According to this talk section Andy and Jinx are baffled by the librul double standards where it's fine to create a feminist bible, but it's stupid to create a conservative bible. Sooo, do they realize that claiming a double standard means that they are admitting the similarity of the projects? If they're bawwwing about double standards, it can be solved in two ways: • Acknowledge that their project is stupid just like the gay/feminist bible, so they should get the ridiculing that CP is getting too. • Claim that the gay/feminist bible is a fine translation project. Since CP's project is just like that, it doesn't deserve the ridiculing. But of course, we all know that what they actually believe is that those other versions are librul claptrap, while their version is conservawesome. This is in fact the exact reverse of the position they're criticizing the liberals on, making it exactly the same double standard.. Only on CP you could find logic this brilliantly retarded.. --GTac 14:20, 7 October 2009 (UTC) "GTac" (obviously not your real name), you have free will to deny logic. I skimmed through your recent edits and you're "sources" are ungrammatical, so anyone with an open mind can see that you're here to do harm to family values. Furthermore, you are in denial that that affirmative action causes rather than prevents athiesm. Observation and logic dictate that Jesus sends people to Hell too. Contribute in an educational way to substantive entries here, or go elsewhere to rant about your view of the world. Please.--Andy Schlafly 08:04, 25 April 2014 (UTC) I did like the idea of removing references to alcoholimg from the bible. Why not remove references to jews as well? Dumbasses. CrundyTalk nerdy to me 15:07, 7 October 2009 (UTC) That's too good to be real. I'm calling Poe on that one. Stu the Foo' 15:22, 7 October 2009 (UTC) The original comment might be poe, but look at the responses from assfly and Jinx hi Jinx!, especially Jinxy's "Noah was obviously a sinner because he was a drinker" comment. CrundyTalk nerdy to me 15:39, 7 October 2009 (UTC) So, they're going to take out the part about Lot's daughters getting him drunk and having sex with him? (Ah, Biblical Family Values. Bet they cut King Solomon down to one wife and no concubines, too.) --Gulik 09:15, 8 October 2009 (UTC) Tghe whole Song of Solomon can go too, and Jacob's many, er, marital side projects. But what about Jacob cheating Esau of his birthright, one one the Bible's most famous acts of deceit? Do they rewrite that altogether or call Jacob a liberal? Totnesmartin 09:22, 8 October 2009 (UTC) ## They're offline again [Conservapedia's down! I tried again and they're back. Proxima Centauri 06:21, 7 October 2009 (UTC) Thanks for that riveting report. - π 06:26, 7 October 2009 (UTC) When CP is in the news you can expect regular outages as the hordes overflow the site. It doesn't really merit commenting. Looking at the stats they have had about 80,000 views of the Bible project page over the last two days alone. My records show: 2009-10-02 : 35648 2009-10-03 : 35675 2009-10-04 : 35703 2009-10-05 : 35723 2009-10-06 : 60011 2009-10-07 : 114020 ГенгисYou have the right to be offended; and I have the right to offend you. 09:11, 7 October 2009 (UTC) Yeah, I don't wanna be a dick, but if I wanted to see if CP was down or not, I could type conservapedia.com into my location bar (or as it's called now, the awesomebar) and press enter. But thanks for the random report. -RedbackOMG, someone get the Raid! 12:32, 7 October 2009 (UTC) They're down intermittently today as well. DOS by RationalWikians couldn't possibly contribute to these outages, could it? Take care, it's illegal in most countries. Proxima Centauri 12:27, 8 October 2009 (UTC) Uh... are you being serious? If you are, you're being a bit silly and need to read the rest of this page. If not, then it's just my sarcasm detector going out of whack - which I think is understandable; I just spent like 5 hours at the hospital (which cost me nothing, and the pills they gave me cost like $5, yay for Universal Health Care!). -RedbackOMG, someone get the Raid! 12:40, 8 October 2009 (UTC) ## Extra credit with Bible Project I'm not to sure what to make of this extra credit. Andy basically asks his students for reinsurance after the wide criticism of his project on the web? I particularily like the afterthought "Oh, and it would be nice if you could find a connection to economics. Like, you know, hum...somehow." --Ireon 15:53, 7 October 2009 (UTC) Well I guess he could sell the translation once he's finished it. That would be... economics...stuff. X Stickman 15:56, 7 October 2009 (UTC) It has just struck me that what Andy's doing with his free-market translation of the Bible is "being economical with the truth" (to use the immortal words of Sir Robert Armstrong). ГенгисYou have the right to be offended; and I have the right to offend you. 16:22, 7 October 2009 (UTC) I'd like to see someone argue option C: that the translation should be "made illegal". Stu the Foo' 16:41, 7 October 2009 (UTC) Any student trying this option would very quickly face the cold harsh truth of Darwin's "survival of the fittest" and be cleansed from the homeschooled pool. Adapt or die! --Ireon 16:49, 7 October 2009 (UTC) WTF? Discouraged, encouraged or made illegal by who exactly? The only bodies I can think of with the power to make it illegal ought to have no opinion at all on the existence of any particular private enterprise, neither encouraging it or discouraging it. Now a reasonably question would be, should anyone who wants to write a conservative bible be scoffed at, ridiculed or burnt at the stake? There's a question we can all enjoy. --JeevesMkII The gentleman's gentleman at the other site 17:04, 7 October 2009 (UTC) I updated the WIGO, but Andy deleted the question and locked the lecture, declaring it complete. Maybe he decided that using his lectures as a way to get his students to praise the glorious Conservative Bible Project was a little much. MDB 12:32, 8 October 2009 (UTC) ## Andy on Liberaland Did anyone else catch this Tuesday night? Intellectually it was what you might expect--Andy would get backed into a corner due to his indefensible positions, Colmes would back off and grab another sword, a couple minutes later Andy would be backed into a different corner. Colmes picked up right away on Andy's raving anti-liberal tendencies, and there was a great moment when Andy talked about how the people writing the liberal translations of the bible are the same ones voting for Obama--Colmes called him out on it and asked Andy if he had investigated the voting record of every bible translator. Back into the corner went Andy, claiming that professors translated the bible and professors voted for Obama. Anyway, I think the most significant thing from the whole interview is that Andy said the translation would be done in about a year. I hadn't seen any commitment language from Andy as to a timeline beyond "if we translate X verses of B book every Y days we'll finish in Z months!!" There has to be some way this can be used to make him look like a fool, because he's obviously going to fail at it. Andy has never been able to maintain a long-term project (remember his one-time goal to make Conservapedia the world's leading free constitutional law resource?). Sandman 16:25, 7 October 2009 (UTC) It all depends... I think it's high time to do everything we can to thrust CP into the limelight. Troll, spam, tell your friends and neighbors. Get your right wing grandparents to take a look, you know it's been a while since you've spoken to them. With any luck, we can get fundies from all corners to make this one of the greatest Christian clusterfucks of the twenty-first century. Imagine, Christians from all over the country, coming together, marring their tome, disagreeing on everything...for the world to see! — Sincerely, Neveruse513 / Talk / Block 16:34, 7 October 2009 (UTC) What? where did this interview occur? Linky? Me!Sheesh!Mine! 16:45, 7 October 2009 (UTC) Linky. I haven't listened to the whole thing, but Alan fucking killed it... "Anyway, uh, Phyllis Schlafly's straight son is, uh, doin' a uh..." Fuck it's not on there... — Sincerely, Neveruse513 / Talk / Block 16:56, 7 October 2009 (UTC) That doesn't have the interview, that's a preview clip. You need to pay (bah!) to listen to the actual interview. No way is anyone getting 5 dollah out of me in order to listen to the Assfly drone on. --JeevesMkII The gentleman's gentleman at the other site 17:06, 7 October 2009 (UTC) Rupert Murdoch is fucking crazy with his pay for news ideas. I have a theory that the ratings for other networks are lower than fox because you can go to the websites and watch full episodes. You have to watch Bill O at these specific times in the day, but you can watch Olberman any time you want. — Sincerely, Neveruse513 / Talk / Block 17:28, 7 October 2009 (UTC) Ah ha, pwned. I found the MP3 of the interview fur free. Here, inflict pain upon yourself: --JeevesMkII The gentleman's gentleman at the other site 18:00, 7 October 2009 (UTC) I added this clip to "pwned" at Andrew Layton Schlafly. If it gets transcribed that can be changed to a link to the transcription page. ħuman 21:25, 7 October 2009 (UTC) It actually hurts to listen to him. — Sincerely, Neveruse513 / Talk / Block 18:03, 7 October 2009 (UTC) Hah, awesome. Alan really fucks the Arsefly in the arse right there. I think I'm in love. --JeevesMkII The gentleman's gentleman at the other site 18:10, 7 October 2009 (UTC) Man. He really comes off as more of an idiot when he can't simply ban someone. All that giggling too, WTF? I love how he quips when he has no answer. "Tyranny" is a synonym for "Government." HarHarHarHarHar! Also, he jumps around from one unsupportable dickhead idea to another unsupportable dickhead idea. Me!Sheesh!Mine! 18:14, 7 October 2009 (UTC) ...I knew the 'Fly was crazy on the internet, but I thought it ended there. Now I see that he's crazy in reality too. It was great to see him be wholly unable to backup his viewpoints with anything other than wild assumptions and sweeping statements. EddyP 18:20, 7 October 2009 (UTC) When he said government with disdain (and then repeated it with more disdain and laughed) I lol'ed hard. — Sincerely, Neveruse513 / Talk / Block 18:21, 7 October 2009 (UTC) Yuh huh. This audio is crying out for a video of Beavis and Butthead overlaid with the Assfly's "HurHurHurHur! Government!" He's just got that perfect Butthead lilt on the last syllable there, like it's a dirty word. --JeevesMkII The gentleman's gentleman at the other site 18:24, 7 October 2009 (UTC) It is painful, but I'm going to write up a transcript. Any thoughts on how we could use the transcript? I'm sure we could use it in some way to illustrate how much of a flailing buffoon Andy is when he doesn't have ye trusty banhammer to save him from awkward questions. I'll pop a post here once it's up.Ask me about your mother 18:33, 7 October 2009 (UTC) I'm sorry, but that's not something you can do. -- Nx / talk 18:50, 7 October 2009 (UTC) I know it isn't going to happen, but please, if the universe is listening, lets see AndyPandy trying that crap with Jeremy Paxman, please, just once.--AndyPandy - because paranoia and abject failure doesn't hold you back, although it should. 18:39, 7 October 2009 (UTC) It's only happened a few times, but I love when Andy goes out into the real world and gets his ass kicked. It happened when he was on the news to debate vaccines and now with Colmes. Ps, when did he find a backbone? I never heard any of this humor (that's right, HUMOR) and intelligent argument during his whole tenor with Hannity. SirChuckBA product of Affirmative Action 18:46, 7 October 2009 (UTC) Yeah, it sounds like he really did his homework, too. I'd even suggest that he may have read some of our work. ħuman 21:30, 7 October 2009 (UTC) Scrub what I said about posting the transcript. I suspect that Nx is thinking of copyright implications, and he's probably right that it can't be posted in its full form. Ta for the warning. Ask me about your mother 18:58, 7 October 2009 (UTC) (unindent) Transcripts can be posted for purposes of critism and commentary, how do you think blogs get away with it? Plus, I seriously doubt that Colmes and his people are gonna come down on us. SirChuckBA product of Affirmative Action 19:00, 7 October 2009 (UTC) I think Nx is severely overreacting here. First, you can't violate copyright without distributing a copy of an original work. We're not doing that. Second, the work in question is the audio. If you write a transcript of an interview, that's a whole other and different work. The interview itself is not eligable for oopyright, only the particular audio master of it being distributed. If you were in the studio, and weren't under contract to Fox to do otherwise, you could perfectly legally tape your own copy of it. --JeevesMkII The gentleman's gentleman at the other site 19:04, 7 October 2009 (UTC) EC x too many -- Nx, I completely disagree with your analysis so far in this thread. If Fox fails at securing its property, why has it not waived any claim to a right to payment? Why do you believe a transcript of the interview with our corresponding talk page commentary or a side by side analysis would not be permissible to the extent Fox would even have any intellectual property right in such a transcript (I'm not sure it would)? I think you're wrong, but I'd like to know what you're thinking since you didn't explain yourself and no answer is immediately self-evident to me. 19:05, 7 October 2009 (UTC) They're asking money from you so that you can listen to the interview. You are depriving them from that profit by linking to the interview without paying. As for the transcript, is it okay if I post a transcript of Dawkins' The Greatest Show on Earth audiobook? -- Nx / talk 19:10, 7 October 2009 (UTC) No, because that's a spoken version of a literary work, something which IS eligible for copyright. Conversations do not form a copyrightable work. Plus, they are asking money for the whole 3 hour thing. As far as I know this clip is something they mean to distribute for free. And even if they didn't mean to distribute it for free, at least in the UK under the misuse of computers act, they've forfeited any right to getting money for it by having no security to bypass. Copyright doesn't enter in to it, since as I point out we're not making a copy. --JeevesMkII The gentleman's gentleman at the other site 19:15, 7 October 2009 (UTC) Without getting my lawyerly hat on I think Nx is correct. A transcript becomes a derivative work and would need the original copyrightholder's permission. Also a conversation is copyrightable if it is broadcast solely in a copyrightable medium. Even if it was freely available that doesn't mean it is exempt from copyright, also deprivation of income is not a necessary condition for copyright infringement. However, as this is not a lengthy piece, it's not like a one hour programme, I