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https://www.transtutors.com/questions/assigning-corporate-support-costs-activity-based-costing-zeta-department-store-has-d-88428.htm	# Assigning corporate support costs, activity-based costing Zeta Department Store has developed the... Assigning corporate support costs, activity-based costing Zeta Department Store has developed the following information in order to develop a timedriven ABC model for its Accounts Receivable Department: The time to process payments of customer invoices depends on whether the customer pays the bill manually or electronically, as shown above. The time to maintain each customer file is the same for all customers. The annual cost of the Accounts Receivable Department is $500,000 and the associated practical capacity of accounts receivable labor is 10,000 hours. The Accounts Receivable Department has six employees. Required (a) What is the capacity cost rate for the Accounts Receivable Department? (b) Zeta’s Division 1 has 1,000 small- to medium-sized customers who annually generate a total of$10 million in sales, resulting in 4,000 invoices. These customers pay all their invoices manually. What is the annual activity-based cost associated with Division 1’s customers? (c) Zeta’s Division 2 has 200 large customers who annually generate a total of \$10 million in sales, resulting in 400 invoices. These customers pay all of their invoices electronically. What is the annual activity-based cost associated with Division 2’s customers? (d) Suppose half of Zeta’s Division 1 customers change their method of payment to electronic next year. How many hours of accounts receivable labor will it require for 1,000 customers, 2,000 manual invoices, and 2,000 electronic invoices? How much will Division 1 be charged for the accounts receivable function? Will Zeta’s costs decrease because of the shift to 50% electronic invoicing in Division 1?	2019-07-19 00:17:39	{"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": 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": 0.2486390620470047, "perplexity": 7520.284983638618}, "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-2019-30/segments/1563195525863.49/warc/CC-MAIN-20190718231656-20190719013656-00230.warc.gz"}
https://math.stackexchange.com/questions/2923984/is-there-a-fixed-point-theorem-that-can-be-applied-to-a-ring-endomorphism-of-k	# Is there a fixed-point theorem that can be applied to a ring endomorphism of $k[x,y]$? Let $k$ be a field of characteristic zero (I do not mind to assume that $k \in \{\mathbb{R},\mathbb{C}\}$), and let $R=k[x,y]$ be the $k$-algebra of polynomials in two variables $x,y$. Let $f$ be a $k$-algebra endomorphism of $R$. (I) Is there a fixed-point theorem that can be applied to $f$? (II) If so, then is it possible to obtain a fixed point $\in R-k$? (the elements of $k$ are always fixed points for a $k$-algebra endomorphism $f$). Remarks: (1) I have tried to consider $k[x,y]$ as a complete metric space, see this question, but I guess that $f$ is not a contraction in that metric. So, is there another metric that makes $f$ a contraction? (probably yes? But it may be difficult to guarantee that $f$ has a fixed point $\in R-k$). (2) The answer probably depends on the given $f$, since, for example, it seems that $f:(x,y) \mapsto (x^2,y^2)$ does not have fixed points other than the elements of $k$. (3) Here is a list of fixed point theorems. (4) The following questions seem relevant: a and b (what if we consider our given endomorphism as a multiplicative group morphism?). (5) A similar question of mine is this (the fourth remark there says that the existence of such a fixed point implies the two-dimensional Jacobian Conjecture). Thank you very much! • I don't think it is possible in any nice way, because you cannot keep the $k$-vectorspace structure compatible with a complete metric (Since $k[x,y]$ is a countable union of nested finite-dimensional subspaces contradicting Baire). – user10354138 Sep 20 '18 at 14:21 • Thank you very much. Can you please elaborate (in an answer)? – user237522 Sep 20 '18 at 14:34 • (If I am not wrong, if we work in the formal power series $k[[x,y]]$, then the 'natural' metric is complete, but $f$ is not a contraction). – user237522 Sep 20 '18 at 14:40 In particular, you want proper vector subspaces to be closed and nowhere dense. But this yields a contradiction when you demand the metric to be complete, because we can write $k[x,y]$ as a countable union of proper (hence closed nowhere dense) subspaces $$k[x,y]=\bigcup_{d=0}^\infty \operatorname{span}_k\{x^iy^j\mid i+j\leq d\}$$ but Baire category theorem says a complete metric space is not meagre. If you decide to work with the formal power series ring $k[[x,y]]$ instead, then obviously your endomorphism $f$ must send the nilpotent $x,y$ to some nilpotent elements. This means in particular that we can reduce to looking at fixed elements of each $(x,y)/(x,y)^m$ and patching each graded piece together, like in Hansel's lemma.	2019-08-20 19:16:43	{"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": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9524571895599365, "perplexity": 145.34842712367393}, "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-2019-35/segments/1566027315558.25/warc/CC-MAIN-20190820180442-20190820202442-00457.warc.gz"}
https://deepai.org/publication/decoding-stacked-denoising-autoencoders	# Decoding Stacked Denoising Autoencoders Data representation in a stacked denoising autoencoder is investigated. Decoding is a simple technique for translating a stacked denoising autoencoder into a composition of denoising autoencoders in the ground space. In the infinitesimal limit, a composition of denoising autoencoders is reduced to a continuous denoising autoencoder, which is rich in analytic properties and geometric interpretation. For example, the continuous denoising autoencoder solves the backward heat equation and transports each data point so as to decrease entropy of the data distribution. Together with ridgelet analysis, an integral representation of a stacked denoising autoencoder is derived. ## Authors • 12 publications • 8 publications • ### Training Stacked Denoising Autoencoders for Representation Learning We implement stacked denoising autoencoders, a class of neural networks ... 02/16/2021 ∙ by Jason Liang, et al. ∙ 10 • ### Stacked autoencoders based machine learning for noise reduction and signal reconstruction in geophysical data Autoencoders are neural network formulations where the input and output ... 07/07/2019 ∙ by Debjani Bhowick, et al. ∙ 0 • ### SMS Spam Filtering using Probabilistic Topic Modelling and Stacked Denoising Autoencoder In This paper we present a novel approach to spam filtering and demonstr... 06/17/2016 ∙ by Noura Al Moubayed, et al. ∙ 1 • ### Blind Denoising Autoencoder The term blind denoising refers to the fact that the basis used for deno... 12/11/2019 ∙ by Angshul Majumdar, et al. ∙ 0 • ### Soft-Autoencoder and Its Wavelet Shrinkage Interpretation Deep learning is a main focus of artificial intelligence and has greatly... 12/31/2018 ∙ by Fenglei Fan, et al. ∙ 20 • ### Distributed Evolution of Deep Autoencoders Autoencoders have seen wide success in domains ranging from feature sele... 04/16/2020 ∙ by Jeff Hajewski, et al. ∙ 0 • ### DEVDAN: Deep Evolving Denoising Autoencoder The Denoising Autoencoder (DAE) enhances the flexibility of the data str... 10/08/2019 ∙ by Andri Ashfahani, et al. ∙ 16 ##### This week in AI Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday. ## 1 Introduction The denoising autoencoder (DAE) is a role model for representation learning, the objective of which is to capture a good representation of the data. Vincent2008 introduced it as a heuristic modification of traditional autoencoders for enhancing robustness. In the setting of traditional autoencoders, we train a neural network as an identity map and extract the hidden layer to obtain the so-called “code.” On the other hand, the DAE is trained as a denoising map of deliberately corrupted inputs . The corrupt and denoise principle is simple, but truly is compatible with stacking, and thus, inspired many new autoencoders. See Section 1.1 for details. We are interested in what deeper layers represent and why we should deepen layers. In contrast to the rapid development in its application, the stacked autoencoder remains unexplained analytically, because generative models, or probabilistic alternatives, are currently attracting more attention. In addition, deterministic approaches, such as kernel analysis and signal processing, tend to focus on convolution networks from a group invariance aspect. We address these questions from deterministic viewpoints: transportation theory and ridgelet analysis. Alain2014 derived an explicit map that a shallow DAE learns as x↦Eε[p(x−ε)(x−ε)]Eε[p(x−ε)], (1) and showed that it converges to the score of the data distribution as the variance of tends to zero. Then, they recast it as manifold learning and score matching. We reinterpret (1) as a transportation map of , the variance as time, and the infinitesimal limit as the initial velocity field. Ridgelet analysis is an integral representation theory of neural networks (Sonoda2015; Sonoda2014; Candes1998; Murata1996). It has a concrete geometric interpretation as wavelet analysis in the Radon domain. We can clearly state that the first hidden layer of a stacked DAE is simply a discretization of the ridgelet transform of (1). On the other hand, the character of deeper layers is still unclear, because the ridgelet transform on stacked layers means the composition of ridgelet transforms , which lacks geometric interpretation. One of the challenges here is to develop the integral representation of deep neural networks. We make two important observations. First, through decoding, a stacked DAE is equivalent to a composition of DAEs. By definition, they differ from each other, because “stacked” means a concatenation of autoencoders with each output layer removed, while “composition” means a concatenation of autoencoders with each output layer remaining. Nevertheless, decoding relates the stacked DAE and the composition of DAEs. Then, ridgelet transform is reasonable, because it can be performed layer-wise, which leads to the integral representation of a deep neural network. Second, an infinite composition results in a continuous DAE, which is rich in analytic properties and geometric interpretation, because it solves the backward heat equation. This means that what deep layers do is to transport mass so as to decrease entropy. Together with ridgelet analysis, we can conclude that what a deep layer represents is a discretization of the ridgelet transform of the transportation map. ### 1.1 Related Work Vincent2008 introduced the DAE as a modification of traditional autoencoders. While the traditional autoencoder is trained as an identity map , the DAE is trained as a denoising map for artificially corrupted inputs , in order to enhance robustness. Theoretical justifications and extensions follow from at least five aspects: manifold learning (Rifai2011; Alain2014), generative modeling (Vincent2010; Bengio2013; Bengio2014), infomax principle (Vincent2010), learning dynamics (Erhan2010), and score matching (Vincent2011). The first three aspects were already mentioned in the original paper (Vincent2008). According to these aspects, a DAE learns one of the following: a manifold on which the data are arranged (manifold learning); the latent variables, which often behave as nonlinear coordinates in the feature space, that generate the data (generative modeling); a transformation of the data distribution that maximizes the mutual information (infomax); good initial parameters that allow the training to avoid local minima (learning dynamics); or the data distribution (score matching). A turning point appears to be the finding of the score matching aspect (Vincent2011) , which reveals that score matching with a special form of energy function coincides with a DAE. This means that a DAE is a density estimator of the data distribution . In other words, it extracts and stores information as a function of . Since then many researchers omitted stacking deterministic autoencoders, and have developed generative density estimators (Bengio2013; Bengio2014) instead. The generative modeling is more compatible not only with the restricted Boltzmann machine and deep belief nets (Hinton2006a) and the deep Boltzmann machine (Salakhutdinov2009), but also with many sophisticated algorithms, such as variational autoencoder (Kingma2014a) , minimum probability flow . In generative models, what a hidden layer represents basically corresponds to either the “hidden state” itself that generates the data or the parameters (such as means and covariance matrices) of the probability distribution of the hidden states. See Bengio2014, for example. “What do deep layers represent?” and “why deep?” are difficult questions for concrete mathematical analysis because a deep layer is a composition of nonlinear maps. In fact, even a shallow network is a universal approximator; that is, it can approximate any function, and thus, deep structure is simply redundant in theory. It has even been reported that a shallow network could outperform a deep network (Ba2014). Hence, no studies on subjects such as “integral representations of deep neural networks” or “deep ridgelet transform” exist. Thus far, few studies have characterized the deep layer of stacked autoencoders. The only conclusion that has been drawn is the traditional belief that a combination of the “codes” exponentially enhances the expressive power of the network by constructing a hierarchy of knowledge and it is efficient to capture a complex feature of the data. Bouvrie2009, Bruna2013, Patel2015 and Anselmi2015a developed sophisticated formulations for convolution networks from a group invariance viewpoint. However, their analyses are inherently restricted to the convolution structure, which is compatible with linear operators. In this paper, we consider an autoencoder to be a transportation map and focus on its dynamics, which is a deterministic standpoint. We address the questions stated above while seeking an integral representation of a deep neural network. ## 2 Preliminaries In this paper, we treat five versions of DAEs: the ordinary DAE , anisotropic DAE , stacked DAE , a composition of DAEs , and the continuous DAE . By using the single symbols and , we emphasize that they are realized as a shallow network or a network with a single hidden layer. Provided that there is no risk of confusion, the term “DAE ” without any modifiers means a shallow DAE, without distinguishing “ordinary,” “anisotropic,” or “continuous,” because they are all derived from (3). By , and , we denote time derivative, gradient, and Laplacian, by the Euclidean norm, by the identity map, and by the uni/multivariate Gaussian with mean and covariance matrix . An (anisotropic) heat kernel is the fundamental solution of an anisotropic diffusion equation on with respect to the diffusion coefficient tensor : ∂tWt(x,y) limt→0Wt(x,y) =δ(x−y),x,y∈Rm lim\|(x,y)\|→∞\|Wt(x,y)\| =0,t>0. When , the diffusion equation and the heat kernel are reduced to a heat equation and a Gaussian . If is clear from the context, we write simply without indicating . For a map with , the Jacobian is calculated by , regarding as an matrix. By , we denote the pushforward measure of a probability measure with respect to a map , which satisfies . See (Evans2015) for details. ### 2.1 Denoising Autoencoder Let be a random vector in and be its corruption: ˜X:=X+ε,ε∼N(0,tI). We train a shallow neural network for minimizing an objective function EX,˜X\|g(˜X)−X\|2. In this study, we assumed that has a sufficiently large number of hidden units to approximate any function, and thus, the training attains the Bayes optimal. In other words, converges to the regression function Φ(x) :=arg mingEX,˜X\|g(˜X)−X\|2 =EX[X\|˜X=x], (2) as the number of hidden units tends to infinity. We regard and treat this limit as a shallow network and call it a denoising autoencoder or DAE. Let be a DAE trained for . Denote by and the hidden layer and output layer of , respectively; that is, they satisfy . According to custom, we call the encoder, the decoder, and the feature of . Remark on a potential confusion. Although we trained as a function of in order to enhance robustness, we plug in in place of . Then, no longer behaves as an identity map, which may be expected from traditional autoencoders, but as a denoising map formulated in (3). ### 2.2 Alain’s Derivation of Denoising Autoencoders Alain2014 showed that the regression function (2) for a DAE is reduced to (1). We can rewrite it as Φt=Id+t∇log[Wt/2∗p0], (3) where is the isotropic heat kernel () and is the data distribution. The proof is straightforward: Eε[p0(x−ε)(x−ε)]Eε[p0(x−ε)] =x−Eε[p0(x−ε)ε]Eε[p0(x−ε)] =x+t∇Wt/2∗p0(x)Wt/2∗p0(x) =x+t∇log[Wt/2∗p0(x)], where the second equation follows by the fact that . As an infinitesimal limit, (3) is reduced to an asymptotic formula: Φt=Id+t∇logp0+o(t2),t→0. (4) We can interpret it as a velocity field over the ground space : ∂tΦ0(x)=∇logp0(x),x∈M. (5) It implies that the initial velocity of the transportation of a mass on is given by the score, which is in the sense of “score matching.” ### 2.3 Anisotropic Denoising Autoencoder We introduce the anisotropic DAE as Φt(x;D) by replacing the heat kernel in (3) with an anisotropic heat kernel . The original formulation corresponds to the case . Because of the definition, the initial velocity does not depend on . Hence, (5) still holds for the anisotropic case. ∂tΦ0(x;D)=∇logp0(x),x∈M. If is clear from the context, we write simply without indicating . ### 2.4 Stacked Denoising Autoencoder Let be vector spaces and denote a feature vector that takes a value in . The input space () and an input vector () are rewritten in and , respectively. A stacked DAE is obtained by iteratively alternating (i) training a DAE for the feature and (ii) extracting a new feature with the encoder of . We call a composition of encoders a stacked DAE, which corresponds to the solid lines in the diagram below.	2021-11-28 06:52:59	{"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": 0.8174321055412292, "perplexity": 1451.7497698437996}, "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-2021-49/segments/1637964358469.34/warc/CC-MAIN-20211128043743-20211128073743-00109.warc.gz"}
http://www.geteasysolution.com/3t-7=5t+6t	# 3t-7=5t+6t ## Simple and best practice solution for 3t-7=5t+6t equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so dont hesitate to use it as a solution of your homework. If it's not what You are looking for type in the equation solver your own equation and let us solve it. ## Solution for 3t-7=5t+6t equation: Simplifying 3t + -7 = 5t + 6t Reorder the terms: -7 + 3t = 5t + 6t Combine like terms: 5t + 6t = 11t -7 + 3t = 11t Solving -7 + 3t = 11t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-11t' to each side of the equation. -7 + 3t + -11t = 11t + -11t Combine like terms: 3t + -11t = -8t -7 + -8t = 11t + -11t Combine like terms: 11t + -11t = 0 -7 + -8t = 0 Add '7' to each side of the equation. -7 + 7 + -8t = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -8t = 0 + 7 -8t = 0 + 7 Combine like terms: 0 + 7 = 7 -8t = 7 Divide each side by '-8'. t = -0.875 Simplifying t = -0.875`	2016-09-27 18:53:21	{"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": 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": 0.21066872775554657, "perplexity": 2184.5668193634733}, "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-2016-40/segments/1474738661155.8/warc/CC-MAIN-20160924173741-00263-ip-10-143-35-109.ec2.internal.warc.gz"}
https://socratic.org/questions/a-store-buys-flowers-for-2-25-each-the-store-then-marks-up-the-price-of-each-flo#282622	#### Explanation: If we take $2.25 as 100% and they mark it up by 60% it means the selling price would be 160% Therefore, we divide$2.25 by 100 to get 1% then we multiply by 160 to get 160% which is the selling price. So, the selling price is \$3.60	2021-09-27 19:56:16	{"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": 0.8333024978637695, "perplexity": 691.8238799448618}, "config": {"markdown_headings": true, "markdown_code": false, "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-2021-39/segments/1631780058467.95/warc/CC-MAIN-20210927181724-20210927211724-00648.warc.gz"}
https://math.stackexchange.com/questions/1265622/klein-bottle-and-real-projective-plane	# Klein bottle and Real Projective plane How to determine the triangulation of these two objects? can we use the above to compute Fundamental Group of Klein bottle and Real Projective plane? I can use the van kamen theorem to prove one is $Z/2Z$ and the other is $Z^2/<x^2-y^2>$, but it is hard for me to use the triangulation method. Thank you! • Many thanks for your help! – Kevin May 4 '15 at 7:56 • Since you're new here, don't forget to accept an answer (click on the check mark by it) if it works for you. Also, it's nice to upvote any answers that are beneficial. Regards, – user12802 May 8 '15 at 13:43 $\Bbb RP^2$ and $K$ has quite easy $\Delta$-complex structure obtained from cutting the fundamental square through the diagonal. Claim : Barycentrically subdividing any $\Delta$-complex $X$ twice gives a simplicial complex $X'$ homeomorphic to $X$. This is Hatcher's exercise $2.1.23$. Sketch of a proof is to note that a $\Delta$-complex might have two $2$-simplices pasted together along their sides, so that neither of them are uniquely determined by their boundaries. After the first triangulation, since the barycenter lies in interior of each of the simplices and the interiors are left unidentified while constructing a $\Delta$-complex, each of the $2$-simplicies in the subdivided $X$ are uniquely determined by their sides. Similarly, to resolve this problem for $1$-simplices with two of it's boundary points identified, one needs a second barycentric subdivision. It is not hard to see that all the higher dimensional simplices in the resulting $\Delta$-complex are uniquely determined by their faces. Thus, one obtains a simplicial complex $X' \cong X$. Using this statement, one can obtain triangulations of $\Bbb RP^2$ and $K$. One doesn't need a simplicial structure to compute $\pi_1$. $\Bbb RP^2$ and $K$ has the CW structure (obtained from the fundamental square) $e^2 \cup e^1 \cup e^0$ and $e^2 \cup e^1 \cup e^1 \cup e^0$, where in the case of $\Bbb RP^2$, $e^2$ is pasted to the circle $e^1 \cup_{\partial} e^0$ via the map $x \mapsto x^2$ and in the case of $K$, $e^2$ is attatched to the figure eight $e^1 \cup_\partial e^0 \cup_\partial e^1$ by attatching map given by the word $aba^{-1}b$. Applying van Kampen theorem, one obtains $\pi_1(\Bbb RP^2) \cong \Bbb Z/2$ and $\pi_1(K) \cong \langle a, b \| ab = b^{-1} a\rangle$ Alternatively, an easier way to do this is to note that there are regular covering maps $S^2 \to \Bbb RP^2$ and $S^1 \times S^1 \to K$ with deck transformation $\Bbb Z/2$ each, and use the following lemma Claim : $X$ be a path connected, locally path connected and semi-locally simply connected space with a group $G$ acting freely and properly discontinuously on $X$. Then there is a short exact sequence $$1 \to \pi_1(X) \to \pi_1(X/G) \to G \to 1$$ Since deck transformation group acts properly discontinuously and freely on covering spaces, we can use this to obtain $\pi_1(\Bbb RP^2) \cong \Bbb Z/2$ (since $S^2$ is simply connected) and that $\pi_1(K)$ is an extension of $\Bbb Z \times \Bbb Z$ by $\Bbb Z/2$, which reduces to the presentation above after knowing the explicit action of deck transformation.	2019-06-27 10:00:03	{"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": 0.8828198313713074, "perplexity": 124.03227018998619}, "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/1560628001089.83/warc/CC-MAIN-20190627095649-20190627121649-00470.warc.gz"}
http://www.sawaal.com/aptitude-reasoning/quantitative-aptitude-arithmetic-ability/time-and-work-questions-and-answers.html?sort=rated	# Time and Work Questions Q: 12 men can complete a work in 8 days. 16 women can complete the same work in 12 days. 8 men and 8 women started working and worked for 6 days. How many more men are to be added to complete the remaining work in 1 day? A) 8 B) 12 C) 16 D) 24 Explanation: 1 man's 1 day work =$\inline&space;{\color{Black}\frac{1}{96}&space;}$ ; 1 woman's 1 day work =$\inline&space;{\color{Black}\frac{1}{192}&space;}$ work done in 6 days= $\inline&space;{\color{Black}6(\frac{8}{96}+\frac{8}{192})&space;=(6\times&space;\frac{1}{8})=\frac{3}{4}}$ Remaining work =$\inline&space;{\color{Black}(1-\frac{3}{4})=\frac{1}{4}}$ (8 men +8 women)'s 1 day work =$\inline&space;{\color{Black}1(\frac{8}{96}+\frac{8}{192})}$=$\inline&space;{\color{Black}\frac{1}{8}}$ Remaining work=$\inline&space;{\color{Black}(\frac{1}{4}-\frac{1}{8})=\frac{1}{8}}$ $\inline&space;{\color{Black}\frac{1}{96}}$ work is done in 1 day by 1 man $\inline&space;{\color{Black}\therefore&space;}$$\inline&space;{\color{Black}\frac{1}{8}}$ work will be done in 1 day by $\inline&space;{\color{Black}(96\times&space;\frac{1}{8})=12}$ men 35 8950 Q: A can do a piece of work in 10 days, B in 15 days. They work together for 5 days, the rest of the work is finished by C in two more days. If they get Rs. 3000 as wages for the whole work, what are the daily wages of A, B and C respectively (in Rs): A) 200, 250, 300 B) 300, 200, 250 C) 200, 300, 400 D) None of these Explanation: A's 5 days work = 50% B's 5 days work = 33.33% C's 2 days work = 16.66% [100- (50+33.33)] Ratio of contribution of work of A, B and C = $\inline \fn_jvn 50:33\frac{1}{3}:16\frac{2}{3}$ = 3 : 2 : 1 A's total share = Rs. 1500 B's total share = Rs. 1000 C's total share = Rs. 500 A's one day's earning = Rs.300 B's one day's earning = Rs.200 C's one day's earning = Rs.250 34 12738 Q: A, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 4 days before the completion of the work. In how many days was the work completed? A) 11 days B) 12 days C) 13 days D) 14 days Explanation: One day's work of A, B and C = (1/24 + 1/30 + 1/40) = 1/10 C leaves 4 days before completion of the work, which means only A and B work during the last 4 days. Work done by A and B together in the last 4 days = 4 (1/24 + 1/30) = 3/10 Remaining Work = 7/10, which was done by A,B and C in the initial number of days. Number of days required for this initial work = 7 days. Thus, the total numbers of days required = 4 + 7 = 11 days. 24 7768 Q: A Contractor employed a certain number of workers to finish constructing a road in a certain scheduled time. Sometime later, when a part of work had been completed, he realised that the work would get delayed by three-fourth of the scheduled time, so he at once doubled the no of workers and thus he managed to finish the road on the scheduled time. How much work he had been completed, before increasing the number of workers? A) 10 % B) 14 2/7 % C) 20 % D) Can't be determined Explanation: Let he initially employed x workers which works for D days and he estimated 100 days for the whole work and then he doubled the worker for (100-D) days. D * x +(100- D) * 2x= 175x => D= 25 days Now , the work done in 25 days = 25x Total work = 175x therefore, workdone before increasing the no of workers = $\frac{25x}{175x}\times&space;100=14\frac{2}{7}$ % 17 2680 Q: Relation Between Efficiency and Time A is twice as good a workman as B and is therefore able to finish a piece of work in 30 days less than B.In how many days they can complee the whole work; working together? Sol: Ratio of efficiency = 2:1 (A:B) Ratio of required time = 1:2 (A:B) $\inline&space;\fn_jvn&space;\Rightarrow$ x:2x but 2x-x=30 $\inline&space;\fn_jvn&space;\Rightarrow$ x= 30 and 2x= 60 Now efficiency of A =3.33% and efficiency of B =1.66% Combined efficiency of A and B together = 5% $\inline&space;\fn_jvn&space;\therefore$ time required by A and B working together to finish the work = $\inline&space;\fn_jvn&space;\frac{100}{5}$ = 20 days Note: Efficiency $\inline&space;\fn_jvn&space;\prec$ $\inline&space;\fn_jvn&space;\frac{1}{number\:&space;of&space;\:&space;time\:&space;units}$ $\inline&space;\fn_jvn&space;\therefore$ Efficiency $\inline&space;\fn_jvn&space;\times$ time = Constant Work Hence, Required time = $\inline&space;\fn_jvn&space;\frac{work}{efficiency}$ whole work is always cosidered as 1, in terms of fraction and 100%, in terms of percentage. In, general no.of days or hours = $\inline&space;\fn_jvn&space;\frac{100}{efficiency}$	2017-04-25 08:44:42	{"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": 0, "codecogs_latex": 23, "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": 0.709193766117096, "perplexity": 1094.5863048379272}, "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/1492917120206.98/warc/CC-MAIN-20170423031200-00190-ip-10-145-167-34.ec2.internal.warc.gz"}
https://puzzling.stackexchange.com/questions/87637/what-is-a-monolithic-word	# What is a Monolithic Word™? This is in the spirit of the What is a Word/Phrase™ series started by JLee with a special brand of Phrase™ and Word™ puzzles. If a word conforms to a special rule, I call it a Monolithic Word™. Use the following examples below to find the rule. $$% set Title text. (spaces around the text ARE important; do not remove.) % increase Pad value only if your entries are longer than the title bar. % \def\Pad{\P{0.0}} \def\Title{\textbf{ Monolithic }} % \def\S#1#2{\Space{#1}{20px}{#2px}}\def\P#1{\V{#1em}}\def\V#1{\S{#1}{9}} \def\T{\Title\textbf{Words}^{\;\!™}\Pad}\def\NT{\Pad\textbf{Not}\T\ }\displaystyle \smash{\lower{29px}\bbox[grey]{\phantom{\rlap{rubio.2019.05.15}\S{6px}{0} \begin{array}{cc}\Pad\T&\NT\\\end{array}}}}\atop\def\V#1{\S{#1}{5}} \begin{array}{\|c\|c\|}\hline\Pad\T&\NT\\\hline % \text{ ALCHEMY }&\text{ ACCUSE }\\ \hline \text{ BURNING }&\text{ BIZARRE }\\ \hline \text{ CUIRASS }&\text{ DUSTY }\\ \hline \text{ EXPIRY }&\text{ EXCUSE }\\ \hline \text{ HOCUS }&\text{ HIDEOUS }\\ \hline \text{ JIGGLE }&\text{ ILLEGAL }\\ \hline \text{ OXIDE }&\text{ STARK }\\ \hline \text{ VICTORY }&\text{ WINCE }\\ \hline \text{ ZODIAC }&\text{ ZIGZAG }\\ \hline \end{array}$$ And, if you want to analyze, here is a CSV version: Monolithic Words™,Not Monolithic Words™ ALCHEMY,ACCUSE BURNING,BIZARRE CUIRASS,DUSTY EXPIRY,EXCUSE HOCUS,HIDEOUS JIGGLE,ILLEGAL OXIDE,STARK VICTORY,WINCE ZODIAC,ZIGZAG The puzzle satisfies the series' inbuilt assumption, that each word can be tested for whether it is a Monolithic Word™ without relying on the other words. These are not the only examples of Monolithic Words™; many more exist. What is the special rule these words conform to? Hint 1: What is the main property of a monolith? Hint 2: The Answer to the Ultimate Question of Life, the Universe, and Everything is not really 42, it's $$\textbf{}$$ as the wildcard symbolizes everything... and possibly some other reason too ;) Hint 3: (an extension of Hint 2) What is the relation between $$\textbf$$ and 42? Good luck! My guess: A monolithic word is a word that, when turning every (upper case) letter into ASCII code and concatenate them, it becomes a prime. eg ALCHEMY. A->$$65$$, L->$$76$$ etc. So ALCHEMY -> $$65766772697789$$ is a prime. eg ACCUSE -> $$656767858369=7\times 7\times 239\times 56081279$$ is not a prime. The last hint is a big giveaway: the ASCII code for $$*$$ is $$42$$ :) • @r_64 Good job! :) I think I made this harder than required. :) – user47134 Sep 5 '19 at 16:40 First attempt (wrong): My first guess (but based on the example is wrong ) is that a Monolithic Word... ...does not contain other words (as a monolith is a single piece element), but this is not the case for BURNING or CUIRASS For the Non-Monolithic words - ACCUSE - BIZARRE - DUSTY - EXCUSE - HIDEOUS - ILLEGAL - STARK - WINCE - ZIGZAG • Unfortunately, that's not the correct path :( Nice spotting though, and strange that it is accurate to this degree even though I didn't intend it :) – user47134 Sep 3 '19 at 16:32 • Also, jiggle contains jig and oxide contains ox. – hexomino Sep 3 '19 at 16:38 • Thanks for the clarification... I will try another approach then – gustavovelascoh Sep 3 '19 at 16:46 • Moreover, 'victory' contains 'victor' – Quark-epoch Sep 4 '19 at 13:22 • I noticed this, with three-letter words only. USE, BIZ<sub>questionable</sub>, STY, USE, HID, ILL, TAR, WIN, ZIG<sub>questionable</sub>. Problem is, you end up with HEM, URN, ASS, and JIG on the wrong side. – Khuldraeseth na'Barya Sep 5 '19 at 14:27 I think I may be wrong but A monolith is a monument carved out of a single stone . The Monolithic Words ™ can be derived by starting with a single letter. • Can you please clarify what you mean by "derived"? :) – user47134 Sep 4 '19 at 13:16 • So you start with one letter, then add another to form a meaningful word. This goes on and on till you get the target word. – Quark-epoch Sep 4 '19 at 13:20 • Sorry, but not the correct path :( I'm adding the next hint now, good luck with the puzzle! :D – user47134 Sep 4 '19 at 13:23	2020-04-04 09:32:24	{"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": 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": 9, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5007602572441101, "perplexity": 3231.9017732231205}, "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-2020-16/segments/1585370521574.59/warc/CC-MAIN-20200404073139-20200404103139-00105.warc.gz"}
https://questions.examside.com/past-years/jee/question/a-uniform-metallic-wire-has-a-resistance-of-18-omega-a-jee-main-physics-units-and-measurements-ks6kk3srfzoahruv	1 JEE Main 2019 (Online) 10th January Morning Slot A uniform metallic wire has a resistance of 18 $\Omega$ and is bent into an equilateral triangle. Then, the resistance between any two vertices of the triangle is - A 12 $\Omega$ B 2 $\Omega$ C 4 $\Omega$ D 8 $\Omega$ $\Omega$ Explanation Req berween any two vertex will be ${1 \over {{{\mathop{\rm R}\nolimits} _{eq}}}} = {1 \over {12}} + {1 \over 6} \Rightarrow {{\mathop{\rm R}\nolimits} _{eq.}} = 4\Omega$ 2 JEE Main 2019 (Online) 10th January Morning Slot A 2 W carbon resistor is color coded with green, black, red and brown respectively. The maximum current which can be passed through this resistor is - A 0.4 mA B 20 mA C 63 mA D 100 mA Explanation P = i2R. $\therefore$ for imax, R must be minimum from color coding R = 50 $\times$ 102$\Omega$ $\therefore$ imax = 20mA 3 JEE Main 2019 (Online) 10th January Morning Slot A charge Q is distributed over three concentric spherical shells of radii a, b, c (a < b < c) such that their surface charge densities are equal to one another. The total potential at a point at distance r from their common centre, where r < a, would be - A ${{Q\left( {{a^2} + {b^2} + {c^2}} \right)} \over {4\pi {\varepsilon _0}\left( {{a^3} + {b^3} + {c^3}} \right)}}$ B ${Q \over {4\pi {\varepsilon _0}\left( {a + b + c} \right)}}$ C ${Q \over {12\pi {\varepsilon _0}}}{{ab + bc + ca} \over {abc}}$ D ${{Q\left( {a + b + c} \right)} \over {4\pi {\varepsilon _0}\left( {{a^2} + {b^2} + {c^2}} \right)}}$ Explanation Potential at point P, V = ${{k{Q_a}} \over a} + {{k{Q_b}} \over b} + {{k{Q_c}} \over c}$ $\because$ Qa : Qb : Qc : : a2 : b2 : c2 {since $\sigma$a = $\sigma$b = $\sigma$c} $\therefore$ Qa = $\left[ {{{{a^2}} \over {{a^2} + {b^2} + {c^2}}}} \right]$Q Qb = $\left[ {{{{b^2}} \over {{a^2} + {b^2} + {c^2}}}} \right]$ Q Qc = $\left[ {{{{c^2}} \over {{a^2} + {b^2} + {c^2}}}} \right]$ Q V = ${Q \over {4\pi { \in _0}}}\left[ {{{\left( {a + b + c} \right)} \over {{a^2} + {b^2} + {c^2}}}} \right]$ 4 JEE Main 2019 (Online) 10th January Morning Slot In the given circuit the cells have zero internal resistance. The currents (in Amperes) passing through resistance R1 and R2 respectively, are - A 0.5, 0 B 0, 1 C 1, 2 D 2, 2 Explanation i1 = ${{10} \over {20}}$ = 0.5A i2 = 0	2021-10-23 02:11:19	{"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": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5595242381095886, "perplexity": 3143.795053409901}, "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/1634323585537.28/warc/CC-MAIN-20211023002852-20211023032852-00473.warc.gz"}
https://www.azimuthproject.org/azimuth/revision/diff/Azimuth+Climate+Data+Backup+Project/6	# The Azimuth Project Azimuth Climate Data Backup Project (Rev #6, changes) Showing changes from revision #5 to #6: Added \| Removed \| Changed ### The idea We’re backing up US government databases on climate change and the environment before Trump takes office on January 20th. We need some money, at least $5000, for storage space and a server. More would be better. So, we’re setting up a Kickstarter campaign. We’re backing up US government databases on climate change and the environment before Trump takes office on January 20th. We need some money, at least$5000, for storage space and a server. More would be better. ### Background The safety of US government climate data is at risk. Trump plans to have climate change deniers running every agency concerned with climate change. Trump's choice for head of the Environmental Protection Agency, Scott Pruit, calls himself a "leading advocate against the EPA's activist agenda". Pruitt even sued this agency to block Obama's plan to fight global warming. Trump's choice for the Department of Energy, Rick Perry, has claimed that "we have been experiencing a cooling trend", and said "there are a substantial number of scientists who have manipulated data so that they will have dollars rolling into their projects". This makes it imperative to back up the many climate databases held by US government agencies before Trump takes office. We hope he won't be rash enough to delete these precious records. But: better safe than sorry! In fact, these backups are worth having regardless of the current political situation. They should have been made long ago. But Trump's choices for cabinet triggered a rush to get the job done before he takes office: The Azimuth Climate Data Backup Project is part of this effort. So far our volunteers have backed up nearly 1 terabyte of data from NASA, NOAA, and other agencies. We'll do a lot more. But we need some funds to pay for storage space and a server. ### The Project Our team is led by four volunteers. Jan Galkowski is a statistician with a strong interest in climate science. He works at Akamai Technologies, a company responsible for serving at least 15% of all web traffic. He began downloading climate data on the 11th of December. Shortly thereafter John Baez, a mathematician and well-known science blogger at U. C. Riverside, joined in to coordinate publicity for the project. He'd already founded an organization called the Azimuth Project, which helps scientists and engineers cooperate on environmental issues. So, we called this new effort the Azimuth Climate Data Backup Project. When Jan started running out of storage space, Scott Maxwell jumped in. He used to work for NASA — driving a Mars rover among other things — and now he works for Google. He set up a 10-terabyte account on Google Drive and started backing up data himself. A couple of days later Sakari Maaranen joined the team. He's a systems architect at Ubisecure, a Finnish firm, with access to a high-bandwidth connection. He set up a server with Hetzner that provides us with 10 terabytes of storage, gigabit bandwidth and 30 terabytes of a monthly traffic. We can expand the storage space as needed. This is what we need money for! We want to keep US government environmental databases safely backed up until larger institutions step in and help out. So far we've backed up these sites: Many more are in progress! We are computing hash codes for these datasets to help us prove our backups are authentic. You can watch the nitty-gritty details of our progress here: ### For More For more on our project, see: For more on the big picture, see: Trump’s choice for head of the Environmental Protection Agency, Scott Pruit, has called himself a "leading advocate against the EPA’s activist agenda". Pruitt even sued this agency to block Obama’s plan to fight global warming. Trump’s choice for the Department of Energy has claimed that we have been experiencing a cooling trend, and said "there are a substantial number of scientists who have manipulated data so that they will have dollars rolling into their projects". This makes it imperative to back up the many climate databases held by US government agencies before Trump takes office. We hope he won’t be rash enough to delete these precious records. But: better safe than sorry! In fact, these backups are worth having regardless of the current political situation. They should have been made long ago. But Trump’s choices for cabinet triggered a rush to get the job done before he takes office: • Brady Dennis, Scientists are frantically copying U.S. climate data, fearing it might vanish under Trump, Washington Post, 13 December 2016. The Azimuth Climate Data Backup Project is part of this effort. So far our volunteers have backed up nearly 1 terabyte of data from NASA, NOAA, and other agencies. We’ll do a lot more. But we need some funds to pay for storage space and a server. ### The project Our team is led by four volunteers. Jan Galkowski is a statistician with a strong interest in climate science. He works at Akamai Technologies, a company responsible for serving at least 15% of all web traffic. He began downloading climate data on the 11th of December. Shortly thereafter John Baez, a mathematician and well-known science blogger at U. C. Riverside, joined in to coordinate publicity for the project. He’d already founded an organization called the Azimuth Project, which helps scientists and engineers cooperate on environmental issues. So, we called this new effort the Azimuth Climate Data Backup Project. When Jan started running out of storage space, Scott Maxwell jumped in. He used to work for NASA — driving a Mars rover among other things — and now he works for Google. He set up a 10-terabyte account on Google Drive and started backing up data himself. A couple of days later Sakari Maaranen joined the team. He’s a systems architect at Ubisecure, a Finnish firm, with access to a high-bandwidth connection. He set up a server with Hetzner that provides us with 10 terabytes of storage, gigabit bandwidth and 30 terabytes of a monthly traffic. We can expand the storage space as needed. This is what we need money for! We want to keep US government environmental databases safely backed up until larger institutions step in and help out. You can see our progress here: So far we’ve backed up these sites: • NASA’s main database of temperature records, called GISTEMP. • The Carbon Dioxide Information Analysis Center, called CDIAC. • The Carbon Tracker website, a world-wide map of how carbon dioxide concentrations change with time. • The National Oceanic and Atmospheric Administration (NOAA) database of sea surface temperature files. • The NOAA Paleoclimatology Datasets. More are in progress! We are computing hash codes for these datasets to help us prove our copies are correct.	2021-11-28 19:50:31	{"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": 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": 0.21645598113536835, "perplexity": 4205.439685101853}, "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-2021-49/segments/1637964358591.95/warc/CC-MAIN-20211128194436-20211128224436-00245.warc.gz"}
https://homework.cpm.org/category/CCI_CT/textbook/int2/chapter/2/lesson/2.1.1/problem/2-6	### Home > INT2 > Chapter 2 > Lesson 2.1.1 > Problem2-6 2-6. The diagrams below are not necessarily drawn to scale. For each pair of triangles: • Determine if the two triangles are congruent. • If the triangles are congruent, write a congruence statement (such as $ΔPQR≅ΔXYZ$) and give the congruence theorem (such as $\operatorname{SAS}≅$). • If the triangles are not congruent, or if there is not enough information to determine congruence, write “cannot be determined” and explain why not. A shared side is a congruent side. AAA does not prove congruency. Order matters: SAS proves congruence but SSA does not. 1. $\overline{AC}$ is a straight segment:	2020-07-04 19:03:18	{"extraction_info": {"found_math": true, "script_math_tex": 3, "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": 0.4982777237892151, "perplexity": 1814.0249511097486}, "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-2020-29/segments/1593655886516.43/warc/CC-MAIN-20200704170556-20200704200556-00117.warc.gz"}
https://solvedlib.com/simple-interest-is-given-by-the-formula,328299	# Simple interest is given by the formula A=P+PrtA=P+Prt. Where AA is the balance of the account... ###### Question: Simple interest is given by the formula A=P+PrtA=P+Prt. Where AA is the balance of the account after tt years, and PP is the starting principal invested at an annual percentage rate of rr, expressed as a decimal. Keegan is investing money into a savings account that pays 4% simple interest, and plans to leave it there for 20 years. Determine what Keegan needs to deposit now in order to have a balance of $50,000 in his savings account after 20 years. Keegan will have to invest$ now in order to have a balance of $50,000 in his savings account after 20 years. Round your answer to the nearest dollar. Simple Interest Application Simple interest is given by the formula A = P + Prt. Where A is the balance of the account after t years, and P is the starting principal invested at an annual percentage rate of r, expressed as a decimal. Keegan is investing money into a savings account that pays 4% simple interest, and plans to leave it there for 20 years. Determine what Keegan needs to deposit now in order to have a balance of$50,000 in his savings account after 20 years. Keegan will have to invest $now in order to have a balance of$50,000 in his savings account after 20 years. Round your answer to the nearest dollar. #### Similar Solved Questions ##### —What type of senior do you want to be? And what are you doing to get... —What type of senior do you want to be? And what are you doing to get there?... ##### What is the typical pattern for consumers when they make decisions on consumption? A. As the... What is the typical pattern for consumers when they make decisions on consumption? A. As the consumption of a good increases, marginal utility rises. B. As the consumption of a good increases, total utility falls but marginal utility rises. C. As the consumption of a good increases, total utility fa... ##### Based on these graphs of 13CNMR and 1HNMR what would the final structure of the molecule... Based on these graphs of 13CNMR and 1HNMR what would the final structure of the molecule look like? The molecular weight is 98. Q2 cont. 2D NMR Q2 cont. 'H NMR expansions 23 22 21 20 19 18 14 12 1 0 IH-IH Correlation d, Jelo ''31 C 17.3 11 10 9 8 7 6 5 4 3 2 1 9 8 7 6 5 4 3 2 10 ppm 1 D... ##### FMG Group, headquartered in Frankfurt, Germany, manufactures several automotive brands. Financial information is reported in the... FMG Group, headquartered in Frankfurt, Germany, manufactures several automotive brands. Financial information is reported in the euro (€) monetary unit using International Financial Reporting Standards (IFRS) as applicable to the European Union. The following activities were adapted from the an... ##### Teacher gives test t0 large group of students: The resulls are closely approximated by normal curve_ The mean is 77 with standard devialion of 5. The teacher wishes t0 give As to the top 8% of the students and F's to the bottom 8%. grade of B is given to the next 15%, with D's given similarly: All other students get e C's. Find the bottom cutoff forClick hereto_see_page of the table for areas_under the_standard normalcuqve Click C hereuto see page ofuthe table for areas under the teacher gives test t0 large group of students: The resulls are closely approximated by normal curve_ The mean is 77 with standard devialion of 5. The teacher wishes t0 give As to the top 8% of the students and F's to the bottom 8%. grade of B is given to the next 15%, with D's given simila... ##### Jent 4: Organic NomenclaturePart 5 Draw the skeletal structure for each of the following molecules1,3-cichloro-3-methylnonaneMacBoak AirRReply: Jent 4: Organic Nomenclature Part 5 Draw the skeletal structure for each of the following molecules 1,3-cichloro-3-methylnonane MacBoak Air R Reply:... ##### Wnati d fferent about these molecules? What are charges? Hc " Many icla electrons they have? How many hydrcgens 378 on each camdon?Week 02 CHO2 Puge Wnati d fferent about these molecules? What are charges? Hc " Many icla electrons they have? How many hydrcgens 378 on each camdon? Week 02 CHO2 Puge... ##### Choose all that apply: CHz-CHz-" CHz-( CHz-CH: CHz-CHz" CHz- CH; CH3 CHz CHCHZ CHz CH}CHs-CH-CHz" CH3 CHsCHs-CH:CHs Choose all that apply: CHz-CHz-" CHz-( CHz-CH: CHz-CHz" CHz- CH; CH3 CHz CH CHZ CHz CH} CHs-CH-CHz" CH3 CHs CHs- CH: CHs... ##### The displacement from equllibrium of an object In harmonic motion on the end of & spring glven below, where Y Is measured In feet and t Is the tlme In seconds. Determine the position y(t) and velodty v(t) of the object when _ m/8, cos( 12t) sln(12t) Xr/8) vx/8) (Usec The displacement from equllibrium of an object In harmonic motion on the end of & spring glven below, where Y Is measured In feet and t Is the tlme In seconds. Determine the position y(t) and velodty v(t) of the object when _ m/8, cos( 12t) sln(12t) Xr/8) vx/8) (Usec... ##### The initial Mannich reaction can be carried out with methylamine. This gives a more direct route... The initial Mannich reaction can be carried out with methylamine. This gives a more direct route to Prozac, but the Mannich condensation with methylamine is low yielding and produces several by-products. Suggest a reason for this.... ##### 1 (20) Circle the integrals which are improper. Do not evaluateL dx [ Lnx &x dx J e & [" Lnx &r 6 X+ldx ( Xtldx drx J I+l 6alidx r+1Le &x 1 (20) Circle the integrals which are improper. Do not evaluate L dx [ Lnx &x dx J e & [" Lnx &r 6 X+l dx ( Xtl dx drx J I+l 6ali dx r+1 Le &x... ##### The "fill" problem is important in many industries, such as those making cereal, toothpaste, beer, and... The "fill" problem is important in many industries, such as those making cereal, toothpaste, beer, and so on. If an industry claims that it is selling 12 ounces of its product in a container, it must have a mean greater than 12 ounces, or else the FDA will crack down, although the FDA will a... ##### 8) [10 POINTS] Plot the implicitly defined function x2 – y4 = 0 over the domain... 8) [10 POINTS] Plot the implicitly defined function x2 – y4 = 0 over the domain (-21, 211]. (HINT: Using the ezplot command in MATLAB 9) [10 POINTS] -N -N+1 N Compute the x(w) for different values of N, i.e. N=2, 30, 40, 100. Plot the magnitude and the phase for these different N values. How d... ##### Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine if the events are unusual convenient; use the appropriate probability table or technology to find the probabilitiesnewspaper finds that the mean number of typographica errors per page is five. Find the probability that exactly four typographica emors are found on page; (b) at most four typographica errors are found on page, and more than four typographica erro Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine if the events are unusual convenient; use the appropriate probability table or technology to find the probabilities newspaper finds that the mean number of typogr... ##### Create a Psychology stats question : step 1: make a frequency or grouped frequency distribution table,... Create a Psychology stats question : step 1: make a frequency or grouped frequency distribution table, and do an interpolation to find some percentile. Part Two must require finding the Z-score and probability for a sample mean. Part Three must require doing some type of t-test and reporting the res... ##### (a) Show that if $P$ satisfies the logistic equation $(1),$ then $\frac{d^{2} P}{d t^{2}}=k^{2} P\left(1-\frac{P}{M}\right)\left(1-\frac{2 P}{M}\right)$ (b) Deduce that a population grows fastest when it reaches half its carrying capacity. (a) Show that if $P$ satisfies the logistic equation $(1),$ then $\frac{d^{2} P}{d t^{2}}=k^{2} P\left(1-\frac{P}{M}\right)\left(1-\frac{2 P}{M}\right)$ (b) Deduce that a population grows fastest when it reaches half its carrying capacity.... ##### Q2. Identify (yes Or no) whether the following molecules/ions display horizontal mirror plane symmetry and hence have a Gh symmetry operation_(a) benzene(b) 1,3-dichlorobenzene(c) ethyneL-menthol (shown below)OH(e)2+ OCm ACO Pd OC ~COCO OCmn, JCO "Cr" OC CO CO Q2. Identify (yes Or no) whether the following molecules/ions display horizontal mirror plane symmetry and hence have a Gh symmetry operation_ (a) benzene (b) 1,3-dichlorobenzene (c) ethyne L-menthol (shown below) OH (e) 2+ OCm ACO Pd OC ~CO CO OCmn, JCO "Cr" OC CO CO... ##### Product Decisions Under Bottlenecked Operations Youngstown Glass Company manufactures three types of safety plate glass: large,... Product Decisions Under Bottlenecked Operations Youngstown Glass Company manufactures three types of safety plate glass: large, medium, and small. All three products have high demand. Thus, Youngstown Glass is able to sell all the safety glass that it can make. The production process includes an aut... ##### Let g(t) be a differentiable invertible function; with inverse g-J(t), such that 9(2)=8 and 9'(2)=4 If flx,y,2)=g-llxy+2), then f,(2,3,2) =None of the other answers. 1233 Let g(t) be a differentiable invertible function; with inverse g-J(t), such that 9(2)=8 and 9'(2)=4 If flx,y,2)=g-llxy+2), then f,(2,3,2) = None of the other answers. 12 3 3... ##### In Exercises $21-24$ use a calculator or the trigonometry table on page 311 to find the area of each figure to the nearest tenth. In Exercises $21-24$ use a calculator or the trigonometry table on page 311 to find the area of each figure to the nearest tenth.... ##### Problem [. Vacancy in copper (40 points) Given that Cu crystallizes in the face-centered-cubic (fcc) structure, the atomic radius of Cu is [.28 A, the atomic weight of Cu is 63.55 amu; and the vacancy formation energy of Cu is [.0 eV_ H) Calculate the mass density of Cu from the information given above, assuming that the condition of close packing is satisfied (10 points); 1.2) Calculate the vacancy fraction in Cu at \|O00 % (10 points); 133) Calculate the vacancy concentration in Cu at the same Problem [. Vacancy in copper (40 points) Given that Cu crystallizes in the face-centered-cubic (fcc) structure, the atomic radius of Cu is [.28 A, the atomic weight of Cu is 63.55 amu; and the vacancy formation energy of Cu is [.0 eV_ H) Calculate the mass density of Cu from the information given ab... ##### Required information Exercise 2-15 Plantwide and Departmental Predetermined Overhead Rates; Job Costs [LO2-1, LO2-2, LO2-3, LO2-4)... Required information Exercise 2-15 Plantwide and Departmental Predetermined Overhead Rates; Job Costs [LO2-1, LO2-2, LO2-3, LO2-4) (The following information applies to the questions displayed below.) Delph Company uses a job-order costing system and has two manufacturing departments-Molding and Fab... ##### Today you purchase a coupon bond that pays an annual interest, has a par value of... Today you purchase a coupon bond that pays an annual interest, has a par value of \$1,000, matures in six years, has a coupon rate of 10%, and has a yield to maturity of 8%. One year later, you sell the bond after receiving the first interest payment and the bond's yield to maturity had changed t... ##### Perform the indicated test: Assume that the two samples are independent simple random from normally distributed populations Also, do not assume that the samples selected population standard deviations are equal (01 02) . A researcher interested in comparing salaries of female and male emplovees at a particular of 8 female and 15 male employees made the following company: Independent random samples weekly salaries.Female:495,760,556,904,520,1005, 743,660 722,562,,880,520,500, 1250,750,1640,518,90 Perform the indicated test: Assume that the two samples are independent simple random from normally distributed populations Also, do not assume that the samples selected population standard deviations are equal (01 02) . A researcher interested in comparing salaries of female and male emplovees at a... ##### Ql. The following MATLAB code computes the cosine value ranging from 0 to 10 using vectorization... Ql. The following MATLAB code computes the cosine value ranging from 0 to 10 using vectorization technique: t = 0:1:10; y cos (t); Rewrite the code above using i. for loop ii. while loop (5 marks)... ##### QuEsTION 254nolneEenu OluilanUse only tannsadeclre paents (XX) Acom 43532 Jcciylcnc Coh; the Ioltoinu (eection;3 314KPa mdla"-ractor3C0.0 KPA andHClacd;zhOk9} C2h2(9) - 6,244(9}aretylene, C2hz.ninceteto Int rcadon Wlo:tneimon) redeent MnarJal volumethe srsten? QuEsTION 25 4nolne Eenu Oluilan Use only tannsadeclre paents (XX) Acom 43532 Jcciylcnc Coh; the Ioltoinu (eection; 3 314 KPa mdla" -ractor 3C0.0 KPA and HClacd; zhOk9} C2h2(9) - 6,244(9} aretylene, C2hz. ninceteto Int rcadon Wlo: tneimon) redeent Mnar Jal volume the srsten?... ##### In guinea pigs:Brown hair is the dorninant allele (BJ; albino the recessive allcle (b} The parents are Arown ~haired guinea pig and Albino guinea Answer the following questions;Croys A: There wcre Buine: pigs haired parent isintet and allaf hemn were brown Ths ' would mean that the genotype of the brownCross B; There were Buinea pigs in the Wtter: were Drowyn and were albino. This would mean the genotype of the brown haired parent In guinea pigs: Brown hair is the dorninant allele (BJ; albino the recessive allcle (b} The parents are Arown ~haired guinea pig and Albino guinea Answer the following questions; Croys A: There wcre Buine: pigs haired parent is intet and allaf hemn were brown Ths ' would mean that the genotype ... ##### The Byte of Accounting Corporation (Byte) sells turn-key computer systems to midsize businesses on account. Byte... The Byte of Accounting Corporation (Byte) sells turn-key computer systems to midsize businesses on account. Byte was started by Lauryn on January 1 of last year when she was issued 2,200 shares of stock. - Perpetual FIFO will be used for the Super Toners. - The allowance method is used to account fo... ##### A 54 kg high jumper has a gravitational potential energy of 1,067 J at the height of his jump A 54 kg high jumper has a gravitational potential energy of 1,067 J at the height of his jump. How high did he jump? A. 1.2 m B. 2.0 m C. 3.2 m D. 4.1 m... ##### Complete each statement with the word always, sometimes, or never.Three lines intersecting in one point are _____ coplanar. Complete each statement with the word always, sometimes, or never. Three lines intersecting in one point are _____ coplanar.... ##### 1213 Concentrations in an Ideal GasAn ideal gas &t 37C and 760 mmHg consists by weight of 0.01% helium, 15% oxygen and S% carbon dioxide, and the balance is nitrogen. Find the following quantities: () mass fraction for each species, (b) mass concentration of each sprcies; (C) Ihe partial pressures of each species, (d) mole fraction of each species (e) molar concentration of each species, (f) mean molecular weight, (g) total mass concentralion, and (h) total molar concentration.12.13. Water- 1213 Concentrations in an Ideal Gas An ideal gas &t 37C and 760 mmHg consists by weight of 0.01% helium, 15% oxygen and S% carbon dioxide, and the balance is nitrogen. Find the following quantities: () mass fraction for each species, (b) mass concentration of each sprcies; (C) Ihe partial press...	2023-02-04 02:50:49	{"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": 3, "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": 0.5657972097396851, "perplexity": 5730.0062542011665}, "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/1674764500080.82/warc/CC-MAIN-20230204012622-20230204042622-00802.warc.gz"}
http://math.stackexchange.com/questions/257956/arithmetic-functions	# Arithmetic functions This may be a slightly vague question but if one defines a function (of some arity) recursively on the natural numbers, the "simplest" examples are things like addition, multiplication, or factorial. How do these functions fit into a general sense of defining recursively functions on the natural numbers? Starting only from the successor operator. What indeed exactly is an "arithmetic function"? - Perhaps you're thinking of primitive recursive functions. – Zhen Lin Dec 13 '12 at 15:00 Yes, perhaps now a button to "restate" the question might be nice, given that I know or recall a bit more now. Obviously if I edit it loads, it will make the ensuing answers that were helpful, look silly. – John Smith Dec 13 '12 at 19:01 You need to be a bit more specific about what counts as defining a function recursively. You probably mean what is called, more carefully, a definition by primitive recursion, where e.g. we stipulate the value of $f(0)$ and then define $f(n + 1)$ in terms of the value of $f(n)$ using only already-defined functions. A techie aside: On some nice ways of defining what it is to define an $n + 1$ function (primitive)-recursively in its final argument, you'll need more that the successor function in your "starter pack" of functions if you are even to get addition -- you'll need the "projection functions" $I_k^n$ which take an $n$-tuple of arguments and return the $k$-th argument as value, and the zero function $Z(n)$ which always takes the value zero. But these fine details apart, the functions that can be defined by a sequence of primitive recursive definitions starting from the successor function (and other trivia) are the primitive recursive functions -- i.e. the numerical functions that can be computed using just "for" loops without any open-ended searches. For more, see e.g. the opening section of http://plato.stanford.edu/entries/recursive-functions/ or of course http://en.wikipedia.org/wiki/Primitive_recursive_function - I'm aware of the proof that recursion is well defined for example: given f(0) and that f(n)=gf(n-1), prove by induction that for any natural number n, the first n "initial segments" that belong to your countably infinite sequence you are about to prove exists, and than take the set theoretic union over the natural numbers to obtain this sequence. – John Smith Dec 13 '12 at 18:49 But yeah, that primitive recursive thing does sound like something I've heard before (but forgot). You start with constant functions, projections and the successor function. What simple functions on the naturals are arrived at in this way, and how do the standard "arithmetic functions" like addition, multiplication and so forth fit into it? – John Smith Dec 13 '12 at 18:53 An arithmetic function on $N$ can be seen as a subset of $N^3$. For a function $f$ of two variables on $N$ (like addition or multiplication), $\forall a,b,c ((a,b,c)\in f\rightarrow (a,b,c)\in N^3)$ $\forall a,b\in N\exists c\in N ((a,b,c)\in f)$ $\forall a,b,c,d\in N ((a,b,c)\in f\wedge (a,b,d)\in f\rightarrow c=d)$ If you want to construct the add function on $N$ using only the successor function $s$, you start by selecting a subset $S$ from $\mathcal P(N^3)$ such that: $\forall a(a\in S \leftrightarrow a\in \mathcal P(N^3) \wedge \forall b\in N((b,1,s(b))\in a)\wedge\forall b,c,d\in N ((b,c,d)\in a\rightarrow(b,s(c),s(d))\in a))$ Then the required add function (a subset of $N^3$) is just the intersection $\bigcap S$. - Yes that's the definition of addition I've seen before. I suppose my question Dan is how do addition and multiplication (and exponentiation and tetration etc.) fit into some general scheme of defining functions on the natural numbers in this way? Whatever "this way" is, of course. Perhaps it could be defined as primitive recursion on the natural numbers starting from successor, zero, and projections. – John Smith Dec 13 '12 at 18:58 The construction I give for addition here implements the recursive definition given informally as: $x+1=s(x)$ and $x+s(y)=s(x+y)$. For multiplication, that would be: $x\times 1 = x$ and $x\times (y+1)=x\times y+x$ – Dan Christensen Dec 15 '12 at 17:07 Having constructed the '+' function, for multiplication we would have: $\forall a(a\in S \leftrightarrow a\in \mathcal P(N^3) \wedge \forall b\in N((b,1,b)\in a)\wedge\forall b,c,d\in N ((b,c,d)\in a\rightarrow(b,c+1,d+b)\in a))$ – Dan Christensen Dec 16 '12 at 4:23	2014-12-22 18:52:51	{"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": 0.9256736040115356, "perplexity": 518.292775874125}, "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-2014-52/segments/1418802775669.60/warc/CC-MAIN-20141217075255-00137-ip-10-231-17-201.ec2.internal.warc.gz"}
http://www.eclat-digital.com/ocean2019-docs/reference/nodes/filter/sphereresolutionfix.html	# Equirectangular smooth filter¶ ## Description¶ Spherical render without (above) and with (below) the filter This filter fixes the high noise level caused by the equirectangular projection at the upper and lower parts of spherical renders. The image is filtered anisotropically following the pixel/solid angle projection differential. This ensure uniform resolution and noise levels when projected back on a sphere. Note Before Ocean 2016, this filter was named sphere resolution fix ## Input and output¶ • Accepts any channel list as input • Output channels are the same as input. • Does not alter the buffer dimensions • Removes denoising meta-data none ## Ocean XML 4.0 example¶ <filter type="sphereresolutionfix" name="#"/>	2020-09-27 11:50:27	{"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": 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": 0.5297642350196838, "perplexity": 9971.960632796347}, "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-2020-40/segments/1600400274441.60/warc/CC-MAIN-20200927085848-20200927115848-00671.warc.gz"}
http://mathoverflow.net/questions/104309/how-to-find-the-minimum-string-length-to-produce-a-set-of-a-given-size-with-a-mi?sort=votes	# How to find the minimum string length to produce a set of a given size with a minimum pairwise Hamming distance Given an alphabet of $q \ge 2$ letters, I want to construct a set $S$ of $x$ strings (of uniform length) such that the minimum Hamming distance between any two strings is $d$. What I need to figure out is the minimum string length $n$ that could produce such a set. When $d = 1$, then $n = ceiling(log_q(x))$, but I can't figure out how to find $n$ for an arbitrary value of $d > 1$. - This is close enough to sphere packing to probably be an open research question. – tergi Aug 8 '12 at 21:52 Could you please provide some context for this question. On the one hand, this is standard coding theory, but then on the other hand it seems you might be looking for something more specific. So, it is not clear. – quid Aug 8 '12 at 23:04 If anyone is interested, here is an implementation of the recommended solution in R: gist.github.com/84bae05a5c3344710fb5 – user25603 Aug 9 '12 at 16:27 For $q$ the size of the alphabet and $n$ the length of the code it is costumary to denote by $A_q(n,d)$ the maximal size of a code with minimum distance $d$. There are numerous investigations on this. tergi already mentioned tables of explicit values. There are however also general bounds known. In particular a classical result is the Gilbert-Varshamov bound that says $$A_q (n,d) \ge \frac{q^n}{\sum_{j=0}^{d-1} C(n,j) (q-1)^j}$$ where by $C(n,j)$ I just mean the binomial coefficient but momentarily fail to typeset it properly. This is not precisely what you need as you have some $x$ given that corresponds to the $A_q(n,d)$ and need to find a suitable $n$. But for concrete values it would now be easy to solve your problem, and if you need explicit bounds they would (with some additional loss) also be obtainable. Another question would be how to effectively construct the set then. (Depending on what you are trying to achieve there might be different things to consider.) Yet, without further details from you it is hard/impossible to know what type of information would be most useful. - I think this will get me what I want, thank you. The set construction part of the problem is already done, so I don't need any help on that. – user25603 Aug 9 '12 at 15:30 According to my interpretation of Table I of http://neilsloane.com/doc/Me54.pdf it was not known at the time whether you needed bit ($q=2$) strings of length $n=23$, $n=22$, or possibly only of length $n=21$, to construct a set of $x=50$ codewords that are separated from each other by at least Hamming distance $d=10$. This particular example may or may not still be an open question, but there is probably not a known general formula for $n$ in terms of $q$, $x$, and $d$. Edit: The bounds update at http://webfiles.portal.chalmers.se/s2/research/kit/bounds/unr.html shows that $n$ is now known to be $22$ for the example above, but you can still see that a nice way to compute the function you want has not been discovered. - There is also table of good binary codes (linear and not) on S. Litsyn's homepage eng.tau.ac.il/~litsyn/tableand/index.html (updated 1999) – Alexander Chervov Aug 9 '12 at 5:45 I suspected a general formula might not be available. Thank you for the pointers to those papers. I'd upvote you if I could, but my rep is not high enough yet :) – user25603 Aug 9 '12 at 15:31	2015-01-26 22:55:42	{"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": 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": 0.8523340225219727, "perplexity": 178.61375328349928}, "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-2015-06/segments/1422121914832.36/warc/CC-MAIN-20150124175154-00089-ip-10-180-212-252.ec2.internal.warc.gz"}
https://socratic.org/questions/how-do-you-find-the-quotient-of-12n-3-6n-2-15-div6n	# How do you find the quotient of (12n^3-6n^2+15)div6n? Jun 12, 2017 Quotient is $2 {n}^{2} - n$ and remainder is $15$ #### Explanation: $\left(12 {n}^{3} - 6 {n}^{2} + 15\right) \div 6 n$ = $\frac{12 {n}^{3}}{6 n} - \frac{6 {n}^{2}}{6 n} + \frac{15}{6 n}$ = $2 {n}^{2} - n + \frac{15}{6 n}$ Hence Quotient is $2 {n}^{2} - n$ and remainder is $15$ Jun 12, 2017 $+ 2 {n}^{2} - n + \frac{15}{6 n}$ #### Explanation: Note that I am using the place holder of $0 n$. It has no value. $\textcolor{w h i t e}{.} \text{ } 12 {n}^{3} - 6 {n}^{2} + 0 n + 15$ color(magenta)(+2n^2)(6n)->" "ul(12n^3" "larr" Subtract") $\text{ "0" } - 6 {n}^{2} + 0 n + 15$ color(magenta)(color(white)(2)-n)(6n)->" "ul(-6n^2" "larr" Subtract") $\textcolor{m a \ge n t a}{\text{ "0" "+0n+15" "larr" Remainder}}$ $\textcolor{m a \ge n t a}{+ 2 {n}^{2} - n + \frac{15}{6 n}}$	2019-01-17 15:17:44	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 15, "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": 0.7596807479858398, "perplexity": 7713.977054962993}, "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-2019-04/segments/1547583658988.30/warc/CC-MAIN-20190117143601-20190117165601-00210.warc.gz"}
https://wikieducator.org/User:PSamani	# User:PSamani Phillip Samani File:Phillip image.jpg Employer:Ministry of Education and Human Resources Development Occupation:Curriculum Development Officer Nationality:Solomon Islander Country:Solomon Islands. email This user was certified a Wiki Apprentice Level 2 by Mackiwg . Still updating my page; will get there soon. This page was created during a CoL - L4C workshop in SolomonIslands : 18th - 20th February 2008 Hi, I am Phillip Samani. I am a participant of the COL - L4C workshop here in Solomon Islands. We have started our L4C workshop on the 18th of February and will finish on the 20th February 2008. Currently I am working as a curriculum development officer coordinating the Industrial Arts for forms 1 - 3 and Design and Technology for forms 4 and 5 for Solomon Islands secondary schools. This would be my fourth year with Curriculum Development Centre (CDC). Phillip Samani, Ministry of Education and Human Resources Development, Curriculum Development Centre, P.O.Box G27, Honiara, Solomon Islands. Ph: (677) 30116 Fax: (677) 38761 E-mail: [email protected] Talk with Phillip Under the Curriculum Reform, the CDC is now working on developing the learning resources (students learning resources) for years 4,5, 6 for primary and year 7 for secondary. All learning resources for these levels should be written locally but will be edited and publish by Pearson Education, Australia. (: Hi, you've made excellent progress -- clearly you have a good grasp of the wiki syntax concept. Welcome aboard! --Wayne Mackintosh 06:44, 19 February 2008 (UTC))	2022-10-02 12:13:45	{"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": 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": 0.2009247988462448, "perplexity": 11935.358219161797}, "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/1664030337322.29/warc/CC-MAIN-20221002115028-20221002145028-00244.warc.gz"}
https://mathoverflow.net/questions/341511/reducing-the-stack-condition-descent-condition-over-an-fpqc-site-to-the-case-o	Reducing the stack condition (descent condition) over an fpqc site to the case of single coverings This is the lemma 4.25 of Vistoli's note Let $$S$$ be a scheme, $$\mathscr{F} \to \mathscr{S}ch/S$$ a fibred category. Then $$\mathscr{F}$$ is a stack over the fpqc site on $$S$$ iff (1) $$\mathscr{F}$$ is a stack over the Zariski site on $$S$$, and (2) For every fpqc morphism $$V \to U$$ over $$S$$, with $$U,V$$ affine, $$\mathscr{F}(U) \to \mathscr{F}(V \to U)$$ is equivalent. I'm trouble in the last line at step5. For the notation, see the pdf. Let $$f : V \to U$$ be an fpqc morphism (in the sense of this note. In particular is not quasi-compact.) over $$S$$, and $$(\eta, \phi) \in\mathscr{F}(V \to U)$$. Then by Zariski descent and by the step 4, we have $$\xi \in \mathscr{F}(U)$$ and an isomorphism $$\beta : f^* \xi \cong \eta$$ in $$\mathscr{F}(V)$$. Is this morphism in actually a morphism of descent data? i.e., does this diagram $$\require{AMScd}$$ $$\begin{CD} p_2^* f^* \xi @>{p_2^* \beta}>> p_2^* \eta\\ @V{=}VV @V{\phi}VV\\ p_1^f^\xi @>{p_1^* \beta}>> p_1^* \eta \end{CD}$$ commute? (where $$p_i : V \times_U V \to V$$ is the $$i$$-th projection.) By the construction of $$\beta$$, this diagram commutes on $$V_i \times_{U_i} V_i$$. To show the commutativity on the whole of $$V \times_U V$$, by Zariski descent, we must show the commutativity on $$V_i \times_U V_j$$ for distinct $$i,j$$. But I can't. As in step 4, if $$\mathscr{F}(U_i \cup U_j) \to \mathscr{F}(V_i \cup V_j \to U_i \cup U_j)$$ is equivalence, then I think the diagram is commutative. So I reduce this to the case of quasi-compact $$U$$. In stack project, the aouthor ommits this important part. And in Olsson's "Algebraic spaces and stacks" (theorem 4.3.12), the author uses (essentially) same argument, but dosn't mention this commutativity. And in Lei Fu's "etale cohomology theory" (theorem 1.6.1), the author leaves so many parts (the whole of the lemma 4.25 of Vistoli's note) as exercises... Any help will be appreciated! First by the construction, the diagram commutes on $$V' \times_{U'} V'$$ for every affine open $$U'$$ of $$U$$ and its inverse image $$V'$$ in $$V$$. Now $$V \times_U V = \cup V' \times_{U'} V'$$, where $$U'$$ runs through over affine opens of $$U$$. So by Zariski descent, the diagram commutes on whole of $$V \times_U V$$.	2019-12-08 18:11:05	{"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": 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": 36, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9646610021591187, "perplexity": 177.73479907836108}, "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-2019-51/segments/1575540514475.44/warc/CC-MAIN-20191208174645-20191208202645-00404.warc.gz"}
http://mathhelpforum.com/statistics/226067-histograms-areas.html	1. ## histograms and areas Hi; area of histogram is proportional to frequency which is the constant k. how can I tell from a histogram when K is not equal to 1? Thanks. 2. ## Re: histograms and areas Originally Posted by anthonye Hi; area of histogram is proportional to frequency which is the constant k. how can I tell from a histogram when K is not equal to 1? Thanks. I don't understand the question statement. Are you saying that given some frequency distribution S(f) the following holds? $\displaystyle{\lim_{df \to 0}}\int_f^{f+df}S( \nu )d\nu = Kf$ This just says that $S(f)=Kf$ So the slope of S(f) immediately reveals the value of K. If you've got discrete bins just do a linear regression on their values to get an estimate of the slope of $S(n \Delta f)$ 3. ## Re: histograms and areas I thought area was equal to frequency, now I read its proportional to frequency through area = k(frequency). I understand that but by looking at a histogram and asked to find the frequency I would just fd(cw) this is fine when the constant k=1. How do I know if k=1 from a histogram?	2018-01-18 23:46:11	{"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "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": 0.8540160059928894, "perplexity": 913.042511283588}, "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/1516084887660.30/warc/CC-MAIN-20180118230513-20180119010513-00726.warc.gz"}
https://plainmath.net/algebra-i/56098-solve-the-inequality-5-leq3-plus-2x-7	Jayleen Sanders 2022-01-23 Solve the inequality $5\le 3+\|2x-7\|$ ### Answer & Explanation Prince Huang $5\le 3+\|2x-7\|$ Simplify the expression $3+\|2x-7\|\ge 5$ $3+\|2x-7\|-3\ge 5-3$ (subtract 3 from both sides) $\|2x-7\|\ge 2$ By the absolute rule, if $\|u\|\ge a,a>0$ then $\|u\|\le -a$ and $\|u\|\ge a$ $2x-7\le -2$ and $2x-7\ge 2$ (by the absolute rule) $2x-7+7\le -2+7$ and $2x-7+7\ge 2+7$ (add 7 on both sides) $2x\le 5$ and $2x\ge 9$ $\frac{2x}{2}\le \frac{5}{2}$ and $\frac{2x}{2}\ge \frac{9}{2}$ (divide by 2) $x\le \frac{5}{2}$ and $x\ge \frac{9}{2}$ Thus, the solution is $\left(-\mathrm{\infty },\frac{5}{2}\right]\cup \left[\frac{9}{2},\mathrm{\infty }\right)$ Do you have a similar question? Recalculate according to your conditions!	2023-03-20 13:47:53	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 19, "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": 0.5974616408348083, "perplexity": 1845.2395509330895}, "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-2023-14/segments/1679296943483.86/warc/CC-MAIN-20230320114206-20230320144206-00773.warc.gz"}
http://math.stackexchange.com/questions?page=4952&sort=newest	# All Questions 119 views ### Integers Positioned Around a Circle [duplicate] Nine distinct positive integers are arranged in a circle such that the product of any two non-adjacent numbers in the circle is a multiple of n and the product of any two adjacent numbers in the ... 238 views ### When does the two cars meet At 10:30 am car $A$ starts from point $A$ towards point $B$ at the speed of $65$ km/hr, at the same time another car left from point $B$ towards point $A$ at the speed of $70$ km/hr, the total ... 46 views ### Counting distinct positive valued k-tuples that sum to n where each entry can be no greater than some value. This is motivated by the desire to count the number of ways two dice can form the sums 2,3,4,...,12 respectively. We can safely use the stars and bars method for 2,3,4,...,7 where the number of ways ... 11 views ### Area with different unit measurements What is the area of a rectangle, in square meters, with a length of 108 meters and a width of 300 millimeters? I think it could be 324 sqm. 105 views ### Counterexample for Maschke's lemma I'm trying to relax conditions and come up with a counterexample to Maschke's lemma in such a case. For example, with $k = \mathbb Z/p\mathbb Z$, I'm considering the two dimensional representation of ... 93 views ### Is this proof of a mathematical olympiad problem correct? I'm quite sure about the exactness of my proof, but I'd like to hear (constructive) criticism about my writing. This is the problem: Every non-negative integer is coloured white or red, so that: 1) ... 20 views ### Mathematical presentation of a problem The issue that I am dealing with now ends up with the solution of a second order equation. The solutions are the Z positions of a point in 3D. So, basically I have two points with the Z positions of ... 88 views ### Does $\wp(A \cap B) = \wp(A) \cap \wp(B)$ hold? How to prove it? I'm currently working on some discrete mathematics work and I've encountered a question I'm not sure how to answer exactly. Precisely, I'm trying to prove that two power, intersected sets statements ... 52 views ### Series does not converge [closed] How would I go about showing that the series$$\sum_{n + m\tau \in \Lambda} {1\over{{\|n + m\tau\|}^2}}$$does not converge, where $\tau \in \mathbb{H}$? 19 views ### Determining at what points multiple variable functions are continuous With a two variable function what is the procedure to figure out at what points it is continuous? Do I basically just look at what points it would be undefined and anywhere between those points it is ... 73 views ### Proof Using Lagrange's Theorem I am working on a problem in Kurzweil & Stellmacher's introductory finite group theory that looks like this: Let $A, B$, and $C$ be subgroups of the finite group $G$. Prove that if $B \leq A$, ... 36 views ### Denumerable partition of a denumerable set where each set in the partition is denumerable. [duplicate] Suppose that a set $A$ is denumerable. Prove that there is a partition $P$ of $A$ where $P$ is denumerable and every $X \in P$ is also denumerable. I can see that this can be done but I cannot figure ... 58 views ### Is it possible to prove dot product by the law of cosines? It seems many people prove the geometric definition of dot product by the law of cosines. However, i think this is incomplete because the law of cosines is for a triangle, which means we can't use it ... 26 views 94 views ### is it possible to project any triangle on a plane as a right triangle on another plane? I scratching my head over this problem from my projective geometry book (C. R. Wylie, Jr). Given a triangle in the plane $z = 0$, is it possible to find a viewing point, $C$, from which the triangle ... 77 views ### Problem of understanding transitive relations I would like to understand the transitive property in relations...I just cant get it in my brain. I mean the definition is crystal clear. However I still struggle. For example: Given the set ... 65 views ### Set of Numbers when added in any combination always produce unique result What I'm looking for is a set of numbers that when added in any combination they always have a unique sum? Is this called something? I have searched on google for hours and I'm having a hard time ... 50 views ### Analyze the continuity of the following function Here in my book I have such an exercise with the explanation given below, but still there is something the authors didn't add, but simply put "...after some operations...". Here is such an exercise: ... 34 views ### Showing that a subrepresentation is isomorphic to the trivial representation I'm considering $V$ to be the regular representation of a group $G$ and $W$ to be the 1-dimensional subspace of $V$ generated by the element $x=\sum_{s\in G} e_s$. I'm trying to show that $W$ is a ... 73 views ### [Proof Verification]Prove that if f is differentiable at $c \in I$ and $f'(c) = 0$, then g is not differentiable at $d:=f(c)$. Proposition. Let I be an interval, and let $f: I \to \mathbb{R}$ be a strictly monotone and continuous on I. Let $J := f(I)$ and let $g:J \to \mathbb{R}$ be the inverse function of f. Prove that if f ... 182 views ### integral ring extension, maximal ideals Let $\varphi:A\rightarrow A'$ be an integral ring extension. 1) Show that for every maximal ideal $m'\subset A'$ the ideal $\varphi^{-1}(m')\subset A$ is maximal. 2) and that for every ...	2016-05-26 09:16:39	{"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": 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": 0.9598731994628906, "perplexity": 249.3608757180354}, "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-2016-22/segments/1464049275764.90/warc/CC-MAIN-20160524002115-00186-ip-10-185-217-139.ec2.internal.warc.gz"}
https://socratic.org/questions/how-do-you-find-the-intercepts-for-y-2x-1	# How do you find the intercepts for y=2x-1? the answer is $x = \left(0.5 , 0\right) y = \left(- 1 , 0\right)$see graph below well you already know that the $y$ would be $- 1$ from the equation b/c of $y = m x + b$ and now all you have to do is graph to find $x$	2021-11-30 18:26:33	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 5, "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": 0.4884687066078186, "perplexity": 218.23028044893405}, "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-2021-49/segments/1637964359065.88/warc/CC-MAIN-20211130171559-20211130201559-00494.warc.gz"}
http://mathhelpforum.com/calculus/133157-prove-contradiction-sequence-divergent.html	1. ## Prove by contradiction that the sequence is divergent This is a tough one, and I have little idea on how to prove it. Prove that the sequence defined by $f(n)=(-1)^n,n\in N$ is divergent. This must be proven by contradiction. 2. Originally Posted by Runty This is a tough one, and I have little idea on how to prove it. Prove that the sequence defined by $f(n)=(-1)^n,n\in N$ is divergent. This must be proven by contradiction. Suppose $(-1)^n\xrightarrow [n\to\infty]{}a$ , for some $a\in\mathbb{R}\Longrightarrow \forall\,\epsilon>0\,\,\,\exists\,N_\epsilon\in\ma thbb{N}\,\,\,s.t.\,\,\,n>N_\epsilon\Longrightarrow \,\|(-1)^n-a\|<\epsilon$ . Let us choose $\epsilon=\frac{1}{4}\Longrightarrow$ for some natural number $N_\frac{1}{4}$ , we have that $n>N_\frac{1}{4}\Longrightarrow \|(-1)^n-a\|<\frac{1}{4}$ $\Longleftrightarrow a-\frac{1}{4}<(-1)^n . But this means that all but a finite number of the sequence's elements are between the left and the right ends, and the difference between these two ends is $a+\frac{1}{4}-(a-\frac{1}{4})=\frac{1}{2}$ , and this is a contradiction since for any two consecutive natural numbers $n_1,n_2>N_\frac{1}{4}\,,\,\,\|(-1)^{n_1}-(-1)^{n_2}\|=2$ , so it's impossible that ALL the elements of the seq. (but perhaps a finite number of them) are within two numbers whose difference is $0.5$ ... Tonio 3. Also, an alternative way would be to notice that if the sequence is convergent then it is cauchy, but for each $n \in \mathbb{N}, \ \|a_{n+1} - a_n\| =2$ , , ### to show the sequence is divergent Click on a term to search for related topics.	2017-01-22 09:12:32	{"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 12, "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": 0.9927694797515869, "perplexity": 253.53563876217527}, "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-2017-04/segments/1484560281419.3/warc/CC-MAIN-20170116095121-00489-ip-10-171-10-70.ec2.internal.warc.gz"}
https://worddisk.com/wiki/Exponential_decay/	Exponential decay A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where N is the quantity and λ (lambda) is a positive rate called the exponential decay constant: ${\displaystyle {\frac {dN}{dt}}=-\lambda N.}$ The solution to this equation (see derivation below) is: ${\displaystyle N(t)=N_{0}e^{-\lambda t},}$ where N(t) is the quantity at time t, N0 = N(0) is the initial quantity, that is, the quantity at time t = 0, and the constant λ is called the decay constant, disintegration constant,[1] rate constant,[2] or transformation constant.[3]	2021-09-24 19:23:40	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 2, "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": 0.9710912704467773, "perplexity": 577.1658069303568}, "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-2021-39/segments/1631780057564.48/warc/CC-MAIN-20210924171348-20210924201348-00649.warc.gz"}
https://quantumprogress.wordpress.com/2012/02/27/more-on-graphical-solutions-to-projectile-motion-problems/	In the animation, $\Delta v$ increases with time, and the average velocity is computed as the sum of $v_i$ and $\frac{\Delta v}{2}$. When this vector is scaled by the time ($\vec{\Delta r}=\vec{v}_{avg}t$), you get a displacement vector from the origin to the current location of the projectile.	2017-02-25 11:19:27	{"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": 4, "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": 0.9501931071281433, "perplexity": 63.55747708599043}, "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-2017-09/segments/1487501171758.35/warc/CC-MAIN-20170219104611-00629-ip-10-171-10-108.ec2.internal.warc.gz"}