would think that use for comment and criticism with attribution to the original source would be acceptable. ГенгисYou have the right to be offended; and I have the right to offend you. 20:11, 7 October 2009 (UTC) I'll eat Darwin's hat if we can't use a transcript of a radio broadcast for commentary. Plus, not a god damned thing about that url is copyrighted. — Sincerely, Neveruse513 / Talk / Block 20:16, 7 October 2009 (UTC) Sure you can, just slap {{fairuse}} on it and problem solved. For extra points, criticize CP when they do the same. -- Nx / talk 20:23, 7 October 2009 (UTC) Seing as how that's the nature of fair use (and you're a fucken vulcan), I don't know if you're joking... — Sincerely, Neveruse513 / Talk / Block 20:27, 7 October 2009 (UTC) (EC) Eh... but if we were critisising it in a side-by-side, it WOULD be fair use, if it's even a derivative of a copyrighted work at all which I'm not sure it is. --JeevesMkII The gentleman's gentleman at the other site 20:28, 7 October 2009 (UTC) It's personal commentary on a freely available excerpt of a publicly broadcast interview. Am I taking crazy pills? — Sincerely, Neveruse513 / Talk / Block 20:31, 7 October 2009 (UTC) No, you ain't. It ticks all three boxes for fair use: not commercial, doesn't affect the value of the original work, used for one of the prescribed purposes ("commentary/criticism") --JeevesMkII The gentleman's gentleman at the other site 20:42, 7 October 2009 (UTC) Sorry NU513 but you don't need to slap a copyright notice on something to make it copyrightable. Copyright is automatically granted when it is created, published or broadcast. That personal diary which you write every night and hide in your lingerie drawer is copyright and can't be published without your consent even if you don't put a © in it. The same applies to any emails or letters you write while the copyright of the ones you receive still resides with the original author, not you as the receiver. It is only if the author or copyright owner explicitly grants a public domain or other free-to-use type of licence that it can be used with impunity. Conservapedia have a free to use license with a rider that they can withdraw it id they don't like what it is being used for. Unfortunately, once it is in the public domain then you can't claim it back. I support fair use but we have to follow the rules, so posting a transcript on its own is a no-no but with critical comment then it I see that as valid. ГенгисYou have the right to be offended; and I have the right to offend you. 20:58, 7 October 2009 (UTC) Who said anything about posting a transcript without commentary? About what I said concerning the copyright of a URL (if we're talking about the same thing - which I don't think we are), I don't think it's even possible. It's like copyrighting your mailing address. Sure, what's in the mailbox is subject to all sorts of laws and regulations, but the address can't be. — Sincerely, Neveruse513 / Talk / Block 21:01, 7 October 2009 (UTC) Well, Concerned Resident suggested just writing up transcript and perhaps I misunderstood your comment about the URL when you said "Plus, not a god damned thing about that url is copyrighted". No the URL itself is not copyrighted but any content on that page is copyrighted. So what do you plan to do with just the URL? Make anagrams? ГенгисYou have the right to be offended; and I have the right to offend you. 21:26, 7 October 2009 (UTC) CR suggested writing it up, but for the purpose of commentary (I presumed). I can't fathom not commenting, or uploading it for any other purpose. About the URL, I was defending posting the URL itself. True, any content on the page it points to is copyrighted, but none of that content is actually here. — Sincerely, Neveruse513 / Talk / Block 21:35, 7 October 2009 (UTC) How about paraphrasing what they said and writing it up in the form of a story? I mean if it is for critical analysis, doing this is pretty much what scholars do all the damn time. --Crazyswordsman 02:38, 8 October 2009 (UTC) Gentlemen, this isn't a pay-per-listen clip. Fox are streaming it for free on their website (you might have to pay for the whole show, but the interview with Andy is available. So nobody's being deprived of legitimate earnings by putting it here. Johann 11:44, 8 October 2009 (UTC) ### Non-negative review You know, it's easy to sneer, but I thought Andy actually did OK considering. The interviewer had him on the defensive, sure, but he made a lot of his main points and some listeners, not you people obviously, but some, might actually think there's something in what he's saying. Plus, credit where it's due, it took some courage to go on a programme that he must have known would be sceptical if not mocking of the whole enterprise.--C0n53rv4p3d14 r00l2 19:06, 7 October 2009 (UTC) Though I only saw the preview clip, I thought the interviewer wasn't really playing fair with the whole 'Where is Hell, if it's a spiritual place it doesn't exist' and Andy did quite well in comparison to his usual CP style. Broccoli 19:14, 7 October 2009 (UTC) I disagree. A good speaker should be able to deabte well, even in hostile situations, Andy looked like a complete idiot. I understand that he was on the defensive and was kinda attacked, but he just looked stupid... All bible translators voted for Obama... How do I know? Well, the bible is translated by professors, professors are all liberal, all liberals voted for Obama.... I WIN!!!!! SirChuckBA product of Affirmative Action 19:24, 7 October 2009 (UTC) Like I said, I haven't heard the whole thing. Also, Andy is not a good speaker at all and did better than I would have, and expected. Broccoli 19:31, 7 October 2009 (UTC) I have a mixed opinion on this interview. I agree with Roolz, in what Andy did surprisingly well. It was a very hostile interview and yet he managed to get most of his points across. Furthermore, it is very easy to mock the project when you announce that it's a "conservative" Bible, but harder to denounce its main points. On the surface, they look quite nice, and you have to dig a bit to uncover all the layers of crazy. That said, it may also be that constant exposure to the wackiness of conservapedia has somehow reduced my WTF level. This interview (and the part about liberals and professors) may well sound batshit crazy to a naive listener! --80.7.149.89 19:35, 7 October 2009 (UTC) Yeah, I was surprised Andy would dare go to liberaland. Anything for the cause, I suppose. He kept himself composed and took a few of Alan's jokes on the chin. In all honesty, I can see the logic of what Andy is trying to do, as poorly as he is executing it. A lot of people have run pretty wild with this to make it out to be something else. — Sincerely, Neveruse513 / Talk / Block 19:49, 7 October 2009 (UTC) To make it out to be something else? Andy is rewriting the Bible because he thinks it teaches economic truths and the groundbreaking 17th century KJV contains socialistic language. Now, I have little to no respect for "liberal" and feminist translations, as they strike me as exercises in incredible cognitive dissonance and rationalization, but this guy is just changing passages so that God agrees with him, allthewhile butchering the language and content. Edit: Need I mention that it's all based in his wingnut pseudolinguistics, where his magical conservative language illuminates biblical conservative concepts which only he can see (since, logically, they can't exist in the inferior greek, latin, hebrew books) 19:54, 7 October 2009 (UTC) But the actual idea that words have changed in meaning and new words could better reflect the original intent of the Bible isn't crazy. 'Free market parables' is though. Broccoli 20:00, 7 October 2009 (UTC) Absolutely true, and that's the basis of most all translations. But Andy isn't looking at original intent, since he can't possibly read the originals. 20:02, 7 October 2009 (UTC) More importantly, some of the passages he mentions are legitimately disputed. And yes, they are some of the ones that liberals love to cite. Not that it makes a difference, because Jesus seems pretty librul anyway. — Sincerely, Neveruse513 / Talk / Block 20:04, 7 October 2009 (UTC) So, think FOX is done with Andy?--Thanatos 20:33, 7 October 2009 (UTC) Nah, with the proper shade of rose-colored glasses, Andy did pretty well last time. — Sincerely, Neveruse513 / Talk / Block 20:42, 7 October 2009 (UTC) ## Waiting for the other shoe to drop I'm waiting for the other shoe to drop: pretty soon the media will be done with Andy's little pet project, and he will be clamoring for attention like he was after the Lenski affair. That, I think, is going to be funnier than all of this media buzz. I give it a week until everyone stops caring--I don't see how the Bible project will stay in the media for much longer. It would, however, be great if Andy makes it to the MSM before this thing blows over. Tetronian 21:52, 7 October 2009 (UTC) Andy on the Daily Show or Colbert would be perfect. ħuman 22:48, 7 October 2009 (UTC) Personally, I'd like to hear Thom Hartmann rip Andy apart. That'd be funny.Punky Your mental puke relief 22:50, 7 October 2009 (UTC) Andy on Colbert would be heavenly. Andy himself probably wouldn't know he was being parodied. Tetronian 22:53, 7 October 2009 (UTC) Well, as I've said, it's never going to happen, but AndyPandy being interviewed by Jeremy Paxman would be worth seeing. Come to think of it, AndyPandy being interviewed by Boris Johnson would also be deeply satisfying (trust me, Boris is a conservative through and through, yet is also one of the most educated, verbiose and clownish men you'll ever listen to).--AndyPandy - because paranoia and abject failure doesn't hold you back, although it should. 23:02, 7 October 2009 (UTC) Andy being interviewed by anyone that's not a right-wing nut would probably be entertaining. But yeah, Colbert would be amazing. I wonder if Colbert is even aware of Andy's existence. Anyway, here is my shameless plug for the latest Conservastan --Composure1 00:04, 8 October 2009 (UTC) Andy would never go on Colbert (despite how much we want to see the two of them in a fistfight). For me, O'Reilly is way to go. Bill calling Andy a pinhead and Andy telling Bill to open his mind. Andy, keep using those statistics during interviews!--Thanatos 01:59, 8 October 2009 (UTC) Lol, nice comic. I like Ed's hat. But an O'Reilly interview would be great. Of course, Andy wouldn't be able to bear being away from his precious Conservapedia for that long, even to promote his Bible project. Btw, if (and it is a very big if) he somehow does get an interview, what are the odds he ends up calling the interviewer a liberal? (Even on Fox News) Tetronian you're clueless 02:17, 8 October 2009 (UTC) Depends. The have to be right-wing yet reasonable. Hannity and Beck are out right away. They would gush and Beck would start contributing (a Beck version of the Book of Mormon). Someone harsh and would attack Andy as a far-right conservative nutjob is basically what we need, with a lot of viewers to spread the lulz.--Thanatos 02:52, 8 October 2009 (UTC) Agreed. Also we need to get Andy on a talk show where he would be socially awkward, like maybe The View. Tetronian you're clueless 13:04, 8 October 2009 (UTC) ## omigod (The Report tips its hat to CP) COLBERT that is all. ħuman 03:32, 8 October 2009 (UTC) Really? No kidding? RaoulDuke 03:35, 8 October 2009 (UTC) Adding Stephen Colbert to the conservative bible would be brilliant, but sadly won't last ten seconds. Z3rotalk 03:39, 8 October 2009 (UTC) Prepare for CP to be unreachable for the next 36 hours. Can an interview be next? Pleeeeeeease? PS, why do these people miss the Schlafly connection?! ħuman 03:44, 8 October 2009 (UTC) What and when? AceMcWicked 03:46, 8 October 2009 (UTC) Explain(503s already)--Thanatos 03:49, 8 October 2009 (UTC) Whaaaaa? Andy's going on Colbert? Zelmerszoetrop 03:51, 8 October 2009 (UTC) Didn't see it, but there's already been a user Colbertbomb123456 registered... --Lesjohn 03:52, 8 October 2009 (UTC) The intro was something along the lines of "does the Bible have a liberal bias", which made me jump. Tip of the hat to Conservapedia, some quotes of the project description, and a call to include Colbert as a Biblical figure. /spoilers ~ Kupochama[1][2] 03:53, 8 October 2009 (UTC) "503" What the hell? Is it the server load? I imagine more people are checking out CP than ever before, maybe they just can't handle it. Zelmerszoetrop 03:51, 8 October 2009 (UTC) Did you read the above? Colbert just told his viewers to go to CP and wreak havoc. The only time the place will be accessible now is when editing/account creation is turned off. ħuman 04:01, 8 October 2009 (UTC) The above didn't much sense however, bahahahaha, Andy is getting all he attention he craved! AceMcWicked 04:03, 8 October 2009 (UTC) Andy with attention is like a great writing team with a prime-time TV slot. Endless source of teh funny. When he has to leave CP and his fake doctor group he has to walk in the real world like back at talk.origins, and makes an utter ass of himself. ħuman 05:01, 8 October 2009 (UTC) MarkGall (Talk \| contribs) blocked Sixsixtysix (Talk \| contribs) with an expiry time of infinite (account creation disabled) (Please recreate your account with your real first name and last initial: just kidding! please leave forever!) I lolled. RaoulDuke 04:04, 8 October 2009 (UTC) Colbert being reported to the FBI in 3...2...1... Seriously, I can see it happening any moment now. -RedbackOMG, someone get the Raid! 04:37, 8 October 2009 (UTC) Moar: Should someone go over to the Colbert forums and tell them they might be reported to the FBI? I don't see why we can't at least warn them. Of course I'm working the night Colbert mentions Conservapedia on the air. Dammit.--EcheNegraMente You are everything you are nothing at all 04:44, 8 October 2009 (UTC) It gets repeated like six times over the next day. Also, someone linked above to what is probably the segment it will probably be available on line. ħuman 05:01, 8 October 2009 (UTC) To those in Australia, Colbert is starting on FoxTel right now and its carrying the story. Rad McCool 08:04, 8 October 2009 (UTC) Andy goes worldwide eh Andr.....Rad! AceMcWicked 09:05, 8 October 2009 (UTC) It does but it was a blink and you missed it segment. Rad McCool 09:07, 8 October 2009 (UTC) (arthurdent)Wikipedia protects its CP article due to "Colbert-inspired vandalism" [9] If you missed it, look on google. There's links on his page and on hulu. His change to the money lender story is good. - CodyH 11:59, 8 October 2009 (UTC) Conservapedia is #5 on Google trends. Sterile gas tank 12:13, 8 October 2009 (UTC) Does anybody know if that Colbert video is available anywhere besides the main website? They seem to have stopped streaming the videos for both the Colbert Report and the Daily Show to the UK...I need my colbert fix! Jammy 12:38, 8 October 2009 (UTC) @Rad - Damn it, why did you wait until after I was out of the hospital to mention that? I could have just suffered a little bit longer - at least TiVo'd it if nothing else. Wah! Now I need to wait until it's on the net. -RedbackOMG, someone get the Raid! 12:44, 8 October 2009 (UTC) Oh wait, I didn't see the latest wigo, I retract my "damn you" and replace it with a "why hello, good sir!" HOLY SHIT. Most amazing thing I have ever seen. Tetronian you're clueless 12:55, 8 October 2009 (UTC) @jammy - just use an American proxy - you can sort them by country on proxy.org. 13:01, 8 October 2009 (UTC) (unindent) Did anyone see Andy's message to Colbert viewers? He plastered it right up on the CP main page... Tetronian you're clueless 13:31, 8 October 2009 (UTC) That's pretty funny. Hey Andypants, I would like to read a bible , honestly I would. Unfortunately, I can't find one that's not full of liberal bias, can you help me? Heh. -RedbackOMG, someone get the Raid! 13:37, 8 October 2009 (UTC) Also look at Recent Changes - he's blocking people for "watching too much television." Tetronian you're clueless 13:44, 8 October 2009 (UTC) But wait, if Colbert viewers picked up any current Bible, wouldn't they be indoctrinated with all the liberal additions that have crept in over the years? --JeevesMkII The gentleman's gentleman at the other site 14:33, 8 October 2009 (UTC) You're right! no-one should read the Bible until the conservative version is finished and distributed to all churches. Totnesmartin 17:30, 8 October 2009 (UTC) Does anybody think that there's even a slight chance that somewhere in a dark corner of Andy's mind, the thought might be - "hell, the entire internet is laughing at me, maybe I should tone things down a bit." Or is this more likely to drive Andy to even greater excesses. I wonder what Mother S thinks about having the family name dragged through the librul media again. --PsygremlinTala! 17:38, 8 October 2009 (UTC) An online link doesn't appear to have been posted yet, so here it is. ГенгисYou have the right to be offended; and I have the right to offend you. 17:41, 8 October 2009 (UTC) I would say no, Andy has flippin' clue about who is laughing at him (apart from Colbert of course). And even if he did, I doubt he would care. Remember, the MSM is a bunch of deceitful libruls that no one listens to, and you can count on Fox to set you free with the truth. Tetronian you're clueless 20:49, 8 October 2009 (UTC) (ui) Did anybody else notice when Colbert used the term "liberal claptrap?" Corry 00:24, 9 October 2009 (UTC) How could you miss it? I was wondering about that actually; is that a common term, or did someone working for Colbert actually peruse the site enough to see it somewhere? I've never heard it outside of CP.EcheNegraMente You are everything you are nothing at all 00:36, 9 October 2009 (UTC) I haven't either, but Colbert is very good at spoofing conservatives, so he might have heard it elsewhere. Tetronian you're clueless 00:44, 9 October 2009 (UTC) ## CONGRATULATIONS JINX!!! To help stem the recent influx of reality into CP, JINX HAS GOT HIS BLOCK RIGHTS BACK!! (No link yet because the site keeps going down). Woooooooo! CONGRATULATIONS JINXY BOY -- Kriss AkabusiAAAWOOOGAAAR!!1 12:30, 8 October 2009 (UTC) Way to go Jinx hi Jinx!! Tetronian you're clueless 12:57, 8 October 2009 (UTC) [[Image:Partytime.png\|thumb\|200px\|left\|Congratulations {{jinx}}!!!!!]] 13:03, 8 October 2009 (UTC) I like how all the other demotees got a "well deserved" but Jinxy only got a stony silence. Perhaps the inquiry only returned a murky "not proven" verdict on master McHue's parodist status? --JeevesMkII The gentleman's gentleman at the other site 13:05, 8 October 2009 (UTC) I wish I could see Jinx hi Jinx!'s horrified expression after viewing Nutty's picture, lol. Tetronian you're clueless 13:21, 8 October 2009 (UTC) Too many dancing bananas!-- Kriss AkabusiAAAWOOOGAAAR!!1 13:29, 8 October 2009 (UTC) I'm gay, and even I didn't enjoy seeing that. Well done to Jinxypoos, enjoy your new/old power to silence those who disagree with you - also known as the power of "la la la, I can't hear you!" -RedbackOMG, someone get the Raid! 13:45, 8 October 2009 (UTC) You don't need block rights to get that power, but yeah, have fun Jinxie. Tetronian you're clueless 13:54, 8 October 2009 (UTC) Erm. Why the cocks? StarFish 14:05, 8 October 2009 (UTC) Another cock! Because we had a very low spending limit and it was all we could afford. -RedbackOMG, someone get the Raid! 14:20, 8 October 2009 (UTC) Heh heh heh. Also ew. Tetronian you're clueless 15:13, 8 October 2009 (UTC) jinx only received his banhammer back because of the rash of new accounts being formed cos of colbert. andy might take it back away when teh flood waters recede. Zelmerszoetrop 17:05, 8 October 2009 (UTC) You're forgetting Andy's limited attention span, he may well forget it ever happened. All Jinxy has to do is stay out of trouble and he should be ok. Totnesmartin 17:28, 8 October 2009 (UTC) @StarFish - because Jinx has a well-known cock bias. 17:22, 8 October 2009 (UTC) Dude! NSFW NSFW!!!! Stile4aly 17:09, 8 October 2009 (UTC) ## Faux News ad Isn't that the ad where the picture was taken from CNN's news tower? Tetronian you're clueless 15:24, 8 October 2009 (UTC) I thought it might have been from a slightly different angle. I'm sure Fox had a tower...it was their protest, after all. — Sincerely, Neveruse513 / Talk / Block 17:29, 8 October 2009 (UTC) No, CNN stole that footage from the trusworthy Fox News, but the liberal media just don't want you to know that Fox is the truth. Just Like the Conservative Bible Project will be the truth once it is published in lieu of the liberal King James Version. You liberals and your deceit are what cause people to think Fox stole footage from CNN when it was the other way around.Conservative Punk 22:15, 8 October 2009 (UTC) ## Where is the religious reaction to the gospel according to Schlafly? Since the Arsefly has once again shown that no stupidity is bad publicity, has anyone seen what any religious figures have to say about the conservative bible project? One would have thought they'd be lining up to beat him with the ceremonial clue crosier, but I haven't seen anything as yet. One can only hope the priest of Schlafly's regular house of worship is a regular Colbert report watcher, and will deliver a stirring sermon this Sunday about the Hubris of twisting religion to meet your own expectations. --JeevesMkII The gentleman's gentleman at the other site 17:49, 8 October 2009 (UTC) Real theologians will not touch this for the same reason that real scientists do not touch creationism. ListenerXTalkerX 17:52, 8 October 2009 (UTC) Here's a (Baptist) Professor of OT criticising the project. €₳$£ΘĪÐMethinks it is a Weasel 17:54, 8 October 2009 (UTC) Well, the AFA has just done an article on this (if you don't know about the AFA they are arch-conservative). Have a look at the comments left, and if you think liberal vandals then you are in for a shock, all comments are moderated and liberals or new commentators rarely have thier comments published.--AndyPandy - because paranoia and abject failure doesn't hold you back, although it should. 17:58, 8 October 2009 (UTC) Fred Clark is a Christian, though an admittedly liberal one. You should definitely read his take on it, but here's a choice pull-quote: "It's ridiculous and extreme and brazenly blasphemous and colossally illiterate, but this is the future of the religious right." --Arcan ¡ollǝɥ 18:28, 8 October 2009 (UTC) I don't know about the religious right, but the netroots have responded with the lolcat Bible.--Tom Moorefiat justitia 05:17, 9 October 2009 (UTC) Hate to rain on your parade, but the lolcat bible has been up for a few years now. - π 05:33, 9 October 2009 (UTC) Pi stole my thunder, but if you like that and are a programmer you might like [10] YorickIs Joe Biden Eva Braun? 05:37, 9 October 2009 (UTC) Tee hee, I like their version of Hello world!. Is there no language in existence that can't be explained with a HW script? Thanks very much for linking that, it already has a place in my bookmarks menu. -RedbackOMG, someone get the Raid! 05:50, 9 October 2009 (UTC) ## Liberal Pharisees I love it. First of all Andy ponders having the "intellectuals" be behind the killing of Jeshua, now he's just gone the whole hog and will blame it on Liberals. It's clear the idiot doesn't even have a clue what a Pharisee was. Once again Andy manages - all on his own - make a complete stuff-up of yet another project. --PsygremlinSermā! 18:06, 8 October 2009 (UTC) Are liberals the new Jews then? First they came for the environmentalists, but I did not speak out because I drive an SUV.... --JeevesMkII The gentleman's gentleman at the other site 18:08, 8 October 2009 (UTC) Jewish high priests are now Liberals? Well, Shalom to you my friends, pass the Bagels. SirChuckBA product of Affirmative Action 18:12, 8 October 2009 (UTC) The Pharisees were liberals when compared with the Sadducees, who were such law-and-order types that the anniversary of their downfall was celebrated annually. ListenerXTalkerX 18:18, 8 October 2009 (UTC) But what Andypandy's doing is comparing a sect to a mindset. Next thing he'll be renaming the Catholic Church (or more likely the Holy Rollers) the Conservative Church and the Anglicans will become Liberals. After all, in Andyland, it's all black and white, no grey anywhere. --Psygremlin말하십시오 18:25, 8 October 2009 (UTC) There's no way Andypandy will ever call the Catholic Church the Conservative Church. After all they hold ultra-liberal views such as social justice and opposition to capital punishment, plus, of course, they repeatedly and deliberately refuse to move the seat of the Catholic Church to the United States which must mean that they are liberal as they deliberately choose to live in Liberal European Vatican City.--AndyPandy - because paranoia and abject failure doesn't hold you back, although it should. 20:10, 8 October 2009 (UTC) Then Andy should just start his own church and call it the Conservative Church. Right next to the cross on the altar he can put a picture of Reagan. Of course, he'll have to watch out for parodists... Tetronian you're clueless 20:46, 8 October 2009 (UTC) Eh, why not cut out the middle man and promote saint Ronnie to deity? --JeevesMkII The gentleman's gentleman at the other site 20:49, 8 October 2009 (UTC) I can see Andy now: "Hmm, I think this sentence translates to "tear down this wall." Tetronian you're clueless 20:51, 8 October 2009 (UTC) I love how this is actually entering media: Salon notes that their parody couldn't match the true crazy[11] 21:35, 8 October 2009 (UTC) Publius, who says the particular crazy they talk about in that article is true? ## Conservative Bible Project talk page Has anyone seen this? It's like the Lenski talk page all over again. I've yet to see any blatant censorship, but it's basically the same typical Andyish justifications. Very amusing. Tetronian you're clueless 20:57, 8 October 2009 (UTC) I've been checking that page every day. Broccoli 21:03, 8 October 2009 (UTC) Well yeah, I know there are a bunch of WIGOs about it, but I mean the page as a whole is pretty damn funny. And 12,000+ views! The page is growing rapidly! Tetronian you're clueless 21:05, 8 October 2009 (UTC) My "favourite" part is the whole slavery bit. The Arsefly seems genuinely unable to see how horribly immoral it is for one human being to own another. He seems to think modern revulsion of slavery is purely the racism factor. I wonder if he thinks it's OK to own someone, as long as they're white. I guess just another example of how fundamentalist religion warps your brain. If you are forced to defend injustice as divine righteousness, then you get in these warped patterns of thought. --JeevesMkII The gentleman's gentleman at the other site 21:22, 8 October 2009 (UTC) Warped doesn't even begin to describe it. He actually thinks that he is preserving the original intent of whoever wrote the Bible. Can anyone really be that thick? Tetronian you're clueless 21:31, 8 October 2009 (UTC) "Every day is a new revelation in this project. Actually it's a dozen new revelations." Yes, and we thank you for the entertainment, Andy. And, yeah, Andy on slavery is just weird and creepy. ħuman 21:32, 8 October 2009 (UTC) Weird and creepy, but not surprising. Actually, it's typical apologetics: find something horribly troubling in the bible, and assuming a priori that the bible is not only true but good, sleaze your way to a poorly cobbled together workaround. Viola! Inerrancy is maintained. Corry 00:34, 9 October 2009 (UTC) Jesus must be facepalming and Buddha must be laughing his ass off. The FSM and Cthulhu are placing bets how long this will last--Thanatos 01:08, 9 October 2009 (UTC) I love the beginning of the page with Addison nearly calling Andy on his shit and even suggesting that conservatism may not be compatible with Christianity.--EcheNegraMente You are everything you are nothing at all 01:55, 9 October 2009 (UTC) ## Gay Penguins So apparently some kind of blogger wrote a spoof mocking liberal activist Wayne Besen [12], and conservapedia sysops jump on that like starving dogs on a bone, genuinely believing these are the rantings of an actual homosexual activist...man, do I love these guys! --Ireon 13:58, 4 October 2009 (UTC) I guess they got confused because his satire isn't much different from his usual rants: "Make no mistake; the sin of homosexuality is the bunker-buster bomb in this war against morality." --Sid 14:38, 4 October 2009 (UTC) Let's not forget that Evilution predicts that all animals will be gay always. The Darwinists will be running for cover from the non-gay penguin that topples the evolutionary paradigm and proves the creation paradigm that the grand canyon formed in a few non-gay hours. Kalliumtalk 14:51, 4 October 2009 (UTC) True, but what really blows my mind is that Kendoll appears to BELIEVE the quotes are from an activist homosexual... One who would say "Harry's as gay today as he's ever been. Mark my words. It's just a matter of time until he ends up slinking around some back alley gay bar in the Castro District, strung out on meth.". Poe's Law indeed.