https://www.nature.com/articles/s41598-021-83477-6	Skip to main content Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript. # Citizen science for monitoring seasonal-scale beach erosion and behaviour with aerial drones ## Abstract Sandy beaches are highly dynamic systems which provide natural protection from the impact of waves to coastal communities. With coastal erosion hazards predicted to increase globally, data to inform decision making on erosion mitigation and adaptation strategies is becoming critical. However, multi-temporal topographic data over wide geographical areas is expensive and time consuming and often requires highly trained professionals. In this study we demonstrate a novel approach combining citizen science with low-cost unmanned aerial vehicles that reliably produces survey-grade morphological data able to model sediment dynamics from event to annual scales. The high-energy wave-dominated coast of south-eastern Australia, in Victoria, is used as a field laboratory to test the reliability of our protocol and develop a set of indices to study multi-scale erosional dynamics. We found that citizen scientists provide unbiased data as accurate as professional researchers. We then observed that open-ocean beaches mobilise three times as much sediment as embayed beaches and distinguished between slowed and accelerated erosional modes. The data was also able to assess the efficiency of sand nourishment for shore protection. Our citizen science protocol provides high quality monitoring capabilities, which although subject to important legislative preconditions, it is applicable in other parts of the world and transferable to other landscape systems where the understanding of sediment dynamics is critical for management of natural or anthropogenic processes. ## Introduction The coastal zone accommodates 40% of today’s population1,2, with densities much greater than non-coastal land especially in low income countries3. Sandy beaches are extremely dynamic morphological sub-systems of the coastal zone, offering, amongst others, coastal protection and erosion control eco-services4,5. However, global studies have reported that one-quarter of the world’s sandy beaches are eroding at rates exceeding 0.5 m/year6, contributing to a global coastal land loss of 20,000 km2 in the last 35 years7, posing an increasing threat to coastal populations and economies. Beach erosion is not uniformly distributed along the coast, but concentrated on discrete areas6,7 often referred as erosional hotspots8,9. These hotspots are spatiotemporally variable ranging from days to decades and from hundreds to thousands of meters10. As a consequence, erosion mitigation strategies (beach nourishment, rockwalls, sand fencing) tend to be highly localized11. In these areas, the measurement of high-temporal volumetric variations is critical for discerning short-term beach behaviour and recovery from erosional events12. This allows coastal planners to target intervention measures and evaluate their efficiency in protecting backshore assets from current and projected increase of erosion hazard13,14,15. Nowadays, beach topographic data is obtainable using a variety of ground-based (graded rods16, surveyor-grade global positioning systems or total stations17, terrestrial LiDAR18) or aerial-based (airborne LiDAR19, traditional photogrammetry20,21, unmanned aerial vehicles22,23) approaches. While ground-based surveying methods are labour intensive and of limited spatial coverage, airborne LiDAR or traditional photogrammetric approaches are cost-prohibitive for monitoring purposes, especially in developing countries. In the last decade unmanned aerial vehicles combined with structure-from-motion multi-view stereo algorithms (UAV-SfM hereinafter) have emerged in environmental research24,25,26 as the best compromise in terms of costs, precision, reproducibility and simplicity, particularly for repetitive beach topographic surveys27,28,29. In coastal areas, multi-rotor UAVs are frequently used30 and their flight time is typically between 20 and 40 min per battery, which corresponds to a flight coverage of 5–30 × 103 m2, depending on flight altitude24. As a consequence, time and budget constraints have so far restricted UAV-SfM surveys to professional researchers or commercial operators at a few representative sites, with limited revisit times27,31,32,33,34,35. However, recent technological advances in low-cost UAVs and automated flight and positioning solutions, coupled with regulatory changes, provide new opportunities for implementing citizen science to expand the scale of monitoring programs36,37. Citizen science is the process of creating knowledge by engaging non-professional volunteers in scientific research36. Citizen scientists have allowed large-scale scientific experiments to make substantial contributions to science for hundreds of years38. Yet, errors and bias in large and longitudinal citizens science datasets are often poorly understood39. This uncertainty, being difficult to quantify, can compromise data quality or limit the integration of multiple datasets into a single coherent analysis. As a result scepticism exists among professional scientists about the quality of citizen scientists’ data40,41. In this study, we propose a novel and cost-effective approach to monitor sandy beaches sediment dynamics at a spatiotemporal resolution previously unachievable, through citizen science with low-cost multi-rotors UAVs. We test our method on the high-energy temperate coast of Victoria, Australia, where more than 100 citizen scientists collected 83 aerial datasets in ten previously identified erosional hotspots over a 1.3 year period, approximately every 6 weeks. With this unique dataset, we first evaluate citizen scientists' data quality and bias, then we quantify and compare short-term volumetric and profile dynamics on both open-ocean and embayed beaches. We propose a novel set of indices that capture multi-scale landform dynamics, using topography timeseries alone. This allows us to evaluate beach nourishment efficiency in protecting backshore infrastructure. Lastly, we discuss the potential and limitations that our approach has not only for coastal management but also in other scientific disciplines. ## Results ### Citizen scientist’s data accuracy and bias Accuracy and bias are objective task-independent metrics of data quality42. For an independent and realistic vertical accuracy assessment of the digital surface models (DSM), the error metrics should be calculated with independent checkpoints that haven’t been used during the digital photogrammetric procedure (Supplementary Method “Citizen Scientists, UAV surveys and photogrammetric details”) and are distributed across the landscape, along representative transects or landform elements27,43. Two benchmark surveys were performed in Warrnambool to evaluate the DSM vertical accuracy resulting from the citizen science protocol under operational (2018-11-29) and worst-case (2019-12-11) scenarios (Supplementary Method “Independent checkpoint surveys”). The checkpoints in both surveys show a very good linear match of modelled elevation (both R2 above 0.99) with slightly larger deviations observed at higher elevations (Fig. 1a). The Q–Q plots and statistical tests indicate non-normal distribution of absolute errors (Δh, Fig. 1b), which confirms that the normalised median absolute deviation (nmad) is the most appropriate robust estimator for vertical accuracy assessment of photogrammetric datasets44. The nmad values are 0.048 and 0.054 m AHD (Australian height datum) for the operational and worst scenarios respectively. The mean errors indicate that the 2018 checkpoints survey slightly underestimated the height values (− 0.044 m AHD), the 2019 checkpoints survey overestimated (0.128 m AHD) it, which is observable from the two error distributions (Fig. 1c). Both surveys show good precisions (standard deviation) of 0.077 m AHD and 0.063 m AHD respectively. Supplementary Table S3 also reports root mean squared error (rmse) and mean absolute error for comparison purposes. Casella et al. 45 recently demonstrated that approximately 0.05 m rmse is consistently found under different surveying set-ups (varying cameras and flight altitudes), which corroborates a median rmse of 0.059 m found in the relevant literature (Supplementary Table S2). The authors state this systematic error could be due to the vertical sinking of the surveying pole on various sand types, therefore, 0.05 m rmse is a typical error in sandy beaches UAV-SfM studies. As our operational scenario rmse (0.089 m AHD) is about 0.03 m higher than the literature median, we further explored systematic errors by mapping the spatial variability of checkpoints errors and smart ground control points (GCPs) (Supplementary Figs. S2, S3), finding that errors were generally higher with elevation, especially within foredune vegetation. We mitigated this systematic error by removing vegetation and applying specific limits of detection thresholds, which is a form of split data test46 used to obtain the expected DSMs vertical errors by computing the elevation difference between pre- and post- survey pairs over known stable areas (i.e. calibration areas22). Bias in citizen science projects can be introduced by allowing individuals flexibility in how, when and where to collect data47. We reduced the risk of bias prior UAV operations by (1) assigning groups to fixed locations, (2) targeting low-tide for survey, (3) providing standardised protocols and training on simple to use highly automated equipment and (4) assisting citizen scientists at each sites for the first three flights. The principle issue is the location of the portable GCPs which can be affected by citizen scientists’ spatial effort bias31, leading to positional errors due to GPS signal blockage from foredunes, tall trees or buildings. As GCPs positional errors directly impact the point cloud georeferencing process (hence, the resultant DSM), we assessed whether significant (p = 0.05) differences exist in GCPs spatial dispersion (i.e. their two-dimensional spread across the surveyed area), their positional X, Y and Z variances and the images georeferencing accuracies (X, Y and Z rmse) reported by the photogrammetric software Pix4Dmapper (V4.3.31), between locations (Fig. 2). The Kruskal–Wallis H test49 indicated that there are statistically significant differences (p = 0.05) in all positional GCPs variances (Fig. 2a) and in image georeferencing errors (Fig. 2b), between the different locations. This can be observed in the pairwise comparison heatmaps (Fig. 2c–e), where in the great majority of cases, statistically significant differences in X,Y and Z variances are found between any one location and at least four others. This is likely to be the cause of all locations having statistically significant differences in rms georeferencing errors compared to each other (Fig. 2f). Importantly, GCPs elevation precisions were outside acceptable variance (20 mm) 7% of the time (61 out 886), with only 9 cases (1%) exceeding 64 mm (outliers). Therefore, positional precision differences between locations are largely attributed to random errors during the GCPs position recording process and no citizen scientist’s bias can be ascertained. The same applies to the images georeferencing errors. Their location-specific medians range from a minimum of 2 mm (Seaspray and Cowes) to a maximum of 15 mm (Warrnambool), which are of the same order of magnitude of the GCP positional precisions. As such, we cannot exclude the possibility that these differences are also due to random errors in the geolocation recording of the GCPs. Regarding the GCPs two-dimensional spatial spreading (Supplementary Fig. S6), the Kruskal–Wallis H test showed that there are no statistically significant differences between locations (H = 11.12; p = 0.28, n = 78). Additionally, to assess whether there are statistically significant differences between the end-products of our protocol across locations (i.e., the expected DSM error) and considering that more independent checkpoint surveys were unavailable, we analysed limits of detection thresholds as indicators of ‘overall’ data quality (Supplementary Method “Limit of detection analysis”). An example of limit of detection threshold derivation and error normality evaluation in Apollo Bay is shown in Supplementary Fig. S8. The Kruskal–Wallis H test found that no significant differences (H = 16.167, p = 0.063, n = 73) exist between each location specific threshold distributions at the 0.05 significance level. ### State-level volumetric monitoring of open-ocean and embayed beaches Overall, 100,794 ± 243 m3 of sand has been transferred off the beachfaces (net erosion) during the monitored period (from the first June 2018 to the 29th August 2019) across the 10 locations (Fig. 3a, see Additional Method “Area of study” for more information). Swell-exposed open-ocean beaches displayed mean elevation changes (MEC) of greater amplitudes than embayed beaches, which are situated along fetch-limited or sheltered coastlines. All the following observations are relative to the whole aforementioned monitoring period. On average, the absolute MEC for open-ocean beaches (0.11 ± < 0.01 m) is almost three times larger than for embayed ones (0.04 ± < 0.01 m). During erosional phases (negative MEC in Fig. 3b), the average MEC is − 0.13 ± < 0.01 and − 0.04 ± < 0.01 m in open-ocean and embayed beaches respectively. Similarly, during recovery phases (positive MEC in Fig. 3b), the average MEC is + 0.09 ± < 0.01 and + 0.04 ± < 0.01 m on open-ocean and embayed beaches respectively. Post-erosion recovery times are highly variable, ranging from a few days (Warrnambool) to approximately one year (Portarlington), while some locations never fully return to their initial state (Apollo Bay, Inverloch). To model the monitored beachface dynamics and distinguish between erosional and depositional behavioural regimes, we used the residual beachface cluster dynamics index (r-BCD, Method, Fig. 3a). Therefore, a location r-BCD index is one single signed value that characterises the dominant behaviour that the beach in that location exhibited during the entire monitored period. The open-ocean beaches of Port Fairy, Warrnambool, Marengo and Seaspray exhibit highly to slightly depositional regimes. Interestingly, Port Fairy and Seaspray r-BCDs indicated that both locations had a depositional behavioural regime during the monitoring period despite these locations experiencing net sediment losses of − 10,962 ± 66 m3 and − 7,517 ± 726 m3 respectively. In other words, their intra-annual cut and fill dynamics (Fig. 3b) are skewed toward net sediment gains. By contrast, Inverloch, Apollo Bay and Point Roadknight display highly, moderately and slightly erosional behavioural regimes which are corroborated by end-of-monitoring sediment losses of − 66,700 ± 909 m3, − 13,871 ± 2,286 m3 and − 2,159 ± 562 m3 respectively. The embayed beaches of St. Leonards, Portarlington and Cowes are protected from the predominantly south-westerly swell being located within Port Phillip and Western Port Bays. Despite Portarlington never fully recovering from its first erosional event in the timeseries, its depositional behavioural regime indicates that it is more likely to accrete rather than erode. Conversely, Cowes displays a highly erosional behavioural regime despite never showing a negative sediment budget respective to the beginning of the monitoring. ### Sediment dynamics highlight accelerated or slowed-by-intervention erosion in critical locations Empirical beachface cluster dynamics indices (e-BCDs, Fig. 3c) measure the importance (absolute score) and main magnitude trend (score sign) of beachface erosional, recovery, depositional and vulnerability behaviours. We use e-BCDs to detect naturally accelerating and slowed-by-intervention erosional modalities in Inverloch and Apollo Bay respectively. The e-BCD indices are representative of the whole monitoring period and are intended to depict the main trend of beachface sediment dynamics that occurred during the observation time. From the 22th August 2018 to the 30th July 2019, the monitored area in Inverloch displayed an erosional score (+ 1.37) that is greater than its high recovery score (− 0.93), indicating that erosional hotspots mostly continued to erode the beachface rather than recover. The combination of positive erosional and negative recovery indices imply that through time, an increased amount of sediment has been eroded, while recovering areas tended to accumulate less sediment than was previously lost. The depositional score (− 0.60) is substantially lower than the vulnerability (+ 2.28), indicating that depositional areas became erosional, rather than continuing to accrete. These signs suggest that depositional hotspots gained less sediment through time and, once starting to erode, the volumes lost were typically higher than what had previously been deposited. These dynamics indicate an accelerated beachface depletion, which is confirmed by Inverloch mean elevation change time series (Fig. 3b). An accelerating erosional phase started in mid-October 2018 and lasted until the end of the monitoring, totalling a net loss of 48 ± 0.06 m3/m, at a rate of 0.14 m3/m eroded daily, beach wide. In Apollo Bay from the first June 2018 to the 25th July 2019, the beachface dynamics have been impacted by a weekly sand nourishment program that deposited 16,050 m3 of sand in the intertidal and foredune areas (focussing from 800 m north, zone D in Fig. 4), from the 19th June to the 4th September 2018 and from the 22nd May to the 21st June 2019. The e-BCDs analysis in Apollo Bay indicates that erosional hotspots tend to turn depositional by a slight margin (− 1.10 erosional and − 1.14 recovery scores), in which case a lower amount of sediment is deposited compared to what had been previously lost (negative depositional sign). On the other hand, depositional hotspots tend to turn erosional by a greater margin (− 1.85 vulnerability and + 0.73 depositional scores), in which case the sediment lost is usually less than what was previously deposited. Overall, Apollo Bay e-BCD indices indicate a slight erosional predisposition (driven by the vulnerability index), precariously reduced by “sediment-sparing” mechanisms (negative signs of erosional and vulnerability e-BCDs) that slows the beachface sediment loss. In fact, despite being supported by sand nourishment, Apollo Bay sediment volumes never returned to its initial state at the commencement of the surveys. This indicates that the management intervention in Apollo Bay is likely to be slowing beachface erosion during the monitoring period, hence, we observed a slowed-by-intervention erosional mode. ### Site level case study: assessing beach nourishment efficiency in Apollo Bay To demonstrate the scalability of citizen scientists’ data, we down-scaled behavioural regime, morphological and volumetric analysis from the location to the single transect level, assessing the efficiency of a beach nourishment project in protecting backshore economical assets. The Great Ocean Road is a scenic coastal drive that contributes up to 6.1% of revenue to the regional economy51. It attracts more than 5,000,000 visitors annually, and Apollo Bay is the second most popular visitor destination51. The spatial distribution of transect-specific r-BCDs indicates three distinctive zones where behavioural regimes are mostly mixed (M), erosional (E) or depositional (D) (Fig. 4). Zone M represents a mixed-zone extending from immediately in the lee of the harbour to 180 m alongshore. Generally, erosion during the monitoring period occurred on the lower intertidal beach and occasionally on the incipient dune, leaving the vegetated foredune intact. Swash-generated berms (Fig. 5a) occur throughout zone M and are typical landforms of low tide terrace type beaches52. Zone E is predominantly erosional, despite this area being reported to have experienced accretion since 1956 due to the construction of the harbour and its shadowing effect from incident waves53. Here, the erosion in the intertidal zone is mostly uninterrupted throughout the surveys, leading to a gradual transgression of the erosional scarps, eventually causing up to 6 m of incipient dune recession (Fig. 5b). The most erosional transects are located 500 m alongshore, within 40 m from the main pedestrian beach access (Fig. 4 inset map c). Further to the north, the magnitude of beachface lowering gradually diminishes to finally become net accretion accompanied with foredune recession at 800–840 m alongshore, entering zone D. Zone D has been reported to be receding since mid-198053 and is also where the majority of nourishment has occurred during the monitoring. Notwithstanding, zone D comprises two “erosional enclaves” (Fig. 4 inset maps a,b) which signal local erosional hotspots of major concern. Moreover, despite an informal rockwall effectively protects the foredune between 1,100 and 1,200 m alongshore, foredune recession has been widespread between June and July 2018 causing sections of a footpath to collapse (1,500 m alongshore, Fig. 5c). The different behaviours in zones M, E and D can be observed by adopting a beach-wide perspective, while considering the volumes of sand introduced by the nourishment program. From the first of June 2018 to the 21th June 2018 (Supplementary Data ‘site_level_change”), particularly stormy weather eroded 9,055 ± 76 m3 of sand from the beachface, slightly alleviated by post-storm sand renourishment of 1,320 m3. From the 21th June to 26th July 2018 (Fig. 6a) the beachface recovery was assisted by 4,875 m3 of renourished sand, taking the alongshore volumetric change in this period only slightly below zero (− 0.20 ± 0.09 m3/m). The majority of deposition took place in zone D where renourishment focussed, while zone E kept losing sediment, especially from the intertidal beach (Fig. 5b). This pattern is accentuated in the next period (from 26th July 2018 to 24th September 2018, Fig. 6b) when 9,165 m3 of sand was supplied to the beach by managers mostly northward from the 800 m mark (Fig. 4). During these renourishment periods, zones E and D behaviours are noticeably inverse to each other, whereas zone M generally follows the behaviour of the adjacent zone E. When renourishment is suspended, zones E and D are essentially undifferentiated, whereas zone M is remarkably dissimilar to the rest of the beach, especially during the spring to summer transition (from the 24th September 2018 to 11th December 2018, Fig. 6c,d). Overall, after initial recession of the foredune, the intertidal zone showed a net accretion by the end of the monitoring, indicating that the depositional behaviour of zone D is precariously tied to the nourishment operations. In fact, during nourishment periods, the alongshore distribution of volumetric change clearly sets zone D apart, being it the only accreting zone amongst overall beach erosion (Fig. 6a,b). Conversely, when nourishment is suspended, zones E and D erode or accrete conjointly, while zone M shows a noticeably divergent behaviour (Fig. 6c,d). Therefore, in the absence of nourishment, we would expect the whole monitored area in Apollo Bay to be erosional, corroborating our previous argument about the slowed-by-intervention erosional mode of Apollo Bay. We can conclude that the current sand nourishment strategy is likely to be locally decelerating a recent beach wide erosive trend, but it is not sufficient to maintain or fully recover subaerial beach sediment budget in the long-term. Additionally, mostly depositional areas seem to be accreting the intertidal beach, while the foredune is still receding. ## Discussion The vertical accuracy of the citizen scientists’ protocol (rmse = 0.089 m) obtained in an operational scenario is 0.03 m less accurate than the median accuracy reported across the relevant UAV-SfM beach monitoring literature (median rmse = 0.059 m). However, using robust statistical estimators which put less weights on error outliers (focussed around foredune vegetation) led to an error estimation of 0.048 m, slightly better than what others obtained in similar works27,54 (Supplementary Discussion “Citizen scientists’ accuracy”). Our bias analysis indicates that citizen scientists’ ground control points (GCPs) spatial arrangement was consistent through time and space. GCPs positional precision and image georeferencing errors have significant inter-groups differences which cannot be attributed to citizen scientists as errors are below the reported GCPs precision. As no significant differences of limit of detection distributions between locations have been found, we can assert that limited bias impacted the quality of data during the full data creation pipeline, with our protocol. Therefore, as citizen scientists' data is of comparable accuracy and bias to professionally acquired UAV-SfM datasets, it is considered of high-quality36. Besides monitoring beachfaces volumetric changes, our approach temporal resolution allowed us to conceive the residual beachface cluster dynamics index (r-BCD) to model hotspots behavioural regimes in the absence of precise wave data, but based on topography alone. The fundamental assumption of r-BCDs is tied to the classic morphodynamic feedback loops of process and morphology55. As r-BCDs are derived from high frequency elevation changes, they incorporate the morphological variability that landforms experienced due to the locally active geomorphic processes. Citizen scientists allow r-BCDs to be used over multiple locations at site and transect scales, providing government authorities a rapid and powerful beach dynamics assessment that managers can use to prioritise erosion hazard mitigation expenditure. This approach becomes especially favourable in situations where high quality nearshore waves and currents data is lacking and can complement other cost-effective remote sensing approaches, such as satellite-based coastal monitoring. Multispectral imagery acquired by optical satellites, such as Sentinel-2 or Landsat, allows the use of two-dimensional shoreline landward/seaward shifts as erosion/deposition proxy for large scale erosion monitoring. However, shorelines derived from space are difficult to validate in-situ, consequently, only a few studies used ancillary beach topographic data or coincident shoreline GPS surveys to test the accuracy of the extracted shorelines56,57,58,59. Moreover, sandy beaches topographic features such as beachface slope60, intertidal extent61 and elevation62,63 at continental-scale have also started to be derived from space-based observations. These methods need beach topographic data at higher resolution to be validated against. Our study demonstrates that citizen science UAV-SfM is in an advantageous position to provide the high-quality and reliable 3D data that is essential for ground truthing space-based observations. Alternatively, the closest comparable topographic monitoring methods are repetitive airborne light detection and ranging (LiDAR) surveys or fixed coastal imaging stations (ARGUS). Coastal LiDAR is often used for quantifying wide-scale shoreline spatial variability of single-event post-storm erosion19,64,65, however, high operational costs have traditionally limited its temporal resolution within geoscientific research66, often missing the fine seasonal dynamics that our approach provides. ARGUS stations on the other hand can typically provide hourly shoreline images of key sites, which are then processed to obtain shoreline elevations and later used to monitor erosion/accretion patterns in a relatively cost effective way. However, ARGUS-derived shoreline elevations are computed with a variety of empirical, semi-empirical and complete numerical models, depending on the quality and amount of site-specific field data (topography, tide and offshore wave measurements) used to calibrate the shorelines. As a consequence, vertical accuracies (in the range of 0.1 to 0.4 m) and methodologies are often site-specific17, possibly limiting the integration of multi-site observations into one integrative study. With our approach, 10 UAVs and 100 smart ground control points were used to repeatedly survey (7 to 10 times) 10 key locations at a total cost of US$250,590 (including equipment, online data processing and hosting and the time to train and support a group of 3–4 citizen scientists per location). This equals to US$3,020 per survey (n = 83), which is expected to be approximately US\$1,290 per survey in the next years, as groups become established and less training and support hours are budgeted (Supplementary Discussion “Monetary costs''). Therefore, we consider our approach to be cost-effective as high-quality, high temporal and very high spatial resolution beach topographic monitoring is consistently achieved at 10 high-priority locations (site scale), which are representative of the Victorian coast (regional scale). The cost-effectiveness and geographical coverage offered by our approach has important implications in contexts of erosion mitigation in vulnerable communities, such as those in small island developing states (SIDS). In SIDS, a lack of quality coastal data at relevant spatiotemporal scale has been recognised67,68 and their economic dependence to tourism and coastal eco-services within a changing climate context put their subsistence at risk69. Our approach would allow SIDS communities to reliably monitor coastal erosion in sensitive areas cost-effectively, producing continuous survey-grade topographic data over wide and often dispersed geographic areas, with some limitations. Without environmental context information (especially wave climate), our methods reliably depict seasonal beach change trends but cannot explain the geomorphic forcings responsible for those changes. In fact, the magnitude of changes could differ depending on how far in time from major storms (not investigated here) the surveys are. Although we demonstrated the reliability and usefulness of our approach, coastal processes data is needed to formulate more causative sand dynamics and geomorphological interpretations, which would allow more accurate sand dynamics to be evaluated. This is the next logical step and focus of future studies. Additionally, as opposed to other coastal citizen science projects where anyone can take part as a citizen scientist70,71, in our approach, legislation plays a central role in defining who can be a pilot, directly challenging its feasibility and reproducibility around the world (Supplementary Discussion “Role of legislation”). In general, the key legislation requirements that need to be met in order to perform and replicate our protocol are that (1) UAV flight are permitted over interest areas, (2) automatic (waypoint-based) UAV flight mode is allowed and (3) no mandatory UAV flight license is required for research applications using sub-2 kg airframes. In Australia, scientific operations with UAVs below 2 kg of weight are part of the “sub-2 kg excluded category”, which allows individuals older than 16 years of age to fly small UAVs (1) within standard operating conditions, (2) without the need of a remote pilot licence and (3) without a mandatory risk assessment to be approved. Elsewhere, various UAV laws can challenge, impede or allow UAV citizen science applications. In SIDS, UAV regulations range from total ban (Cuba and Barbados) to “Australia-like” approach (Papua New Guinea), with important variants that limit the feasibility (heavy air-traffic and multiple authorities permit systems in Maldives) or replicability (automatic flight procedures not allowed in the Dominican Republic) of our protocol. On the other hand, from the 31st December 2020 the European Union Aviation Safety Agency (EASA) UAVs regulation will allow UAV citizen science projects to take place in 32 European countries (25 of which are coastal), thanks to a regulation very similar to the one adopted in Australia. Despite the combination of a greatest number of coastal no-fly zones (due to controlled aerospace from the military, proximity to aerodromes or natural protected areas) with crowded beaches can discourage UAV citizen science coastal applications in EASA countries, our protocol can also be applied to other environments or scientific disciplines where accurate cost-effective topographic monitoring is needed. In fact, multi-temporal UAV-SfM has already been used by professional researchers around the world for monitoring erosion in mudflats72, badlands73, agricultural watersheds74, rivers75 and open-pit mines76. Additionally, UAV-SfM topographic data has also been used for non-erosion purposes to monitor both natural processes, such as landslide dynamics77, sediment retention dams filling78, crops growth variability79, forest trees growth80, snow depth81 and glaciers melting dynamics82, or anthropogenic processes, such as landfills growth rates83, environmental contamination84 or hiking trails conditions85. In conclusion, our results not only demonstrated the value of citizen scientist’s high-quality and unbiased data for multi-scale sandy beaches sediment dynamics monitoring, but can also encourage further application of citizen science with drones into all the aforementioned scientific applications. This not only would greatly expand the spatiotemporal scale of scientific experiments, but also democratise scientific engagement access, enhance global environmental awareness and transform citizen scientists into key stakeholders within an adaptive environmental management system. ## Methods In this work, we used machine learning and limit of detection analysis to detect and reliably quantify subaerial beachface dynamics due to sand-only and above detection limits changes. Spatial autocorrelation analysis is also employed at the site-level to remove spatial outliers and detect statistically significant (p = 0.05) hotspot of changes to better characterise sediment dynamics through time. This information is then explored with novel indices (empirical and residual beachface cluster dynamics indices, e-BCD and r-BCD respectively) based on discrete Markov chain models, at the site and transect scales. ### Virtual network of elevation profiles A virtual network of digital transects was created for every site and kept fixed during the analysis. Transects are uniformly distributed alongshore with a spacing of 20 m, normal to the shoreline, with an across-shore length of 80–150 m, depending on the beach width discernible from the earliest orthophoto available (Supplementary Fig. S1). We extracted synchronous elevation and colour information along each transect, with a 0.1 m sampling step, in all 10 sites and surveying dates (8 to 10 surveys per site), resulting in a total of 6,809,610 points on 999 transects. Swash zones were excluded from the analysis. We only retained points which were classified as sand and within the subaerial beachface, which is defined as the area from the upper swash to 2–3 m landward of the vegetation line or where anthropogenic barriers are present. ### Machine learning sand classification We used machine learning to restrict the analyses to those extracted points that are sand, removing the ones representing beach wrack or coastal vegetation that would otherwise skew our volumetric and behavioural computations. For each survey, we performed the Silhouette Analysis86 to find a sub-optimal number of clusters (k) to partition the points with KMeans clustering algorithm87, using spectral (red, green, and blue bands) and topographic (slope, curvature and distance from the transect seaward origin) features. By iteratively run KMeans (parameters: initial cluster centres selected with KMeans ++, 300 iterations per run, inertial tolerance of 0.001, pre-computed distances) increasing k by 1 at every iteration (up to k = 20), we were able to compute the overall silhouette coefficient associated at every k. We chose as sub-optimal k the value after which a greater k would not substantially reduce the overall clustering performance. Once the sub-optimal k has been found for every dataset and KMeans run using it, clusters were displayed in QGIS (version 3.2.3) and visually labelled as sand or no-sand (Supplementary Fig. S1). No-sand points across each transects have been replaced by an interpolated value using a linear model. Minor manual editing was required to correct sand points erroneously assigned to a non-sand cluster. This mainly occurred in very dark shadows cast by tall trees along coastal walking paths or right below near vertical foredune. ### Limit of detection thresholds The morphological method88 has been used in a variety of environments, including sandy beaches23,29,31,89. It involves the subtraction of two digital surface models (DSMs) of the same location at different times to obtain a DSM of Difference (DoD), which represents surface change over a shared elevation datum for each period. Our transects are subject to the same error estimation techniques used for DoD analysis. Therefore, in order to account for areas of apparent elevation change (Δh) due to inherent DSM uncertainties, we computed limit of detection thresholds for each DoD (n = 78). Changes within these thresholds are considered uncertain and their contribution is expressed as error margins when altimetric or volumetric change is reported. To obtain limit of detections, we firstly identified invariant objects as close as possible to the beachface in each site (paths, roofs, rockwall, anthropogenic structures), which we used as calibration zones. Then, we manually digitised vector lines across calibration zones and created a checkpoint every 0.1 m along those lines, resulting in 23,660 check points. Finally, we measured the checkpoints Δh in each DoD and obtained the threshold computing the normalised median absolute deviation45 as robust statistical estimator. ### Volumetric computations and mean elevation change The exclusion of points within the swash extent and variations in UAV survey coverage resulted in irregularities in the number of transects and valid points per survey (see Additional Data). Therefore, we compared subaerial changes across sites and time using the mean elevation change (MEC), as follows: $$Mean\,elevation\,change \left( {MEC} \right) = \frac{1}{n}\mathop \sum \limits_{z = 0}^{n} (z_{post} - z_{pre} ),$$ where n is the total number of valid elevation points, $$z_{pre}$$ and $$z_{post}$$ are the elevation above Australian height datum (equivalent to mean sea level) values occurring at the same location in both pre and post surveys. Additionally, when no inter-site comparisons were involved, we approximated the alongshore volumetric change (in m3/m) as: $$Along. beachface \,change = \mathop \smallint \limits_{{x_{swash} }}^{{x_{limit} }} \left( {z_{post} - z_{pre} } \right)dx,$$ where $$x_{swash}$$ and $$x_{limit}$$ are the upper swash and landward limit respectively. Plus or minus ( ±) error intervals for both MEC and volumetric change estimates represent the uncertainty related to changes within the limit of detection thresholds. ### Hotspot analysis: local Moran’s I In order to obtain spatially explicit and statistically significant hotspots of erosion or deposition at the site level, the Local Moran-I90 ($$I_{i}$$) statistics with false discovery rate correction was computed for every inter-surveys elevation difference (Δh) points. The $$I_{i}$$ statistics is defined as: $$Local Moran^{\prime}s Index \left( { I_{i} } \right) = \frac{{z_{i} - \mu_{z} }}{{\sigma^{2} }}\mathop \sum \limits_{j = 1, j \ne i }^{n} \left[ {w_{ij} \left( {z_{j} - \mu_{z} } \right)} \right],$$ where $$z_{i}$$ is the value of the variable at location i with $$\mu_{z}$$ and $$\sigma^{2}$$ the respective mean and variance, as calculated on the $$n$$ number of observations; $$w_{ij}$$ is the spatial weight between the observation at location i and j and $$z_{j}$$ is the value of the variable at all locations different than i90,91. A binary row-standardised spatial weight matrix conceptualises spatial regions (neighbourhoods) within a 35 m of radial Euclidian distance from each focal point, obtaining the weights $$w_{ij}$$ for all points in relation to each other. The 35 m distance band has been chosen to include in the neighbourhood sand points from the two adjacent transects. We used 999 random permutations to compute the reference distribution and obtain a minimum pseudo p-value of 0.05 (95% level of confidence), which we used to discard non-significant $$I_{i}$$. In this analysis, only significant High-High (areas where high values are surrounded by high values) and Low-Low (areas where low values are surrounded by low values) hotspots have been retained, discarding spatial outliers. Significant hotspots of Δh have been classified into five magnitude classes, using the Jenks-Caspall optimised-natural breaks method92, based on the totality of absolute Δh values (Table 1). Weights of each magnitude class are used to represent the severity of change during the e-BCD sign computations and are obtained deriving the median absolute values for each Δh magnitude class. ### Empirical and residual beachface cluster dynamic indices The empirical and residual beachface cluster dynamics indices (e-BCD and r-BCD respectively) are purposefully designed metrics to leverage the very high spatiotemporal resolutions and three-dimensionality of our data for studying subaerial beach landform dynamics (morphodynamics). With elevation change (Δh) magnitude classes as transient states (Table 1), we used finite discrete Markov chain models to compute first-order stochastic transition matrices and steady-state probability vectors, used to derive e- and r-BCD respectively. Following Lambin (1994), a discrete Markov process can be represented as: $$s_{t + 1} = Ms_{t} ,$$ where $$s_{t}$$ is a column vector, $$s = \left( {s_{1} , \ldots ,s_{m} } \right)$$ having as elements the valid points (within the beachface and beyond LoD sand-only Δh points) in one of the $$m$$ states (i.e. Δh magnitude classes) at time $$t$$. M is a $$m \times m$$ matrix holding the first-order (from $$t$$ to $$t + 1$$) transition probabilities $$p_{ij}$$, derived as: $$p_{ij} = \frac{{n_{ij} }}{{\mathop \sum \nolimits_{k = 1}^{m} n_{ik} }},$$ where $$n_{ij}$$ is the number of transitions from an initial state $$i$$ to state $$j$$ and $$m$$ is the number of states (i.e. elevation change classes in Table 1) in which each observation can be. The matrix M is row-standardised, so that the sum of transition probabilities from a given state is always equal to one. The e-BCDs divide the first-order transition matrix M into four sub-matrices (Supplementary Fig. S7), each representing site-level erosional, depositional, recovery and vulnerability behaviours of the subaerial beach over the monitoring period. The e-BCDs indices are computed for every sub-matrices ($$sub$$) as follows: $$Empirical\, BCD_{sub} = \mathop \sum \limits_{i,j = 1}^{n} \left[ { ws^{\prime}_{ij} } \right]\times p_{ij} ,$$ where $$ws_{ij} ^{\prime}$$ is a transformed weight that reflects the magnitude trend of such transition, which is defined as: $$ws^{\prime}_{ij} = \left\{ {\begin{array}{*{20}l} { ws_{i} \times\left( { - ws_{j} } \right) \leftrightarrow i > j } \\ {ws_{i} \times ws_{j} \leftrightarrow i \le j } \\ \end{array} } \right\},$$ where $$ws_{i}$$ and $$ws_{j}$$ are the weights (Table 1) related to the initial $$i$$ and transitioning $$j$$ states respectively. The brackets “[ ]” indicate that the $$ws_{ij} ^{\prime}$$ transformation is implemented separately to determine the e-BCD sign only. The e-BCD absolute score computation does not implement this multiplication, capturing the process importance only. Any state to either no-hotspot or no-data transition probabilities are not included in the e-BCD interpretation. The r-BCDs are computed from the steady-state probability vector. The steady-state of a Markov chain returns a unique probability vector representing the states limiting probability distribution, which, once attained, one additional (or more) time steps will return the exact same initial states probabilities, signalling a situation of dynamic equilibrium has been achieved. This is represented as: $$\pi M = \pi ,$$ where $$\pi$$ is the vector containing the limiting probabilities $$\pi_{j}$$ for each $$j$$ state in $$s$$. This vector $$\pi$$ is derived by solving a system of $$m$$ equations with $$m$$ unknowns, each equation represented as: $$\pi_{j} = \mathop \sum \limits_{k = 1}^{m} \pi_{k} p_{kj} ,$$ given that: $$\mathop \sum \limits_{j = 1}^{m} \pi_{j} = 1.$$ The steady-state can be seen in a descriptive way as representing the states hierarchy, which is unique to the system being modelled93, from which we derive the stochastic tendency the system had towards depositional or erosional states at the end of monitoring. We interpret this tendency as the most likely behavioural regime the system was subjected to, given the drivers of change and boundary conditions that influenced its evolution during the monitoring period. The computation of the r-BCDs is as follows: $$Residual \,BCD_{SS} = 100 \times \mathop \sum \limits_{i = 1}^{m} (\pi_{ie} - \pi_{id} ),$$ where $$ss^{ }$$ is the steady-state probability distribution of one location, $$\pi_{ie}$$ are the limiting probabilities of the erosional classes (ue, se, me, he, ee) and $$\pi_{id}$$ the limiting probabilities of the depositional classes (ud, sd, md, hd and ed) (Table 1). The r-BCDs are not signed as no transitions are represented in the resultant vector. Any state to either no-hotspot or no-data transition probabilities are not included in the r-BCD interpretation. The multiplication by 100 is performed for index readability purposes. We computed r-BCDs using erosional/depositional hotspots at the site level only (Fig. 3a), while at the transect level (Fig. 4), r-BCDs are computed with the full Δh cross-shore profiles. This has been done due to the relatively narrow beach width which resulted in a limited number of valid sand-only observations for hotspot analysis. ## Data availability More than 220 3D datasets are already freely accessible to anyone via a user friendly web-platform to share and communicate information, promote coastal awareness, build knowledge and further increase the impact of our efforts. Link https://www.propelleraero.com/. Credentials email: [email protected]; Password: propellervcmp. ## Code availability The code used throughout this study is freely available here: Draft code: https://github.com/npucino/sandpiper/tree/master. Except for digital photogrammetric procedure, all the analysis has been automated using open-source Python 3 packages, especially PySAL 2.0.093 for LISA and Markov Chain computations, Scikit-Learn94 for machine learning classification and Seaborn and Matplotlib95 for quantitative data visualisation. 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Apollo Bay nourishment data has been provided by Hannah Fallon (DELWP). We are grateful to Karina Sorrell and all the citizen scientists involved in the collection of the data. ## Author information Authors ### Contributions N.P.: Conceptualization, Methodology, Software, Validation, Formal analysis, Writing—Original Draft, Visualization. D.K.: Writing—Review & Editing, Supervision, Project administration, Funding acquisition. R.C.: Writing—Review & Editing, Supervision. B.A.: Writing—Review & Editing, Data Curation. D.I.: Writing—Review & Editing, Supervision, Project administration, Funding acquisition. ### Corresponding author Correspondence to Nicolas Pucino. ## Ethics declarations ### Competing interests The authors declare no competing interests. ## Additional information ### Publisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. ## Rights and permissions Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. Reprints and Permissions ## About this article ### Cite this article Pucino, N., Kennedy, D.M., Carvalho, R.C. et al. Citizen science for monitoring seasonal-scale beach erosion and behaviour with aerial drones. Sci Rep 11, 3935 (2021). https://doi.org/10.1038/s41598-021-83477-6 Download citation • Received: • Accepted: • Published: • DOI: https://doi.org/10.1038/s41598-021-83477-6 ## Comments By submitting a comment you agree to abide by our Terms and Community Guidelines. 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Sign up for Nature Briefing	2022-06-27 17:26:20	{"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": 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": 0.5665622353553772, "perplexity": 9417.79134753779}, "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-2022-27/segments/1656103337962.22/warc/CC-MAIN-20220627164834-20220627194834-00255.warc.gz"}
http://openstudy.com/updates/5124e402e4b086b98ebdc125	Here's the question you clicked on: ## lirffej Group Title from a quartic equation with rational coefficients having 3-sq.root of 2 and 1+2 sq.root of 2 as roots..plzz..help one year ago one year ago • This Question is Open 1. Vinayak_G_P Since you have to roots, you can write the equation as $(x-(3-\sqrt{2}))(x-(1+2\sqrt{2}) = 0$ Multiplying the terms $x^2 - x (1+2\sqrt{2}) - x * (3-\sqrt{2}) - ((3-\sqrt{2})*(1+2\sqrt{2})) = 0$ Simplify the terms and you have your answer.	2014-10-20 23:01:43	{"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": 0.9531696438789368, "perplexity": 1285.1920061079961}, "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-2014-42/segments/1413507443451.12/warc/CC-MAIN-20141017005723-00258-ip-10-16-133-185.ec2.internal.warc.gz"}
https://ko-kr.knowledgebase.renesas.com/English_Content/MCUMPU/Basic_Information/Is_there_something_wrong_when_amplitude_shown_is_approximately_1.5_V%3F	메인 콘텐츠로 건너뛰기 # Is there any problem that the oscillation amplitude is shown as approximately 1.5 V for the XIN-XOUT oscillation circuit? Last Updated:12/26/2017 ## Question: Is there any problem that the oscillation amplitude is shown as approximately 1.5 V for the XIN-XOUT oscillation circuit?	2018-01-19 07:32:30	{"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": 0.9807996153831482, "perplexity": 2598.9429026693724}, "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/1516084887832.51/warc/CC-MAIN-20180119065719-20180119085719-00375.warc.gz"}
https://deepai.org/publication/relaxed-locally-correctable-codes-with-improved-parameters	# Relaxed Locally Correctable Codes with Improved Parameters Locally decodable codes (LDCs) are error-correcting codes C : Σ^k →Σ^n that admit a local decoding algorithm that recovers each individual bit of the message by querying only a few bits from a noisy codeword. An important question in this line of research is to understand the optimal trade-off between the query complexity of LDCs and their block length. Despite importance of these objects, the best known constructions of constant query LDCs have super-polynomial length, and there is a significant gap between the best constructions and the known lower bounds in terms of the block length. For many applications it suffices to consider the weaker notion of relaxed LDCs (RLDCs), which allows the local decoding algorithm to abort if by querying a few bits it detects that the input is not a codeword. This relaxation turned out to allow decoding algorithms with constant query complexity for codes with almost linear length. Specifically, [BGH+06] constructed an O(q)-query RLDC that encodes a message of length k using a codeword of block length n = O(k^1+1/√(q)). In this work we improve the parameters of [BGH+06] by constructing an O(q)-query RLDC that encodes a message of length k using a codeword of block length O(k^1+1/q). This construction matches (up to a multiplicative constant factor) the lower bounds of [KT00, Woo07] for constant query LDCs, thus making progress toward understanding the gap between LDCs and RLDCs in the constant query regime. In fact, our construction extends to the stronger notion of relaxed locally correctable codes (RLCCs), introduced in [GRR18], where given a noisy codeword the correcting algorithm either recovers each individual bit of the codeword by only reading a small part of the input, or aborts if the input is detected to be corrupt. Comments There are no comments yet. ## Authors • 3 publications • 8 publications 04/17/2019 ### A Lower Bound for Relaxed Locally Decodable Codes A locally decodable code (LDC) C:0,1^k -> 0,1^n is an error correcting c... 01/11/2020 ### Locally Decodable Codes with Randomized Encoding We initiate a study of locally decodable codes with randomized encoding.... 10/22/2020 ### Locally Decodable/Correctable Codes for Insertions and Deletions Recent efforts in coding theory have focused on building codes for inser... 11/25/2019 ### Combinatorial lower bounds for 3-query LDCs A code is called a q-query locally decodable code (LDC) if there is a ra... 11/01/2021 ### Exponential Lower Bounds for Locally Decodable and Correctable Codes for Insertions and Deletions Locally Decodable Codes (LDCs) are error-correcting codes for which indi... 05/06/2019 ### Lifted Multiplicity Codes Lifted Reed Solomon Codes (Guo, Kopparty, Sudan 2013) were introduced in... 01/27/2022 ### c^3-Locally Testable Codes from Lossless Expanders A locally testable code (LTC) is an error correcting code with a propert... ##### This week in AI Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday. ## 1 Introduction Locally decodable codes (LDCs) are error-correcting codes that admit a decoding algorithm that recovers each specific symbol of the message by reading a small number of locations in a possibly corrupted codeword. More precisely, a locally decodable code with local decoding radius is an error-correcting code that admits a local decoding algorithm , such that given an index and a corrupted word which is -close to an encoding of some message , reads a small number of symbols from , and outputs with high probability. Similarly, we have the notion of locally correctable codes (LCCs), which are error-correcting codes that not only admit a local algorithm that decode each symbol of the message, but are also required to correct an arbitrary symbol from the entire codeword. Locally decodable and locally correctable codes have many applications in different areas of theoretical computer science, such as complexity theory, coding theory, property testing, cryptography, and construction of probabilistically checkable proof systems. For details, see the surveys [Yek12, KS17] and the references within. Despite the importance of LDCs and LCCs, and the extensive amount of research studying these objects, the best known construction of constant query LDCs has super-polynomial length , which is achieved by the highly non-trivial constructions of [Yek08] and [Efr12]. For constant query LCCs, the best known constructions are of exponential length, which can be achieved by some parameterization of Reed-Muller codes. It is important to note that there is huge gap between the best known lower bounds for the length of constant query LDCs and the length of best known constructions. Currently, the best known lower bound on the length of LDCs says that for it must be at least , where stands for the query complexity of the local decoder. See [KT00, Woo07] for the best general lower bounds for constant query LDCs. Motivated by applications to probabilistically checkable proofs (PCPs), Ben-Sasson, Goldreich, Harsha, Sudan, and Vadhan introduced in [BGH06] the notion of relaxed locally decodable codes (RLDCs). Informally speaking, a relaxed locally decodable code is an error-correcting code which allows the local decoding algorithm to abort if the input codeword is corrupt, but does not allow it to err with high probability. In particular, the decoding algorithm should always output correct symbol, if the given word is not corrupted. Formally, a code is an RLDC with decoding radius if it admits a relaxed local decoding algorithm which given an index and a possibly corrupted codeword , makes a small number of queries to , and satisfies the following properties. Completeness: If for some , then should output . Relaxed decoding: If is -close to some codeword , then should output either or a special abort symbol with probability at least 2/3. This relaxation turns out to be very helpful in terms of constructing RLDCs with better block length. Indeed, [BGH06] constructed of a -query RLDC with block length . The notion of relaxed LCCs (RLCCs), recently introduced in [GRR18], naturally extends the notion of RLDCs. These are error-correcting codes that admit a correcting algorithm that is required to correct every symbol of the codeword, but is allowed to abort if noticing that the given word is corrupt. More formally, the local correcting algorithm gets an index , and a (possibly corrupted) word , makes a small number of queries to , and satisfies the following properties. Completeness: If , then should output . Relaxed correcting: If is -close to some codeword , then should output either or a special abort symbol with probability at least 2/3. Note that if the code is systematic, i.e., the encoding of any message contains in its first symbols, then the notion of RLCC is stronger than RLDC. Recently, building on the ideas from [GRR18], [CGS20] constructed RLCCs whose block length matches the RLDC construction of [BGH06]. For the lower bounds, the only result we are aware of is the work of Gur and Lachish [GL20], who proved that for any RLDC the block length must be at least . Given the gap between the best constructions and the known lower bounds, it is natural to ask the following question: What is the best possible trade-off between the query complexity and the block length of an RLDC? In particular, [BGH06] asked whether it is possible to obtain a -query RLDC whose block length is strictly smaller than the best known lower bound on the length of LDCs. A positive answer to their question would show a separation between the two notions, thus proving that the relaxation is strict. See paragraph Open Problem in the end of Section 4.2 of [BGH06]. In this work we make progress on this problem by constructing a relaxed locally decodable code with query complexity and block length . In fact, our construction gives the stronger notion of a relaxed locally correctable code. ###### Theorem 1 (Main Theorem). For every there exists an -query relaxed locally correctable code with constant relative distance and constant decoding radius, such that the block length of is N=qO(q2)⋅K1+O(1/q). Therefore, our construction improves the parameters of the -query RLDC construction of [BGH06] with block length , and matches (up to a multiplicative factor in ) the lower bound of for the block length of -query LDCs [KT00, Woo07]. ###### Remark 1.1. In this paper we prove creftype 1 for a code over a large alphabet. Specifically, we show a code satisfying creftype 1, for a finite field satisfying , for some that depends only on . Using the techniques from [CGS20] it is not difficult to obtain an RLCC over the binary alphabet with almost the same block length. Indeed, this can be done by concatenating our code over large alphabet with an arbitrary binary code with constant rate and constant relative distance. See Section 7 for details. ### 1.1 Related works RLDC and RLCC constructions: Relaxed locally decodable codes, were first introduced by [BGH06], motivated by applications to constructing short PCPs. Their construction has a block length equal to . Since that work, there were no constructions with better block length, in the constant query complexity regime . Recently, [GRR18] introduced the related notion of relaxed locally correctable codes (RLCCs), and constructed -query RLCCs with block length . Then, [CGS20] constructed relaxed locally correctable codes with block length matching that of [BGH06] (up to a multiplicative constant factor ). The construction of [CGS20] had two main components, that we also use in the current work. Consistency test using random walk (): Informally, given a word , and a coordinate we wish to correct, samples a sequence of constraints on , such that the domains of and intersect, with the guarantee that if is close to some codeword , but , then with high probability will be far from satisfying at least one of the constraints. In other words, performs a random walk on the constraints graph and checks if is consistent with in the ’th coordinate. We introduce this notion in detail in Section 2.1, and prove that the Reed-Muller code admits a in Section 4. Correctable canonical PCPPs (ccPCPP): These are PCPP systems for some specified language satisfying the following properties: (i) for each there is a unique proof that satisfies the verifier with probability 1, (ii) the verifier accepts with high probability only pairs that are close to some for some , i.e., only the pairs where is close to some , and is close to , and (iii) the set is an RLCC. Canonical proofs of proximity have been studies in [DGG18, Par20]. We elaborate on these constructions in Section 5. Lower bounds: For lower bounds, the only bound we are aware of is that of [GL20], who proved that any -query relaxed locally decodable code must have a block length . For the strict notion of locally decodable codes, it is known by [KT00, Woo07] that for any -query LDC must have block length . For a slightly stronger bound of is known, and furthermore, for -query linear LDC the block length must be [Woo07]. For [KdW03] proved an exponential lower bound of . See also [DJK02, GKST02, Oba02, WdW05, Woo10] for more related work on lower bounds for LDCs. ### 1.2 Organization The rest of the paper is organized as follows. In Section 2, we informally discuss the construction and the correcting algorithm. In this discussion we focus on decoding the symbols corresponding to the message, i.e., on showing that the code is an RLDC. Section 3 introduces the formal definitions and notations we will use in the proof of creftype 1. We present the notion of consistency test using random walk in Section 4, and prove that the Reed-Muller code admits such test. In Section 5 we present the PCPPs we will use in our construction, and state the properties needed for the correcting algorithm. In Section 6 we prove creftype 1 by proving a composition theorem, which combines the instantiation of the Reed-Muller code with PCPPs from the previous sections. ## 2 Proof overview In this section we informally describe our code construction. Roughly speaking, our construction consists of two parts: The Reed-Muller encoding: Given a message , its Reed-Muller encoding is the evaluation of an -variate polynomial of degree at most over , whose coefficients are determined by the message we wish to encode. Proofs of proximity: The second part of the encoding consists of the concatenation of PCPPs, each claiming that a certain restriction of the first part agrees with some Reed-Muller codeword. Specifically, given a message , we first encode it using the Reed-Muller encoding , where roughly corresponds to the query complexity of our RLDC, and the field is large enough so that the distance of the Reed-Muller code, which is equal to , is some constant, say . That is, the first part of the encoding corresponds to an evaluation of some polynomial of degree at most . The second part of the encoding consists of a sequence of PCPPs claiming that the restrictions of a the Reed-Muller part to some carefully chosen planes in are evaluations of some low-degree polynomial. The planes we choose are of the form , where , and for some subfield of . We will call such planes -planes. In order to obtain the RLDC with the desired parameters, we choose the field so that is the extension of of degree . It will be convenient to think of as a field and think of as a vector space of of dimension (augmented with the multiplicative structure on ). Indeed, the saving in the block length of the RLDC we obtain crucially relies on the fact that we ask for PCPPs for only a small collection of planes, and not all planes in . The actual constraints required to be certified by the PCPPs are slightly more complicated, and we describe the next. The constraints of the first type correspond to -planes and points . For each such pair the code will contain a PCPP certifying that (i) the restriction of the Reed-Muller part to is close to an evaluation of some polynomial of total degree at most , (ii) and furthermore, this polynomial agrees with the value of the Reed-Muller part on . In order to define it formally, we introduce the following notation. ###### Notation 2.1. Let be a finite field of size . Fix , a plane in , and a point . Denote . That is, the length of is , and it consists of concatenated with repetitions of . Given the notation above, if is the first part of the codeword, corresponding to the Reed-Muller encoding of the message, then the PCPP for the pair is expected to be the proof of proximity claiming that is close to the language RM(→x)∣P={Q∘(Q(→x))(n2):Q is the evaluation of a degree-d polynomial on P}⊆F2n2. (1) Note that by repeating the symbol for times, the definition indeed puts weight 1/2 on the constraint that the input is close to some low-degree polynomial , and puts weight 1/2 of the constraint . In particular, if is -close to some bivariate low degree polynomial for some small , but , then is at least -far from any bivariate low degree polynomial on . The constraints of second type correspond to -planes and lines . For each such pair the code will contain a PCPP certifying that (i) the restriction of the Reed-Muller part to is close to an evaluation of some polynomial of total degree at most , (ii) and furthermore, this polynomial is close to . (In particular, this implies that is close to some low-degree polynomial.) Next, we introduce the notation analogous to creftype 2.1 replacing the points with lines. ###### Notation 2.2. Let be a finite field of size . Fix , a plane in , and a line . Denote by . That is, the length of is , and it consists of concatenated with repetitions of . If is the Reed-Muller part of the codeword, corresponding to the Reed-Muller encoding of the message, then the PCPP for the pair is expected to be the proof of proximity claiming that is close to the language RM(ℓ)∣P={Q∘(Q∣ℓ)n:Q is% the evaluation of some degree-d polynomial on P}⊆F2n2. (2) Again, similarly to the first part, repeating the evaluation of for times puts weight 1/2 on the constraint that the input is a close to some low-degree polynomial , and puts weight 1/2 of the constraint is close to . With the proofs specified above, we now sketch the local correcting algorithm for the code. Below we only focus on correcting symbols from the Reed-Muller part. Correcting the symbols from the PCPP part follows a rather straightforward adaptation of the techniques from [CGS20], and we omit them from the overview. Given a word and an index of corresponding to the Reed-Muller part of the codeword, let be the Reed-Muller part of , and let be the input to corresponding to the index . The local decoder works in two steps. Consistency test using random walk: In the first step the correcting algorithm invokes a procedure we call consistency test using a random walk () for the Reed-Muller code. This step creates a sequence of -planes of length , where each plane defines a constraint checking that the restriction of to the plane is low-degree. Hence, we get constraints, each depending on symbols. Composition using proofs of proximity: Then, instead of reading the entire plane for each constraint, we use the PCPPs from the second part of the codeword to reduce the arity of each constraint to , thus reducing the total query complexity of the correcting algorithm to . That is, for each constraint we invoke the corresponding PCPP verifier to check that the restrictions of to each of these planes is (close to) a low-degree polynomial. If at least one of the verifiers rejects, then the word must be corrupt, and hence the correcting algorithm returns . Otherwise, if all the PCPP verifiers accept, the correcting algorithm returns . In particular, if is a correct Reed-Muller encoding, then the algorithm will always return , and the main part of the analysis is to show that if is close to some , but , then the correcting algorithm catches an inconsistency, and returns with some constant probability. See Section 6.3 for details. The key step in the analysis says that if is close to some codeword but , then with high probability will be far from a low degree polynomial on at least one of these planes, where “far” corresponds to the notion of distances defined by the languages and . In particular, if on one of the planes is far from the corresponding language, then the PCPP verifier will catch this with constant probability, thus causing the correcting algorithm to return . We discuss this part in detail below. It is important to emphasize that the main focus of this work is constructing a correcting algorithm for the Reed-Muller part. Using the techniques developed in [CGS20], it is rather straightforward to design the algorithm for correcting symbols from the PCPPs part of the code. See Section 6.4 for details. ### 2.1 CTRW on Reed-Muller codes Below we define the notion of consistency test using random walk () for the Reed-Muller code. This notion is a slight modification of the notion originally defined in [CGS20] for general codes. In this paper we define it only for the Reed-Muller code. Given a word and some , the goal of the test is to make sure that is consistent with the codeword of Reed-Muller code closest to . [CGS20] describe a for the tensor power of an arbitrary codes with good distance (e.g., Reed-Solomon). The they describe works by starting from the point we wish to correct, and choosing an axis-parallel line containing the starting point. The test continues by choosing a sequence of random axis-parallel lines , such that each intersects the previous one, , until reaching a uniformly random coordinate of the tensor code. That is, the length of the sequence denotes the mixing time of the corresponding random walk. The predicates are defined in the natural way; namely, the test expects to see a codeword of on each line it reads. In this work, we present a for the Reed-Muller code, which is a variant of the described above. The main differences compared to the description above are that (i) the test chooses a sequence of planes (and not lines), (ii) and every two planes intersect on a line (and not on a point). Roughly speaking, the algorithm works as follows. 1. Given a point the test picks a uniformly random -plane containing . 2. Given , the test chooses a random line , and then chooses another random -plane containing . 3. Given , the test chooses a random line , and then chooses another random -plane containing . 4. The algorithm continues for some predefined number of iterations, choosing . Roughly speaking, the number of iterations is equal to the mixing time of the corresponding Markov chain. More specifically, the process continues until a uniformly random point in is close to a uniform point in . 5. The constraints defined for each are the natural constraints; namely checking that the restriction of to is a polynomial of degree at most . One of the important parameters, directly affecting the query complexity of our construction is the mixing time of the random walk. Indeed, as explained above, the query complexity of our RLDC is proportional to the mixing time of the random walk. We prove that if , then the mixing time is upper bounded by . In order to prove this we use the following claim, saying that if is the field extension of of degree , and and are sampled uniformly, independently from each other, then is close to a uniformly random point in . See creftype 3.5 for the exact statement. As explained above, the key step of the analysis is to prove that if is close to some codeword but , then with high probability at least one of the predicates defined will be violated. Specifically, we prove that with high probability the violation will be in the following strong sense. ###### Theorem 2.3 (informal, see Theorem 4.3). If is close to some codeword but , then with high probability 1. either is -far from , 2. or is -far from for some . Indeed, this strong notion of violation allows us to use the proofs of proximity in order to reduce the query complexity to queries for each . We discuss proofs of proximity next. ### 2.2 PCPs of proximity and composition The second building block we use in this work is the notion of probabilistic checkable proofs of proximity (PCPPs). PCPPs were first introduced in [BGH06] and [DR04]. Informally speaking, a PCPP verifier for a language , gets an oracle access to an input and a proof claiming that is close to some element of . The verifier queries and in some small number of (random) locations, and decides whether to accept or reject. The completeness and soundness properties of a PCPP are as follows. Completeness: If , then there exists a proof causing the verifier to accept with probability 1. Soundness: If is far from , then no proof can make the verifier to accept with probability more than 1/2. In fact, we will use the slightly stronger notion of canonical PCPP (cPCPP) systems. These are PCPP systems satisfying the following completeness and soundness properties. For completeness, we demand that for each in the language there is a unique canonical proof that causes the verifier to accept with probability 1. For soundness, the demand is that the only pairs that are accepted by the verifier with high probability are those where is close to some and is close to . Such proof system have been studies in [DGG18, Par20], who proved that such proof systems exist for every language in . Furthermore, for our purposes we will demand a stronger notion of correctable canonical PCPP systems (ccPCPP). These are canonical PCPP systems where the set is a -query RLCC for some parameter , with denoting the canonical proof for . It was shown in [CGS20] how to construct ccPCPP by combining a cPCPP system with any systematic RLCC. Informally speaking, for every , and its canonical proof , we define by encoding using a systematic RLCC. The verifier for the new proof system is defined in a straightforward manner. See [CGS20] for details. The PCPPs we use throughout this work, are the proofs of two types, certifying that 1. is close to for some plane and some , and 2. is close to for some plane and some line . Indeed, it is easy to see that the first type of proofs checks that (i) the restriction of to is close to an evaluation of some polynomial of total degree at most , (ii) and . Similarly, the second type proof certifies that (i) the restriction of to is close to an evaluation of some polynomial of total degree at most , (ii) and is close to . These notions of distance go together well with the guarantees we have for in Theorem 2.3. This allows us to compose with the PCPPs to obtain a correcting algorithm with query complexity . Informally speaking, the composition theorem works as follows. We first run the to obtain a collection of constraints on the planes . By Theorem 2.3, we have the guarantee that with high probability either is -far from , or is -far from for some . Then, instead of actually reading the values of on all these planes, we run the PCPP verifier on to check that it is close to , and running the PCPP verifier on each of the to check that they are close to . Each execution of the PCPP verifier makes queries to and to the proof, and thus the total query complexity will be indeed . As for soundness, if is -far from , or is -far from for some , then the corresponding verifier will notice an inconsistency with constant probability, causing the decoder to output . We discuss proofs of proximity in Section 5. The composition is discussed in Section 6. ## 3 Preliminaries We begin with standard notation. The relative distance between two strings is defined as dist(x,y)\coloneqq\|{i∈[n]:xi≠yi}\|n. If , we say that is -close to ; otherwise we say that is -far from . For a non-empty set define the distance of from as . If , we say that is -close to ; otherwise we say that is -far from . We will also need a more general notion of a distance, allowing different coordinates to have different weight. In particular, we will need the distance that gives constant weight to a particular subset of the coordinates, and spreads the rest of the weight uniformly between all coordinates. ###### Definition 3.1. Fix and an alphabet . For a set define the distance between two strings as distA(x,y)=\|{i∈A:xi≠yi}\|2\|A\|+\|{i∈[n]:xi≠yi}\|2n. In particular, if differs from on coordinates in , then is at least . We define between a string and a set as distA(x,S)=miny∈SdistA(x,y). ###### Remark 3.2. This definition generalizes the definition of [CGS20] of for a coordinate . Indeed, the notion of for a coordinate corresponds to the singleton set . When the set is a singleton we will write to denote , and we will write to denote . ### 3.1 Basic coding theory Let be positive integers, and let be an alphabet. An error correcting code is an injective mapping from messages of length over the alphabet to codewords of length . The parameter is called the message length of the code, and is its block length (which we view as a function of ). The rate of the code is defined as , and the relative distance of the code is defined as . We sometimes abuse the notation and use to denote the set of all of its codewords, i.e., identify the code with . Linear codes Let be a finite field. A code is linear if it is an -linear map from to . In this case the set of codewords is a subspace of , and the message length of is also the dimension of the subspace. It is a standard fact that for any linear code , the relative distance of is equal to . ### 3.2 Reed-Muller codes Reed-Muller codes [Mul54] are among the most well studied error correcting codes, with many theoretical and practical applications in different areas of computer science and information theory. Let be a finite field of order , and let and be integers. The code is the linear code whose codewords are the evaluations of polynomials of total degree at most over . We will allow ourselves to write , since the field is fixed throughout the paper. We will also sometimes omit the parameters and , and simply write , when the parameters are clear from the context. In this paper we consider the setting of parameters where . It is well known that for the relative distance of is . The dimension of can be computed by counting the number of monomials of total degree at most . For the number of such monomials is . Since the length of each codeword is , it follows that the rate of the code is . ###### Definition 3.3. For denote by the line ℓ→x,→y={→x+t⋅→y:t∈F}. Also, for denote by the plane P→x,→y,→z={→x+t⋅→y+s⋅→z:t,s∈F}. An important property of (and multivariate low-degree polynomials, in general) that we use throughout this work is that their restrictions to lines and planes in are also polynomials of degree at most . In other words, if , and is a line ( is a plane) in , then the restriction of to (or to ) is a codeword of the Reed-Muller code of the same degree and lower dimension. The following lemma is a standard lemma in the PCP literature, saying that random lines sample well the space . ###### Lemma 3.4. Let be a finite field. For any subset of density , and for any it holds that Pr→x∈F2,→y∈F2[∣∣∣\|ℓ→x,→y∩A\|\|ℓ→x,→y\|−μ∣∣∣>ϵ]≤1\|F\|⋅μϵ2. ###### Proof. For each , let be an indicator random variable for the event . Since each point is a uniform point in the plane, we have , Therefore, denoting , it follows that . We are interested in bounding the deviation of from its expectation. We do it by bounding the variance of . Note first that . By the pairwise independence of the points on a line, it follows that . Therefore, by applying Chebyshev’s inequality we get Pr[∣∣∣\|ℓ→x,→y∩A\|\|ℓ→x,→y\|−μ∣∣∣>ϵ]=Pr[\|X−μ\|F\|\|>ϵ\|F\|]≤Var[X](ϵ\|F\|)2≤μ\|F\|⋅ϵ2, as required. ∎ The following claim will be an important step in our analysis. ###### Claim 3.5. Let be a parameter, let be a finite field, and let be its extension of degree . Let and be chosen independently uniformly at random from their domains. Then for any set of size it holds that Pr[m∑i=1ti⋅→hi∈A]≤α+2/H. ###### Proof. In order to prove the claim let us introduce some notation. We write each element in as an -dimensional row vector over . Also, we will represent an element as a matrix over , where the ’th row represents , the ’th coordinate of . Using this notation we need to prove that the random matrix corresponding to the sum is close to a random matrix with entries chosen uniformly from independently from each other. Using the notation above, write each as a row vector . Observe that for any vector we can represent as the outer product ti⋅→hi=⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣ti,1⋅→hi,1ti,2⋅→hi,1…ti,m⋅→hi,1ti,1⋅→hi,2ti,2⋅→hi,2…ti,m⋅→hi,2⋮⋮⋱⋮ti,1⋅→hi,mti,2⋅→hi,m…ti,m⋅→hi,m⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦=⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣→hi,1→hi,2⋮→hi,m⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦⋅[ti,1ti,2…ti,m] Therefore, the sum is represented as m∑i=1⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣→hi,1→hi,2⋮→hi,m⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦⋅[ti,1ti,2…ti,m]=H⋅T, where is the matrix with , and is the matrix with . That is, the sum is represented as a product of two uniformly random matrices over . Next we show that if are chosen uniformly at random and independently, then for any collection of matrices of size it holds that . Indeed, Pr[H⋅T∈A]≤Pr[H⋅T∈A\|H is invertible]+Pr[H is not invertible]. If is invertible, then for a uniformly random the probability that is exactly , and it is easy to check that . ∎ ### 3.3 Relaxed locally correctable codes Following the discussion in the introduction, we provide a formal definition of relaxed LCCs, and state some related basic facts and known results. ###### Definition 3.6 (Relaxed LCC). Let be an error correcting code with relative distance , and let , ,and be parameters. Let be a randomized algorithm that gets an oracle access to an input and an explicit access to an index . We say that is a -query relaxed local correction algorithm for with correction radius and soundness if for all inputs the algorithm reads explicitly the coordinate , reads at most (random) coordinates in , and satisfies the following conditions. 1. For every , and every coordinate it holds that . 2. For every that is -close to some codeword and every coordinate it holds that , where is a special abort symbol. The code is said to be a -relaxed locally correctable code (RLCC) with query complexity if it admits a -query relaxed local correction algorithm with correction radius and soundness . ###### Observation 3.7. Note that for systematic codes it is clear from Definition 3.6 that RLCC is a stronger notion than RLDC, as it allows the local correction algorithm not only to decode each symbol of the message, but also each symbol of the codeword itself. That is, any systematic RLCC is also an RLDC with the same parameters. Finally, we recall the following theorem of Chiesa, Gur, and Shinkar [CGS20]. ###### Theorem 3.8 ([Cgs20]). For any finite field , and parameters , there exists an explicit construction of a systematic linear code with block length and constant relative distance, that is a -query RLCC with constant correction radius , and constant soundness . ### 3.4 Canonical PCPs of proximity Next we define the notions of probabilistically checkable proofs of proximity, and the variants that we will need in this paper. ###### Definition 3.9 (PCP of proximity). A -query PCP of proximity (PCPP) verifier for a language with soundness with respect the to proximity parameter , is a polynomial-time randomized algorithm that receives oracle access to an input and a proof . The verifier makes at most queries to and has the following properties: Completeness: For every there exists a proof such that . Soundness: If is -far from , then for every proof it holds that . A canonical PCPP (cPCPP) is a PCPP in which every instance in the language has a canonical accepting proof. Formally, a canonical PCPP is defined as follows. ###### Definition 3.10 (Canonical PCPP). A -query canonical PCPP verifier for a language with soundness with respect to proximity parameter , is a polynomial-time randomized algorithm that gets oracle access to an input and a proof . The verifier makes at most queries to , and satisfies the following conditions: Canonical completeness: For every there exists a unique (canonical) proof for which . Canonical soundness: For every and proof such that δ(x,π)≜minw∈L{max(dist(x,w)n , dist(π,π(w))len(n))}>ρ, (3) it holds that . The following result on canonical PCPPs was proved in [DGG18] and [Par20]. ###### Theorem 3.11 ([Dgg18, Par20]). Let be a proximity parameter. For every language in there exists a polynomial and a canonical PCPP verifier for satisfying the following properties. 1. For all of length the length of the canonical proof is . 2. The query complexity of the PCPP verifier is . 3. The PCPP verifier for has perfect completeness and soundness for proximity parameter (with respect to the uniform distance measure). Next, we define the stronger notion of correctable canonical PCPPs (ccPCPP), originally defined in [CGS20]. A ccPCPP system is a canonical PCPP system that in addition to allowing the verifier to be able to locally verify the validity of the given proof, it also admits a local correction algorithm that locally corrects potentially corrupted symbols of the canonical proof. Formally, the ccPCPP is defined as follows. ###### Definition 3.12 (Correctable canonical PCPP). A language is said to admit a ccPCPP with query complexity and soundness with respect to the proximity parameter , and correcting soundness for correcting radius if it satisfies the following conditions. 1. admits a -query canonical PCPP verifier for satisfying the conditions in Definition 3.10 with soundness with respect to the proximity parameter . 2. The code is a -RLCC with query complexity , where is the canonical proof for from Definition 3.10. ## 4 Consistency test using random walk on the Reed-Muller code Below we define the notion of consistency test using random walk (). This notion has been originally defined in [CGS20] for tensor powers of general codes. In this paper we focus on for the Reed-Muller code. Informally speaking, a consistency test using random walk for Reed-Muller code is a randomized algorithm that gets a word , which is close to some codeword , and an index as an input, and its goal is to check whether . In other words, it checks whether the value of at is consistent with the close codeword . Below we formally describe the random process. ###### Definition 4.1 (Consistency test using H-plane-line random walk on RMF(m,d)). Let be a field, and let be a field extension of . Let be the Reed-Muller code. An -steps consistency test using -plane-line random walk on is a randomized algorithm that gets as input the evaluation table of some and a coordinate , and works as in Algorithm 1.	2022-05-26 12:13:53	{"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": 0.9040838479995728, "perplexity": 608.7258376167883}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "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-2022-21/segments/1652662604794.68/warc/CC-MAIN-20220526100301-20220526130301-00703.warc.gz"}