--Ireon 14:52, 4 October 2009 (UTC) I thought that looked suspicious. A gay penguin flap was the plot of the first episode of that Amy Pollard show, 'Parks and Recreation.' Czolgolz 13:30, 5 October 2009 (UTC) ### Gay swans Andy won't like this, these swans are satannic black, gay and unchivalrous! I suppose Andy thinks God made them that way. Proxima Centauri 12:29, 8 October 2009 (UTC) Natural selection made the swans that way, they rear cygnets that one or both have fathered and their cygnets tend to survive. Proxima Centauri 08:14, 9 October 2009 (UTC) ## What is happening with cp traffic? Alexa shows a lazy trajectory even with the media attention, and quantcast seems to think they died in the end of august and gave up on statistics about them, any ideas? --129.19.139.172 14:32, 6 October 2009 (UTC) Alexa lags a few days behind, and the Diggrush etc. pretty much started yesterday? ħuman 19:29, 6 October 2009 (UTC) I wonder if RW traffic will increase as well? Tetronian 21:03, 6 October 2009 (UTC) We got a few after the Cracked article, so a few people should drift our way. Keep an eye on RationalWiki:How I found RationalWiki to see if this brought anyone here, perhaps? Totnesmartin 17:16, 7 October 2009 (UTC) Alexa tends to update on Thursdays. Last week it was about as high as the Cracked article. After Colbert I actual expect to see this as CP largest ever spike in traffic, in a few weeks it will probably drop back around 65,000. - π 08:38, 9 October 2009 (UTC) I'm not suprised at the number of hits CP is getting, YouTube insight says my vids (link in case someone hasn't seen them) have gotten a larger number of views over the last few days. Not an incredibly high number, but larger than average. For some reason, the top vid is still the Lenski Affair, probably because it's the top result for Conservapedia. With any luck it'll have a carry-on effect, as I always place this site's address somewhere in my vids and the description. If people see my vids and decide to come here and laugh at CP, that's great - if they decide to stay and contribute, that's just gravy. GreatAtheismo 08:55, 9 October 2009 (UTC) ## Fretful porpentine It's good to see him out and about. EddyP 14:41, 6 October 2009 (UTC) Not me, sadly. Fretfulporpentine 12:29, 9 October 2009 (UTC) Whoever he is, he's doing well. He's got Andy eating out of his hand. StarFish 15:50, 6 October 2009 (UTC) Are you kidding? A bot that automatically blocks liberals? I bet Andy would give one of his children for such a thing. Z3rotalk 16:07, 6 October 2009 (UTC) ## Daniel1212 roundly pwns Assfly For some reason, Andy takes Daniel's exegesis out of archive to dismissively respond. Funny, considering Daniel runs circles around Andy biblically. He tears apart Andy's armchair exegesis one by one. Andy really doesn't like to be proven wrong (I know!), so he's being extremely rude ("WAAHHH!!! This is supposed to be easy...and concise!!"). It's very funny. I think I'm feeling a parthian from Daniel coming on. — Sincerely, Neveruse513 / Talk / Block 02:04, 9 October 2009 (UTC) I love how Andy responds to his huge block comment with a few sentences, and then ends by saying "go fuck yourself Godspeed." You're right, there's no way Daniel's patience is going to last much longer. Tetronian you're clueless 02:12, 9 October 2009 (UTC) It reminds me of PJR, who thumbs his nose at any sort of organized theology in favor of picking up a Bible and reading it, acting as if the meaning is obvious. ListenerXTalkerX 02:29, 9 October 2009 (UTC) Well, that depends on what you mean by meaning. Though I would think that the meaning of meaning that you mean is OBVIOUS to everyone. HumanisticJones 12:43, 9 October 2009 (UTC) Glad to see you're back. — Sincerely, Neveruse513 / Talk / Block 02:43, 9 October 2009 (UTC) As this goes on, I suspect more and more Cthulhudiddit--Thanatos 02:52, 9 October 2009 (UTC) Well, someone's a smarmy bastard, aren't they? I can't remember, is Jacob a homeschooler or a parodist? --Arcan ¡ollǝɥ 06:53, 9 October 2009 (UTC) And we are supposed to keep track of that? Isn't that TK's job? ħuman 07:37, 9 October 2009 (UTC) (UD) Andy reminds me of senior management, straight out of Dilbert but also in the real world a well. Really he wants everything presented as Powerpoint slides with no more than three bullet points each, otherwise he can't comprehend the message. If an argument can be put in just one sentence the most likely it is just sloganeering and is pretty much what Andy does himself all the time. He can't sit down, read a piece, comprehend the nuances of the arguments and draw up a rebuttal. Which is why his amicus curae briefs are so crap. His desire for conciseness is really some sort of attention deficit disorder. The more I know about this guy, the more disdain I have for him. ГенгисYou have the right to be offended; and I have the right to offend you. 09:47, 9 October 2009 (UTC) Nice comparison. You were thinking of something like this? Replace "technical jargon" with "liberal claptrap" and we have a perfect match! -RedbackOMG, someone get the Raid! 12:58, 9 October 2009 (UTC) That's certainly the sort of thing I was thinking of. Nice find, I don't remember that one but my memory isn't ... To be fair, Daniel does go on a bit, and Jacob's response is priceless. All we need now is for Andy to change the title to "Another liberal rant".-- Kriss AkabusiAAAWOOOGAAAR!!1 10:01, 9 October 2009 (UTC) To be fair, it is a subject worth going on about (to a Christian, let alone a Biblical scholar). Andy's intellectual laziness is priceless. — Sincerely, Neveruse513 / Talk / Block 12:54, 9 October 2009 (UTC) ## Schlafly citation challenge I'll give 1000% internets to the user who is able to determine the last time Andrew Schlafly actually cited the Bible in a talk page response. — Sincerely, Neveruse513 / Talk / Block 02:12, 9 October 2009 (UTC) Can someone help with a script to process a user's contribution lists? It'd be really easy to make (a fucking ugly beast of) a regex to find a bible citation. I'd really like to figure out how often Pope Andy uses the bible. — Sincerely, Neveruse513 / Talk / Block 02:17, 9 October 2009 (UTC) I win! From the archived Conservapedia Bible Project talk page: "Language is never 100% precise. Sometimes it is obvious what was meant, despite the inartful articulation provided by the best terminology available. Mark 6:22 has an example of this, and we improved on the Greek word for "girl". See Gospel of Mark (Translated).--Andy Schlafly 23:31, 5 October 2009 (EDT)" Ha ha! Tetronian you're clueless 02:24, 9 October 2009 (UTC) Well, that was anti-climactic. tosses half-baked script in the trash, hands over the internets to Tetronian, grabs coat, leaves — Sincerely, Neveruse513 / Talk / Block 02:30, 9 October 2009 (UTC) Really this ought to be a part of the liberalism formula... hasn't Andy criticized people for not citing the Bible enough? Maybe MarkGall will share his scripts with you... --Pyfgcr 02:31, 9 October 2009 (UTC) Actually, a Bible searching script isn't a bad idea (although I have no idea how to write one). And if MarkGall got wind of such an idea, the possibilities would be endless! With all the Colbert-inspired vandalism, I bet Andy us desperate for a way to stop wandals. (Hopefully desperate enough to try Mark's equation) But anyways, I have 1000 internets!! That's over 9000!! Ok, maybe not that many. Tetronian you're clueless 02:35, 9 October 2009 (UTC) I'm going to try and ignore the CBP, as it deals so directly with the subject of the Bible. I want to know, in the course of discussion, how often Andy really cites the Bible. I need the perl practice anyway... — Sincerely, Neveruse513 / Talk / Block 02:39, 9 October 2009 (UTC) Wouldn't a bot that just searched for anything in the format of x:x (with the x being a number) make finding bible citations fairly easy, since the only time anyone uses x:x is referring to a bible passage (at least, the x:x matches that aren't the bible are going to be fairly rare)? I hope my astonishing insight into making bots has been useful, because I'm going back to not knowing anything about any form of coding now. X Stickman 06:53, 9 October 2009 (UTC) REGEX matching-wise you could look for /[A-Z][a-z]+\s[0-9]+:[0-9]+(-[0-9])?/ This would match any string that started in a capitalized string and ends in number:number or optionally number:number-number. That should catch things like "Lev 11:9-12" or "John 3:16". HumanisticJones 12:49, 9 October 2009 (UTC) ## So who the hell is "Scott Schlafly" anyway? Where did they get that from? --127․0․0․1 10:26, 9 October 2009 (UTC) Scott of Conservapedia tried to build an encyclopaedia using only homskollars, and ended up freezing to death on the vast tundra of neglected blog while his rivals streaked past and were back at base camp enjoying bacon butties. --JeevesMkII The gentleman's gentleman at the other site 10:36, 9 October 2009 (UTC) And most importantly, are they really insinuating that getting Schlafly's name wrong was the only sin and biggest flaw in the article? If so, that's brilliant. --wwwwolf (barks/growls) 16:39, 9 October 2009 (UTC) I was thinking they may have got confused with one of his brothers, but there's not Scott anywhere. Obviously a crossed wire while rehashing the blogs. moral 16:50, 9 October 2009 (UTC) I just thought the funniest part of it was that Andy took that as proof that the article was full of librul deceit. It reminded me of him correcting people's spelling. Tetronian you're clueless 00:46, 10 October 2009 (UTC) Would have been funny if they confused Andy with his brother John.--Thanatos 02:09, 10 October 2009 (UTC) ## Massive WIGO breakdown The last dozen or so wigos have been numbered wrong. It is poll=wigo#### not poll=####. Could we please watch this in the future? - π 10:40, 9 October 2009 (UTC) Shit. That's partially my bad. Tetronian you're clueless 11:59, 9 October 2009 (UTC) ## wtf? [13]. What the hell does Jacob think he's doing? He's not going to last long with that kind of attitude. Zob 14:16, 9 October 2009 (UTC) Actually, hasty prosecution of Acorn is just the kind of thing that will earn him his stripes. — Sincerely, Neveruse513 / Talk / Block 14:19, 9 October 2009 (UTC) Oh, come on. There was far too much liberal-speak there: "I have [...]read what you said"? "I overreacted"? "I owe you an apology"!?!?!?? Someone has to put a stop to this madness. Zob 14:27, 9 October 2009 (UTC) Oh...that attitude. I am willing to open my mind and I owe you a lengthy ban. — Sincerely, Neveruse513 / Talk / Block 14:33, 9 October 2009 (UTC) ## I guess they really ARE having a meltdown over the Obama/Nobel news... When they use Al Jazeera instead of Newsbusters or Fox as their front-page headline source to question the reasoning behind the award. Way to embrace multiculturalism, Joaquin. --SpinyNorman 15:08, 9 October 2009 (UTC) Hellhell, it's better than WorldNutDaily. Tetronian you're clueless 15:15, 9 October 2009 (UTC) The committee has sole responsibility to decides who deserves it. If they chose him, then he deserves it as a matter of fact. Asking does he really deserve it is meaningless, because whoever is asking really isn't on the selection committee (and probably for a good reason). — Sincerely, Neveruse513 / Talk / Block 15:23, 9 October 2009 (UTC) What's the best they can hope for by saying "does he deserve the award?" For the Nobel Peace Prize to be revoked? That'd be a fucking sight. Nobel Committee Head: Gentlemen, I have bad news! Since awarding the Nobel Peace Price of 2009 to the current President of the United States of America, Barack HUSSEIN Obama, a two-bit, far right, Christian, conservative, American wiki-based website had the following to post on their Homepage "News Feed:" After less than a year in office does the US president deserve the award? Is the decision a clever political move by the Nobel committee? Will it help or hinder Obama's presidency? After these remarks, I move we strip Mr Hussein-Obama of his Prize and give it to a far more suitable candidate, such as George W Bush! I don't think so. SJ Debaser 16:03, 9 October 2009 (UTC) I don't know....even some rather prominent people are being critical. But I don't think it would be enough to merit taking it away. Tetronian you're clueless 19:22, 9 October 2009 (UTC) More salt rubbed into an already mortally wounded Assfly ego. After being elected Prez, I thought it would take Obama way longer to pwn Andy's shitty post-HLR career curve still further. But, nope, a motherfucking Nobel Peace Prize to add to the list just ten months in. Sweetness. :) --Robledo 19:18, 9 October 2009 (UTC) Hopefully that will mean more batshit crazy conspiracy theories about Obama (on CP), which will mean more controversy, which will mean many, many more lulz. Tetronian you're clueless 00:43, 10 October 2009 (UTC) I like TK's rewrite to the "news". Oodon 01:29, 10 October 2009 (UTC) ## Conservapedia web comic I stumbled upon a website that lets you easily make your own web comics and as an experiment made one about Conservapedia. The premise is that Andy is ruler of a fictional land called Conservastan. Unless I get very lazy I hope to make more, but here is the first one. --Composure1 02:54, 6 October 2009 (UTC) No no no, Andy is leader of Andyland, not this liberal "Conservastan" you speak of - sorry, just having fun. Well done, I quite enjoyed it. It has a pretty believable ending too, which is unfortunate but funny. -RedbackOMG, someone get the Raid! 03:26, 6 October 2009 (UTC) Nice work, I like it. --EcheNegraMente You are everything you are nothing at all 04:14, 6 October 2009 (UTC) Yes, good. But shouldn't "Andy come down for dinner" have a thought balloony series of dots indicating that it comes from Heaven above? ħuman 05:15, 6 October 2009 (UTC) Come to think of it, why are the speech bubbles coming out of his mouth? Everyone knows he talks out of his ass. Tetronian 20:48, 6 October 2009 (UTC) Why does Conservastan look like a mashup of Auckland and Wellington?Beastiepaws 00:23, 7 October 2009 (UTC) I second this query. You are implying that New Zealand, a nation which, if I remember correctly, has been IP blocked in its entirety, is Conservastan.WazzaHello? Is there anybody in there? Just nod if you can hear me... 16:05, 10 October 2009 (UTC) The Google automatic translation to Finnish is hilarious. This is the linguistic equivalent of uncanny valley: machine translation that actually looks like someone who has rudimentary knowledge of the language and is translating the stuff badly using a dictionary that doesn't show the words being used in real contexts. "Deep <Conservastan>'s presidential to palace" "Joaquin, how could you?" "This painting was made, a liberal!" "It is a gun - I thought it was healthy." "[it is] that the weapon is 'security' to initiate." "I am sorry, dear leader." "Andy! Go down <for dinner>" "sigh..." "[It is] coming, mother!" --wwwwolf (barks/growls) 20:49, 7 October 2009 (UTC) ## TK's got our goat! ONOZ!img --User:Theemperor/Sig 01:59, 9 October 2009 (UTC) Ha ha, "I know what to do with those." Can you WIGO it? Tetronian you're clueless 02:06, 9 October 2009 (UTC) Let's face it, it's not even "us", it's the Colbert Nation. They are wiki-savvy, and they are legion. ħuman 03:02, 9 October 2009 (UTC) But we have Ace... --User:Theemperor/Sig 03:08, 9 October 2009 (UTC) Yes, but he can't insert pickled sausage pictures where they belong on CP, he can only freak people out on RW who are at work... ħuman 07:43, 9 October 2009 (UTC) (ui) Is TK spoofing Andy with this? It seems like he's mocking Andy's style. Tetronian you're clueless 13:07, 9 October 2009 (UTC) Yeah, he is. TK's a parodist. The bloody best there ever was. He didn't say "get your goat" by accident, and starting a sentence with "It is a well known fact that liberals..." is just showing how stupid Andy is. SJ Debaser 20:38, 9 October 2009 (UTC) That prick is a blocking machine! I had a nice little account going, was slipping some good parody under the radar, then BANG!. Looks like I made the mistake of logging in from an IP address that had previously been blocked. Are there scripts that check for this, or does this little man sit there checking everyone's IP address? (Incidentally, they've not reverted any of my edits yet!) DeltaStar 13:08, 10 October 2009 (UTC) Typical. They still haven't reverted some of the edits that obvious parodists like Bugler and RodWeathers made. And right now Pope Andy is too busy to focus on anything but his precious little project. Tetronian you're clueless 13:44, 10 October 2009 (UTC) ## CBP mentioned on Jay Leno!! CBP was mentioned (briefly) on the Jay Leno Show. It was literally 8 minutes ago (the show just started, it was mentioned in the first 4 minutes.) After it ends, can someone try to find a link? (Also: countdown to CP response in 3...2...1... ) Tetronian you're clueless 02:14, 10 October 2009 (UTC) Wow, he is not three days late to the party or anything. No wonder everyone criticises Leno, he has a nightly show and he can only cover this a few days after Colbert. - π 02:23, 10 October 2009 (UTC) And it was right after a joke about South Carolina governor Mark Sanford. (paraphrase: they caught him doing 85 miles per hour on a 65 mph road, like the time they caught him doing 69 in Argentina...) Still, it's better than nothing. Tetronian you're clueless 02:28, 10 October 2009 (UTC) This summarises Leno's humour. - π 02:39, 10 October 2009 (UTC) I wonder if Andy is going to replace John as the untalked about member of the family.