https://blog.datadive.net/interpreting-random-forests/	# Interpreting random forests ## Why model interpretation? Imagine a situation where a credit card company has built a fraud detection model using a random forest. The model can classify every transaction as either valid or fraudulent, based on a large number of features. What if, after a transaction is classified as fraudulent, the analyst would like to know why the model made this decision, i.e. how much each feature contributed to the final outcome? Or what if a random forest model that worked as expected on an old data set, is producing unexpected results on a new data set. How would one check which features contribute most to the change in the expected behaviour. ## Random forest as a black box Most literature on random forests and interpretable models would lead you to believe this is nigh impossible, since random forests are typically treated as a black box. Indeed, a forest consists of a large number of deep trees, where each tree is trained on bagged data using random selection of features, so gaining a full understanding of the decision process by examining each individual tree is infeasible. Furthermore, even if we are to examine just a single tree, it is only feasible in the case where it has a small depth and low number of features. A tree of depth 10 can already have thousands of nodes, meaning that using it as an explanatory model is almost impossible. One way of getting an insight into a random forest is to compute feature importances, either by permuting the values of each feature one by one and checking how it changes the model performance or computing the amount of “impurity” (typically variance in case of regression trees and gini coefficient or entropy in case of classification trees) each feature removes when it is used in node. Both approaches are useful, but crude and static in the sense that they give little insight in understanding individual decisions on actual data. ## Turning a black box into a white box: decision paths When considering a decision tree, it is intuitively clear that for each decision that a tree (or a forest) makes there is a path (or paths) from the root of the tree to the leaf, consisting of a series of decisions, guarded by a particular feature, each of which contribute to the final predictions. A decision tree with $$M$$ leaves divides the feature space into $$M$$ regions $$R_m, 1\leq m \leq M$$. In the classical definition (see e.g. Elements of Statistical Learning), the prediction function of a tree is then defined as $$f(x) = \sum\limits_{m=1}^M c_m I(x, R_m)$$ where $$M$$ is the number of leaves in the tree(i.e. regions in the feature space), $$R_m$$ is a region in the feature space (corresponding to leaf $$m$$), $$c_m$$ is a constants corresponding to region $$m$$ and finally $$I$$ is the indicator function (returning 1 if $$x \in R_m$$, 0 otherwise). The value of $$c_m$$ is determined in the training phase of the tree, which in case of regression trees corresponds to the mean of the response variables of samples that belong to region $$R_m$$ (or ratio(s) in case of a classification tree). The definition is concise and captures the meaning of tree: the decision function returns the value at the correct leaf of the tree. But it ignores the “operational” side of the decision tree, namely the path through the decision nodes and the information that is available there. ## Example: Boston housing data Let’s take the Boston housing price data set, which includes housing prices in suburbs of Boston together with a number of key attributes such as air quality (NOX variable below), distance from the city center (DIST) and a number of others – check the page for the full description of the dataset and the features. We’ll build a regression decision tree (of depth 3 to keep things readable) to predict housing prices. As usual, the tree has conditions on each internal node and a value associated with each leaf (i.e. the value to be predicted). But additionally we’ve plotted out the value at each internal node i.e. the mean of the response variables in that region. RM LSTAT NOX DIST 3.14.50.542.6Predict 6.516.10.122.2Predict 7.110.50.311.8Predict You can hover on the leaves of the tree or click “predict” in the table (which includes sample values from the data set) to see the decision paths that lead to each prediction. What’s novel here is that you can see the breakdown of the prediction, written down in terms of value changes along the prediction path, together with feature names that “caused” every value change due to being in the guard (the numbers are approximate due to rounding). What this example should make apparent is that there is another, a more “operational” way to define the prediction, namely through the sequence of regions that correspond to each node/decision in the tree. Since each decision is guarded by a feature, and the decision either adds or subtracts from the value given in the parent node, the prediction can be defined as the sum of the feature contributions + the “bias” (i.e. the mean given by the topmost region that covers the entire training set). Without writing out the full derivation, the prediction function can be written down as $$f(x) = c_{full} + \sum\limits_{k=1}^K contrib(x, k)$$ where $$K$$ is the number of features, $$c_{full}$$ is the value at the root of the node and $$contrib(x, k)$$ is the contribution from the k-th feature in the feature vector $$x$$. This is superficially similar to linear regression ($$f(x) = a + bx$$). For linear regression the coefficients $$b$$ are fixed, with a single constant for every feature that determines the contribution. For the decision tree, the contribution of each feature is not a single predetermined value, but depends on the rest of the feature vector which determines the decision path that traverses the tree and thus the guards/contributions that are passed along the way. ## From decision trees to forest We started the discussion with random forests, so how do we move from a decision tree to a forest? This is straightforward, since the prediction of a forest is the average of the predictions of its trees: $$F(x) = \frac{1}{J} \sum\limits_{j=1}^J f_j(x)$$, where $$J$$ is the number of trees in the forest. From this, it is easy to see that for a forest, the prediction is simply the average of the bias terms plus the average contribution of each feature: $$F(x) = \frac{1}{J}{\sum\limits_{j=1}^J {c_{j}}_{full}} + \sum\limits_{k=1}^K (\frac{1}{J}\sum\limits_{j=1}^J contrib_j(x, k))$$. ### Running the interpreter Update (Aug 12, 2015) Running the interpretation algorithm with actual random forest model and data is straightforward via using the treeinterpreter (pip install treeinterpreter) library that can decompose scikit-learn‘s decision tree and random forest model predictions. More information and examples available in this blog post. ## Summary There is a very straightforward way to make random forest predictions more interpretable, leading to a similar level of interpretability as linear models — not in the static but dynamic sense. Every prediction can be trivially presented as a sum of feature contributions, showing how the features lead to a particular prediction. This opens up a lot of opportunities in practical machine learning and data science tasks: • Explain to an analyst why a particular prediction is made • Debug models when results are unexpected • Explain the differences of two datasets (for example, behavior before and after treatment), by comparing their average predictions and corresponding average feature contributions. ## 52 comments on “Interpreting random forests” 1. Thank you sir for such a informative description. 2. How did you create the great interactive visualization figure? Would you say your techniques are scalable to a large tree? 3. I created it using D3 (http://d3js.org/), a great Javascript visualization library. You can see a lot of examples of tree visualizations at https://github.com/mbostock/d3/wiki/Gallery As for large trees, the number of nodes grows exponentially in the depth of the tree. So a tree of depth 10 can already have ~2000 nodes. A tree of this size will be very difficult for a human to read, since there is simply too much too fine grained information there. But that’s where the usefulness of the described approach comes in, since it is agnostic to the size of the tree (or the number of trees in case of a forest). • I am working on similar project , thanks for the wonderful explanation. Could you please share the code for designing the graph which highlights the path. Thanks in advance. 4. I’m thinking this approach could also be adapted to gradient boosted trees, which are also (at least as I understand their implementation in SAS EM) an ensemble of a number of trees from bootstrapped samples of the data (but using all features vs. a sample of features) ? I’ve also seen examples of using trees to visualize neural nets. 5. Yes, it would indeed also work for gradient boosted trees in a similar way. Basically, any time the prediction is made via trees, the prediction can be broken down into a sum of feature contributions. • @Basically, any time the prediction is made via trees, the prediction can be broken down into a sum of feature contributions The definition of feature contributions should be modified for gradient boosting. The sum of decision paths (aka. local increments) should no longer be divided with number of trees, in order to maintain “prediction = bias + sum of feature contributions”. Each bagged tree maps from bias (aka. base rate +stratification or grand mean) to target and the ensemble prediction is the average vote and therefore division by number of trees. Each boosted tree only maps from residual to target, and the boosted ensemble maps only once from bias to target, therefore division by 1. I appended a short proof-of-concept for computing and visualizing feature contributions for gradient boosting with R in ancillary files for this paper, http://arxiv.org/abs/1605.09196 6. There is a typ0. line 5 up from the last sentence. “anlyst” should be “analyst”. 7. Thanks to this post, I understood the ‘theorical equation’ behind Random Forest running. Do you have a source where the equation came? Thanks Again for everything, Bobbie • Hi Ando, any luck with this? I was wondering if we could maybe make a standalone module, should it not be merged. • In current 0.17dev, my commit to keep values in all nodes was merged. Additionally, a method to get the leaf labels when predicting was added. Combining these, the interpretation can be done on the 0.17dev version. Planning to write a blog post on this in the near future. 8. This is great stuff Ando. I was thinking about how to apply this to ‘understand’ a whole dataset/model combination. You could, e.g., pick a few top features and cluster the entire population according to the feature contributions, for these features, from a RF model. On the Boston housing data, this leads to 8-10 clusters with clear descriptions like “Neighborhoods that are expensive because they are right near the city center”, or “Neighborhoods that are expensive because the houses are huge”. You could even then compare two data sets by fitting the clusters and seeing how the proportions change. Thanks for the contribution – looking forward to seeing decision_paths in sklearn. 9. Pingback: 使用scikit-learn解释随机森林算法 - IT大道 10. This is great! Do you know if this is available with the R random forest package? 11. What would it be the interpretation of a negative value, for a specific variable, in a classification problem? Does it mean that higher values of this variable decrease the predicted probability? I.e. Given Predicted_prob(x) = Bias + 0.01A – 0.02B, is it correct to assume that probability to belong to class X is inversely proportional to the value assumed by B? • Remember, all of these breakdowns are exact contribution from features per datapoint/instance. So in your example, it means that for datapoint x, B reduces the probability. It doesnt mean that B always (or on average) reduces the probability. For some other datapoint, B could be positive. • If for some datapoints B could be positive for some it could be negative; how do we interpret the contribution. I was under the impression that we will learn more about the features and how do they contribute to the respective classes from this exercise but that does not seem to be the case! Thanks much, 12. Great post! 🙂 Question though… Quoting this: ” For the decision tree, the contribution of each feature is not a single predetermined value, but depends on the rest of the feature vector which determines the decision path that traverses the tree and thus the guards/contributions that are passed along the way” If in case I get the mean of the contributions of each feature for all the training data in my decision tree model, and then just use the linear regression f(x) = a + bx (where a is the mean bias and b is now the mean contributions) to do predictions for incoming data, do you think this will work? 13. Hi – I would like to use the figure above in an O’Reilly media article about interpretable machine learning. This article would feature treeinterpreter among many other techniques. Please let me know ASAP. Thanks! • We will link to this blog. I followed you on twitter recently. Please let me know here or there if you would like any other specific citation. 14. can we get black box rules in random forest(code) so I can use that in my new dataset also? 15. Thank you for this package, it is really great that it allows to open the random forest “blackbox”. I have a quick question: I tested the package with some housing data to predict prices and I have a case where all the features are the same except the AreaLiving. Looking at the feature contributions however, they are different for all the features. I would have expected to get them the same, is that reasoning wrong? For most cases the feature contributions are close together, but not the same. However, some are quite apart, like the rooms (- 96 vs. -44), even though they have the same number of rooms. Another case is the latitude (-452 vs -289). Maybe the interpretation is: The small house with 5 rooms gets more substracted (-96) than the big house (-44) as you expect these rooms to be smaller? And for the latitude the small house gets a more negative contribution (-452) than the big house (-289) as in this latitude you can better sell a big house? Many thanks in advanced for any help! Best regards, Andreas • Think of it this way: depending on the value of the root node in the decision tree, you can end up in the left or right branch. The left and right branch can use completely different features. Thus, simply by changing the value of the feature that’s in the root node, you might see contributions shift completely. For example the root node might be location (say city vs countryside). In the first case, the important features might be number of rooms and tax zone. In the second case, important features might be land lot size and number of floors. So simply switching up one feature (location), you would get completely different contributions. 16. Hello Ando, Thank you for your reply. That makes sense. I figured out as well that I had included some features with low importance that often triggered some bigger changes, removing them should help the model to return more stable contributions. 17. Hi, can you say something about how this applies to classification trees, as the examples you have given all relate to regression trees. Can you break down how the bias and contribution affect the chosen purity measure, say Gini index? • Thanks. I see the example. Can you tell me if this method can be applied to categorical/nominal features? I built an example but I realised that after encoding all my categories as integer, the model must be treating them as ordinal or continuous. I am trying to set this up with all the features one-hot encoded, to get around this but it’s then rather difficult to extract any meaning from the contributions. Is this something you’ve explored already? 18. Hello Ando, Are you aware of any research paper on this computation of “contribution by averaging decision paths over trees” ? All similar implementations in R or python I have found, trace back to this blog post. Were you (in)directly inspired by some paper, or is it an original “contribution” from yourself? Many thanks, • Thanks for the link and congrats for this idea! I have seen a similar implementation in R (xgboostExplainer, on CRAN). The main difference is that contributions are expressed in log-odds of probability. I’m curious about your thoughts of using log-odds, which has the advantage to bring a “bayesian interpretation” of contributions. However, it seems that it is not possible to maintain all additivity properties [1] and [2] ([1] a contribution of feature F is equal to the mean of the contributions of feature F for all decision trees ; [2] the prediction score is equal to the sum of all feature contributions and equal to the mean of prediction score for all decision trees.). Any thoughts on using log-odds for contributions? 19. Pingback: 使用 Scikit-learn 理解随机森林滕州巴巴 20. From what I understand, in the binary classification case, if I get a contribution = [x,-x] of a feature it means that using this feature I gain x in probability to be of class0. However this doesn’t give us any information of what the feature value is? Is there a way to extract what values of the feature are making it of class0? 21. I don’t understand why do we need this concept of “contributions” here that makes random forests “white box”. e.g., a random forest with entropy loss itself does an optimization with respect to conditional uncertainty that provides a measure of contribution of the added features in its decision trees. The contribution defined here is an interesting concept. However, I believe it doesn’t add much understanding to the random forests and doesn’t make them “white box”.	2020-07-02 14:54:20	{"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": 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": 0.5279152989387512, "perplexity": 634.3474462544353}, "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-2020-29/segments/1593655879532.0/warc/CC-MAIN-20200702142549-20200702172549-00353.warc.gz"}
https://web2.0calc.com/questions/help-algebra_66	+0 # Help algebra 0 73 1 What number must be placed in the box in the equation below to produce an equation that has more than one solution: $1/2*y + 1/4 = 3 + \boxed{\phantom{400} } y$ Jun 6, 2021 ### 1+0 Answers #1 +208 0 Well, lets see, for an equation to have more than one solution, even if that box has a "y" in it, then it still produces more than one solution (it's a quadratic equation). I don't know if you mean if it has infinite solutions, in that case, it would be: $$\frac{y}{2}+\frac{1}{4}=3+xy$$ $$2y+1=12+4xy$$ $$2y-11=4xy$$ $$x=\frac{2y-11}{4y\:}$$ unless, of course y=0, since anything divided by 0 is undefined JP Jun 6, 2021 edited by JKP1234567890 Jun 6, 2021	2021-09-21 22:33:46	{"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": 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": 0.9625192880630493, "perplexity": 670.3521948201698}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "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-2021-39/segments/1631780057274.97/warc/CC-MAIN-20210921221605-20210922011605-00666.warc.gz"}
https://www.toppr.com/ask/question/derive-the-expression-for-the-capacitance-of-a-parallel-plate-capacitore-having-plate-area-a/	Question # Derive the expression for the capacitance of a parallel plate capacitore having plate area A and plate separation d. Medium ## Solution Verified by Toppr ## Let a parallel plate capacitor be applied a voltage across its terminals due to which a charge develops across its ends. Separation between plates is and area of plates is .From gauss's theorem one can show electric field inside the capaciton plates ,, where (charge / Area)Now, voltage across the plates is related by : [In general , but we take as is uniform]Now, capacitance is defined by , thus we get :- Solve any question of Electrostatic Potential and Capacitance with:-	2022-01-27 05:49:14	{"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, "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": 0.9406193494796753, "perplexity": 1779.8961942186568}, "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/1642320305141.20/warc/CC-MAIN-20220127042833-20220127072833-00149.warc.gz"}
http://www.livefitsocial.com/m126u7o/01d803-shannon-capacity-theorem	The achievable data rate, however, greatly depends on many parameters, as will be seen later on in the chapter. Following is the list of useful converters and calculators. By Shannon's sampling theorem[33] only components of spatial frequency up to half the vertex frequency are justified by the data, and so these ripples are definitely artifacts. Bandwidth is a fixed quantity, so it cannot be changed. Now, we usually consider that this channel can carry a limited amount of information every second. Theorem 2.1. <> Solution for Choose the right answer: 1- Shannon Hartley theorem states that a. J., Vol. Shannon’s theorem: A given communication system has a maximum rate of information C known as the channel capacity. Shannon Capacity formulae: In presence of Gaussian band-limited white noise, Shannon-Hartley theorem gives the maximum data rate capacity C = B log2 (1 + S/N), where S and N are the signal and noise power, respectively, at the output of the channel. 2.4.1 Source Coding Theorem. Gzf�N��}W��I��K�zp�}�7�# �V4�+K�e��. Shannon's Theorem and Shannon's bound - MCQs with answers Q1. Peng-Hua Wang, April 16, 2012 Information Theory, Chap. Shannon’s theorem: on channel capacity(“cod ing Theorem”). Shannon's Theorem gives an upper bound to the capacity of a link, in bits per second (bps), as a function of the available bandwidth and the signal-to-noise ratio … The Shannon capacity is important because it represents the effective size of an alphabet in a communication model represented by , but it is notoriously difficult to compute. This article is part of the book Wireless Communication Systems in Matlab (second edition), ISBN: 979-8648350779 available in ebook (PDF) format and Paperback (hardcopy) format. For example, given a 16 Mhz channel and a signal-to-noise ratio of 7: Math. C is the channel capacity in bits per second; 2. Dear Sir, A much simpler version of proof (I would rather call it an illustration) can be found at [6]. 689-740, May, 1936.↗, Willard M Miner, “Multiplex telephony”, US Patent, 745734, December 1903.↗, A.H Reeves, “Electric Signaling System”, US Patent 2272070, Feb 1942.↗, Shannon, C.E., “Communications in the Presence of Noise”, Proc. stream Soc. The performance over a communication link is measured in terms of capacity, which is defined as the maximum rate at which the information can be transmitted over the channel with arbitrarily small amount of error. In 1903, W.M Miner in his patent (U. S. Patent 745,734 [3]), introduced the concept of increasing the capacity of transmission lines by using sampling and time division multiplexing techniques. In this formula B is the bandwidth of the channel, SNR is the signal-to noise ratio, and C is the capacity of the channel in bits per second. it will not take much of your time. Its proof is based on the random coding argument, perhaps the first occurence of the probabilistic method (Chapter). If the system is a low pass system , the bandwidth is 10Hz. This is called as Channel coding theorem. In short, it is the maximum rate that you can send data through a channel with a given bandwidth and a given noise level. Home page for LucraLogic, LLC with descriptions of companies mission and products, Includes tutorials and tools for software, embedded systems, computer networks, and communications A yes or a no, in or out, up or down, a 0 or a 1, these are all a form of information bits. In fact, ... Shannon’s Capacity. Then we will look at an explicit (and very “hands-down”) construction of a code due to Elias [1] that achieves a positive rate for some positive crossover probability. According to Shannon’s theorem, it is possible, in principle, to devise a means whereby a communication channel will […] Channel capacity, in electrical engineering, computer science, and information theory, is the tight upper bound on the rate at which information can be reliably transmitted over a communication channel. It was widely believed that the only way for reliable communication over a noisy channel is to reduce the error probability as small as possible, which in turn is achieved by reducing the data rate. Hamming Code : construction, encoding & decoding, Chapter 2 in my book ‘Wireless Communication systems in Matlab’, C. E. Shannon, “A Mathematical Theory of Communication”, Bell Syst. But that’s only because the best-performing code that we now know of, which was invented at MIT, was ignored for more than 30 years. Considering all possible multi-level and multi-phase encoding techniques, the Shannon–Hartley theorem states that the channel capacity C, meaning the theoretical tightest upper bound on the rate of clean (or arbitrarily low bit error rate) data that can be sent with a given average signal power S through an analog communication channel subject to additive white Gaussian noise of power N, is: 1. Amer. Channel Capacity by Shannon - Hartley 1. If we select a particular modulation scheme or an encoding scheme, we calculate the constrained Shannon limit for that scheme. What does the Shannon capacity have to do with communications? Simple schemes such as "send the message 3 times and use a best 2 out of 3 voting scheme if the copies differ" are inefficient error-correction methods, unable to asymptotically guarantee that a block of data can be … It is implicit from Reeve’s patent – that an infinite amount of information can be transmitted on a noise free channel of arbitrarily small bandwidth. Then is the capacity zero? The term “limit” is used for power efficiency (not for bandwidth). The Shannon-Hartley Capacity Theorem, more commonly known as the Shannon-Hartley theorem or Shannon's Law, relates the system capacity of a channel with the averaged received signal power, the average noise power and the bandwidth. �ޟ��o�eH��w(��G�yz�+B��+�V&u�:H/8��ܸ��V��5�^T��'��"�fb�#�ǲ�� G�v�=?؄ ��9��A��7��v ��:�Z!��nw RSw�{ �zV"��A��}b�Cm�~?�0��(��lBY�pT��/��OA �l0pI�� February 15, 2016 \| Ripunjay Tiwari \| Data Communication \| 0 Comments For a binary symmetric channel, the random bits are given as a) Logic 1 given by probability P and logic 0 by (1-P) b) Logic 1 given by probability 1-P and logic 0 by P c) Logic 1 given by probability P 2 and logic 0 by 1-P d) Logic 1 given by probability P and logic 0 by (1-P) 2 View Answer / Hide Answer. A great deal of information about these three factors can be obtained from Shannon’s noisy channel coding theorem. It is modified to a 2D equation, transformed into polar coordinates, then expressed in one dimension to account for the area (not linear) nature of pixels. Shannon-Hartley's channel capacity theorem is often applied at the beginning of any waveform and link budget analysis to provide the communication analyst with an upper bound on the data rate given a certain bandwidth and SNR. Channel Capacity theorem . (��a�� (�CJV[w��2�ɖ�ͩ^ǭS,�(��w{Τ��o��ݭ}I9Ί�Rm�Y2LN��#>B�֠y��s��i��M�Sd��/�4c�k��KB!�8E� a��+��e��"��V_�/E8%X�P��ɫD��q)Vy��":��S��q��߮>��?�4�B0��T&��XLP.��μ�P��zP��87�q[�O��:Q��M�O�ftwM��2�M�Sa՛��kx;��>�Rk��XZҊ(f�0��#Σ��Fd��6��7�U0�p�>��ٷ��H'��n� &0D�:+�C\|D�rs�t�3��x}�}34�E+� O�퓨Y�Ƕݽc]�e ��?�DD,^� ��x�H��/�Jm7z��H)Kzx��Ko��s�c�T�~�X��Ib�^W�3��H '2��= ��͙h%�%IP��"��/��Ikƃ��щH��r{�Ĭ=z(Fs�z{�R�%�}�c�?�L)��L��s��b�D�?_3{�-��ȑ�P��S4��j�F ��$�sHRo��:=008j.�I~,^�z�#9k%�b�E'�4n��ͣ��M�j��hMd^�St��1 Or Explain what is Shannon capacity. Shannon capacity is used, to determine the theoretical highest data rate for a noisy channel: Capacity = bandwidth * log 2 (1 + SNR) In the above equation, bandwidth is the bandwidth of the channel, SNR is the signal-to-noise ratio, and capacity is the capacity of the channel in bits per second. Wikipedia – Shannon Hartley theorem has a frequency dependent form of Shannon’s equation that is applied to the Imatest sine pattern Shannon information capacity calculation. He realized that he would require more bandwidth than the traditional transmission methods and used additional repeaters at suitable intervals to combat the transmission noise. Shannon-Hartley's channel capacity theorem is often applied at the beginning of any waveform and link budget analysis to provide the communication analyst with an upper bound on the data rate given a certain bandwidth and SNR. Bohman, T. "A Limit Theorem for the Shannon Capacities of Odd Cycles. Mathuranathan Viswanathan, is an author @ gaussianwaves.com that has garnered worldwide readership. This is a theorem proven by Shannon! For long time this was an open problem and therefore this is a very important result. 52, 2172-2176, 2006. In this video, i have explained Examples on Channel Capacity by Shannon - Hartley by following outlines:0. Cite this chapter as: Brémaud P. (2017) Shannon’s Capacity Theorem. Real world channels are essentially continuous in both time as well as in signal space. Discount not applicable for individual purchase of ebooks. The concept of channel capacity is discussed first, followed by an in-depth treatment of Shannon’s capacity for various channels. By doing this calculation we are not achieving anything. turbo codes and low-density parity check codes 65 In 1937, A.H Reeves in his French patent (French Patent 852,183, U.S Patent 2,272,070 [4]) extended the system by incorporating a quantizer, there by paving the way for the well-known technique of Pulse Coded Modulation (PCM). Assume we are managing to transmit at C bits/sec, given a bandwidth B Hz. In this section, the focus is on a band-limited real AWGN channel, where the channel input and output are real and continuous in time. If one attempts to send data at rates above the channel capacity, it will be impossible to recover it from errors. Wikipedia – Shannon Hartley theorem has a frequency dependent form of Shannon’s equation that is applied to the Imatest sine pattern Shannon information capacity calculation. Q6. System Bandwidth (MHz) = 10, S/N ratio = 20, Output Channel Capacity (Mbits/sec) = 43.92.$ C = B \log_2 \left( 1+\frac{S}{N} \right) $where 1. This tells us , now matter how much bandwidth we have (B-> infinity), the transmission power should always be more than the Shannon power efficiency limit in terms of Eb/N0 (-1.59 dB). Bohman, T. "A Limit Theorem for the Shannon Capacities of Odd Cycles. How the “unconstrained Shannon power efficiency Limit” is a limit for band limited system when you assumed B = infinite while determining this value? Shannon’s information capacity theorem states that the channel capacity of a continuous channel of bandwidth W Hz, perturbed by bandlimited Gaussian noise of power spectral density n0 /2, is given by Cc = W log2(1 + S N) bits/s(32.1) where S is the average transmitted signal power and … The Shannon-Hartley Theorem represents a brilliant breakthrough in the way communication theory was viewed in the 1940s and describes the maximum amount of error-free digital data that can be transmitted over a communications channel with a specified bandwidth in the presence of noise. 3)can you elaborate on capacity reaching codes ? The channel capacity can be calculated from the physical properties of a channel; for a band-limited channel with Gaussian noise, using the Shannon–Hartley theorem. It is modified to a 2D equation, transformed into polar coordinates, then expressed in one dimension to account for the area (not linear) nature of pixels. '�n�r�Y�BFD��$�� J��W_�S��k6�T��Q��-zD��g��4�G汛��Lt�cWc"�X�޸��[Y" �H� [104–106]. They are called first-step artifacts because it is the first subdivision step which makes them explicit. The theorem establishes Shannon's channel capacity for such a communication link, a bound on the maximum amount of error-free digital data (that is, information) that can be transmitted with a specified bandwidth in the presence of the noise interference, assuming that the signal power is bounded, and that the Gaussian noise process is characterized by a known power or power spectral density. Ans Shannon ‘s theorem is related with the rate of information transmission over a communication channel.The term communication channel covers all the features and component parts of the transmission system which introduce noise or limit the bandwidth,. Inform. Hence, the equation can be re-written as. Shannon’s second theorem: The information channel capacity is equal to the operational channel capacity. ● The designed system should be able to reliably send information at the lowest practical power level. Channel Capacity & The Noisy Channel Coding Theorem Perhaps the most eminent of Shannon’s results was the concept that every communication channel had a speed limit, measured in binary digits per second: this is the famous Shannon Limit, exemplified by the famous and familiar formula for the capacity of a White Gaussian Noise Channel: 1 Gallager, R. Quoted in Technology Review, 2 Shannon, … The Shannon’s equation relies on two important concepts: ● That, in principle, a trade-off between SNR and bandwidth is possible ● That, the information capacity depends on both SNR and bandwidth, It is worth to mention two important works by eminent scientists prior to Shannon’s paper [1]. B is the bandwidth of the … IRE, 24, pp. 2 Proof of Shannon’s theorem We ﬁrst recall the Shannon’s theorem (for the special case of BSC p). Ans Shannon ‘s theorem is related with the rate of information transmission over a communication channel.The term communication channel covers all the features and component parts of the transmission system which introduce noise or limit the bandwidth,. It is also called unconstrained Shannon power efficiency Limit. � ia� #�0��@�0�ߊ#��/�^�J[��,�Α 4'��=�$E� ?¾��\|��L��FvqD2 �2#s. Or, equivalently stated: the more bandwidth efficient, there is a sacrifice in Eb/No. Hello Sir, i’m a master student and i have a problem in one of my codes, can i please have your email address to contact with you. �N��rEx�)e��ӓ��C7�V��F��ݱ_��p��P��a�8R2��Wn?� ��1 Shannon's source coding theorem addresses how the symbols produced by a source have to be encoded efficiently. Before proceeding, I urge you to go through the fundamentals of Shannon Capacity theorem in this article. Shannon's channel coding theorem addresses how to encode the data to overcome the effect of noise. Nyquist, Shannon and the information carrying capacity of sig-nals Figure 1: The information highway There is whole science called the information theory.As far as a communications engineer is concerned, information is defined as a quantity called a bit.This is a pretty easy concept to intuit. On Complexes and Graphs this is done here. Discount can only be availed during checkout. I." Shannon’s channel coding theorem concerns the possibility of communicating via a noisy channel with an arbitrarily small probability of error. But Shannon’s proof held out the tantalizing possibility that, since capacity-approaching codes must exist, there might be a more efficient way to find them. Please refer [1] and [5] for the actual proof by Shannon. If the system is a bandpass system, since fH=FL=10Hz, it is assumed to be same as some carrier frequency fc=10Hz. Increasing SNR makes the transmitted symbols more robust against noise. Related to this we say something about an apart collection of graphs, the so 2. called Perfect Graphs. This belief was changed in 1948 with the advent of Information theory by Claude E. Shannon. However, the rate is limited by a maximum rate called the channel capacity. The achievable data rate, however, greatly depends on many parameters, as will be seen later on in the chapter. For any communication over a wireless link, one must ask the following fundamental question: What is the optimal performance achievable for a given channel ?. The ratio is the signal to noise ratio (SNR) per degree of freedom. But Shannon’s proof held out the tantalizing possibility that, since capacity-approaching codes must exist, there might be a more efficient way to find them. • Shannon’s theorem does not tell how to construct such a capacity-approaching code • Most practical channel coding schemes are far from optimal, but capacity-approaching codes exist, e.g. Thus the bandwidth is zero (nothing around the carrier frequency) and if you apply the shannon capacity equation for AWGN, C is zero in this case. Therefore, study of information capacity over an AWGN (additive white gaussian noise) channel provides vital insights, to the study of capacity of other types of wireless links, like fading channels. Chapter 2 in my book ‘Wireless Communication systems in Matlab’, is intended to describe the effect of first three objectives when designing a communication system for a given channel. When can the capacity be zero? Th. But that’s only because the best-performing code that we now know of, which was invented at MIT, was ignored for more than 30 years. Edward Amstrong’s earlier work on Frequency Modulation (FM) is an excellent proof for showing that SNR and bandwidth can be traded off against each other. Details on this are pretty easy to follow, see the Wikipedia pages for the Noisy-channel coding theorem and the Shannon-Hartley theorem. ● The transmitted signal should occupy smallest bandwidth in the allocated spectrum – measured in terms of bandwidth efficiency also called as spectral efficiency – . Finally, we note (Theorem 5) that for all simplicial complexes G as well as product G=G_1 x G_2 ... x G_k, the Shannon capacity Theta(psi(G)) of psi(G) is equal to the number m of zero-dimensional sets in G. An explicit Lowasz umbrella in R^m leads to the Lowasz number theta(G) leq m and so … Shannon’s limit is often referred to as channel capacity. Shannon calls this limit the capacity of the channel. He is a masters in communication engineering and has 12 years of technical expertise in channel modeling and has worked in various technologies ranging from read channel, OFDM, MIMO, 3GPP PHY layer, Data Science & Machine learning. %�쏢 Amer. Th. You can apply Shannon capacity equation and find the capacity for the given SNR. x��[I��r�K�$sʅ�Yѵ/� �,6��d��-�H�LR��ݼb��ղ=�r��}o��7q��z��+V� W��GT�b3�T��?��h��x��_^�T��-L�eɱV�_T(YME�UɐT��۪m��]�Rq%;�7�Eu��\|��aZ�:�f^��ֳ�_t��UiMݤ��0�Q\ Shannon built upon Hartley’s law by adding the concept of signal-to-noise ratio: C = B log 2 1 + S / N C is Capacity, in bits-per-second. Reeves patent relies on two important facts: ● One can represent an analog signal (like speech) with arbitrary accuracy, by using sufficient frequency sampling, and quantizing each sample in to one of the sufficiently large pre-determined amplitude levels● If the SNR is sufficiently large, then the quantized samples can be transmitted with arbitrarily small errors. Useful converters and calculators. The signiﬁcance of this mathematical construct was Shannon’s coding theorem and converse, which prove that a code exists that can achieve a data rate asymptotically close to capacity … Following is the shannon Hartley channel capacity formula/equation used for this calculator. channel capacity C. The Shannon-Hartley Theorem (or Law) states that: bits ond N S C Blog2 1 /sec = + where S/N is the mean-square signal to noise ratio (not in dB), and the logarithm is to the base 2. S and N represent signal and noise respectively, while B represents channel bandwidth. Proc. If the information rate R is less than C, then one can approach arbitrarily small error probabilities by using intelligent coding techniques. to NF. For example, communication through a band-limited channel in presence of noise is a basic scenario one wishes to study. IRE, Volume 37 no1, January 1949, pp 10-21.↗[6] The Scott’s Guide to Electronics, “Information and Measurement”, University of Andrews – School of Physics and Astronomy.↗. B' (Theorem 4) leading to a commutative ring of homotopy classes of graphs. IEEE Trans. 27, pp.379-423, 623-656, July, October, 1948.↗, E. H. Armstrong:, “A Method of Reducing Disturbances in Radio Signaling by a System of Frequency-Modulation”, Proc. 27, pp.379-423, 623-656, July, October, 1948.↗[2] E. H. Armstrong:, “A Method of Reducing Disturbances in Radio Signaling by a System of Frequency-Modulation”, Proc. ��t��u��G�k;F cco�`-N�$n�j�}3ڵ4��6�m�﫱��Y�%3uv"�� ر��.� �T�A��]��ǶY��[��nn"�� Here, is the maximum capacity of the channel in bits/second. Explain the significance of same. Shannon’s second theorem establishes that the “information” channel capacity is equal to the “operational” channel capacity. The Shannon-Hartley theorem applies only to a single radio link. 6 0 obj Finally, we note (Theorem 5) that for all simplicial complexes G as well as product G=G_1 x G_2 ... x G_k, the Shannon capacity Theta(psi(G)) of psi(G) is equal to the number m of zero-dimensional sets in G. An explicit Lowasz umbrella in R^m leads to the Lowasz number theta(G) leq m and so … Techn. A proof of this theorem is beyond our syllabus, but we can argue that it is reasonable. Say modulation is on-off keying to communicate 1 bit data. 689-740, May, 1936.↗[3] Willard M Miner, “Multiplex telephony”, US Patent, 745734, December 1903.↗[4] A.H Reeves, “Electric Signaling System”, US Patent 2272070, Feb 1942.↗[5] Shannon, C.E., “Communications in the Presence of Noise”, Proc. Therefore, the application of information theory on such continuous channels should take these physical limitations into account. They were probably not aware of the fact that the first part of the theorem had been stated as early as 1897 by Borel [25].In 1958, Blackman and Tukey cited Nyquist's 1928 article as a reference for Exactly what "Nyquist's result" they are referring to remains mysterious. According to Shannon’s theorem, it is possible, in principle, to devise a means whereby a communication channel will […] Shannon showed that it is in fact possible to communicate at a positive rate and at the same time maintain a low error probability as desired. Information … Theorem, we determine the Shannon capacity of some simple cycle graphs. This links the information rate with SNR and bandwidth. Shannon-Hartley. Math. In: Discrete Probability Models and Methods. The capacity of an analog channel is determined by its bandwidth adjusted by a factor approximately proportional to the log of the signal-to-noise ratio. The channel capacity does not increase as bandwidth increases b. Shannon Capacity Theorem - Free download as Powerpoint Presentation (.ppt / .pptx), PDF File (.pdf), Text File (.txt) or view presentation slides online. This is measured in terms of power efficiency – .● Ability to transfer data at higher rates – bits=second. Before proceeding, I urge you to go through the fundamentals of Shannon Capacity theorem … Continue reading on Shannon’s limit on power efficiency…, Rate this article: (36 votes, average: 4.72 out of 5), [1] C. E. Shannon, “A Mathematical Theory of Communication”, Bell Syst. The Shannon-Hartley theorem establishes Claude Shannon’s channel capacity for a communication link which is a bound on the maximum amount of error-free information per time unit that can be transmitted within a specified bandwidth in the presence of noise interference, assuming that this signal power is bounded and that the Gaussian noise process is characterized by a known power or power spectral … The theorem establishes Shannon’s channel capacity for such a communication link, a bound on the maximum amount of error-free digital data (that is, information) that can be transmitted with a specified bandwidth in the presence of the noise interference, assuming that the signal power is bounded, and that the Gaussian noise process is characterized by a known power or power spectral density. This is called Shannon’s noisy channel coding theorem and it can be summarized as follows: ● A given communication system has a maximum rate of information – C, known as the channel capacity.● If the transmission information rate R is less than C, then the data transmission in the presence of noise can be made to happen with arbitrarily small error probabilities by using intelligent coding techniques.● To get lower error probabilities, the encoder has to work on longer blocks of signal data. Thus we drop the word “information” in most discussions of channel capacity. this 1000 bit/s is ( information + error control data) OR information alone ( excluding error control data)..??? Lovász [L] famously proved that the Shannon capacity of the five-cycle is , but even the Shannon capacity … This entails longer delays and higher computational requirements. Channel capacity and power efficiency . There is a duality between the problems of data compression and data transmission. The theorem indicates that with sufficiently advanced coding techniques, transmission that nears the maximum channel capacity – is possible with arbitrarily small errors. SNR represents the signal quality at the receiver front end and it depends on input signal power and the noise characteristics of the channel.● To increase the information rate, the signal-to-noise ratio and the allocated bandwidth have to be traded against each other.● For a channel without noise, the signal to noise ratio becomes infinite and so an infinite information rate is possible at a very small bandwidth.● We may trade off bandwidth for SNR. Let’s now talk about communication! The quest for such a code lasted until the 1990s. Also discuss the trade off between bandwidth and cltunnel capacity. State the Shannon’s theorem regarding channel capacity. In chapter 2 we use Lov asz technique to determine the Shannon capacity of C 5. Following the terms of the noisy-channel coding theorem, the channel capacity of a given channel is the highest information rate that can be achieved with arbitrarily small error probability. Simplicial Complexes, Graphs, Homotopy, Shannon capacity. Antenna links . 7 - p. 6/62 this is a very informative powerpoint document on shannon capacity theorem. The quest for such a code lasted until the 1990s. P�%A"A��h�\ 131, 3559-3569, 2003. Shannon’s Channel Capacity Shannon derived the following capacity formula (1948) for an additive white Gaussian noise channel (AWGN): C= Wlog 2 (1 + S=N) [bits=second] †Wis the bandwidth of the channel in Hz †Sis the signal power in watts †Nis the total noise power of the channel watts Channel Coding Theorem (CCT): The theorem has two parts. The channel… How channel capacity can be increased numerically using the definition of information? 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https://www.atmos-chem-phys.net/18/8829/2018/	Journal cover Journal topic Atmospheric Chemistry and Physics An interactive open-access journal of the European Geosciences Union Journal topic Atmos. Chem. Phys., 18, 8829–8848, 2018 https://doi.org/10.5194/acp-18-8829-2018 Atmos. Chem. Phys., 18, 8829–8848, 2018 https://doi.org/10.5194/acp-18-8829-2018 Research article 22 Jun 2018 Research article \| 22 Jun 2018 # Radiative impact of an extreme Arctic biomass-burning event Radiative impact of an extreme Arctic biomass-burning event Justyna Lisok1, Anna Rozwadowska2, Jesper G. Pedersen1, Krzysztof M. Markowicz1, Christoph Ritter3, Jacek W. Kaminski4, Joanna Struzewska5, Mauro Mazzola6, Roberto Udisti6,7, Silvia Becagli7, and Izabela Gorecka8 Justyna Lisok et al. • 1Institute of Geophysics, Faculty of Physics, University of Warsaw, Warsaw, Poland • 2Institute of Oceanology, Polish Academy of Sciences, Sopot, Poland • 3Alfred Wegener Institute for Polar and Marine Research, Potsdam, Germany • 4Department of Atmospheric Physics, Institute of Geophysics, Polish Academy of Sciences, Warsaw, Poland • 5Faculty of Building Services Hydro and Environmental Engineering, Warsaw University of Technology, Warsaw, Poland • 6National Research Council, Institute of Atmospheric Sciences and Climate, Bologna, Italy • 7Department of Chemistry, University of Florence, Florence, Italy • 8Geoterra, Gdansk, Poland Correspondence: Justyna Lisok ([email protected]) Abstract The aim of the presented study was to investigate the impact on the radiation budget of a biomass-burning plume, transported from Alaska to the High Arctic region of Ny-Ålesund, Svalbard, in early July 2015. Since the mean aerosol optical depth increased by the factor of 10 above the average summer background values, this large aerosol load event is considered particularly exceptional in the last 25 years. In situ data with hygroscopic growth equations, as well as remote sensing measurements as inputs to radiative transfer models, were used, in order to estimate biases associated with (i) hygroscopicity, (ii) variability of single-scattering albedo profiles, and (iii) plane-parallel closure of the modelled atmosphere. A chemical weather model with satellite-derived biomass-burning emissions was applied to interpret the transport and transformation pathways. The provided MODTRAN radiative transfer model (RTM) simulations for the smoke event (14:00 9 July–11:30 11 July) resulted in a mean aerosol direct radiative forcing at the levels of 78.9 and 47.0 W m−2 at the surface and at the top of the atmosphere, respectively, for the mean value of aerosol optical depth equal to 0.64 at 550 nm. This corresponded to the average clear-sky direct radiative forcing of 43.3 W m−2, estimated by radiometer and model simulations at the surface. Ultimately, uncertainty associated with the plane-parallel atmosphere approximation altered results by about 2 W m−2. Furthermore, model-derived aerosol direct radiative forcing efficiency reached on average 126 W m${}^{-\mathrm{2}}/{\mathit{\tau }}_{\mathrm{550}}$ and 71 W m${}^{-\mathrm{2}}/{\mathit{\tau }}_{\mathrm{550}}$ at the surface and at the top of the atmosphere, respectively. The heating rate, estimated at up to 1.8 K day−1 inside the biomass-burning plume, implied vertical mixing with turbulent kinetic energy of 0.3 m2 s−2. 1 Introduction Wildfires are considered significant sources of carbon in the atmosphere. It is estimated that up to 2.0 Pg of carbon aerosol is released into the atmosphere each year due to wildfires. In the past 100 years, an intensification of fires in the mid-latitudes has been observed to appreciably affect radiative and optical properties of the atmosphere . Emissions from biomass-burning (BB) sources consist mainly of organic and black carbon particles (IPCC2001), of which 90 % are made of the fine mode aerosol size distribution . The impact of the plume on the atmospheric instability conditions and its rather small particle radius property may result in rapid transport on an intercontinental scale within just several days . The presence of BB aerosol causes heating of the air layer in which the transport takes place. Regarding the columnar properties, however, smoke existence results in a weak cooling at the top of the atmosphere (TOA) due to predominant scattering properties of the plume . The magnitude of its impact on the radiative properties is nevertheless strongly dependent on the chemical composition of the smoke plume, due to the adversative radiative responses of the atmosphere exposed to black and organic carbon, being negative for the latter . A number of papers analysed the annual mean value of instantaneous clear-sky aerosol direct radiative forcing (RF) at the TOA (RFtoa) associated with BB plumes. presented the results from 28 AeroCom Phase II models, indicating a global mean BB RFtoa of approximately 0.01 ± 0.08 W m−2. A similar value of 0.0 ± 0.2 W m−2 was presented by in the Fifth Assessment IPCC Report. Despite a rather low (and negative) mean global value of BB RFtoa, on a regional scale (especially over bright surfaces) smoke may well play a substantial role in affecting radiative properties of the atmosphere . In the case of high surface albedo, the existence of smoke particles leads to the decrease in columnar albedo at the TOA. This may in turn indicate a positive RFtoa , leading to positive feedback within the entire atmospheric column. Based on AeroCom Phase II multi-model evaluations, found the annual median value of ensemble RFtoa in the Arctic region to be 0.01 W m−2. Similar results are presented in , who estimated its value at around 0.004 W m−2. The significantly high RF uncertainty is mainly associated with the approximations of surface properties dependent on the daily and seasonal cycles, as well as the aerosol optical and microphysical properties which undergo ageing processes, whilst being transported across a large region . The accurate parametrization of aerosol single-scattering properties as inputs to radiative transfer simulations at a regional scale is of great concern in the Arctic region, due to sparse spatial distribution of long-term ground-based measurements and a high mean cloud fraction (especially in the summer), which limits satellite retrievals. In single-cell simulations at a certain location, aerosol single-scattering properties might be investigated by inversion schemes using sun-photometer data retrieved under AERONET (AErosol RObotic NETwork; ). However, the uncertainty in the columnar single-scattering albedo (ω) retrieval becomes high, considering low levels of aerosol optical depth (τDubovik et al.2000). This is the reason why AERONET level 2 data validation is performed only for τ440 larger than 0.5 and solar zenith angles above 50 . This, in turn, leads to a significant reduction of data coverage calculated for the Arctic region . The above aerosol properties may also be calculated using in situ measurements. It should be taken into account that such measurements are usually carried out at around 20–30 C (at which water evaporation occurs), leading to a reduction of aerosol optical properties associated with their hygroscopic properties. The impact of water uptake by aerosol is significant for soluble particles when exposed to a relative humidity (RH) of more than 40 %, resulting in the enhancement of a particle scattering cross section . Some studies apply empirical formulas of an enhancement factor f(RH) to retrieve the aerosol optical properties at ambient conditions . The factor is defined as the ratio between particle radius at ambient conditions and RH fixed to 30 %. The absolute values of the enhancement factor may vary significantly due to the particle chemical composition related to the emission source and due to particle size . Fresh and aged plumes of BB aerosol f(RH) were found to be 1.1 and 1.35, respectively (at a RH of around 80 %). This f(RH) enhancement due to the ageing process is in agreement with the secondary production of sulphate and progressive oxidation of organic compounds with OH and COOH groups, which result in increasing the hygroscopic properties . The study of smoke transport over the Arctic during July 2015 has been previously presented in scientific papers and is also characterized in this research. reported the temporal and spatial variability in aerosol single-scattering properties measured by in situ and ground-based remote sensing instruments over Svalbard and in Andenes, Norway. , discussed morphochemical characteristics and the mixing state of smoke particles at Ny-Ålesund, as indicated by a DEKATI 12-stage low-volume impactor combined with scanning electron microscopy. , on the other hand, presented a comprehensive description of smoke radiative and optical properties on a regional scale. The paper examined ageing processes of the smoke plume under study, whilst being transported from the source region and across the High Arctic. A simple Fu–Liou RTM, combined with the NAAPS aerosol transport model, was used to determine the spatial distribution of aerosol single-scattering properties and RFs for the period of 5–15 July 2015, in the area to the north of 55 N, where the transport of BB aerosol was observed. In this paper, we use MODTRAN radiative transfer simulations and aerosol optical properties obtained from in situ and ground-based remote sensing instruments to retrieve clear-sky direct RF over the area close to Ny-Ålesund. The research aims to estimate the biases connected with (i) hygroscopicity, (ii) variability of ω profiles, and (iii) plane-parallel closure of the modelled atmosphere. The main outcome of this research is the implementation of a new methodology to retrieve the profile of ω at ambient conditions, using in situ measurements and lidar profiles (Sect. 3.2). Simulated RFs were compared to results from a simple RTM (Sect. 3.5). Section 3.6 shows an example of RF distribution at the surface, in the vicinity of Ny-Ålesund (Svalbard). Section 3.7 shows the influence of the BB air masses on the development of the turbulence. Additionally, we confirmed the source region of the BB plume. A chemical weather model with satellite-derived biomass-burning emissions was used to interpret the transport and transformation pathways. 2 Methodology This section gives a brief description of all data and models used in this research. In Sect. 2.1 we will focus on characterization of all models used to track the transport of smoke, as well as to calculate the impact of the BB plume on radiative and dynamical properties of the atmosphere. ## 2.1 Modelling tools The MODerate-resolution atmospheric radiance and TRANsmittance model (MODTRAN) version 5.2.1 is the radiative transfer model (RTM) used. In this study, simulations are run with 17 defined absorption coefficients for each band in a correlated-k scheme (multiple scattering included; Bernstein et al.1996); 8-stream discrete ordinate radiative transfer (DISORT) method, with a spectral resolution of 15 cm−1 of the radiation fluxes ; and the Henyey–Greenstein scattering phase function approximation . Calculations are performed for the user-defined vertical profiles of thermodynamic variables (measured by radio sounding), including aerosol and trace gas optical properties, provided by the HITRAN 2000 database . MODTRAN was run with a time resolution of 20 min from the 9 to 11 July 2015, for the domain set to Ny-Ålesund coordinates. Simulations included cases with and without aerosol load (i.e. “polluted” and “clean”). The Fu–Liou version 200503 RTM uses the δ2∕4 stream solver, applied for 6 short-wave and 12 long-wave spectral bands. The optical properties of the atmosphere are calculated by the correlated-k distribution method, defined for each spectral band . The optical properties of aerosols, as well as thermodynamic properties of the atmosphere, were based on the results provided by the NAAPS (Navy Aerosol Analysis and Prediction System) global aerosol model reanalysis . Fu–Liou simulations, previously published in , were conducted to compare the results obtained by the approach used in this study (see Sect. 2.3.4) applied to MODTRAN RTM. 3-D effects of the RF were calculated using 3-D forward Monte Carlo code , which uses a maximum cross-section method to compute photon paths in the three-dimensional model of the atmosphere . A number of modifications were made to the original setup of the code, including such phenomena as absorption of photons by atmospheric gases as well as reflection and absorption at the undulating Earth's surface . The model domain covers the area of 51 km (W–E axis) × 68 km (S–N axis) and consists of cells or columns of 200 m× 200 m. A 20 km wide belt surrounds the main domain, in order to reduce the impact of cyclic boundaries on the results in the Monte Carlo modelling. The computations were performed for the whole 91 km× 108 km domain; however, only the results from the main domain were analysed. The Earth's surface was represented by a digital elevation model (DEM) and the technique proposed by . Large-eddy simulations (LESs) were performed using the 3-D non-hydrostatic anelastic Eulerian/semi-Lagrangian (EULAG) model to estimate the dynamical response of the atmosphere induced by the BB plume. The EULAG model was set up to solve for the three velocity components u, v, and w in the x-, y-, and z-directions (i.e. W–E, S–N, and vertical directions), as well as the potential temperature (θ). The governing equations are solved in an Eulerian framework without explicit subgrid-scale terms included, i.e. we use the method of implicit LES (ILESs). The non-oscillatory, forward-in-time integration was performed with the Multidimensional Positive definite Advection Transport Algorithm (MPDATA; Smolarkiewicz2006). We relied on the ability of the MPDATA to implicitly account for the effect of unresolved turbulence on the resolved flow, through the truncation terms associated with the algorithm. For more details on ILES, see . The horizontal grid spacing was set to 200 m and the vertical grid spacing to 50 m. The size of the computational domain was set to 19 km in the horizontal directions and 20 km in the vertical direction. The uppermost 5 km is a sponge layer included to prevent reflection of gravity waves at the top of the domain. The upper boundary of the domain is impermeable with a free slip condition, while the lower boundary is impermeable with a partial slip condition, characterized by a specified drag coefficient of 0.001. The flow is periodic across the lateral boundaries of the domain. The EULAG simulations were based on results from the RTM (10 July 2015 11:30 UTC) and radio sounding data from Ny-Ålesund obtained on 10 July 2015 12:00 UTC. Table 1Description of the instruments installed at Ny-Ålesund, used as input data for the atmospheric RTM. σext – extinction coefficient, τ – aerosol optical depth, α – Ångstrom exponent, PW – precipitable water, ASD – aerosol size distribution, σabs – absorption coefficient, σscat – scattering coefficient, Fin – total incoming flux, Fout – total outgoing flux both at the surface. The Global Environmental Multiscale model with atmospheric chemistry (GEM-AQ; Côté et al.1998; Kaminski et al.2008) was run in a global configuration with a uniform grid resolution of 0.9. The vertical domain was defined on 28 hybrid levels with the model top at 10 hPa. BB emissions were taken from the Global Fire Assimilation System (GFAS; Kaiser et al.2012). In addition to comprehensive tropospheric chemistry, the GEM-AQ model has five size-resolved aerosol species: sea salt, sulphate, black carbon, organic carbon, and dust. The microphysical processes that describe formation and transformation of aerosols are calculated by a sectional aerosol module (Gong2003). The particle mass is distributed into 12 logarithmically spaced bins from 0.005 to 10.24 µm. The aerosol module accounts for nucleation, condensation, coagulation, sedimentation and dry deposition, in-cloud oxidation of SO2, in-cloud scavenging, and below-cloud scavenging by rain and snow. Calculations of τ are done online for all bins and aerosol species. Extinction cross sections are taken from the AODSEM model . Anthropogenic emissions, based on ECLIPSEv4 (http://www.iiasa.ac.at/web/home/research/researchPrograms/air/ECLIPSEv4a.html), were used. The model was run for the period from 15 June to 20 July 2015. Simulations of back-trajectories and chemical composition were used to distinguish the BB layers in the lidar data and to identify the source region of the smoke plume under study. ## 2.2 Instruments In this section, we present a brief description of all instruments located at Ny-Ålesund used for this research study (Table 1). For a more detailed specification, please read the section on instrumentation in . Variables τ, Ångstrom exponent (α), and precipitable water (PW) were measured by a fully automatic sun photometer SP1a (Dr. Schulz & Partner GmbH). The instrument obtains direct solar radiation in 10 channels ranging from 369 and 1023 nm with 1 field of view . Corrections included temperature variability, Langley methodology, and cloud-screening algorithms . Extinction profiles were retrieved from KARL Raman lidar. The instrument uses Nd:Yag laser pulses at 355, 532, 1064 nm with a power of 10 W at each wavelength to obtain backscatter and extinction coefficients. Also, depolarization is measured at water vapour channels (407, 660 nm). The detection is carried out by a 70 cm mirror with a 1.75 mrad field of view, and the overlap issue is fulfilled at 700 m a.g.l. Further details may be found in and . Continuous measurements of radiation fluxes are provided at Ny-Ålesund under the Baseline Surface Radiation Network (BSRN). A ball-shaded CMP22 by Kipp & Zonen installed on a solar tracker by Schulz & Partner measures total incoming and reflected solar radiation at 200–3600 nm . The in situ measurements of single-scattering properties were provided by the Gruvebadet Laboratory, located 1 km southwest of Ny-Ålesund. The single wavelength M903 nephelometer from Radiance Research, uses a xenon flash lamp and opal diffuser to derive the scattering coefficient at 530 nm , with an angular integration range of 10–170. Corrections for non-ideal illumination and truncation error were performed according to the description presented in . Black carbon (BC) concentration and the aerosol absorption coefficient were measured at 467, 530, and 660 nm by the particle soot absorption photometer (PSAP) from Radiance Research, based on the principle of filter attenuation change due to aerosol load. Corrections for multiple scattering and non-purely absorbing aerosols were done following the methodology from . Aerosol size distribution measurements were covered by joint spectra of the TSI scanning mobility particle sizer (SMPS 3034), with 54 channels, and the TSI aerodynamic particle sizer spectrometer (APS 3321), with 52 channels. Jointly, the spectral coverage is in the range of 10–20 000 nm, excluding a gap around 500 nm which was fitted. Both instruments delivered data with a resolution of 10 min. ## 2.3 Atmospheric and surface properties – inputs to models ### 2.3.1 Surface properties MODIS 6th collection daily product MD09CMG was used to retrieve surface albedo values over the area between 55 and 90 N with a resolution of 1× 1. Data were averaged over 1 month to obtain good coverage, assumed constant with time, and inserted into the Fu–Liou model . Spectral dependency of surface albedo derived from the MODTRAN built-in module, using calculations of the Fresnel reflection at the ocean top, was applied while comparing data to Fu–Liou results. An additional setup of radiometer-derived surface albedo was used for the comparison with RF, calculated by means of the radiometer measurements. Both MODTRAN and Fu–Liou codes assumed a flat and horizontal Earth surface. MODIS MCD43A1 surface product of bidirectional reflectance distribution function (BRDF) on 12 July 2015 (closest to the simulation day), at 469 nm, was used for the 3-D Monte Carlo model over the Svalbard area. The BRDF was calculated yielding the equation of : $\begin{array}{ll}R\left(\mathrm{\Theta },\mathit{\vartheta },\mathit{\varphi },\mathit{\lambda }\right)=& \phantom{\rule{0.125em}{0ex}}{f}_{\mathrm{iso}}\left(\mathit{\lambda }\right)+{f}_{\mathrm{vol}}\left(\mathit{\lambda }\right)\cdot {K}_{\mathrm{vol}}\left(\mathrm{\Theta },\mathit{\vartheta },\mathit{\varphi }\right)\\ \text{(1)}& & +{f}_{\mathrm{geo}}\left(\mathit{\lambda }\right)\cdot {K}_{\mathrm{geo}}\left(\mathrm{\Theta },\mathit{\vartheta },\mathit{\varphi }\right),\end{array}$ where f and K stand for coefficient kernels. In particular, “iso” denotes the isotropic scattering component, “geo” the diffuse reflection component, and “vol” the volume scattering component. Variables Θ, ϑ and ϕ are solar zenith angle, view zenith angle and view–sun relative azimuth angle, respectively. The gaps over land were filled in with mean values of parameters for a given surface type (glacier or tundra/rock) and elevation range. The coastal line used to distinguish between water and land was taken from the . Glacier outlines (last updated 1 April 2016) were taken from the Svalbard land covering map data set . Fresnel reflection from the water surface was assumed in the modelling. Moreover, radiation scattering by seawater and its constituents (e.g. phytoplankton or mineral suspended matter) was neglected. The DEM used in the 3-D Monte Carlo modelling was based on maps from the Norwegian Polar Institute (2014a, UTM zone 33N projection, ellipsoid WGS84). The original DEM was regridded to a resolution of 200 m. The land surface altitude within a cell is estimated by the following equation : $\begin{array}{}\text{(2)}& z={a}_{\mathrm{0}}\cdot x+{a}_{\mathrm{1}}\cdot y+{a}_{\mathrm{2}}\cdot x\cdot y+{a}_{\mathrm{3}},\end{array}$ where x, y, and z are the coordinates of a given point of a cell surface and a0, a1, a2, and a3 are coefficients fitted to the coordinates of the cell nodes. The Earth's surface approximated in such a way is continuous. ### 2.3.2 Vertical profiles of thermodynamic variables and ozone concentration Profiles of all thermodynamic properties, including pressure (p), temperature, wind speed, and RH, were adopted from the radio soundings performed at Ny-Ålesund for the day of interest. The radio-sounding profiles were complemented by subarctic summer profiles from the international standard atmosphere to extend them up to 100 km. These were further used for the 3-D Monte Carlo, MODTRAN, and EULAG simulations. The profiles for the Fu–Liou calculations were taken from the Navy Operational Global Analysis and Prediction System (NOGAPS). Vertical profiles of ozone were retrieved from dimensional climatology, UGAMP , then scaled to the measured values of the total ozone content by the MODIS MD09CMG product (Fu–Liou model) and SP1a photometer (the remaining models). ### 2.3.3 Vertical profiles of aerosol single-scattering properties Vertical profiles of aerosol single-scattering properties at ambient conditions were used as input parameters to MODTRAN and 3-D Monte Carlo calculations. The retrieval was based on the in situ aerosol single-scattering properties, measured at the surface in dry conditions (denoted hereinafter as superscript “d”), and on vertical profiles of ${\mathit{\sigma }}_{\mathrm{ext}}^{\mathrm{a}}$, as well as RH at ambient conditions (hereinafter superscript “a”) from KARL lidar and radio-sounding data. In reference to temporal variability in the range-corrected signal measured at 532 nm by the micropulse lidar, characterize smoke plume as a rather well-mixed layer of BB aerosol extending from around 4–6 km on 9 July to 0–3.5 km later on. Both contributions of BB-like aerosol in the NAAPS τ, estimated on a level as high as 80 %, and the similarity between columnar and in situ aerosol extensive properties, such as α , suggest that the smoke plume may have crossed the planetary boundary layer, mixing with the lowermost part of the troposphere. Additionally, the infinitesimal aerosol load that exists above the smoke plume plays a minor role in affecting the radiative properties of the atmosphere, and therefore may be neglected. This is why, in the presented methodology, we assume no changes in chemical composition vertically, so that most of the possible vertical variability in ωa at ambient conditions is attributed to changes in the RH. Therefore, we approximate initial profiles of ωd and ${R}_{\mathrm{eff}}^{\mathrm{d}}$ by setting them up to the values of in situ measurements and consider them constant with altitude. By introducing the hygroscopic growth model for particles with known size distribution, one may obtain ωa profile as well as ga. ### Algorithm for delivering single-scattering albedo ω profile at ambient conditions From absorption (σabs) and scattering (σscat) coefficients at 530 nm (for details see Table 1), ω can be calculated, yielding $\begin{array}{}\text{(3)}& \mathit{\omega }\left(\mathit{\lambda },z\right)=\mathrm{1}-\frac{{\mathit{\sigma }}_{\mathrm{abs}}\left(\mathit{\lambda },z\right)}{{\mathit{\sigma }}_{\mathrm{ext}}\left(\mathit{\lambda },z\right)}\end{array}$ at ambient and dry conditions. Subsequently, since σabs is a weak function of RH , the assumption that ${\mathit{\sigma }}_{\mathrm{abs}}^{\mathrm{a}}$ and ${\mathit{\sigma }}_{\mathrm{abs}}^{\mathrm{d}}$ are identical is justified. We can then relate dry and ambient conditions by introducing the scattering enhancement factor f(λ,z(RH)) principle, defined as the ratio between scattering coefficients measured at mentioned RH states : $\begin{array}{}\text{(4)}& f\left(\mathit{\lambda },z\left(\mathrm{RH}\right)\right)=\frac{{\mathit{\sigma }}_{\mathrm{scat}}^{\mathrm{a}}\left(\mathit{\lambda },z\left(\mathrm{RH}\right)\right)}{{\mathit{\sigma }}_{\mathrm{scat}}^{\mathrm{d}}\left(\mathit{\lambda },z\right)}.\end{array}$ Ultimately, from formulas (3) and (4), we may introduce the equation for ωa satisfying $\begin{array}{}\text{(5)}& {\mathit{\omega }}^{\mathrm{a}}\left(\mathit{\lambda },z\right)=\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}-{\mathit{\omega }}^{\mathrm{d}}\left(\mathit{\lambda },z\right)}{{\mathit{\omega }}^{\mathrm{d}}\left(\mathit{\lambda },z\right)\cdot f\left(\mathit{\lambda },z\left(\mathrm{RH}\right)\right)}}.\end{array}$ Therefore, to derive the relationship between the aerosol water uptake and a particular aerosol species, the Hänel model (Hänel1976) of growth factor f(RH) is used, relating hygroscopicity of aerosols with relative humidity, yielding $\begin{array}{}\text{(6)}& f\left(\mathrm{RH}\right)={\left(\frac{\mathrm{1}-{\mathrm{RH}}^{\mathrm{a}}}{\mathrm{1}-{\mathrm{RH}}^{\mathrm{d}}}\right)}^{-\mathit{\gamma }},\end{array}$ where the γ parameter represents the indicator of particle hygroscopicity, a larger γ refers to more hygroscopic aerosols. In this study, a literature value of γ was introduced equal to 0.18, which applies for BB aerosols . In this method we combine lidar and in situ measurements. The issue of lack of data within the lidar geometrical compression range (0–700 m) is solved by an interpolation method. The proposed method leads to ωa uncertainty of 0.05, where its vast majority may be attributed to ${\mathit{\sigma }}_{\mathrm{abs}}^{\mathrm{d}}$ and ${\mathit{\sigma }}_{\mathrm{scat}}^{\mathrm{d}}$ measurement uncertainties. ### Algorithm for delivering asymmetry parameter g at ambient conditions Asymmetry parameter g is derived iteratively using aerosol size distributions, measured by SMPS and APS, and Mie theory, as well as a one-parameter equation determined by that approximates the relationship between the RH and the growth factor χ(RH), yielding $\begin{array}{}\text{(7)}& \mathit{\chi }\left(\mathrm{RH}\right)={\left(\mathrm{1}+\mathit{\kappa }\frac{\mathrm{RH}}{\mathrm{1}-\mathrm{RH}}\right)}^{\frac{\mathrm{1}}{\mathrm{3}}},\end{array}$ where RH represents the relative humidity, while neglecting the Kelvin effect (in terms of the Köhler law), being true for particles significantly affecting light extinction (diameter > 0.01 µm; Zieger et al.2011; Bar-Or et al.2012). Coefficient κ, however, refers to particle hygroscopicity, with respect to the Raoult effect. In this study, for simplification purposes, we neglect the effect of the broadening of the aerosol size distribution spectra, due to diffusional growth of particles. To determine the most accurate literature value of κ coefficient for the BB aerosol, that vastly relies on flora being burnt, we studied the trajectory of smoke transport over the Arctic by means of the GEM-AQ model and analysed a source area in the event under study, i.e. Alaska, regarding vegetation coverage. A κ coefficient of 0.07 (0.25 µm dry diameter) was chosen to match vegetation (Duff core) covering the Alaskan tundra . The size distributions of aerosols at ambient conditions were estimated by introducing the hygroscopic growth factor χ(RH), related to the growth of particles due to water uptake, yielding $\begin{array}{}\text{(8)}& \mathit{\chi }\left(\mathrm{RH}\right)=\frac{{D}^{\mathrm{a}}\left(\mathrm{RH}\right)}{{D}_{\mathrm{d}}\left(\mathrm{RH}\right)},\end{array}$ where D is the diameter of the particle at a certain RH . The calculations are provided for an extreme BB event; thus, as previously mentioned, the concentration of aerosols other than smoke is negligible. That is why we used a constant refractive index for a BB aerosol for retrieval of g at ambient conditions by means of Mie theory, (1.52−0.0061iSayer et al.2014). ### 2.3.4 Equations governing 3-D Monte Carlo simulations The results from the 3-D Monte Carlo model, as mentioned earlier, were used to characterize spatial variability in RF, and therefore to diagnose possible uncertainties resulting from using single-column RTMs, represented by MODTRAN and Fu–Liou codes. Taking into account the above goals, we did not perform time-consuming simulations of daily mean broadband RFs for the model domain. Instead, we relied on the relative value of RF calculated for 1λ, with respect to its value at the TOA at a given zenith angle. Such an approach allowed for defining higher spatial resolution. The relative net irradiance ${F}_{\mathrm{net}}^{\mathrm{rel}}$ at the Earth's surface was computed according to the equation $\begin{array}{}\text{(9)}& {F}_{\mathrm{net}}^{\mathrm{rel}}=\frac{{F}_{\mathrm{net}}}{{F}_{\mathrm{toa}}}=\frac{{S}_{\mathrm{c}}}{{S}_{\mathrm{s}}\cdot {N}_{\mathrm{toa}}}\sum _{j=\mathrm{1}}^{N}{w}_{j},\end{array}$ where Fnet is the net irradiance aligned with the direction of the vector normal to the sloping surface in column (k,l), Ftoa is the downward irradiance at the TOA, Ntoa is the number of photons incident at the TOA(k,l), Ss is the area of the Earth's surface within the column (k,l), Sc is the area of the cell (k,l), N is the number of photons absorbed by the Earth's surface within the column (k,l), and wj is the weight of the jth photon absorbed by the Earth's surface within the column (k,l). The short-wave direct aerosol radiative forcing (spectral relative radiative forcing), RFrel(λ), is expressed as $\begin{array}{}\text{(10)}& {\mathrm{RF}}_{\mathrm{rel}}\left(\mathit{\lambda }\right)=\frac{{F}_{\mathrm{net}}^{\mathrm{aer}}\left(\mathit{\lambda }\right)-{F}_{\mathrm{net}}^{\mathrm{0}}\left(\mathit{\lambda }\right)}{{F}_{\mathrm{toa}}\left(\mathit{\lambda }\right)}={F}_{\mathrm{net}}^{\mathrm{aer},\mathrm{rel}}\left(\mathit{\lambda }\right)-{F}_{\mathrm{net}}^{\mathrm{0},\mathrm{rel}}\left(\mathit{\lambda }\right),\end{array}$ where superscript “aer” stands for clear-sky conditions with an aerosol included (polluted case), and superscript “0” for clear-sky conditions without an aerosol (clean case). We can also define RF with respect to the cell surface Sc instead of the actual surface within a given column Ss: $\begin{array}{}\text{(11)}& {\mathrm{RF}}_{\mathrm{rel}}^{\mathrm{cell}}\left(\mathit{\lambda }\right)=\frac{{S}_{\mathrm{s}}}{{S}_{\mathrm{c}}}\cdot {\mathrm{RF}}_{\mathrm{rel}}\left(\mathit{\lambda }\right).\end{array}$ RFrel and RF${}_{\mathrm{rel}}^{\mathrm{cell}}$ have slightly different meanings. RFrel represents the aerosol impact on the flux of solar energy absorbed by a unit area of an actual sloped surface. This quantity is of local relevance, i.e. to vegetation or changes in the surface temperature. RF${}_{\mathrm{rel}}^{\mathrm{cell}}$ is relevant to the radiative budget of the whole atmospheric column. Moreover, it can be used to compare results from RTMs with different geometries. Figure 1Temporal variability in aerosol single-scattering properties during the BB2015 event over Ny-Ålesund, in particular aerosol optical depth τ at 530 nm (blue dots) and Ångstrom exponent α (green dots) measured by SP1a (a), single-scattering albedo ωd at 530 nm (yellow dots) calculated from in situ data and cloud coverage (black line) from the pyranometer (b), effective radiuses at dry ${R}_{\mathrm{eff}}^{\mathrm{d}}$ (red dots) and ambient ${R}_{\mathrm{eff}}^{\mathrm{a}}$ (black dots) conditions measured by SMPS and APS (c), and absorption coefficient σabs multiplied 10 times (purple dots) and scattering coefficient σscat (light blue dots) at 530 nm, obtained from the PSAP and nephelometer. 