--Thanatos 02:30, 10 October 2009 (UTC) Oh, come now, you know they won't talk about John either... Stu the Foo' 02:36, 10 October 2009 (UTC) Andy and John are the only ones willing to show up to Phyllis' idiot convention. - π 02:39, 10 October 2009 (UTC) Just you wait 'til Roger gets his unabomber on, then we'll see who the black sheep really is. --JeevesMkII The gentleman's gentleman at the other site 07:31, 10 October 2009 (UTC) (ui) Here's the link! (It takes a while to load, though....) Tetronian you're clueless 13:40, 10 October 2009 (UTC) ## Conservapedia is picking up speed on YouTube! But not for the reasons they were hoping Sorry, I know I should be above posting YouTube vids "just coz dere funny lol" but, um... lol. What he does at the end is just priceless. Childish, but priceless. I wonder who (if anyone) monitors that address. hope this hasn't already been posted somewhere -RedbackOMG, someone get the Raid! 14:16, 10 October 2009 (UTC) I like this video better.Lord of the Goons The official spikey-haired skeptical punk 18:39, 10 October 2009 (UTC) This one is also really good.Punky Your mental puke relief 18:58, 10 October 2009 (UTC) ## It should be fun... .... to see Conservapedia's response to Barack Obama winning the Nobel Peace Prize. And actually, there's at least one valid point that can be made, and not from frothing Obama-hate -- it is far too early in Obama's career for a move like this. MDB 09:35, 9 October 2009 (UTC) The only thing more premature than this award is the clown who WIGOed it before Conservapedia had even said a word about it.-- Kriss AkabusiAAAWOOOGAAAR!!1 10:05, 9 October 2009 (UTC) No shit. It is 4 in the morning on the server clock, nobody that can edit the front page would be awake and we have a WIGO already. - π 10:13, 9 October 2009 (UTC) I actually like it.... It's kind of a before and after... We all know it's gonna happen, so we start the countdown and wait for the explosion to come. SirChuckBA product of Affirmative Action 10:20, 9 October 2009 (UTC) Never mind the Conservapedia reaction, my reaction was WTF? Shouldn't you get the nobel peace prize for what you've done rather than who you are? --JeevesMkII The gentleman's gentleman at the other site 10:31, 9 October 2009 (UTC) I'm not so concerned with whether he's 'earned' it but with the the fact that this may well make things more difficult for him back him the US, making the wingnuts even more nutty in the healthcare shouting match. I wouldn't be too surprised if Obama is rather wishing they hadn't picked him. Jammy 10:37, 9 October 2009 (UTC) Yeah, apart from the whole "why wigo when it hasn't even happened" thing, I also agree that it should not have been awarded to Obama. I mean, he hasn't really done anything to earn it (not from lack of effort or intention). Maybe it would have been a teeny bit more sensible to wait and see how his plans work out. If Andy throws a mental over this, I think it would be rather justified - and unless he really goes apeshit which is always a probability with Andy, I won't be joining in making fun of him about this issue. -RedbackOMG, someone get the Raid! 11:11, 9 October 2009 (UTC) Apparently it is ironic. How many wars has Obama started then? - π 11:13, 9 October 2009 (UTC) Started? None? Escalated/helped to expand beyond its borders? One. RaoulDuke 13:03, 9 October 2009 (UTC) Mh, well, at least Andy isn't pissing on anything new. The Nobel Prize has always been one of his targets (if I recall, because Gore won one and because this Hoyle fellow didn't win one or something). --Sid 12:14, 9 October 2009 (UTC) "The Nobel Prize is an often-politicized award that is criticized for increasing evidence of bias and possibly even corruption....As an unwritten rule, the award is not given to a conservative (such as Ronald Reagan or Pope John Paul II), and it is not given to anyone who challenges the scientific establishment on the issues of the theory of evolution or theory of relativity." Nothing new to add to that really. - π 12:18, 9 October 2009 (UTC) But simultaneously in Conservathink the fact that Einstein didn't get a Nobel Prize for Relativity proves that relativity = teh evil. Cantabrigian 12:34, 9 October 2009 (UTC) TK, darling, I... don't get the irony, sorry. Am I too tired to see it, or are you using big boy words without understanding their definition? Be careful, misuse of the word irony is more Ed's thing. Speaking of which, has Ed been around lately? I've been sort of in and out for the last few weeks; I haven't seen any creepy Uncle Ed rants pop up in wigo lately. That aside, I kinda have to agree, the Nobel is more of a political stunt than anything else. That doesn't mean former Nobel Prize holders weren't worthy, it just means that... well, if politics had nothing to do with Obama receiving it, I don't know what did. I mean, he hasn't done anything worth a Nobel yet - give him a bit more time and I trust that'll change. Ugh, I feel dirty now. -RedbackOMG, someone get the Raid! 12:38, 9 October 2009 (UTC) You don't get the irony because it's not ironic. TK's just a lying grievance collector who has to invent controversy to get lathered up about. He's admitted to me that some of his news posts are just lightning rods put out to draw unsuspecting fodder to the blocking block. This should have been ignored. 20:14, 9 October 2009 (UTC) Yeah, my reaction when I heard it on the radio last night was "what the fuck did he get it for?" I guess it's for promoting international diplomacy and working to reduce nuclear arms or something. Maybe it's just for not being King Bush II? ħuman 20:37, 9 October 2009 (UTC) Almost everyone I've spoken to has expressed the same opinion. According to the BBC web site Nobel Committee head Thorbjoern Jagland said: "It was because we would like to support what he is trying to achieve". To me that does seem quite a political stance but I suspect it's largely because of what he has replaced. ГенгисYou have the right to be offended; and I have the right to offend you. 21:15, 9 October 2009 (UTC) Orwell was right about memory. Please to read his Cairo speech in full and then tell me he's not worthy of this year's prize. --Robledo 22:50, 9 October 2009 (UTC) I suppose (if I were Andy) I would argue that the speech in question hasn't led to anything monumental. (It is a damn good speech though, which of course Andy would never, ever admit.) Tetronian you're clueless 00:52, 10 October 2009 (UTC) Yes, a great speech - among several other great speeches (we host the text of one here on this site, the one about race in America). But truly "great" speeches are measured in hindsight by the results achieved. ħuman 01:14, 10 October 2009 (UTC) ONE SPEECH? A speech that has led to no real changes in policy? Instead of speeches, let's count Afghani and Pakistani civilians killed in aerial bombardments (152 in the first three months of the Obama administration according to one Pakistani news source). Let's count men held in indefinite detention at the Baghram air base in Afghanistan. This award is total bullshit. RaoulDuke 01:00, 10 October 2009 (UTC) Besides that, the speech doesn't count--it came months after nominations were closed. One doesn't get nominated for a prize for something that hasn't happened. RaoulDuke 01:07, 10 October 2009 (UTC) Yes, but the judging was done recently, and would include it. ħuman 01:14, 10 October 2009 (UTC) The Nobel Prize vote is usually conducted on the day or the day before it is announced. Last year a stalemate pushed the literature prize announcement back nearly a week. As for nominations, our own article shows that nearly anyone can be nominated including such luminaries as Stalin, Mussolini and Rush Limbaugh. What actually is important is the vote and that took place this week. - π 01:22, 10 October 2009 (UTC) Actually once nominated you can never be unnominated, for all we know he may have been nominated 2 or 3 years ago. - π 01:26, 10 October 2009 (UTC) Maybe all of the other nominees were just absolutely terrible.X Stickman 10:52, 10 October 2009 (UTC) I'm not even sure who the other nominees were, except for Morgan Tsvangirai and I was kinda rooting for him. We had a commentator on the radio here saying Obama won it for aspirational purposes, rather than for actual achievements. Still came as a huge surprise though. Andy must be having kittens. No doubt in his mind, if he'd been HLR Pres, then he would be US Pres and a Nobel laureate today, instead of lurking in some dingy church basement. --PsygremlinParla! 11:41, 10 October 2009 (UTC) According to the nobel prize site, "The names of the nominees and other information about the nominations cannot be revealed until 50 years later." I didn't know that. Anyway, I wonder if Andy really is taking this personally somehow. Poor dear. X Stickman 14:27, 10 October 2009 (UTC) I gotta say; elected in (late) January and nominated by the end of the same month. Wow. In effect he got the prize for winning an election. I can imagine previous recipients demoting theirs from the pool room to the throne room. Tricksy 01:42, 12 October 2009 (UTC) He potentially could have been nominated 20 years ago when he was a community organiser in Chicago for all we know. How about instead of running your mouth you find out how the actual process works? Also, I suspect you are being metaphoric and trying to show how aussie you are with the now done to death pool room line (I hate that fucking movie now everyone discovered it about 5 years later), but I doubt any one leave a 200 gram chunk of gold lying around their house - π 02:04, 12 October 2009 (UTC) Wow, hair trigger. Yes I suppose he could have, but the committee chose to mention "international diplomacy", so I was assuming it was a recent nomination. I don't know how on earth some suspects someone else of being metaphoric. Nevertheless, the only reason the line worked in the movie (which was still not well known the first time I saw it, btw) is because it is a real line. I admit that I aimed my phrasing at the Aussies here, but what of it? I was in fact toning down my instinctive occerism a little, for which you seem to be accusing me of being faux-Aussie (and "throne room" flowed better than "dunny" anyway). (I do recall reading somewhere that Qld as a state retains more "occerisms" in normal usage than NSW and VIC, but I thought that WA and SA did as well). I was simply expressing my thought that if the Peace Prize can be awarded for not actually achieving anything (yet) then other recipients could well see their own prizes as having less value - thus the metaphor (yes metaphor, but what else would it be?) of moving it from publicly displayed with pride to somewhere not much short of putting it away altogether. I am not, by the way, faulting Obama for this. He didn't award himself the prize, and I think his self-deprecation in this respect is come by honestly. Tricksy 02:57, 12 October 2009 (UTC) For some fullblown mock-Aussie, here is an occerisation of said previous recipients imagined reaction. "Sufferin dooley, I was flat out like a lizard drinkin for years before I got one, and I thought it was better than a poke in the eye with a sharp stick, but if a bloke can get one just for bumpin his gums then I reckon it's about as much use to me as a bucket under a bull and I'll chuck it in the long grass." Tricksy 03:08, 12 October 2009 (UTC) (EC)Whilst I am baffled by Obama receiving the award myself, the "twelve day" Republican party convenient lie talking point is starting to shit me of because it is a simplification of the process in an attempt to discredit Obama. We don't speak Ocker where I live, we prefer English. - π 03:12, 12 October 2009 (UTC) Sorry, I am not aware of the "12 day talking point", but on the face of it I assume it means the period from the US election to PP close of nominations. I can see why you would think I was repeating that, but I was not. I think I already addressed the point about dicrediting Obama, but to be clear; I was criticising the prize committee, not Obama. Although now I am curious about when he was nominated and who nominated him. Some friends of ours moved from our city to yours, and when we went for a visit they did comment on getting a little bit of a reaction to their choice of slang (not a big reaction, just a sort of "do people really stay that?" kind of thing). Although nobody I know would string so much together as in my example, any one of those phrases could be used in casual conversation without being greatly noticed (even 2 or maybe 3 in a sentence if someone was a little bit "exercised"), and I do have one or two friends who would come close to that sentence above when they get worked up. Oh well, I believe even other Aussies consider us Queenslanders a little odd. Come the secession, none of it will matter. Tricksy 03:35, 12 October 2009 (UTC) I am not an Aussie and I know Queenslanders are weird, queer looking folks. AceMcWicked 03:36, 12 October 2009 (UTC) Aah, speaking of mock-Aussies how goes the land of the long white cloud? :) We had the big red cloud a couple of weeks ago. Weird fact - our constitution lists NZ as a state of the Australian Federation. Apparently any time NZ wants to join up, you can. No need to ask permission of anyone but New Zealenders. I thought the constitution thing was a bit condescending, but actually it's empowering. It's like a country being able to join