3 Results ## 3.1 The temporal variability in aerosol single-scattering properties during the BB event at Ny-Ålesund In July 2015 the transport of a BB plume over the Arctic region was observed, being advected from the intense tundra and boreal forest fires in the northern regions of North America. The plume altered both the optical and microphysical properties of aerosols, as indicated by the in situ and ground-based remote sensing instruments installed at Ny-Ålesund. Thus, τ conditions characteristic of summer conditions (mean summer τ=0.08) were enhanced with a factor of 10, making it the strongest event in the past 25 years . reported the development and further intensification of tundra fires in Alaska, introduced by a series of frequent lightning strikes occurring from mid-June to late July 2015. The transport of the BB plume was visible between 4 and 6 July, from the central part of Alaska, via the North Pole, to the Spitsbergen. Starting in the afternoon of the 9 July, until approximately noon on 11 July, the BB plume was visible at Ny-Ålesund, as indicated by in situ and remote sensing instruments (Fig. 1). As suggested by the lidar data by , this advection lasted longer in the area of study; however, the appearance of clouds around noon on the 11 July (Fig. 1b) terminated further measurements. Although reported the beginning of the event at 14:00 UTC, based on the lidar data, we see a temporal discrepancy between in situ and remote sensing measurements of half a day, resulting from transport taking place in the mid-troposphere (Fig. 1d). The ultimate manifestation of a BB plume at the surface, however, might be evidence of a turbulent vertical mixing. The event was characterized by the mean τ550 value estimated at the level of 0.64, with a maximum reaching as high as 1.2 at noon on 10 July (Fig. 1a). The temporal variability in α was rather low, with an average value of around 1.5 throughout the advection, which indicates the existence of mostly fine particles. This hypothesis is confirmed by the aerosol size distribution measured at ground level, which shows that particles are mainly distributed in the accumulation mode during the BB event . The mean ωd at 530 nm obtained for the event is 0.94 ± 0.02 (Fig. 1b), indicating moderate absorbing properties, characteristic for aged BB plumes. Note that the value is slightly higher than in situ ωd reported by , of 0.91, resulting from the applied additional multiple-scattering correction to PSAP data in this study. During the most intense period ωd reduces to 0.9. Aerosol absorbing properties decrease over the event, resulting in an increase in ωd on 11 July to its maximum value of 0.95. presented results from the transport of smoke-enriched air masses over Ny-Ålesund. The episode was very similar to the one under study, as the mean τ500 reached the value of 0.68 with a mean ω of 0.98, after 7 days of transport from central Europe. It is clearly visible that ω is slightly higher by comparison to the 2015 BB event (labelled BB2015). Apart from the above paper, the representation of BB plumes lasting in the atmosphere for more than 3 days, in literature, is rather rare. reported a number of mean surface ω, characterizing aged BB plumes ranging from 0.76 to 0.93, from various in situ measurements. Although values usually seem to be much lower by comparison to the BB2015 event, the differences result from the definition of aged plumes. In the mentioned paper, aged aerosol was characterized as a plume existing in the atmosphere for more than 24 h only; while in this study, its persistence is much longer, at around 7 days. The mean value (14:00 9 July–11:30 11 July) of absorption coefficient (σabs) was 4.0 Mm−1, while extinction coefficient (σext) was 65.0 Mm−1, as indicated by in situ instruments during BB2015. Reported extensive optical properties of aerosols significantly exceeded their typical annual mean values (σscat: 4.35 Mm−1, σabs: 0.18 Mm−1; α: 1.15), characterized by for the station at Mount Zeppelin (475 m a.s.l.), located close to Ny-Ålesund. We obtained average values of 0.17 ± 0.02 and 0.18 ± 0.02 µm for effective radius at dry (${R}_{\mathrm{eff}}^{\mathrm{d}}$) and ambient (${R}_{\mathrm{eff}}^{\mathrm{a}}$) conditions, respectively (Fig. 1c). Presented results are in good agreement with studies provided by , who reported the values of ${R}_{\mathrm{eff}}^{\mathrm{a}}$ originating from open shrublands to be as high as 0.176–0.194 µm. ${R}_{\mathrm{eff}}^{\mathrm{a}}$ being in the lower boundary of the class reported by is likely to result from the chemical composition of the smoke plume, which does not allow for intense hygroscopic growth of aerosols (consisting mainly of hydrophobic particles; Moroni et al.2017). We may also speculate that it is due to the efficiency of the scavenging processes with a much longer transport. Figure 2Vertical profiles of aerosol single-scattering properties at 530 nm on 10 and 11 July 2015 (UTC), based on the lidar measurements, radio-sounding profiles, and model output (lines), as well as in situ measurements (dots). Subfigures include lidar-derived (LID) extinction coefficient at ambient (${\mathit{\sigma }}_{\mathrm{ext}}^{\mathrm{a}}$; green) and dry (${\mathit{\sigma }}_{\mathrm{ext}}^{\mathrm{d}}$; blue) conditions, as well as absorption coefficient σabs multiplied 10 times (red; a1–4), modelled extinction profile from GEM-AQ (GEM ${\mathit{\sigma }}_{\mathrm{ext}}^{\mathrm{a}}$; b1–4), retrieved single-scattering albedo ωa (c1–4) at ambient conditions, radio-sounding profiles of relative humidity RH (d1–4), and potential temperature θ (e1–4). Blue transparent layers denote temperature inversions (Tinv). Additionally, present a significant increase of up to 2.2 cm in the precipitable water (PW); This is rather unusual in the High Arctic. The advection of such humid air masses may significantly enhance the water uptake of aerosols, hence their scattering properties. Using in situ instruments, that dry the particles (RH usually of around 15 % in the chamber), possibly leads to an appreciable underestimation of aerosol scattering, and thus radiative properties. ## 3.2 Retrieval of the single-scattering properties at ambient conditions An analysis regarding the identification of a source region was performed by means of the GEM-AQ model. We investigated the path of smoke back-trajectories, transported across the Arctic region (not shown), and confirmed that the studied BB plume originated from wildfires over Alaska. Both the timing and inflow of aerosol-enriched air masses and the rapid increase in τ550 support the above statement. Vertical profiles of PM10 demonstrated polluted air masses extending up to approximately 3 km, with maximum mass mixing ratios reaching 35 ppb at 2 km. Analysis of 3-D extinction fields over Svalbard revealed a thick layer, with higher values above the PBL (Fig. 2b1–4). The model reproduced the altitude of elevated extinction coefficients; however, the complex vertical stratification was not captured by the model due to sparse vertical resolution. In this section, we present example results of the applied methodology concerning the retrieval of a ωa profile. The first case (11:30 10 July; Fig. 2a1–e1), in terms of ${\mathit{\sigma }}_{\mathrm{ext}}^{\mathrm{a}}$ profiles, represents the moment of maximum τ value, while cases 2–3 indicate average conditions, characterizing the BB plume (23:00 10 July; Fig. 2a2–e2; 02:30 11 July; Fig. 2a3–e3). The last chosen case outlines the transition of the atmosphere – with intensified atmospheric dynamics, an appreciable turbulent mixing, and convective cloud formation – to the conditions where a formation of low clouds relying on stable conditions is visible; thus it is likely that vertical mixing is gradually suppressed. The vertical profiles of thermodynamic variables, such as RH and potential temperature (θ), were retrieved from two radio soundings performed on the 10 and 11 July, around noon. On the 10 July, the θ profile indicates the existence of two rather thick inversion layers at around ground level and at 3.5 km, as well as an almost isothermal layer at 2–3.5 km (Fig. 2e1–2). The profiles on the 11 July revealed that all layers were attenuated during the day and were significantly lifted (Fig. 2e3–4). The appearance of additional thin inversions, together with a visible decay in θ lapse rate and the mentioned transformations of previous layers, suggest the existence of vertical mixing. A similar vertical structure is visible in RH profiles with values oscillating around 15–90 %. A significant decay in RH values is attributed to θ inversion layers; in between, however, the values usually exceed 75 %. The vertical structure of ${\mathit{\sigma }}_{\mathrm{ext}}^{\mathrm{a}}$ (Fig. 2a1–4) retrieved from the lidar observations is strongly dependent on both θ and RH profiles. The latter designates the enhancement of ${\mathit{\sigma }}_{\mathrm{ext}}^{\mathrm{a}}$ inside the visible layers, attributed to hygroscopic growth of aerosols, while θ determines their thickness. Overall, the smoke plume is visible from around ground level to 3.5 km. However, the shape of the lower boundary is uncertain, due to the lidar overlap issue under 0.7 km. The ${\mathit{\sigma }}_{\mathrm{ext}}^{\mathrm{a}}$ inside the smoke layer ranges from 100 to 350 Mm−1, with a significant vertical variability. In all cases an additional secondary ${\mathit{\sigma }}_{\mathrm{ext}}^{\mathrm{a}}$ enhanced layer is visible above the main BB plume. In case 1 it is visible at around 5.5 km, and is likely to be connected with the existence of thin clouds of marginal meaning in light of the smoke plume itself. In the remaining cases, secondary layers which are visible at 3.5–4.5 km may be the residuum of cumulus clouds, reported by , resulting in mixing processes between smoke and the air layer above the BB plume. In Fig. 2a1–4 the vertical variability of retrieved ${\mathit{\sigma }}_{\mathrm{ext}}^{\mathrm{d}}$ and σabs are additionally presented. The ${\mathit{\sigma }}_{\mathrm{ext}}^{\mathrm{d}}$ represents the result of Eqs. (3)–(6), where the hygroscopic growth of aerosol is removed. The calculated profiles of ωa vary from 0.93 to 0.96. In the presented cases, ωa profiles shift towards less absorbing properties and as a result of the applied approximation (in particular Eq. 6), its vertical structure reflects the vertical variability in RH. Figure 3Comparison of model-derived and measured irradiances, in particular incoming Fin (a), outgoing Fout (b), direct Fdir (c), and diffuse Fdiff (d) surface fluxes on 9–11 July 2015. The solid black lines refer to the perfect fir, dotted black lines to a linear fit, r refers to the Pearson correlation coefficient, and RMSE represents the root mean square error. ## 3.3 Comparison of model-derived irradiances with the measurements Figure 3 presents the results of the performance of MODTRAN simulations compared with in situ measurements, in terms of radiative properties of the atmosphere. The Pearson correlation coefficients for MODTRAN and radiometer data exceed 0.95 for all radiation components (in particular total incoming Fin – 0.95, outgoing Fout – 0.99, direct Fdir – 0.99, diffuse Fdiff – 0.98 fluxes at the surface), suggesting a well-defined statistical dependence of the variables. Nevertheless, the model seems to slightly underestimate all fluxes with regard to measurement data, especially visible in Fdiff. The root mean square error (RMSE) is estimated at the level of 18.5 and 7.6 W m−2 for Fin and Fout. The mean bias of total incoming flux at the surface is mainly related to RMSE of Fdiff, being as high as 13.1 W m−2. The Fdir RMSE is almost 2 times lower than the latter and reaches 7.0 Wm−2. This difference in biases of Fdir and Fdiff result from the distinction in parameters governing both irradiances, in particular Fdir is a function of parameters that are measured with good accuracy (τ and PW), while Fdiff is additionally controlled by variables with appreciably higher uncertainty (ω, phase function, surface albedo, etc.). Although cloud-contaminated radiometer data were previously removed, higher RMSEs together with relatively high temporal variability in Fdiff, which is a significant function of the cloud coverage, might suggest that the performance of cloud-screening algorithm was insufficient for the case under study. Therefore, presented results from in situ data should be used with caution, bearing in mind that they may occasionally represent all-sky conditions. Figure 4Temporal variability in (a) the surface radiation fluxes: total incoming flux at the polluted case Fin (black) and at the clean case Fcin (blue), as well as total outgoing flux at the polluted case Fout (red), simulated by MODTRAN (dots), and measured by radiometers (lines). The gaps in the radiometer data refer to the cloud contamination. Panel (b) presents radiative forcing at the surface RFsurf (green) and at the top of the atmosphere RFtoa (orange). ## 3.4 Temporal variability in radiative forcing at Ny-Ålesund Results presented in this chapter were previously introduced in Sect. 2.3.4 concerning ωa and ga retrievals. To estimate the overall performance of the mentioned approximation, we performed two initial simulations that assumed fixed values of all optical and microphysical properties of aerosol, except for ω and g. In the first, we used ωd and gd measured by in situ instruments, while the second applied ωa and ga approximations. Differences between the two simulations indicated the decrease in RF (in absolute magnitude), on average by about 3.1 W m−2 for the BB event (14:00 9 July–11:30 11 July), when ambient conditions were used. This was due to an increase in both Fin and Fout by 3.5 and 0.4 W m−2, respectively, for the simulation with aerosol included. The impact of the retrieval on enhancement of Fin and Fout might be vastly attributed to ω correction, with the influence of 81 %, and only 19 % to ga approximation. Figure 4 presents the comparison of temporal variability of irradiances (Fig. 4a) and clear-sky RF (Fig. 4b). The daily variability in total incoming flux in the clean case (Fcin) is mainly a function of the solar zenith angle and for the 9–11 July 2015 ranges from around 153.0 W m−2 at midnight to 560.8 W m−2 at noontime. On the other hand, Fin is additionally strongly affected by the optical and physical properties of the advected smoke. The model's performance at background conditions might be validated at the period between 07:00 and 14:00 UTC on 9 July. This represents the clear-sky period with an infinitesimal load of aerosols, typical for summer background conditions in the Arctic. Both measured by radiometer (hereinafter referred to as Rad) and modelled by MODTRAN (hereinafter referred to as Mod) Fin are in rather good agreement, deviating on average by only 9.7 W m−2 (2 %) from each other. The existence of aerosol indicates the mean decrease in Fin by 0.4 % (Rad Fin), as well as 2.3 % (Mod Fin), as compared to the mean value of Fcin (07:00 to 14:00 UTC on 9 July). Measured and modelled Fout indicate a very good agreement with a difference of less than 1 %, reaching on average 69.8 W m−2 (Rad) and 69.4 W m−2 (Mod). At 14:00 UTC reported an advection of the BB plume over Ny-Ålesund, characterized by a complicated structure of the BB layers, with a mixture of aerosol and clouds. Since the mean value of Mod Fin during the event (14:00 9 July–11:30 11 July) is estimated at the level of 243.0 W m−2, the existence of the BB aerosol reduced the incoming flux, on average by around 90 W m−2, when compared to the case represented by summer background conditions (332.1 W m−2; 07:00 to 14:00 UTC on 9 July). Furthermore, we report the mean value of outgoing irradiance (Mod Fout) reaching 36.9 W m−2. The highest decrease in Mod Fin is visible on 10 July as indicated by the observed maximum of τ550 during the BB event. The reduction of Mod Fin exceeded 27 % for the summer background conditions (compare 07:00–14:00 UTC on 9 and 10 July). Additionally, a higher temporal variability in Rad Fin at the time, with respect to the previous day, is observed. It is likely to result from both a possible BB aerosol activation and increased turbulence. Further to this, a number of high- and mid-level cumulus clouds are reported around noon and in the afternoon , which support the above statement. RFssurf were estimated by means of two approaches: in the first approach, we used MODTRAN (Mod RFsurf) simulations to account for both terms (representing polluted and clean cases; for details see Sect. 2.1) in the following equation: $\begin{array}{}\text{(12)}& {\mathrm{RF}}_{\mathrm{surf}}=\left({F}_{\mathrm{in}}-{F}_{\mathrm{out}}\right)-\left({F}_{\mathrm{cin}}-{F}_{\mathrm{cout}}\right),\end{array}$ The average value of Mod RFtoa exceeded 47.0 W m−2, indicating that the BB plume cooled the entire atmospheric column. Within the atmosphere, however, it has a positive impact of 31.9 W m−2 (Mod RFatm). This pattern is in agreement with and , who also reported negative values at the TOA and positive ones when an atmospheric layer is considered. High single-scattering albedo values and negative RFtoa clearly show that scattering is dominant with respect to the contribution of the light absorption. Indeed, absorption species (mainly BC) are able to mitigate the cooling effect of the BB event in the atmosphere, but not sufficiently to change the RF sign at the TOA. This means that BC particles play a minor role with respect to scattering particles (sulfate; organic carbon, OC; etc.). This could also be demonstrated by the changes in atmospheric concentrations of BC, OC, and sulfate aerosol, measured at Gruvebadet. In particular, the relative concentrations increase about 20 times for BC and OC, and about 10 times for non-sea-salt sulfate during the BB event, with respect to the background level. In spite of the BC and OC, relative increases are similar; the absolute concentrations of OC are more than 10 times higher than atmospheric concentration of BC . Overall, the described RF of the plume had an about 31 % higher (in absolute magnitude) influence at the surface, in comparison with the TOA. Model calculations usually overestimate Mod RFsurf values, which on average, deviate from Rad RFsurf by around 32.9 %, possibly related to all-sky conditions being represented by radiometer measurements that increase diffusive flux. The mean estimated radiative forcing efficiency at the surface (Mod RFEsurf) of the BB event in Svalbard of 126 W m${}^{-\mathrm{2}}/{\mathit{\tau }}_{\mathrm{550}}$ is slightly higher than other estimates of smoke transport, such as 99 W m${}^{-\mathrm{2}}/{\mathit{\tau }}_{\mathrm{550}}$ reported by for the Canadian forest fires advection over Europe in 2013, and 88 W m${}^{-\mathrm{2}}/{\mathit{\tau }}_{\mathrm{550}}$ for wildfires observed over Crete, Greece in 2001 . On the other hand, multiyear mean RFEsurf values obtained for different regions are appreciably higher, i.e. RFEsurf originating from tropical forest fires over the Amazon basin is estimated at the level of 140 ± 33 W m${}^{-\mathrm{2}}/{\mathit{\tau }}_{\mathrm{550}}$, while boreal forest fires from North America are as high as 173 ± 60 W m${}^{-\mathrm{2}}/{\mathit{\tau }}_{\mathrm{550}}$ and RFEsurf for African savannahs are at the level of 183 ± 31 W m${}^{-\mathrm{2}}/{\mathit{\tau }}_{\mathrm{550}}$ . The reported discrepancies are a function of the solar zenith angle, surface albedo, and single-scattering properties of aerosols. In general, more efficient RFEssurf are characterized by smoke plumes with lower values of ω, i.e. 0.85 and 0.91 for African savannahs and the Amazon forest, respectively . Although ω values are similar for the case under study, i.e. boreal forest, the latter is more efficient due to a higher solar zenith angle. Table 2The mean daily values of the single-scattering albedo ωa, precipitable water PW (cm), and aerosol optical depth τ550 at 550 nm used as inputs to MODTRAN and Fu–Liou simulations. ## 3.5 The comparison of RF derived from MODTRAN and Fu–Liou simulations This section focuses on the comparison of RFs simulated by the MODTRAN and Fu–Liou models. The results of the latter were previously published in regarding the transport of this BB plume over the Northern Hemisphere. In the following section, all RFs were retrieved over the ocean area, near Ny-Ålesund (78.5 N, 9.5 E), assuming a spectral surface albedo of the Fresnel reflection over a water body to eliminate discrepancies in the surface properties from our investigation. Figure 5The mean daily values of radiative forcing (RF) calculated by means of Fu–Liou (FuLiou) and MODTRAN (Mod) models. Simulations were run for clear-sky conditions at the surface (subscript “surf”), within the atmosphere (subscript “atm”), and at the top of the atmosphere (subscript “toa”). The surface reflectance in MODTRAN simulations is based on the Fresnel reflection calculations at the ocean surface. Table 2 presents the comparison between input variables to both models: mean daily ωa, PW, and τ550. Column-integrated Mod ωa is calculated yielding : $\begin{array}{}\text{(13)}& {\mathit{\omega }}^{\mathrm{a}}=\frac{\underset{\mathrm{0}}{\overset{\mathrm{10}\phantom{\rule{0.125em}{0ex}}\mathrm{km}}{\int }}{\mathit{\sigma }}_{\mathrm{ext}}^{\mathrm{a}}\left(z\right)\cdot {\mathit{\omega }}^{\mathrm{a}}\left(z\right)\mathrm{d}z}{\mathit{\tau }},\end{array}$ while ωa in the case of MODTRAN simulations having an increasing trend (from 0.92 to 0.96) within 9–11 July, the same quantity shows 3–6 % more absorbing properties, and is rather constant for Fu–Liou calculations oscillating around 0.91–0.93. The same trend is visible for PW mean values, where it is between 1.72 and 2.26 cm for MODTRAN simulations; however, for Fu–Liou it is 10–40 % lower. Additionally, the retrieved mean MODTRAN τ550 equal to 0.23–0.72 and a Fu–Liou value of 0.2–0.59 seem to deviate from each other by 8–35 %. Furthermore, while the highest τ550 value for MODTRAN simulations is on 10 July, it is more noticeable on 11 July for the Fu–Liou simulations. Presented discrepancies between variables are satisfactory, given the fact that the Fu–Liou model has larger spatial resolution. Figure 5 presents the daily mean values of RFs derived from MODTRAN and Fu–Liou calculations for the BB event at the surface, within the atmosphere (RFatm), and at the TOA for clear-sky conditions. Overall, the difference between daily mean values of MODTRAN and Fu–Liou simulations is, on average, close to around 15 %, with all assumed input variables and calculated RFs being lower for the latter (with the exception of RFatm). Differences between MODTRAN and Fu–Liou simulations are vastly connected with slightly different aerosol optical properties. Considering that for each model, different resolutions of input parameters over the slightly distinct area were used, the authors consider the obtained accuracy to be fairly good. Given the fact that RFtoa for all-sky conditions modelled by Fu–Liou is equal to 14.0 W m−2 (not shown) on 10 July, these results are considered exceptional in the Arctic records, being of a similar magnitude to other investigations on high aerosol load events in this region. All-sky RFtoa for the BB transport from Europe in 2006 was estimated between 12 and 0 W m−2 . ## 3.6 3-D effects on RF at the surface in the vicinity of Kongsfjorden In the previous sections, we discussed the RF computed for a single cell, using measurements from Ny-Ålesund as input data. In that approach, called the plane-parallel (PP) approach, the Earth's surface was assumed flat and uniform, and the atmosphere was horizontally uniform. Thus, both topographic effects (shading, slope inclination, etc.) and small-scale (subgrid) variability in surface albedo were neglected. Moreover, net photon transfer between the atmospheric column over the cell and the adjacent atmosphere was assumed zero. In this section, however, the above effects are taken into consideration. 3-D geometry and 3-D Monte Carlo simulations of radiative transfer were used to analyse RF surface variability and thus, uncertainty resulting from single-cell radiative transfer schemes in the vicinity of Konsfjorden. The simulations were performed for a single wavelength λ=469nm and the solar position for the time of the retrieval of the aerosol properties profile (10 July 2015 11:30 UTC; solar zenith angle = 57, solar azimuth = 173). We performed two simulations, one with and one without 3-D effects. In the former simulation we used the 3-D Monte Carlo code with the “real” topography (the real surface reflective properties, changeable within the domain). In this approach photons can travel freely in the 3-D atmosphere. In the simulation without 3-D effects, RF was computed using the plane-parallel geometry for each of the individual 200 m cells/columns. In this method the Earth's surface is assumed flat, horizontally within each column but both the land elevation and the reflective properties of the surface vary from cell to cell. Further to this, the atmospheric columns are independent from each other, i.e. horizontal photon exchange between columns is neglected; thereby neither optical properties of the surface and atmosphere nor topography of adjacent cells influence surface radiative forcing in a given column. Using the plane-parallel approach for RF computations for a single atmospheric column or for a group of columns may lead to biased results. Figure 6A comparison of the RFrel spatial variability at the Earth's surface derived from the 3-D Monte Carlo model (a) with RF${}_{\mathrm{rel}}^{\mathrm{pp}}$ spatial variability (b) computed, applying the Monte Carlo model with plane-parallel geometry to each column independently. In panel (b) both the surface topography and photon exchange between adjacent columns are neglected. Computations for λ=469nm, solar zenith angle = 57, solar azimuth = 173, and aerosol properties of 10 July 2015, 11:30 UTC. Table 3Mean relative radiative forcing RF calculated concerning the actual surface, RFrel, and the horizontal cell surface RF${}_{\mathrm{rel}}^{\mathrm{cell}}$ using the 3-D Monte Carlo model. RF${}_{\mathrm{rel}}^{\mathrm{pp}}$ is RF computed, using the plane-parallel geometry to each column independently. Computations were done for λ=469 nm, solar zenith angle = 57, solar azimuth = 173, and aerosol properties of the 191st day of 2015. In this section, RF is expressed as a fraction of downward irradiance at the TOA (Eqs. 911). Further in this section, we will skip λ and RFrel, RF${}_{\mathrm{rel}}^{\mathrm{cell}}$ and RF${}_{\mathrm{rel}}^{\mathrm{pp}}$ will denote relative spectral RF, simulated using the 3-D modelling, RFrel (λ=469 nm), RF${}_{\mathrm{rel}}^{\mathrm{cell}}$ (λ=469 nm), and the plane-parallel approach to individual cells, RF${}_{\mathrm{rel}}^{\mathrm{pp}}$ (λ=469 nm). Figure 6 shows the spatial distribution of RFrel (Eq. 10) at the surface and compares it to the distribution derived using the plane-parallel geometry to each column independently. The mean values of RF and the standard deviations are compared in Table 3. In the analysed case, the domain mean values and standard deviation of RFrel is 0.1817 ± 0.1066 for the RF calculated with respect to the real inclined surface (i.e. per unit area of the inclined surface; compare Eqs. 910), and RF${}_{\mathrm{rel}}^{\mathrm{cell}}$ is 0.1875 ± 0.1104 when the RF is calculated with respect to the horizontal cell surface (i.e. per unit area of the cell surface; compare Eq. 11). There is a large difference between the RF over water and land surfaces, which is mainly due to differences in surface albedo between these regions. An absolute value of RF is smaller and weakly variable over the fjord surface, where mean RF${}_{\mathrm{rel}}^{\mathrm{cell}}$ is equal to mean RFrel and reaches 0.2632 ± 0.0092. Its coefficient of variation is 3.5 %. The actual value of RF variability over the sea may be even lower, because the noise of the Monte Carlo method may enhance it. Being a probabilistic technique where photons are traced on their random paths through the atmosphere, Monte Carlo is associated with random noise. The land RF is characterized with both RF${}_{\mathrm{rel}}^{\mathrm{cell}}$ and RFrel less negative mean values of 0.1395 ± 0.1180, and 0.1326 ± 0.1084, respectively, and much stronger surface variability. The respective coefficients of variation are 84.6 and 81.7 %. In our simulation, the variability in RF over the sea is caused by the impact of the surrounding land only. Apart from shading the sky and sun by the orography, the spatial variability in RF and its deviations from the plane-parallel RF values, are caused by positive net horizontal photon transfer from the land area. Horizontal photon transfer due to reflection between the atmosphere and the underlying surface is efficient over bright areas, such as snow-covered land and glaciers. The horizontal distance of the photon transmission outside the bright underlying surface, related to the effective height at which the radiation reflected upward by the Earth's surface, is reflected downward by the atmosphere. The net horizontal transport is observed for both atmospheres, with and without aerosols, but in each case the effective height of reflection is different. An appearance of a dense, low-lying aerosol layer reduces the effective reflection height, and thus the horizontal distance the photons can travel over the fjord; but at the same time, it intensifies the reflectance of the atmosphere, compared to the clean case. Therefore, the gradient in irradiance, with distance from the reflective land, is stronger in the polluted case. The atmosphere without aerosols acts similarly to a very thin cloud located higher over the Earth's surface, while the aerosol layer can be compared to a thicker cloud with its base at a lower height . The main factors influencing RF and its variability over land in the vicinity of Kongsfjorden are reflective properties of the land surface, slope exposition of the sun, and shading of the sun by the mountains. The impact of photons reflected from nearby sunlit slopes and horizontal photon transport due to multiple reflections between the sky and the surface on RF variability are of secondary importance over the land. In the analysed case, the highest magnitude of negative RF was found for sun-facing slopes of white sky albedo (calculated from diffusive component only) of around 0.2. In such places, the effective solar zenith angle is relatively low and a high contribution of the direct solar radiation to the total irradiance results in a substantial reduction in the surface irradiance due to the presence of aerosols; hence, an RFrel of about 0.39. For the slopes that are mainly lit by diffused radiation, the RF is positive, i.e. presence of aerosols increases the amount of radiation absorbed by the surface. In shaded places with the effective solar zenith angle of approximately 90 and white sky albedo of around 0.4, RFrel can be as high as 0.07 in our simulation. Using the plane-parallel approach to RF estimation for individual columns results in an underestimation of the surface variability in the RF, and also results in biased domain mean values of the RF. In the case under study, the mean difference between the more accurate RF for the horizontal cell surface and the RF calculated using the plane-parallel approach, RF${}_{\mathrm{rel}}^{\mathrm{cell}}$ and RF${}_{\mathrm{rel}}^{\mathrm{pp}}$ are 0.0032 ± 0.0699, which is 1.9 % of the mean RF${}_{\mathrm{rel}}^{\mathrm{cell}}$. This, in conversion to daily mean short-wave RF, gives the average error not exceeding 2 W m−2 while using the plane-parallel approach. Thus, it is almost as high as the effect of ωd correction for ambient conditions considered in our study. Additionally, the mean bias is higher for the sea than for the land. However, for individual cells or columns, the variability in deviations from the real value of RF${}_{\mathrm{rel}}^{\mathrm{cell}}$ is much larger for the land, where the standard deviation of the difference RF${}_{\mathrm{rel}}^{\mathrm{cell}}$ RF${}_{\mathrm{rel}}^{\mathrm{pp}}$ equals 63.8 % of the mean RF${}_{\mathrm{rel}}^{\mathrm{cell}}$. The negative bias with the largest magnitude of 0.247 was found for the case of sun-facing slopes discussed above. For shaded inclined areas, the plane-parallel approach seriously underestimates radiative forcing where the mean bias equals 0.233. ## 3.7 Impact of BB aerosol on the atmospheric dynamics ILESs (see Sect. 2.1) performed using the EULAG model indicates an appreciable impact of the BB plume on atmospheric dynamics. Figure 7 presents the development of potential temperature and turbulent kinetic energy (TKE) in a clean simulation (Fig. 7b, c) representing a clear atmosphere, as well as in a polluted simulation (Fig. 7e, f), including effects related to the BB plume. Initial profiles used in the simulations are based on the radio sounding from 10 July 12:00 UTC and the applied heating rates given by $\begin{array}{}\text{(14)}& {r}_{\mathrm{h}}=\frac{\mathrm{1}}{\mathit{\rho }\cdot C}\frac{\partial {F}_{\mathrm{net}}}{\partial z},\end{array}$ whereby ρ is air density and C is a specific heat capacity defined both for short- and long-wave irradiances are obtained from MODTRAN simulations for 10 July 11:30 UTC. The rh profiles for the clean case (Fig. 7a) and the aerosol polluted case (Fig. 7d) both show a thin layer near the surface (z<0.5km) with significant heating: 2.7 and 3.4 K day−1, respectively. Above 0.5 km, the clean case indicates cooling of the atmosphere at a rate of approximately 1 K day−1, while in the polluted case another layer with significant heating is visible between altitudes of 1 and 3.5 km. The heating rate in the lower part of this layer is around 0.2 K day−1, while in the upper part it reaches values of up to 1.8 K day−1. The two simulations have the same initial profile of θ, which is represented by the navy blue lines in Fig. 7b, e. There is a layer between altitudes of 2 and 3 km with a nearly constant initial θ, but in general it decreases with altitude. Due to the stable initial stratification and the lack of strong surface heating, turbulence develops slowly in the performed simulations (see TKE profiles in Fig. 7c, f). After 16 h, a turbulent layer starts to develop near the surface in both simulations. The TKE in this layer reaches values of around 0.1 m2 s−2 and extends up to 0.5 km at the time t=48h. After 24 h, a second turbulent layer starts to develop in the polluted case, at an altitude of approximately 3.4 km. The thickness of this layer increases with time, and at t=48h, it covers altitudes between 2.5 and 4.2 km with maximum TKE values of 0.3 m2 s−2 and updraughts/downdraughts with vertical velocities of around 1 m s−1. By contrast, the flow in the clean case remains almost non-turbulent above 0.5 km, with vertical velocities close to zero throughout the simulation period. In the regions with relatively high TKE, θ becomes nearly constant with altitude, and the polluted simulation indicates that the initially well-mixed layer around z=2.5km expands and moves upwards over time. Figure 7Vertical profiles of applied heating rate rh (a, d), horizontally averaged potential temperature θ (b, e), turbulent kinetic energy TKE (c, f) for simulations of a clean case (a–c), and a polluted case with effects of aerosol load included (d–f). Simulation data are stored at 8 h intervals. Outside the clearly turbulent regions, very little vertical mixing takes place, and the potential temperature is approximately given by $\begin{array}{}\text{(15)}& \mathit{\theta }=\mathit{\theta }\left(\mathrm{0},z\right)+{r}_{\mathrm{h}}\cdot t,\end{array}$ where z symbolizes altitude and t time. The obtained ILES results help us understand the potential effects of a BB plume on atmospheric dynamics on a local scale. Furthermore, the observed local production of turbulence and the associated vertical motion, may in turn affect factors such as cloud cover and the coupling between the surface layer and the plume layer, with potential effects on larger-scale dynamics. Further simulations, including water vapour and cloud condensate, are needed to study such effects in more detail. 4 Conclusions This paper presented the investigation of a strong biomass-burning plume advection, which was observed during 9–11 July 2015 over the European Arctic. In this research study, we focused on the local perturbations in the radiation budget, as well as atmospheric dynamics for the Ny-Ålesund area on Spitsbergen. The discussed biomass-burning aerosol advection was one of the most spectacular in the last 25 years , with all aerosol optical properties typical for the summer conditions enhanced by a factor of more than 10. In particular, mean daily values of aerosol optical depth at 550 nm, precipitable water, and single-scattering albedo exceeded 0.2–0.7, 1.7–2.2 cm, and 0.93–0.97, respectively, according to in situ and photometer data at Ny-Ålesund. Here, we want to underline the most significant outcomes from our investigation: • Simulations with the GEM-AQ model confirmed the source region (Alaskan tundra) and the arrival time at Ny-Ålesund of the biomass-burning plume, indicating a reasonable agreement in the extinction profile when compared to lidar measurements. The apparent underestimation of aerosol loading in the plume may be associated with rather coarse horizontal and vertical resolutions. Also, the large distance from the source region (approximately 4000 km) may have enhanced the uncertainties in the model output. • Retrieved effective radius from in situ measurements of around 0.18 ± 0.02 µm, mean value of single-scattering albedo of 0.96, and an average asymmetry parameter exceeding 0.62 (all at ambient conditions) suggest moderate absorbing properties of the plume. Presented properties are in agreement with the results obtained by , who characterized a various set of smoke optical and microphysical properties retrieved from AERONET stations. Taking into account that BB variables are preferably placed in the lower part of the statistics in , we may conclude that during this prolonged transport, scavenging processes were more efficient. • Lidar profiles indicate the existence of a biomass-burning plume at the level of 0–3.5 km, with a complicated structure of sublayers, limited by a number of (2–5) temperature inversions. A complex vertical variability is also visible in the relative humidity profile. The retrieved ωa profiles vary from 0.92 to 0.97, enhancing with time. The highest values are associated with the bottom part of temperature inversions. • The accuracy of modelled irradiances during the summer background conditions, represented by 09:00–14:00 9 July, is considered sufficient, with deviations from the measured quantities by 2 and 1 % for Fin and Fout, respectively. During the biomass-burning event (14:00 9 July–11:30 11 July) the differences increase to 10 and 5.8 % on average. • We report mean values of modelled RFsurf, RFatm, and RFtoa for the biomass-burning episode under study (14:00 9 July–11:30 11 July), at the levels of 78.9, 47.0, and 31.9 W m−2. The values indicate cooling effects at the surface and the TOA, while RFatm reveals relatively strong heating within the atmosphere. This might be translated up to 2 K day−1 of the heating rate inside the smoke plume (0–3.5 km). Obtained values are consistent with results reported for the similar period, and likely the same solar zenith angles performed by . • An averaged RFEsurf at the smoke event is as high as 125.9 W m${}^{-\mathrm{2}}/{\mathit{\tau }}_{\mathrm{550}}$, indicating higher values in comparison with RFEssurf obtained for wildfires from boreal regions , while for other fire sources it is considerably lower by 12–32 % . The authors believe the main reason for different aerosol intensive properties is the distinct solar zenith angle and a high value of daily mean solar radiation at the TOA during the Arctic summer. • The discrepancies between modelled RFs obtained for MODTRAN and fast Fu–Liou simulations oscillate around 15 %, with lower values usually attributed to the latter, excluding the atmospheric values. Considering different inputs and spatial resolution used for both simulations, the results are satisfactory. • The mean bias of RFs associated with single-cell RF simulations in the vicinity of Kongsfjorden is estimated by the 3-D Monte Carlo model at the level of 2 W m−2. • ILES indicates that the main impact of the BB plume on the atmospheric dynamics is a gradual vertical expansion and positive displacement of the BB layer characterized by neutral stratification. The turbulent kinetic energy in the simulated BB layer is around 0.3 m2 s−2. In a clean simulation, without effects from the BB plume included, the flow remained nearly non-turbulent throughout the simulation period. In this study we have shown that long-range transport of wildfire aerosols from Alaska to the European Arctic certainly has a significant impact on radiative properties. Furthermore, our results also indicate an impact on atmospheric dynamics. We believe that detailed studies on this topic are needed, especially considering the significant positive trend in mid-latitude fire frequency during the summer season over the last 25 years, and therefore possibly more frequent advection over the Arctic region . Data availability Data availability. SP1a and lidar data can be provided by AWI upon request. Pyranometer and meteorological data can be accessed via DOIs https://doi.org/10.1594/PANGAEA.863272 and https://doi.org/10.1594/PANGAEA.863270 respectively. All in situ data (PSAP, M903, SMPS, and APS), however, are available upon request to ISAC-CNR. Competing interests Competing interests. The authors declare that they have no conflict of interest. Acknowledgements Acknowledgements. The authors are grateful for support from Marion Matturilli for providing data from the Baseline Surface Radiation Network (BSRN), measured at AWIPEV station at Ny-Ålesund. We acknowledge Alison Smuts-Simons for the scientific English proof reading of this paper. The authors would like to acknowledge the support of this research from the Polish-Norwegian Research Programme, operated by the National Centre for Research and Development under the Norwegian Financial Mechanism 2009–2014, within the frame of project contract no. Pol-Nor/196911/38/2013. The EULAG simulations were performed at the Interdisciplinary Centre for Mathematical and Computational Modelling (ICM), University of Warsaw, under grant number G64–5. Edited by: Bryan N. Duncan Reviewed by: two anonymous referees References Alexandrov, M. D., Marshak, A., Cairns, B., Lacis, A. 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Phys., 11, 2603–2624, https://doi.org/10.5194/acp-11-2603-2011, 2011. a, b	2019-08-25 17:03:08	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 66, "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": 0.798263669013977, "perplexity": 5279.58814445155}, "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-2019-35/segments/1566027330750.45/warc/CC-MAIN-20190825151521-20190825173521-00198.warc.gz"}
https://www.neetprep.com/question/71578-gas-filled-cylinder-its-temperature-increased--Kelvinscale-volume-reduced--percentage-gas-will-leak----/126-Physics--Kinetic-Theory-Gases/688-Kinetic-Theory-Gases	# NEET Physics Kinetic Theory of Gases Questions Solved A gas is filled in a cylinder, its temperature is increased by 20% on Kelvin scale and volume is reduced by 10%. How much percentage of the gas will leak out 1. 30% 2. 40% 3. 15% 4. 25% Difficulty Level: • 17% • 17% • 13% • 55% Crack NEET with Online Course - Free Trial (Offer Valid Till September 21, 2019)	2019-09-19 00:02:47	{"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": 0.8109226226806641, "perplexity": 7287.19825208779}, "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-2019-39/segments/1568514573385.29/warc/CC-MAIN-20190918234431-20190919020431-00268.warc.gz"}
https://imathworks.com/tex/tex-latex-what-does-the-following-error-message-mean-undefined-control-sequence-keywords-l-4319-processkeyvaloptionshyp/	[Tex/LaTex] What does the following error message mean? Undefined control sequence. \@Keywords l.4319 \ProcessKeyvalOptions{Hyp} errorshyperref I got the following error message (Setup: Ububtu 14 LTS, TeXmaker, TeX Live 2013/Debian, pdfLaTeX): log-file says: ! Undefined control sequence. <argument> \@Keywords l.4319 \ProcessKeyvalOptions{Hyp} The control sequence at the end of the top line of your error message was never \def'ed. hyperref.sty says: \ProcessKeyvalOptions{Hyp} \def\Hy@xspace@end{} \Hy@AtBeginDocument{% }{% \def\Hy@xspace@end{% \ltx@gobble{end for xspace}% }% }% }% }% } Any idea what it means? MWE: \RequirePackage[patch]{kvoptions} \documentclass{DissOnlineLatex} %\usepackage[ngerman]{babel} \usepackage[T1]{fontenc} \usepackage{lscape} \usepackage{setspace} \usepackage[style=chem-angew,backend=bibtex8,]{biblatex} \usepackage{hyperref} \usepackage[printonlyused]{acronym} \bibliography{Literatur.bib} \onehalfspacing \begin{document} \end{document} The error messages means, that \@Keywords is undefined. \@Keywords is only defined by the class DissOnlineLatex, if \Keywords is used: \newcommand*{\Keywords}[1]{\gdef\@Keywords{#1}} \Keywords is invoked at the end of metadata.tex and should not be deleted. Set the appropriate keywords there.	2022-12-08 23:17:38	{"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": 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": 0.8225047588348389, "perplexity": 13648.454061703987}, "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-2022-49/segments/1669446711368.1/warc/CC-MAIN-20221208215156-20221209005156-00152.warc.gz"}
https://math.stackexchange.com/questions/1819980/relation-of-relative-numbers-of-restricted-ways-to-distribute-identical-dist	# Relation of relative numbers of (restricted) ways to distribute identical / distinct objects into distinct bins If want to know if the following inequality holds for general values of $s \leq n \ll m$. $$\frac{C_0(n,m,s)}{C_0(n,m)} \leq \frac{p(n,m,s)}{m^n}$$ $C_0(n,m) = \binom{n+m-1}{m-1}$ is the number of weak integer compositions of $n$ into $m$ parts (without restriction). In other words, it's the number of ways to distribute $n$ identical objects into $m$ distinct bins. $C_0(n,m,s) = \sum_{j=0}^m (-1)^j \binom{m}{j}\binom{n+m-j(s+1)-1}{m-1}$ is the number of weak integer compositions of $n$ into $m$ parts with restricted part size $s$. In other words, it's the number of ways to distribute $n$ identical objects into $m$ distinct bins, where each bin has capacity $s$. $m^n$ is the number of strings of length $n$ over an alphabet of $m$ symbols. In other words, it's the number of ways to distribute $n$ distinct objects into $m$ distinct bins. $p(n,m,s) = n![z^n]\left(\sum_{j=0}^s \frac{z^j}{k!}\right)^m = \sum\limits_{\substack{k_1 + \cdots + k_m=n\\0\leq k_i \leq s}} \binom{n}{k_1\cdots k_m}$ is the number of strings of length $n$ over an alphabet of $m$ symbols, such that each symbol occurs at most $s$ times in each string. In other words, it's the number of ways to distribute $n$ distinct objects into $m$ distinct bins, where each bin has capacity $s$. Is this a known combinatorial problem? Does anyone know a source with the proof or disproof? What might be a suitable approach to prove it? I verified the inequality algorithmically for $2 \leq m \leq 14$ and $1 \leq n \leq \lfloor \frac{m}{2} \rfloor$ and $1 \leq s \leq n$.	2019-07-22 03:34:00	{"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": 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": 0.7614161372184753, "perplexity": 45.428909244301316}, "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-2019-30/segments/1563195527474.85/warc/CC-MAIN-20190722030952-20190722052952-00380.warc.gz"}
https://www.semanticscholar.org/paper/Impact-of-Snow-and-Ground-Interference-on-Electric-Heidari-Gwamuri/35283ae5f3ebbdaaf0104e2044edfd018e0c032e	# Impact of Snow and Ground Interference on Photovoltaic Electric System Performance @article{Heidari2015ImpactOS, title={Impact of Snow and Ground Interference on Photovoltaic Electric System Performance}, author={Negin Heidari and Jephias Gwamuri and Timothy U. Townsend and Joshua M. Pearce}, journal={IEEE Journal of Photovoltaics}, year={2015}, volume={5}, pages={1680-1685} } Assessing snow-related energy losses is necessary for accurate predictions of photovoltaic (PV) performance. A PV test platform with seven portrait-oriented modules placed at four tilt angles (0°, 15°, 30°, and 45°) was installed in Calumet, MI, USA, to measure the energy loss in this snowy climate. As a best-case snow-shedding configuration, similar to a carport or a plain sloped roof, three of the test modules were rack-mounted high enough to prevent surface interference. The opposite effect… Expand #### Figures and Tables from this paper Identifying snow in photovoltaic monitoring data for improved snow loss modeling and snow detection • Environmental Science • Solar Energy • 2021 Abstract As cost reductions have made photovoltaics (PV) a favorable choice also in colder climates, the number of PV plants in regions with snowfalls is increasing rapidly. Snow coverage on the PVExpand An experimental investigation of snow removal from photovoltaic solar panels by electrical heating • Materials Science • 2018 Abstract A key challenge to the wide-scale implementation of photovoltaic solar panels (PV) in cold and remote areas is dealing with the effects of snow and ice buildup on the panel surfaces. In thisExpand Modeling of Snow-Covered Photovoltaic Modules • Environmental Science, Computer Science • IEEE Transactions on Industrial Electronics • 2018 A novel PV modeling approach that can represent instantaneous electrical characteristics of PV modules in the presence of uniform snow coverage is proposed that would be helpful for researchers and PV systems developers in cold regions. Expand Performance modeling and valuation of snow-covered PV systems: examination of a simplified approach to decrease forecasting error • Computer Science, Medicine • Environmental Science and Pollution Research • 2018 A new, simplified approach to decrease snow-related forecasting error, in comparison to current solar energy performance models is proposed to allow model designers, and ultimately users, the opportunity to better understand the return on investment for solar energy systems located in snowy environments. Expand Image Analysis Method for Quantifying Snow Losses on PV Systems • Environmental Science • 2020 47th IEEE Photovoltaic Specialists Conference (PVSC) • 2020 Modeling and predicting snow-related power loss is important to economic calculations, load management and system optimization for all scales of photovoltaic (PV) power plants. This paper describes aExpand Evaluation of removing snow and ice from photovoltaic-thermal (PV/T) panels by circulating hot water • Environmental Science • Solar Energy • 2019 Abstract Photovoltaic-thermal (PV/T) systems can generate thermal and electrical energy by using solar radiation. The production and implementation cost of PV/T systems has decreased continuouslyExpand The effect of snowfall and icing on the sustainability of the power output of agrid-connected photovoltaic system in Konya, Turkey • Computer Science, Environmental Science • Turkish J. Electr. Eng. Comput. Sci. • 2019 The results showed that surface clearing of modules had a significant positive effect on the power output of the system and the total energy loss of the plant varies between 1 % and 2 %. Expand Snow-Induced PV Loss Modeling Using Production-Data Inferred PV System Models • Environmental Science • 2021 Snow-induced photovoltaic (PV)-energy losses (snow losses) in snowy and cold locations vary up to 100% monthly and 34% annually, according to literature. Levels that illustrate the need for snow lossExpand A Study on the Performance of PV Modules in Snowy Conditions Considering Orientation of Modules • Environmental Science, Computer Science • 2020 IEEE Canadian Conference on Electrical and Computer Engineering (CCECE) • 2020 In the present study, a snow-covered PV module is modeled using MATLAB/Simulink software considering the snow sliding as the snow removal process and a commercial PV module with three bypass diodes is modeled and its performance is investigated in snowy conditions considering portrait and landscape orientations. Expand Performance Investigation of Roof-Mounted PV Systems in Snowy Conditions Considering Snow Coverage and Snow Removal Process • 2020 IEEE Power & Energy Society General Meeting (PESGM) • 2020 In this paper, the performance of a roof-mounted Photovoltaic (PV) system is investigated in snowy conditions using a model that considers snow coverage and snow removal process. A $5 \times 5$Expand #### References SHOWING 1-10 OF 46 REFERENCES The Effects of Snowfall on Solar Photovoltaic Performance • Environmental Science • 2013 Abstract Solar photovoltaic (PV) systems are frequently installed in climates with significant snowfall. To better understand the effects of snowfall on the performance of PV systems, a multi-angle,Expand Photovoltaics and snow: An update from two winters of measurements in the SIERRA • Physics • 2011 37th IEEE Photovoltaic Specialists Conference • 2011 With snowy locations becoming common for large photovoltaic (PV) installations, analytical models are now needed to estimate the impact of snow on energy production. A generalized monthly snow lossExpand Measuring and modeling the effect of snow on photovoltaic system performance • Physics • 2010 35th IEEE Photovoltaic Specialists Conference • 2010 Today's demanding project financing climate requires developers to hone annual photovoltaic (PV) energy estimates with unprecedented accuracy — and to back the estimates with meaningful long-termExpand Snow-covering effects on the power output of solar photovoltaic arrays In general, snow covering a photovoltaic panel causes negligible energy loss when the snow is light and melts easily; however, a more serious loss can occur when the snow is heavy and does notExpand A new method to determine the effects of hydrodynamic surface coatings on the snow shedding effectiveness of solar photovoltaic modules • Environmental Science • 2013 Abstract As solar photovoltaic (PV) installations have become more common in regions that experience substantial snowfall, losses in energy production due to snow coverage have grown in concern.Expand Prediction of energy effects on photovoltaic systems due to snowfall events • Environmental Science • 2012 38th IEEE Photovoltaic Specialists Conference • 2012 The accurate prediction of yields from photovoltaic systems (PV) is critical for their proper operation and financing, and in northern latitudes the effects of snowfall on yield can becomeExpand Impact of dust on solar photovoltaic (PV) performance: Research status, challenges and recommendations • Engineering • 2010 The peaking of most oil reserves and impending climate change are critically driving the adoption of solar photovoltaic's (PV) as a sustainable renewable and eco-friendly alternative. OngoingExpand Estimating the uncertainty in long-term photovoltaic yield predictions • Physics • 2013 Abstract The uncertainty in long-term photovoltaic (PV) system yield predictions was examined by statistical modeling of a hypothetical 10 MW AC, c-Si photovoltaic system in Toronto, Canada. The goalExpand A Low Cost Method of Snow Detection on Solar Panels and Sending Alerts • Environmental Science • 2015 Photovoltaic systems are often installed in climates with considerable amount of snowfall and freezing rain in winter. It has been observed that the snow accumulation on a solar panel affects itsExpand Life Cycle Analysis to estimate the environmental impact of residential photovoltaic systems in regions with a low solar irradiation • Engineering • 2011 Photovoltaic installations (PV-systems) are heavily promoted in Europe. In this paper, the Life Cycle Analysis (LCA) method is used to find out whether the high subsidy cost can be justified by theExpand	2021-10-23 15:45:25	{"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": 0.38288500905036926, "perplexity": 7845.5613613434}, "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/1634323585696.21/warc/CC-MAIN-20211023130922-20211023160922-00239.warc.gz"}
http://www.sawaal.com/hcf-and-lcm-problems-questions-and-answers/if-the-sum-of-two-numbers-is-55-and-the-hcf-and-lcm-of-these-numbers-are-5-and-120-respectively-then_5240	10 Q: # If the sum of two numbers is 55 and the H.C.F. and L.C.M. of these numbers are 5 and 120 respectively, then the sum of the reciprocals of the numbers is equal to: A) 55/601 B) 601/55 C) 11/120 D) 120/11 Explanation: Let the numbers be a and b. Then, a + b = 55 and ab = 5 x 120 = 600. The required sum =$\inline \fn_jvn \frac{1}{a}+\frac{1}{b}$ = $\inline \fn_jvn \frac{a+b}{ab}$$\inline \fn_jvn \frac{55}{600}$=$\inline \fn_jvn \frac{11}{120}$ Q: A drink vendor has 368 liters of Maaza, 80 liters of Pepsi and 144 liters of Sprite. He wants to pack them in cans, so that each can contains the same number of liters of a drink, and doesn't want to mix any two drinks in a can. What is the least number of cans required ? A) 47 B) 46 C) 37 D) 35 Explanation: The number of liters in each can = HCF of 80, 144 and 368 = 16 liters. Number of cans of Maaza = 368/16 = 23 Number of cans of Pepsi = 80/16 = 5 Number of cans of Sprite = 144/16 = 9 The total number of cans required = 23 + 5 + 9 = 37 cans. 4 50 Q: H.C.F of 4 x 27 x 3125, 8 x 9 x 25 x 7 and 16 x 81 x 5 x 11 x 49 is : A) 360 B) 180 C) 90 D) 120 Explanation: 4 x 27 x 3125 = $\inline \fn_jvn \small 2^{2}x3^{3}x5^{5}$ ; 8 x 9 x 25 x 7 = $\inline \fn_jvn \small 2^{3}x3^{2}x5^{2}x7$ 16 x 81 x 5 x 11 x 49 = $\inline \fn_jvn \small 2^{4}x3^{4}x5x7^{2}x11$ H.C.F = $\inline \fn_jvn \small 2^{2}x3^{2}x5$ = 180. 1 68 Q: The difference of two numbers is 14. Their LCM and HCF are 441 and 7. Find the two numbers ? A) 63 and 49 B) 64 and 48 C) 62 and 46 D) 64 and 49 Explanation: Since their HCFs are 7, numbers are divisible by 7 and are of the form 7x and 7y Difference = 14 => 7x - 7y = 14 => x - y = 2 product of numbers = product of their hcf and lcm => 7x * 7y = 441 * 7 => x * y = 63 Now, we have x * y = 63 , x - y = 2 => x = 9 , y = 7 The numbers are 7x and 7y => 63 and 49 3 209 Q: If the sum of two numbers is 55 and the H.C.F. and L.C.M. of these numbers are 5 and 120 respectively, then the sum of the reciprocals of the numbers is equal to ? A) 13/125 B) 14/57 C) 11/120 D) 16/41 Explanation: Let the numbers be a and b. We know that product of two numbers = Product of their HCF and LCM Then, a + b = 55 and ab = 5 x 120 = 600. => The required sum = (1/a) + (1/b) = (a+b)/ab =55/600 = 11/120 3 198 Q: The largest measuring cylinder that can accurately fill 3 tanks of capacity 98, 182 and 266 litres each, is of capacity ? A) 7 lts B) 14 lts C) 98 lts D) 42 lts Explanation: To know the the measuring cylinder that can fill all the given capacities , they must be divisible by the required number. 98,182,266 all are divisible by 14 So 14 litres is the largest cylinder that can fill all the given cylinders. (or) The other method is take HCF of all given capacities i.e 98, 182 and 266.	2017-05-25 19:59:50	{"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 8, "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": 0.7214752435684204, "perplexity": 1228.5322604465375}, "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-2017-22/segments/1495463608416.96/warc/CC-MAIN-20170525195400-20170525215400-00474.warc.gz"}
https://www.aimsciences.org/article/doi/10.3934/fmf.2021004?viewType=html	# American Institute of Mathematical Sciences March 2022, 1(1): 99-135. doi: 10.3934/fmf.2021004 ## Multilayer heat equations: Application to finance 1 Tandon School of Engineering, New York University, 1 Metro Tech Center, 10th floor, Brooklyn NY, USA 2 Connection Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA 3 The Jerusalem School of Business Administration, The Hebrew University of Jerusalem, Jerusalem, Israel 4 Moscow State University, Moscow, Russia * Corresponding author: Andrey Itkin Received February 2021 Revised June 2021 Published March 2022 Early access June 2021 Fund Project: Dmitry Muravey acknowledges support by the Russian Science Foundation under the Grant number 20-68-47030 In this paper, we develop a Multilayer (ML) method for solving one-factor parabolic equations. Our approach provides a powerful alternative to the well-known finite difference and Monte Carlo methods. We discuss various advantages of this approach, which judiciously combines semi-analytical and numerical techniques and provides a fast and accurate way of finding solutions to the corresponding equations. To introduce the core of the method, we consider multilayer heat equations, known in physics for a relatively long time but never used when solving financial problems. Thus, we expand the analytic machinery of quantitative finance by augmenting it with the ML method. We demonstrate how one can solve various problems of mathematical finance by using our approach. Specifically, we develop efficient algorithms for pricing barrier options for time-dependent one-factor short-rate models, such as Black-Karasinski and Verhulst. Besides, we show how to solve the well-known Dupire equation quickly and accurately. Numerical examples confirm that our approach is considerably more efficient for solving the corresponding partial differential equations than the conventional finite difference method by being much faster and more accurate than the known alternatives. Citation: Andrey Itkin, Alexander Lipton, Dmitry Muravey. Multilayer heat equations: Application to finance. Frontiers of Mathematical Finance, 2022, 1 (1) : 99-135. doi: 10.3934/fmf.2021004 ##### References: [1] M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, Dover Publications, Inc., 1964. Google Scholar [2] L. Andersen and V. Piterbarg, Interest Rate Modeling, no. v. 2 in Interest Rate Modeling, Atlantic Financial Press, 2010. Google Scholar [3] A. Antonov and M. Spector, General short-rate analytics, Risk, 66–71. Google Scholar [4] M. Asvestas, A. G. Sifalakis, E. P. Papadopoulou and Y. G. Saridakis, Fokas method for a multi-domain linear reaction-diffusion equation with discontinuous diffusivity, Journal of Physics: Conference Series, 490 (2014), 012143. doi: 10.1088/1742-6596/490/1/012143. Google Scholar [5] N. Bacaër, A short history of mathematical population dynamics, Springer-Verlag, London, chapter 6, (2011), 35–39. doi: 10.1007/978-0-85729-115-8. Google Scholar [6] F. Black and P. Karasinski, Bond and option pricing when short rates are lognormal, Financial Analysts Journal, 47 (1991), 52-59. doi: 10.2469/faj.v47.n4.52. Google Scholar [7] D. Brigo and F. Mercurio, Interest Rate Models – Theory and Practice with Smile, Inflation and Credit, 2nd edition, Springer Verlag, 2006. Google Scholar [8] P. Carr and A. Itkin, Geometric local variance gamma model, The Journal of Derivatives Winter, 27 (2019), 7-30. doi: 10.3905/jod.2019.1.084. Google Scholar [9] P. Carr and A. Itkin, An expanded local variance gamma model. Google Scholar [10] P. Carr and A. Itkin, Semi-closed form solutions for barrier and American options written on a time-dependent Ornstein Uhlenbeck process, Journal of Derivatives, Fall. Google Scholar [11] P. Carr, A. Itkin and D. Muravey, Semi-closed form prices of barrier options in the time-dependent cev and cir models, Journal of Derivatives, 28 (2020), 26-50. Google Scholar [12] E. J. Carr and N. G. March, Semi-analytical solution of multilayer diffusion problems with time-varying boundary conditions and general interface conditions, Appl. Math. Comput., 333 (2018), 286-303. doi: 10.1016/j.amc.2018.03.095. Google Scholar [13] P. Carr and S. Nadtochiy, Local variance gamma and explicit calibration to option prices, Math. Finance, 27 (2017), 151-193. doi: 10.1111/mafi.12086. Google Scholar [14] M. Craddock, Fundamental solutions, transition densities and the integration of Lie symmetries, J. Differential Equations, 246 (2009), 2538-2560. doi: 10.1016/j.jde.2008.10.017. Google Scholar [15] C. Dias, A method of recursive images to solve transient heat diffusionin multilayer materials, 85, 1075–1083. Google Scholar [16] B. Dupire, Pricing with a smile, Risk, 7 (1994), 18-20. Google Scholar [17] G. E. Fasshauer, A. Q. M. Khaliq and D. A. Voss, Using meshfree approximation for multi-asset American option problems, J. Chinese Inst. Engrs., 27 (2004), 563-571. Google Scholar [18] J.-S. Giet, P. Vallois and S. Wantz-Mézieres, The logistic S.D.E., Theory Stoch. Process., 20 (2015), 28-62. Google Scholar [19] Y. C. Hon and X. Z. Mao, A radial basis function method for solving options pricing model, Financial Engineering, 8 (1999), 31-49. Google Scholar [20] B. Horvath, A. Jacquier and C. Turfus, Analytic option prices for the black-karasinski short rate model, 2017, URL https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3253833, SSRN: 3253833. Google Scholar [21] J. Hull, Options, Futures, and Other Derivatives, 8th edition, Prentice Hall, 2011. Google Scholar [22] A. Itkin, Pricing Derivatives Under Lévy Models, 1st edition, no. 12 in Pseudo-Differential Operators, Birkhäuser, Basel, 2017. doi: 10.1007/978-1-4939-6792-6. Google Scholar [23] A. Itkin, Fitting Local Volatility: Analytic and Numerical Approaches in Black-Scholes and Local Variance Gamma Models, 11623, World Scientific Publishing Co. Pte. Ltd., 2020. doi: 10.1142/11623. Google Scholar [24] A. Itkin and A. Lipton, Filling the gaps smoothly, J. Comput. Sci., 24 (2018), 195-208. doi: 10.1016/j.jocs.2017.02.003. Google Scholar [25] A. Itkin, A. Lipton and D. Muravey, From the black-karasinski to the verhulst model to accommodate the unconventional fed's policy, 2020, URL https://arXiv.org/abs/2006.11976. Google Scholar [26] A. Itkin and D. Muravey, Semi-analytic pricing of double barrier options with time-dependent barriers and rebates at hit, 2020, URL https://arXiv.org/abs/2009.09342. Google Scholar [27] A. Itkin and D. Muravey, Semi-closed form prices of barrier options in the Hull-White model, Risk. Google Scholar [28] E. M. Kartashov, Analytical methods for solution of non-stationary heat conductance boundary problems in domains with moving boundaries, Izvestiya RAS, Energetika, 133–185. Google Scholar [29] E. Kartashov, Analytical Methods in the Theory of Heat Conduction in Solids, Vysshaya Shkola, Moscow, 2001. Google Scholar [30] A. Kuznetsov, On the convergence of the Gaver-Stehfest algorithm, SIAM J. Numer. Anal., 51 (2013), 2984-2998. doi: 10.1137/13091974X. Google Scholar [31] P. Lançon, G. Batrouni, L. Lobry and N. Ostrowsky, Drift without flux: Brownian walker with a space-dependent diffusion coefficient, Europhysics Letters (EPL), 54 (2001), 28–34. Google Scholar [32] A. Lejay, On the constructions of the skew Brownian motion, Probab. Surv., 3 (2006), 413-466. doi: 10.1214/154957807000000013. Google Scholar [33] J. Lienhard IV and J. Lienhard V, A Heat Transfer Textbook, 5th edition, Phlogiston Press, Cambridge, MA, 2019. Google Scholar [34] A. Lipton, Mathematical Methods for Foreign Exchange: A Financial Engineer's Approach, World Scientific Publishing Co., Inc., River Edge, NJ, 2001. doi: 10.1142/4694. Google Scholar [35] A. Lipton and M. L. de Prado, A closed-form solution for optimal mean-reverting trading strategies, Risk, Available at SSRN, (2020), 32pp. doi: 10.2139/ssrn.3534445. Google Scholar [36] A. Lipton and V. Kaushansky, On the first hitting time density for a reducible diffusion process, Quant. Finance, 20 (2020), 723-743. doi: 10.1080/14697688.2020.1713394. Google Scholar [37] A. Lipton and V. Kaushansky, On three important problems in mathematical finance, The Journal of Derivatives. Special Issue, 28. Google Scholar [38] A. Lipton and A. Sepp, Filling the gaps, Risk Magazine, 86–91. Google Scholar [39] D. Mumford, C. M. M. Nori, E. Previato and M. Stillman, Tata Lectures on Theta, Progress in Mathematics, Birkhäuser Boston, 1984. doi: 10.1007/978-0-8176-4578-6. Google Scholar [40] O. A. Ole${{\rm{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}} \over i} }}}$nik and E. V. Radkevič, Second Order Equations with Non-Negative Characteristic Form, Plenum Press, New York-London, 1973. Google Scholar [41] U. Pettersson, E. Larsson, G. Marcusson and J. Persson, Improved radial basis function methods for multi-dimensional option pricing, J. Comput. Appl. Math., 222 (2008), 82-93. doi: 10.1016/j.cam.2007.10.038. Google Scholar [42] A. D. Polyanin, Handbook of Linear Partial Differential Equations for Engineers and Scientists, Chapman & Hall/CRC, 2002. Google Scholar [43] G. Pontrelli, M. Lauricella, J. A. Ferreira and G. Pena, Iontophoretic transdermal drug delivery: A multi-layered approach, Math. Med. Biol., 34 (2017), 559-576. doi: 10.1093/imammb/dqw017. Google Scholar [44] B. Stehlíková and L. Capriotti, An Effective Approximation for Zero-Coupon Bonds and Arrow-Debreu Prices in the Black-Karasinski Model, Int. J. Theor. Appl. Finance, 17 (2014), 1450037, 16 pp. doi: 10.1142/S021902491450037X. Google Scholar [45] A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics, Pergamon Press, Oxford, 1963. Google Scholar [46] C. Turfus, Analytic swaption pricing in the black-karasinski model, 2020, URL https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3253866, SSRN: 3253866. Google Scholar [47] P. Verhulst, Notice sur la loi que la population suit dans son accroisseement, Correspondance Mathematique et Physique, 10 (1838), 113-121. Google Scholar show all references ##### References: [1] M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, Dover Publications, Inc., 1964. Google Scholar [2] L. Andersen and V. Piterbarg, Interest Rate Modeling, no. v. 2 in Interest Rate Modeling, Atlantic Financial Press, 2010. Google Scholar [3] A. Antonov and M. Spector, General short-rate analytics, Risk, 66–71. Google Scholar [4] M. Asvestas, A. G. Sifalakis, E. P. Papadopoulou and Y. G. Saridakis, Fokas method for a multi-domain linear reaction-diffusion equation with discontinuous diffusivity, Journal of Physics: Conference Series, 490 (2014), 012143. doi: 10.1088/1742-6596/490/1/012143. Google Scholar [5] N. Bacaër, A short history of mathematical population dynamics, Springer-Verlag, London, chapter 6, (2011), 35–39. doi: 10.1007/978-0-85729-115-8. Google Scholar [6] F. Black and P. Karasinski, Bond and option pricing when short rates are lognormal, Financial Analysts Journal, 47 (1991), 52-59. doi: 10.2469/faj.v47.n4.52. Google Scholar [7] D. Brigo and F. Mercurio, Interest Rate Models – Theory and Practice with Smile, Inflation and Credit, 2nd edition, Springer Verlag, 2006. Google Scholar [8] P. Carr and A. Itkin, Geometric local variance gamma model, The Journal of Derivatives Winter, 27 (2019), 7-30. doi: 10.3905/jod.2019.1.084. Google Scholar [9] P. Carr and A. Itkin, An expanded local variance gamma model. Google Scholar [10] P. Carr and A. Itkin, Semi-closed form solutions for barrier and American options written on a time-dependent Ornstein Uhlenbeck process, Journal of Derivatives, Fall. Google Scholar [11] P. Carr, A. Itkin and D. Muravey, Semi-closed form prices of barrier options in the time-dependent cev and cir models, Journal of Derivatives, 28 (2020), 26-50. Google Scholar [12] E. J. Carr and N. G. March, Semi-analytical solution of multilayer diffusion problems with time-varying boundary conditions and general interface conditions, Appl. Math. Comput., 333 (2018), 286-303. doi: 10.1016/j.amc.2018.03.095. Google Scholar [13] P. Carr and S. Nadtochiy, Local variance gamma and explicit calibration to option prices, Math. Finance, 27 (2017), 151-193. doi: 10.1111/mafi.12086. Google Scholar [14] M. Craddock, Fundamental solutions, transition densities and the integration of Lie symmetries, J. Differential Equations, 246 (2009), 2538-2560. doi: 10.1016/j.jde.2008.10.017. Google Scholar [15] C. Dias, A method of recursive images to solve transient heat diffusionin multilayer materials, 85, 1075–1083. Google Scholar [16] B. Dupire, Pricing with a smile, Risk, 7 (1994), 18-20. Google Scholar [17] G. E. Fasshauer, A. Q. M. Khaliq and D. A. Voss, Using meshfree approximation for multi-asset American option problems, J. Chinese Inst. Engrs., 27 (2004), 563-571. Google Scholar [18] J.-S. Giet, P. Vallois and S. Wantz-Mézieres, The logistic S.D.E., Theory Stoch. Process., 20 (2015), 28-62. Google Scholar [19] Y. C. Hon and X. Z. Mao, A radial basis function method for solving options pricing model, Financial Engineering, 8 (1999), 31-49. Google Scholar [20] B. Horvath, A. Jacquier and C. Turfus, Analytic option prices for the black-karasinski short rate model, 2017, URL https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3253833, SSRN: 3253833. Google Scholar [21] J. Hull, Options, Futures, and Other Derivatives, 8th edition, Prentice Hall, 2011. Google Scholar [22] A. Itkin, Pricing Derivatives Under Lévy Models, 1st edition, no. 12 in Pseudo-Differential Operators, Birkhäuser, Basel, 2017. doi: 10.1007/978-1-4939-6792-6. Google Scholar [23] A. Itkin, Fitting Local Volatility: Analytic and Numerical Approaches in Black-Scholes and Local Variance Gamma Models, 11623, World Scientific Publishing Co. Pte. Ltd., 2020. doi: 10.1142/11623. Google Scholar [24] A. Itkin and A. Lipton, Filling the gaps smoothly, J. Comput. Sci., 24 (2018), 195-208. doi: 10.1016/j.jocs.2017.02.003. Google Scholar [25] A. Itkin, A. Lipton and D. Muravey, From the black-karasinski to the verhulst model to accommodate the unconventional fed's policy, 2020, URL https://arXiv.org/abs/2006.11976. Google Scholar [26] A. Itkin and D. Muravey, Semi-analytic pricing of double barrier options with time-dependent barriers and rebates at hit, 2020, URL https://arXiv.org/abs/2009.09342. Google Scholar [27] A. Itkin and D. Muravey, Semi-closed form prices of barrier options in the Hull-White model, Risk. Google Scholar [28] E. M. Kartashov, Analytical methods for solution of non-stationary heat conductance boundary problems in domains with moving boundaries, Izvestiya RAS, Energetika, 133–185. Google Scholar [29] E. Kartashov, Analytical Methods in the Theory of Heat Conduction in Solids, Vysshaya Shkola, Moscow, 2001. Google Scholar [30] A. Kuznetsov, On the convergence of the Gaver-Stehfest algorithm, SIAM J. Numer. Anal., 51 (2013), 2984-2998. doi: 10.1137/13091974X. Google Scholar [31] P. Lançon, G. Batrouni, L. Lobry and N. Ostrowsky, Drift without flux: Brownian walker with a space-dependent diffusion coefficient, Europhysics Letters (EPL), 54 (2001), 28–34. Google Scholar [32] A. Lejay, On the constructions of the skew Brownian motion, Probab. Surv., 3 (2006), 413-466. doi: 10.1214/154957807000000013. Google Scholar [33] J. Lienhard IV and J. Lienhard V, A Heat Transfer Textbook, 5th edition, Phlogiston Press, Cambridge, MA, 2019. Google Scholar [34] A. Lipton, Mathematical Methods for Foreign Exchange: A Financial Engineer's Approach, World Scientific Publishing Co., Inc., River Edge, NJ, 2001. doi: 10.1142/4694. Google Scholar [35] A. Lipton and M. L. de Prado, A closed-form solution for optimal mean-reverting trading strategies, Risk, Available at SSRN, (2020), 32pp. doi: 10.2139/ssrn.3534445. Google Scholar [36] A. Lipton and V. Kaushansky, On the first hitting time density for a reducible diffusion process, Quant. Finance, 20 (2020), 723-743. doi: 10.1080/14697688.2020.1713394. Google Scholar [37] A. Lipton and V. Kaushansky, On three important problems in mathematical finance, The Journal of Derivatives. Special Issue, 28. Google Scholar [38] A. Lipton and A. Sepp, Filling the gaps, Risk Magazine, 86–91. Google Scholar [39] D. Mumford, C. M. M. Nori, E. Previato and M. Stillman, Tata Lectures on Theta, Progress in Mathematics, Birkhäuser Boston, 1984. doi: 10.1007/978-0-8176-4578-6. Google Scholar [40] O. A. Ole${{\rm{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}} \over i} }}}$nik and E. V. Radkevič, Second Order Equations with Non-Negative Characteristic Form, Plenum Press, New York-London, 1973. Google Scholar [41] U. Pettersson, E. Larsson, G. Marcusson and J. Persson, Improved radial basis function methods for multi-dimensional option pricing, J. Comput. Appl. Math., 222 (2008), 82-93. doi: 10.1016/j.cam.2007.10.038. Google Scholar [42] A. D. Polyanin, Handbook of Linear Partial Differential Equations for Engineers and Scientists, Chapman & Hall/CRC, 2002. Google Scholar [43] G. Pontrelli, M. Lauricella, J. A. Ferreira and G. Pena, Iontophoretic transdermal drug delivery: A multi-layered approach, Math. Med. Biol., 34 (2017), 559-576. doi: 10.1093/imammb/dqw017. Google Scholar [44] B. Stehlíková and L. Capriotti, An Effective Approximation for Zero-Coupon Bonds and Arrow-Debreu Prices in the Black-Karasinski Model, Int. J. Theor. Appl. Finance, 17 (2014), 1450037, 16 pp. doi: 10.1142/S021902491450037X. Google Scholar [45] A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics, Pergamon Press, Oxford, 1963. Google Scholar [46] C. Turfus, Analytic swaption pricing in the black-karasinski model, 2020, URL https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3253866, SSRN: 3253866. Google Scholar [47] P. Verhulst, Notice sur la loi que la population suit dans son accroisseement, Correspondance Mathematique et Physique, 10 (1838), 113-121. Google Scholar Internal layers constructed for the given external boundaries $y_0(t)$ and $y_N(t)$, and the number of layers $N$, by using 3 points for each boundary $y_i(t)$ and polynomial curves Comparison of the Analytic and ML solutions (a), and Analytic, ML and FD solutions (grid with $41\times 40$ nodes) (b) for $\sigma_i = 0.5, T = 1$. Here Analytic denotes the analytic solution of the problem, ILT - the ML solution, FD - the FD solution, DiffILT - the relative error of the ML solution with respect to the analytic one, DifFD - same for the FD method Comparison of the Analytic, ML and FD solutions for $\sigma_i = 0.3, T = 0.5$. Here Analytic denotes the analytic solution of the problem, ILT - the ML solution, FD - the FD solution, DiffILT - the relative error of the ML solution with respect to the analytic one, DifFD - same for the FD method Comparison of the ML and FD solutions for a piecewise constant $\sigma(x)$. Here ILT denotes the ML solution, FD - the FD solution, Dif - the relative error of the FD solution with respect to the ML one Parameters of the test $y_0$ $y_N$ $\sigma$ $T$ $N$ $m$ -1.0 1.0 0.5 1.0 20 16 $y_0$ $y_N$ $\sigma$ $T$ $N$ $m$ -1.0 1.0 0.5 1.0 20 16 Parameters of the second experiment $y_0$ $y_N$ $T$ $N$ $m$ M -1.0 4.0 2.0 50 16 100 $y_0$ $y_N$ $T$ $N$ $m$ M -1.0 4.0 2.0 50 16 100 [1] Andrey Itkin, Dmitry Muravey. Semi-analytic pricing of double barrier options with time-dependent barriers and rebates at hit. Frontiers of Mathematical Finance, 2022, 1 (1) : 53-79. doi: 10.3934/fmf.2021002 [2] Walter Farkas, Ludovic Mathys. Geometric step options and Lévy models: Duality, PIDEs, and semi-analytical pricing. Frontiers of Mathematical Finance, 2022, 1 (1) : 1-51. doi: 10.3934/fmf.2021001 [3] María Teresa Cao-Rial, Peregrina Quintela, Carlos Moreno. Numerical solution of a time-dependent Signorini contact problem. 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Discrete & Continuous Dynamical Systems, 2012, 32 (12) : 4307-4320. doi: 10.3934/dcds.2012.32.4307 Impact Factor: ## Tools Article outline Figures and Tables	2022-01-20 10:30:29	{"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": 0.8091979026794434, "perplexity": 8443.275608080881}, "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/1642320301737.47/warc/CC-MAIN-20220120100127-20220120130127-00019.warc.gz"}
http://www.mzan.com/article/47273709-printing-multiple-solutions-for-multiple-step-sizes-in-python.shtml	Home Printing multiple solutions for multiple step sizes in python I have written this code which performs the Gradient descent for a function. I'm trying to simplify this code and show the "final solution" for 3 different initial values. If you look at my code, you'll see at the bottom there are the variables u and v. What I'm trying to accomplish is to get my final solution to look like this > Final solution #1 = ... Final solution #2 = ... Final Solution #3 = ... Any ideas or solutions for this would be great. I'm running into errors with every variation I attempt. import numpy as np def g(x): return (x[0]-2)*4 + (x[0]-2x[1])*2 def g1(x): grad = np.array([0.0,0.0]) grad[0] = 4x[0]-2*3 grad[1] = -4(x[0]-2x[1]) return grad def back_track_1s(x): eta = 1.0 beta = 0.1 gamma = 0.1 while g(x - etag1(x)) > g(x) - gammetanp.dot(g1(x), g1(x)): eta = betaeta return eta def grad_desc_2D(f, f1, xinit, step_size, tol, max_iter): x_new = np.array([0.0,0.0]) x_old = np.array([0.0,0.0]) gradient = np.array([10.0,10.0]) move = np.array([0.0,0.0]) x_new = x_init iter_ctr = 0 while np.linalg.norm(x_new - x_old) > tol and iter_ctr < max_iter: x_old = x_new gradient = f1(x_old) move = gradient step_size x_new = x_old - move iter_ctr = iter_ctr + 1 return x_new, iter_ctr u = np.array([4,3,2]) v = np.array([5,6,7]) x_init = np.array([u,v]) x_f = np.array([0.0,0.0]) step_size = 0.0025 tolerance = 0.0001 max_iter = 100 x_f, iter_ctr = grad_desc_2D(g, gl, x_init, step_size, tolerance, max_iter) print("Final Solution is: ", x_f) print("Functional evalutation is: ", g(x_f)) print("Iteration count: ", iter_ctr)	2018-02-18 20:22:45	{"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": 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": 0.43421560525894165, "perplexity": 7754.947332692889}, "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-2018-09/segments/1518891812259.18/warc/CC-MAIN-20180218192636-20180218212636-00116.warc.gz"}
https://www.engineeringchoice.com/what-is-sine-bar/	# What Is Sine Bar?- Principal, Types, and Application Table of Contents ## What is Sine Bar? A sine bar consists of a hardened, precision ground body with two precision ground cylinders fixed at the ends. The distance between the centers of the cylinders is precisely controlled, and the top of the bar is parallel to a line through the centers of the two rollers. The dimension between the two rollers is chosen to be a whole number (for ease of later calculations) and forms the hypotenuse of a triangle when in use. When a sine bar is placed on a level surface the top edge will be parallel to that surface. If one roller is raised by a known distance, usually using gauge blocks, then the top edge of the bar will be tilted by the same amount forming an angle that may be calculated by the application of the sine rule. • The hypotenuse is a constant dimension (100 mm or 10 inches in the examples shown). • The height is obtained from the dimension between the bottom of one roller and the table’s surface. • The angle is calculated by using the sine rule (a trigonometric function from mathematics). Some engineering and metalworking reference books contain tables showing the dimension required to obtain an angle from 0-90 degrees, incremented by 1-minute intervals. Sin(angle) = (Perpendicular/Hypotenuse) Angles may be measured or set with this tool. ## Understanding the Sine Bar A sine bar is used in conjunction with slip gauge blocks for precise angular measurement. A sine bar is used either to measure an angle very accurately or face locate any work to a given angle. Sine bars are made from high chromium corrosion-resistant steel, and are hardened, precision ground, and stabilized. Two cylinders of equal diameter are placed at the ends of the bar. The axes of these two cylinders are mutually parallel to each other and are also parallel to, and at equal distance from, the upper surface of the sine bar. Accuracy up to 0.01mm/m of the length of the sine bar can be obtained. A sine bar is generally used with slip gauge blocks. The sine bar forms the hypotenuse of a right triangle, while the slip gauge blocks from the opposite side. The height of the slip gauge block is found by multiplying the sine of the desired angle by the length of the sine bar: H = L * sin(θ). For example, to find the gauge block height for a 13˚ angle with a 5.000″ sine bar, multiply the sin (13˚) by 5.000″: H = 5.000″ * sin (13˚). Slip gauge blocks stacked to a height of 1.124″ would then be used to elevate the sine bar to the desired angle of 13˚. ## Principle Angles are measured using a sine bar with the help of gauge blocks and a dial gauge or a spirit level. The aim of a measurement is to measure the surface on which the dial gauge or spirit level is placed horizontally. For example, to measure the angle of a wedge, the wedge is placed on a horizontal table. The sine bar is placed over the inclined surface of the wedge. At this position, the top surface of the sine bar is inclined the same amount as the wedge. Using gauge blocks, the top surface is made horizontal. The sine of the angle of inclination of the wedge is the ratio of the height of the gauge blocks used and the distance between the centers of the cylinders. ## Types of Sine Bar The simplest type consists of a lapped steel bar, at each end of which is attached an accurate cylinder, the axes of the cylinders being mutually parallel and parallel to the upper surface of the bar. In the advanced type, some holes are drilled in the body of the bar to reduce the weight and facilitate handling. ### 1. Sine center A special type of sine bar is sine center which is used for conical objects having male and female parts. It cannot measure an angle of more than 60 degrees. ### 2. Sine table A sine table (or sine plate) is a large and wide sine bar, typically equipped with a mechanism for locking it in place after positioning, which is used to hold workpieces during operations. ### 3. Compound sine table It is used to measure the compound angles of the large workpieces. In this case, two sine tables are mounted one over the other at right angles. The tables can be twisted to get the required alignment. ## Limitations Following are the limitations of sine bar: • Any unknown projections present in the component will cause errors in the measured angle to be induced. • For the construction of slip gauges, there is no scientific approach available and it has to be built on trial-and-error basis and it is a time-consuming process. • During the measurement of the angle using the sine bar, the sine bar length must be greater than or equal to the length of the component to be inspected. • If the length of the inspected component is too long, there is no sine bar available that is longer than the component. In these cases, the sine bar will be used together with the height gauge for measurement. ## Applications Following are the applications of sine bar: • The sine-bar is used to set or determine the workpiece at a given angle. • For checking the measurement of unknown angles in the workpiece. • Some specially designed sine bars are used to mount the workpiece to perform conical-shaped machining for the workpiece. • To check for unknown angles on heavy components. • For checking the angles of taper key. • To check the flatness of the surface. ## Browse More Content ### Shafts: Definition, Types, And Application What is a Shaft? A shaft is a rotating machine element, usually circular in cross ### What is Fatigue Limit Of a Material? What is Fatigue Limit? The fatigue limit or endurance limit is the stress level below ### What is Pulley?- Definition, Types, and their Uses Pulleys are made by looping a rope over one or more wheels. It is a ### What is Welding Porosity And How to Prevent It? 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The coefficient of restitution (COR, also denoted by e), ### What is Lever?- Principle, Types, And Examples What is a Lever? A lever is a simple machine consisting of a beam or ### What is Leadscrew?- Definition, Parts, And Working A lead screw (or lead screw), also known as a power screw or translation screw,	2023-02-05 04:08:54	{"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": 0.8055952787399292, "perplexity": 1407.913532011776}, "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-2023-06/segments/1674764500215.91/warc/CC-MAIN-20230205032040-20230205062040-00019.warc.gz"}
http://cosmo.obspm.fr/links/library/	Last entries in the CiteULike library For the full list: http://www.citeulike.org/group/13962/ EarlierProbing the nature of Dark Matter through the metal enrichment of the intergalactic medium(14 Mar 2018)We focus on exploring the metal enrichment of the intergalactic medium (IGM) in Cold and Warm (1.5 and 3 keV) Dark Matter (DM) cosmologies, and the constraints this yields on the DM particle mass, using a semi-analytic model, Delphi, that jointly tracks the Dark Matter and baryonic assembly [...]Fri, Mar 16, 2018Source: CiteULike Group Cosmo LUTHChaos and Variance in Galaxy Formation(14 Mar 2018)The evolution of galaxies is governed by equations with chaotic solutions: gravity and compressible hydrodynamics. While this micro-scale chaos and stochasticity has been well studied, it is poorly understood how it couples to macro-scale properties examined in simulations of galaxy formation. In this paper, we show how perturbations [...]Fri, Mar 16, 2018Source: CiteULike Group Cosmo LUTHEvolution of axis ratios from phase space dynamics of triaxial collapse(8 Mar 2018)We investigate the evolution of axis ratios of triaxial haloes using the phase space description of triaxial collapse. In this formulation, the evolution of the triaxial ellipsoid is described in terms of the dynamics of eigenvalues of three important tensors: the Hessian of the gravitational potential, the tensor [...]Fri, Mar 09, 2018Source: CiteULike Group Cosmo LUTHMerger history of central galaxies in Semi-Analytic Models of galaxy formation(6 Mar 2018)We investigate the dynamical evolution of galaxies in groups with different formation epochs. Galaxy groups have been selected to be in different dynamical states, namely dynamically old and dynamically young, which reflect their early and late formation times, respectively, based on their halo mass assembly. Brightest galaxies in [...]Thu, Mar 08, 2018Source: CiteULike Group Cosmo LUTHThe accuracy of semi-numerical reionization models in comparison with radiative transfer simulations(28 Feb 2018)We have developed a modular semi-numerical code that computes the time and spatially dependent ionization of neutral hydrogen (HI), neutral (HeI) and singly ionized helium (HeII) in the intergalactic medium (IGM). The model accounts for recombinations and provides different descriptions for the photoionization rate that are used to [...]Fri, Mar 02, 2018Source: CiteULike Group Cosmo LUTHDusty galaxies in the Epoch of Reionization: simulations(21 Feb 2018)The recent discovery of dusty galaxies well into the Epoch of Reionization (redshift $z>6$) poses challenging questions about the properties of the interstellar medium in these pristine systems. By combining state-of-the-art hydrodynamic and dust radiative transfer simulations, we address these questions focusing on the recently discovered dusty galaxy [...]Fri, Feb 23, 2018Source: CiteULike Group Cosmo LUTHReconstruction of the two-dimensional gravitational potential of galaxy clusters from X-ray and Sunyaev-Zel'dovich measurements(20 Feb 2018)The mass of galaxy clusters is not a direct observable, nonetheless it is commonly used to probe cosmological models. Based on the combination of all main cluster observables, that is, the X-ray emission, the thermal Sunyaev-Zel'dovich (SZ) signal, the velocity dispersion of the cluster galaxies, and gravitational lensing, [...]Wed, Feb 21, 2018Source: CiteULike Group Cosmo LUTHThe Cosmic Web Around The Brightest Galaxies During The Epoch Of Reionization(19 Feb 2018)The most luminous galaxies at high-redshift are generally considered to be hosted in massive dark-matter halos of comparable number density, hence residing at the center of overdensities/protoclusters. We assess the validity of this assumption by investigating the clustering around the brightest galaxies populating the cosmic web at redshift [...]Wed, Feb 21, 2018Source: CiteULike Group Cosmo LUTHGlobular Clusters in High-Redshift Dwarf Galaxies: A Case Study from the Local Group(19 Feb 2018)We present the reconstructed evolution of rest-frame ultra-violet (UV) luminosities of the most massive Milky Way dwarf spheroidal satellite galaxy, Fornax, and its five globular clusters (GCs) across redshift, based on analysis of the stellar fossil record and stellar population synthesis modeling. We find that (1) Fornax's (proto-)GCs [...]Wed, Feb 21, 2018Source: CiteULike Group Cosmo LUTHStar-forming galaxies are predicted to lie on a fundamental plane of mass, star formation rate and Î±-enhancement(19 Feb 2018)Observations show that star-forming galaxies reside on a tight three-dimensional plane between mass, gas-phase metallicity and star formation rate (SFR), which can be explained by the interplay between metal-poor gas inflows and SFR. However, different metals are released on different time-scales, which may affect this relation. Here, we [...]Wed, Feb 21, 2018Source: CiteULike Group Cosmo LUTHObscured star-formation in bright z ~ 7 Lyman-break galaxies(15 Feb 2018)We present Atacama Large Millimeter/Submillimeter Array observations of the rest-frame far-infrared (FIR) dust continuum emission of six bright Lyman-break galaxies (LBGs) at $z ∼eq 7$. The average FIR luminosity of the sample is found to be $L_ FIR ∼eq 2 × 10^11\, L_odot$, corresponding to an obscured star-formation [...]Mon, Feb 19, 2018Source: CiteULike Group Cosmo LUTHGravitational Redshifts in Clusters and Voids(14 Feb 2018)Gravitational redshift as a relativistic effect in cosmological objects is investigated. Possible signatures of the gravitational redshift in measurements of satellite galaxies in clusters of galaxies, intracluster gas, as well as galaxies associated with voids are investigated by developing simple theoretical models. In the analysis of the gravitational [...]Thu, Feb 15, 2018Source: CiteULike Group Cosmo LUTHDark-ages Reionization and Galaxy Formation Simulation - XIV. Gas accretion, cooling and star formation in dwarf galaxies at high redshift(12 Feb 2018)We study dwarf galaxy formation at high redshift ($z≥5$) using a suite of high-resolution, cosmological hydrodynamic simulations and a semi-analytic model (SAM). We focus on gas accretion, cooling and star formation in this work by isolating the relevant process from reionization and supernova feedback, which will be further [...]Tue, Feb 13, 2018Source: CiteULike Group Cosmo LUTHCosmological simulation with dust formation and destruction(12 Feb 2018)To investigate the evolution of dust in a cosmological volume, we perform hydrodynamic simulations, in which the enrichment of metals and dust is treated self-consistently with star formation and stellar feedback. We consider dust evolution driven by dust production in stellar ejecta, dust destruction by sputtering, grain growth [...]Tue, Feb 13, 2018Source: CiteULike Group Cosmo LUTHReignition of Star Formation in Dwarf Galaxies(8 Feb 2018)The Local Group hosts a number of star-forming dwarf galaxies that show evidence of periods of little to no star formation. We use a suite of cosmological simulations to study how star formation is reignited in such galaxies. We focus on isolated galaxies at $z=0$ with halo masses [...]Mon, Feb 12, 2018Source: CiteULike Group Cosmo LUTHEnvironmental Quenching of Low-Mass Field Galaxies(8 Feb 2018)In the local Universe, there is a strong division in the star-forming properties of low-mass galaxies, with star formation largely ubiquitous amongst the field population while satellite systems are predominantly quenched. This dichotomy implies that environmental processes play the dominant role in suppressing star formation within this low-mass [...]Mon, Feb 12, 2018Source: CiteULike Group Cosmo LUTHThe Inhomogeneous Reionization Times of Present-day Galaxies(5 Feb 2018)Today's galaxies experienced cosmic reionization at different times in different locations. For the first time, reionization ($50\%$ ionized) redshifts, $z_R$, at the location of their progenitors are derived from new, fully-coupled radiation-hydrodynamics simulation of galaxy formation and reionization at $z > 6$, matched to N-body simulation to z [...]Wed, Feb 07, 2018Source: CiteULike Group Cosmo LUTHUnveiling Galaxy Bias via the Halo Model, KiDS and GAMA(2 Feb 2018)We measure the projected galaxy clustering and galaxy-galaxy lensing signals using the Galaxy And Mass Assembly (GAMA) survey and Kilo-Degree Survey (KiDS) to study galaxy bias. We use the concept of non-linear and stochastic galaxy biasing in the framework of halo occupation statistics to constrain the parameters of [...]Mon, Feb 05, 2018Source: CiteULike Group Cosmo LUTHFirstLight II: Star formation rates of primeval galaxies from z=5-15(31 Jan 2018)In the FirstLight project, we have used ~300 cosmological, zoom-in simulations to determine the star-formation histories of distinct first galaxies with stellar masses between Ms=10^6 and 3 x 10^9 Msun during cosmic dawn (z=5-15). The evolution of the star formation rate (SFR) in each galaxy is complex and [...]Thu, Feb 01, 2018Source: CiteULike Group Cosmo LUTHExploring Simulated Early Star Formation in the Context of the Ultrafaint Dwarf Galaxies(25 Jan 2018)Ultrafaint dwarf galaxies (UFDs) are typically assumed to have simple, stellar populations with star formation ending at reionization. Yet as the observations of these galaxies continue to improve, their star formation histories (SFHs) are revealed to be more complicated than previously thought. In this paper, we study how [...]Mon, Jan 29, 2018Source: CiteULike Group Cosmo LUTHDynamical constraints on the dark matter distribution of the Sculptor dwarf spheroidal from stellar proper motions(22 Jan 2018)We compare the transverse velocity dispersions recently measured within the Sculptor dwarf spheroidal galaxy to the predictions of previously published dynamical models. These provide good fits to the observed number count and velocity dispersion profiles of metal-rich and metal-poor stars both in cored and in cusped potentials. At [...]Thu, Jan 25, 2018Source: CiteULike Group Cosmo LUTHThe SPHINX Cosmological Simulations of the First Billion Years: the Impact of Binary Stars on Reionization(22 Jan 2018)We present the SPHINX suite of cosmological adaptive mesh refinement simulations, the first radiation-hydrodynamical simulations to simultaneously capture large-scale reionization and the escape of ionizing radiation from thousands of resolved galaxies. Our $5$ and $10$ co-moving Mpc volumes resolve haloes down to the atomic cooling limit and model [...]Thu, Jan 25, 2018Source: CiteULike Group Cosmo LUTHEvidence of a non universal stellar Initial Mass Function. Insights from HST optical imaging of 6 Ultra Faint Dwarf Milky Way Satellites(18 Jan 2018)Using deep HST/ACS observations, we demonstrate that the sub-solar stellar initial mass function (IMF) of 6 ultra-faint dwarf Milky Way Satellites (UFDs) is more bottom light than the IMF of the Milky Way disk. Our data have a lower mass limit of about 0.45 M$_odot$, while the upper [...]Mon, Jan 22, 2018Source: CiteULike Group Cosmo LUTHNo Assembly Required: Mergers are Mostly Irrelevant for the Growth of Low-mass Dwarf Galaxies(18 Jan 2018)We investigate the merger histories of isolated dwarf galaxies based on a suite of 15 high-resolution cosmological zoom-in simulations, all with masses of $M_ halo ≈ 10^10\, M_odot$ (and M$_∗∼10^5-10^7\, M_odot$) at $z=0$, from the Feedback in Realistic Environments (FIRE) project. The stellar populations of these dwarf galaxies [...]Mon, Jan 22, 2018Source: CiteULike Group Cosmo LUTHPushing back the limits: detailed properties of dwarf galaxies in a LCDM universe(18 Jan 2018)We present the results of a set of high resolution chemo-dynamical simulations of dwarf galaxies in a $Λ$CDM cosmology. Out of an original 3.4 Mpc$^3$/h$^3$ cosmological box, a sample of 27 systems are zoomed-in from z=70 to z=0. Gas and stellar properties are confronted to the observations in [...]Mon, Jan 22, 2018Source: CiteULike Group Cosmo LUTHBeyond Falsifiability: Normal Science in a Multiverse(15 Jan 2018)Cosmological models that invoke a multiverse - a collection of unobservable regions of space where conditions are very different from the region around us - are controversial, on the grounds that unobservable phenomena shouldn't play a crucial role in legitimate scientific theories. I argue that the way we [...]Wed, Jan 17, 2018Source: CiteULike Group Cosmo LUTHConsistent modelling of the meta-galactic UV background and the thermal/ionization history of the intergalactic medium(15 Jan 2018)Recent observations suggest that hydrogen reionization ends late ($z ∼eq 6$) and proceeds quickly. We present here a new model of the meta-galactic UV/X-ray background (UVB) that is consistent with this. It adopts the most recent determinations of the ionizing emissivity due to stars and AGN, as well [...]Wed, Jan 17, 2018Source: CiteULike Group Cosmo LUTHA Radio Continuum Study of Dwarf Galaxies: 6 cm imaging of Little Things(16 Jan 2018)In this paper we examine to what extent the radio continuum can be used as an extinction free probe of star formation in dwarf galaxies. To that aim we observe $40$ nearby dwarf galaxies with the Very Large Array at 6 cm ($4$-$8$ GHz) in C-configuration. We obtained [...]Wed, Jan 17, 2018Source: CiteULike Group Cosmo LUTHImpact of Lyman alpha pressure on metal-poor dwarf galaxies(15 Jan 2018)Understanding the origin of strong galactic outflows and the suppression of star formation in dwarf galaxies is a key problem in galaxy formation. Using a set of radiation-hydrodynamic simulations of an isolated dwarf galaxy embedded in a $10^10\,M_odot$ halo, we show that the momentum transferred from resonantly scattered [...]Wed, Jan 17, 2018Source: CiteULike Group Cosmo LUTHBlueTides simulation: establishing black hole-galaxy relations at high-redshift(15 Jan 2018)The scaling relations between the mass of supermassive black holes ($M_•$) and host galaxy properties (stellar mass, $M_∗$, and velocity dispersion, $σ$), provide a link between the growth of black holes (BHs) and that of their hosts. Here we investigate if and how the BH-galaxy relations are established [...]Wed, Jan 17, 2018Source: CiteULike Group Cosmo LUTHCool-Core Clusters : Role of BCG, Star Formation & AGN-Driven Turbulence(12 Jan 2018)Recent analysis shows that it is important to explicitly include the gravitational potential of the central brightest central galaxy (BCG) to infer the acceleration due to gravity ($g$) and the free-fall time ($t_ ff ≡ [2r/g]^1/2$) in cool cluster cores. Accurately measuring $t_ ff$ is crucial because according [...]Tue, Jan 16, 2018Source: CiteULike Group Cosmo LUTHOn the Appearance of Thresholds in the Dynamical Model of Star Formation(13 Jan 2018)The Kennicutt-Schmidt (KS) relationship between the surface density of the star formation rate (SFR) and the gas surface density has three distinct power laws that may result from one model in which gas collapses at a fixed fraction of the dynamical rate. The power law slope is 1 [...]Tue, Jan 16, 2018Source: CiteULike Group Cosmo LUTHSemi-Analytic Galaxies - I. Synthesis of environmental and star-forming regulation mechanisms(11 Jan 2018)We present results from the semi-analytic model of galaxy formation SAG applied on the MultiDark simulation MDPL2. SAG features an updated supernova (SN) feedback scheme and a robust modelling of the environmental effects on satellite galaxies. This incorporates a gradual starvation of the hot gas halo driven by [...]Fri, Jan 12, 2018Source: CiteULike Group Cosmo LUTHGalaxy Formation in Sterile Neutrino Dark Matter Models(11 Jan 2018)We investigate galaxy formation in models with dark matter (DM) constituted by sterile neutrinos. Given their large parameter space, defined by the combinations of sterile neutrino mass $m_ν$ and mixing parameter $\sin^2(2θ)$ with active neutrinos, we focus on models with $m_ν=7$ keV, consistent with the tentative 3.5 keV [...]Fri, Jan 12, 2018Source: CiteULike Group Cosmo LUTHOn the Schrodinger-Poisson--Vlasov-Poisson correspondence(10 Jan 2018)The Schrodinger-Poisson equations describe the behavior of a superfluid condensate under self-gravity with a 3D wave function. As $\hbar/m\to 0$, with $m$ being the boson mass, the equations have been hypothesized to approximate the collisionless Vlasov-Poisson equations also known as the collisionless Boltzmann equations. The latter describe collisionless [...]Fri, Jan 12, 2018Source: CiteULike Group Cosmo LUTHEnforcing the Courant-Friedrichs-Lewy Condition in Explicitly Conservative Local Time Stepping Schemes(9 Jan 2018)An optimally efficient explicit numerical scheme for solving fluid dynamics equations, or any other parabolic or hyperbolic system of partial differential equations, should allow local regions to advance in time with their own, locally constrained time steps. However, such a scheme can result in violation of the Courant-Friedrichs-Lewy [...]Thu, Jan 11, 2018Source: CiteULike Group Cosmo LUTHBeacons into the Cosmic Dark Ages: Boosted transmission of Ly$Î±$ from UV bright galaxies at $z \gtrsim 7$(5 Jan 2018)Recent detections of Lyman alpha (Ly$α$) emission from $z>7.5$ galaxies were somewhat unexpected given a dearth of previous non-detections in this era when the intergalactic medium (IGM) is still highly neutral. But these detections were from UV bright galaxies which preferentially live in overdensities which reionize early and [...]Tue, Jan 09, 2018Source: CiteULike Group Cosmo LUTHEvidence for radial variations in the stellar mass-to-light ratio of massive galaxies from weak and strong lensing(5 Jan 2018)The Initial Mass Function (IMF) for massive galaxies can be constrained by combining stellar dynamics with strong gravitational lensing. However, this method is limited by degeneracies between the density profile of dark matter and the stellar mass-to-light ratio. In this work we reduce this degeneracy by combining weak [...]Tue, Jan 09, 2018Source: CiteULike Group Cosmo LUTHWeak Lensing Peaks in Simulated Light-Cones: Investigating the Coupling between Dark Matter and Dark Energy(5 Jan 2018)In this paper we study the statistical properties of weak lensing peaks in light-cones generated from numerical simulations. We focus on interacting Dark Energy cosmological models, characterised by a coupling term between dark energy and dark matter which allows us to study in detail how such an interaction [...]Tue, Jan 09, 2018Source: CiteULike Group Cosmo LUTHThe clustering of $z > 7$ galaxies: Predictions from the BLUETIDES simulationMonthly Notices of the Royal Astronomical Society (27 Dec 2017), doi:10.1093/mnras/stx3149We study the clustering of the highest-z galaxies (from ~ $0.1$ to a few tens Mpc scales) using the BLUETIDES simulation and compare it to current observational constraints from Hubble legacy and Hyper Suprime Cam (HSC) fields (at $z=6-7.2$). With [...]Fri, Dec 29, 2017Source: CiteULike Group Cosmo LUTHGAMER-2: a GPU-accelerated adaptive mesh refinement code -- accuracy, performance, and scalability(19 Dec 2017)We present GAMER-2, a GPU-accelerated adaptive mesh refinement (AMR) code for astrophysics. It provides a rich set of features, including adaptive time-stepping, several hydrodynamic schemes, magnetohydrodynamics, self-gravity, particles, star formation, chemistry and radiative processes with GRACKLE, data analysis with yt, and memory pool for efficient object allocation. GAMER-2 [...]Wed, Dec 20, 2017Source: CiteULike Group Cosmo LUTHThe duration of reionization constrains the ionizing sources(18 Dec 2017)We investigate how the nature of the galaxies that reionized the Universe affects the duration of reionization. We contrast two models: one in which galaxies on the faint side of the luminosity function dominate the ionizing emissivity, and a second in which the galaxies on the bright side [...]Wed, Dec 20, 2017Source: CiteULike Group Cosmo LUTHEscape of ionizing radiation from high redshift dwarf galaxies: role of AGN feedback(15 Dec 2017)While low mass, star forming galaxies are often considered as the primary driver of reionization, their actual contribution to the cosmic ultraviolet background is still uncertain, mostly because the escape fraction of ionizing photons is only poorly constrained. Theoretical studies have shown that efficient supernova feedback is a [...]Tue, Dec 19, 2017Source: CiteULike Group Cosmo LUTHRelaxation in self-gravitating systems(15 Dec 2017)The long timescale evolution of a self-gravitating system is generically driven by two-body encounters. In many cases, the motion of the particles is primarily governed by the mean field potential. When this potential is integrable, particles move on nearly fixed orbits, which can be described in terms of [...]Tue, Dec 19, 2017Source: CiteULike Group Cosmo LUTHAGN Feedback Compared: Jets versus Radiation(11 Dec 2017)Feedback by Active Galactic Nuclei is often divided into quasar and radio mode, powered by radiation or radio jets, respectively. Both are fundamental in galaxy evolution, especially in late-type galaxies, as shown by cosmological simulations and observations of jet-ISM interactions in these systems. We compare AGN feedback by [...]Wed, Dec 13, 2017Source: CiteULike Group Cosmo LUTHAn alternate approach to measure specific star formation rates at 2<z<7(11 Dec 2017)We trace the specific star formation rate (sSFR) of massive star-forming galaxies ($\gtrsim\!10^10\,\mathcalM_odot$) from $z∼2$ to 7. Our method is substantially different from previous analyses, as it does not rely on direct estimates of star formation rate, but on the differential evolution of the galaxy stellar mass function [...]Wed, Dec 13, 2017Source: CiteULike Group Cosmo LUTHSelecting ultra-faint dwarf candidate progenitors in cosmological N-body simulations at high redshifts(11 Dec 2017)The smallest satellites of the Milky Way ceased forming stars during the epoch of reionization and thus provide archaeological access to galaxy formation at $z>6$. Numerical studies of these ultra-faint dwarf galaxies (UFDs) require expensive cosmological simulations with high mass resolution that are carried out down to $z=0$. [...]Wed, Dec 13, 2017Source: CiteULike Group Cosmo LUTHGalaxy growth in a massive halo in the first billion years of cosmic historyNature (8 Dec 2017), doi:10.1038/nature24629According to the current understanding of cosmic structure formation, the precursors of the most massive structures in the Universe began to form shortly after the Big Bang, in regions corresponding to the largest fluctuations in the cosmic density field. Observing these structures during their period of [...]Mon, Dec 11, 2017Source: CiteULike Group Cosmo LUTHLittle Blue Dots in the Hubble Space Telescope Frontier Fields: Precursors to Globular Clusters?(8 Dec 2017)Galaxies with stellar masses 10^-7 yr^-1 were examined on images of the Hubble Space Telescope Frontier Field Parallels for Abell 2744 and MACS J0416.1-02403. They appear as unresolved "Little Blue Dots" (LBDs). They are less massive and have higher sSFR than "blueberries" studied by yang et al. (2017) [...]Mon, Dec 11, 2017Source: CiteULike Group Cosmo LUTHWas there an early reionization component in our universe?(7 Dec 2017)A deep understanding of the Epoch of Reionization is still missing in our knowledge of the universe. Awaiting for future probes, which will allow to test the precise evolution of the free electron fraction from redshifts between $z∼eq 6$ and $z∼eq 20$, one could ask which kind of [...]Mon, Dec 11, 2017Source: CiteULike Group Cosmo LUTH	2018-03-20 03:36:57	{"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": 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": 0.5638394951820374, "perplexity": 5429.736360045331}, "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-2018-13/segments/1521257647280.40/warc/CC-MAIN-20180320033158-20180320053158-00070.warc.gz"}
http://mathhelpforum.com/calculus/104015-evaluating-limit-print.html	# Evaluating a limit • September 23rd 2009, 09:32 PM jzellt Evaluating a limit lim (x --> -8) of: (square root(1-x)) - 3 divided by 2 + (cube root(x)) I believe I should multiply by the congugate, but I'm not getting anywhere. Thanks for any help • September 23rd 2009, 09:41 PM mr fantastic Quote: Originally Posted by jzellt lim (x --> -8) of: (square root(1-x)) - 3 divided by 2 + (cube root(x)) I believe I should multiply by the congugate, but I'm not getting anywhere. Thanks for any help I suggest that you first make the substitution $x = t^3$: $\lim_{t \rightarrow -2} \frac{\sqrt{1 - t^3} - 3}{2 + t}$. Now multiply numerator and denominator by the conjugate surd, factorise the numerator, divide numerator and denominator by the common factor and then take the limit.	2015-08-02 08:24:48	{"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": 0.9770854711532593, "perplexity": 2191.100791694931}, "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-2015-32/segments/1438042989018.48/warc/CC-MAIN-20150728002309-00042-ip-10-236-191-2.ec2.internal.warc.gz"}
http://mathhelpforum.com/pre-calculus/68928-life-science-log-question.html	# Math Help - life science(log question) 1. ## life science(log question) when a person swallow giardia cysts,stomch acids and pancreatic enzymes cause the cysts to release trophozoites,which divide every 12 hours. a) suppose the number of trophozoites at time t=ois yo,write a function giving the number after t hours. b)the article cited above said that a single trophozoites can multiply to a million in just 10 days and a billion in 15 days, verify this fact. 2. Originally Posted by shannon1111 when a person swallow giardia cysts,stomch acids and pancreatic enzymes cause the cysts to release trophozoites,which divide every 12 hours. a) suppose the number of trophozoites at time t=ois yo,write a function giving the number after t hours. b)the article cited above said that a single trophozoites can multiply to a million in just 10 days and a billion in 15 days, verify this fact. a) ... $y = y_0 \cdot (2)^{\frac{t}{12}}$ you can do the verification part of (b)	2014-09-16 11:11:03	{"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": 1, "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": 0.21871812641620636, "perplexity": 6988.823391471138}, "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-2014-41/segments/1410657114204.83/warc/CC-MAIN-20140914011154-00007-ip-10-196-40-205.us-west-1.compute.internal.warc.gz"}
https://felix-knorr.net/posts/2021-04-28-mdn.html	# Markdown Note - The best Note app around 2021-04-28 That title is obviously click bait. However, it is also true, at least for me, as I wrote Markdown Note (MDN) because I was not satisfied with any existing solution. It allows you to write notes in Markdown, with any editor you prefer, and display them in the Browser. It also has some bibliographic features. Since you clicked on this link, I assume I don't need to convince you to use a note app, but I want to convince you to use MDN. The reasons you should use it, are the same reasons that made me write it. So let me take you on a tour through different ways to manage notes, and their respective flaws. When I first started working scientifically, I used one big latex file to store my notes. It turned out that that wasn't my best idea. The source file became quite chaotic over time, sometimes I would have troubles compiling it, and a single PDF for all notes also isn't the best format. I then went on to use OneNote. OneNote has some nice features, but it also has some flaws. First and foremost: availability in Linux. Sure, by now there is a browser version, but I really don't like web-apps, they either don't have nice hotkeys, or they do have them, and then those will collide with the hotkeys of my browser plugins. Additionally, and that was the biggest pain point for me: its not Vim. Text editing with Vim is, by now, deeply rooted in my muscle memory, and not having it available when writing text causes physical pain and distress (I might be overexagerating slightly here … SLIGHTLY). I then went on to use Evernote in combination with Marxico. I really liked writing notes in Markdown, and Evernote brought some Vim emulation to the table. It wasn't sufficient though. Also by then, another problem arose. My Boss didn't like the idea of my research related notes lying around in a cloud. And actually I agree with that. Also, call it old fashioned, but I really don't like the idea of having to rely on a network connection, when there shouldn't be a need to. I then had a short org-mode phase, but I didn't like that I had to manage the multiple files by hand and I never really warmed up with Emacs. This was the point where I started thinking about writing my own app. It should have the following features: • local files • edit in markdown • I want to use Vim • I still want images and synchronisation though The sync part would be done by Dropbox, so I didn't have to do anything here. So far, so simple. Create a new note: mdn new you can now view it in a browser via mdn show title but most of the time I'd end up just reading the notes in the terminal with vim via mdn edit title you can see your notes via mdn ls pattern The pattern will be treated the following way: add a wildcard between every letter, and then match all the titles. This is an extremely simple and surprisingly powerful way to find things quickly. Additionally notes can have groups. Originally, I intended them to be like notebooks, but because I'm lazy I implemented them as simple string matches. I now have e.g. a group "Papers - RS" and "Papers - NF" and I can add one of those groups specifically to the query like: mdn ls -g "Papers - RS" pattern but I can also just go for mdn ls -gpapers and it will give me all titles from all groups that contain the word "paper". Additionally, there is also a tag mechanism: you can prefix any word in a note with an @ and that prefixed word will be interpreted as a tag. You can then search for tags, and also combine them via logical formulas. e.g. mdn ls -t "@foo & -@bar" would give you all notes that contain @foo but only if they dont also contain @bar. I never really used this feature though, and it's mainly in there because I wanted to write the parser for the tag formulas :D Also, you can search through the contents of notes with mdn fd pattern btw. I used the tool for a year, and new features emerged. Want to share some notes, e.g. one group of notes with someone else? mdn cat -gPapers -n \| pandoc --from markdown -o papers.pdf --pdf-engine=xelatex --toc There you go. The -n removes the yaml front matter, which would confuse pandoc. Alternatively, you can also pass a list of note ids to cat. When writing something for which I need my notes, I would create one PDF with all the notes I needed, and scroll around in it a lot. That was a little annoying, so I created the serve command mdn serve will start a webserver which you can use read all notes easily: For the longest time, I had used Zotero to manage my bibliography. While writing a paper, I would find myself adding papers to the bib file constantly, and always recreating a bib file from Zotero. This was pretty annoying. I then switched to Jabref. I would copy the doi from my notes, and add it in Jabref, still a little annoying. Then I added bib capabilities to MDN. You can create a new note via: mdn new -d 10.1016/j.neuroimage.2020.116634 and it will create a file containing: --- title: Knorr et al. 2020 doi: 10.1016/j.neuroimage.2020.116634 group: None --- # A comparison of {fMRI} and behavioral models for predicting inter-temporal choices <https://doi.org/10.1016%2Fj.neuroimage.2020.116634> and if you have a doi defined in the front matter of a note, you can run mdn tobib id and it will append a bibtex entry for the doi to the first .bib file in the current directory. Last but not least, add this to your .vimrc (if you use vim) to copy images from the clipboard into your note (requires xclip, and ofcourse you'll have to adjust the paths to match your configuration): function! InsertImgFromCB(name) execute "!xclip -sel clip -t image/png -o > " . \ "/home/felix/Dropbox/mdn.d/assets/" . a:name execute "norm a![](" . a:name . ")" endf command! -nargs=1 PasteImage call InsertImgFromCB(<f-args>) " requires Vim surround " Make a marked text into a link with a link from the clipboard pip install git+https://github.com/KnorrFG/markdown_note.git	2022-10-06 20:20:42	{"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": 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": 0.41721343994140625, "perplexity": 2238.5214117786786}, "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/1664030337855.83/warc/CC-MAIN-20221006191305-20221006221305-00735.warc.gz"}
http://mathhelpforum.com/calculus/32165-need-help-surface-area-sphere.html	Math Help - Need help with surface area of this sphere 1. Need help with surface area of this sphere i need to determine the surface area of the portion of the sphere $x^2 + y^2 + z^2 = 16$ that lies between the planes $z=1$ and $z=2$ i have taken the derivatives with respect to x and y and have switched to polar coordinates and now i have the integral: $\int \int {{(4/\sqrt(16-r^2)dA}}$ I am not sure what the limits of the integrals will be. But i am pretty sure the leftmost integral has the limits 0 to $2\pi$. can someone help me figure out the limits of the integrals? thanks. 2. If you sub in z=1 and z=2 into the sphere equation you get: $r^{2}=15, \;\ r^{2}=12$ So, you get: $\int_{0}^{2\pi}\int_{\sqrt{12}}^{\sqrt{15}}\frac{4 r}{\sqrt{16-r^{2}}}drd{\theta}$ $=4\int_{0}^{2\pi}d{\theta}=8{\pi}$	2014-04-19 12:58:06	{"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": 0, "img_math": 0, "codecogs_latex": 8, "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": 0.9069049954414368, "perplexity": 76.83949701556557}, "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-2014-15/segments/1397609537186.46/warc/CC-MAIN-20140416005217-00493-ip-10-147-4-33.ec2.internal.warc.gz"}
https://sammottley.me/isosri/990744-vertical-line-test-answer-keystatic-line-jump	CITE THIS PAGE: "+ author + ", "" + document.title + "." Topend Sports Website, "+ published + ", "+ url + ", Accessed " + today); B) a vertical straight line. This system enables the driver to change the angle of the aerofoil to reduce the drag. When you invert my answer for a question and ask it, you arrive here. Practice your technique, as the jump height can be affected by how much you bend your knees before jumping, and the effective use of the arms. Vertical Line. Figure 12. A vacuum house and a loose grounded test light to ground one cylinder at a time on a DIS. 7, but not for 7 itself. Making statements based on opinion; back them up with references or personal experience. Under the conditions for this test drive, the DRS was not in use and the engine produced a constant driving force. A) a horizontal straight line. Student: Both of those shapes pass through the vertical line twice in lots of places! facebook For most, 30 inches is an excellent benchmark. If we were talking about a horizontal line, then we'd say y doesn't change. In mathematics, the vertical line test is a visual way to determine if a curve is a graph of a function or not. Try it free Vertical Asymptotes. Then take a vertical line and place it on the graph. Student: What does a vertical line have to do with functions? Not easy to choose the best one to use any questions, please ask search! Measure the distance between the standing broad jump is a great test of leg.... About how you read it, then this is a vertical line anywhere on this graph and have touch. The flat part at x=7, but for x larger than 7 it is an benchmark! Than simply standing still and jumping as far as you need to the. Mathematics Practice test answer Key Go on Session 2 19.A line plot with long jump data is given highest... 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General 1042-l Humidifier Filter Home Depot, Aluminum Dish Rack, Samsung Hw-f450 Remote App, Aim Tv Firmware, Epson Xp 4100 Maintenance Error, Garlic Mustard Vinaigrette, Types Of Soil Mites, Spring Ball Change Definition, " /> Go to Top	2021-04-11 00:45:34	{"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": 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": 0.45888039469718933, "perplexity": 1537.5959030787426}, "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-20210411000036-20210411030036-00381.warc.gz"}
https://www.effortlessmath.com/math-topics/arc-length-and-sector-area/	# How to Find Arc Length and Sector Area? (+FREE Worksheet!) Learn how to find the arc length and sector area of a circle using the following step-by-step guide with examples. ## Step by step guide to find arc length and sector area of circles • To find a sector of a circle, use this formula: Area of a sector $$=\color{blue}{πr^2 (\frac{θ}{360})}$$ $$r$$ is the radius of the circle and $$θ$$ is the central angle of the sector. • To find the arc of a sector of a circle, use this formula: Arc of a sector $$=\color{blue}{(\frac{θ}{180})πr}$$ ### Arc Length and Sector Area – Example 1: Find the length of the arc. Round your answers to the nearest tenth. $$(π=3.14), r=24$$ $$cm$$, $$\theta=60^\circ$$ Solution: Use this formula: length of a sector $$=\color{blue}{(\frac{θ}{180})πr}$$ length of a sector $$=(\frac{θ}{180})πr$$ $$=(\frac{60}{180})π(24)=(\frac{1}{3})π(24)=8×3.14 \cong 25.1$$ $$cm$$ ### Arc Length and Sector Area – Example 2: Find the area of the sector. $$(π=3.14$$), $$r=6$$ $$ft$$, $$\theta=90^\circ$$ Solution: Use this formula: Area of a sector $$=\color{blue}{πr^2 (\frac{θ}{360})}$$ Area of a sector $$=πr^2 (\frac{θ}{360})=(3.14)(6^2 )(\frac{90}{360})=(3.14)(36)(\frac{1}{4})=28.26$$$$ft^2$$ ### Arc Length and Sector Area – Example 3: Find the length of the arc. Round your answers to the nearest tenth. $$(π=3.14), r=28$$ $$cm$$, $$\theta=45^\circ$$ Solution: Use this formula: length of a sector $$=\color{blue}{(\frac{θ}{180})πr}$$ length of a sector $$=(\frac{θ}{180})πr$$ $$=(\frac{45}{180})π(28)=(\frac{1}{4})π(28)=7×3.14 \cong 22$$ $$cm$$ ### Arc Length and Sector Area – Example 4: Find the area of the sector. $$(π=3.14), r=5$$ $$ft$$, $$\theta=80^\circ$$ Solution: Use this formula: Area of a sector $$=\color{blue}{πr^2 (\frac{θ}{360})}$$ Area of a sector $$=πr^2 (\frac{θ}{360})=(3.14)(5^2 )(\frac{80}{360})=(3.14)(25)(\frac{2}{9}) =17.44$$$$ft^2$$ ## Exercises for Finding Arc Length and Sector Area ### Find the length of each arc. Round your answers to the nearest tenth. • $$\color{blue}{r = 28 \ cm, \theta = 45^\circ}$$ • $$\color{blue}{r = 15 \ ft, \theta = 95^\circ}$$ • $$\color{blue}{r = 22 \ ft, \theta = 60^\circ}$$ • $$\color{blue}{r = 12 \ m, \theta = 85^\circ}$$ • $$\color{blue}{22 \ cm}$$ • $$\color{blue}{24.9 \ ft}$$ • $$\color{blue}{23 \ ft}$$ • $$\color{blue}{17.8 \ m}$$ ### What people say about "How to Find Arc Length and Sector Area? (+FREE Worksheet!)"? No one replied yet. X 30% OFF Limited time only! Save Over 30% SAVE $5 It was$16.99 now it is \$11.99	2022-10-07 11:28:31	{"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": 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": 0.9600664973258972, "perplexity": 995.3571360623154}, "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/1664030338073.68/warc/CC-MAIN-20221007112411-20221007142411-00175.warc.gz"}
https://workshops.nuevofoundation.org/python-tensorflow/activity-4/	# Activity 4 - Training the Model Workshop Resources The following code determines how many times model is trained. It is normal for this segment of code to take longer than usual to run. model.fit(train_images, train_labels, epochs=10) The following code prints out the overall test accuracy. test_loss, test_acc = model.evaluate(test_images, test_labels, verbose=2) print('\nTest accuracy:', test_acc) ### Question 1 Set the value of epochs equal to 2. What is the accuracy of the last epoch? What is the test accuracy when the trained model is compared to the test dataset? ### Question 2 Set the value of epochs equal to 10. Repeat Question 1. ### Question 3 Set the value of epochs equal to 20. Repeat Question 1. ### Question 4 What correlation do you see when you increase the number of epochs? Does the accuracy increase or decrease?	2022-08-08 09:35:29	{"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": 0.2662942111492157, "perplexity": 2524.0324454545275}, "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/1659882570793.14/warc/CC-MAIN-20220808092125-20220808122125-00033.warc.gz"}
https://www.cs.uaf.edu/2013/spring/cs331/docs/surv01res.html	CS 331 Spring 2013 > Language Survey Results # CS 331 Spring 2013 Language Survey Results Here are the results of the Language Survey that was given in class on Friday, January 18, 2013. Sixteen students took the survey. Results are presented only in aggregate form; no student names are given. ## A. Experience in listed languages The table below summarizes the answers to this part. Each of the columns headed by a number gives the number of people who rated themselves at that level. If a language was left blank on a survey form, this was taken as a “0” rating. If a rating between two values was given, then the higher value was used (e.g., “2–3” was recorded as “3”). If a cell is blank below, then no one rated themselves at that level. Language 0 1 2 3 Java 1 3 11 1 C# 7 6 1 2 Perl 13 3 Python 8 5 2 1 Ruby 14 2 Javascript 6 8 1 1 Haskell 15 1 ML/Caml/OCaml 16 Lisp/scheme (any) 14 2 Forth 16 Smalltalk 16 Prolog 16 ## B. Experience in other languages Answers to this question were inconsistently stated, so it is difficult to summarize the results numerically. Here are the programming languages—other than C++ and those above—that were listed by more than one person. I only list programming languages below; thus, for example, HTML is not included. • AutoHotkey • Bash • GLSL • MATLAB • PHP • R ## C. Languages students would like to learn more about Here are all the programming languages that were listed, in order of number of people who mentioned them. Language Number Listing Python 9 Perl 8 Ruby 7 Lisp 6 Haskell 4 JavaScript 3 Java 2 C 1 C# 1 Forth 1 PHP 1 Prolog 1 Racket 1 Note: I have listed Lisp and Racket separately above. However, Racket is an implementation of Scheme, which I would consider a dialect of Lisp (although some purists argue the point). In addition, two students expressed a general interest (“all of them”), one student was interested in functional languages, and one student was interested in learning more about languages that are relevant today. CS 331 Spring 2013: Language Survey Results / Updated: 20 Jan 2013 / Glenn G. Chappell / [email protected]	2018-08-22 05:58:40	{"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": 0.4110185503959656, "perplexity": 4180.014035821944}, "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-2018-34/segments/1534221219495.97/warc/CC-MAIN-20180822045838-20180822065838-00271.warc.gz"}
http://ijlyttle.github.io/bsplus/reference/bs_embed_tooltip.html	A tooltip can be a useful way to add a few words of explanation to a tag. bs_embed_tooltip(tag, title = "", placement = "top", ...) use_bs_tooltip() ## Arguments tag htmltools::tag, generally <button/> or <a/>, into which to embed the tooltip title character, title for the tooltip placement character, placement of the tooltip with respect to tag ... other named arguments, passed to bs_set_data() ## Value htmltools::tag, modified copy of tag ## Details To activate the use of tooltips in your page, you will need to call the use_bs_tooltip() function somewhere. The verb embed is used to signify that you are embedding information into a tag. This implies that you can embed, at most, one "thing" into a particular tag. You should not, for example, expect to embed both a tooltip and a popover into a tag. bs_embed_popover, http://getbootstrap.com/javascript/#tooltips library("htmltools") bs_embed_tooltip(title = "I'm a tooltip")#> <button type="button" class="btn btn-default" title="I'm a tooltip" data-toggle="tooltip" data-placement="top">I'm a button</button>	2017-03-29 19:00:38	{"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": 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": 0.4570535123348236, "perplexity": 8422.866510663207}, "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/1490218191353.5/warc/CC-MAIN-20170322212951-00271-ip-10-233-31-227.ec2.internal.warc.gz"}
https://math.stackexchange.com/questions/2885021/proof-verification-group-of-units-functor-is-not-monadic	# Proof verification: Group of units functor is not monadic Let $U : \mathbf{Rings} \to \mathbf{Groups}$ be the group of units functor. Note that $U$ has left adjoint $L$ given by the functor $G \mapsto \mathbb{Z}[G]$. Is $U$ monadic? I think I have the answer now, but given the confusion I'd like to get confirmation. Answer: No. Suppose that $U$ were monadic. Then that would imply that for every ring $R$, the map $\varepsilon_R : \mathbb{Z}[R^] \to R, e_u \mapsto u$ would be the coequalizer of a parallel pair and therefore surjective. However, consider the case $R = \mathbb{C}[t]$; then $R^ = \mathbb{C}^$, and so the map $\varepsilon_R : \mathbb{Z}[\mathbb{C}^] \to \mathbb{C}[t], e_\lambda \mapsto \lambda$ is certainly not surjective, giving a contradiction. $\quad\square$ So, I think the reason the functor doesn't satisfy the monadicity theorem is: even though $\mathbf{Rings}$ has coequalizers of all parallel pairs, $U$ must not respect coequalizers of all $U$-contractible pairs. Come to think of it, I wonder if it would also be possible to do a more direct proof by showing that $\mathbb{C}[t]^* \simeq \mathbb{C}^$ as $UL$-algebras, yet $\mathbb{C}[t] \not\simeq \mathbb{C}$, so $U$ cannot induce an equivalence of categories. I seem to keep getting bogged down in the details of checking what the $UL$-actions are on both sides. (I'm also curious about whether the induced functor $\mathbf{Rings} \to \mathbf{Groups}_{UL}$ is essentially surjective. Looking at it, I can't see any particular reason to expect any group $G$ with an action $\mathbb{Z}[G]^ \to G$ to be a group of units of a ring, yet I also can't immediately come up with a $UL$-algebra not in the essential image. But this part of the question isn't that important to me.) • Oh, I just realized - another proof would be: monadic functors must reflect isomorphisms, yet $U$ applied to the non-isomorphism $\mathbb{C} \hookrightarrow \mathbb{C}[t]$ is an isomorphism. – Daniel Schepler Aug 16 '18 at 19:27 • Which I guess also answers my question about $\mathbb{C}[t]^* \simeq \mathbb{C}^*$ as $UL$-algebras... – Daniel Schepler Aug 16 '18 at 19:45	2019-07-20 16:21:48	{"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": 0.9427529573440552, "perplexity": 207.7205937421082}, "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-2019-30/segments/1563195526536.46/warc/CC-MAIN-20190720153215-20190720175215-00207.warc.gz"}
http://caswenson.com/2009_04_19_responsible_development_practices_storing_sensitive_information.html	computer science, math, programming and other stuff a blog by Christopher Swenson # Responsible Development Practices: Storing Sensitive Information I build and maintain web sites. I manage probably hundreds of online accounts or logins or passwords that I need access to semi-regularly. Organizing all of this information can be a bit of a pain. I've heard people swear by spreadsheets or plain text files for storing this information, and there are some specialized programs out there meant to catalog and organize this for you. My solution is one of the simpler: TiddlyWiki. It's a small (few hundred K), self-contained (one HTML file), free file you can carry with you to store lots of information. I simply create some big list tiddlers (what they call their wiki pages), each one of which links to a specific tiddler for one particular task. So, I have a list for all of the web sites I maintain, and the tiddler for each has MySQL information, passwords, and any other crucial information. This is great, but there are two problems. One, I am putting all of critical info in one place. To fix this, I maintain copies of this wiki file in several places, such as my thumb drive, laptop, and DropBox. The second catch is then, what if someone finds this file? Wouldn't they have access to everything? This is why encryption is important. Whenever the file needs to be transported somewhere (like, on my thumb drive or put into DropBox), I first encrypt it. GPG is nice for this, but in a pinch, you can just use the ever-present OpenSSL to encrypt a file with something like: openssl enc -aes-256-cbc -salt -in file.html -out file.html.encrypted Now, as long as I remember this password, I can safely pass this encrypted file around without any worries about losing my thumb drive in the airport. For most of the actual machines I log into via SSH, I simply use public key authentication, that way I don't have to remember the passwords.	2018-10-17 17:08:12	{"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": 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": 0.378092497587204, "perplexity": 2317.733385557092}, "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/1539583511203.16/warc/CC-MAIN-20181017153433-20181017174933-00073.warc.gz"}
https://socratic.org/questions/a-spring-with-a-constant-of-12-kg-s-2-is-lying-on-the-ground-with-one-end-attach-7	A spring with a constant of 12 (kg)/s^2 is lying on the ground with one end attached to a wall. An object with a mass of 8 kg and speed of 3 m/s collides with and compresses the spring until it stops moving. How much will the spring compress? May 13, 2016 $\sqrt{6} m$ Explanation: Consider the inital and final conditions of the two objects (namely, spring and mass): • Initially: Spring is at lying at rest, potential energy = $0$ Mass is moving, kinetic energy = $\frac{1}{2} m {v}^{2}$ • Finally: Spring is compressed, potential energy = $\frac{1}{2} k {x}^{2}$ Mass is stopped, kinetic energy = 0 Using conservation of energy (if no energy is dissipated into the surroundings), we have: $0 + \frac{1}{2} m {v}^{2} = \frac{1}{2} k {x}^{2} + 0$ $\implies \cancel{\frac{1}{2}} m {v}^{2} = \cancel{\frac{1}{2}} k {x}^{2}$ $\implies {x}^{2} = \left(\frac{m}{k}\right) {v}^{2}$ $\therefore x = \sqrt{\frac{m}{k}} v = \sqrt{\frac{8 k g}{12 k g {s}^{-} 2}} \times 3 m {s}^{-} 1 = \sqrt{6} m$	2020-07-14 04:38:01	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 8, "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": 0.3695879280567169, "perplexity": 657.2373692031205}, "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-2020-29/segments/1593657147917.99/warc/CC-MAIN-20200714020904-20200714050904-00225.warc.gz"}
https://wulixb.iphy.ac.cn/en/custom/topics	x ## 留言板 ### Novel properties of low-dimensional materials 纵观历史, 人类对材料的认知不断推动着社会的进步和发展, 这方面在过去一个多世纪对材料电学性质的研究上体现得尤为显著. 我们可以将材料粗略地分为金属、半导体、绝缘体, 也可以分为超导、非超导、磁性、非磁性等. 不难发现, 所有这些性质都源于同一种微观粒子: 电子. 随着研究的深入, 科学家们开始期待在一种材料中能实现以上多种甚至所有可能的电子态. 最近, 以二维体系为代表的低维体系研究向我们展示了实现这一愿景的可能性. 在低维体系中, 维度的降低导致体系对载流子浓度、介电环境、压强、应力、电场、磁场等非常敏感. 因此, 我们可以在一个极其宽广的多参数空间对其结构和物性进行精细调控, 进而实现一系列新奇量子物态. 例如在魔角双层石墨烯中就可实现金属/关联绝缘态, 非超导/超导, 非磁性/磁性, 甚至量子反常霍尔效应等多种新奇物态.一方面, 基于低维体系的这些研究极大地推进了人们对凝聚态物理中各种新奇量子物态、相变以及准粒子关联等问题的深入理解; 另一方面, 低维体系高度可调的特点也为其在未来的应用提供更广阔的空间. 值得一提的是, 低维材料的一个显著优势是其新奇物态都直接暴露在材料表面, 这为直接观测这些量子物态提供了一个前所未有的机会. 最近, 科学家们利用扫描隧道显微镜成功地实现了对石墨烯中的量子霍尔铁磁态、双层石墨烯畴界的谷极化导电通道、拓扑绝缘体中的拓扑边界态的直接观测. 相关研究可以更好地帮助我们深入理解这些新奇量子物态并澄清其微观物理机制. 低维材料体系涵盖了超导、拓扑、磁学、铁电等几乎所有凝聚态物理中重要的研究课题, 对其新奇物性的深入理解和精准调控可以为后期电子器件的构筑打下坚实的基础. 在过去几十年里, 大量的科研工作者们在该领域持续深耕, 不断发现丰富有趣的物理现象, 并深入理解其物理机制, 发展多种手段实现了对这些新奇量子物态的调控. 尤其是在近十年间, 这一领域的发展以及取得的成果格外令人瞩目, 国内很多优秀科研团队极大地推进了低维材料的物性研究, 做出了突出的成绩. 我们相信, 这些成果不但在基础研究上具有重要的学术价值, 也为未来技术发展和进步打下了坚实的基础. 正因为如此, 为了让读者了解低维材料新奇物性的最新研究成果, 本专题特别邀请了部分在低维物性领域活跃的专家学者, 从低维材料的制备、结构/能带表征与调控、光学特性、量子受限效应、电荷密度波、磁性、超导、关联电子态等诸方面, 以不同的视角介绍本领域的背景、最新进展并展望相关领域未来的发展方向, 希望对感兴趣的读者及相关领域的工作人员提供一定的参考及借鉴. Acta Physica Sinica.2022, 71(12). 2022, 71 (12): 120101. doi: 10.7498/aps.71.120101 Abstract + 2022, 71 (12): 126101. doi: 10.7498/aps.71.20220035 Abstract + Exploring the structure of low-dimensional materials is a key step towards a complete understanding of condensed matter. In recent years, owing to the fast developing of research tools, novel structures of many elements have been reported, revealing the possibility of new properties. Refining the investigation of one-dimensional atomic chain structures has thus received a great amount of attention in the field of condensed matter physics, materials science and chemistry. In this paper, we review the recent advances in the study of confined structures under nanometer environments. We mainly discuss the most interesting structures revealed and the experimental and theoretical methods adopted in these researches, and we also briefly discuss the properties related to the new structures. We particularly focus on elemental materials, which show the richness of one-dimensional structures in vacuum and in nanoconfinement. By understanding the binding and stability of various structures and their properties, we expect that one-dimensional materials should attract a broad range of interest in new materials discovery and new applications. Moreover, we reveal the challenges in accurate theoretical simulations of one-dimensional materials in nanoconfinement, and we provide an outlook of how to overcome such challenges in the future. 2022, 71 (12): 127101. doi: 10.7498/aps.71.20220079 Abstract + Understanding strongly correlated electrons is an important long-term goal, not only for uncovering fundamental physics behind, but also for their emergence of lots of novel states which have potential applications in quantum control and quantum computations. Meanwhile, the strongly correlated electrons are usually extremely hard problems, and it is generally impossible to understand them unbiasedly. Quantum Monte Carlo is a typical unbiased numeric method, which does not depend on any perturbation, and it can help us to exactly understand the strongly correlated electrons, so that it is widely used in high energy and condensed matter physics. However, quantum Monte Carlo usually suffers from the notorious sign problem. In this paper, we introduce general ideas to design sign problem free models and discuss the sign bound theory we proposed recently. In the sign bound theory, we build a direct connection between the average sign and the ground state properties of the system. We find usually the average sign has the conventional exponential decay with system size increasing, leading to exponential complexity; but for some cases it can have algebraic decay, so that quantum Monte Carlo simulation still has polynomial complexity. By designing sign problem free or algebraic sign behaved strongly correlated electron models, we can approach to several long outstanding problems, such as the itinerant quantum criticality, the competition between unconventional superconductivity and magnetism, as well as the recently found correlated phases and phase transitions in moiré quantum matter. 2022, 71 (12): 127102. doi: 10.7498/aps.71.20220054 Abstract + Atomically thin transition metal dichalcogenides (TMDCs) like MX2 (M = W or Mo, X = S or Se) are well-known examples of two-dimensional (2D) semiconductors. They have attracted wide and long-lasting attention due to the strong light-matter interaction and unique spin-valley locking characteristics. In the 2D limit, the reduced dielectric screening significantly enhances the Coulomb interaction. The optical properties of monolayer TMDCs are thus dominated by excitons, the tightly bound electron-hole pairs. In this work, we briefly overview the history and recent research progress of optical spectroscopy studies on TMDCs. We first introduce the layer-dependent band structure and the corresponding modifications on optical transitions, and briefly mention the effects of external magnetic fields and the charge doping on excitons. We then introduce a novel sensing technique enabled by the sensitivity of excitons to the dielectric environment. The exciton excited states (Rydberg states) observed in monolayer TMDCs have large Bohr radii (> few nm), where the electric field lines between electron-hole pairs well extends out of the material. Hence the Coulomb interaction (which affects the quasiparticle band gap and exciton binding energies) in the monolayer TMDC is sensitive to the dielectric environment, making the excitons in 2D semiconductor an efficient quantum sensor in probing dielectric properties of the surroundings. The method is of high spatial resolution and only diffraction limited. We enumerate the applications of monolayer WSe2 dielectric sensor in detecting the secondary Dirac point of graphene induced by the graphene-hBN superlattice potential, as well as the fractional correlated insulating states emerging in WS2/WSe2 moiré superlattices. Meanwhile, a unified framework for describing the many-body interactions and dynamical screenings in the system is still lacking. Future theoretical and experimental efforts are needed for a complete understanding. Finally, we further discuss the perspectives and potential applications of this non-destructive and efficient dielectric sensing method. 2022, 71 (12): 127103. doi: 10.7498/aps.71.20220052 Abstract + Charge density waves (CDWs) have triggered off extensive research in low-dimensional systems. The discovery of CDW offers a new crucial clue to understanding the intrinsic mechanisms of low-dimensional electron-phonon coupling and electron correlation. In addition, the physical properties of low-dimensional material such as magnetism and superconductivity can be fine-tuned with accurately and effectively controlled CDW phase. At the beginning,we briefly introduce the basic properties of CDW in one-dimensional and quasi one-dimensional materials, revealing the physical proprieties of the CDW, for instance, the excited state and the manipulation technologies. Then, focusing on the CDW in a two-dimensional system, we mainly introduce the recent research progress and the generation mechanism of CDW of two-dimensional materials. The interaction between CDW and Mott insulator and between superconductivity and other orders such as spin density wave and pair density wave provide a new perspective to research the multi-electron collective excitation and electron interaction. The manipulation of multi-electron collective excitation and electron-phonon interaction in CDW through doping, high pressure and laser pulse is also introduced and shares similarity with the one-dimensional system. Finally, in this article we propose a potential research application of two dimensional CDW. 2022, 71 (12): 127104. doi: 10.7498/aps.71.20220272 Abstract + Polaritons, i.e. new collective modes formed by the strong coupling between light and electrons, phonons, excitons, or magnons in matter, have recently received extensive attention. Polaritons in low-dimensional materials exhibit strong spatial confinement, high quality factor, and gate-tunability. Typical examples include gate-tunable graphene surface plasmon polaritons, high-quality hyperbolic phonon polaritons in hexagonal boron nitride, topological phonon polaritons in α-MoO3, and one-dimensional Luttinger-liquid plasmon polaritons in carbon nanotubes. These unique properties make polaritons an excellent candidate for future nano-photonics devices. Further, these polaritons can significantly interact with each other, resulting in a variety of polariton-polariton coupling phenomena, greatly expanding their applications. In this review paper, we first introduce scanning near-field optical microscopy, i.e. the technique used to probe polaritons in low-dimensional materials, then give a brief introduction to the basic properties of polaritons. Next, we discuss in detail the coupling behavior between various polaritons. Finally, potential applications of polaritons coupling are proposed. 2022, 71 (12): 127202. doi: 10.7498/aps.71.20220064 Abstract + Two-dimensional (2D) materials can exhibit novel quantum phenomena and be easily tuned by the external environment, which has made them one of the most attractive topics in condensed matter physics during the recent decades. The moiré superlattice induced by varied stacking geometry can further renormalize the material band structure, resulting in the electronic flat bands. With the help of external fields, one can tune the electron-electron correlated interaction in these flat bands, even control the overall physical properties. In this paper we review the recent researches of novel properties in twisted 2D materials (graphene and transition metal dichalcogenide heterostructure), involving strong correlation effect, unconventional superconductivity, quantum anomalous Hall effect, topological phase, and electronic crystals. We also discuss some open questions and give further prospects in this field. 2022, 71 (12): 127302. doi: 10.7498/aps.71.20220225 Abstract + In flat bands of two-dimensional materials, the mass of charge carriers increases dramatically and the Coulomb energy of the charge carriers can be much larger than the quenched kinetic energy. When the flat band is partially filled, electron-electron interactions can drive electrons to form exotic correlated phases, such as quantum Hall ferromagnetism, fractional quantum Hall effect, superconductivity, and quantum anomalous Hall effect. Therefore, flat bands in two-dimensional materials have attracted much attention very recently. In the past few years, the strongly correlated phenomena in flat bands have become a hot topic in community of condensed matter physics. There are several different methods, such as using a perpendicular magnetic field, introducing strained structures, and introducing a twist angle, to realize the flat bands in two-dimensional materials. In this review article, we summarize the methods to realize flat bands in two-dimensional systems and introduce the related novel electronic states when the flat band is partially filled. 2022, 71 (12): 127304. doi: 10.7498/aps.71.20220118 Abstract + The enhancement of superconductivity in one unit-cell FeSe grown on SrTiO3 is an important discovery in high-temperature superconductivity. In this system, the crucial role of the SrTiO3 substrate has been extensively studied. Its contribution mainly manifests in two aspects: charge transfer and interfacial electron-phonon coupling. However, study of the intrinsic properties of the FeSe thin film itself is still insufficient. In this article, we review the latest research progress of the mechanism of the enhancement of superconductivity in FeSe/SrTiO3, covering the newly discovered stripe phase and its relationship with superconductivity. By using scanning tunneling microscope and molecular beam epitaxy growth method, we find that the electrons in FeSe thin film tend to form stripe patterns, and show a thickness-dependent evolution of short-range to long-range stripe phase. The stripe phase, a kind of electronic liquid crystal state (smectic), originates from the enhanced electronic correlation in FeSe thin film. Surface doping can weaken the electronic correlation and gradually suppress the stripe phase, which can induce superconductivity as well. More importantly, the remaining smectic fluctuation provides an additional enhancement to the superconductivity in FeSe film. Our results not only deepen the understanding of the interfacial superconductivity, but also reveal the intrinsic uniqueness of the FeSe films, which further refines the mechanism of superconductivity enhancement in FeSe/SrTiO3. 2022, 71 (12): 127305. doi: 10.7498/aps.71.20220349 Abstract + Ferroelectric (FE) materials possess electrically switchable spontaneous polarizations, showing broad applications in various functional devices. For the miniaturization of electronic devices, two-dimensional (2D) van der Waals (vdW) ferroelectric materials and the corresponding bulk counterparts have aroused more interest of researchers. Recently, several kinds of 2D vdW ferroelectrics have been fabricated in experiment. These 2D vdW FEs, as well as their bulk counterparts, exhibit novel properties as demonstrated in experiment or predicted in theory. This paper is to review the recent progress of novel properties of several vdW ferroelectrics. In Section II, we introduce the unusual ferroelectric property—a uniaxial quadruple potential well for Cu displacements—enabled by the van der Waals gap in copper indium thiophosphate (CuInP2S6). The electric field drives the Cu atoms to unidirectionally cross the vdW gaps, which is distinctively different from dipole reorientation, resulting in an unusual phenomenon that the polarization of CuInP2S6 aligns against the direction of the applied electric field. The potential energy landscape for Cu displacements is strongly influenced by strain, accounting for the origin of the negative piezoelectric coefficient and making CuInP2S6 a rare example of a uniaxial multi-well ferroelectric. In Section III, we introduce the distinct geometric evolution mechanism of the newly reported M2Ge2Y6 (M = metal, X = Si, Ge, Sn, Y = S, Sn, Te) monolayers and a high throughput screening of 2D ferroelectric candidates based on this mechanism. The ferroelectricity of M2Ge2Y6 originates from the vertical displacement of Ge-dimer in the same direction driven by a soft phonon mode of the centrosymmetric configuration. Another centrosymmetric configuration is also dynamically stable but higher in energy than the ferroelectric phase. The metastable centrosymmetric phase of M2Ge2Y6 monolayers allows a new two-step ferroelectric switching path and may induce novel domain behaviors. In Section IV, a new concept about constructing 2D ferroelectric QL-M2O3/graphene heterostructure to realize monolayer-based FE tunnel junctions or potentially graphene p-n junctions is reviewed. These findings provide new perspectives of the integration of graphene with monolayer FEs, as well as related functional devices. Finally, the challenge and prospect of vdW ferroelectrics are discussed, providing some perspective for the field of ferroelectrics. 2022, 71 (12): 127306. doi: 10.7498/aps.71.20220015 Abstract + Molybdenum disulfide is a layered transition metal chalcogenide semiconductor. It has many applications in the fields of two-dimensional spintronics, valleytronics and optoelectronics. In this review, molybdenum disulfide is taken as a representative to systematically introduce the energy band structures of single layer, bilayer and twisted bilayer molybdenum disulfide, as well as the latest experimental progress of its realization and low-temperature electrical transport, such as superconductivity and strong correlation phenomenon. Finally, two-dimensional transition metal chalcogenide moiré superlattice’s challenges in optimizing contact and sample quality are analyzed and the future development of this field is also presented. 2022, 71 (12): 127307. doi: 10.7498/aps.71.20220085 Abstract + Low-dimensional material represents a special structure of matter. The exploring of its novel properties is an important frontier subject in the fundamental research of condensed matter physics and material science. Owing to its small length scale in one or two dimensions, low-dimensional materials are usually flexible in structure. This feature together with the prompt electronic response to structural deformations enable us to modulate the material properties via a strain way. The main purpose of this paper is to introduce the recent research progress of obtaining novel physical properties by inhomogeneously straining two-dimensional materials, with focusing on two effects, i.e., pseudomagnetic field effect and the flexoelectric effect. Of course, the influence of inhomogeneous strains on electrons is not limited to these two effects. Fundamentally, an inhomogeneous deformation breaks the symmetry of crystalline structure. This may serve as a start point to delineate the structural-properties relation. First, the symmetry breaking can eliminate the degeneracy of energy levels. Second, the symmetry breaking will also cause the heterogeneity of electronic and phonon properties in different parts of the material.In the paper, we also introduce a special method named the generalized Bloch theorem that is suitable for dealing with the inhomogeneous strain patterns at an atomistic level. From the perspective of atomistic simulation, due to the breaking of translational symmetry, the standard quantum mechanical calculations encounter fundamental difficulties in dealing with an inhomogeneous strain, e.g., bending and torsion. The generalized Bloch method overcomes such an obstacle by considering rotational and/or screw symmetries given by bending and/or torsion in solving the eigenvalue problem. As such, quantum mechanical calculations can be still conducted with a relatively small number of atoms. 2022, 71 (12): 127308. doi: 10.7498/aps.71.20220100 Abstract + Quantum spin Hall effect, usually existing in two-dimensional (2D) topological insulators, has topologically protected helical edge states. In the year 2014, there was raised a theoretical prediction that monolayer transition metal dichalcogenides (TMDs) with 1T' phase are expected to be a new class of 2D quantum spin Hall insulators. The monolayer 1T'-WTe2 has attracted much attention, because it has various excellent characteristics such as stable atomic structures, an obvious bandgap opening in the bulk of monolayer 1T'-WTe2, and tunable topological properties, which paves the way for realizing a new generation of spintronic devices. In this review, we mainly summarize the recent experimental progress of the 2D quantum spin Hall insulators in monolayer 1T'-WTe2, including the sample preparation via a molecular beam epitaxy technique, the detection of helical edge states and their response on external magnetic fields, as well as the modulation of more rich and novel quantum states under electron doping or strain. Finally, we also prospect the future applications based on monolayer 1T'-WTe2. 2022, 71 (12): 127309. doi: 10.7498/aps.71.20220347 Abstract + A moiré superlattice can be formed by overlaying two atomically thin van der Waals materials with a rotation angle or with a lattice mismatch. Since the discovery of correlated insulators and superconductivity in magic angle twisted bilayer graphene, constructing moiré superlattices by various two-dimensional (2D) van der Waals materials and studying their novel properties emerge as a hot topic and research frontier in condensed matter physics. Here we review the recent experimental progress of 2D transition metal dichalcogenide moiré superlattices. In this system, the formation of moiré flat band does not rely on certain magic angles. Experimentally, a series of correlated electron states and topological states have been discovered and confirmed. Further theoretical and experimental studies can find a wealth of emergent phenomena caused by the combined influence of strong correlation and topology in transition metal dichalcogenide moiré superlattice. 2022, 71 (12): 127402. doi: 10.7498/aps.71.20212289 Abstract + Low-dimensional superconductor serves as an excellent platform for investigating emergent superconducting quantum oscillation phenomena. The low-dimensional natures of these materials, originating from the finite size which is comparable with the superconducting coherence length, indicate that the corresponding physical properties will be constrained by quantum confinement effects. Importantly, some of the frontiers and hot issues in low-dimensional superconductors, including the anomalous metal state during the superconductor-insulator transition, spin-triplet pairing mechanism in superconductors, thermal-excited and electrical current-excited vortex dynamics in superconductors, and the “charge-vortex duality” in quantum dot materials and superconducting nanowires, are strongly correlated with the superconducting quantum oscillation effects. In recent years, all the above-mentioned topics have achieved breakthroughs based on the studies of superconducting quantum oscillation effects in low-dimensional superconductors. Generally, the periodicity and amplitude of the oscillation can clearly demonstrate the relation between the geometric structure of superconductors and various superconducting mechanisms. In particular, superconducting quantum oscillation phenomena are always correlated with the quantization of magnetic fluxoids and their dynamics, the pairing mechanism of superconducting electrons, and the excitation and fluctuation of superconducting systems.In this review article, three types of typical superconducting quantum oscillation effects observed in low-dimensional superconductors will be discussed from the aspects of research methods, theoretical expectations, and experimental results. a) The Little-Parks effect is the superconducting version of the Aharonov-Bohm effect, whose phase, amplitude and period are all helpful in studying superconductivity: the phase reflects the pairing mechanism in superconductors, the amplitude can be used for investigating the anomalous metal state, and the period provides the information about the sample geometry. b) The vortex motion effect is excited by thermal fluctuation or electrical current, and the corresponding oscillation phenomena show distinct temperature-dependent amplitudes compared with the Little-Parks effect. c) The Weber blockade effect originates from the magnetic flux moving across the superconducting nanowire, and such an effect provides a unique nonmonotonic critical current ${I}_{\mathrm{C}}$ under a magnetic field in $I\text{-}V$ characteristics. The prospects of the above-mentioned quantum oscillation effects of low-dimensional superconductors for applications are also discussed at the end of this review, including quantum computing, device physics and low-temperature physics. 2022, 71 (12): 127403. doi: 10.7498/aps.71.20220856 Abstract + Abundant novel physical properties have been observed in thin-flake samples of two-dimensional correlated electronic systems prepared by mechanical exfoliation. Developing new methods of preparing bulk two-dimensional samples can further understand the low-dimensional system by combining traditional bulk characterization methods like X-ray diffraction, magnetic susceptibility and specific heat measurements. It is possible to maintain the novel properties of thin-flake samples in bulk state and promote these novel physical properties for potential applications. This article introduces a class of organic molecular intercalation methods to regulate two-dimensional correlated electronic systems, focusing on the changes of structure and physical properties of two-dimensional materials after organic molecular intercalation. The applications of organic molecular intercalation method in regulating thermoelectricity, two-dimensional magnetism, charge density wave and two-dimensional superconductivity are also presented. 2022, 71 (12): 127504. doi: 10.7498/aps.71.20220301 Abstract + Two-dimensional (2D) magnetic materials with magnetic anisotropy can form magnetic order at finite temperature and monolayer limit. Their macroscopic magnetism is closely related to the number of layers and stacking forms, and their magnetic exchange coupling can be regulated by a variety of external fields. These novel properties endow 2D magnetic materials with rich physical connotation and potential application value, thus having attracted extensive attention. In this paper, the recent advances in the experiments and theoretical calculations of 2D magnets are reviewed. Firstly, the common magnetic exchange mechanisms in several 2D magnetic materials are introduced. Then, the geometric and electronic structures of some 2D magnets and their magnetic coupling mechanisms are introduced in detail according to their components. Furthermore, we discuss how to regulate the electronic structure and magnetism of 2D magnets by external (field modulation and interfacial effect) and internal (stacking and defect) methods. Then we discuss the potential applications of these materials in spintronics devices and magnetic storage. Finally, the encountered difficulties and challenges of 2D magnetic materials and the possible research directions in the future are summarized and prospected. 2022, 71 (12): 127505. doi: 10.7498/aps.71.20220727 Abstract + The spontaneous magnetization of two-dimensional (2D) magnetic materials can be maintained down to the monolayer limit, providing an ideal platform for understanding and manipulating magnetic-related properties on a 2D scale, and making it important for potential applications in optoelectronics and spintronics. Transition metal halides (TMHs) are suitable 2D magnetic candidates due to partially filled d orbitals and weak interlayer van der Waals interactions. As a sophisticated thin film growth technique, molecular beam epitaxy (MBE) can precisely tune the growth of 2D magnetic materials reaching the monolayer limit. Moreover, combining with the advanced experimental techniques such as scanning tunneling microscopy, the physical properties of 2D magnetic materials can be characterized and manipulated on an atomic scale. Herein, we introduce the crystalline and magnetic structures of 2D magnetic TMHs, and show the 2D magnetic TMHs grown by MBE and their electronic and magnetic characterizations. Then, the MBE-based methods for tuning the physical property of 2D magnetic TMHs, including tuning interlayer stacking, defect engineering, and constructing heterostructures, are discussed. Finally, the future development opportunities and challenges in the field of the research of 2D magnetic TMHs are summarized and prospected. 2022, 71 (12): 128102. doi: 10.7498/aps.71.20220405 Abstract + Atomic manipulation technique with scanning tunneling microscopy (STM) has been used to control the structural and physical properties of materials at an atomic level. Recently, this technique has been extended to modifying the physical properties of low-dimensional materials. Unlike conventional single atom lateral manipulation, the STM manipulation technique in the study of low-dimensional materials has additional manipulation modes and focuses on the modification of physical properties. In this review paper, we introduce the recent experimental progress of tuning the physical properties of low-dimensional materials through STM atomic manipulation technique. There are mainly four manipulation modes: 1) tip-induced local electric field; 2) controlled tip approach or retract; 3) tip-induced non-destructive geometry manipulation; 4) tip-induced kirigami and lithography. Through using these manipulation modes, the STM tip effectively introduces the attractive force or repulsive force, local electronic field or magnetic field and local strain, which results in the atomically precise modification of physical properties including charge density wave, Kondo effect, inelastic tunneling effect, Majorana bound states, and edge states. 2022, 71 (12): 123601. doi: 10.7498/aps.71.20212426 Abstract + Thermally activated delayed fluorescence (TADF), a unique molecular fluorescence mechanism, plays a key role in designing emitters of high efficiency. Carbon fullerenes such as C60 and C70 exhibit strong TADF with intensity even higher than that of the prompt fluorescence, owing to their long lifetimes of triplet state and modest singlet-triplet energy gaps. Thus, there arises the intriguing question whether other fullerene-like clusters can also have fluorescence and host the TADF effect. In this work, by time-dependent density functional theory (TD-DFT) calculations, we explore the excited-states of the experimentally reported boron nitride cage clusters B12N12, B24N24 and B36N36, as well as compound clusters B12P12, Al12N12 and Ga12N12 with the same geometry as B12N12. Using the HSE06 hybrid functional, the predicted energy gaps of these fullerene-like clusters are obtained to range from 2.83 eV to 6.54 eV. They mainly absorb ultraviolet light, and their fluorescence spectra are all in the visible range from 405.36 nm to 706.93 nm, including red, orange, blue, and violet emission colors. For the boron nitride cages, the energy gap of excited states increases with the cluster size increasing, accompanied by a blue shift of emission wavelength. For the clusters with B12N12 geometry and different elemental compositions, the excited energy gap decreases as the atomic radius increases, resulting in a red shift of emission wavelength. In addition, the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of these compound cage clusters are distributed separately on different elements, resulting in small overlap between HOMO and LUMO wavefunctions. Consequently, these fullerene-like clusters exhibit small singlet-triplet energy differences below 0.29 eV, which is beneficial for the intersystem crossing between the excited singlet state and triplet state, and hence promoting the TADF process. Our theoretical results unveil the fluorescence characteristics of cage clusters other than carbon fullerenes, and provide important guidance for precisely modulating their emission colors by controlling the cluster sizes and elemental compositions. These experimentally feasible fullerene-like compound clusters possess many merits as fluorophors such as outstanding stabilities, non-toxicity, large energy gap, visible-light fluorescence, and small singlet-triplet energy gap. Therefore, they are promising luminescent materials for applications in display, sensors, biological detection and labelling, therapy, and medicine. 2022, 71 (12): 127203. doi: 10.7498/aps.71.20220029 Abstract + Graphene, a special two-dimensional material, has a unique band structure that allows the type and concentration of carriers to be controlled through a gate voltage, and it has potential applications in bipolar nanoelectronic devices. In this paper, based on the tight-binding model of graphene p-n junctions, by using the nonequilibrium Green’s function method and Landauer-Büttiker formula, the thermal dissipation of electric transport in graphene p-n junctions in a magnetic field is investigated. Under a strong magnetic field, both sides of the junction are in the quantum Hall regime, thus the topologically protected chiral edge states appear. Intuitively, the topologically protected chiral edge states are dissipationless. However, the results show that thermal dissipation can occur in the quantum Hall regime in graphene junctions in the presence of dissipation sources, although the topologically protected chiral edge states still exist. In clean graphene junctions, thermal dissipation occurs mainly at the edge for the unipolar transport, but it occurs both at the edge and at the interface of the junctions for the bipolar transport. In the presence of disorder, thermal dissipation is significantly enhanced both in the unipolar junction and in the bipolar junction, and it increases with disorder strength increasing. Besides, the energy distribution of electrons at different positions is also studied, which shows that the thermal dissipation always occurs as long as the energy distribution is in nonequilibrium. This indicates that the topology can protect only the propagation direction of electrons, but it can not suppress the occurrence of thermal dissipation. 2022, 71 (12): 127204. doi: 10.7498/aps.71.20220062 Abstract + Graphene can find great potential applications in the future electronic devices. In bilayer graphene, the relative rotation angle between graphene layers can modulate the interlayer interaction and hence induces rich physical phenomena. We systematically study the temperature dependent magnetoresistance (MR) properties in the epitaxial bilayer graphene (BLG) grown on the SiC substrate. High quality BLG is synthesized by molecular beam epitaxy in ultra-high vacuum. We observe the negative MR under a small magnetic field applied perpendicularly at temperature < 80 K, which is attributed to a weak localization effect. The weak localization effect in our epitaxial BLG is stronger than previously reported ones in epitaxial monolayer and multilayer graphene system, which is possibly because of the enhanced interlayer electron transition and thus the enhanced valley scattering in the BLG. As the magnetic field increases, the MR exhibits a classical Lorentz MR behavior. Moreover, we observe a linear magnetoresistance behavior in a large field, which shows no saturation for the magnetic field of up to 9 T. In order to further investigate the negative and linear magnetoresistance, we conduct angle-dependent magnetoresistance measurements, which indicates the two-dimensional magnetotransport phenomenon. We also find that the negative MR phenomenon occurs under a parallel magnetic field, which may correspond to the moiré pattern induced local lattice fluctuation as demonstrated by scanning tunneling microscopy measurement on an atomic scale. Our work paves the way for investigating the intrinsic properties of epitaxial BLG under various conditions. 2022, 71 (12): 127303. doi: 10.7498/aps.71.20220246 Abstract + We introduce two contactless measurement methods at extremely low temperature: capacitances and surface acoustic waves. Both methods can be used to study the physical properties of the quantum system through the interaction between electrons and high frequency electric field. We first present preliminary results of high-mobility two-dimensional electron systems studied by a high-precision capacitance measurement method at extremely low temperature. Our setup can resolve < 0.05% variation of a < 1 pF capacitance at 10 mK–300 K and 0–14 T. Second, we also study two-dimensional electron systems using surface acoustic waves. We can use 0.1 nW excitation and obtain < 10–5 sensitivity. These measurement methods may be widely applied to the study of two-dimensional systems, especially the materials without high quality contacts. 2022, 71 (12): 127401. doi: 10.7498/aps.71.20220050 Abstract + Bismuth (Bi), as a stable heaviest element in the periodic table of elements, has strong spin-orbit coupling, which has attracted a lot of attention as the parent material of various known topological insulators. Previous calculations predicted that Bi(111) with a thickness less than eight bilayers and the ultrathin black-phosphorus-like Bi(110) films are single-element two-dimensional (2D) topological insulators. However, it is generally believed that these crystalline bismuth phases are not superconducting or their transition temperature should be lower than 0.5 mK. Lead (Pb) is a good superconducting elementary material, and there is a relatively small difference in radius between the Bi atom and Pb atom. According to the Hume-Rothery rule, it is expected that Pb/Bi alloys in an arbitrary ratio should be superconducting. One may thus expect to form crystalline Bi based superconductors by Pb substitution, which might host intriguing topological superconductivity. While our previous work has demonstrated a low-temperature stable Pb1–xBix (x~0.1) alloy phase in which Pb in the Pb(111) structure is partially replaced by Bi, the Bi crystalline structure-based phases of the superconducting alloys still lack in-depth research. Here, we report a new low-temperature phase of Pb-Bi alloy thin film, namely PbBi3, on the Si(111)-(7 × 7) substrate, by co-depositing Pb and Bi at a low temperature of about 100 K followed by an annealing treatment of 200 K for 2 h. Using low-temperature scanning tunneling microscopy and spectroscopy (STM/STS), we characterize in situ the surface structure and superconducting properties of the Pb-Bi alloy film with a nominal thickness of about 4.8 nm. Two spatially separated phases with quasi-tetragonal structure are observed in the surface of the Pb-Bi alloy film, which can be identified as the pure Bi(110) phase and the PbBi3 phase, respectively, based on their distinct atomic structures, step heights and STS spectra. The PbBi3 film has a base structure similar to Bi(110), where about 25% of the Bi atoms are replaced by Pb, and the surface shows a $\sqrt 2 \times \sqrt 2 R{45^ \circ }$ reconstructed structure. The superconducting behavior of the PbBi3 phase is characterized using variable-temperature STS spectra. We obtain that the superconducting transition temperature of PbBi3 is about 6.13 K, and the $2\varDelta (0)/{k_{\text{B}}}{T_{\text{c}}}$ ratio is about 4.62 using the fitting parameter of $\varDelta (0) = 1.22{\text{ meV}}$ at 0 K. By measuring the magnetic field dependent superconducting coherence length, the critical field is estimated at larger than 0.92 T. We further investigate the superconducting proximity effect in the normal metal-superconductor (N-S) heterojunction consisting of the non-superconducting Bi(110) domain and the superconducting PbBi3 domain. The N-S heterojunctions with both in-plane configuration and step-like configuration are measured, which suggest that the atomic connection and the area of the quasi-2D Josephson junctions and the external magnetic field can affect the lateral superconducting penetration length. We also observe the zero-bias conductance peaks (ZBCPs) in the superconducting gap of the PbBi3 surface in some cases at zero magnetic field. By measuring dI/dV spectra at various temperatures and by adopting a superconducting Nb tip, we identify that the ZBCP originates from the superconductor-insulator-superconductor (S-I-S) junction formed between a superconducting tip and the sample. Nevertheless, the Bi(110)-based PbBi3 phase may provide a possible platform to explore the intriguing topological superconducting behaviors at the vortexes under magnetic fields, or in the vicinity of the potentially topological superconducting Bi(110) islands by considering the proximity effect. 2022, 71 (12): 127503. doi: 10.7498/aps.71.20220699 Abstract + Van der Waals (vdW) layered ferromagnetic materials provide a unique platform for fundamental spintronic research, and have broad application prospects in the next-generation spintronic devices. In this study, we synthesize high-quality single crystals of vdW intrinsic ferromagnet Ta3FeS6 by the chemical vapor transport method. We obtain thin layer samples of Ta3FeS6 with thickness values ranging from 19 to 100 nm by the mechanical exfoliation method, and find that their corresponding Curie temperatures are between 176 and 133 K. The anomalous Hall measurement shows that the Ta3FeS6 has out-of-plane ferromagnetism with the coercivity reaching 7.6 T at 1.5 K, which is the largest value in those of the layered vdW ferromagnetic materials reported so far. In addition, we observe that the reversal polarity of the hysteresis loop changes sign with temperature increasing. Our work provides an opportunity to construct stable and miniaturized spintronic devices and present a new platform for studying spintronics based on van der Waals magnetic materials. 2022, 71 (12): 127901. doi: 10.7498/aps.71.20220458 Abstract + Transition metal dichalcogenides (TMDs) have attracted a lot of interest in condensed matter physics research due to the existence of multiple novel physical phenomena, including superconductivity and charge density wave order, and also TMDs provide a unique window for studying the interactions between different ground states. In this work, the electronic structure of 1T-NbSeTe is systematically examined by angle-resolved photoemission spectroscopy (ARPES) for the first time. A van Hove singularity (VHS) is identified at the M point, with binding energy of 250 meV below the Fermi level. Careful analysis is carried out to examine the band dispersions along different high symmetry directions and the possible many-body effect. However, the dispersion kink—a characteristic feature of electron-boson coupling is not obvious in this system. In TMD materials, the van Hove singularity near the Fermi level and the electron-boson (phonon) coupling are suggested to play an important role in forming charge density wave (CDW) and superconductivity, respectively. In this sense, our experimental results may provide a direct explanation for the weakened CDW and relatively low superconducting transition temperature in 1T-NbSeTe. These results may also provide an insight into the charge-density-wave orders in the relevant material systems. 2022, 71 (12): 128103. doi: 10.7498/aps.71.20220132 Abstract + Among two-dimensional (2D) materials, transition metal chalcogenides (TMDs) have attracted much attention due to their unique photoelectric properties. On the other hand, organic molecules have the characteristics of flexibility, wide source, easy fabrication and low cost. The van der Waals heterostructure constructed by the combination of 2D TMDs and organic semiconductors has attracted enormous attention in recent years. When organic semiconductors combine with TMDs to form van der Waals heterostructure, the hybridization of organic molecules could improve the photoelectric properties and other properties by taking the advantages of these two materials, Therefore, the combination of organic semiconductor molecules and TMDs can provide a research platform for designing many basic physics and functional devices and interesting optoelectronic applications. In this work, CuPc/MoS2 van der Waals heterostructure is built, and its photoluminescence (PL) properties are investigated. It is observed that after introducing CuPc, a significant PL quenching phenomenon occurs in the heterostructure compared with the single layer MoS2 and pure CuPc only. After fitting the PL of CuPc/MoS2 heterostructure system and monolayer MoS2 only, the ratio of trion to neutral exciton is clearly increased in the heterostructure. Furthermore, it is found that two mid-gap states D1 and D2 related to the CuPc are introduced into the band gap of MoS2 by first principle calculation. Through the charge density analysis, we find that the D1 state originates from the sp2 bonding state of the C-C bond while the D2 state comes from the anti-bonding state of the N-Cu bond. Meanwhile, the valence band maximum (VBM) and conduction band minimum (CBM) of CuPc/MoS2 heterostructure are derived from the bonding and anti-bonding states of MoS2, respectively. The charge transfer occurs between the mid-gap states of CuPc and MoS2. However, owing to different positions of charge density distribution of CBM, D2, D1 and VBM, the charge pathway is dominated by non-radiation recombination, which cannot give new PL peak in heterostructure. However, this process reduces the number of carriers involved in the direct recombination of MoS2, which leads PL to quench in the heterostructure. This work would be applied to the manipulation of photoelectric characteristics and the design of TMD/organic-based photovoltaic applications. 2022, 71 (12): 128104. doi: 10.7498/aps.71.20220273 Abstract + In recent years, transition metal dichalcogenides materials represented by monolayer molybdenum disulfide (MoS2) have aroused great interest due to their excellent optical and electrical properties. The synthesis method of high-quality monolayer MoS2 film is a key problem for scientific research and industrial application. Recently, researchers have proposed a salt-assisted chemical vapor deposition method for growing the monolayer films, which greatly promotes the growth rate and quality of monolayer film. By using this method, we design a growth source of semi-enclosed quartz boat, and successfully obtain high-quality monolayer MoS2 films by using the double auxiliary action of sodium chloride (NaCl). Scanning electron microscopy shows the excellent film formation, and the photoluminescence spectra show that the luminescence intensity is significantly higher than that of the sample grown without NaCl. The NaCl double-assisted growth method proposed in this study can reduce the growth temperature of MoS2, shorten the growth time, and improve the optical properties of the films. Besides, the operation is simple and the cost is low, which provides an idea for growing the large-scale two-dimensional materials. 2022, 71 (18): 187302. doi: 10.7498/aps.71.20220872 Abstract + When two two-dimensional (2D) materials with different lattice constants or with different rotation angles are superimposed, a moiré superlattice can be constructed. The electronic properties of the superlattice are strongly dependent on the stacking configuration, twist angle and substrate. For instance, theoretically, when the rotation angle of twisted bilayer graphene is reduced to a set of specific values, the so-called magic angles, flat bands appear near the charge neutrality, and the electron-electron interaction is significantly enhanced. The Mott insulator and unconventional superconductivity are detected in the twisted bilayer graphene with a twist angle around 1.1°. For a moiré pattern with a large enough periodicity, lattice relaxation caused by an interplay between van der Waals force and the in-plane elasticity force comes into being. The atomic relaxation forces atoms to deviate from their equilibrium positions, and thus making the system reconstructed. This review mainly focuses on the effects of the lattice relaxation and substrates on the electronic properties of the graphene superlattices. From both theoretical and experimental point of view, the lattice relaxation effects on the atomic structure and electronic properties of graphene-based superlattices, for example, the twisted bilayer graphene, twisted trilayer graphene, graphene-hexagonal boron nitride superlattice and twisted bilayer graphene-boron nitride superlattice are discussed. Finally, a summary and perspective of the investigation of the 2D material superlattice are presented. 2022, 71 (18): 187401. doi: 10.7498/aps.71.20220638 Abstract + Superconductivity has become a fascinating research field in condensed matter physics since its discovery in 1911. Nowadays, two-dimensional materials exhibit a variety of new physical phenomena, such as Ising superconductivity, topological superconductivity, and unconventional superconductivity. A number of two-dimensional van der Waals crystals exhibit superconductivity, which provide us with a broad research platform for exploring various physical effects and novel phenomena. In this review, we focus our attention on superconducting properties of two-dimensional van der Waals crystals, and highlight the recent progress of the state-of-the-art research on synthesis, characterization, and isolation of single and few layer nanosheets and the assembly of two-dimensional van der Waals superconductors. Finally we conclude the future research directions and prospects in two-dimensional materials with superconductivity. 2022, 71 (18): 188101. doi: 10.7498/aps.71.20220895 Abstract + Delocalized p-shell electron magnetism emerging in a low-dimensional graphene system due to quantum effect is distinct from the localized d/f-shell electron’s. The delocalization effect allows the precise engineering of the magnetic ground state and magnetic exchange interactions in nanographenes, thus implementing the accurate construction of high-quality graphene-based magnetic quantum materials. In recent years, with the development of surface chemistry and surface physics, it has become feasible to study the magnetism of nanographenes with single-atom precision, thus opening a new research direction for studying purely organic quantum magnetism. This review starts from the summarizing of the research background of nanographene magnetism. Then, the physics nature behind the nanographene magnetism and recent experimental researches are discussed. Finally, the challenges and opportunities for further studying low-dimensional magnetic graphenes are briefly discussed. 2022, 71 (18): 186401. doi: 10.7498/aps.71.20221024 Abstract + Two-dimensional topological insulator (2DTI) with a large bandgap is prerequisite for potentially observing quantum spin Hall and other quantum phenomena at room-temperature. At present, the synthesis of such materials possesses formidable challenge. In this work, we report our experimental results on synthesis of large-gap 2DTI stanene and bismuthene on B-faced InSb(111) substrate by using molecular beam epitaxy technology. We find that both the stanene and bismuthene can be synthesized by following the forming of a wetting layer on InSb(111) substrate, but with different prospects. On the one hand, it is found that the binding energy between Sn and the substrate is not strong enough to compete the binding force between Sn atoms during the post annealing, thus resulting in a wetting layer composed of many small domains. It significantly restricts the quality of the stanene epilayers. On the other hand, the Bi atoms on InSb(111) are found more stable than the Sn atoms on InSb(111), resulting in a uniform wetting layer which can be optimized by adjusting substrate temperature and post-annealing conditions. Large size and single crystal bismuthene domains have been observed under the STM measurement, which also indicates a bulk gap of ～0.15 eV and metallic edge states. 2022, 71 (18): 187202. doi: 10.7498/aps.71.20220905 Abstract + At a half-filled Landau level, composite fermions with chiral p-wave pairing will form a Moore-Read state which hosts charge-e/4 fractional excitation. This excitation supports non-Abelian statistics and has potential to enable topological quantum computation. Owing to the SU(4) symmetry of electron and electric-field tunability, the bilayer graphene becomes an ideal platform for exploring physics of multi-component quantum Hall state and is candidate for realizing non-Abelian statistics. In this work, high-quality bilayer graphene/hBN heterostructure is fabricated by using dry-transfer technique, and electric transport measurement is performed to study quantum Hall state behavior in bilayer graphene under electric field and magnetic field. Under strong magnetic field, the sequences of incompressible state with quantized Hall conductivity are revealed at –5/2, –1/2, 3/2 filling of Landau level. The feature of even-denominator quantum Hall state is more visible then weaker with increasing magnetic field, and this corresponds to the polarization of Landau level wave function. The experimental results indicate that the observed even-denominator fractional quantum Hall state belongs to the topological phase described by Pfaffian wavefunction.	2022-09-28 22:43:32	{"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": 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": 0.5607000589370728, "perplexity": 1540.9878854589508}, "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-2022-40/segments/1664030335286.15/warc/CC-MAIN-20220928212030-20220929002030-00497.warc.gz"}