the EU without applying (not that I am saying we are like the EU). Tricksy 04:11, 12 October 2009 (UTC) Queensland is Australia's equivalent to the South in so many ways. - π 03:52, 12 October 2009 (UTC) Yeah. Better climate, better food, better looking. Tricksy 04:11, 12 October 2009 (UTC) He was referring to the U.S. South, which is altogether too hot, swarming with alligators and mosquitoes, and has more than its share of inbred hillbillies, voodoo practitioners, and creationists. ListenerXTalkerX 04:26, 12 October 2009 (UTC) Replace alligators with crocodiles, hillbillies with bogans and do away with the voodoo business and yer, that's pretty much it. -RedbackOMG, someone get the Raid! 04:32, 12 October 2009 (UTC) Replace voodoo with astrologers. The Gold Coast is basically mini-Miami, full of old people and drunk barely legals once a year. - π 04:36, 12 October 2009 (UTC) ## shut up and depart from him http://conservapedia.com/Mark_1-8_(Translated) Mark 1:25: "Jesus then rebuked the evil spirit, "Shut up and depart from him." Come on, they missed a wonderful opportunity to use powerful new conservative words. This should be translated: "Jesus Christ (Talk \| contribs) blocked Evil Spirit (Talk \| contribs) with an expiry time of 5 years (account creation disabled) (Vandalism / Liberal vandalism. Bye!)" Secret Squirrel 13:50, 10 October 2009 (UTC) I think this is about the first time I remember seeing you make a CP related post and it is by far the most sublimely funny thing posted on this page. - π 13:54, 10 October 2009 (UTC) Oh I make a CP related post now and then... Secret Squirrel 13:57, 10 October 2009 (UTC) I smell a LOLcat Bible type spoof of the CP Bible coming soon. Just a hunch. :) Secret Squirrel 14:07, 10 October 2009 (UTC) We could start a "Rational Bible Project"...just make it redirect to the atheism article. Tetronian you're clueless 14:12, 10 October 2009 (UTC) Rational Bible Project might be fun, but there's already the S.A.B. where most of the hard work has been done. Who had the decent parody one again? moral 11:31, 11 October 2009 (UTC) A project of that scope would probably get about as far as Andy's version is going to. Sure, Mark and Philemon are easy, but let's see him wade through the Pentateuch. He'll have a blast with Leviticus, if he ever gets past the instructions for the tabernacle in Exodus. Corry 14:45, 11 October 2009 (UTC) That was my Torah portion for my bar mitzvah! I can still chant it in Hebrew. If only I had chanted it in Conservative. Oh the places I would have gone. 03:15, 12 October 2009 (UTC) ## Not WIGO-worthy, but... ...I found this very amusing for several reasons. First, the article in question is the first I've seen that does not blatantly portray Andy as a complete nutjob (other than those written by fundie loons, of course). They even gave him an interview. Second, Andy admits that he is "without sin," which I never would have expected. And finally, I can imagine him smirking as he plasters this up on the main page. Tetronian you're clueless 13:55, 10 October 2009 (UTC) "We're not without sin". - π 14:03, 10 October 2009 (UTC) Isn't that a double negative? Also, there already is a wiki without sin. Oodon 18:11, 10 October 2009 (UTC) Oh, whoops, I meant "not without sin." But what is the wiki without sin? Tetronian you're clueless 18:19, 10 October 2009 (UTC) I can't tell you yet... because it doesn't even have 100 articles yet. But it is without sin because everything is on lockdown... all the time! Oh, and there's only one user too. Oodon 05:19, 11 October 2009 (UTC) What's so unusual about Andy saying he's without sin? That's standard Christian belief. Totnesmartin 09:30, 11 October 2009 (UTC) The Christian position is that no one is without sin... ListenerXTalkerX 03:29, 12 October 2009 (UTC) ## A proposal A complete moratorium on WIGOs based entirely on the actions of un-noteworthy editors who have not been endorsed by Andy. For example, take the homeschoolers WIGO; it's by an unknown guy who has no rights; he could easily be pissing around. Someone making an account and saying something stupid isn't funny; what is funny is when the Assfly goes "BRILLIANT IDEA!!!". So I say no more WIGOs involving new editors saying stupid things until the fly himself endorses them. EddyP 14:48, 11 October 2009 (UTC) That is usual policy; I think people are getting too excited about the Bible Project, and are WIGOing anything related to it. Broccoli 15:11, 11 October 2009 (UTC) Yeah, anything that comes from a user with a red name or red talk page link gets an instant -1 from me. I think most regulars understand that redlinks are usually newbies or parodists, and don't usually represent the Andychrist's views. Probably just as well you brought it up, people (and newcomers, who are also a type of people) are just getting a bit carried away with the extraordinarily large amount of crazy that's going on at the moment and could do with a reminder. -RedbackOMG, someone get the Raid! 15:19, 11 October 2009 (UTC) Sounds like a good plan. Tetronian you're clueless 15:58, 11 October 2009 (UTC) I agree with all of the above. Anyway, it looks like this WIGO is being voted down, so the system works. --Ireon 17:26, 11 October 2009 (UTC) Agreed. That being said, if Andy ends up agreeing that "homeschooler" is an appropriate replacement for "disciple", I might not stop laughing for the rest of the day.--EcheNegraMente You are everything you are nothing at all 17:35, 11 October 2009 (UTC) I think the proposed moratorium is already covered by our guideline not to out parody. ListenerXTalkerX 17:41, 11 October 2009 (UTC) In his response to the "homeschoolers = disciples" comment, Andy says that translating the bible is "not hard". I found this more amusing than the original wigo. X Stickman 21:43, 11 October 2009 (UTC) A random Aschlafly edit would probably have been funnier than the "original wigo". ħuman 00:26, 12 October 2009 (UTC) ## Colbert's influx new accounts created at CP larronsicut fur in nocte 15:22, 11 October 2009 (UTC) The 9th has low account creation as account creation was shut off for a majority of the day. Aboriginal Noise with 4 M's and a silent Q 15:38, 11 October 2009 (UTC) Interesting that only slightly more than half of the accounts have been blocked. Hopefully there are many potential parodists... Tetronian you're clueless 17:35, 11 October 2009 (UTC) Can you whip up a version of that showing the week previous to the Nation's call to battle? ħuman 00:42, 12 October 2009 (UTC) new accounts at CP Something like this? larronsicut fur in nocte 05:55, 12 October 2009 (UTC) Nice, thank you. It makes it all clearer. Thank you again! ħuman 06:02, 12 October 2009 (UTC) ## Econ homework Re: "(because 10+8+5+6+5 =/= 10+8+6+5+5)", doesn't the activity's reward reset? That is, the third hour of hiking in a row is only 5 points, but if it comes after a two hour reading break, it ought to be good for more? Of course, then the best course would score 10+8+6+10+8 = 42! (2 two hour hikes separated by one hour of reading porn). Maybe I'd better go re-read the question... ħuman 20:41, 11 October 2009 (UTC) ## Charity and Free Market: WTF? Could someone please enlighten me on this one? The student's answer exposed by the wigo is scary, scary stuff. But I can not make sense of the question itself anyway, and the model answers here are just baffling, not to mention mutually exclusive. So, what is exactly Andy's point? --Ireon 18:02, 11 October 2009 (UTC) See cp:Liberals and uncharitableness. ListenerXTalkerX 18:04, 11 October 2009 (UTC) Thanks for the read, but it's more a general statement about liberals and uncharitableness, no mention of free market there. Has Andy tried to explain himself? BTW, great job on the wigo.--Ireon 18:15, 11 October 2009 (UTC) He thinks that "liberal" and "socialist" are synonyms. ListenerXTalkerX 18:18, 11 October 2009 (UTC) Of course, but to put that as a question for his lectures, surely he has some way of justifying his position? It's kind of a big leap from 'liberal = socialists' to 'free market causes charity'. --Ireon 18:36, 11 October 2009 (UTC) I guess Andy never stops to think about how most liberals are effing poor! And the ones who aren't, so-called "Elitists", do donate. You just don't hear about it because they aren't famous. Oodon 18:32, 11 October 2009 (UTC) Most liberals are poor? I think that's false. This doesn't exactly prove the opposite, but it's worth noting that the ten poorest states by median income all voted red in the last election. Also, of the ten highest income states only one (Alaska) didn't go blue.--EcheNegraMente You are everything you are nothing at all 19:26, 11 October 2009 (UTC) There is something to the points that (1) a free market allows for the freest operation of organized charities; (2) less people will donate to charity if they think the State is taking at least halfway proper care of those who would otherwise be its recipients; (3) those who squawk the loudest about the conditions of the poor are usually too busy squawking to donate any time in direct aid of altering these conditions. ListenerXTalkerX 19:39, 11 October 2009 (UTC) Okay, that makes sense. The model answers, on the other hand, make none whatsoever. I have the feeling Andy just picked the one saying 'Free market, gooooood' --Ireon 20:09, 11 October 2009 (UTC) ...That's pretty much what all his contributions boils down to? conservative=free market=faith=open-mindedness=homeschooling=prayer=charity=good! liberalism=socialism=obama=public schools=vaccines=evolution=atheism=bad. It's all interchangeable, you can just pick and choose and create a random answer with it and it'll be 10/10 will use as model answer. --GTac 15:57, 12 October 2009 (UTC) ## WIGO worthy? Not sure if thisimg is WIGO worthy, so I'm just going to put it here and let everyone comment. Tetronian you're clueless 01:04, 12 October 2009 (UTC) ...They finally realize not all press is good press. YAY, my homeland is now officially atheist according to CP. No wonder it's so peaceful--Thanatos 02:31, 12 October 2009 (UTC) (EC)I dunno if it is, but at least you didn't add one more lame wigo to the list. I like the word "panic", though. I also really love the "sentence" "Panic sweeps liberals about our Conservative Bible Project." Back when wigo CP was a mere babe (mid 2007?), Sid used to accumulate these edits and make them tell a story. Nowadays, everything on recent changes at CP gets wigoed nine seconds after it happens. Don't let the +40 votes fool you, we just have more readers these days. Oh, Sid's "best ofs" used to be so droll, so perfect, so considered and polished. Sorry for yelling at the kids to get off my lawn ;) ħuman 02:34, 12 October 2009 (UTC) Point taken. There are a lot of short and dumb wigos nowadays. I suppose we kiddies are the reason. gingerly steps off Human's lawn Tetronian you're clueless 02:53, 12 October 2009 (UTC) Yeah well, what's wrong with completely rewriting a WIGO (or several) to attempt to capture that great Sid style? I completely agree with you Human. Sid's WIGO's captivated me for the first month I read this site before I realized the Best of Conservapedia was different than regular WIGOs. The stories told themselves through simple setups. We've gotten ahead of ourselves with editorializing rather than letting the crazy and wicked speak for itself. I'm guilty too. I wish I was there back in the day. 03:21, 12 October 2009 (UTC) Maybe we should all collaborate and write a policy on how to write good wigos? Tetronian you're clueless 03:24, 12 October 2009 (UTC) There is a guide already, but I doubt too many people read it. We don't do policy as such. - π 03:26, 12 October 2009 (UTC) I know, Conservapedia:What is going on at CP?/Instructions. But it doesn't include all of what Human was talking about. But perhaps instead of policy we can just informally agree to be funnier? Tetronian you're clueless 03:32, 12 October 2009 (UTC) The problem, I think (if there is one), is that posting wigoes has a fairly competitive and possessive aspect. Meaning that 1) the slightest blips get posted the instant they are on RC as individual wigoes, and 2) people tend not to rewrite them as much as one would expect on a wiki. The "race to the bottom" effect means that some stories never get told as well as they might be, since their segments are already spread over 3 or 4 wigoes. Sometimes the stories are told best in non-chronological order, after they have unfolded, and the way we "do" this nowadays doesn't lend itself to that style. I don't think there's a solution other than people being bold and bundling wigoes or carefully rewriting them when they have five "UPDATE" sentence fragments appended. ħuman 19:39, 12 October 2009 (UTC) ### Moar not WIGO-worthy stuff I don't know what's funnier, Daniel's comment or Andy's responseimg Tetronian you're clueless 02:57, 12 October 2009 (UTC) Already WIGO'd. ListenerXTalkerX 02:58, 12 October 2009 (UTC) Dammit. Human, I agree with you completely. (and I suppose I should actually look at WIGOCP next time before commenting....silly me.) Tetronian you're clueless 03:05, 12 October 2009 (UTC)	2014-04-25 08:04:32	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 2, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4713742434978485, "perplexity": 5325.882432363599}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1398223211700.16/warc/CC-MAIN-20140423032011-00052-ip-10-147-4-33.ec2.internal.warc.gz"}
http://openstudy.com/updates/507f4c55e4b0b56960051084	## babydoll332 3 years ago Find the exact value of sin-1(-0.5). 1. babydoll332 pi/3 correct? 2. satellite73 no because $\sin(\frac{\pi}{3})=\frac{1}{2}$ not $$-\frac{1}{2}$$ but you have the right idea 3. satellite73 go the other way on the unit circle to $$-\frac{\pi}{3}$$ 4. babydoll332 ok so -pi/3 5. babydoll332 it makes sense 6. satellite73 yup don't forget your answer has to be between $$-\frac{\pi}{2}$$ and $$\frac{\pi}{2}$$ which is why you are not allowed to say $$\frac{2\pi}{3}$$ for example 7. babydoll332 got :)) 8. satellite73 good!	2015-11-29 23:24:57	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5965721011161804, "perplexity": 2221.056809172262}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398460263.61/warc/CC-MAIN-20151124205420-00250-ip-10-71-132-137.ec2.internal.warc.gz"}
https://mathematica.stackexchange.com/questions/187463/hessian-matrix-product-in-taylor-expansion-of-vector-function/187476	# Hessian matrix product in Taylor expansion of vector function I am trying to get the 2nd order coefficient of the Taylor expansion at $$\pmb{x}=\pmb{0}$$ of f[{x1_, x2_}] = {{c1 x1^2 + c2 x1 x2 + c3 x2^2}, {d1 x1^2 + d2 x1 x2 + d3 x2^2}} so, taking these notes into account, I calculated the Hessian matrix, x1 /: Dt[x1, x2] = 0; x2 /: Dt[x2, x1] = 0; H = Dt[f[{x1, x2}], {{x1, x2}, 2},Constants -> {c1, c2, c3, d1, d2, d3}] (* {{{{2c1, c2}, {c2, 2c3}}}, {{{2d1, d2}, {d2, 2d3}}}} ) and, as described in the notes, multiplied it by $$\pmb{x^T}$$ on the left and $$\pmb{x}$$ on the right X = {{x1}, {x2}} Expand[X\[Transpose].H.X] ( {{{{2c1x1^2 + c2x2x1 + 2d1x2x1 + d2x2^2}, {c2x1^2 + 2c3x2x1 + d2x2x1 + 2d3x2^2}}}} ) but the result is not as expected, as it should be equal to $$\pmb{f}$$ (ignoring the 1/2 factor). I think I followed Mathematica's matrix/vector product rules, so what am I missing? Note: I am aware there are other simpler solutions such as Normal[Series[f[{(x1 - 0) t, (x2 - 0) t}], {t, 0, 2}]] /. t -> 1 ( {c1 x1^2+c2 x1 x2+c3 x2^2,d1 x1^2+d2 x1 x2+d3 x2^2} ) but I still want to know what I might have done wrong. • – Michael E2 Feb 24 at 15:44 Since f is vector-values, you should better multiply from the right: f[{x1_, x2_}] = {{c1 x1^2 + c2 x1 x2 + c3 x2^2}, {d1 x1^2 + d2 x1 x2 + d3 x2^2}}; H = D[f[{x1, x2}], {{x1, x2}, 2}]; X = {x1, x2}; f[X] == 1/2 (H.X).X // Expand True • Seriously? I tried quite a few possibilities with f and x written as {{a},{b}} or {a,b} because of the issue with vectors in the link I posted, but missed that one. Oh well... Thanks! – xihiro Dec 7 '18 at 8:47 One problem (or difference from the notes) is that your function f[] is matrix-valued instead of scalar-valued. Your H turns out to be a matrix of Hessian matrices. Your method of computing the Hessian turns out to replace each scalar component of f[{x1, x2}] by its Hessian matrix. To recover f[], you need to apply Dot[] at the appropriate level. Another difference is that X is a matrix (depth-2 array) instead of a vector (depth-1 array). While there is a natural isomorphism from $$(2\times1)$$-matrices to $$2$$-vectors, programmatically it makes a difference, since X\[Transpose].mat.X results in a $$1\times1$$ matrix {{q}} instead of a scalar q. So H turns out to be a $$2 \times 1$$ matrix whose entries are $$2 \times 2$$ matrices. Dimensions[H] ( {2, 1, 2, 2} ) The entries are the Hessian matrices h of the corresponding scalar entry of f[]. Addressing the first point, we can apply X\[Transpose].h.X/2 to each Hessian component matrix h by using Map. The entries h of the matrix H are at level 2. The following then gets the Dot[] product right: Map[Expand[X\[Transpose].#.X/2] &, H, {2}] ( {{{{c1 x1^2 + c2 x1 x2 + c3 x2^2}}}, {{{d1 x1^2 + d2 x1 x2 + d3 x2^2}}}} ) The following breaks down the computation and illustrates the parts, which can get lost in the braces; pr[] prints each Dot[] result and highlights them in red: pr[result_] := (Print["res -> ", result, ", dim -> ", Dimensions[result]]; Style[result, Red]); Map[pr@Expand[X\[Transpose].#.X/2] &, H, {2}] // MatrixForm The above shows that output as a $$2 \times 1$$ matrix with $$1 \times 1$$ matrix entries. That's why the OP's code wasn't working. The principal problem is making X a matrix instead of a vector. One might wonder whether the function f[] should be matrix- or vector-valued, since most vectors in the question appear as column matrices; but both types of functions are valid. If we use a vector, Dot[] contracts the last level of the tensor H: X2 = {x1, x2}; H.X2 // Dimensions H.X2.X2 // Dimensions ( {2, 1, 2} {2, 1} *) The product H.X2.X2/2 is practically equivalent to use of Map at level {2}, but has the desired dimensions and is equal to f[X2]. This is the solution that @Henrik shows in his answer.	2019-11-16 23:57:26	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 11, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.661392092704773, "perplexity": 3577.343210557418}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496668772.53/warc/CC-MAIN-20191116231644-20191117015644-00017.warc.gz"}
http://mathhelpforum.com/calculus/86089-multiple-solutions.html	# Math Help - Multiple Solutions 1. ## Multiple Solutions find all the solutions from 0 to 2pi 2cos^2x = 13sinx-5 2. Originally Posted by jumpman23 find all the solutions from 0 to 2pi 2cos^2x = 13sinx-5 $\cos^2{x} = 1 - \sin^2{x}$ ... solve the resulting quadratic for $\sin{x}$ btw ... why are these basic trig problems on the calculus page?	2015-05-05 08:55:27	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8013499975204468, "perplexity": 4440.472392658217}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1430455283053.76/warc/CC-MAIN-20150501044123-00070-ip-10-235-10-82.ec2.internal.warc.gz"}
https://learn.careers360.com/ncert/question-the-radius-of-a-circle-is-increasing-uniformly-at-the-rate-of-3-cms-find-the-rate-at-which-the-area-of-the-circle-is-increasing-when-the-radius-is-10-cm/	# 3) The radius of a circle is increasing uniformly at the rate of 3 cm/s. Find the rate at which the area of the circle is increasing when the radius is 10 cm. Radius of a circle is increasing uniformly at the rate = 3 cm/s Area of circle(A) = (by chain rule) It is given that the value of r = 10 cm So, Hence, the rate at which the area of the circle is increasing when the radius is 10 cm is ## Related Chapters ### Preparation Products ##### JEE Main Rank Booster 2021 This course will help student to be better prepared and study in the right direction for JEE Main.. ₹ 13999/- ₹ 9999/- ##### Rank Booster NEET 2021 This course will help student to be better prepared and study in the right direction for NEET.. ₹ 13999/- ₹ 9999/- ##### Knockout JEE Main April 2021 (Easy Installments) An exhaustive E-learning program for the complete preparation of JEE Main.. ₹ 4999/- ##### Knockout NEET May 2021 An exhaustive E-learning program for the complete preparation of NEET.. ₹ 22999/- ₹ 14999/-	2020-10-24 09:09:52	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8867395520210266, "perplexity": 3456.639745728004}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107882103.34/warc/CC-MAIN-20201024080855-20201024110855-00133.warc.gz"}
https://www.qb365.in/materials/stateboard/8th-standard-term-1-two-marks-model-question-paper-6587.html	#### Term 1 Two Mark Model Questions 8th Standard EM Reg.No. : • • • • • • Maths Time : 01:00:00 Hrs Total Marks : 50 25 x 2 = 50 1. List five rational numbers between –2 and 0 2. List five rational numbers between –1.2 and -2.3 3. Verify that -(- x) is the same x for: $x=\frac { -31 }{ 45 }$ 4. Divide: $\frac { -3 }{ 13 }$ by -3 5. Arrange the following rational numbers in ascending and descending order $\frac { -5 }{ 12 } ,\frac { -11 }{ 8 } ,\frac { -15 }{ 24 } ,\frac { -7 }{ -9 } ,\frac { 12 }{ 36 }$ 6. Use commutative and distributive properties to simplify $\frac { 4 }{ 5 } \times \frac { -3 }{ 8 } -\frac { 3 }{ 8 } \times \frac { 1 }{ 4 } +\frac { 19 }{ 20 }$ 7. Subbu spends $\frac { 1 }{ 3 }$ of his monthly earnings on rent, $\frac { 2 }{ 5 }$ on food and $\frac { 1 }{ 10 }$ on monthly usuals. What fractional part of his earnings is left with him for other expenses? 8. Show that $\left( \frac { \frac { 7 }{ 9 } -5 }{ \frac { 4 }{ 3 } } \right) \div \frac { 3 }{ 2 } +\frac { 4 }{ 9 } -\frac { 1 }{ 3 } =-2$ 9. The difference between a number and its two third is 30 more than one -fifth of the number. Find the number. 10. Find the area of a sector whose length of the arc is 50 mm and radius is 14 mm. 11. Dhamu fixes a square tile of 30 cm on the floor. The tile has a sector design on it as shown in the figure. Find the area of the sector. (π=3.14). 12. Find the perimeter and area of the combined figures given below. $\left( \pi =\frac { 22 }{ 7 } \right)$ 13. Find the area of the combined figure given, formed by joining a semicircle of diameter 6 cm with a triangle of base 6 cm and height 9 cm. ( π = 3.14 ) 14. A rocket drawing has the measures as given in the figure. Find its area. 15. Which 3-D shapes do the following nets represent? Draw them. 16. Multiply a monomial by a monomial 6x,4 17. Multiply a monomial by a monomial 2p2q3, −9pq2 18. Find the product of (2x+3)(2x−4) 19. Expand (3m+5)2 20. Multiply (4x2+9) and (3x-2) 21. In the given fi gure YH\|\|TE . Prove that ΔWHY～ΔWET and also fi nd HE and TE. 22. In the given fi gure, AC ≡ AD and ∠CBD≡∠DEC. Prove that DBCF ≡ DEDF. 23. Construct the following quadrilaterals with the given measurements and also find their area. AGRI, AG= 4.5 cm, GR = 3.8 cm, ∠A = 60°, ∠G = 110° and ∠R = 90°. 24. In how many ways, can the teacher choose 3 students in all, one each from 10 students in VI std, 15 students in VII std and 20 students in VIII std to go to an excursion? 25. An examination paper has 3 sections, each with five questions and students are instructed to answer one question from each section. In how many different ways of can the questions be answered?	2020-01-23 16:14:12	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6566049456596375, "perplexity": 2086.2392294262745}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250611127.53/warc/CC-MAIN-20200123160903-20200123185903-00190.warc.gz"}
https://www.physicsforums.com/threads/double-slit-experiment-one-slit-covered-with-glass.522303/	# Double-slit experiment, one slit covered with glass 1. Aug 17, 2011 ### cep 1. The problem statement, all variables and given/known data In a double-slit experiment, He-Ne laser light of wavelength 633 nm produced an interference pattern on a screen placed at some distance from the slits. When one of the slits was covered with a thin glass slide of thickness 12.0 um, the central fringe shifted to the point occupied earlier by the 10th dark fringe. What is the refractive index of the glass slide? Here's a link to a similar problem with a figure: www.physics.ohio-state.edu/~gohlke/pedagogy/Phys133I_Diffraction.pdf[/URL] [b]2. Relevant equations[/b] n=c/v; $\Delta$x (constructive) = m$\lambda$ = dsin$\Theta$; $\Delta$x (destructive) = (m+1/2)$\lambda$ = dsin$\Theta$; Snell's law (maybe?) [b]3. The attempt at a solution[/b] I understand that the glass slide will slow the passage of light, thus effectively increasing $\Delta$x between the two light paths. I guess i need to figure out how many wavelengths the light going through the glass is "behind" the other beam. However, I don't understand how to incorporate this into the problem. It seems to get very complicated very quickly-- since the light isn't traveling straight through the glass, the distance is not equal to the thickness of the glass. Then, the light is refracted when leaving the glass, according to Snell's law. The only examples in my textbook were very simplistic, we didn't cover anything like this in class, and I'm really not sure what to do. I tried working out the problem as indicated in the link (though they solve for the thickness of the slide, and n is given), but got like -0.5 for n (and I was suspicious of their answer anyway, because it seems to neglect so many complicating factors). Can anyone help me think about this? Thanks a lot, sorry if this post is tl;dr :). -CEP Last edited by a moderator: Apr 26, 2017 2. Aug 17, 2011 ### vela Staff Emeritus It's easiest to think of these problems in terms of optical path length, which is just the number of wavelengths between two points. The interference pattern is caused by light reaching a point along two different paths. For the central fringe, by definition, the optical path lengths are equal. For the first-order fringe, the difference in optical path length is ±1, and so on. Come up with expressions for the optical path length for the two rays when the slide is present. Then set them equal to each other because you're working with the central fringe. The only unknown left should be n. 3. Aug 17, 2011 ### PeterO Last edited by a moderator: Apr 26, 2017 4. Aug 17, 2011 ### cep Also, Peter, my question is different as I am supposed to determine the refractive index (n) of the glass-- not the thickness of the slide. Thank you both for the responses-- very helpful. To clarify, I shouldn't be worried about the path length THROUGH the glass, just the change in wavelength? I'll keep working on it :) 5. Aug 17, 2011 ### PeterO Yes that's it. The piece of glass is a certain number of "wavelengths in air" thick, but 9.5 more "wavelengths in glass" thick. That enables you to get the wavelength in glass, and so the refractive index. 6. Aug 17, 2011 ### vela Staff Emeritus So is your problem the way you stated or the way the problem PeterO found is stated? 7. Aug 18, 2011 ### cep The question in the original post is copied, verbatim, from my textbook. The attachment is a solution to a similar problem, with a figure identical to the one in the book.	2018-02-21 18:11:10	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7490419149398804, "perplexity": 574.1917377923974}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891813691.14/warc/CC-MAIN-20180221163021-20180221183021-00667.warc.gz"}
http://www.sciforums.com/showthread.php?76495-Welding-without-heat	1. ## Welding without heat... I was giving some thought of how to bind two metals together without using any heat or welding wires/rods and an idea struck me. Seeing that the atoms are similar to each other why not excite them using a frequency that would be applied to make them energetic enough to just bond together? If a sound frequency could be found that could make the atoms so energetic couldn't this actually be done? Just a thought, what's your thinking along this line? 2. Sonic fusing is a common way to join plastics. They probably do it for metals too, but metals do this naturally. Perfectly clean metals will fuse to each other instantly. 3. Originally Posted by spidergoat Sonic fusing is a common way to join plastics. They probably do it for metals too. If you have the time, metals do this naturally. Put a flat piece of silver next to a flat piece of gold and eventually they will diffuse into each other, assuming there is no oxidation. What about steel? Have you ever heard of steel being "fused" this way as well? 4. Any kind of energy that will heat the metal up will work. Sound energy is as good as anything. "energetic" is the same as heat. 5. Originally Posted by spidergoat Any kind of energy that will heat the metal up will work. Sound energy is as good as anything. "energetic" is the same as heat. So why hasn't anyone come along and made a sound wave welder? It would be cheaper and easier plus better for the metals to combine with. 6. Originally Posted by cosmictraveler So why hasn't anyone come along and made a sound wave welder? It would be cheaper and easier plus better for the metals to combine with. Easy - because it's SUPER dangerous under any conditions other than factory applications (which is where it's also applied to plastics - as was mentioned). The transducer is impossible to control by hand and the welder (person) would be injured immediately by the stray (powerful!) sound waves. It's also conducted by the metal even better than through air so there is no safe place anywhere near the operation. Edit: and forget about ear protection - we're talking about BONE conduction. Easy - because it's SUPER dangerous under any conditions other than factory applications (which is where it's also applied to plastics - as was mentioned). The transducer is impossible to control by hand and the welder (person) would be injured immediately by the stray (powerful!) sound waves. It's also conducted by the metal even better than through air so there is no safe place anywhere near the operation. Edit: and forget about ear protection - we're talking about BONE conduction. So why not use electromagnets to attach the device onto the pieces that need to be fused together and leave it without anyone around it until its done with its job? 8. Originally Posted by cosmictraveler I was giving some thought of how to bind two metals together without using any heat or welding wires/rods and an idea struck me. Seeing that the atoms are similar to each other why not excite them using a frequency that would be applied to make them energetic enough to just bond together? If a sound frequency could be found that could make the atoms so energetic couldn't this actually be done? Just a thought, what's your thinking along this line? "Making the atoms energetic" means heating them up. Plastics can be bonded chemically with certain saturated solvents absent heat, but not metals. ...beaten by spidergoat 9. wow 10. Sonic welding has been done on aluminum since the 1960's. They have also tried it for steel, although you need to heat it up a certain degree. It shows much promise. You might be able to clear a free surface by abrading in oil or a nonreactive liquid, then applying ultrasound to assist the free energy spontaneous bonding in metals. 