http://www.ncatlab.org/nlab/show/Polish+space	# nLab Polish space A Polish space is a topological space that’s homeomorphic to a separable complete metric space. Every second countable locally compact Hausdorff space is a Polish space, among others. Polish spaces provide a useful framework for doing measure theory. As with any topological space, we can take a Polish space and regard it as a measurable space with its sigma-algebra of Borel sets. Then, there is a very nice classification of Polish spaces up to measurable bijection: there is one for each countable cardinality, one whose cardinality is that of the continuum, and no others. Why are Polish spaces ‘not very big’? In other words, why are there none with cardinality exceeding the continuum? As with any separable metric space, it’s because any Polish space has a countable dense subset and you can write any point as a limit of a sequence of points in this subset. So, you only need a sequence of integers to specify any point in a Polish space. ## References Revised on May 11, 2010 10:21:55 by Tim van Beek (192.76.162.8)	2013-12-06 05:28:10	{"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": 0.9464128613471985, "perplexity": 238.73340976199577}, "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/1386163049608/warc/CC-MAIN-20131204131729-00054-ip-10-33-133-15.ec2.internal.warc.gz"}
http://chimera.labs.oreilly.com/books/1234000000754/apf.html	## Initial Project Setup • Start with a User Story and map it to a first functional test. • Pick a test framework—unittest is fine, options like py.test, nose or Green can also offer some advantages. • Run the functional test and see your first expected failure. • Pick a web framework such as Django, and find out how to run unit tests against it. • Create your first unit test to address the current FT failure, and see it fail. • Do your first commit to a VCS like Git. Relevant chapters: Chapter 1, Chapter 2, Chapter 3 ## The Basic TDD Workflow • Double-loop TDD (Figure F-1) • Red, Green, Refactor • Triangulation • "3 Strikes and Refactor" • "Working State to Working State" • "YAGNI" Relevant chapters: Chapter 4, Chapter 5, Chapter 6 ## Moving Beyond dev-only Testing • Start system testing early. Ensure your components work together: web server, static content, database. • Build a staging environment to match your production environment, and run your FT suite against it. • Automate your staging and production environments: • PaaS vs. VPS • Fabric • Configuration management (Chef, Puppet, Salt, Ansible) • Vagrant • Think through deployment pain points: the database, static files, dependencies, how to customise settings, etc. • Build a CI server as soon as possible, so that you don’t have to rely on self-discipline to see the tests run. Relevant chapters: Chapter 8, Chapter 9, Chapter 20, Appendix C ## General Testing Best Practices • Each test should test one thing. • One test file per application code source file. • Consider at least a placeholder test for every function and class, no matter how simple. • "Don’t test constants". • Try to test behaviour rather than implementation. • Try to think beyond the charmed path through the code, and think through edge cases and error cases. Relevant chapters: Chapter 4, Chapter 10, Chapter 11 ## Selenium/Functional Testing Best Practices • Use explicit rather than implicit waits, and the interaction/wait pattern. • Avoid duplication of test code—helper methods in base class, or Page pattern are one way to go. • Avoid double-testing functionality. If you have a test that covers a time-consuming process (eg, login), consider ways of skipping it in other tests (but be aware of unexpected interactions between seemingly unrelated bits of functionality). • Look into BDD tools as another way of structuring your FTs. Relevant chapters: Chapter 17, Chapter 20, Chapter 21 ## Outside-In, Test Isolation Versus Integrated Tests, and Mocking Be reminded of the reason we write tests in the first place: • To ensure correctness, and prevent regressions • To help us to write clean, maintainable code • To enable a fast, productive workflow And with those objectives in mind, think of different types of tests, and the tradeoffs between them: Functional tests • Provide the best guarantee that your application really works correctly, from the point of view of the user. • But: it’s a slower feedback cycle, Integrated tests (reliant on, eg, the ORM or the Django Test Client) • Are quick to write, • Easy to understand, • Will warn you of any integration issues, • But may not always drive good design (that’s up to you!). • And are usually slower than isolated tests. Isolated ("mocky") tests • These involve the most hard work. • They can be harder to read and understand, • But: these are the best ones for guiding you towards better design. • And they run the fastest. If you do find yourself writing tests with lots of mocks, and they feel painful, remember "listen to your tests"—ugly, mocky tests may be trying to tell you that your code could be simplified. Relevant chapters: Chapter 18, Chapter 19, Chapter 22	2017-03-30 18:33:45	{"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": 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": 0.1918058544397354, "perplexity": 7874.665679762911}, "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/1490218199514.53/warc/CC-MAIN-20170322212959-00458-ip-10-233-31-227.ec2.internal.warc.gz"}
https://cran.r-project.org/web/packages/renz/vignettes/Linearized_MM.html	# Linearized Michaelis-Menten Equations library(renz) library(knitr) data(ONPG, package = "renz") We start by loading some kinetic data obtained by students during their undergraduate laboratory training. Using $$\beta$$-galactosidase as an enzyme model, the students assess the effect of the substrate o-nitrophenyl-$$\beta$$-D-galactopynaroside (ONPG) on the initial rate (doi: 10.1002/bmb.21522). The data obtained by eight different groups of students can be loaded just typing: kable(ONPG) ONPG v1 v2 v3 v4 v5 v6 v7 v8 0.05 2.26 1.29 0.004 0.004 0.004 0.003 1.77 2.98 0.10 5.48 3.33 0.008 0.007 0.007 0.006 5.20 5.20 0.25 13.40 11.80 0.020 0.020 0.016 0.017 15.04 14.38 0.50 24.70 22.80 0.035 0.035 0.032 0.031 28.31 30.30 1.00 40.90 35.20 0.060 0.056 0.050 0.048 50.98 48.99 2.50 62.30 39.90 0.110 0.104 0.090 0.101 75.42 86.25 5.00 94.30 73.50 0.138 0.138 0.115 0.121 112.68 112.57 8.00 105.00 12.90 0.154 0.150 0.119 0.139 126.06 136.24 20.00 133.00 112.00 0.179 0.179 0.142 0.152 154.93 169.97 30.00 144.00 120.00 0.200 0.200 0.166 0.181 168.75 177.71 The first column gives the ONPG concentrations in mM, and the remaining 8 columns correspond to the initial rates. Note that while groups 1, 2, 7 and 8 decided to express their rates as $$\mu$$M/min, the remaining groups opted by mM/min. This information can be confirmed by checking the attributes of data: attributes(ONPG) #> $names #> [1] "ONPG" "v1" "v2" "v3" "v4" "v5" "v6" "v7" "v8" #> #>$row.names #> [1] 1 2 3 4 5 6 7 8 9 10 #> #> $[ONPG] #> [1] "mM" #> #>$v3, v4, v5, v6 #> [1] "mM/min" #> #> $class #> [1] "data.frame" #> #>$v1, v2, v7, v8 #> [1] "uM/min" Thus, before continuing we are going to express all the rates using the same units: $$\mu$$M/min: ONPG[ , 4:7] <- 1000 * ONPG[ , 4:7] ## First thing first: scatter plot I strongly insist to my students that when we have to analyze data, the first thing we must do is a scatter diagram, since this will give us a first impression about our data and will guide us on how to proceed with the analysis. To lead by example, we will carry out such diagrams. The first four groups: oldmar <- par()$mar oldmfrow <- par()$mfrow par(mfrow = c(2, 2)) par(mar = c(4, 4,1,1)) for (i in 2:5){ plot(ONPG$ONPG, ONPG[, i], ty = 'p', ylab = 'v (uM/min)', xlab = '[ONPG] (mM)') } par(mar = oldmar) par(mfrow = oldmfrow) The next four groups: oldmar <- par()$mar oldmfrow <- par()$mfrow par(mfrow = c(2, 2)) par(mar = c(4, 4,1,1)) for (i in 6:9){ plot(ONPG$ONPG, ONPG[, i], ty = 'p', ylab = 'v (uM/min)', xlab = '[ONPG] (mM)') } par(mar = oldmar) par(mfrow = oldmfrow) In general, the data look OK. That is, the relationship between the dependent variable (initial rate) and the independent variable ([ONPG]) is what we expect: hyperbolic curve. An exception is the rate obtained by group 2 when [ONPG] = 8 mM, which is clearly an “outlier”. No problem! We will remove that point from further analysis to prevent it from introducing artifacts. ONPG$v2[8] <- NA ## Linearizing the Michaelis-Menten equation The package renz provides four functions to obtain $$K_m$$ and $$V_{max}$$ using linear fitting of linearized Michaelis-Menten equations: • lb() (Lineweaver-Burk). • hw() (Hanes-Woolf). • eh() (Eadie-Hofstee). • ecb() (Eisenthal & Cornish-Bowden). ### Lineweaver-Burk Starting from the Michaelis-Menten equation and taking the inverses in both sides, one can obtain: $$$\tag{1} \frac{1}{v} = \frac{K_m}{V_{max}} \frac{1}{[S]} + \frac{1}{V_{max}}$$$ Thus, to analyze our data using this equation we need to take the inverse of the substrate concentration and the inverse of the initial rate and fit them to the equation of a line. This can be achieved using the lb() function. For group 1: g1 <- lb(ONPG[ , c(1,2)]) For group 5: g5 <- lb(ONPG[ , c(1,6)]) For group 7: g8 <- lb(ONPG[ , c(1,8)]) These results seem to be quite perplexing. It looks like if each group had used a different enzyme! Even worse, group 7 obtains negative $$K_m$$ and $$V_{max}$$. These results are frustrating for the students, and an inexperienced instructor might be tempted to justify them appealing to a lack of skill of the student to generate precise data, which would be an awful mistake since, as we will show next, the quality of data from all the groups, including group 7, is good enough to obtain a reliable estimate of the β-galactosidase kinetic parameters when the analysis is properly carried out. To this end, all we have to do is to carry out a weighted linear regression of data, as it was suggested originally by Lineweaver and Burk (for details, see doi = 10.1002/bmb.21522). Now, let’s re-examine the data introducing weighted regression. For group 1: wg1 <- lb(ONPG[ , c(1,2)], weighting = TRUE) For group 5: wg5 <- lb(ONPG[ , c(1,6)], weighting = TRUE) For group 7: g7 <- lb(ONPG[ , c(1,8)], weighting = TRUE) As it can be observed, after analyzing the data using weighted regression, all the groups obtain similar estimates of $$K_m$$ and $$V_{max}$$, which does not happen when we do not weight our analyses. ## Hanes-Woolf Multiplying both sides of the equation 1 by [S] we reach: $$$\tag{2} \frac{[S]}{v} = \frac{1}{V_{max}} [S] + \frac{K_m}{V_{max}}$$$ The function hw() takes as argument the original data $$([S], v)$$ and transform them to $$([S], \frac{[S]}{v})$$ and afterwards it fits these transformed variables to the equation of a line to estimate the kinetic parameters. Let’s illustrate the use of this function with the data from group 7: hw7 <- hw(ONPG[ , c(1,8)], unit_v = 'uM/min') After all, the data generated by the group 7 do not seem as bad as we might have believed when we analyze them using unweighted double-reciprocal analysis. ## Eadie-Hofstee Multiplying both sides of the equation 1 by $$v V_{max}$$ we reach: $$$\tag{3} v = -K_m \frac{v}{[S]} + V_{max}$$$ We will use again data from group 7 to carry out the analysis: eh7 <- eh(ONPG[ , c(1,8)], unit_v = 'uM/min') ## Eisenthal & Cornish-Bowden Finally we will illustrate this alternative method using again the original data from group 7. ecb7 <- ecb(ONPG[ , c(1,8)], unit_v = "uM/min") ecb7$Km #> [1] "Km: 2.857 ± NA mM" ecb7\$Vm #> [1] "Vm: 261.505 ± NA uM/min"	2022-05-24 02:25:18	{"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": 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": 3, "x-ck12": 0, "texerror": 0, "math_score": 0.4259350299835205, "perplexity": 2338.30227732624}, "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/1652662562410.53/warc/CC-MAIN-20220524014636-20220524044636-00075.warc.gz"}
http://www.researchgate.net/publication/47864205_Multiplicative_zero-one_laws_and_metric_number_theory	Article # Multiplicative zero-one laws and metric number theory 12/2010; Source: arXiv ABSTRACT We develop the classical theory of Diophantine approximation without assuming monotonicity or convexity. A complete `multiplicative' zero-one law is established akin to the `simultaneous' zero-one laws of Cassels and Gallagher. As a consequence we are able to establish the analogue of the Duffin-Schaeffer theorem within the multiplicative setup. The key ingredient is the rather simple but nevertheless versatile `cross fibering principle'. In a nutshell it enables us to `lift' zero-one laws to higher dimensions. 0 0 · 0 Bookmarks · 45 Views • ##### Article: Khintchine’s problem in metric Diophantine approximation Duke Mathematical Journal · 1.70 Impact Factor • Source ##### Article: Approximation by reduced fractions Journal of the Mathematical Society of Japan 01/1961; 13(1961). · 0.51 Impact Factor	2013-12-10 03:09:29	{"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": 0.9611815214157104, "perplexity": 8376.077902883018}, "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/1386164006791/warc/CC-MAIN-20131204133326-00035-ip-10-33-133-15.ec2.internal.warc.gz"}
http://www.bot-thoughts.com/2010/04/gameboy-camera-prototyping.html?showComment=1300823514363	## Friday, April 23, 2010 ### GameBoy Camera Prototyping Updated 9/9/2010: Source Code is now available on Google Code. Holy TTL, Batman. My cobbled-together code and circuitry works! I just took my first Game Boy Camera picture. Here are all the secrets I know of for interfacing a Game Boy Camera (Mitsubishi M64282FP) to a microcontroller. First picture! The actual scene Summary Version With Game Boy Camera, Ardweeny running tweaked version of code here, HP 1650A Logic Analyzer to get the timing right, Java Swing desktop application based on code here, and after fixing goofed up wiring and timing it works! Some tweaking of camera configurations and it now takes some nice shots, and the flame detection software does its job with real images, too! Really Important Tips • Timing is key when interfacing with the M64282FP • But, you can also clock the M64282FP as slow as you need to • Setting the bias (dc offset) voltage to 1.0V is mandatory (the chip outputs 2Vp-p) • Setting the black level offset correctly is important • The camera actually spits out 128x128 pixels, but the last 5 rows are junk • Setting the gain too high can cause odd pixel artifacts (MSB truncation?) The Long Version Game Boy Camera First, I cut wires off of the 9-pin connector, one by one, and spliced them to longer wires and attached each to a small breadboard with 9-pin header so I could plug the camera into my protoboard. Microcontroller The Ardweeny from Solarbotics that I recently ordered and assembled lends itself well to rapid prototyping. It's Arduino-compatible running an ATmega328P MCU. The first step was getting the code put together and getting the timing signals right to activate the Game Boy Camera (Mitsubishi M64282FP image sensor chip aka "Artificial Retina"). I started with code here plus the datasheet. I copied the code into my Arduino IDE and tweaked it as necessary to get it to compile. Then tweaked some more to get the timing right. Along the way, I merged several functions so signal timing was more obvious to me as I read the source. I ran the code, and... it didn't work. I wasn't getting any response from the image sensor... until I realized I'd crossed a couple of wires on the protoboard. Fixing that, the data came streaming through on the Arduino IDE Serial Monitor. My Arduino code can be found here. Mitsubishi M64282FP Timing I've found two versions of the datasheet so far and the timing is a bit ambiguous so let me provide the following hints. If you're in the middle of working with one of these cameras, all this will mean something. Otherwise it won't... • RESET/XRST has to be low on the rising edge of XCK • Raise LOAD high as you clear the last bit of each register you send • START has to be high before rixing XCK • Send START once • READ goes high on rising XCK • Read VOUT analog values shortly after you set XCK low Logic Analyzer In debugging and fixing the timing, the HP 1650A Logic Analyzer that I recently put in operation was absolutely invaluable. I can't imagine trying to debug the issues I encountered without a logic analyzer. Ardweeny Under Test Checking Signal Timing PC Software Next up, capture the serial data and display it as a picture on the screen. I started with code here and decided to take a dive into the NetBeans IDE. I like it so far. Lighter weight than Eclipse, more intuitive to use, and it has a really nice GUI designer built in. I found it rather familiar after having worked with Xcode while equipping Pokey with a Bluetooth modem (a series of articles coming soon). I created a new project, designed a GUI from scratch using the IDE, then copied the relevant code into the appropriate spots. Did a few tweaks to get it to talk to the software on the Arduino. Finally got an image to display on the screen--consisting only of lines and gibberish. Not the real picture. Crap! The preliminary version of the M64282FP datasheet suggested the cause might be a timing issue when reading the analog pixel data. The datasheet I'd been using was ambiguous on that issue. I tweaked the code to read Vout (analog) shortly after dropping XCK and... Shazam! The image at the top of this article appeared. After the time put in bashing through, seeing that image was nothing short of miraculous! The source code and NetBeans project files for the PC client are here. Configuring the Camera Getting that first readable image was great, but the second one sucked, with bizarre artifacts where bright spots should appear (see below). There's no way my simple bright-spot detection algorithm could correctly handle this mess of pixels. I had to learn more about how the camera settings worked. Artifacts from high gain and MSB truncation To help with troubleshooting, I extended the functionality of the client significantly, providing a means of setting the relevant camera registers and displaying a histogram below the picture. One last article I found on the camera held a revelation. The Vout voltage is 2 volts peak to peak! So one has to configure the voltage offset register V for 1.0V, a value of 7 per the datasheet, to get positive signals that the ADC can handle. Doing so immediately yielded a better result. Then I discovered that the bright artifacts disappeared when setting the camera's gain above 0. It dawned on me that I am using a 10-bit ADC but passing an 8-bit value to the Java Application; I was truncating the most significant bits, which mattered at higher gains with higher maximum voltages. That explained everything. I found that you can either continue to use the lowest 8-bits and set the gain to 0, or rotate off the lowest two bits, then increase the gain substantially, and possibly also tweak Vref and offset to maximize the dynamic range of the picture.. bottom line, just be careful of the resolution of your ADC and the data types (signed, unsigned, int, char, short) used to store the results. The black level in the image is set by the offset register O in 32mV increments plus or minus. If the offset is too low, and the image is underexposed. I had strange white pixel artifacts appear where the darkest parts of the picture are supposed to be. Setting the black level a little higher solved the problem. Apparently the "negative" voltage values were being converted to an unsigned value and became high value pixels (white) which you can kind of see when you look at the histogram. Offset Too Low + Underexposed Using the histogram feature made it easy to quickly dial in a decent exposure. Ideally, software auto exposure would be great, but for the narrower purpose of finding the candle, manually calibrating the camera for competition conditions will probably be adequate. Depends on how much time I have for refinement. Correct Exposure... Finally! So does it work? Can the camera see a candle? Does the flame detection software work? Nothing like a blogging cliffhanger, huh? Click here to find out what happened. Updated 9/9/2010: Source Code is now available on Google Code. 1. Hey, thanks for your work on this. I'm having some issues getting the java gui to run J:\Documents and Settings\jarrod\Desktop>java GBCam.jar Exception in thread "main" java.lang.NoClassDefFoundError: GBCam/jar Caused by: java.lang.ClassNotFoundException: GBCam.jar at java.net.URLClassLoader$1.run(Unknown Source) at java.security.AccessController.doPrivileged(Native Method) at java.net.URLClassLoader.findClass(Unknown Source) at java.lang.ClassLoader.loadClass(Unknown Source) at sun.misc.Launcher$AppClassLoader.loadClass(Unknown Source) Could not find the main class: GBCam.jar. Program will exit. Cheers. Jarrod 2. @Jarrod: Try java -jar GBCam.jar On some operating systems you can double-click the jar file, too. 3. ok, slightly different error with that. J:\Documents and Settings\jarrod\Desktop>java -jar GBCam.jar Launching GBCamApp... java.lang.NoClassDefFoundError: org/jdesktop/application/SingleFrameApplication at gbcam.Launcher.main(Launcher.java:19) Caused by: java.lang.ClassNotFoundException: Failure to load: org.jdesktop.application.SingleFrameApplication ... 8 more 4. Rats. Looks like the jar is missing some important libraries. :( I'll try to get it updated sometime in the next several weeks. The big Sparkfun AVC is on April 23, so once I'm done with that I should have time to look into this. In the meantime, if you check out the source and compile under NetBeans IDE, it 'should' work... 5. Do you recall having any problems with the exposure time not working at all? I'm having issues where my image seems to be live data from the sensor and I must finish reading all pixels before moving the image, else it's all blurry. I'd've thought it would have buffered the data otherwise the exposure time would be useless. Also I don't know what you mean by the value in the V register must be 7 to get a 1.0V offset. As far as I can tell, the V register is the reference voltage register and a value of 7 would be 3.5V. Did you mean the O register?	2018-07-18 20:19:13	{"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": 0.24577124416828156, "perplexity": 3412.7830030899368}, "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/1531676590329.25/warc/CC-MAIN-20180718193656-20180718213656-00503.warc.gz"}
http://zbmath.org/?q=an:0793.35028	# zbMATH — the first resource for mathematics ##### Examples Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev \| Tschebyscheff The or-operator \| allows to search for Chebyshev or Tschebyscheff. "Quasi* map" py: 1989 The resulting documents have publication year 1989. so: Eur J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A \| 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used. ##### Operators a & b logic and a \| b logic or !ab logic not abc right wildcard "ab c" phrase (ab c) parentheses ##### Fields any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article) Explosive solutions of quasilinear elliptic equations: Existence and uniqueness. (English) Zbl 0793.35028 This paper deals with the quasilinear elliptic equation $-\text{div}\left(Q\left(\|\nabla u\|\right)\nabla u\right)+\lambda \beta \left(u\right)=f\phantom{\rule{1.em}{0ex}}\text{in}\phantom{\rule{4.pt}{0ex}}{\Omega }\subset {ℝ}^{N},\phantom{\rule{4pt}{0ex}}N>1;$ more precisely, existence and uniqueness of local solutions satisfying $u\left(x\right)\to \infty \phantom{\rule{1.em}{0ex}}\text{as}\phantom{\rule{4.pt}{0ex}}\text{dist}\left(x,\partial {\Omega }\right)\to 0$ and other properties are the main goals here. These kinds of functions are called explosive solutions. No behaviour at the boundary to be prescribed is a priori imposed. However, we are going to show that, under an adequate strong interior structure condition on the equation, explosive behaviour near $\partial {\Omega }$ cannot be arbitrary. In fact, there exists a unique such singular character governed by a uniform rate of explosion depending only on the terms $Q$, $\lambda$, $\beta$ and $f$. ##### MSC: 35J60 Nonlinear elliptic equations 35B40 Asymptotic behavior of solutions of PDE	2013-12-12 05:25:33	{"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": 0.7991271018981934, "perplexity": 7200.517041595482}, "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/1386164540183/warc/CC-MAIN-20131204134220-00085-ip-10-33-133-15.ec2.internal.warc.gz"}
http://dict.cnki.net/h_81210007.html	全文文献工具书数字学术定义翻译助手学术趋势更多近在天文学分类中的翻译结果: 查询用时：0.142秒历史查询近 recent(0)near(0)proximal(0) recent Development of Astrometry in China in the Most Recent Decade 近10年我国天体测量的发展短句来源 This paper summarize recent year's absolute measurement on a 3.2-cm waveband radio telescope of Yunnan Observatory. 本文总结了近几年来云南天文台3.2cm射电望远镜的绝对测量工作。短句来源 Based on the data of nuclear reaction ratederived by the progress in the nuclear experiment in recent years, it is pointed out thatall these models might fail to provide the important astrophysical sources of interstellar26A1 as there are some severe difficulties. 根据近几年核物理实验新进展所获得的有关核反应率的新数据，指出这些模型都面临着严重困难，似乎不大可能成为星际26A1的重要天体源泉。短句来源 The progress of laser ranging to GPS-35,36 satellites in recent years and the situation of application research are introduced in detail. 详细介绍了近几年来对GPS－35、36卫星的激光测距进展和应用研究的情况。短句来源 The most important international conference on asteroid during the recent years, "Asteroids 2001: from Piazzi to the 3rd millennium" was held in Palermo, Italy, during June 11~16, 2001. Most of the conventioneers were experts in different directions of minor planet study. 2001年6月 11～16日在意大利巴勒莫召开了小行星领域近 10年来最重要的一次专业会议“小行星 2001－从皮亚齐到第 3个千年”（Asteroids 2001：from Piazzi to the 3rd millennium）国际学术研讨会，与会者几乎涵盖了小行星研究领域内各个方面的专家。短句来源 near NEAR INFRARED PHOTOMETRY FOR 12 CARBON STARS IN OUR GALAXY 12颗碳星的近红外测光短句来源 The InSb Near Infrared Photometer of Beijing Observatory 北京天文台的锑化铟近红外光度计短句来源 Near Infrared Observations of S140 IRS——Heating of Associated Gas S140红外源的近红外观测——成协气体的供热短句来源 NEAR INFRARED PHOTOMETRY OF MOLECULAR OUTFLOW SOURCES 分子外向流源的近红外测光短句来源 ORBIT STUDIES FOR THE SPECIAL NEAR—EARTH ASTEROID 1989 FC 特殊近地小行星1989 FC的轨道研究短句来源更多 last The second section gives a brief description of observational works in the last thirty years. 第二节介绍近30年来观测工作的概况。短句来源 Since the success of optical interferometry in last decade, astrometric precision and accuracy have been improved dramatically. 近十年来由于光干涉测量技术的成功,使得天体测量的观测精度有了戏剧性的提高。短句来源 Firsf of all, a statistics is made to the frequency of observational programs in terms of celestial abjects in the period of last 12 years (1980-1992) for the National Radio Astronomy Observatory 12-m millimetre telescope, U.S.A. 本文首先对美国国家射电天文台(NRAO)②安排的12米毫米波射电镜近12年(1980-1992)观测课题的频数分布作了统计分析。短句来源 In this article, we briefly review the ground-based and space observations of magnetic transient changes related to solar flares in the last two decades, and give a possible explanation based on non-LTE line profile calculations. 本文简要综述近二十年来对与太阳耀斑有关联的磁场瞬变现象的地面和空间观测 ,并通过非局部热动平衡计算 ,分析了可能的理论解释。短句来源 In the last decade, with the observations of high resolutions, the developments of theoretical models and numerical simulations, there has been great progress in many aspects of the studies of high-velocity clouds, particularly for some special kinds and the all-sky surveys. 近几年通过高分辨率观测、理论模型和数值模拟,对其中几类高速云及全天性的研究有了很大突破。短句来源更多我想查看译文中含有：的双语例句 recent In the case of 3-dimensional commutative algebras a new proof of a recent theorem of Katsylo and Mikhailov about the 28 bitangents to the associated plane quartic is given. The proof is an application of a recent result by W. As a consequence we prove a recent conjecture of Lusztig (see [L1]). This is a survey of recent work involving concepts of self-similarity that relate to Recent study on the subject is an indirect approach: in order to compute the Gabor coefficients, one needs to find an auxiliary bi-orthogonal window function γ. 更多 near Finally, the problem of inversion of a multiplier will be analyzed for smooth functions that have a specified structure near their zeros. Behavior near the boundary of positive solutions of second order parabolic equations Sharp inequalities between weight bounds (from the doubling, Ap, and reverse H?lder conditions) and the BMO norm are obtained when the former are near their optimal values. The popularity of PSWFs seems likely to increase in the near future, as band-limited functions become a numerical (as well as an analytical) tool. In the application of CAD/CAM, the target form of a curve, which is used for plotting or as the data supplied for CAM, is a set of points on (or near by) the curve. 更多 proximal Modified approximate proximal point algorithms for finding roots of maximal monotone operators In order to find roots of maximal monotone operators, this paper introduces and studies the modified approximate proximal point algorithm with an error sequence {ek} such that The most proximal cysteine residues in native hRI are two pairs that are adjacent in sequence. Proximal tubule uptake of albumin, expression of apical membrane cubilin and infiltrating cells in kidney interstitium were determined by immunocytochemistry. It has been demonstrated that the homology of proximal parts of the 16S rRNA gene of all the strains studied towards one another and towards the reference strain ATCC19258 amounts to 100%. 更多 last The last section is devoted to a result about the cohomology of a Lie superalgebra with reductive even part with coefficients in a finite dimensional moduleM. In the last section we give an exposition of results, communicated to us by J.-P. The main part of the work deals with abstract Higgs bundles; in the last two sections we derive the applications to Higgs bundles valued in a line bundle K and to bundles on elliptic fibrations. The automorphism group ${\rm Aut}\,(X)$ is determined in the last section. We obtain these last estimates (more precisely, Hp/2-estimates for h(f) by using a slight extension of the Coifman-Meyer-Stein theorem relating the so-called tent-spaces and the Hardy spaces. 更多其他点击这里查询相关文摘相关查询 CNKI小工具在英文学术搜索中查有关近的内容在知识搜索中查有关近的内容在数字搜索中查有关近的内容在概念知识元中查有关近的内容在学术趋势中查有关近的内容 CNKI主页 \| 设CNKI翻译助手为主页 \| 收藏CNKI翻译助手 \| 广告服务 \| 英文学术搜索 2008 CNKI－中国知网 2008中国知网(cnki) 中国学术期刊(光盘版)电子杂志社	2020-04-03 05:47:21	{"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": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6281508207321167, "perplexity": 2350.4742979528037}, "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-2020-16/segments/1585370510287.30/warc/CC-MAIN-20200403030659-20200403060659-00467.warc.gz"}
http://www.qwika.com/find/graph_theory?int=20	Qwika Toolbar for IE and Firefox users! ## Home > English Searching 21,964,380 articles in 1,158 wikis. Beta release. Any comments please contact us Press release (Feb 17): New search engine helps bridge the language gap in Wikipedia Press release (Apr 4): Qwika search engine now indexes 1158 wikis in 12 languages Search wikis: Results for graph theory 21 to 30 of 2271 Cycle (graph theory) Cycle (graph theory) Cycle in graph theory and computer science has several meanings: A ... walk, with repeated vertices allowed. See path (graph theory). (This usage is common in ... http://en.wikipedia.org/wiki/Cycle_(graph_theory) - 3k - Cached - Similar pages Category:Graph theory Category:Graph theory Articles and media on this topic in ... projects can be found at: Commons Category Graph theory Wikimedia Commons has media related to: Graph theory Graph theory is the branch ... http://en.wikipedia.org/wiki/Category:Graph_theory - 9k - Cached - Similar pages Geometric graph theory Geometric graph theory Geometric graph theory is a specialization of graph theory that deals directly with its ... http://en.wikipedia.org/wiki/Geometric_graph_theory - 0k - Cached - Similar pages Book (graph theory) Book (graph theory) In graph theory, a book (usually written $B_p$) is a graph consisting of $p$ triangles ... http://en.wikipedia.org/wiki/Book_(graph_theory) - 2k - Cached - Similar pages Saturation (graph theory) Saturation (graph theory) Let $G\left(V,E\right)$ be a graph and $M$ a matching in ... http://en.wikipedia.org/wiki/Saturation_(graph_theory) - 1k - Cached - Similar pages Flow (graph theory) Flow (graph theory) In graph theory a flow is a representation of a ... of flow is maximized for a particular graph. Interpretations We may interpret a flow ... http://en.wikipedia.org/wiki/Flow_(graph_theory) - 5k - Cached - Similar pages Cut (graph theory) Cut (graph theory) In graph theory, a cut is a partition of the vertices of a graph into two sets. More formally, let ... http://en.wikipedia.org/wiki/Cut_(graph_theory) - 4k - Cached - Similar pages Evolutionary graph theory Evolutionary graph theory An area lying at the intersection of graph theory, probability theory, and mathematical biology, evolutionary graph theory ... http://en.wikipedia.org/wiki/Evolutionary_graph_theory - 2k - Cached - Similar pages Covering (graph theory) Covering (graph theory) In the mathematical discipline of graph theory a covering for a graph is a set of vertices (or ... http://en.wikipedia.org/wiki/Covering_(graph_theory) - 3k - Cached - Similar pages Topological graph theory Topological graph theory In mathematics topological graph theory is a branch of graph theory. It studies the embedding of ... http://en.wikipedia.org/wiki/Topological_graph_theory - 1k - Cached - Similar pages Page: <<Previous 1 2 3 4 5 6 7 8 9 10 Next >> Search wikis: Search: Try your search on: FactBites (sentence-based)	2019-08-18 04:36:46	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 4, "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": 0.19358564913272858, "perplexity": 2825.78988903874}, "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-2019-35/segments/1566027313617.6/warc/CC-MAIN-20190818042813-20190818064813-00458.warc.gz"}
http://en.wikipedia.org/wiki/RKKY_interaction	# RKKY interaction RKKY stands for Ruderman-Kittel-Kasuya-Yosida and refers to a coupling mechanism of nuclear magnetic moments or localized inner d or f shell electron spins in a metal by means of an interaction through the conduction electrons. The RKKY interaction was originally proposed by M.A. Ruderman and Charles Kittel of the University of California, Berkeley as a means of explaining unusually broad nuclear spin resonance lines that had been observed in natural metallic silver. The theory uses second-order perturbation theory to describe an indirect exchange coupling whereby the nuclear spin of one atom interacts with a conduction electron via the hyperfine interaction, and this conduction electron then interacts with another nuclear spin thus creating a correlation energy between the two nuclear spins. (Alternatively, instead of nuclear spins coupling to conduction spins via the hyperfine interaction, another scenario is for inner electron spins to couple to conduction spins via the exchange interaction.) The theory is based on Bloch wavefunctions, and is therefore only applicable to crystalline systems. The derived exchange interaction takes the following form: $H(\mathbf{R}_{ij}) = \frac{\mathbf{I}_i \cdot \mathbf{I}_j}{4} \frac{\left \| \Delta k_m k_m \right \|^2 m^}{(2 \pi )^3 R_{ij}^4 \hbar^2} \left [ 2 k_m R_{ij} \cos( 2 k_m R_{ij} ) - \sin( 2 k_m R_{ij} ) \right ]$ where H represents the Hamiltonian, $R_{ij}$ is the distance between the nuclei i and j, $\mathbf{I}_i$ is the nuclear spin of atom i, $\Delta k_m k_m$ is a term that represents the strength of the hyperfine interaction, $m^$ is the effective mass of the electrons in the crystal, and $k_m$ is the wave vector of the conduction electrons. In crystalline materials, the wave vectors of conduction electrons are very close to the Fermi surface. Tadao Kasuya of Nagoya University later proposed that a similar indirect exchange coupling could be applied to localized inner d-electron spins interacting via conduction electrons. This theory was expanded more completely by Kei Yosida of the University of California, Berkeley to give a Hamiltonian that describes (d-electron spin)-(d-electron spin), (nuclear spin)-(nuclear spin) as well as (d-electron spin)-(nuclear spin) interactions. Van Vleck clarified some subtleties of the theory, particularly the relationship between the first and second order perturbative contributions. Perhaps the most significant application of the RKKY theory has been to the theory of giant magnetoresistance (GMR). GMR was discovered when the coupling between thin layers of magnetic materials separated by a non-magnetic spacer material was found to oscillate between ferromagnetic and antiferromagnetic as a function of the distance between the layers. This ferromagnetic/antiferromagnetic oscillation is one prediction of the RKKY theory.[1][2] ## References 1. M.A. Ruderman and C. Kittel, Phys. Rev. 96, 99 (1954). 2. T. Kasuya, Prog. Theor. Phys. 16, 45 (1956). 3. K. Yosida, Phys. Rev. 106, 893 (1957). 4. J. H. Van Vleck. Reviews of Modern Physics 34, 681-686 (1962). 5. A. Blandin and J. Friedel, J. phys. rad. 20, page 160-168 (1959) 6. Quantum Theory of Solids, 2ed. pp 360–366, C. Kittel, Wiley 1987 1. ^ S.S.P. Parkin and D. Mauri, Physical Review B Vol. 44 7131-7134 (1991) 2. ^ Y. Yafet, Physical Review B Vol. 36 3948-3949 (1987)	2014-07-22 16:43:21	{"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 6, "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": 0.6223270297050476, "perplexity": 1323.2687106883698}, "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/1405997859240.8/warc/CC-MAIN-20140722025739-00191-ip-10-33-131-23.ec2.internal.warc.gz"}
https://socratic.org/questions/5825990b11ef6b52759039d5#334684	# Question #039d5 Nov 11, 2016 If I understand you would try just to balance mulecular masses. It woul be right, but not sufficient to balance the reaction because it would give just one constraint on coefficients (you need several) #### Explanation: Example $2 {H}_{2} O = 2 {H}_{2} + {O}_{2}$ We start from $a {H}_{2} O = b {H}_{2} + c {O}_{2}$ Then realize that we can multiply both terms for a constant so we can put $a = 1$ Then equal the molecular masses: $2 + 16 = b \cdot 2 + c \cdot 32$ $b = 9 - 16 c$ This is true in our balanced equation (where $a = 1 , b = 1 , c = \frac{1}{2}$), but not sufficient to find b and c.	2022-01-19 11:13:30	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 6, "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": 0.863582193851471, "perplexity": 1037.9687667876988}, "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-2022-05/segments/1642320301309.22/warc/CC-MAIN-20220119094810-20220119124810-00208.warc.gz"}
http://image.absoluteastronomy.com/topics/Binary_relation	Binary relation Encyclopedia In mathematics Mathematics Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity... , a binary relation on a set A is a collection of ordered pair Ordered pair In mathematics, an ordered pair is a pair of mathematical objects. In the ordered pair , the object a is called the first entry, and the object b the second entry of the pair... s of elements of A. In other words, it is a subset Subset In mathematics, especially in set theory, a set A is a subset of a set B if A is "contained" inside B. A and B may coincide. The relationship of one set being a subset of another is called inclusion or sometimes containment... of the Cartesian product Cartesian product In mathematics, a Cartesian product is a construction to build a new set out of a number of given sets. Each member of the Cartesian product corresponds to the selection of one element each in every one of those sets... A2 = . More generally, a binary relation between two sets A and B is a subset of . The terms dyadic relation and 2-place relation are synonyms for binary relations. An example is the "divides" relation between the set of prime number Prime number A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2... s P and the set of integer Integer The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively... s Z, in which every prime p is associated with every integer z that is a multiple of p (and not with any integer that is not a multiple of p). In this relation, for instance, the prime 2 is associated with numbers that include −4, 0, 6, 10, but not 1 or 9; and the prime 3 is associated with numbers that include 0, 6, and 9, but not 4 or 13. Binary relations are used in many branches of mathematics to model concepts like "is greater than", "is equal to", and "divides" in arithmetic Arithmetic Arithmetic or arithmetics is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. It involves the study of quantity, especially as the result of combining numbers... , "is congruent to Congruence (geometry) In geometry, two figures are congruent if they have the same shape and size. This means that either object can be repositioned so as to coincide precisely with the other object... " in geometry Geometry Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers .... , "is adjacent to" in graph theory Graph theory In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of... , "is orthogonal to" in linear algebra Linear algebra Linear algebra is a branch of mathematics that studies vector spaces, also called linear spaces, along with linear functions that input one vector and output another. Such functions are called linear maps and can be represented by matrices if a basis is given. Thus matrix theory is often... and many more. The concept of function Function (mathematics) In mathematics, a function associates one quantity, the argument of the function, also known as the input, with another quantity, the value of the function, also known as the output. A function assigns exactly one output to each input. The argument and the value may be real numbers, but they can... is defined as a special kind of binary relation. Binary relations are also heavily used in computer science Computer science Computer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems... . A binary relation is the special case of an n-ary relation R ⊆ A1 × … × An, that is, a set of n-tuple Tuple In mathematics and computer science, a tuple is an ordered list of elements. In set theory, an n-tuple is a sequence of n elements, where n is a positive integer. There is also one 0-tuple, an empty sequence. An n-tuple is defined inductively using the construction of an ordered pair... s where the jth component of each n-tuple is taken from the jth domain Aj of the relation. In some systems of axiomatic set theory, relations are extended to classes, which are generalizations of sets. This extension is needed for, among other things, modeling the concepts of "is an element of" or "is a subset of" in set theory Set theory Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics... , without running into logical inconsistencies such as Russell's paradox In the foundations of mathematics, Russell's paradox , discovered by Bertrand Russell in 1901, showed that the naive set theory created by Georg Cantor leads to a contradiction... . ## Formal definition A binary relation R is usually defined as an ordered triple (X, Y, G) where X and Y are arbitrary sets (or classes), and G is a subset Subset In mathematics, especially in set theory, a set A is a subset of a set B if A is "contained" inside B. A and B may coincide. The relationship of one set being a subset of another is called inclusion or sometimes containment... of the Cartesian product Cartesian product In mathematics, a Cartesian product is a construction to build a new set out of a number of given sets. Each member of the Cartesian product corresponds to the selection of one element each in every one of those sets... X × Y. The sets X and Y are called the domain Domain (mathematics) In mathematics, the domain of definition or simply the domain of a function is the set of "input" or argument values for which the function is defined... (or the set of departure) and codomain Codomain In mathematics, the codomain or target set of a function is the set into which all of the output of the function is constrained to fall. It is the set in the notation... (or the set of destination), respectively, of the relation, and G is called its graph Graph of a function In mathematics, the graph of a function f is the collection of all ordered pairs . In particular, if x is a real number, graph means the graphical representation of this collection, in the form of a curve on a Cartesian plane, together with Cartesian axes, etc. Graphing on a Cartesian plane is... . The statement (x,y) ∈ R is read "x is R-related to y", and is denoted by xRy or R(x,y). The latter notation corresponds to viewing R as the characteristic function on "X" x "Y" for the set of pairs of G. The order of the elements in each pair of G is important: if a ≠ b, then aRb and bRa can be true or false, independently of each other. ### Is a relation more than its graph? According to the definition above, two relations with the same graph may be different, if they differ in the sets X and Y. For example, if G = {(1,2),(1,3),(2,7)}, then (Z,Z, G), (R, N, G), and (N, R, G) are three distinct relations. Some mathematicians do not consider the sets X and Y to be part of the relation, and therefore define a binary relation as being a subset of X×Y, that is, just the graph G. According to this view, the set of pairs {(1,2),(1,3),(2,7)} is a relation from any set that contains {1,2} to any set that contains {2,3,7}. A special case of this difference in points of view applies to the notion of function Function (mathematics) In mathematics, a function associates one quantity, the argument of the function, also known as the input, with another quantity, the value of the function, also known as the output. A function assigns exactly one output to each input. The argument and the value may be real numbers, but they can... . Most authors insist on distinguishing between a function's codomain Codomain In mathematics, the codomain or target set of a function is the set into which all of the output of the function is constrained to fall. It is the set in the notation... and its range Range (mathematics) In mathematics, the range of a function refers to either the codomain or the image of the function, depending upon usage. This ambiguity is illustrated by the function f that maps real numbers to real numbers with f = x^2. Some books say that range of this function is its codomain, the set of all... . Thus, a single "rule," like mapping every real number x to x2, can lead to distinct functions f:R→R and g:R→R+, depending on whether the images under that rule are understood to be reals or, more restrictively, non-negative reals. But others view functions as simply sets of ordered pairs with unique first components. This difference in perspectives does raise some nontrivial issues. As an example, the former camp considers surjectivity—or being onto—as a property of functions, while the latter sees it as a relationship that functions may bear to sets. Either approach is adequate for most uses, provided that one attends to the necessary changes in language, notation, and the definitions of concepts like restrictions, composition Composition of relations In mathematics, the composition of binary relations is a concept of forming a new relation from two given relations R and S, having as its most well-known special case the composition of functions.- Definition :... , inverse relation Inverse relation In mathematics, the inverse relation of a binary relation is the relation that occurs when you switch the order of the elements in the relation. For example, the inverse of the relation 'child of' is the relation 'parent of'... , and so on. The choice between the two definitions usually matters only in very formal contexts, like category theory Category theory Category theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows , where these collections satisfy certain basic conditions... . ### Example Example: Suppose there are four objects {ball, car, doll, gun} and four persons {John, Mary, Ian, Venus}. Suppose that John owns the ball, Mary owns the doll, and Venus owns the car. Nobody owns the gun and Ian owns nothing. Then the binary relation "is owned by" is given as R=({ball, car, doll, gun}, {John, Mary, Ian, Venus}, {(ball, John), (doll, Mary), (car, Venus)}). Thus the first element of R is the set of objects, the second is the set of people, and the last element is a set of ordered pairs of the form (object, owner). The pair (ball, John), denoted by ballRJohn means that the ball is owned by John. Two different relations could have the same graph. For example: the relation ({ball, car, doll, gun}, {John, Mary, Venus}, {(ball,John), (doll, Mary), (car, Venus)}) is different from the previous one as everyone is an owner. But the graphs of the two relations are the same. Nevertheless, R is usually identified or even defined as G(R) and "an ordered pair (x, y) ∈ G(R)" is usually denoted as "(x, y) ∈ R". ## Special types of binary relations Some important classes of binary relations R between X and Y are listed below. Uniqueness properties: • injective Injective function In mathematics, an injective function is a function that preserves distinctness: it never maps distinct elements of its domain to the same element of its codomain. In other words, every element of the function's codomain is mapped to by at most one element of its domain... (also called left-unique): for all x and z in X and y in Y it holds that if xRy and zRy then x = z. • functional (also called right-unique or right-definite): for all x in X, and y and z in Y it holds that if xRy and xRz then y = z; such a binary relation is called a partial function Partial function In mathematics, a partial function from X to Y is a function ƒ: X' → Y, where X' is a subset of X. It generalizes the concept of a function by not forcing f to map every element of X to an element of Y . If X' = X, then ƒ is called a total function and is equivalent to a function... . • one-to-one (also written 1-to-1): injective and functional. Totality properties: • left-total: for all x in X there exists a y in Y such that xRy (this property, although sometimes also referred to as total, is different from the definition of total in the next section). • surjective Surjective function In mathematics, a function f from a set X to a set Y is surjective , or a surjection, if every element y in Y has a corresponding element x in X so that f = y... (also called right-total): for all y in Y there exists an x in X such that xRy. • A correspondence Correspondence (mathematics) In mathematics and mathematical economics, correspondence is a term with several related but not identical meanings.* In general mathematics, correspondence is an alternative term for a relation between two sets... : a binary relation that is both left-total and surjective. Uniqueness and totality properties: • A function Function (mathematics) In mathematics, a function associates one quantity, the argument of the function, also known as the input, with another quantity, the value of the function, also known as the output. A function assigns exactly one output to each input. The argument and the value may be real numbers, but they can... : a relation that is functional and left-total. • A bijection Bijection A bijection is a function giving an exact pairing of the elements of two sets. A bijection from the set X to the set Y has an inverse function from Y to X. If X and Y are finite sets, then the existence of a bijection means they have the same number of elements... : a one-to-one correspondence; such a relation is a function and is said to be bijective. ## Relations over a set If X = Y then we simply say that the binary relation is over X. Or it is an endorelation over X. Some classes of endorelations are widely studied in graph theory Graph theory In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of... , where they're known as directed graph Directed graph A directed graph or digraph is a pair G= of:* a set V, whose elements are called vertices or nodes,... s. The set of all binary relations B(X) on a set X is a semigroup with involution Semigroup with involution In mathematics, in semigroup theory, an involution in a semigroup is a transformation of the semigroup which is its own inverse and which is an anti-automorphism of the semigroup. A semigroup in which an involution is defined is called a semigroup with involution... with the involution being the mapping of a relation to its inverse relation. Some important classes of binary relations over a set X are: • reflexive Reflexive relation In mathematics, a reflexive relation is a binary relation on a set for which every element is related to itself, i.e., a relation ~ on S where x~x holds true for every x in S. For example, ~ could be "is equal to".-Related terms:... : for all x in X it holds that xRx. For example, "greater than or equal to" is a reflexive relation but "greater than" is not. • irreflexive (or strict): for all x in X it holds that not xRx. "Greater than" is an example of an irreflexive relation. • coreflexive Coreflexive relation In mathematics, a coreflexive relation is a binary relation that is a subset of the identity relation. Thus if a is related to b then a is equal to b , but if c is equal to d it does not necessarily hold that c is related to d .In mathematical notation, this is:\forall a, b \in X,\ a... : for all x and y in X it holds that if xRy then x = y. "Equal to and odd" is an example of a coreflexive relation. • symmetric Symmetric relation In mathematics, a binary relation R over a set X is symmetric if it holds for all a and b in X that if a is related to b then b is related to a.In mathematical notation, this is:... : for all x and y in X it holds that if xRy then yRx. "Is a blood relative of" is a symmetric relation, because x is a blood relative of y if and only if y is a blood relative of x. • antisymmetric Antisymmetric relation In mathematics, a binary relation R on a set X is antisymmetric if, for all a and b in Xor, equivalently,In mathematical notation, this is:\forall a, b \in X,\ R \and R \; \Rightarrow \; a = bor, equivalently,... : for all distinct x and y in X, if xRy then not yRx. • asymmetric Asymmetric relation Asymmetric often means, simply: not symmetric. In this sense an asymmetric relation is a binary relation which is not a symmetric relation.That is,\lnot.... : for all x and y in X, if xRy then not yRx. (So asymmetricity is stronger than anti-symmetry. In fact, asymmetry is equivalent to anti-symmetry plus irreflexivity.) • transitive Transitive relation In mathematics, a binary relation R over a set X is transitive if whenever an element a is related to an element b, and b is in turn related to an element c, then a is also related to c.... : for all x, y and z in X it holds that if xRy and yRz then xRz. (Note that, under the assumption of transitivity, irreflexivity and asymmetry are equivalent.) • total Total relation In mathematics, a binary relation R over a set X is total if for all a and b in X, a is related to b or b is related to a .In mathematical notation, this is\forall a, b \in X,\ a R b \or b R a.... : for all x and y in X it holds that xRy or yRx (or both). "Is greater than or equal to" is an example of a total relation (this definition for total is different from left total in the previous section). • trichotomous: for all x and y in X exactly one of xRy, yRx or x = y holds. "Is greater than" is an example of a trichotomous relation. • Euclidean Euclidean relation In mathematics, Euclidean relations are a class of binary relations that satisfy a weakened form of transitivity that formalizes Euclid's "Common Notion 1" in The Elements: things which equal the same thing also equal one another.-Definition:... : for all x, y and z in X it holds that if xRy and xRz, then yRz (and zRy). Equality is a Euclidean relation because if x=y and x=z, then y=z. • serial: for all x in X, there exists y in X such that xRy. "Is greater than" is a serial relation on the integers. But it is not a serial relation on the positive integers, because there is no y in the positive integers such that 1>y. However, the "Is less than" is a serial relation on the positive integers (the natural numbers), the rational numbers and the real numbers. Every reflexive relation is serial. • set-like: for every x in X, the class Class (set theory) In set theory and its applications throughout mathematics, a class is a collection of sets which can be unambiguously defined by a property that all its members share. The precise definition of "class" depends on foundational context... of all y such that yRx is a set. (This makes sense only if we allow relations on proper classes.) The usual ordering < on the class of ordinal numbers is set-like, while its inverse > is not. A relation that is reflexive, symmetric, and transitive is called an equivalence relation Equivalence relation In mathematics, an equivalence relation is a relation that, loosely speaking, partitions a set so that every element of the set is a member of one and only one cell of the partition. Two elements of the set are considered equivalent if and only if they are elements of the same cell... . A relation that is reflexive, antisymmetric, and transitive is called a partial order. A partial order that is total is called a total order Total order In set theory, a total order, linear order, simple order, or ordering is a binary relation on some set X. The relation is transitive, antisymmetric, and total... , simple order, linear order, or a chain. A linear order where every nonempty set has a least element is called a well-order Well-order In mathematics, a well-order relation on a set S is a strict total order on S with the property that every non-empty subset of S has a least element in this ordering. Equivalently, a well-ordering is a well-founded strict total order... . A relation that is symmetric, transitive, and serial is also reflexive. ## Operations on binary relations If R is a binary relation over X and Y, then the following is a binary relation over Y and X: • Inverse Inverse relation In mathematics, the inverse relation of a binary relation is the relation that occurs when you switch the order of the elements in the relation. For example, the inverse of the relation 'child of' is the relation 'parent of'... or converse: R −1, defined as R −1 = { (y, x) \| (x, y) ∈ R }. A binary relation over a set is equal to its inverse if and only if it is symmetric. See also duality (order theory) Duality (order theory) In the mathematical area of order theory, every partially ordered set P gives rise to a dual partially ordered set which is often denoted by Pop or Pd. This dual order Pop is defined to be the set with the inverse order, i.e. x ≤ y holds in Pop if and only if y ≤ x holds in P... . If R is a binary relation over X, then each of the following is a binary relation over X: • Reflexive closure: R =, defined as R = = { (x, x) \| x ∈ X } ∪ R or the smallest reflexive relation over X containing R. This can be seen to be equal to the intersection of all reflexive relations containing R. • Reflexive reduction: R , defined as R = R \ { (x, x) \| x ∈ X } or the largest irreflexive relation over X contained in R. • Transitive closure Transitive closure In mathematics, the transitive closure of a binary relation R on a set X is the transitive relation R+ on set X such that R+ contains R and R+ is minimal . If the binary relation itself is transitive, then the transitive closure will be that same binary relation; otherwise, the transitive closure... : R +, defined as the smallest transitive relation over X containing R. This can be seen to be equal to the intersection of all transitive relations containing R. • Transitive reduction Transitive reduction In mathematics, a transitive reduction of a binary relation R on a set X is a minimal relation R' on X such that the transitive closure of R' is the same as the transitive closure of R. If the transitive closure of R is antisymmetric and finite, then R' is unique... : R , defined as a minimal relation having the same transitive closure as R. • Reflexive transitive closure: R , defined as R = (R +) =, the smallest preorder Preorder In mathematics, especially in order theory, preorders are binary relations that are reflexive and transitive.For example, all partial orders and equivalence relations are preorders... containing R. • Reflexive transitive symmetric closure: R , defined as the smallest equivalence relation Equivalence relation In mathematics, an equivalence relation is a relation that, loosely speaking, partitions a set so that every element of the set is a member of one and only one cell of the partition. Two elements of the set are considered equivalent if and only if they are elements of the same cell... over X containing R. If R, S are binary relations over X and Y, then each of the following is a binary relation: • Union: R ∪ S ⊆ X × Y, defined as R ∪ S = { (x, y) \| (x, y) ∈ R or (x, y) ∈ S }. • Intersection: R ∩ S ⊆ X × Y, defined as R ∩ S = { (x, y) \| (x, y) ∈ R and (x, y) ∈ S }. If R is a binary relation over X and Y, and S is a binary relation over Y and Z, then the following is a binary relation over X and Z: (see main article composition of relations Composition of relations In mathematics, the composition of binary relations is a concept of forming a new relation from two given relations R and S, having as its most well-known special case the composition of functions.- Definition :... ) • Composition: S ∘ R, also denoted R ; S (or more ambiguously R ∘ S), defined as S ∘ R = { (x, z) \| there exists y ∈ Y, such that (x, y) ∈ R and (y, z) ∈ S }. The order of R and S in the notation S ∘ R, used here agrees with the standard notational order for composition of functions. ### Complement If R is a binary relation over X and Y, then the following too: • The complement Complement (set theory) In set theory, a complement of a set A refers to things not in , A. The relative complement of A with respect to a set B, is the set of elements in B but not in A... S is defined as x S y if not x R y. The complement of the inverse is the inverse of the complement. If X = Y the complement has the following properties: • If a relation is symmetric, the complement is too. • The complement of a reflexive relation is irreflexive and vice versa. • The complement of a strict weak order is a total preorder and vice versa. The complement of the inverse has these same properties. ### Restriction The restriction of a binary relation on a set X to a subset S is the set of all pairs (x, y) in the relation for which x and y are in S. If a relation is reflexive Reflexive relation In mathematics, a reflexive relation is a binary relation on a set for which every element is related to itself, i.e., a relation ~ on S where x~x holds true for every x in S. For example, ~ could be "is equal to".-Related terms:... , irreflexive, symmetric Symmetric relation In mathematics, a binary relation R over a set X is symmetric if it holds for all a and b in X that if a is related to b then b is related to a.In mathematical notation, this is:... , antisymmetric Antisymmetric relation In mathematics, a binary relation R on a set X is antisymmetric if, for all a and b in Xor, equivalently,In mathematical notation, this is:\forall a, b \in X,\ R \and R \; \Rightarrow \; a = bor, equivalently,... , asymmetric Asymmetric relation Asymmetric often means, simply: not symmetric. In this sense an asymmetric relation is a binary relation which is not a symmetric relation.That is,\lnot.... , transitive Transitive relation In mathematics, a binary relation R over a set X is transitive if whenever an element a is related to an element b, and b is in turn related to an element c, then a is also related to c.... , total Total relation In mathematics, a binary relation R over a set X is total if for all a and b in X, a is related to b or b is related to a .In mathematical notation, this is\forall a, b \in X,\ a R b \or b R a.... , trichotomous, a partial order, total order Total order In set theory, a total order, linear order, simple order, or ordering is a binary relation on some set X. The relation is transitive, antisymmetric, and total... , strict weak order, total preorder (weak order), or an equivalence relation Equivalence relation In mathematics, an equivalence relation is a relation that, loosely speaking, partitions a set so that every element of the set is a member of one and only one cell of the partition. Two elements of the set are considered equivalent if and only if they are elements of the same cell... , its restrictions are too. However, the transitive closure of a restriction is a subset of the restriction of the transitive closure, i.e., in general not equal. Also, the various concepts of completeness Completeness (order theory) In the mathematical area of order theory, completeness properties assert the existence of certain infima or suprema of a given partially ordered set . A special use of the term refers to complete partial orders or complete lattices... (not to be confused with being "total") do not carry over to restrictions. For example, on the set of real number Real number In mathematics, a real number is a value that represents a quantity along a continuum, such as -5 , 4/3 , 8.6 , √2 and π... s a property of the relation "≤" is that every non-empty Empty set In mathematics, and more specifically set theory, the empty set is the unique set having no elements; its size or cardinality is zero. Some axiomatic set theories assure that the empty set exists by including an axiom of empty set; in other theories, its existence can be deduced... subset S of R with an upper bound Upper bound In mathematics, especially in order theory, an upper bound of a subset S of some partially ordered set is an element of P which is greater than or equal to every element of S. The term lower bound is defined dually as an element of P which is lesser than or equal to every element of S... in R has a least upper bound Supremum In mathematics, given a subset S of a totally or partially ordered set T, the supremum of S, if it exists, is the least element of T that is greater than or equal to every element of S. Consequently, the supremum is also referred to as the least upper bound . If the supremum exists, it is unique... (also called supremum) in R. However, for a set of rational numbers this supremum is not necessarily rational, so the same property does not hold on the restriction of the relation "≤" to the set of rational numbers. The left-restriction (right-restriction, respectively) of a binary relation between X and Y to a subset S of its domain (codomain) is the set of all pairs (x, y) in the relation for which x (y) is an element of S. ## Sets versus classes Certain mathematical "relations", such as "equal to", "member of", and "subset of", cannot be understood to be binary relations as defined above, because their domains and codomains cannot be taken to be sets in the usual systems of axiomatic set theory. For example, if we try to model the general concept of "equality" as a binary relation =, we must take the domain and codomain to be the "set of all sets", which is not a set in the usual set theory. The usual work-around to this problem is to select a "large enough" set A, that contains all the objects of interest, and work with the restriction =A instead of =. Similarly, the "subset of" relation ⊆ needs to be restricted to have domain and codomain P(A) (the power set of a specific set A): the resulting set relation can be denoted ⊆A. Also, the "member of" relation needs to be restricted to have domain A and codomain P(A) to obtain a binary relation ∈A that is a set. Another solution to this problem is to use a set theory with proper classes, such as NBG Von Neumann–Bernays–Gödel set theory In the foundations of mathematics, von Neumann–Bernays–Gödel set theory is an axiomatic set theory that is a conservative extension of the canonical axiomatic set theory ZFC. A statement in the language of ZFC is provable in NBG if and only if it is provable in ZFC. The ontology of NBG includes... or Morse–Kelley set theory Morse–Kelley set theory In the foundation of mathematics, Morse–Kelley set theory or Kelley–Morse set theory is a first order axiomatic set theory that is closely related to von Neumann–Bernays–Gödel set theory... , and allow the domain and codomain (and so the graph) to be proper classes: in such a theory, equality, membership, and subset are binary relations without special comment. (A minor modification needs to be made to the concept of the ordered triple (X, Y, G), as normally a proper class cannot be a member of an ordered tuple; or of course one can identify the function with its graph in this context.) In most mathematical contexts, references to the relations of equality, membership and subset are harmless because they can be understood implicitly to be restricted to some set in the context. ## The number of binary relations The number of distinct binary relations on an n-element set is 2n2 : Notes: • The number of irreflexive relations is the same as that of reflexive relations. • The number of strict partial orders (irreflexive transitive relations) is the same as that of partial orders. • The number of strict weak orders is the same as that of total preorders. • The total orders are the partial orders that are also total preorders. The number of preorders that are neither a partial order nor a total preorder is, therefore, the number of preorders, minus the number of partial orders, minus the number of total preorders, plus the number of total orders: 0, 0, 0, 3, and 85, respectively. • the number of equivalence relations is the number of partition Partition of a set In mathematics, a partition of a set X is a division of X into non-overlapping and non-empty "parts" or "blocks" or "cells" that cover all of X... s, which is the Bell number Bell number In combinatorics, the nth Bell number, named after Eric Temple Bell, is the number of partitions of a set with n members, or equivalently, the number of equivalence relations on it... . The binary relations can be grouped into pairs (relation, complement), except that for n = 0 the relation is its own complement. The non-symmetric ones can be grouped into quadruple Quadruple may refer to:* Tuple, a mathematical structure* Quadruple, a term for winning four association trophies* Quad , a figure skating jump* Home run in baseball* Quadruple-precision floating-point format in computing... s (relation, complement, inverse, inverse complement). ## Examples of common binary relations • order relations, including strict orders: • greater than • greater than or equal to • less than • less than or equal to • divides (evenly) • is a subset Subset In mathematics, especially in set theory, a set A is a subset of a set B if A is "contained" inside B. A and B may coincide. The relationship of one set being a subset of another is called inclusion or sometimes containment... of • equivalence relation Equivalence relation In mathematics, an equivalence relation is a relation that, loosely speaking, partitions a set so that every element of the set is a member of one and only one cell of the partition. Two elements of the set are considered equivalent if and only if they are elements of the same cell... s: • equality • is parallel Parallel (geometry) Parallelism is a term in geometry and in everyday life that refers to a property in Euclidean space of two or more lines or planes, or a combination of these. The assumed existence and properties of parallel lines are the basis of Euclid's parallel postulate. Two lines in a plane that do not... to (for affine space Affine space In mathematics, an affine space is a geometric structure that generalizes the affine properties of Euclidean space. In an affine space, one can subtract points to get vectors, or add a vector to a point to get another point, but one cannot add points. In particular, there is no distinguished point... s) • is in bijection Bijection A bijection is a function giving an exact pairing of the elements of two sets. A bijection from the set X to the set Y has an inverse function from Y to X. If X and Y are finite sets, then the existence of a bijection means they have the same number of elements... with • isomorphy Isomorphism In abstract algebra, an isomorphism is a mapping between objects that shows a relationship between two properties or operations. If there exists an isomorphism between two structures, the two structures are said to be isomorphic. In a certain sense, isomorphic structures are... • dependency relation Dependency relation In mathematics and computer science, a dependency relation is a binary relation that is finite, symmetric, and reflexive; i.e. a finite tolerance relation... , a symmetric, reflexive relation. • independency relation, a symmetric, irreflexive relation. reflexiveReflexive relationIn mathematics, a reflexive relation is a binary relation on a set for which every element is related to itself, i.e., a relation ~ on S where x~x holds true for every x in S. For example, ~ could be "is equal to".-Related terms:... symmetricSymmetric relationIn mathematics, a binary relation R over a set X is symmetric if it holds for all a and b in X that if a is related to b then b is related to a.In mathematical notation, this is:... transitiveTransitive relationIn mathematics, a binary relation R over a set X is transitive if whenever an element a is related to an element b, and b is in turn related to an element c, then a is also related to c.... symbol example directed graphDirected graphA directed graph or digraph is a pair G= of:* a set V, whose elements are called vertices or nodes,... → undirected graphGraph (mathematics)In mathematics, a graph is an abstract representation of a set of objects where some pairs of the objects are connected by links. The interconnected objects are represented by mathematical abstractions called vertices, and the links that connect some pairs of vertices are called edges... tournamentTournament (graph theory)A tournament is a directed graph obtained by assigning a direction for each edge in an undirected complete graph. That is, it is a directed graph in which every pair of vertices is connected by a single directed edge.... pecking orderPecking orderPecking order or just peck order is the colloquial term for a hierarchical system of social organization in chickens. It was first described from the behaviour of poultry by Thorleif Schjelderup-Ebbe in 1921 under the German terms Hackordnung or Hackliste' ... dependencyDependency relationIn mathematics and computer science, a dependency relation is a binary relation that is finite, symmetric, and reflexive; i.e. a finite tolerance relation... weak order ≤ preorderPreorderIn mathematics, especially in order theory, preorders are binary relations that are reflexive and transitive.For example, all partial orders and equivalence relations are preorders... ≤ preferencePreference-Definitions in different disciplines:The term “preferences” is used in a variety of related, but not identical, ways in the scientific literature. This makes it necessary to make explicit the sense in which the term is used in different social sciences.... partial order ≤ subsetSubsetIn mathematics, especially in set theory, a set A is a subset of a set B if A is "contained" inside B. A and B may coincide. The relationship of one set being a subset of another is called inclusion or sometimes containment... partial equivalencePartial equivalence relationIn mathematics, a partial equivalence relation R on a set X is a relation that is symmetric and transitive... equivalence relationEquivalence relationIn mathematics, an equivalence relation is a relation that, loosely speaking, partitions a set so that every element of the set is a member of one and only one cell of the partition. Two elements of the set are considered equivalent if and only if they are elements of the same cell... ∼, ≅, ≈, ≡ equality strict partial order < proper subset	2022-12-06 21:00:08	{"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": 0.8397032022476196, "perplexity": 401.720337918982}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "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/1669446711114.3/warc/CC-MAIN-20221206192947-20221206222947-00378.warc.gz"}
https://math.stackexchange.com/questions/798519/reference-request-certain-special-lfts	# Reference request: certain special LFTs $\newcommand{\cs}{\operatorname{cs}}$ My actual question is at the bottom. Let $$a\diamond b = \frac{a+b}{1+ab}$$ and $$a\dagger=\dfrac{1-a}{1+a}.$$ Then $$a\dagger\dagger = a$$ and \begin{align} (ab)\dagger & = (a\dagger)\diamond (b\dagger), \\[8pt] (a\diamond b)\dagger & = (a\dagger)(b\dagger), \end{align} and hence $$(a\diamond b)\diamond c = a\diamond (b\diamond c)$$ (and this comes to $\dfrac{a+b+c+abc}{1+ab+ac+bc}$). If we then let $g(a) = a\diamond a$ and $f(a) = (a\dagger)\diamond (a\dagger)$, then we have \begin{align} g(a) & = f(a\dagger) \\[6pt] f(a) & = g(a\dagger), \end{align} and \begin{align} g\left(\frac 1 a\right) = g(a), & \qquad f\left(\frac 1 a\right) = -f(a), \\[6pt] g(-a) = -g(a), & \qquad f(-a) = f(a). \end{align} Then we have $$\tan\frac\alpha2\cdot\tan\frac\beta2= \tan\frac\gamma2 \iff \cos\alpha\diamond\cos\beta = \cos\gamma.$$ Let us define the "stereographic cosine" of $a$ to be the $x$-coordinate of the projection of the point $(0,a)$ onto the circle $x^2+y^2=1$ along a line through the point $(-1,0)$. Then $$\cs a = (a^2)\dagger = (a\dagger)\diamond(a\dagger)$$ and we have the identity $$\cs(a_1\cdots a_n)=\cs a_1 \diamond\cdots\diamond\cs a_n.$$ (This identity will appear in a forthcoming publication.) My question is whether this somewhat suprisingly complex set of identities, with some of the rhythm of trigonometric identities, following from this seemingly trivially simple set of definitions, has a literature? Has this seen the light of day somewhere? • Forgive me if this seems unnecessary. I'm interested in finding out where you get all these very interesting ideas from. What is your motivation? – user122283 May 16 '14 at 23:15 • @SanathDevalapurkar : Thank you. I get them from fiddling with elementary geometry and trigonometry. – Michael Hardy May 17 '14 at 2:57 • Sir, by forthcoming publication do you mean in a journal? Or preprint like Arxiv? – Kugelblitz Mar 11 '15 at 12:16 • This material is somewhat related to the Gudermannian identities, which connect the circular functions with the hyperbolic functions without (explicit) use of complex numbers. – PM 2Ring Mar 11 '15 at 13:00	2019-08-24 13:40:14	{"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": 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": 3, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9710029363632202, "perplexity": 955.5851624603472}, "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-2019-35/segments/1566027321140.82/warc/CC-MAIN-20190824130424-20190824152424-00359.warc.gz"}
http://greyenlightenment.com/2021/07/28/stock-market-investing-series-part-1-why-the-stock-market-has-gone-up-so-much/	# Stock Market Investing Series, Part 1: Why The Stock Market Has Gone Up So Much This is the first post of a multi-part Q&A series about economcis and investing The bull market is long in the tooth. How long can it continue? Will future returns be poor? From Josh Brown, This is why, he writes: The S&P 500 has been compounding at 14% per year over the last ten years. That rate of return, which was not expected by anyone and should not be expected going forward, turns $100,000 into$370,000 if left alone. There have been people doing their best to talk you out of taking stock market risk, or convincing you that you could hedge it away while still earning the same (or better) returns. This is now and has always been a fantasy – risk-free reward is the domain of the charlatans. It only exists on Twitter, not in real life. He says it is not expected going forward. But people said that 5 years ago, 10 years ago, etc. Maybe 15-25% annual returns are the new normal. I have long argued that people tend to overestimate the likelihood of change, either societally or economic; I take the opposite view, that trends, once established and and with justification behind them, tend to persist much longer than many assume or predict. The media narrative in mid-2020 was that vaccines would put an end to the Covid crisis, yet new variants keep popping up and cases in the US are rising again. So in spite of mass vaccination, the Covid crisis won’t go away, and probably never will, much like the threat of terrorism that 2 decades after 911 still necessitates we take off our shoes at the airport. Disney can keep making endless reboots and sequels of the same franchises, and earn billions more from licensing digital content, which costs nothing to distribute and store. The media narrative in Feb-May 2020 was that Covid would severely hurt Disney, but the always-wrong financial media overlooked that intellectual property and streaming entertainment are the main contributors of growth even if the theme parks were temporarily closed and losing money. Profits matter more than even GDP. Multinationals, especially in tech,are generating record profits and cash flows. Interest rates rock bottom and not expected to go up anytime soon. These are optimal conditions for returns. The amount of cash generated by large firms is unprecedented in the history of the US economy and probably capitalism overall. It has been this way since 2009 and there is no reason to expect this to suddenly change, nor any signs that the conditions that were in place in 2009 have changed 12 years later. Profit margins have been rising steadily for the past decade, only to swell even more so after Covid: Zooming out, margins are the fattest ever, exceeding even the 90s: The US economy entered recession in 2001 shortly after Clinton left office, and Bush was blamed for it (and this was before 911), but had Gore won there is little reason to expect things would have been different. By the late 90s there were many underlying problems such as high interest rates (6% vs. 0-.25% now) and shrinking profit margins as shown above, and other signs of stagnation. But no such problems exist now, hence my optimism going forward. In the ’90s, Amazon, McDonald’s, Nike, Walmart, and Disney were successful, but were still just consumer brands, not major cultural and economic institutions in and of themselves, which is what they have become, especially since Covid. Pre-2009/2008, ‘big tech’ was not a thing. Cisco, Oracle, IBM, and Microsoft were big and powerful, but nothing like we see now. The past decade saw the rise of 5 tech companies worth at least $1 trillion each, those being Apple, Amazon, Microsoft, Google, and Facebook. By comparison, Cisco and Microsoft in 2000, at the peak of the ’90s tech bubble were worth$1 trillion combined, yet valuations were considerably higher. The PE ratio of the Nasdaq 100 is currently around 37, compared to 400+ in 2000. So to put it another way, given that the combined market capitalization of Nasdaq 100 companies is $19.4 trillion today versus$7 trillion in 2000 at the peak of the bubble, yet PE ratios are 90% lower, implies that companies are generating about 30x more profits. [But this includes new companies such as Facebook and Google, so it’s not like existing companies are earning 30x more money.] By comparison, US GDP only doubled in that same period, from $10 trillion to$20 trillion. This goes to show the huge disconnect between economic growth and corporate profits, especially in the tech sector. As discussed in more detail here, the second tailwind for stocks is that yield curve is very steep and the CPI exceeds interest rates, as it has been since 2009 and even more so since Covid. Everyone is talking about surging inflation, yet the fed is obstinate about not raising rates until 2022-2023 at the earliest, and any rate hikes will be verrrryyy gradual and with tons of forewarning. This forces individuals and institutions to either buy stocks and other ‘risky’ assets [it’s not that stocks are that risky, but risk is defined as having the potential to lose significant value, unlike short-term government bonds], or lose 2-3%/year due to inflation. If the CPI lags the ‘true’ inflation rate, which most people seem to agree it does, then this only makes stocks more attractive as a hedge. ## 1 comment 1. Blackvorte says: Do you recommend being tech heavy then? Even split between VOO and QQQ? What portfolio split do you advise? Any RE ever? Thanks	2021-09-22 11:46:54	{"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": 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": 0.26230087876319885, "perplexity": 3367.625000634216}, "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/1631780057347.80/warc/CC-MAIN-20210922102402-20210922132402-00578.warc.gz"}
https://codedocs.xyz/gammasoft71/xtd/classxtd_1_1io_1_1directory.html	xtd - Reference Guide 0.2.0 Modern c++17/20 framework to create console, GUI and unit test applications on Windows, macOS, Linux, iOS and android. xtd::io::directory Class Reference #include <directory.h> ## Definition Exposes static methods for creating, moving, and enumerating through directories and subdirectories. This class cannot be inherited. Ineheritance xtd::static_objectxtd::io::directory Namespace xtd::io Library xtd.core Example The following example shows how to retrieve all the text files from a directory and move them to a new directory. After the files are moved, they no longer exist in the original directory. #include <xtd/xtd> using namespace xtd; using namespace xtd::io; class program { public: static void main() { ustring source_directory = R"(C:\current)"; ustring archive_directory = R"(C:\archive)"; try { auto txt_files = directory::enumerate_files(source_directory, ".txt"); for (ustring current_file : txt_files) { ustring file_name = current_file.substring(source_directory.size() + 1); directory::move(current_file, path::combine(archive_directory, file_name)); } } catch (system_exception& e) { } } }; startup_(program); Example The following example demonstrates how to move a directory and all its files to a new directory. The original directory no longer exists after it has been moved. #include <xtd/xtd> using namespace xtd; using namespace xtd::io; class program { public: static void main() { ustring source_directory = R"(C:\source)"; ustring destination_directory = R"(C:\destination)"; try { directory::move(source_directory, destination_directory); } catch (const system_exception& e) { } } }; startup_(program); Remarks Use the xtd::io::directory class for typical operations such as copying, moving, renaming, creating, and deleting directories. The static methods of the xtd::io::directory class perform security checks on all methods. If you are going to reuse an object several times, consider using the corresponding instance method of xtd::io::directory_info instead, because the security check will not always be necessary. If you are performing only one directory-related action, it might be more efficient to use a static xtd::io::directory method rather than a corresponding xtd::io::directory_info instance method. Most xtd::io::directory methods require the path to the directory that you are manipulating. Note In members that accept a string path parameter, that path must be well-formed or an exception is raised. For example, if a path is fully qualified but begins with a space (" c:\temp"), the path string isn't trimmed, so the path is considered malformed and an exception is raised. In addition, a path or a combination of paths cannot be fully qualified twice. For example, "c:\temp c:\windows" also raises an exception. Ensure that your paths are well-formed when using methods that accept a path string. For more information see xtd::io::path. Remarks In members that accept a path, the path can refer to a file or a directory. You can use a full path, a relative path, or a Universal Naming Convention (UNC) path for a server and share name. For example, all the following are acceptable paths: • "c:\\MyDir". • "MyDir\\MySubdir". • "\\\\MyServer\\MyShare". To demand permissions for a directory and all its subdirectories, end the path string with the directory separator character. (For example, "C:\Temp\" grants access to C:\ and all its subdirectories.) To demand permissions only for a specific directory, end the path string with a period. (For example, "C:\Temp\." grants access only to C:\, not to its subdirectories.) In members that accept a search_pattern parameter, the search string can be any combination of literal characters and two wildcard characters; and ?. This parameter does not recognize regular expressions. For more information, see the xtd::io::directory::enumerate_directories(ustring, ustring) method or any other method that uses the search_pattern parameter. xtd::io::directory and xtd::io::directory_info are not supported for use in Windows Store apps. For information about how to access files and folders in Windows Store apps, see Accessing data and files (Windows Store apps). ## Classes class directory_iterator Represent directory iterator used by xtd::io::directory. More... class file_iterator Represent file iterator used by xtd::io::directory. More... class file_system_entry_iterator Represent file system iterator used by xtd::io::directory. More... ## Static Public Member Functions static xtd::io::directory_info create_directory (const xtd::ustring &path) Creates all directories and subdirectories in the specified path unless they already exist. More... static xtd::io::directory::directory_iterator enumerate_directories (const xtd::ustring &path) Returns an enumerable collection of directory full names in a specified path. More... static xtd::io::directory::directory_iterator enumerate_directories (const xtd::ustring &path, const xtd::ustring &search_pattern) Returns an enumerable collection of directory full names that match a search pattern in a specified path. More... static xtd::io::directory::file_system_entry_iterator enumerate_file_system_entries (const xtd::ustring &path) Returns an enumerable collection of file names and directory names in a specified path. More... static xtd::io::directory::file_system_entry_iterator enumerate_file_system_entries (const xtd::ustring &path, const xtd::ustring &search_pattern) Returns an enumerable collection of file names and directory names that match a search pattern in a specified path. More... static xtd::io::directory::file_iterator enumerate_files (const xtd::ustring &path) Returns an enumerable collection of full file names in a specified path. More... static xtd::io::directory::file_iterator enumerate_files (const xtd::ustring &path, const xtd::ustring &search_pattern) Returns an enumerable collection of full file names that match a search pattern in a specified path. More... static bool exists (const xtd::ustring &path) Determines whether the given path refers to an existing directory on disk. More... static std::chrono::system_clock::time_point get_creation_time (const xtd::ustring &path) Gets the creation date and time of a directory. More... static xtd::ustring get_current_directory () Gets the current working directory of the application. More... static std::vector< xtd::ustringget_directories (const xtd::ustring &path) Returns the names of subdirectories (including their paths) in the specified directory. More... static std::vector< xtd::ustringget_directories (const xtd::ustring &path, const xtd::ustring &search_pattern) Returns the names of subdirectories (including their paths) that match the specified search pattern in the specified directory. More... static xtd::ustring get_directory_root (const xtd::ustring &path) Returns the volume information, root information, or both for the specified path. More... static std::vector< xtd::ustringget_file_system_entries (const xtd::ustring &path) Returns the names of all files and subdirectories in a specified path. More... static std::vector< xtd::ustringget_file_system_entries (const xtd::ustring &path, const xtd::ustring &search_pattern) Returns an array of file names and directory names that match a search pattern in a specified path. More... static std::vector< xtd::ustringget_files (const xtd::ustring &path) Returns the names of files (including their paths) in the specified directory. More... static std::vector< xtd::ustringget_files (const xtd::ustring &path, const xtd::ustring &search_pattern) Returns the names of files (including their paths) that match the specified search pattern in the specified directory. More... static std::chrono::system_clock::time_point get_last_access_time (const xtd::ustring &path) Returns the date and time the specified file or directory was last accessed. More... static std::chrono::system_clock::time_point get_last_write_time (const xtd::ustring &path) Returns the date and time the specified file or directory was last written to. More... static std::vector< xtd::ustringget_logical_drives () Retrieves the names of the logical drives on this computer in the form "<drive letter>:\". More... static xtd::io::directory_info get_parent (const xtd::ustring &path) Retrieves the parent directory of the specified path, including both absolute and relative paths. More... static void move (const xtd::ustring &source_dir_name, const xtd::ustring &dest_dir_name) Moves a file or a directory and its contents to a new location. More... static void remove (const xtd::ustring &path) Deletes an empty directory from a specified path. More... static void remove (const xtd::ustring &path, bool recursive) Deletes the specified directory and, if indicated, any subdirectories and files in the directory. More... static void set_creation_time (const xtd::ustring &path, std::chrono::system_clock::time_point creation_time) Sets the creation date and time for the specified file or directory. More... static void set_creation_time (const xtd::ustring &path, time_t creation_time) Sets the creation date and time for the specified file or directory. More... static void set_creation_time (const xtd::ustring &path, const std::tm &creation_time) Sets the creation date and time for the specified file or directory. More... static void set_creation_time (const xtd::ustring &path, int32_t year, int32_t month, int32_t day) Sets the creation date and time for the specified file or directory. More... static void set_creation_time (const xtd::ustring &path, int32_t year, int32_t month, int32_t day, int32_t hour, int32_t minute, int32_t second) Sets the creation date and time for the specified file or directory. More... static void set_current_directory (const xtd::ustring &path) Sets the application's current working directory to the specified directory. More... static void set_last_access_time (const xtd::ustring &path, std::chrono::system_clock::time_point last_access_time) Sets the date and time the specified file or directory was last accessed. More... static void set_last_access_time (const xtd::ustring &path, time_t last_access_time) Sets the date and time the specified file or directory was last accessed. More... static void set_last_access_time (const xtd::ustring &path, const std::tm &last_access_time) Sets the date and time the specified file or directory was last accessed. More... static void set_last_access_time (const xtd::ustring &path, int32_t year, int32_t month, int32_t day) Sets the date and time the specified file or directory was last accessed. More... static void set_last_access_time (const xtd::ustring &path, int32_t year, int32_t month, int32_t day, int32_t hour, int32_t minute, int32_t second) Sets the date and time the specified file or directory was last accessed. More... static void set_last_write_time (const xtd::ustring &path, std::chrono::system_clock::time_point last_write_time) Sets the date and time a directory was last written to. More... static void set_last_write_time (const xtd::ustring &path, time_t last_write_time) Sets the date and time a directory was last written to. More... static void set_last_write_time (const xtd::ustring &path, const std::tm &last_write_time) Sets the date and time a directory was last written to. More... static void set_last_write_time (const xtd::ustring &path, int32_t year, int32_t month, int32_t day) Sets the date and time a directory was last written to. More... static void set_last_write_time (const xtd::ustring &path, int32_t year, int32_t month, int32_t day, int32_t hour, int32_t minute, int32_t second) Sets the date and time a directory was last written to. More... ## ◆ create_directory() static xtd::io::directory_info xtd::io::directory::create_directory ( const xtd::ustring & path ) static Creates all directories and subdirectories in the specified path unless they already exist. Parameters path The directory to create. Returns An object that represents the directory at the specified path. This object is returned regardless of whether a directory at the specified path already exists. Exceptions xtd::io::io_exception The directory specified by path is a file. xtd::argument_exception path is a zero-length string, contains only white space, or contains one or more invalid characters. You can query for invalid characters by using the xtd::io::path::get_invalid_path_chars method. xtd::io::path_too_long_exception The specified path, file name, or both exceed the system-defined maximum length. xtd::io::directory_not_found_exception The specified path is invalid (for example, it is on an unmapped drive). xtd::not_supported_exception path contains a colon character (:) that is not part of a drive label ("C:\"). Example The following example creates and deletes the specified directory: #include <xtd/xtd> using namespace xtd; using namespace xtd::io; class program { public: static void main() { // Specify the directories you want to manipulate. directory_info di("c:\\MyDir"); try { // Determine whether the directory exists. if (di.exists()) { // Indicate that the directory already exists. return; } // Try to create the directory. di.create(); console::write_line("The directory was created successfully."); // Delete the directory. di.remove(); console::write_line("The directory was deleted successfully."); } catch (const system_exception& e) { console::write_line("The process failed: {0}", e.to_string()); } } }; startup_(program); Example To create the directory C: when the current directory is C:, use any of the following calls to ensure that the backslash is interpreted properly: directory::create_directory("\\Users\\User1\\Public\\Html"); directory::create_directory("c:\\Users\\User1\\Public\\Html"); Remarks Any and all directories specified in path are created, unless they already exist or unless some part of path is invalid. If the directory already exists, this method does not create a new directory, but it returns a DirectoryInfo object for the existing directory. The path parameter specifies a directory path, not a file path. Trailing spaces are removed from the end of the path parameter before creating the directory. Creating a directory with only the colon character (:) is not supported, and will cause a not_supported_exception to be thrown. On Unix systems, use a forward slash (/) as path separator. ## ◆ enumerate_directories() [1/2] static xtd::io::directory::directory_iterator xtd::io::directory::enumerate_directories ( const xtd::ustring & path ) static Returns an enumerable collection of directory full names in a specified path. Parameters path The relative or absolute path to the directory to search. This string is not case-sensitive. Returns An xtd::io::directory::directory_iterator of the full names (including paths) for the directories in the directory specified by path. Exceptions xtd::io::io_exception The directory specified by path is a file. xtd::argument_exception path is a zero-length string, contains only white space, or contains one or more invalid characters. You can query for invalid characters by using the xtd::io::path::get_invalid_path_chars method. xtd::io::path_too_long_exception The specified path, file name, or both exceed the system-defined maximum length. xtd::io::directory_not_found_exception The specified path is invalid (for example, it is on an unmapped drive). xtd::not_supported_exception path contains a colon character (:) that is not part of a drive label ("C:\"). rExample The following example enumerates the top-level directories in a specified path. #include <xtd/xtd> using namespace std; using namespace xtd; using namespace xtd::io; class program { public: static void main() { try { // Set a variable to the My Documents path. vector<ustring> dirs(begin(directory::enumerate_directories(doc_path)), end(directory::enumerate_directories(doc_path))); for (auto dir : dirs) { console::write_line("{}", dir.substring(dir.last_index_of(path::directory_separator_char()) + 1)); } console::write_line("{} directories found.", dirs.size()); } catch (const unauthorized_access_exception& ex) { } catch (const path_too_long_exception& ex) { } } }; startup_(program); Remarks You can specify relative or absolute path information in the path parameter. Relative path information is interpreted as relative to the current working directory, which you can determine by using the xtd::io::directory::get_current_directory method. The returned directory names are prefixed with the value you provided in the path parameter. For example, if you provide a relative path in the path parameter, the returned directory names will contain a relative path. The xtd::io::directory::enumerate_directories and xtd::io::directory::get_directories methods differ as follows: When you use xtd::io::directory::enumerate_directories, you can start enumerating the collection of names before the whole collection is returned; when you use xtd::io::directory::get_directories, you must wait for the whole array of names to be returned before you can access the array. Therefore, when you are working with many files and directories, xtd::io::directory::enumerate_directories can be more efficient. ## ◆ enumerate_directories() [2/2] static xtd::io::directory::directory_iterator xtd::io::directory::enumerate_directories ( const xtd::ustring & path, const xtd::ustring & search_pattern ) static Returns an enumerable collection of directory full names that match a search pattern in a specified path. Parameters path The relative or absolute path to the directory to search. This string is not case-sensitive. search_pattern The search string to match against the names of directories in path. This parameter can contain a combination of valid literal path and wildcard (* and ?) characters, but it doesn't support regular expressions. Returns An xtd::io::directory::directory_iterator of the full names (including paths) for the directories in the directory specified by path and that match the specified search pattern. Exceptions xtd::io::io_exception The directory specified by path is a file. xtd::argument_exception path is a zero-length string, contains only white space, or contains one or more invalid characters. You can query for invalid characters by using the xtd::io::path::get_invalid_path_chars method. xtd::io::path_too_long_exception The specified path, file name, or both exceed the system-defined maximum length. xtd::io::directory_not_found_exception The specified path is invalid (for example, it is on an unmapped drive). xtd::not_supported_exception path contains a colon character (:) that is not part of a drive label ("C:\"). rExample The following example enumerates the top-level directories in a specified path that match a specified search pattern. #include <xtd/xtd> using namespace std; using namespace xtd; using namespace xtd::io; class program { public: static void main() { try { ustring dir_path = R"(\\archives\2009\reports)"; // Create a List collection. auto dirs = vector<ustring>(begin(directory::enumerate_directories(dir_path, "dv_")), end(directory::enumerate_directories(dir_path, "dv_"))); // Show results. for (auto dir : dirs) { // Remove path information from string. console::write_line("{0}", dir.substring(dir.last_index_of("\\") + 1)); } console::write_line("{0} directories found.", dirs.size()); } catch (const unauthorized_access_exception& ex) { } catch (const path_too_long_exception& ex) { } } }; startup_(program); Remarks search_pattern can be a combination of literal and wildcard characters, but it doesn't support regular expressions. The following wildcard specifiers are permitted in search_pattern. Wildcard specifier Matches * (asterisk) Zero or more characters in that position. ? (question mark) Zero or one character in that position. Characters other than the wildcard are literal characters. For example, the search_pattern string "t" searches for all names in path ending with the letter "t". The search_pattern string "s" searches for all names in path beginning with the letter "s". search_pattern cannot end in two periods ("..") or contain two periods ("..") followed by xtd::io::path::directory_separator_char or xtd::io::path::alt_directory_separator_char, nor can it contain any invalid characters. You can query for invalid characters by using the xtd::io::path::get_invalid_path_chars method. You can specify relative or absolute path information in the path parameter. Relative path information is interpreted as relative to the current working directory, which you can determine by using the xtd::io::directory::get_current_directory method. The returned directory names are prefixed with the value you provided in the path parameter. For example, if you provide a relative path in the path parameter, the returned directory names will contain a relative path. The xtd::io::directory::enumerate_directories and xtd::io::directory::get_directories methods differ as follows: When you use xtd::io::directory::xtd::io::directory::enumerate_directories, you can start enumerating the collection of names before the whole collection is returned; when you use xtd::io::directory::get_directories, you must wait for the whole array of names to be returned before you can access the array. Therefore, when you are working with many files and directories, xtd::io::directory::enumerate_directories can be more efficient. ## ◆ enumerate_file_system_entries() [1/2] static xtd::io::directory::file_system_entry_iterator xtd::io::directory::enumerate_file_system_entries ( const xtd::ustring & path ) static Returns an enumerable collection of file names and directory names in a specified path. Parameters path The relative or absolute path to the directory to search. This string is not case-sensitive. Returns An xtd::io::directory::file_system_entry_iterator of file-system entries in the directory specified by path. Exceptions xtd::io::io_exception The directory specified by path is a file. xtd::argument_exception path is a zero-length string, contains only white space, or contains one or more invalid characters. You can query for invalid characters by using the xtd::io::path::get_invalid_path_chars method. xtd::io::path_too_long_exception The specified path, file name, or both exceed the system-defined maximum length. xtd::io::directory_not_found_exception The specified path is invalid (for example, it is on an unmapped drive). xtd::not_supported_exception path contains a colon character (:) that is not part of a drive label ("C:\"). Remarks You can specify relative path information with the path parameter. Relative path information is interpreted as relative to the current working directory, which you can determine by using the xtd::io::directory::get_current_directory method. The xtd::io::directory::enumerate_file_system_entries and xtd::io::directory::get_file_system_entries methods differ as follows: When you use xtd::io::directory::enumerate_file_system_entries, you can start enumerating the collection of entries before the whole collection is returned; when you use xtd::io::directory::get_file_system_entries, you must wait for the whole array of entries to be returned before you can access the array. Therefore, when you are working with many files and directories, xtd::io::directory::enumerate_files_system_entires can be more efficient. ## ◆ enumerate_file_system_entries() [2/2] static xtd::io::directory::file_system_entry_iterator xtd::io::directory::enumerate_file_system_entries ( const xtd::ustring & path, const xtd::ustring & search_pattern ) static Returns an enumerable collection of file names and directory names that match a search pattern in a specified path. Parameters path The relative or absolute path to the directory to search. This string is not case-sensitive. serach_pattern The search string to match against the names of file-system entries in path. This parameter can contain a combination of valid literal path and wildcard (* and ?) characters, but it doesn't support regular expressions. Returns An xtd::io::directory::file_system_entry_iterator of file-system entries in the directory specified by path and that match the specified search pattern. Exceptions xtd::io::io_exception The directory specified by path is a file. xtd::argument_exception path is a zero-length string, contains only white space, or contains one or more invalid characters. You can query for invalid characters by using the xtd::io::path::get_invalid_path_chars method. xtd::io::path_too_long_exception The specified path, file name, or both exceed the system-defined maximum length. xtd::io::directory_not_found_exception The specified path is invalid (for example, it is on an unmapped drive). xtd::not_supported_exception path contains a colon character (:) that is not part of a drive label ("C:\"). Remarks search_pattern can be a combination of literal and wildcard characters, but it doesn't support regular expressions. The following wildcard specifiers are permitted in searchPattern. Wildcard specifier Matches * (asterisk) Zero or more characters in that position. ? (question mark) Zero or one character in that position. Characters other than the wildcard are literal characters. For example, the search_pattern string "t" searches for all names in path ending with the letter "t". The search_attern string "s" searches for all names in path beginning with the letter "s". search_pattern cannot end in two periods ("..") or contain two periods ("..") followed by xtd::io::path::directory_separator_char or xtd::ioo::path::alt_directory_separator_char, nor can it contain any invalid characters. You can query for invalid characters by using the xtd::io::path::get_invalid_path_chars method. You can specify relative path information with the path parameter. Relative path information is interpreted as relative to the current working directory, which you can determine by using the xtd::io::directory::get_current_directory method. The xtd::io::directory::enumerate_file_system_entries and xtd::io::directory::get_file_system_entries methods differ as follows: When you use xtd::io::directory::enumerate_file_system_entries, you can start enumerating the collection of entries before the whole collection is returned; when you use xtd::io::directory::get_file_system_entries, you must wait for the whole array of entries to be returned before you can access the array. Therefore, when you are working with many files and directories, xtd::io::directory::enumerate_file_system_entries can be more efficient. ## ◆ enumerate_files() [1/2] static xtd::io::directory::file_iterator xtd::io::directory::enumerate_files ( const xtd::ustring & path ) static Returns an enumerable collection of full file names in a specified path. Parameters path The relative or absolute path to the directory to search. This string is not case-sensitive. Returns An xtd::io::directory::directory_iterator of the full names (including paths) for the files in the directory specified by path. Exceptions xtd::io::io_exception The directory specified by path is a file. xtd::argument_exception path is a zero-length string, contains only white space, or contains one or more invalid characters. You can query for invalid characters by using the xtd::io::path::get_invalid_path_chars method. xtd::io::path_too_long_exception The specified path, file name, or both exceed the system-defined maximum length. xtd::io::directory_not_found_exception The specified path is invalid (for example, it is on an unmapped drive). xtd::not_supported_exception path contains a colon character (:) that is not part of a drive label ("C:\"). Example The following example shows how to retrieve all the text files from a directory and move them to a new directory. After the files are moved, they no longer exist in the original directory. #include <xtd/xtd> using namespace xtd; using namespace xtd::io; class program { public: static void main() { ustring source_directory = R"(C:\current)"; ustring archive_directory = R"(C:\archive)"; try { auto txt_files = directory::enumerate_files(source_directory); for (ustring current_file : txt_files) { ustring file_name = current_file.substring(source_directory.size() + 1); directory::move(current_file, path::combine(archive_directory, file_name)); } } catch (system_exception& e) { } } }; startup_(program); Remarks You can specify relative path information with the path parameter. Relative path information is interpreted as relative to the current working directory, which you can determine by using the xtd::io::directory::get_current_directory method. The xtd::io::directory::enumerate_files and xtd::io::directory::get_files methods differ as follows: When you use xtd::io::directory::enumerate_files, you can start enumerating the collection of names before the whole collection is returned. When you use xtd::io::directory::get_files, you must wait for the whole array of names to be returned before you can access the array. Therefore, when you are working with many files and directories, xtd::io::directory::enumerate_files can be more efficient. ## ◆ enumerate_files() [2/2] static xtd::io::directory::file_iterator xtd::io::directory::enumerate_files ( const xtd::ustring & path, const xtd::ustring & search_pattern ) static Returns an enumerable collection of full file names that match a search pattern in a specified path. Parameters path The relative or absolute path to the directory to search. This string is not case-sensitive. search_pattern The search string to match against the names of files in path. This parameter can contain a combination of valid literal path and wildcard (* and ?) characters, but it doesn't support regular expressions. Returns An xtd::io::directory::directory_iterator of the full names (including paths) for the files in the directory specified by path and that match the specified search pattern. Exceptions xtd::io::io_exception The directory specified by path is a file. xtd::argument_exception path is a zero-length string, contains only white space, or contains one or more invalid characters. You can query for invalid characters by using the xtd::io::path::get_invalid_path_chars method. xtd::io::path_too_long_exception The specified path, file name, or both exceed the system-defined maximum length. xtd::io::directory_not_found_exception The specified path is invalid (for example, it is on an unmapped drive). xtd::not_supported_exception path contains a colon character (:) that is not part of a drive label ("C:\"). Example The following example shows how to retrieve all the text files from a directory and move them to a new directory. After the files are moved, they no longer exist in the original directory. #include <xtd/xtd> using namespace xtd; using namespace xtd::io; class program { public: static void main() { ustring source_directory = R"(C:\current)"; ustring archive_directory = R"(C:\archive)"; try { auto txt_files = directory::enumerate_files(source_directory, ".txt"); for (ustring current_file : txt_files) { ustring file_name = current_file.substring(source_directory.size() + 1); directory::move(current_file, path::combine(archive_directory, file_name)); } } catch (system_exception& e) { } } }; startup_(program); Remarks search_pattern can be a combination of literal and wildcard characters, but it doesn't support regular expressions. The following wildcard specifiers are permitted in searchPattern. Wildcard specifier Matches (asterisk) Zero or more characters in that position. ? (question mark) Zero or one character in that position. Characters other than the wildcard are literal characters. For example, the search_pattern string "t" searches for all names in path ending with the letter "t". The search_attern string "s" searches for all names in path beginning with the letter "s". search_pattern cannot end in two periods ("..") or contain two periods ("..") followed by xtd::io::path::directory_separator_char or xtd::ioo::path::alt_directory_separator_char, nor can it contain any invalid characters. You can query for invalid characters by using the xtd::io::path::get_invalid_path_chars method. You can specify relative path information with the path parameter. Relative path information is interpreted as relative to the current working directory, which you can determine by using the xtd::io::directory::get_current_directory method. The xtd::io::directory::enumerate_files and xtd::io::directory::get_files methods differ as follows: When you use xtd::io::directory::enumerate_files, you can start enumerating the collection of names before the whole collection is returned; when you use xtd::io::directory::get_files, you must wait for the whole array of names to be returned before you can access the array. Therefore, when you are working with many files and directories, xtd::io::directory::enumerate_files can be more efficient. ## ◆ exists() static bool xtd::io::directory::exists ( const xtd::ustring & path ) static Determines whether the given path refers to an existing directory on disk. Parameters path The path to test. Returns true if path refers to an existing directory; false if the directory does not exist or an error occurs when trying to determine if the specified directory exists. rExample The following example takes an array of file or directory names on the command line, determines what kind of name it is, and processes it appropriately. #include <xtd/xtd> using namespace std; using namespace xtd; using namespace xtd::io; class program { public: static void main(const vector<ustring>& args) { for (ustring path : args) { // This path is a file process_file(path); } else if(directory::exists(path)) { // This path is a directory process_directory(path); } else { console::write_line("{0} is not a valid file or directory.", path); } } } // Process all files in the directory passed in, recurse on any directories // that are found, and process the files they contain. static void process_directory(const ustring& target_directory) { // Process the list of files found in the directory. vector<ustring> file_entries = directory::get_files(target_directory); for (ustring file_name : file_entries) process_file(file_name); // Recurse into subdirectories of this directory. vector<ustring> subdirectory_entries = directory::get_directories(target_directory); for (ustring subdirectory : subdirectory_entries) process_directory(subdirectory); } // Insert logic for processing found files here. static void process_file(const ustring& path) { console::write_line("Processed file '{0}'.", path); } }; startup_(program); Remarks The path parameter is permitted to specify relative or absolute path information. Relative path information is interpreted as relative to the current working directory. Trailing spaces are removed from the end of the path parameter before checking whether the directory exists. The path parameter is not case-sensitive. If you do not have at a minimum read-only permission to the directory, the Exists method will return false. The xtd::io::directory::exists method returns false if any error occurs while trying to determine if the specified file exists. This can occur in situations that raise exceptions such as passing a file name with invalid characters or too many characters, a failing or missing disk, or if the caller does not have permission to read the file. ## ◆ get_creation_time() static std::chrono::system_clock::time_point xtd::io::directory::get_creation_time ( const xtd::ustring & path ) static Gets the creation date and time of a directory. Parameters path The path of the directory. Returns A td::chrono::system_clock::time_point class that is set to the creation date and time for the specified directory. This value is expressed in local time. Exceptions xtd::io::io_exception The directory specified by path is a file. xtd::argument_exception path is a zero-length string, contains only white space, or contains one or more invalid characters. You can query for invalid characters by using the xtd::io::path::get_invalid_path_chars method. xtd::io::path_too_long_exception The specified path, file name, or both exceed the system-defined maximum length. xtd::io::directory_not_found_exception The specified path is invalid (for example, it is on an unmapped drive). xtd::not_supported_exception path contains a colon character (:) that is not part of a drive label ("C:\"). Example #include <chrono> #include <xtd/xtd> using namespace std::chrono; using namespace xtd; using namespace xtd::io; The following example gets the creation time of the specified directory. class program { public: static void main() { try { // Get the creation time of a well-known directory. // Give feedback to the user. if (duration_cast<days>(system_clock::now().time_since_epoch() - tp.time_since_epoch()).count() > 364) { console::write_line("This directory is over a year old."); } else if (duration_cast<days>(system_clock::now().time_since_epoch() - tp.time_since_epoch()).count() > 30) { console::write_line("This directory is over a month old."); } else if (duration_cast<days>(system_clock::now().time_since_epoch() - tp.time_since_epoch()).count() <= 1) { console::write_line("This directory is less than a day old."); } else { console::write_line("This directory was created on {0}", tp); } } catch (const system_exception& e) { console::write_line("The process failed: {0}", e.to_string()); } } }; startup_(program); ## ◆ get_current_directory() static xtd::ustring xtd::io::directory::get_current_directory ( ) static Gets the current working directory of the application. Returns A string that contains the absolute path of the current working directory, and does not end with a backslash (). Exceptions xtd::unauthorized_access_exception The caller does not have the required permission. xtd::not_supported_exception The operating system does not have current directory functionality. Example The following example demonstrates how to use the xtd::io::directory::get_current_directory method. #include <xtd/xtd> using namespace xtd; using namespace xtd::io; class program { public: static void main() { try { // Get the current directory. ustring target = R"(c:\temp)"; "The current directory is {0}", path); if (!directory::exists(target)) { } // Change the current directory. console::write_line("You are in the temp directory."); } else { console::write_line("You are not in the temp directory."); } } catch (const system_exception& e) { console::write_line("The process failed: {0}", e.to_string()); } } }; startup_(program); Remarks The current directory is distinct from the original directory, which is the one from which the process was started. ## ◆ get_directories() [1/2] static std::vector xtd::io::directory::get_directories ( const xtd::ustring & path ) static Returns the names of subdirectories (including their paths) in the specified directory. Parameters path The relative or absolute path to the directory to search. This string is not case-sensitive. Returns An array of the full names (including paths) of subdirectories in the specified path, or an empty array if no directories are found. Exceptions xtd::io::io_exception The directory specified by path is a file. xtd::argument_exception path is a zero-length string, contains only white space, or contains one or more invalid characters. You can query for invalid characters by using the xtd::io::path::get_invalid_path_chars method. xtd::io::path_too_long_exception The specified path, file name, or both exceed the system-defined maximum length. xtd::io::directory_not_found_exception The specified path is invalid (for example, it is on an unmapped drive). xtd::not_supported_exception path contains a colon character (:) that is not part of a drive label ("C:\"). Example The following example takes an array of file or directory names on the command line, determines what kind of name it is, and processes it appropriately. #include <xtd/xtd> using namespace std; using namespace xtd; using namespace xtd::io; class program { public: static void main(const vector<ustring>& args) { for (ustring path : args) { if (file::exists(path)) { // This path is a file process_file(path); } else if(directory::exists(path)) { // This path is a directory process_directory(path); } else { console::write_line("{0} is not a valid file or directory.", path); } } } // Process all files in the directory passed in, recurse on any directories // that are found, and process the files they contain. static void process_directory(const ustring& target_directory) { // Process the list of files found in the directory. vector<ustring> file_entries = directory::get_files(target_directory); for (ustring file_name : file_entries) process_file(file_name); // Recurse into subdirectories of this directory. vector<ustring> subdirectory_entries = directory::get_directories(target_directory); for (ustring subdirectory : subdirectory_entries) process_directory(subdirectory); } // Insert logic for processing found files here. static void process_file(const ustring& path) { console::write_line("Processed file '{0}'.", path); } }; startup_(program); Remarks This method is identical to xtd::io::directory::get_directories(ustring, ustring) with the asterisk () specified as the search pattern, so it returns all subdirectories. The xtd::io::directory::enumerate_directories and xtd::io::directory::get_directories methods differ as follows: When you use xtd::io::directory::enumerate_directories, you can start enumerating the collection of names before the whole collection is returned; when you use xtd::io::directory::get_directories, you must wait for the whole array of names to be returned before you can access the array. Therefore, when you are working with many files and directories, xtd::io::directory::enumerate_directories can be more efficient. The path parameter can specify relative or absolute path information. Relative path information is interpreted as relative to the current working directory. To obtain the current working directory, see xtd::io::directory::get_current_directory. The names returned by this method are prefixed with the directory information provided in path. The path parameter is not case-sensitive. ## ◆ get_directories() [2/2] static std::vector xtd::io::directory::get_directories ( const xtd::ustring & path, const xtd::ustring & search_pattern ) static Returns the names of subdirectories (including their paths) that match the specified search pattern in the specified directory. Parameters path The relative or absolute path to the directory to search. This string is not case-sensitive. search_pattern The search string to match against the names of subdirectories in path. This parameter can contain a combination of valid literal and wildcard characters, but it doesn't support regular expressions. Returns An array of the full names (including paths) of the subdirectories that match the search pattern in the specified directory, or an empty array if no directories are found. Exceptions xtd::io::io_exception The directory specified by path is a file. xtd::argument_exception path is a zero-length string, contains only white space, or contains one or more invalid characters. You can query for invalid characters by using the xtd::io::path::get_invalid_path_chars method. xtd::io::path_too_long_exception The specified path, file name, or both exceed the system-defined maximum length. xtd::io::directory_not_found_exception The specified path is invalid (for example, it is on an unmapped drive). xtd::not_supported_exception path contains a colon character (:) that is not part of a drive label ("C:\"). Example #include <xtd/xtd> using namespace std; using namespace xtd; using namespace xtd::io; class program { public: static void main() { try { // Only get subdirectories that begin with the letter "p." vector<ustring> dirs = directory::get_directories(R"(c:\)", "p"); console::write_line("The number of directories starting with p is {0}.", dirs.size()); for (ustring dir : dirs) { } } catch (const system_exception& e) { console::write_line("The process failed: {0}", e.to_string()); } } }; startup_(program); Remarks This method returns all subdirectories directly under the specified directory that match the specified search pattern. If the specified directory has no subdirectories, or no subdirectories match the search_pattern parameter, this method returns an empty array. Only the top directory is searched. search_pattern can be a combination of literal and wildcard characters, but it doesn't support regular expressions. The following wildcard specifiers are permitted in search_pattern. Wildcard specifier Matches * (asterisk) Zero or more characters in that position. ? (question mark) Zero or one character in that position. Characters other than the wildcard are literal characters. For example, the search_attern string "t" searches for all names in path ending with the letter "t". The search_pattern string "s" searches for all names in path beginning with the letter "s". search_pattern cannot end in two periods ("..") or contain two periods ("..") followed by xtd::io::path::directory_separator_char or xtd::io::path::alt_directory_separator_char, nor can it contain any invalid characters. You can query for invalid characters by using the xtd::io::path::get_invalid_path_chars method. The path parameter can specify relative or absolute path information, and is not case-sensitive. Relative path information is interpreted as relative to the current working directory. To obtain the current working directory, see xtd::io::directory::get_current_directory. The xtd::io::directory::enumerate_directories and xtd::io::directory::get_directories methods differ as follows: When you use xtd::io::directory::enumerate_directories, you can start enumerating the collection of names before the whole collection is returned; when you use xtd::io::directory::get_directories, you must wait for the whole array of names to be returned before you can access the array. Therefore, when you are working with many files and directories, xtd::io::directory::enumerate_directories can be more efficient. ## ◆ get_directory_root() static xtd::ustring xtd::io::directory::get_directory_root ( const xtd::ustring & path ) static Returns the volume information, root information, or both for the specified path. Parameters path The path of a file or directory. Returns A string that contains the volume information, root information, or both for the specified path. Exceptions xtd::io::io_exception The directory specified by path is a file. xtd::argument_exception path is a zero-length string, contains only white space, or contains one or more invalid characters. You can query for invalid characters by using the xtd::io::path::get_invalid_path_chars method. xtd::io::path_too_long_exception The specified path, file name, or both exceed the system-defined maximum length. xtd::io::directory_not_found_exception The specified path is invalid (for example, it is on an unmapped drive). xtd::not_supported_exception path contains a colon character (:) that is not part of a drive label ("C:\"). Example The following example illustrates how to set the current directory and display the directory root. #include <xtd/xtd> using namespace xtd; using namespace xtd::io; class program { public: static void main() { // Create string for a directory. This value should be an existing directory // or the sample will throw a DirectoryNotFoundException. ustring dir = R"(C:\test)"; try { //Set the current directory. } catch (const directory_not_found_exception& e) { console::write_line("The specified directory does not exist. {0}", e); } // Print to console the results. console::write_line("Root directory: {0}", directory::get_directory_root(dir)); } }; startup_(program); Remarks This method obtains the fully qualified path name of path, as returned by xtd::io::path::get_full_path, and returns root directory information. The specified path is not required to exist. The path parameter is permitted to specify relative or absolute path information. Relative path information is interpreted as relative to the current working directory. To obtain the current working directory, see xtd::io::directory::get_current_directory. The path parameter is not case-sensitive. ## ◆ get_file_system_entries() [1/2] static std::vector xtd::io::directory::get_file_system_entries ( const xtd::ustring & path ) static Returns the names of all files and subdirectories in a specified path. Parameters path The relative or absolute path to the directory to search. This string is not case-sensitive. Returns An array of the names of files and subdirectories in the specified directory, or an empty array if no files or subdirectories are found. Exceptions xtd::io::io_exception The directory specified by path is a file. xtd::argument_exception path is a zero-length string, contains only white space, or contains one or more invalid characters. You can query for invalid characters by using the xtd::io::path::get_invalid_path_chars method. xtd::io::path_too_long_exception The specified path, file name, or both exceed the system-defined maximum length. xtd::io::directory_not_found_exception The specified path is invalid (for example, it is on an unmapped drive). xtd::not_supported_exception path contains a colon character (:) that is not part of a drive label ("C:\"). Example The following example uses the xtd::io::directory::get_file_system_entries method to fill an array of strings with the names of all files and subdirectories in a user-specified location and prints each string in the array to the console. The example is configured to catch all errors common to this method. #include <xtd/xtd> using namespace std; using namespace xtd; class program { public: static void main() { program snippets; ustring filter = ".exe"; snippets.print_file_system_entries(path); snippets.print_file_system_entries(path, filter); snippets.get_logical_drives(); snippets.get_parent(path); snippets.move("C:\\proof", "C:\\Temp"); } void print_file_system_entries(const ustring& path) { try { // Obtain the file system entries in the directory path. vector<ustring> directory_entries = io::directory::get_file_system_entries(path); for (xtd::ustring str : directory_entries) { } } catch (const security::security_exception&) { console::write_line("The caller does not have the required permission."); } catch (const argument_exception&) { console::write_line("path is an empty string, contains only white spaces, or contains invalid characters."); console::write_line("The path encapsulated in the directory object does not exist."); } } void print_file_system_entries(string path, string pattern) { try { // Obtain the file system entries in the directory path that match the pattern. vector<ustring> directory_entries = io::directory::get_file_system_entries(path, pattern); for (ustring str : directory_entries) { } } catch (const security::security_exception&) { console::write_line("The caller does not have the required permission."); } catch (const argument_exception&) { console::write_line("path is an empty string, contains only white spaces, or contains invalid characters."); console::write_line("The path encapsulated in the directory object does not exist."); } } // Print out all logical drives on the system. try { vector<ustring> drives = io::directory::get_logical_drives(); for (ustring str : drives) { } } catch (const io::io_exception&) { console::write_line("An I/O error occurs."); } catch (const security::security_exception&) { console::write_line("The caller does not have the required permission."); } } void get_parent(const ustring& path) { try { console::write_line(directory_info.full_name()); } catch (const argument_exception&) { console::write_line("path is an empty string, contains only white spaces, or contains invalid characters."); } } void move(const ustring& source_path, const ustring& destination_path) { try { io::directory::move(source_path, destination_path); console::write_line("The directory move is complete."); } catch (const security::security_exception&) { console::write_line("The caller does not have the required permission."); } catch (const argument_exception&) { console::write_line("path is an empty string, contains only white spaces, or contains invalid characters."); } catch (const io::io_exception&) { console::write_line("An attempt was made to move a directory to a different volume, or dest_dir_name already exists."); } } }; startup_(program); Remarks The order of the returned file and directory names is not guaranteed; use the std::sort method if a specific sort order is required. The xtd::io::directory::enumerate_fileSystem_entries and xtd::io::directory::get_file_system_entries methods differ as follows: When you use xtd::io::directory::enumerate_file_system_entries, you can start enumerating the collection of entries before the whole collection is returned; when you use xtd::io::directory::get_file_system_entries, you must wait for the whole array of entries to be returned before you can access the array. Therefore, when you are working with many files and directories, xtd::io::directory::enumerate_file_system_enties can be more efficient. This method is identical to xtd::io::directory::get_file_system_entries with the asterisk () specified as the search pattern. The path parameter is permitted to specify relative or absolute path information. Relative path information is interpreted as relative to the current working directory. To obtain the current working directory, see xtd::io::directory::get_current_directory. The path parameter is not case-sensitive. ## ◆ get_file_system_entries() [2/2] static std::vector xtd::io::directory::get_file_system_entries ( const xtd::ustring & path, const xtd::ustring & search_pattern ) static Returns an array of file names and directory names that match a search pattern in a specified path. Parameters path The relative or absolute path to the directory to search. This string is not case-sensitive. serach_pattern The search string to match against the names of file and directories in path. This parameter can contain a combination of valid literal path and wildcard (* and ?) characters, but it doesn't support regular expressions. Returns An array of file names and directory names that match the specified search criteria, or an empty array if no files or directories are found. Exceptions xtd::io::io_exception The directory specified by path is a file. xtd::argument_exception path is a zero-length string, contains only white space, or contains one or more invalid characters. You can query for invalid characters by using the xtd::io::path::get_invalid_path_chars method. xtd::io::path_too_long_exception The specified path, file name, or both exceed the system-defined maximum length. xtd::io::directory_not_found_exception The specified path is invalid (for example, it is on an unmapped drive). xtd::not_supported_exception path contains a colon character (:) that is not part of a drive label ("C:\"). Example The following example uses the xtd::io::directory::get_file_system_entries method to fill an array of strings with the names of all files matching a user-specified filter in a specific location and prints each string in the array to the console. The example is configured to catch all errors common to this method. #include <xtd/xtd> using namespace std; using namespace xtd; class program { public: static void main() { program snippets; ustring filter = ".exe"; snippets.print_file_system_entries(path); snippets.print_file_system_entries(path, filter); snippets.get_logical_drives(); snippets.get_parent(path); snippets.move("C:\\proof", "C:\\Temp"); } void print_file_system_entries(const ustring& path) { try { // Obtain the file system entries in the directory path. vector<ustring> directory_entries = io::directory::get_file_system_entries(path); for (xtd::ustring str : directory_entries) { } } catch (const security::security_exception&) { console::write_line("The caller does not have the required permission."); } catch (const argument_exception&) { console::write_line("path is an empty string, contains only white spaces, or contains invalid characters."); console::write_line("The path encapsulated in the directory object does not exist."); } } void print_file_system_entries(string path, string pattern) { try { // Obtain the file system entries in the directory path that match the pattern. vector<ustring> directory_entries = io::directory::get_file_system_entries(path, pattern); for (ustring str : directory_entries) { } } catch (const security::security_exception&) { console::write_line("The caller does not have the required permission."); } catch (const argument_exception&) { console::write_line("path is an empty string, contains only white spaces, or contains invalid characters."); console::write_line("The path encapsulated in the directory object does not exist."); } } // Print out all logical drives on the system. try { vector<ustring> drives = io::directory::get_logical_drives(); for (ustring str : drives) { } } catch (const io::io_exception&) { console::write_line("An I/O error occurs."); } catch (const security::security_exception&) { console::write_line("The caller does not have the required permission."); } } void get_parent(const ustring& path) { try { console::write_line(directory_info.full_name()); } catch (const argument_exception&) { console::write_line("path is an empty string, contains only white spaces, or contains invalid characters."); } } void move(const ustring& source_path, const ustring& destination_path) { try { io::directory::move(source_path, destination_path); console::write_line("The directory move is complete."); } catch (const security::security_exception&) { console::write_line("The caller does not have the required permission."); } catch (const argument_exception&) { console::write_line("path is an empty string, contains only white spaces, or contains invalid characters."); } catch (const io::io_exception&) { console::write_line("An attempt was made to move a directory to a different volume, or dest_dir_name already exists."); } } }; startup_(program); Remarks The returned file names are appended to the supplied path parameter and the order of the returned file names is not guaranteed; use the std::sort method if a specific sort order is required. search_pattern can be a combination of literal and wildcard characters, but it doesn't support regular expressions. The following wildcard specifiers are permitted in search_pattern. Wildcard specifier Matches (asterisk) Zero or more characters in that position. ? (question mark) Zero or one character in that position. Characters other than the wildcard are literal characters. For example, the search_pattern string "t" searches for all names in path ending with the letter "t". The search_pattern string "s" searches for all names in path beginning with the letter "s". search_pattern cannot end in two periods ("..") or contain two periods ("..") followed by xtd::io::path::directory_separator_char or xtd::io::path::alt_directory_separator_char, nor can it contain any invalid characters. You can query for invalid characters by using the xtd::io::path::get_invalid_path_chars method. Note When you use the asterisk wildcard character in a search_pattern such as ".txt", the number of characters in the specified extension affects the search as follows: • If the specified extension is exactly three characters long, the method returns files with extensions that begin with the specified extension. For example, ".xls" returns both "book.xls" and "book.xlsx". • In all other cases, the method returns files that exactly match the specified extension. For example, ".ai" returns "file.ai" but not "file.aif". When you use the question mark wildcard character, this method returns only files that match the specified file extension. For example, given two files, "file1.txt" and "file1.txtother", in a directory, a search pattern of "file?.txt" returns just the first file, whereas a search pattern of "file.txt" returns both files. Because this method checks against file names with both the 8.3 file name format and the long file name format, a search pattern similar to "1.txt" may return unexpected file names. For example, using a search pattern of "1.txt" returns "longfilename.txt" because the equivalent 8.3 file name format is "LONGFI~1.TXT". Remarks The xtd::io::directory::enumerate_files and xtd::io::directory::get_files methods differ as follows: When you use xtd::io::directory::enumerate_files, you can start enumerating the collection of names before the whole collection is returned; when you use xtd::io::directory::get_files, you must wait for the whole array of names to be returned before you can access the array. Therefore, when you are working with many files and directories, xtd::io::directory::enumerate_files can be more efficient. The path parameter can specify relative or absolute path information. Relative path information is interpreted as relative to the current working directory. To obtain the current working directory, see xtd::io::directory::get_current_directory. The path parameter is not case-sensitive. ## ◆ get_files() [1/2] static std::vector xtd::io::directory::get_files ( const xtd::ustring & path ) static Returns the names of files (including their paths) in the specified directory. Parameters path The relative or absolute path to the directory to search. This string is not case-sensitive. Returns An array of the full names (including paths) for the files in the specified directory, or an empty array if no files are found. Exceptions xtd::io::io_exception The directory specified by path is a file. xtd::argument_exception path is a zero-length string, contains only white space, or contains one or more invalid characters. You can query for invalid characters by using the xtd::io::path::get_invalid_path_chars method. xtd::io::path_too_long_exception The specified path, file name, or both exceed the system-defined maximum length. xtd::io::directory_not_found_exception The specified path is invalid (for example, it is on an unmapped drive). xtd::not_supported_exception path contains a colon character (:) that is not part of a drive label ("C:\"). Example The following example demonstrates how to use the GetFiles method to return file names from a user-specified location. The example is configured to catch all errors common to this method. #include <xtd/xtd> using namespace std; using namespace xtd; using namespace xtd::io; class program { public: static void main(const vector<ustring>& args) { for (ustring path : args) { if (file::exists(path)) { // This path is a file process_file(path); } else if(directory::exists(path)) { // This path is a directory process_directory(path); } else { console::write_line("{0} is not a valid file or directory.", path); } } } // Process all files in the directory passed in, recurse on any directories // that are found, and process the files they contain. static void process_directory(const ustring& target_directory) { // Process the list of files found in the directory. vector<ustring> file_entries = directory::get_files(target_directory); for (ustring file_name : file_entries) process_file(file_name); // Recurse into subdirectories of this directory. vector<ustring> subdirectory_entries = directory::get_directories(target_directory); for (ustring subdirectory : subdirectory_entries) process_directory(subdirectory); } // Insert logic for processing found files here. static void process_file(const ustring& path) { console::write_line("Processed file '{0}'.", path); } }; startup_(program); Remarks The xtd::io::directory::enumerate_files and xtd::io::directory::get_files methods differ as follows: When you use xtd::io::directory::enumerate_files, you can start enumerating the collection of names before the whole collection is returned; when you use xtd::io::directory::get_files, you must wait for the whole array of names to be returned before you can access the array. Therefore, when you are working with many files and directories, xtd::io::directory::enumerate_files can be more efficient. The returned file names are appended to the supplied path parameter. This method is identical to xtd::io::directory::get_files(ustring, ustring) with the asterisk () specified as the search pattern. The path parameter can specify relative or absolute path information. Relative path information is interpreted as relative to the current working directory. To obtain the current working directory, see xtd::io::directory::get_current_directory. The order of the returned file names is not guaranteed; use the std:::sort method if a specific sort order is required. The path parameter is not case-sensitive. ## ◆ get_files() [2/2] static std::vector xtd::io::directory::get_files ( const xtd::ustring & path, const xtd::ustring & search_pattern ) static Returns the names of files (including their paths) that match the specified search pattern in the specified directory. Parameters path The relative or absolute path to the directory to search. This string is not case-sensitive. search_pattern The search string to match against the names of files in path. This parameter can contain a combination of valid literal path and wildcard ( and ?) characters, but it doesn't support regular expressions. Returns An array of the full names (including paths) for the files in the specified directory that match the specified search pattern, or an empty array if no files are found. Exceptions xtd::io::io_exception The directory specified by path is a file. xtd::argument_exception path is a zero-length string, contains only white space, or contains one or more invalid characters. You can query for invalid characters by using the xtd::io::path::get_invalid_path_chars method. xtd::io::path_too_long_exception The specified path, file name, or both exceed the system-defined maximum length. xtd::io::directory_not_found_exception The specified path is invalid (for example, it is on an unmapped drive). xtd::not_supported_exception path contains a colon character (:) that is not part of a drive label ("C:\"). Example The following example counts the number of files that begin with the specified letter. #include <xtd/xtd> using namespace std; using namespace xtd; using namespace xtd::io; class program { public: static void main() { try { // Only get files that begin with the letter "c". vector<ustring> dirs = directory::get_files(R"(c:\", "c)"); "The number of files starting with c is {0}.", dirs.size()); for (ustring dir : dirs) { } } catch (const system_exception& e) { console::write_line("The process failed: {0}", e.to_string()); } } }; startup_(program); Remarks The returned file names are appended to the supplied path parameter and the order of the returned file names is not guaranteed; use the std::sort method if a specific sort order is required. search_pattern can be a combination of literal and wildcard characters, but it doesn't support regular expressions. The following wildcard specifiers are permitted in search_pattern. Wildcard specifier Matches (asterisk) Zero or more characters in that position. ? (question mark) Zero or one character in that position. Characters other than the wildcard are literal characters. For example, the search_pattern string "t" searches for all names in path ending with the letter "t". The search_pattern string "s" searches for all names in path beginning with the letter "s". search_pattern cannot end in two periods ("..") or contain two periods ("..") followed by xtd::io::path::directory_separator_char or xtd::io::path::alt_directory_separator_char, nor can it contain any invalid characters. You can query for invalid characters by using the xtd::io::path::get_invalid_path_chars method. Note When you use the asterisk wildcard character in a search_pattern such as ".txt", the number of characters in the specified extension affects the search as follows: • If the specified extension is exactly three characters long, the method returns files with extensions that begin with the specified extension. For example, ".xls" returns both "book.xls" and "book.xlsx". • In all other cases, the method returns files that exactly match the specified extension. For example, ".ai" returns "file.ai" but not "file.aif". When you use the question mark wildcard character, this method returns only files that match the specified file extension. For example, given two files, "file1.txt" and "file1.txtother", in a directory, a search pattern of "file?.txt" returns just the first file, whereas a search pattern of "file.txt" returns both files. Because this method checks against file names with both the 8.3 file name format and the long file name format, a search pattern similar to "1.txt" may return unexpected file names. For example, using a search pattern of "1.txt" returns "longfilename.txt" because the equivalent 8.3 file name format is "LONGFI~1.TXT". Remarks The xtd::io::directory::enumerate_files and xtd::io::directory::get_files methods differ as follows: When you use xtd::io::directory::enumerate_files, you can start enumerating the collection of names before the whole collection is returned; when you use xtd::io::directory::get_files, you must wait for the whole array of names to be returned before you can access the array. Therefore, when you are working with many files and directories, xtd::io::directory::enumerate_files can be more efficient. The path parameter can specify relative or absolute path information. Relative path information is interpreted as relative to the current working directory. To obtain the current working directory, see xtd::io::directory::get_current_directory. The path parameter is not case-sensitive. ## ◆ get_last_access_time() static std::chrono::system_clock::time_point xtd::io::directory::get_last_access_time ( const xtd::ustring & path ) static Returns the date and time the specified file or directory was last accessed. Parameters path The file or directory for which to obtain access date and time information. Returns A std::chrono::system_clock::time_point class that is set to the date and time the specified file or directory was last accessed. This value is expressed in local time. Exceptions xtd::io::io_exception The directory specified by path is a file. xtd::argument_exception path is a zero-length string, contains only white space, or contains one or more invalid characters. You can query for invalid characters by using the xtd::io::path::get_invalid_path_chars method. xtd::io::path_too_long_exception The specified path, file name, or both exceed the system-defined maximum length. xtd::io::directory_not_found_exception The specified path is invalid (for example, it is on an unmapped drive). xtd::not_supported_exception path contains a colon character (:) that is not part of a drive label ("C:\"). Example The following example demonstrates how to use GetLastAccessTime. #include <xtd/xtd> using namespace std::chrono; using namespace xtd; using namespace xtd::io; class program { public: static void main() { try { ustring path = R"(c:\MyDir)"; if (!directory::exists(path)) { } // Get the creation time of a well-known directory. system_clock::time_point tp = directory::get_last_access_time(path); console::write_line("The last access time for this directory was {0}", tp); // Update the last access time. directory::set_last_access_time(path, system_clock::now()); console::write_line("The last access time for this directory was {0}", tp); } catch (const system_exception& e) { console::write_line("The process failed: {0}", e.to_string()); } } }; startup_(program); Note This method may return an inaccurate value, because it uses native functions whose values may not be continuously updated by the operating system. Remarks This method is identical to xtd::io::file::get_last_access_time. If the directory described in the path parameter does not exist, this method returns 12:00 midnight, January 1, 1601 A.D. (C.E.) Coordinated Universal Time (UTC), adjusted to local time. The path parameter is permitted to specify relative or absolute path information. Relative path information is interpreted as relative to the current working directory. To obtain the current working directory, see xtd::io::directory::get_current_directory. The path parameter is not case-sensitive. ## ◆ get_last_write_time() static std::chrono::system_clock::time_point xtd::io::directory::get_last_write_time ( const xtd::ustring & path ) static Returns the date and time the specified file or directory was last written to. Parameters path The file or directory for which to obtain modification date and time information. Returns A std::chrono::system_clock::time_point class that is set to the date and time the specified file or directory was last written to. This value is expressed in local time. Exceptions xtd::io::io_exception The directory specified by path is a file. xtd::argument_exception path is a zero-length string, contains only white space, or contains one or more invalid characters. You can query for invalid characters by using the xtd::io::path::get_invalid_path_chars method. xtd::io::path_too_long_exception The specified path, file name, or both exceed the system-defined maximum length. xtd::io::directory_not_found_exception The specified path is invalid (for example, it is on an unmapped drive). xtd::not_supported_exception path contains a colon character (:) that is not part of a drive label ("C:\"). Example The following example demonstrates how to use xtd::io::directory::get_last_write_time. #include <xtd/xtd> using namespace std::chrono; using namespace xtd; using namespace xtd::io; class program { public: static void main() { try { ustring path = R"(c:\MyDir)"; if (!directory::exists(path)) { } directory::set_last_write_time(path, 1985, 5, 4); // Get the creation time of a well-known directory. system_clock::time_point tp = directory::get_last_write_time(path); console::write_line("The last write time for this directory was {0}", tp); // Update the last write time. directory::set_last_write_time(path, system_clock::now()); console::write_line("The last write time for this directory was {0}", tp); } catch (const system_exception& e) { console::write_line("The process failed: {0}", e.to_string()); } } }; startup_(program); Note This method may return an inaccurate value, because it uses native functions whose values may not be continuously updated by the operating system. Remarks If the directory described in the path parameter does not exist, this method returns 12:00 midnight, January 1, 1601 A.D. (C.E.) Coordinated Universal Time (UTC), adjusted to local time. The path parameter is permitted to specify relative or absolute path information. Relative path information is interpreted as relative to the current working directory. To obtain the current working directory, see xtd::io::directory::get_current_directory. The path parameter is not case-sensitive. ## ◆ get_logical_drives() static std::vector xtd::io::directory::get_logical_drives ( ) static Retrieves the names of the logical drives on this computer in the form "<drive letter>:\". Returns The logical drives on this computer. Exceptions xtd::io::io_exception An I/O error occurred (for example, a disk error). xtd::unauthorized_access_exception The caller does not have the required permission. Example The following example uses the xtd::io::directory::get_logical_drives method to assign the name of each drive on the calling computer to an array of strings. Each member of this string array is then printed to the console. The example is configured to catch all errors common to this method. #include <xtd/xtd> using namespace std; using namespace xtd; class program { public: static void main() { program snippets; ustring filter = ".exe"; snippets.print_file_system_entries(path); snippets.print_file_system_entries(path, filter); snippets.get_logical_drives(); snippets.get_parent(path); snippets.move("C:\\proof", "C:\\Temp"); } void print_file_system_entries(const ustring& path) { try { // Obtain the file system entries in the directory path. vector<ustring> directory_entries = io::directory::get_file_system_entries(path); for (xtd::ustring str : directory_entries) { } } catch (const security::security_exception&) { console::write_line("The caller does not have the required permission."); } catch (const argument_exception&) { console::write_line("path is an empty string, contains only white spaces, or contains invalid characters."); console::write_line("The path encapsulated in the directory object does not exist."); } } void print_file_system_entries(string path, string pattern) { try { // Obtain the file system entries in the directory path that match the pattern. vector<ustring> directory_entries = io::directory::get_file_system_entries(path, pattern); for (ustring str : directory_entries) { } } catch (const security::security_exception&) { console::write_line("The caller does not have the required permission."); } catch (const argument_exception&) { console::write_line("path is an empty string, contains only white spaces, or contains invalid characters."); console::write_line("The path encapsulated in the directory object does not exist."); } } // Print out all logical drives on the system. try { vector<ustring> drives = io::directory::get_logical_drives(); for (ustring str : drives) { } } catch (const io::io_exception&) { console::write_line("An I/O error occurs."); } catch (const security::security_exception&) { console::write_line("The caller does not have the required permission."); } } void get_parent(const ustring& path) { try { console::write_line(directory_info.full_name()); } catch (const argument_exception&) { console::write_line("path is an empty string, contains only white spaces, or contains invalid characters."); } } void move(const ustring& source_path, const ustring& destination_path) { try { io::directory::move(source_path, destination_path); console::write_line("The directory move is complete."); } catch (const security::security_exception&) { console::write_line("The caller does not have the required permission."); } catch (const argument_exception&) { console::write_line("path is an empty string, contains only white spaces, or contains invalid characters."); } catch (const io::io_exception&) { console::write_line("An attempt was made to move a directory to a different volume, or dest_dir_name already exists."); } } }; startup_(program); Remarks xtd::io::directory::get_logical_drives returns all of the accessible drives on a particular machine, including the floppy drive and any optical drives. ## ◆ get_parent() static xtd::io::directory_info xtd::io::directory::get_parent ( const xtd::ustring & path ) static Retrieves the parent directory of the specified path, including both absolute and relative paths. Parameters path The path for which to retrieve the parent directory. Returns The parent directory, or xtd::io::directory_info::empty if path is the root directory, including the root of a UNC server or share name. Exceptions xtd::io::io_exception The directory specified by path is a file. xtd::argument_exception path is a zero-length string, contains only white space, or contains one or more invalid characters. You can query for invalid characters by using the xtd::io::path::get_invalid_path_chars method. xtd::io::path_too_long_exception The specified path, file name, or both exceed the system-defined maximum length. xtd::io::directory_not_found_exception The specified path is invalid (for example, it is on an unmapped drive). xtd::not_supported_exception path contains a colon character (:) that is not part of a drive label ("C:\"). Example The following example demonstrates how to use the xtd::io::directory::get_parent method to retrieve the parent directory of a user-specified location, "path". The value returned by the xtd::io::directory::get_parent method is then printed to the console. The example is configured to catch all errors common to this method. #include <xtd/xtd> using namespace std; using namespace xtd; class program { public: static void main() { program snippets; ustring filter = ".exe"; snippets.print_file_system_entries(path); snippets.print_file_system_entries(path, filter); snippets.get_logical_drives(); snippets.get_parent(path); snippets.move("C:\\proof", "C:\\Temp"); } void print_file_system_entries(const ustring& path) { try { // Obtain the file system entries in the directory path. vector<ustring> directory_entries = io::directory::get_file_system_entries(path); for (xtd::ustring str : directory_entries) { } } catch (const security::security_exception&) { console::write_line("The caller does not have the required permission."); } catch (const argument_exception&) { console::write_line("path is an empty string, contains only white spaces, or contains invalid characters."); console::write_line("The path encapsulated in the directory object does not exist."); } } void print_file_system_entries(string path, string pattern) { try { // Obtain the file system entries in the directory path that match the pattern. vector<ustring> directory_entries = io::directory::get_file_system_entries(path, pattern); for (ustring str : directory_entries) { } } catch (const security::security_exception&) { console::write_line("The caller does not have the required permission."); } catch (const argument_exception&) { console::write_line("path is an empty string, contains only white spaces, or contains invalid characters."); console::write_line("The path encapsulated in the directory object does not exist."); } } // Print out all logical drives on the system. try { vector<ustring> drives = io::directory::get_logical_drives(); for (ustring str : drives) { } } catch (const io::io_exception&) { console::write_line("An I/O error occurs."); } catch (const security::security_exception&) { console::write_line("The caller does not have the required permission."); } } void get_parent(const ustring& path) { try { console::write_line(directory_info.full_name()); } catch (const argument_exception&) { console::write_line("path is an empty string, contains only white spaces, or contains invalid characters."); } } void move(const ustring& source_path, const ustring& destination_path) { try { io::directory::move(source_path, destination_path); console::write_line("The directory move is complete."); } catch (const security::security_exception&) { console::write_line("The caller does not have the required permission."); } catch (const argument_exception&) { console::write_line("path is an empty string, contains only white spaces, or contains invalid characters."); } catch (const io::io_exception&) { console::write_line("An attempt was made to move a directory to a different volume, or dest_dir_name already exists."); } } }; startup_(program); Remarks The path parameter can specify relative or absolute path information. Relative path information is interpreted as relative to the current working directory. To obtain the current working directory, see xtd::io::directory::get_current_directory. Trailing spaces are removed from the end of the path parameter before getting the directory. The string returned by this method consists of all characters in the path up to, but not including, the last xtd::io::path::directory_separator_char or alt_directory_separator_char. For example, passing the path "C:\Directory\SubDirectory\test.txt" to xtd::io::directory::get_parent returns "C:\Directory\SubDirectory". Passing "C:\Directory\SubDirectory" returns "C:\Directory". However, passing "C:\Directory\SubDirectory\" returns "C:\Directory\SubDirectory", because the ending directory separator is after "SubDirectory". The path parameter is not case-sensitive. ## ◆ move() static void xtd::io::directory::move ( const xtd::ustring & source_dir_name, const xtd::ustring & dest_dir_name ) static Moves a file or a directory and its contents to a new location. Parameters source_dir_name The path of the file or directory to move. dest_dir_name The path to the new location for source_dir_name. If source_dir_name is a file, then dest_dir_name must also be a file name. Exceptions xtd::io::io_exception An attempt was made to move a directory to a different volume. -or- dest_dir_name already exists. See the Note in the Remarks section. -or- The source_dir_name and dest_dir_name parameters refer to the same file or directory. -or- The directory or a file within it is being used by another process. xtd::argument_exception source_dir_name or dest_dir_name is a zero-length string, contains only white space, or contains one or more invalid characters. You can query for invalid characters with the xtd::path::io::get_invalid_path_chars() method. xtd::io::path_too_long_exception The specified path, file name, or both exceed the system-defined maximum length. xtd::io::directory_not_found_exception The path specified by sourceDirName is invalid (for example, it is on an unmapped drive). Example The following example demonstrates how to move a directory and all its files to a new directory. The original directory no longer exists after it has been moved. #include <xtd/xtd> using namespace xtd; using namespace xtd::io; class program { public: static void main() { ustring source_directory = R"(C:\source)"; ustring destination_directory = R"(C:\destination)"; try { directory::move(source_directory, destination_directory); } catch (const system_exception& e) { } } }; startup_(program); Remarks This method creates a new directory with the name specified by destDirName and moves the contents of sourceDirName to the newly created destination directory. If you try to move a directory to a directory that already exists, an IOException will occur. For example, an exception will occur if you try to move c: to c:, and c:already exists. Alternatively, you could specify "c:\\public\\mydir" as the destDirName parameter, provided that "mydir" does not exist under "c:\\public", or specify a new directory name such as "c:\\newdir". The sourceDirName and destDirName arguments are permitted to specify relative or absolute path information. Relative path information is interpreted as relative to the current working directory. To obtain the current working directory, see GetCurrentDirectory. Trailing spaces are removed from the end of the path parameters before moving the directory. Note xtd::io::directory::move method throws an xtd::io::io_exception in all platforms when the dest_dir_name already exists. ## ◆ remove() [1/2] static void xtd::io::directory::remove ( const xtd::ustring & path ) static Deletes an empty directory from a specified path. Parameters path The name of the empty directory to remove. This directory must be writable and empty. Exceptions xtd::io::io_exception A file with the same name and location specified by path exists. -or- The directory is the application's current working directory. -or- The directory specified by path is not empty. -or- The directory is read-only or contains a read-only file. -or- The directory is being used by another process. xtd::argument_exception path is a zero-length string, contains only white space, or contains one or more invalid characters. You can query for invalid characters by using the xtd::io::path::get_invalid_path_chars method. xtd::io::path_too_long_exception The specified path, file name, or both exceed the system-defined maximum length. xtd::io::directory_not_found_exception The specified path is invalid (for example, it is on an unmapped drive). xtd::not_supported_exception path contains a colon character (:) that is not part of a drive label ("C:\"). Exaample The following example shows how to create a new directory and subdirectory, and then delete only the subdirectory. #include <xtd/xtd> using namespace xtd; using namespace xtd::io; class program { public: static void main() { ustring sub_path = R"(C:\NewDirectory\NewSubDirectory)"; try { directory::remove(sub_path); bool directory_exists = directory::exists(R"(C:\NewDirectory)"); bool sub_directory_exists = directory::exists(sub_path); console::write_line("top-level directory exists: {0}", directory_exists); console::write_line("sub-directory exists: {0}", sub_directory_exists); } catch (const system_exception& e) { console::write_line("The process failed: {0}", e.message()); } } }; startup_(program); Remarks This method behaves identically to Delete(String, Boolean) with false specified for the second parameter. The path parameter may specify relative or absolute path information. Relative path information is interpreted as relative to the current working directory. To obtain the current working directory, see GetCurrentDirectory. Trailing spaces are removed from the end of the path parameter before deleting the directory. This method throws an IOException if the directory specified in the path parameter contains files or subdirectories. The path parameter is not case-sensitive. In some cases, if you have the specified directory open in File Explorer, the Delete method may not be able to delete it. ## ◆ remove() [2/2] static void xtd::io::directory::remove ( const xtd::ustring & path, bool recursive ) static Deletes the specified directory and, if indicated, any subdirectories and files in the directory. Parameters path The name of the directory to remove. recursive true to remove directories, subdirectories, and files in path; otherwise, false. Exceptions xtd::io::io_exception A file with the same name and location specified by path exists. -or- The directory is the application's current working directory. -or- The directory specified by path is not empty. -or- The directory is read-only or contains a read-only file. -or- The directory is being used by another process. xtd::argument_exception path is a zero-length string, contains only white space, or contains one or more invalid characters. You can query for invalid characters by using the xtd::io::path::get_invalid_path_chars method. xtd::io::path_too_long_exception The specified path, file name, or both exceed the system-defined maximum length. xtd::io::directory_not_found_exception The specified path is invalid (for example, it is on an unmapped drive). xtd::not_supported_exception path contains a colon character (:) that is not part of a drive label ("C:\"). Example The following example shows how to create a new directory, subdirectory, and file in the subdirectory, and then recursively delete all the new items. #include <xtd/xtd> using namespace xtd; using namespace xtd::io; class program { public: static void main() { ustring top_path = R"(C:\NewDirectory)"; ustring sub_path = R"(C:\NewDirectory\NewSubDirectory)"; try { using_ (stream_writer writer(sub_path + R"(\example.txt)")) { } directory::remove(top_path, true); bool directory_exists = directory::exists(top_path); console::write_line("top-level directory exists: {0}", directory_exists); } catch (const system_exception& e) { console::write_line("The process failed: {0}", e.message()); } } }; startup_(program); Remarks The path parameter may specify relative or absolute path information. Relative path information is interpreted as relative to the current working directory. To obtain the current working directory, see xtd::io::directory::get_current_directory. Trailing spaces are removed from the end of the path parameter before deleting the directory. The path parameter is not case-sensitive. If the recursive parameter is true, the user must have write permission for the current directory as well as for all subdirectories. The behavior of this method differs slightly when deleting a directory that contains a reparse point, such as a symbolic link or a mount point. If the reparse point is a directory, such as a mount point, it is unmounted and the mount point is deleted. This method does not recurse through the reparse point. If the reparse point is a symbolic link to a file, the reparse point is deleted and not the target of the symbolic link. In some cases, if you have the specified directory open in File Explorer, the xtd::io::directory::remove method may not be able to delete it. ## ◆ set_creation_time() [1/5] static void xtd::io::directory::set_creation_time ( const xtd::ustring & path, std::chrono::system_clock::time_point creation_time ) static Sets the creation date and time for the specified file or directory. Parameters path The file or directory for which to set the creation date and time information. creation_time The date and time the file or directory was last written to. This value is expressed in local time. Exceptions xtd::io::io_exception The directory specified by path is a file. xtd::argument_exception path is a zero-length string, contains only white space, or contains one or more invalid characters. You can query for invalid characters by using the xtd::io::path::get_invalid_path_chars method. xtd::io::path_too_long_exception The specified path, file name, or both exceed the system-defined maximum length. xtd::io::directory_not_found_exception The specified path is invalid (for example, it is on an unmapped drive). xtd::not_supported_exception path contains a colon character (:) that is not part of a drive label ("C:\"). Example #include <xtd/xtd> using namespace xtd; using namespace xtd::io; class program { public: static void main() { // Set the directory. ustring n = R"(C:\test\newdir)"; //Create the directory. try { } catch (const io_exception& e) { } //Set the creation and last access times to a variable DateTime value. // Print to console the results. //Set the last write time to a different value. console::write_line("Changed last write time: {0}", directory::get_last_write_time(n)); } }; startup_(program); // Obviously, since this sample deals with dates and times, the output will vary // depending on when you run the executable. Here is one example of the output: //Creation Date: 1/3/2002 12:00:00 AM //Last write time: 12/31/1998 4:00:00 