11. Originally Posted by cosmictraveler So why not use electromagnets to attach the device onto the pieces that need to be fused together and leave it without anyone around it until its done with its job? That sounds like a far too complicated process if you're doing more than just a quick and fairly simple job. And for something of THAT nature (quick and simple) it would still be pretty complicated and expensive. Just grab the old arc welder or MIG/TIG and be done in a few minutes. That sounds like a far too complicated process if you're doing more than just a quick and fairly simple job. And for something of THAT nature (quick and simple) it would still be pretty complicated and expensive. Just grab the old arc welder or MIG/TIG and be done in a few minutes. I was only considering a device that large for BIG pieces of steel to be welded not smaller ones. I don't think smaller ones would be as hard to use the device with because a small job would only need a small machine to weld it with, not a large machine. 13. To weld witout heat with LARGE pieces of steel is something I've come up with. No one seems to understand how to do this but myself, to bad. 14. I'd like to hear what you've come up with, cosmic. Because it can overthrow just about everything in the welding and construction industries. 15. Originally Posted by spidergoat Sonic fusing is a common way to join plastics. They probably do it for metals too, but metals do this naturally. Perfectly clean metals will fuse to each other instantly. I hate sonic welding. Eventually you get used to the high pitched squeal, but...eeeeeeeeee for hrs, is spine tingling. Lots of parts in your car are sonic welded. 16. Originally Posted by cosmictraveler So why hasn't anyone come along and made a sound wave welder? It would be cheaper and easier plus better for the metals to combine with. They have. http://en.wikipedia.org/wiki/Ultrasonic_welding I maintain that metal will weld with each other with no added heat if the mating surfaces are perfect, and there is no oxidation. I used to work at a company that produced a cold-welded material for dental fillings. The material was just a kind of metal with a coating of copper. It's easy to remove the oxidation from the copper with an activating solution, after which the metal particles naturally weld to each other. A film of oxidation or foreign material is the only reason metals don't weld to each other when touching. 17. It's easier to do for low-$T_m$ metals like dental amalgams, solder, tin, aluminum, and even brass, but much harder to do for other metals such as iron and titanium. You have to heat close to the creep temperature (roughly $0.4T_m$) to successfully use ultrasound welding on them. Solder creeps at room temperature, and aluminum can creep at around the boiling point of water. 18. I think cosmictraveller is referring to a process of chemically welding two peices of metal together. It's a fictional device used in the Honor Harrington novels by David Weber for spaceship construction and repair. Whether there is a real world capability of doing this I just don't know. 19. Gold will naturally cold-weld to form alluvial gold nuggests. Flakes of gold wash down, settle into cracks in a stream-bed, and form alluvial nuggets over long periods of time. This gold is much more valuable than ordinary gold, as it is prized by collectors. #### Posting Permissions • You may not post new threads • You may not post replies • You may not post attachments • You may not edit your posts •	2014-07-31 01:17:49	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 2, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.40590354800224304, "perplexity": 1514.5755378820297}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1406510272256.16/warc/CC-MAIN-20140728011752-00108-ip-10-146-231-18.ec2.internal.warc.gz"}
http://libros.duhnnae.com/2017/sep/15051624912-Holographic-Techni-dilaton-High-Energy-Physics-Phenomenology.php	# Holographic Techni-dilaton - High Energy Physics - Phenomenology Holographic Techni-dilaton - High Energy Physics - Phenomenology - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online. Abstract: Techni-dilaton, a pseudo-Nambu-Goldstone boson of scale symmetry, waspredicted long ago in the Scale-invariant-Walking-Conformal TechnicolorSWC-TC as a remnant of the approximate scale symmetry associated with theconformal fixed point, based on the conformal gauge dynamics of ladderSchwinger-Dyson SD equation with non-running coupling. We study thetechni-dilaton as a flavor-singlet bound state of techni-fermions by includingthe techni-gluon condensate tGC effect into the previous bottom-upholographic approach to the SWC-TC, a deformation of the holographic QCD with$\gamma m \simeq 0$ by large anomalous dimension $\gamma m \simeq 1$. Withincluding a bulk scalar field corresponding to the gluon condensate, we firstimprove the Operator Product Expansion of the current correlators so as toreproduce gluonic $1-Q^4$ term both in QCD and SWC-TC. We find in QCD about$10\%$ negative contribution of gluon condensate to the $ho$ meson mass. Wealso calculate the oblique electroweak $S$-parameter in the presence of theeffect of the tGC and find that for the fixed value of $S$ the tGC effectsdramatically reduce the flavor-singlet scalar techni-dilaton mass $M { mTD}$ in the unit of $F \pi$, while the vector and axial-vector masses$M ho$ and $M {a 1}$ are rather insensitive to the tGC, where $F \pi$ is thedecay constant of the techni-pion. If we use the range of values of tGC impliedby the ladder SD analysis of the non-perturbative scale anomaly in the large$N f$ QCD near the conformal window, the phenomenological constraint $S \simeq0.1$ predicts the techni-dilaton mass $M { m TD} \sim 600$ GeV which is withinreach of LHC discovery. Autor: Kazumoto Haba, Shinya Matsuzaki, Koichi Yamawaki Fuente: https://arxiv.org/	2018-10-22 08:27:07	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8658797144889832, "perplexity": 6358.924240358113}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583514879.30/warc/CC-MAIN-20181022071304-20181022092804-00423.warc.gz"}
https://www.physicsforums.com/threads/help-finding-the-transfer-function-h-s-vi-s-ii-s.784670/	# Help Finding the Transfer Function H(s)=Vi(s)/Ii(s) Tags: 1. Nov 28, 2014 ### Captain1024 1. The problem statement, all variables and given/known data Find the transfer function $H(s)=\frac{Vi(s)}{Ii(s)}$ The circuit consists of a voltage source and a 5H Inductor in series with a 10Ohm Resistor which are in parallel with a 10uF Capacitor in series with a 500Ohm Resistor. $\rightarrow$ Diagram here. 2. Relevant equations Parallel Impedances: $Z_{eq}=\frac{Z1Z2}{Z1+Z2}$ $s=j\omega$ 3. The attempt at a solution $5H\ \rightarrow\ j\omega5$ $10\mu F\ \rightarrow\ \frac{1}{j\omega10^{-5}}$ $Z_1=j\omega5+10$ $Z_2=\frac{1}{j\omega10^{-5}}+500$ $V_i=\frac{Z_1Z_2}{Z_1+Z_2}I$ $V_i=\frac{\frac{j\omega5}{j\omega10^{-5}}+j\omega2500+\frac{10}{j\omega10^{-5}}+5000}{j\omega5+\frac{1}{j\omega10^{-5}}+510}I$ $H(s)=\frac{V_i}{I}=\frac{5.05e5+(1.0025e6)s}{5s+\frac{10e5}{s}+510}$ 2. Nov 28, 2014 ### Staff: Mentor Before you replace jw by s, multiply both numerator and denominator by jw to get a tidier form. 3. Nov 28, 2014 ### Captain1024 I have to go to sleep now. I will be back at it tomorrow afternoon. 4. Nov 29, 2014 ### Staff: Mentor You could have used s right from the start. 5H → s5 10uF → 1/(s10-5) Then V(s) = Z(s).I(s) 5. Nov 29, 2014 ### Captain1024 Problem reworked: $j\omega5\ \rightarrow\ 5s$ $\frac{1}{j\omega10^{-5}}\ \rightarrow\ \frac{1}{10^{-5}} \frac{1}{s}\ \rightarrow\ \frac{10^5}{s}$ $Z_1=5s+10$ $Z_2=\frac{10^5}{s}+500$ $V_i=Z_{eq} I_i$ $\frac{V_i}{I_i}=\frac{(5s+10)(\frac{10^5}{s}+500)}{5s+10+\frac{10^5}{s}+500}$ $=\frac{5e5+2500s+\frac{10^6}{s}+5000}{5s+\frac{10^5}{s}+510}$ $=\frac{5.05e5+2500s+\frac{10^6}{s}}{5s+\frac{10^5}{s}+510}(\frac{s}{s})$ $=\frac{2500s^2+(5.05e5)s+10^6}{5s^2+510s+10^5}$ Correct answer: $H(s)=\frac{0.25s^2+5.05s+10}{(5e-5)s^2+(5.1e-3)s+1}$ These two answers do not seem equivalent to me? Where am I going wrong? 6. Nov 29, 2014 ### Captain1024 I just verified by finding the zeros and poles. My answer matches. Thanks for the guidance. 7. Nov 29, 2014 ### Staff: Mentor When you don't have the correct answer to compare yours with, a simple check you can do is ask: what is H(s) when s=0. This is the DC value, which inspection of your circuit indicates is the inductor branch with its 10 ohms. Also, when s → infinity you have the high frequency impedance, here being the 500 ohms in the capacitive branch. If these two extremes of H(s) check okay, there's good reason to be optimistic the rest of your work is right. 8. Nov 30, 2014 ### rude man Rather than introduce numbers early in the solution, you should retain the component symbols until the end.	2018-01-20 17:48:13	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3781517744064331, "perplexity": 2762.7616967575286}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084889677.76/warc/CC-MAIN-20180120162254-20180120182254-00657.warc.gz"}
https://cs.stackexchange.com/questions/80343/if-problem-is-conl-complete-is-it-nl-complete/80346	# If problem is coNL-complete, is it NL-complete We know from Immerman-Szelepcsényi theorem that $coNL=NL$. But, what about: If problem is $coNL\text{-}complete$, is it $NL\text{-}complete$? And why? • Isn't it trivial? Did you try to prove yourself? What confuses you? – fade2black Aug 22 '17 at 20:25 • You can see *-complete as a function that takes a class $C$ of problems and returns the class $C'$ of $C-complete$ problems, i.e., $\operatorname{Complete}(C):=\{P : P \in C\text{ and }P\text{ is }C\text{-hard}\}$. Your question becomes: Since $coNL = NL$, do we have $\operatorname{Complete}(coNL)=\operatorname{Complete}(NL)$ to which the answer is obviously yes: You applied the same function to the same argument so the result will be the same. – xavierm02 Aug 23 '17 at 12:57 If the language $A$ is $NL$-complete then 1. $A \in NL$ 2. Each problem in $NL$ is logspace reducible to $A$ Since $coNL = NL$ each problem in $coNL$ is logspace reducible to $A$ as well. Thus $A$ is $coNL$-complete. • Oh, yeah. It is trival in the fact :) – Logic Aug 22 '17 at 20:39 Yes, if a problem is $coNL-complete$ it's $NL-complete$. Take a language $L$ which is $coNL-complete$. 1. By theorem (that you mentioned) there exist a TM which accepts it in $NL$ so $L \in NL$. 2. Now, take a language $L_1 \in NL$. By theorem $L_1 \in coNL$ and by $L$ being $coNL-Hard$ there exist a log-space reduction $L_1 <_L L$. So, $L$ is $NL-Hard$. Therefore, $L$ is $NL-complete$. The theorem : Immerman–Szelepcsényi theorem	2020-03-30 17:46:56	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9300021529197693, "perplexity": 611.4213729333238}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370497171.9/warc/CC-MAIN-20200330150913-20200330180913-00427.warc.gz"}
https://www.physicsforums.com/threads/trigonometric-integral.90852/	Trigonometric integral 1. Sep 25, 2005 Stevecgz Problem: $$\int sin^6 x dx$$ Progress so far: $$\int (sin^2 x)^3 dx$$ $$\frac{1}{8} \int (1-cos2x)^3 dx$$ $$\frac 1 8 \int (1 - 3cos2x + 3cos^22x - cos^32x) dx$$ Any help is appreciated. I can see using a half angle identity for cos^2(2x), but what do I do with the cos^3(2x)? Steve Last edited: Sep 25, 2005 2. Sep 25, 2005 whozum Try looking up some sine integral reduction formulas on google. They take care of integrals involving powers of sine pretty nicely. 3. Sep 25, 2005 Stevecgz I've found one in my text. Would I simply continue using the reduction formula until I get to sin^0(x)? Steve 4. Sep 25, 2005 whozum Yes thats pretty much how we did it. 5. Sep 25, 2005 Stevecgz Thanks whozum. Steve	2017-05-25 14:52:33	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9502844214439392, "perplexity": 2988.4384961500805}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463608084.63/warc/CC-MAIN-20170525140724-20170525160724-00257.warc.gz"}
https://www.gamedev.net/forums/topic/575823-circular-dependencies/	Public Group Circular Dependencies This topic is 3006 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic. Recommended Posts i have a problem of Circular Dependencies class A #include "B.h" and Class B #include "A.h to solve would i write a seperate class , C, is this way or another way please class A #include "C.h" Class B #include "C.h Share on other sites It depends on what you are doing exactly. Why do they need to include the header containing the other class? Do they both just have pointers to the other one? If thats the case, you can just forward declare the class and not have to include the header file. For example... class B;class A{ B* m_b;}; class A;class B{ A* m_a;}; If the problem is they both require something else that is in each header file, such as some enumerations, the solution may be to split the enumerations to a third file or to redesign the classes to not have the dependency on each other. Share on other sites Which language? I presume it is C++. What are the reason for you need class A to include class B and viceversa? If your class A needs to include instances of class B and the same in class B you can have these instances declared as pointer in class definition, use class forward as explained in http://www-subatech.in2p3.fr/~photons/subatech/soft/carnac/CPP-INC-1.shtml 1. 1 2. 2 3. 3 Rutin 16 4. 4 5. 5 • 10 • 10 • 14 • 10 • 25 • Forum Statistics • Total Topics 632647 • Total Posts 3007640 • Who's Online (See full list) There are no registered users currently online ×	2018-09-25 11:06:31	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1838287115097046, "perplexity": 4609.784115496644}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267161501.96/warc/CC-MAIN-20180925103454-20180925123854-00438.warc.gz"}