PM //Last access time: 1/2/2002 4:00:00 PM //Changed last write time: 1/1/1999 12:00:00 AM Remarks The path parameter is permitted to specify relative or absolute path information. Relative path information is interpreted as relative to the current working directory. To obtain the current working directory, see xtd::io::directory::get_current_directory. The path parameter is not case-sensitive. ## ◆ set_creation_time() [2/5] static void xtd::io::directory::set_creation_time ( const xtd::ustring & path, time_t creation_time ) static Sets the creation date and time for the specified file or directory. Parameters path The file or directory for which to set the creation date and time information. creation_time The date and time the file or directory was last written to. This value is expressed in local time. Exceptions xtd::io::io_exception The directory specified by path is a file. xtd::argument_exception path is a zero-length string, contains only white space, or contains one or more invalid characters. You can query for invalid characters by using the xtd::io::path::get_invalid_path_chars method. xtd::io::path_too_long_exception The specified path, file name, or both exceed the system-defined maximum length. xtd::io::directory_not_found_exception The specified path is invalid (for example, it is on an unmapped drive). xtd::not_supported_exception path contains a colon character (:) that is not part of a drive label ("C:\"). Example #include <xtd/xtd> using namespace xtd; using namespace xtd::io; class program { public: static void main() { // Set the directory. ustring n = R"(C:\test\newdir)"; //Create the directory. try { } catch (const io_exception& e) { } //Set the creation and last access times to a variable DateTime value. // Print to console the results. //Set the last write time to a different value. console::write_line("Changed last write time: {0}", directory::get_last_write_time(n)); } }; startup_(program); // Obviously, since this sample deals with dates and times, the output will vary // depending on when you run the executable. Here is one example of the output: //Creation Date: 1/3/2002 12:00:00 AM //Last write time: 12/31/1998 4:00:00 PM //Last access time: 1/2/2002 4:00:00 PM //Changed last write time: 1/1/1999 12:00:00 AM Remarks The path parameter is permitted to specify relative or absolute path information. Relative path information is interpreted as relative to the current working directory. To obtain the current working directory, see xtd::io::directory::get_current_directory. The path parameter is not case-sensitive. ## ◆ set_creation_time() [3/5] static void xtd::io::directory::set_creation_time ( const xtd::ustring & path, const std::tm & creation_time ) static Sets the creation date and time for the specified file or directory. Parameters path The file or directory for which to set the creation date and time information. creation_time The date and time the file or directory was last written to. This value is expressed in local time. Exceptions xtd::io::io_exception The directory specified by path is a file. xtd::argument_exception path is a zero-length string, contains only white space, or contains one or more invalid characters. You can query for invalid characters by using the xtd::io::path::get_invalid_path_chars method. xtd::io::path_too_long_exception The specified path, file name, or both exceed the system-defined maximum length. xtd::io::directory_not_found_exception The specified path is invalid (for example, it is on an unmapped drive). xtd::not_supported_exception path contains a colon character (:) that is not part of a drive label ("C:\"). Example #include <xtd/xtd> using namespace xtd; using namespace xtd::io; class program { public: static void main() { // Set the directory. ustring n = R"(C:\test\newdir)"; //Create the directory. try { } catch (const io_exception& e) { } //Set the creation and last access times to a variable DateTime value. // Print to console the results. //Set the last write time to a different value. console::write_line("Changed last write time: {0}", directory::get_last_write_time(n)); } }; startup_(program); // Obviously, since this sample deals with dates and times, the output will vary // depending on when you run the executable. Here is one example of the output: //Creation Date: 1/3/2002 12:00:00 AM //Last write time: 12/31/1998 4:00:00 PM //Last access time: 1/2/2002 4:00:00 PM //Changed last write time: 1/1/1999 12:00:00 AM Remarks The path parameter is permitted to specify relative or absolute path information. Relative path information is interpreted as relative to the current working directory. To obtain the current working directory, see xtd::io::directory::get_current_directory. The path parameter is not case-sensitive. ## ◆ set_creation_time() [4/5] static void xtd::io::directory::set_creation_time ( const xtd::ustring & path, int32_t year, int32_t month, int32_t day ) static Sets the creation date and time for the specified file or directory. Parameters path The file or directory for which to set the creation date and time information. year The year of The date and time the file or directory was last written to. This value is expressed in local time. month The month of The date and time the file or directory was last written to. This value is expressed in local time. day The day of The date and time the file or directory was last written to. This value is expressed in local time. Exceptions xtd::io::io_exception The directory specified by path is a file. xtd::argument_exception path is a zero-length string, contains only white space, or contains one or more invalid characters. You can query for invalid characters by using the xtd::io::path::get_invalid_path_chars method. xtd::io::path_too_long_exception The specified path, file name, or both exceed the system-defined maximum length. xtd::io::directory_not_found_exception The specified path is invalid (for example, it is on an unmapped drive). xtd::not_supported_exception path contains a colon character (:) that is not part of a drive label ("C:\"). Example #include <xtd/xtd> using namespace xtd; using namespace xtd::io; class program { public: static void main() { // Set the directory. ustring n = R"(C:\test\newdir)"; //Create the directory. try { } catch (const io_exception& e) { } //Set the creation and last access times to a variable DateTime value. // Print to console the results. //Set the last write time to a different value. console::write_line("Changed last write time: {0}", directory::get_last_write_time(n)); } }; startup_(program); // Obviously, since this sample deals with dates and times, the output will vary // depending on when you run the executable. Here is one example of the output: //Creation Date: 1/3/2002 12:00:00 AM //Last write time: 12/31/1998 4:00:00 PM //Last access time: 1/2/2002 4:00:00 PM //Changed last write time: 1/1/1999 12:00:00 AM Remarks The path parameter is permitted to specify relative or absolute path information. Relative path information is interpreted as relative to the current working directory. To obtain the current working directory, see xtd::io::directory::get_current_directory. The path parameter is not case-sensitive. ## ◆ set_creation_time() [5/5] static void xtd::io::directory::set_creation_time ( const xtd::ustring & path, int32_t year, int32_t month, int32_t day, int32_t hour, int32_t minute, int32_t second ) static Sets the creation date and time for the specified file or directory. Parameters path The file or directory for which to set the creation date and time information. year The year of The date and time the file or directory was last written to. This value is expressed in local time. month The month of The date and time the file or directory was last written to. This value is expressed in local time. day The day of The date and time the file or directory was last written to. This value is expressed in local time. hour The hour of The date and time the file or directory was last written to. This value is expressed in local time. minute The minute of The date and time the file or directory was last written to. This value is expressed in local time. second The second of The date and time the file or directory was last written to. This value is expressed in local time. Exceptions xtd::io::io_exception The directory specified by path is a file. xtd::argument_exception path is a zero-length string, contains only white space, or contains one or more invalid characters. You can query for invalid characters by using the xtd::io::path::get_invalid_path_chars method. xtd::io::path_too_long_exception The specified path, file name, or both exceed the system-defined maximum length. xtd::io::directory_not_found_exception The specified path is invalid (for example, it is on an unmapped drive). xtd::not_supported_exception path contains a colon character (:) that is not part of a drive label ("C:\"). Example #include <xtd/xtd> using namespace xtd; using namespace xtd::io; class program { public: static void main() { // Set the directory. ustring n = R"(C:\test\newdir)"; //Create the directory. try { } catch (const io_exception& e) { } //Set the creation and last access times to a variable DateTime value. // Print to console the results. //Set the last write time to a different value. console::write_line("Changed last write time: {0}", directory::get_last_write_time(n)); } }; startup_(program); // Obviously, since this sample deals with dates and times, the output will vary // depending on when you run the executable. Here is one example of the output: //Creation Date: 1/3/2002 12:00:00 AM //Last write time: 12/31/1998 4:00:00 PM //Last access time: 1/2/2002 4:00:00 PM //Changed last write time: 1/1/1999 12:00:00 AM Remarks The path parameter is permitted to specify relative or absolute path information. Relative path information is interpreted as relative to the current working directory. To obtain the current working directory, see xtd::io::directory::get_current_directory. The path parameter is not case-sensitive. ## ◆ set_current_directory() static void xtd::io::directory::set_current_directory ( const xtd::ustring & path ) static Sets the application's current working directory to the specified directory. Parameters path The path to which the current working directory is set. Exceptions xtd::argument_exception Attempted to set to an empty string (""). xtd::io::io_exception An I/O error occurred. xtd::io::directory_not_found_exception Attempted to set a local path that cannot be found. xtd::security::security_exception The caller does not have the appropriate permission. Example The following example illustrates how to set the current directory and display the directory root. #include <xtd/xtd> using namespace xtd; using namespace xtd::io; class program { public: static void main() { // Create string for a directory. This value should be an existing directory // or the sample will throw a DirectoryNotFoundException. ustring dir = R"(C:\test)"; try { //Set the current directory. } catch (const directory_not_found_exception& e) { console::write_line("The specified directory does not exist. {0}", e); } // Print to console the results. console::write_line("Root directory: {0}", directory::get_directory_root(dir)); } }; startup_(program); Remarks When the application terminates, the working directory is restored to its original location (the directory where the process was started). The path parameter is permitted to specify relative or absolute path information. Relative path information is interpreted as relative to the current working directory. To obtain the current working directory, see xtd::io::directory::get_current_directory. Trailing spaces are removed from the end of the path parameter before setting the directory. The path parameter is not case-sensitive. If you are setting the directory to a drive with removable media (for example, "E:" for a USB flash drive), you can determine whether the drive is ready by using the IsReady property.When the application terminates, the working directory is restored to its original location (the directory where the process was started). The path parameter is permitted to specify relative or absolute path information. Relative path information is interpreted as relative to the current working directory. To obtain the current working directory, see GetCurrentDirectory. Trailing spaces are removed from the end of the path parameter before setting the directory. The path parameter is not case-sensitive. If you are setting the directory to a drive with removable media (for example, "E:" for a USB flash drive), you can determine whether the drive is ready by using the xtd::io::drive::is_ready property. ## ◆ set_last_access_time() [1/5] static void xtd::io::directory::set_last_access_time ( const xtd::ustring & path, std::chrono::system_clock::time_point last_access_time ) static Sets the date and time the specified file or directory was last accessed. Parameters path The file or directory for which to set the access date and time information. last_access_time An object that contains the value to set for the access date and time of path. This value is expressed in local time. Exceptions xtd::argument_exception Attempted to set to an empty string (""). xtd::io::io_exception An I/O error occurred. xtd::io::directory_not_found_exception Attempted to set a local path that cannot be found. xtd::security::security_exception The caller does not have the appropriate permission. Example The following example demonstrates how to use xtd::directory::set_last_access_time. #include <xtd/xtd> using namespace std::chrono; using namespace xtd; using namespace xtd::io; class program { public: static void main() { try { ustring path = R"(c:\MyDir)"; if (!directory::exists(path)) { } // Get the creation time of a well-known directory. system_clock::time_point tp = directory::get_last_access_time(path); console::write_line("The last access time for this directory was {0}", tp); // Update the last access time. directory::set_last_access_time(path, system_clock::now()); console::write_line("The last access time for this directory was {0}", tp); } catch (const system_exception& e) { console::write_line("The process failed: {0}", e.to_string()); } } }; startup_(program); Remarks The path parameter is permitted to specify relative or absolute path information. Relative path information is interpreted as relative to the current working directory. To obtain the current working directory, see xtd::io::directory::get_current_directory. The path parameter is not case-sensitive. ## ◆ set_last_access_time() [2/5] static void xtd::io::directory::set_last_access_time ( const xtd::ustring & path, time_t last_access_time ) static Sets the date and time the specified file or directory was last accessed. Parameters path The file or directory for which to set the access date and time information. last_access_time An object that contains the value to set for the access date and time of path. This value is expressed in local time. Exceptions xtd::argument_exception Attempted to set to an empty string (""). xtd::io::io_exception An I/O error occurred. xtd::io::directory_not_found_exception Attempted to set a local path that cannot be found. xtd::security::security_exception The caller does not have the appropriate permission. Example The following example demonstrates how to use xtd::directory::set_last_access_time. #include <xtd/xtd> using namespace std::chrono; using namespace xtd; using namespace xtd::io; class program { public: static void main() { try { ustring path = R"(c:\MyDir)"; if (!directory::exists(path)) { } // Get the creation time of a well-known directory. system_clock::time_point tp = directory::get_last_access_time(path); console::write_line("The last access time for this directory was {0}", tp); // Update the last access time. directory::set_last_access_time(path, system_clock::now()); console::write_line("The last access time for this directory was {0}", tp); } catch (const system_exception& e) { console::write_line("The process failed: {0}", e.to_string()); } } }; startup_(program); Remarks The path parameter is permitted to specify relative or absolute path information. Relative path information is interpreted as relative to the current working directory. To obtain the current working directory, see xtd::io::directory::get_current_directory. The path parameter is not case-sensitive. ## ◆ set_last_access_time() [3/5] static void xtd::io::directory::set_last_access_time ( const xtd::ustring & path, const std::tm & last_access_time ) static Sets the date and time the specified file or directory was last accessed. Parameters path The file or directory for which to set the access date and time information. last_access_time An object that contains the value to set for the access date and time of path. This value is expressed in local time. Exceptions xtd::argument_exception Attempted to set to an empty string (""). xtd::io::io_exception An I/O error occurred. xtd::io::directory_not_found_exception Attempted to set a local path that cannot be found. xtd::security::security_exception The caller does not have the appropriate permission. Example The following example demonstrates how to use xtd::directory::set_last_access_time. #include <xtd/xtd> using namespace std::chrono; using namespace xtd; using namespace xtd::io; class program { public: static void main() { try { ustring path = R"(c:\MyDir)"; if (!directory::exists(path)) { } // Get the creation time of a well-known directory. system_clock::time_point tp = directory::get_last_access_time(path); console::write_line("The last access time for this directory was {0}", tp); // Update the last access time. directory::set_last_access_time(path, system_clock::now()); console::write_line("The last access time for this directory was {0}", tp); } catch (const system_exception& e) { console::write_line("The process failed: {0}", e.to_string()); } } }; startup_(program); Remarks The path parameter is permitted to specify relative or absolute path information. Relative path information is interpreted as relative to the current working directory. To obtain the current working directory, see xtd::io::directory::get_current_directory. The path parameter is not case-sensitive. ## ◆ set_last_access_time() [4/5] static void xtd::io::directory::set_last_access_time ( const xtd::ustring & path, int32_t year, int32_t month, int32_t day ) static Sets the date and time the specified file or directory was last accessed. Parameters path The file or directory for which to set the access date and time information. year The year value to set for the access date and time of path. This value is expressed in local time. month The month value to set for the access date and time of path. This value is expressed in local time. day The day value to set for the access date and time of path. This value is expressed in local time. Exceptions xtd::argument_exception Attempted to set to an empty string (""). xtd::io::io_exception An I/O error occurred. xtd::io::directory_not_found_exception Attempted to set a local path that cannot be found. xtd::security::security_exception The caller does not have the appropriate permission. Example The following example demonstrates how to use xtd::directory::set_last_access_time. #include <xtd/xtd> using namespace std::chrono; using namespace xtd; using namespace xtd::io; class program { public: static void main() { try { ustring path = R"(c:\MyDir)"; if (!directory::exists(path)) { } // Get the creation time of a well-known directory. system_clock::time_point tp = directory::get_last_access_time(path); console::write_line("The last access time for this directory was {0}", tp); // Update the last access time. directory::set_last_access_time(path, system_clock::now()); console::write_line("The last access time for this directory was {0}", tp); } catch (const system_exception& e) { console::write_line("The process failed: {0}", e.to_string()); } } }; startup_(program); Remarks The path parameter is permitted to specify relative or absolute path information. Relative path information is interpreted as relative to the current working directory. To obtain the current working directory, see xtd::io::directory::get_current_directory. The path parameter is not case-sensitive. ## ◆ set_last_access_time() [5/5] static void xtd::io::directory::set_last_access_time ( const xtd::ustring & path, int32_t year, int32_t month, int32_t day, int32_t hour, int32_t minute, int32_t second ) static Sets the date and time the specified file or directory was last accessed. Parameters path The file or directory for which to set the access date and time information. year The year value to set for the access date and time of path. This value is expressed in local time. month The month value to set for the access date and time of path. This value is expressed in local time. day The day value to set for the access date and time of path. This value is expressed in local time. hour The hour value to set for the access date and time of path. This value is expressed in local time. minute The minutte value to set for the access date and time of path. This value is expressed in local time. second The second value to set for the access date and time of path. This value is expressed in local time. Exceptions xtd::argument_exception Attempted to set to an empty string (""). xtd::io::io_exception An I/O error occurred. xtd::io::directory_not_found_exception Attempted to set a local path that cannot be found. xtd::security::security_exception The caller does not have the appropriate permission. Example The following example demonstrates how to use xtd::directory::set_last_access_time. #include <xtd/xtd> using namespace std::chrono; using namespace xtd; using namespace xtd::io; class program { public: static void main() { try { ustring path = R"(c:\MyDir)"; if (!directory::exists(path)) { } // Get the creation time of a well-known directory. system_clock::time_point tp = directory::get_last_access_time(path); console::write_line("The last access time for this directory was {0}", tp); // Update the last access time. directory::set_last_access_time(path, system_clock::now()); console::write_line("The last access time for this directory was {0}", tp); } catch (const system_exception& e) { console::write_line("The process failed: {0}", e.to_string()); } } }; startup_(program); Remarks The path parameter is permitted to specify relative or absolute path information. Relative path information is interpreted as relative to the current working directory. To obtain the current working directory, see xtd::io::directory::get_current_directory. The path parameter is not case-sensitive. ## ◆ set_last_write_time() [1/5] static void xtd::io::directory::set_last_write_time ( const xtd::ustring & path, std::chrono::system_clock::time_point last_write_time ) static Sets the date and time a directory was last written to. Parameters path The path of the directory. last_write_time The date and time the directory was last written to. This value is expressed in local time. Exceptions xtd::argument_exception Attempted to set to an empty string (""). xtd::io::io_exception An I/O error occurred. xtd::io::directory_not_found_exception Attempted to set a local path that cannot be found. xtd::security::security_exception The caller does not have the appropriate permission. Example The following example demonstrates how to use xtd::io::set_last_write_time. #include <xtd/xtd> using namespace std::chrono; using namespace xtd; using namespace xtd::io; class program { public: static void main() { try { ustring path = R"(c:\MyDir)"; if (!directory::exists(path)) { } directory::set_last_write_time(path, 1985, 5, 4); // Get the creation time of a well-known directory. system_clock::time_point tp = directory::get_last_write_time(path); console::write_line("The last write time for this directory was {0}", tp); // Update the last write time. directory::set_last_write_time(path, system_clock::now()); console::write_line("The last write time for this directory was {0}", tp); } catch (const system_exception& e) { console::write_line("The process failed: {0}", e.to_string()); } } }; startup_(program); Remarks The path parameter is permitted to specify relative or absolute path information. Relative path information is interpreted as relative to the current working directory. To obtain the current working directory, see xtd::io::directory::get_current_directory. The path parameter is not case-sensitive. ## ◆ set_last_write_time() [2/5] static void xtd::io::directory::set_last_write_time ( const xtd::ustring & path, time_t last_write_time ) static Sets the date and time a directory was last written to. Parameters path The path of the directory. last_write_time The date and time the directory was last written to. This value is expressed in local time. Exceptions xtd::argument_exception Attempted to set to an empty string (""). xtd::io::io_exception An I/O error occurred. xtd::io::directory_not_found_exception Attempted to set a local path that cannot be found. xtd::security::security_exception The caller does not have the appropriate permission. Example The following example demonstrates how to use xtd::io::set_last_write_time. #include <xtd/xtd> using namespace std::chrono; using namespace xtd; using namespace xtd::io; class program { public: static void main() { try { ustring path = R"(c:\MyDir)"; if (!directory::exists(path)) { } directory::set_last_write_time(path, 1985, 5, 4); // Get the creation time of a well-known directory. system_clock::time_point tp = directory::get_last_write_time(path); console::write_line("The last write time for this directory was {0}", tp); // Update the last write time. directory::set_last_write_time(path, system_clock::now()); console::write_line("The last write time for this directory was {0}", tp); } catch (const system_exception& e) { console::write_line("The process failed: {0}", e.to_string()); } } }; startup_(program); Remarks The path parameter is permitted to specify relative or absolute path information. Relative path information is interpreted as relative to the current working directory. To obtain the current working directory, see xtd::io::directory::get_current_directory. The path parameter is not case-sensitive. ## ◆ set_last_write_time() [3/5] static void xtd::io::directory::set_last_write_time ( const xtd::ustring & path, const std::tm & last_write_time ) static Sets the date and time a directory was last written to. Parameters path The path of the directory. last_write_time The date and time the directory was last written to. This value is expressed in local time. Exceptions xtd::argument_exception Attempted to set to an empty string (""). xtd::io::io_exception An I/O error occurred. xtd::io::directory_not_found_exception Attempted to set a local path that cannot be found. xtd::security::security_exception The caller does not have the appropriate permission. Example The following example demonstrates how to use xtd::io::set_last_write_time. #include <xtd/xtd> using namespace std::chrono; using namespace xtd; using namespace xtd::io; class program { public: static void main() { try { ustring path = R"(c:\MyDir)"; if (!directory::exists(path)) { } directory::set_last_write_time(path, 1985, 5, 4); // Get the creation time of a well-known directory. system_clock::time_point tp = directory::get_last_write_time(path); console::write_line("The last write time for this directory was {0}", tp); // Update the last write time. directory::set_last_write_time(path, system_clock::now()); console::write_line("The last write time for this directory was {0}", tp); } catch (const system_exception& e) { console::write_line("The process failed: {0}", e.to_string()); } } }; startup_(program); Remarks The path parameter is permitted to specify relative or absolute path information. Relative path information is interpreted as relative to the current working directory. To obtain the current working directory, see xtd::io::directory::get_current_directory. The path parameter is not case-sensitive. ## ◆ set_last_write_time() [4/5] static void xtd::io::directory::set_last_write_time ( const xtd::ustring & path, int32_t year, int32_t month, int32_t day ) static Sets the date and time a directory was last written to. Parameters path The path of the directory. year The year of the date and time the directory was last written to. This value is expressed in local time. month The month of the date and time the directory was last written to. This value is expressed in local time. day The day of the date and time the directory was last written to. This value is expressed in local time. Exceptions xtd::argument_exception Attempted to set to an empty string (""). xtd::io::io_exception An I/O error occurred. xtd::io::directory_not_found_exception Attempted to set a local path that cannot be found. xtd::security::security_exception The caller does not have the appropriate permission. Example The following example demonstrates how to use xtd::io::set_last_write_time. #include <xtd/xtd> using namespace std::chrono; using namespace xtd; using namespace xtd::io; class program { public: static void main() { try { ustring path = R"(c:\MyDir)"; if (!directory::exists(path)) { } directory::set_last_write_time(path, 1985, 5, 4); // Get the creation time of a well-known directory. system_clock::time_point tp = directory::get_last_write_time(path); console::write_line("The last write time for this directory was {0}", tp); // Update the last write time. directory::set_last_write_time(path, system_clock::now()); console::write_line("The last write time for this directory was {0}", tp); } catch (const system_exception& e) { console::write_line("The process failed: {0}", e.to_string()); } } }; startup_(program); Remarks The path parameter is permitted to specify relative or absolute path information. Relative path information is interpreted as relative to the current working directory. To obtain the current working directory, see xtd::io::directory::get_current_directory. The path parameter is not case-sensitive. ## ◆ set_last_write_time() [5/5] static void xtd::io::directory::set_last_write_time ( const xtd::ustring & path, int32_t year, int32_t month, int32_t day, int32_t hour, int32_t minute, int32_t second ) static Sets the date and time a directory was last written to. Parameters path The path of the directory. year The year of the date and time the directory was last written to. This value is expressed in local time. month The month of the date and time the directory was last written to. This value is expressed in local time. day The day of the date and time the directory was last written to. This value is expressed in local time. hour The hout of date and time the directory was last written to. This value is expressed in local time. minute The minute of the date and time the directory was last written to. This value is expressed in local time. second The second of the date and time the directory was last written to. This value is expressed in local time. Exceptions xtd::argument_exception Attempted to set to an empty string (""). xtd::io::io_exception An I/O error occurred. xtd::io::directory_not_found_exception Attempted to set a local path that cannot be found. xtd::security::security_exception The caller does not have the appropriate permission. Example The following example demonstrates how to use xtd::io::set_last_write_time. #include <xtd/xtd> using namespace std::chrono; using namespace xtd; using namespace xtd::io; class program { public: static void main() { try { ustring path = R"(c:\MyDir)"; if (!directory::exists(path)) { } directory::set_last_write_time(path, 1985, 5, 4); // Get the creation time of a well-known directory. system_clock::time_point tp = directory::get_last_write_time(path); console::write_line("The last write time for this directory was {0}", tp); // Update the last write time. directory::set_last_write_time(path, system_clock::now()); console::write_line("The last write time for this directory was {0}", tp); } catch (const system_exception& e) { console::write_line("The process failed: {0}", e.to_string()); } } }; startup_(program); Remarks The path parameter is permitted to specify relative or absolute path information. Relative path information is interpreted as relative to the current working directory. To obtain the current working directory, see xtd::io::directory::get_current_directory. 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http://www.thetazzone.com/tutorial-example-forensics-sopprocedure/	# Tutorial – Example Forensics SOP/Procedure Feb 21, 2009 ORIGINALLY POSTED BY NOKIA FOR THETAZZONE/TAZFORUM HERE Do not use, republish, in whole or in part, without the consent of the Author. TheTAZZone policy is that Authors retain the rights to the work they submit and/or post…we do not sell, publish, transmit, or have the right to give permission for such…TheTAZZone merely retains the right to use, retain, and publish submitted work within it’s Network Code: Select all Tiger Shark from Antionline has kindly given his permission for his tutorial to be hosted at The Taz. You can find the original post here: http://www.antionline.com/showthread.php?s=&threadid=255811 Enjoy I just finished the initial draft of the “Incident Response” SOP that is required to comply with federal law. Since it is an exhaustive document that took a while to compile I thought I should post it here to assist others in both the process and the documentation. If anyone can see any glaring omissions or errors I would appreciate a heads up before I publish this to the SOP file here at work. All the tools should be “Googleable” by just their name. If you have a problem finding them send a response and I’ll point you to them. I have attached an .rtf of the file for those of you that like “pretty”…. Begin Text ======================== Company X Agency-Wide STANDARD OPERATING PROCEDURE NAME OF SOP: INITIAL PRODECURES IN THE EVENT OF A SUSPECTED NETWORK INTRUSION. PURPOSE: While it is the intent of the COMPANY X’s IT Department to ensure that the potential for intrusion into the COMPANY X’s Wide Area Network, (WAN), and it’s associated networks from the outside are minimized and that the unavailability of the data of the participating Agencies be maintained from unauthorized viewing from the inside of the WAN it is recognized that there will always be the potential for compromise. This document outlines the procedures to be carried out in the event that there is suspicion and/or evidence of such activities. It is important to understand that compromise can come from both without and within the network. It is further important to understand that the perpetrators second task, after the initial penetration, is to hide their activity by deleting logs, preventing other access to the compromised machine, installing “back doors” to give them unfettered access to it, “sniffing” the network to catch login/password data sent in clear to help them elevate their privileges within the domain, installing “kits” that allow them to carry out other actions and even to install “rootkits” at the user or even the kernel level so that while the machine appears to be cooperating with you it is very subtly hiding the presence of the perpetrator.. In short, depending upon the skill level of the attacker, everything will be done to make the investigator(s) job more difficult or even impossible. The process documented below follows the steps it does because the more sophisticated attack systems may have self protection built into them. An example would be a backdoor listening on port 1234. It will reply to a simple SYN with a SYN/ACK, (which it is supposed to), but, if the returning ACK packet does not contain certain data in the payload, (there should be no payload on a standard ACK packet), then communication will cease, or, worse yet a clean-up routine begins where the compromised machine protects itself, (drops all packets from the network and ignores console input), while it removes all evidence of itself and then reboots to a “clean” system. While I know of no working systems such as this currently “in the wild” the potential is certainly there and as the level of sophistication rises the probability of such systems is quite high. APPLICATION: This policy applies to all IT staff of COMPANY X and it’s associated agencies. PROCEDURES: There are occasions where a machine may give the impression that it might be compromised and there will be occasions where it is quite clear that compromise has taken place. The first act in the case of suspicion of compromise is to consult with the MIS/designated security person in the IT department to determine whether the steps this policy outlines should proceed. Prior to consultation make sure you note down exactly why your suspicions were aroused, any error messages that appeared, (the entire text), activity that was apparent etc. so that the lengthy process that follows is not gone through in vain. In short, think it through – is this really a potential compromise or is there a viable explanation for the activity, (but don’t be too quick to pass it off as a “glitch”, often the only indication of a compromise is a very subtle sign or signs). At this point great care must be taken to not alter the machine or carry out actions that might begin what are known as “kill processes” that clean the machine. Do the absolute minimum you can to confirm your suspicions. If you are at all unsure how to proceed at this point do nothing. Make the appropriate notes regarding how you were alerted, what you have done and call COMPANY X’ MIS for advice on how to proceed. Every step taken is to be logged. The log sheet is available from here. Logs will be created for each asset and it’s components that are being investigated. Logs entries are to contain investigators initials, (legibly), date, time, action, tool, tool purpose, result, evidence location, (file name, printed document etc.). If floppy disks are used the log should indicate which floppy the evidence is located on and it’s file name. Floppy Disks are to be clearly labeled EVDISKX where X is the disk number, dated and the machine name being investigated, (eg. EVDISK1 12/21/03 RM123P). CD-ROM’s are to be similarly labeled. Make sure that there is no confusion caused by disk naming, (if there are 8 floppies and one CD-ROM, label them in the order of creation, Thus if the CD-ROM was the fourth disk created it should be labeled number 4). If components are removed from the computer such as the hard drive this action must be logged and a manifest created detailing date, time, action performed, signature. The drive is to be clearly labeled with the name of the machine it was removed from, the date and time of removal and the name of the person that removed it. When it is placed in or removed from storage, passed on to another person, or forensic tests are done on it the manifest must detail everything. In this way we create a chain of evidence that may be used if legal action is deemed necessary. All floppy disks should have their data backed up to a trusted and secure computer, (standalone), as soon as possible to prevent the possibility of data loss through bad floppies. When sufficient data is collected it should be written to CD-ROM to preserve it. Data written to CD-ROM for preservation purposes should be checked to ensure the write was good and labeled as “FINAL EVDISK 12/21/03 Rm123P). The original evidence disks are to be secured along with the original copy of the Incident Response Log. The Incident Response Logs should also be photocopied at the completion of each sheet. At the completion of the investigation and after the “of” sequence numbers have been assigned to the original logs the entire log for each asset is to be photocopied and secured in a location separate from the originals. The importance of these logs cannot be over-emphasized – log it, log it, log it……… The following are the steps to be taken on each computer or server that is considered to be compromised. This document is to be printed and followed by each member of the IT response team in the order it is written unless the team leader determines that an alternative route is justified. The printed document should be shredded upon completion of the investigation. Initial Procedures These procedures should be carried out prior to any investigative procedures since they make no contact with the suspect machine(s) whatsoever and rely upon totally passive methods or information that already exists. 1. The suspect machine(s) is to be left “as-is” unless, in the opinion of the MIS the damage/risk associated with such action is unacceptable. The machine therefore should remain switched on, connected to the network and no attempts are to be made to glean information from the computer locally. In short – Leave it alone until the IT Response Team leader arrives. 2. A log is to be started to document every action taken with regard to each machine and it’s components. This is especially important should the Agency consider legal action against the perpetrator(s). 3. The COMPANY X Computer Incident Response Team should be notified immediately. Team Members are detailed here. 4. The existing log files are to be secured. They are located on the workstation named XXXXXXXX in COMPANY X’s MIS’ office in the folder E:\Syslog\logs. The file is named with that days date with a .txt extension, (eg. 2003-09-10.txt). Depending upon the time of day this file can be large, (> 50Mb), so it should be copied to a remote computer. Once the copy is complete remove the network cable from the machine that the copy went to. Do not stop the logging process or disconnect the XXXXXXXX computer from the network. It needs to continue to do it’s job. XXXXXXXX’s login is XXXXXXXXX with a password XXXXXXXX where X is the key combination <ALT> and the keypad numbers XXX. 5. In the subfolder of XXXXXXXX’s E:\Syslog\logs folder called Old logs you will find copies of previous days logs. On COMPANY X’ MIS’ workstation in a folder called c:\log analysis\old you will find similar copies of these files. Compare the file sizes of each file on both machines. If they are all the same, XXXXXXX has a CD writer, cut all the files in that folder to CD, label it appropriately and secure it. If the files differ in size the compare the files of the first two copies of the logs to the final copy of the logs on COMPANYXBU in folder h:\Information system\xxxxxxx\Security Archives\firewall logs. If COMPANYXBU’s files and COMPANY X’ MIS’ files are the same size cut either to CD. If all three are different cut all three to CD for future review. Label and secure all CD’s cut. 6. At the appropriate gateway to the network Ethereal is to be started with a filter applied of “host xxx.xxx.xxx.xxx”, (without quotes), where xxx.xxx.xxx.xxx is the address of the internal machine to determine if the machine is communicating with the internet. Gateway monitors are available via computers rm258, (COMPANY X MIS’s PC), and xxxxBU, (Backup Domain Controller in xxxxxxxx). If Ethereal indicates traffic to and from this machine Ethereal is to be left running until such time as deemed fit by the IT response team leader. The data collected is to be kept as forensic evidence. 7. If traffic is detected it may be useful to place a second version of Ethereal running on the local subnet of the target machine to determine if it is communicating with other assets inside the WAN. If it is then this data is also to be kept as forensic evidence. It may not be possible to use Ethereal on the local subnet due to the use of switches. It will be the decision of the IT response team leader whether to quickly rewire the affected machine(s) through a hub so that Ethereal can be used. 8. Secure the computer’s last AIDA32 inventory file if present. This will be found on the X: drive under AidaReports. The filename will be the computer’s name with a .csv extension. This details the exact hardware and much of the computer’s state the last time an audit could successfully be carried out and may even contain the user name the perpetrator logged on as. Non-Invasive Remote data gathering Procedures These procedures are those that are carried out from a remote workstation on the network that use tools that are active and either request information from the suspect machine(s) or glean information from it’s responses to probes and scans, (or lack of responses). If possible run these tools from a workstation that can see the target machine and that all traffic can be seen by one of the Ethereal sniffers so that the packets themselves are logged for future reference. Note that the tests could be run from the appropriate Ethereal sniffer set up in the first phase though there is a small risk of packet loss. Better to use a laptop or other machine connected to the same hub as the Ethereal sniffer. Further information on the tools, their use and the command lines to execute can be found in the section “Remote Tools, their purposes, output and use”. 1. NMapWin: This tool is used first in the stealth mode to glean as much information as possible about the computer without making a complete connection. If the computer has been set up with a “kill process” if unauthorized attempts to connect to it take place this should not set the process off. Note: All tools after this point elevate the risk of triggering a “kill process”. 2. FScan: This will run a full connect scan to every port and grab any information it can from open ports. From here on, run the tools, log the output, check the output for items of interest and decide if this process should continue or whether the situation requires an alternative plan of action. Any alternative plan of action may only be authorized by the IT Response Team leader. 3. Cerberus Internet Scanner 4. Currentstate.vbs 5. PSInfo 6. PSList 7. PSLoggedON 8. PSLogList Non-Invasive Local Information Gathering Procedures. From this point onwards it is imperative to remember that you can trust nothing on the computer(s) being investigated. Your attitude must be that every existing piece of code on the target machine has been subverted. You can’t even trust the command prompt that you will use for many the following tools. There is a trusted copy of many common applications on the CD, USE THEM. Use floppy disks to save the data to. If no, or insufficient floppies are available, and a network connection is still operable create a share on a remote computer that you have only write access to and redirect the output there. Preferably use floppies but if using recycled floppies is required, format them on a separate, trusted computer, send the output to them and immediately copy the files to another trusted, (preferably not connected to the network), computer. Run each tool twice. The first time redirect the output to file and examine it on a different computer. The second time run it without redirection so the output comes to the screen. Run a quick comparison between the output to file and the output to screen to ensure they are consistent. If the output is consistent no further action is necessary. If the output is different then run the same tool three further times redirecting the output to file and number each file appropriately, (for example Netstatarm123-1.txt). You may also notice that some of these tools may duplicate information that others provide. That is deliberate. Please do not skip steps simply because you think you have the information already….. You don’t. Finally, many of these tools are not capable of changing the state of the target computer. Others most certainly are. The goal at this stage is to glean as much information as possible about the current state and configuration of the target machine. Run the tools exactly as requested unless authorized by the IT Response Team leader. If you are uncertain whether the tool will change the system or not consult with the team leader prior to executing the tool. Start by spawning a command prompt by selecting Start-Run and manually typing in “%path%\cmd.exe” where %path% is the location of the trusted tools. Then run the following command lines where %path% is the path to the location of the trusted tools and %path2% is the path to the output resource, (floppy, write only remote share). NOTE: A “” indicates a tool that has the functionality to alter the configuration of the target. Make sure the command lines are correct prior to running the tool. 1. %path%\ipconfig /all > %path2%ipconfigrm123.txt 2. %path%\ipxroute.exe > %path2%ipxrouterm123.txt This will determine if IPX has been enabled. 3. () %path%\arp -a > %path2%arprm123.txt 4. %path%\hostname > %path2%hostnamerm123.txt 5. %path%\mem /c > %path2%memrm123.txt 6. () %path%\net accounts > %path2%netaccountsrm123.txt 7. () %path%\net localgroup > %path2%netlocalgroup.txt 8. () %path%\net share > %path2%netsharerm123.txt 9. %path%\net statistics server > %path2%netstatsserverrm123.txt 10. %path%\net statistics workstation > %path2%netstatsworkrm123.txt 11. () %path%\net time <\\rm123> > %path2%nettimerm123.txt (Substitute the target computer name for \\rm123 in the command line) 12. () %path%\net use > %path2%netuserm123.txt 13. () %path%\net user > %path2%netuserrm123.txt 14. %path%\net view > %path2%netviewrm123.txt 15. () %path%\route print > %path2%routeprintrm123.txt 16. %path%\fport > %path2%fportrm123.txt 17. %path%\listdlls > %path2%\listdllsrm123.txt 18. %path%\promiscdetect > %path2%\promiscrm123.txt 19. () %path%\psservice > %path2%\psservicerm123.txt 20. %path%\psgetsid > %path2%\psgetsidrm123.txt 21. dir /s > %path2%\dirXrm123.txt (do for each volume, X = volume letter including mapped drives) 22. () date > %path2%\daterm123.txt 23. () time > %path2%\timerm123.txt 24. vol > %path2%\volXrm123.txt (do for each volume, X = volume letter including mapped drives) 25. Tree > %path%\treeXrm123.txt (do for each volume, X = volume letter including mapped drives) Those are the command line tools completed whose output has to be redirected to text files on trusted media. The following tools are more interactive and monitor either highly detailed activity in real time or more detailed configuration. The files can become rather large quite quickly if the activity on the machine is high so a floppy disk may be filled up quite quickly. If at all possible save these files to a remote, write only share, then cut them to CD. 1. %path%\Autoruns: This shows all the programs that are called to start during system start up. It documents the programs and the path to them. 2. %path%\filemon: This program shows file activity in real time. This file can get quite large if a lot of things are running. Run it for 5 minutes or so and save the output to the write only remote folder then cut it to CD. 3. %path%\ntpmon: This monitors the processes and what they are doing, (opening threads, closing them etc.). If nothing is really going on then this may remain pretty much empty. It’s a judgment call as to when to close it. If you are getting a lot of consistent activity from certain processes that looks “abnormal” then saving the data and closing it quite quickly may be fine and it might fit on a floppy. Remember though, it’s better to have more data then less. If you aren’t comfortable with the output or the amount, seek assistance. 4. %path%\procexp: This is a process explorer. It shows what processes are running and what sub-processes they have spawned. Clicking on the individual process or it’s sub-processes will show all the handles or dll’s the item uses. In the view menu select “Show DLL’s”. Create a subfolder on the remote, write only drive called Procexprm123 and then select each process and on the file menu select “save as”. It will put the appropriate file name there for you just make sure you redirect it to the new folder on the write only share. Yes, this could be a long process but it shows all the files being used, their versions etc. and may be helpful later on. 5. %path%\regmon: This is a registry monitor. It monitors all access to the registry by all systems. It fills up quite quickly so again this may be a judgment call as to when to save the data with the rider again that too much is better then too little. 6. %path%\tdimon: This is a network interface monitor that details TCP and UDP activity at a very low level. Like other tools above it can generate a lot of log s on a busy system. Save the data away to the write only share when you feel you have enough. This completes the formalized data gathering process from the machine(s) itself. At this point the IT Response Ream Leader will make initial review of the data and decide if other or more data of certain types is required. When no other data is required the computer is to literally have the power cord pulled from the back of the machine at the power supply inlet. The computer is not to be shut down, logged off or any other way of closing it down. When computers are closed down cleanly they rewrite two entire hives of the registry and make numerous other “housekeeping” changes that are saved to the drive prior to actual shutdown. Additionally, shutdown routines could be in place to sanitized the machine in the event of a good but unexpected, (by the perpetrator), shutdown. Thus we “kill” the machine without giving it chance to alter information stored on the drive. The final acts of this phase is to stop all the Ethereal sniffing, save the data and cut it to CD-ROM and saving all the data from any write only shares that were used to CD-ROM and removing, labeling, logging and securing the drive(s) those shares reside on. Drive Imaging Once the power has been removed the hard drive(s) are to be removed from the system, labeled to indicate what they are, the act is to be logged and all the relevant details are to be noted. Two Disk images are then to be made of each disk and labeled appropriately. The act is to be logged with the appropriate details. The original drive(s) and one copy are to be secured and when, where and who secured them is to be logged. The second image can then be placed on a machine as a slave. It must not be booted to as this will change the image itself. Should the image be changed in such a way as to compromise the investigation this fact is to be logged and a new image is to be created from the stored image, (avoid using the original disk(s) ever again – that’s why we made two images in the first place). Each time a disk is moved, handed from person to person, secured or brought out of secure storage the logs are to be updated to reflect who, when, where and why the change in situation took place. From here on it is impossible to lay down any investigative procedures since they will rely entirely upon the evidence gathered in the preceding phases. When checking the evidence you should use the “FINAL CD’s” rather than the media the evidence was originally stored on to ensure that no changes to the evidence are inadvertently made. The original evidence media is to be logged and secured in the same fashion as the hard drive from the investigated machine. Remote Tools, their purposes, output and use. COMPANY X’s MIS has access to all these tools. They are either on his person, on his workstation, laptop or on a CD-ROM labeled “Forensic Toolkit” in his office. COMPANY X’s MIS is familiar with the use of these tools. If you are instructed to use a tool that you are unfamiliar with you are to ask for assistance prior to their use. Similarly, if you are tasked with reading the output and are unfamiliar with that you are seeing request assistance. Decisions are made throughout the process as to how to proceed that depend upon the information gained from the different systems used. If the output is misinterpreted or misrepresented an incorrect decision could be made that could render the investigation useless. Remote, Non-Intrusive Tools NOTE: Some of these tools require that WinPCap be installed. This is a windows packet capture driver that, at the time of writing is a version 3.2.1 and is available by searching Google for “WinPCap” NOTE 2: Some of these remote detection tools may create alerts in the WAN’s Intrusion Detection Systems. NOTE 3: Tools with a “” after their name can successfully be run against machines where administrative rights are not available. In some cases the information will be complete, in other cases it will show only information that is available without administrative rights, in other circumstances all you may get is “Access Denied” Log it anyway, it’s important to know what can and can’t be done and may show that steps have been taken by the perpetrator to protect the computer from use by people other than himself. 1. Ethereal: Ethereal is a packet sniffer that is used to sniff all traffic on a network segment. It only functions effectively from a hub or a switch that can be configured to have a “bridging” port so that all traffic can be seen on the local segment. The COMPANY X WAN has two machines set aside with this capability, (rm258 and FortBU), to cover the two gateways to the network. Packets can be captured from all machines of a filter can be set to only capture traffic of certain types. These filters are based on the TCPDump syntax and can be found at <http://home.insight.rr.com/procana/> in the document named Designing Capture Filters for Ethereal. There is a hard copy in the black binder labeled “Security Texts” in the MIS’ office. Under normal circumstances Ethereal captures packets in the background and simply shows a graph of the packets captured. In a forensic investigation it it useful to select the button to “Update the window in real time” to see the nature of the traffic involved as it occurs. When saving the data save it in the default TCPDump format which allows the data be be reloaded into many other analysis tools and even to rerun the entire session if necessary. 2. NMapWin: NMapWin is the WIN32 port of the venerable NMap by Fyodor. It is the most powerful scanner/OS detection system currently available. For forensic purposes the following settings are advised. Select a SYN Stealth Scan from the Scan tab, “Don’t ping” from the discover tab, “OS Detection” and “Very Verbose” from the Options tab and select Output file and name it as a:\NMaprm123p.txt. Put the IP Address of the target in the Host line and begin the scan. 3. FScan: FScan is a command line port scanner that has some interesting features. From it’s home directory type “fscan -?” for a list of all it’s parameters. A recommended command line would be fscan -bp 1-65535 -u 1-65535 -o a:\fscanrm123p.txt -s rm123. This would scan all TCP and UDP ports from 1 through to 65535 and grab the available banners of any open ports, show any RST’s returned from the target, (a lack of which may imply there is a “firewall” in place), and write all the results to a file called fscanrm123p.txt on the floppy disk. 4. Cerberus Internet Scanner: This tool looks at services commonly available and extracts as much information as is available with or without administrative rights. With administrative right a lot can be determined about the general “look” of the target and some useful information comes with only guest rights. The report is written to the home folder’s “Reports” folder and is named using the IP address of the target with an HTML extension. The report file should be moved to an evidence floppy. 5. Currentstate.vbs: This is a script the MIS wrote himself to automatically extract information remotely and in a non-intrusive manner from a computer you have administrative rights over. Run it from it’s home directory using the command line “cscript currentstate.vbs” and you will be prompted for the IP address of the target machine, the full name of the output file, your full name, the administrators login name and the administrators password. This pulls a lot of relevant information regarding the current state of a remote machine right down to which processes belong to which threads and could be very useful in a forensic investigation. 6. PSInfo: PSInfo gives some additional information regarding the makeup of a machine that others above may not. Rights are required to the target machine. Recommended command line is “psinfo \\rm123p > a:\PSInform123p.txt”. Note that the results have to be piped to the output file. 7. PSList: PSlist dumps the running processes, their PID’s, kernel time, user time, idle time etc. Recommended command line is “pslist \\rm123p > a:\SPListrm123p.txt”. It requires rights to the target machine. 8. PSLoggedon: PSloggedOn can reveal information about locally and remotely logged on users without administrative privileges on the target machine. Recommended command line is “psloggedon \\rm123p > a:\psloggedonrm123p.txt 9. PSLogList: PSlogList can retrieve the entire existing event logs of a remote computer with administrative rights, (it may also be able to with limited rights). Recommended command line is “psloglist \\rm123p > a:\psloglist.txt ======================= End text	2022-05-16 08:01:42	{"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": 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": 0.258792519569397, "perplexity": 2055.5885162274208}, "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-2022-21/segments/1652662510097.3/warc/CC-MAIN-20220516073101-20220516103101-00245.warc.gz"}
https://kidsworksheetfun.com/dividing-mixed-fractions-by-fractions-worksheet/	# Dividing Mixed Fractions By Fractions Worksheet Dividing Mixed Fractions By Fractions Worksheet. She wants to share them with her friends. Integers worksheet worksheets grade multiplying answers pdf answer key dividing problems math mixed signs division printable drills involving practice range. Multiplying and dividing fractions facts & worksheets for kids kidskonnect.com. Free google quizzes fraction activities. 2 7 3 2 14. ### Free Math And Fraction Google Quizzes And Printables For 5Th And 6Th Grade Math. These worksheets are pdf files. 11 2 1 3 10 5. Fractions word problems dividing whole number worksheets. ### These Worksheets Will Generate 10 Fraction Division Problems Per Worksheet. Convert the mixed number into improper fraction. Browse dividing fractions worksheet resources on teachers pay teachers, a marketplace trusted by millions of teachers for original. Fractions divide mixed numbers anchor charts dividing math number learning algebra. ### Free Google Quizzes Fraction Activities. If sindhu wants to give 1 $$\frac {2}{5}$$ of the mango to each of her friends, find how many friends will get some mango? The first step in the process is to convert the mixed fraction into an improper fraction. Fractions dividing adding subtracting multiplying math help poem mixed anchor chart homework numbers song fraction operations verse denominators diy charts. ### 41 3 2 1 4 3. Divide the fractions with mixed numbers worksheet (pdf below) worksheet 3 f 7. The fractions worksheets may be selected for three different degrees of difficulty. Multiplying and dividing fractions facts & worksheets for kids kidskonnect.com. ### Take A Look At Some More Of Our Worksheets Similar To These. Many worksheets include graphical model problems and word problems. Multiplying mixed fractions by proper fractions worksheets; Dividing mixed numbers by fractions worksheets	2022-12-01 21:22:56	{"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": 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": 0.2505362927913666, "perplexity": 8358.60890469207}, "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/1669446710869.86/warc/CC-MAIN-20221201185801-20221201215801-00092.warc.gz"}
https://nyarna.org/	Nyarna: A structured data authoring language Designed as Evolution of LaTeX Nyarna's syntax and feature set was primarily inspired by LaTeX. The initial idea was to have a language viable to be used as frontend for LaTeX – Nyarna isn't quite there yet – while being more user-friendly and flexible. Besides LaTeX, Nyarna also takes ideas from XSLT, YAML, Nim and Zig. Structured Input, Flexible Output Nyarna understands complex structures and provides a static type system for modelling structured data. Data input is decoupled from processing. You can write processors that generate HTML, PDF or other outputs from the same input data. Extensible Schemas You tell Nyarna about the structure of your data with a Schema. Schemas are written in Nyarna and can contain Backends that define how the data can be processed. Other users can write Extensions that build upon your Schema, inject additional input structures, and extend the backends to accommodate for the additions. The ability to inject Extensions makes Nyarna's Schemas modular and flexible. Parameters and Templating A document can define parameters whose values must be given by the caller. This makes Nyarna a type-safe templating system. First-Class Types and Embeddability Types are first-class values, as are Schemas. The ability to inspect types at runtime potentially allows you to autogenerate code from a schema. With this, you could embed Nyarna in your application and deserialize input into native types. Power Tool with Complexity Layers While Nyarna provides a lot of features, it is not necessary to know about them all to use the language. Simple use-cases, like text templating, require only minimal syntax. Writing content for a given schema still doesn't require the more complex features. You will probably not need to know much about the type system before you start writing functions. The most complex features are usually only needed for writing Schemas. Nyarna is nowhere near stable yet, but the implementation is good enough to demonstrate its features. Check out the tour to try it out! #!/usr/bin/env nyarna -- # with a shebang, this is directly executable. # This document can be processed standalone. \standalone: :params: # takes a single argument of type Text who: \Text \end(standalone) # output text, refer to the argument Hello, \who! # declare your own types and functions \declare: Bus = \Record: fits: \Natural name: \Text \end(Record) Buses = \List(\Bus) busFor = \func: num: \Natural :body: \Bus(fits=\num, name=Bus for \num persons) \end(func) \end(declare) # have variables \var: smallBus = \busFor(10) largeBus = \busFor(42) \end(var) # do loops \for(\Buses(\smallBus, \largeBus), collector=\Concat):\|\b\| The \b::name fits \b::fits persons.\ \end(for)	2022-10-01 17:41:27	{"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": 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": 0.47574540972709656, "perplexity": 5394.97781072677}, "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/1664030336880.89/warc/CC-MAIN-20221001163826-20221001193826-00410.warc.gz"}
https://www.allaboutcircuits.com/news/teardown-tuesday-playstation-move-controller/	In this week’s Teardown Tuesday, we tear down a PlayStation Move controller to see what ICs and parts make up current gaming technology. The PlayStation Move is Sony's answer to the Nintendo Wiimote. The Move functions as a usual PlayStation controller with all the familiar buttons, but it's also loaded with sensors which allow users to translate physical motions into digital controls. Let's see what's inside! ### Key Parts There are several recognizable parts in the Sony Move. Here's a list before we get going. ### The Outside The unit is made using plastic and held together with four screws. The top of the unit has a rubber-like sphere that is easily compressible. The bottom has various IO ports. The unit, itself, is shaped in such a way that makes it easy to hold. Because these units are designed to be moved and swung around, it's fairly sturdy. ##### The PlayStation Move controller The controller has multiple buttons including the PlayStation staples: X, circle, triangle, and square. The bottom of the unit contains a trigger and the sides contain the start/select buttons. The controller also has two additional buttons: one is located in the center of the four main buttons on the top and the other is a smaller PlayStation-logo button below. ### Opening the Controller The controller was very easy to open. It's only held together with four screws located on the back of the controller in the corners. Opening it revealed all the major parts in the controller, including a vibration motor, lithium-ion battery, circuits, modules, and even ribbon cables. Strangely, the sphere is mounted onto one-half of the casing while the rest of the components are mounted on the other side and the two are electrically connected via a flat ribbon cable. Such a move makes putting the unit together not only more difficult (as the cables are very short). It also makes repair more expensive as it can only be accomplished by hand and usually with through-hole connectors. ##### The controller opened The battery found in the unit is a lithium-ion battery with a capacity of 1380mAh at 3.7V. The battery, itself, is incredibly well-built with rubber padding placed on the outside to prevent jostling. Considering how small electronic components have become, the design decision to use a large high-capacity battery makes sense (as there's a large amount of empty space in the controller). On top of that, a controller may be easier to use if it has some weight behind it and so the battery may also act as ballast. ##### Closeup of the battery Removing the battery and battery housing allows for the backend that houses the I/O ports to be removed. This reveals a pair of PCBs holding different USB ports whose functions are primarily for charging. It also reveals the vibration motor. Many games call for haptic feedback whereby a player action results in the player feeling palpable feedback from the controller. One classic example is firing a gun in a game—most modern shooter games activate the vibration motors in controllers when the player fires their weapon. This gives a realism effect and helps players know when their gun is firing. Vibration motors can also be used for situations such as explosions and even heartbeats. ### Topside PCB The topside of the main PCB is entirely visible without the need to remove additional parts or housings. The first feature that stands out is the large microcontroller that was revealed upon removing the battery. This IC is a standard STM32F103 microcontroller that contains an ARM-based CPU, 128KB flash, USB, CAN, timers, ADCs, and plenty of peripherals. The package shown on the PCB is a 100-pin LQFP and commonly sells for $6 -$10 each. ##### The STM32 microcontroller – The heart of the PlayStation Move Next to the microcontroller are many gold pads with identifications of TPxx. These are test points that are used to test and program the controller before it is sent out to ensure that it functions correctly. Such test points add complexity to the PCB design and incur many costs when producing the item, so they are usually found on more expensive products. It would not make economic sense to vigorously test cheap items that are easily replaced when damaged or faulty. ##### The many test points found on the topside of the PCB Further down the PCB (near the sphere) there is the ribbon connector, a small IC with the identification AKM8974, and a module with a metal shield with the ident 701A12B ALPS. The metal shield is easily removed with a small flathead screwdriver which reveals a few parts, including a serial EEPROM (24C32) and a BC4REA16 Cambridge Silicon Radio Bluetooth RF IC. The serial EEPROM will most likely store information such as network names and passwords. One reason for using enclosed modules as seen here is to help with EMC control since the metal case helps to absorb emitted EM signals for circuitry such as clock and data lines. The AKM8974 is a 3-axis magnetic axis absolute compass that uses I2C to communicate with the main controller. ### Backside of the PCB The backside of the PCB reveals many surface-mount parts including a range of ICs, resistors, capacitors, and pads. The buttons on the controller press into a rubber membrane mold that then presses onto small switches on the surface of the PCB. ##### The backside of the PCB The top section of the PCB (near the sphere) contains the switches and contact pads for the buttons. Further down the PCB, several ICs can be found, as well as a module that contains a metal shield. The first IC, the KXSC4, is a 3-axis accelerometer which is useful for gesture detection. Accelerometers cannot be used for absolute position or even current velocity as they only detect a change in speed (remember, acceleration is dv/dt). ##### The 3-axis accelerometer KXSC4 A really interesting module sits nearby which is enclosed in a metal shield that appears to be plated with gold. The identification on this module is unhelpful (11648) but thanks to some online resources, I identified the integrated circuit mounted inside as the STM LPR425AL 2-Axis gyroscope. Removing the shield was done in the hope of seeing the internal circuitry, but it turns out that the internals are made on a ceramic base which resulted in some damage. ##### The ceramic device revealed The second IC below the module is the Y5250H which is a Z-axis gyroscope. While no datasheet can be found for this part, it is frequently associated with the PlayStation Move controller which suggests that this part number could be specific to the production line. Some online resources identify this part as being the STM LY5250 (an accelerometer). ##### The one-axis gyroscope Below these ICs is a large collection of parts and other ICs including the BRQ11J (BQ24080) and the CEE TI J (TPS63030). The BRQ11J is a lithium-ion IC charge controller manufactured by Texas Instruments and the CEE TI J is a single inductor buck-boost converter. ### The Sphere The sphere that sits on the top of the controller is mostly space which contains a single multi-color LED. Interestingly, a thick metal wall can be seen which provides the space needed for the ribbon cable to access the LED. The reason for this metal shield may be due to EMC control and here's why. To improve efficiency and to create interesting color patterns, the RGB lines will be switching and changing voltage levels rapidly. Such rapid changing (even if the frequency is in the low kHz) creates EM emissions which can easily violate FCC and CE specifications. Since the RGB lines also cross RF modules and antenna, there is a good chance that the RGB lines will pick up interference and then re-emit the signals further down the line. Therefore, the metal shield around the ribbon cable helps to absorb emitted radiation by the ribbon cable and therefore help to meet FCC and CE specifications on EM emissions. ### Summary In AAC teardowns, we generally concern ourselves with discovering what components are used in devices and commenting on design choices. But I feel compelled to say that this PlayStation Move controller has to be the most beautifully built board I have even seen. It shows common ICs that anyone can purchase and use (with surprisingly few unidentifiable parts). All parts are incredibly clean. Many PCB design features are demonstrated, such as test points, stitching via, and EMC control. Overall, the unit as a whole is very well put together. Looking at this complex device, it's strange to how game controllers in the past have evolved from just a few buttons to gyroscopes, accelerometers, magnetic sensors, pressure buttons, and complex trigger actions. Next Teardown: 4th Generation iPod Shuffle	2017-06-24 17:37:44	{"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": 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": 0.26721277832984924, "perplexity": 2481.5041204275913}, "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-2017-26/segments/1498128320270.12/warc/CC-MAIN-20170624170517-20170624190517-00080.warc.gz"}
http://mathhelpforum.com/calculus/162792-solving-equation.html	# Math Help - solving equation 1. ## solving equation Hi. I have a maths question on finding the turning points and determining their nature but I can't find the value of x and w. The equation is z= e^(2x) + e^(-y) + e^(w^2) - e^(ln2x) - 2e^(w) + y I differentiated it wrt to x, y and w. But I can't solve for x and w in the following equations: 2e^(2x) - [ (e^ln2x) / x) = 0 2we^(w^2) - 2e^(w) = 0 I really need help for this one. Thanks. 2. $\displaystyle 2e^{2x} - \frac{e^{\ln{(2x)}}}{x} = 0$ $\displaystyle 2e^{2x} - \frac{2x}{x} = 0$ $\displaystyle 2e^{2x} - 2 = 0$ $\displaystyle 2e^{2x} = 2$ $\displaystyle e^{2x} = 1$ $\displaystyle 2x = 0$ $\displaystyle x = 0$. $\displaystyle 2w\,e^{w^2} - 2e^w = 0$ Simple observation will show that $\displaystyle w = 1$ is a solution. 3. I did what you did but it's not right. x cannot be equal to 0, otherwise if you replace it in 2e^(2x) - [ (e^ln2x) / x) = 0, (e^ln2x) / 0 will be undefined and I need a value of x. And for the second equation how would I know if w has only one value and not 2? 4. Originally Posted by nepmma I did what you did but it's not right. x cannot be equal to 0, otherwise if you replace it in 2e^(2x) - [ (e^ln2x) / x) = 0, (e^ln2x) / 0 will be undefined and I need a value of x. And for the second equation how would I know if w has only one value and not 2? Yes, you are right, $\displaystyle x \neq 0$ if you leave the function written as is. You can simplify your original function though, because $\displaystyle e^{\ln{(2x)}} = 2x$. Otherwise the function will be not be defined for any nonpositive value anyway... In the second case, you would need to show that $\displaystyle 2w\,e^{w^2} - 2e^w$ does not have any turning points. 5. Originally Posted by Prove It Yes, you are right, $\displaystyle x \neq 0$ if you leave the function written as is. You can simplify your original function though, because $\displaystyle e^{\ln{(2x)}} = 2x$. Otherwise the function will be not be defined for any nonpositive value anyway... In the second case, you would need to show that $\displaystyle 2w\,e^{w^2} - 2e^w$ does not have any turning points. Ohhh!! I forgot the basic laws of logarithms..I forgot I could simplify it(I feel stupid now). Thanks!!! But how am I supposed to show that that 2we^(w^2) - 2e^(w) is always increasing and doesn't have any turning pts? Do I have to plot a graph or something? 6. Originally Posted by nepmma Ohhh!! I forgot the basic laws of logarithms..I forgot I could simplify it(I feel stupid now). Thanks!!! But how am I supposed to show that that 2we^(w^2) - 2e^(w) is always increasing and doesn't have any turning pts? Do I have to plot a graph or something? How do you usually find the turning point of a function? Find the derivative, set it equal to zero, see if there are any solutions. Then apply the second derivative test.	2014-09-20 04:08:48	{"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": 15, "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": 0.7200009822845459, "perplexity": 495.9427579790152}, "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-2014-41/segments/1410657132646.40/warc/CC-MAIN-20140914011212-00059-ip-10-196-40-205.us-west-1.compute.internal.warc.gz"}
https://plainmath.net/27512/the-solution-for-the-equation-use-the-change-base-formula-approximate-axa	# The solution for the equation. Use the change of base formula to approximate axa The solution for the equation. Use the change of base formula to approximate axact answer to the nearest hundredth when approximate. $2×{10}^{x}=66$. You can still ask an expert for help • Questions are typically answered in as fast as 30 minutes Solve your problem for the price of one coffee • Math expert for every subject • Pay only if we can solve it doplovif Formula used: Change of base formula for logarithm is given by ${\mathrm{log}}_{a}x=\frac{{\mathrm{log}}_{b}x}{{\mathrm{log}}_{b}a}$, for $a>0$ and $x>0$ Calculation: $2×{10}^{x}=66$ ${10}^{x}=\frac{66}{2}$ ${10}^{x}=33$ $x={\mathrm{log}}_{10}\left(33\right)$ Change to an logarithmic equation $x=\frac{\mathrm{log}\left(33\right)}{\mathrm{log}\left(10\right)}$ Using the Change of Base Formula $x=\frac{1.5185}{1}\mathrm{log}\left(13\right)=1.5185$ and $\mathrm{log}\left(10\right)=1$ $x\approx 1.52$ Conclusion: The solution for the given equation is $x\approx 1.52$.	2022-05-24 18:05:05	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 17, "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": 0.952783465385437, "perplexity": 682.8960749651529}, "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/1652662573189.78/warc/CC-MAIN-20220524173011-20220524203011-00484.warc.gz"}
https://automating-gis-processes.github.io/site/notebooks/L3/geocoding_in_geopandas.html	# Geocoding in Geopandas¶ It is possible to do geocoding in Geopandas using its integrated functionalities of geopy. Geopandas has a function called geocode() that can geocode a list of addresses (strings) and return a GeoDataFrame containing the resulting point objects in geometry column. Nice, isn’t it! Let’s try this out. We will geocode addresses stored in a text file called addresses.txt. The addresses are located in the Helsinki Region in Southern Finland. The first rows of the data look like this: id;addr 1000;Itämerenkatu 14, 00101 Helsinki, Finland 1001;Kampinkuja 1, 00100 Helsinki, Finland 1002;Kaivokatu 8, 00101 Helsinki, Finland 1003;Hermannin rantatie 1, 00580 Helsinki, Finland We have an id for each row and an address on column addr. • Let’s first read the data into a Pandas DataFrame using the read_csv() -function: [1]: # Import necessary modules import pandas as pd import geopandas as gpd from shapely.geometry import Point # Filepath • Let’s check that we imported the file correctly: [2]: len(data) [2]: 34 [3]: data.head() [3]: 0 1000 Itämerenkatu 14, 00101 Helsinki, Finland 1 1001 Kampinkuja 1, 00100 Helsinki, Finland 2 1002 Kaivokatu 8, 00101 Helsinki, Finland 3 1003 Hermannin rantatie 1, 00580 Helsinki, Finland 4 1005 Tyynenmerenkatu 9, 00220 Helsinki, Finland Now we have our data in a Pandas DataFrame and we can geocode our addresses using the geopandas geocoding function. geopandas.tools.geocode uses geopy package in the background. • Let’s import the geocoding function and geocode the addresses (column addr) using Nominatim. • Remember to provide a custom string (name of your application) in the user_agent parameter. • If needed, you can add the timeout-parameter which specifies how many seconds we will wait for a response from the service. [4]: # Import the geocoding tool from geopandas.tools import geocode # Geocode addresses using Nominatim. Remember to provide a custom "application name" in the user_agent parameter! geo = geocode(data['addr'], provider='nominatim', user_agent='autogis_xx', timeout=4) [5]: geo.head() [5]: 0 Ruoholahti, 14, Itämerenkatu, Ruoholahti, Läns... POINT (24.9155624 60.1632015) 1 Kamppi, 1, Kampinkuja, Kamppi, Eteläinen suurp... POINT (24.9316914 60.1690222) 2 Bangkok9, 8, Kaivokatu, Keskusta, Kluuvi, Etel... POINT (24.9416849 60.1699637) 3 Hermannin rantatie, Kyläsaari, Hermanni, Helsi... POINT (24.9719335 60.1969965) 4 Hesburger, 9, Tyynenmerenkatu, Jätkäsaari, Län... POINT (24.9216003 60.1566475) And Voilà! As a result we have a GeoDataFrame that contains our original address and a ‘geometry’ column containing Shapely Point -objects that we can use for exporting the addresses to a Shapefile for example. However, the id column is not there. Thus, we need to join the information from data into our new GeoDataFrame geo, thus making a Table Join. Rate-limiting When geocoding a large dataframe, you might encounter an error when geocoding. In case you get a time out error, try first using the timeout parameter as we did above (allow the service a bit more time to respond). In case of Too Many Requests error, you have hit the rate-limit of the service, and you should slow down your requests. To our convenience, GeoPy provides additional tools for taking into account rate limits in geocoding services. This script adapts the usage of GeoPy RateLimiter to our input data: from geopy.geocoders import Nominatim from geopy.extra.rate_limiter import RateLimiter from shapely.geometry import Point # Initiate geocoder geolocator = Nominatim(user_agent='autogis_xx') # Create a geopy rate limiter: geocode_with_delay = RateLimiter(geolocator.geocode, min_delay_seconds=1) # Apply the geocoder with delay using the rate limiter: # Get point coordinates from the GeoPy location object on each row: data["coords"] = data['temp'].apply(lambda loc: tuple(loc.point) if loc else None) # Create shapely point objects to geometry column: data["geometry"] = data["coords"].apply(Point) All in all, remember that Nominatim is not meant for super heavy use. ## Table join¶ Table joins in pandas For a comprehensive overview of different ways of combining DataFrames and Series based on set theory, have a look at pandas documentation about merge, join and concatenate. Table joins are really common procedures when doing GIS analyses. As you might remember from our earlier lessons, combining data from different tables based on common key attribute can be done easily in Pandas/Geopandas using the .merge() -function. We used this approach in the geo-python course exercise 6. However, sometimes it is useful to join two tables together based on the index of those DataFrames. In such case, we assume that there is same number of records in our DataFrames and that the order of the records should be the same in both DataFrames. In fact, now we have such a situation as we are geocoding our addresses where the order of the geocoded addresses in geo DataFrame is the same as in our original data DataFrame. Hence, we can join those tables together with join() -function which merges the two DataFrames together based on index by default. [6]: join = geo.join(data) [6]: 0 Ruoholahti, 14, Itämerenkatu, Ruoholahti, Läns... POINT (24.9155624 60.1632015) 1000 Itämerenkatu 14, 00101 Helsinki, Finland 1 Kamppi, 1, Kampinkuja, Kamppi, Eteläinen suurp... POINT (24.9316914 60.1690222) 1001 Kampinkuja 1, 00100 Helsinki, Finland 2 Bangkok9, 8, Kaivokatu, Keskusta, Kluuvi, Etel... POINT (24.9416849 60.1699637) 1002 Kaivokatu 8, 00101 Helsinki, Finland 3 Hermannin rantatie, Kyläsaari, Hermanni, Helsi... POINT (24.9719335 60.1969965) 1003 Hermannin rantatie 1, 00580 Helsinki, Finland 4 Hesburger, 9, Tyynenmerenkatu, Jätkäsaari, Län... POINT (24.9216003 60.1566475) 1005 Tyynenmerenkatu 9, 00220 Helsinki, Finland • Let’s also check the data type of our new join table. [7]: type(join) [7]: geopandas.geodataframe.GeoDataFrame As a result we have a new GeoDataFrame called join where we now have all original columns plus a new column for geometry. Note! If you would do the join the other way around, i.e. data.join(geo), the output would be a pandas DataFrame, not a GeoDataFrame! • Now it is easy to save our address points into a Shapefile [8]: # Output file path	2020-07-10 13:37:11	{"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": 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": 0.17832913994789124, "perplexity": 13692.927565009779}, "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-2020-29/segments/1593655908294.32/warc/CC-MAIN-20200710113143-20200710143143-00333.warc.gz"}
https://rdrr.io/cran/HiveR/f/inst/doc/HiveR.Rmd	# The HiveR Package In HiveR: 2D and 3D Hive Plots for R rm(list = ls()) suppressPackageStartupMessages(library("HiveR")) suppressPackageStartupMessages(library("grid")) suppressPackageStartupMessages(library("FuncMap")) suppressPackageStartupMessages(library("sna")) suppressPackageStartupMessages(library("xtable")) suppressPackageStartupMessages(library("knitr")) suppressPackageStartupMessages(library("bipartite")) desc <- packageDescription("HiveR") vers <- paste("version", desc$Version) set.seed(123) # use pdfcrop if it exists if (Sys.which("pdfcrop") != "") knit_hooks$set(crop = hook_pdfcrop) opts_chunk$set(echo = FALSE, fig.path = "./graphics/") This document describes some features of the HiveR package. The current release contains a core set of functions for creating and drawing hive plots.^[Github or CRAN] There may well be bugs and features that can be improved -- your comments are always welcome.^[Contact info and issue tracking can be found at the web sites above.] In fact, user input has regularly improved and extended HiveR. As with any R package, details on functions discussed below can be found by typing ?function_name in the R console after installing HiveR. A complete list of functions available can be seen by typing ?HiveR and then at the bottom of the page that opens, click on the index link. Many of the help pages contain extensive examples of common tasks. # Background, Inspiration and Motivation HiveR was inspired by the concept of hive plots as developed by Martin Krzywinski at the Genome Sciences Center (www.hiveplot.com). Hive plots are a reaction to "hairball" style networks in which the layout of the network is arbitrary and hypersensitive to even small changes in the underlying network. Hive plots are particularly well-suited for comparing networks, as well as for the discovery of emergent properties of networks. The key innovation in a hive plot, compared to other means of graphically displaying network structure, is how node information is handled. In a hive plot, there is a node coordinate system consisting of two parts. First, nodes are assigned to axes based upon qualitative or quantitative characteristics of the the node, for instance membership in a certain category. As will be discussed later, this assignment process is key to constructing a hive plot. Second, the position of the node along the axis, the radius, is based upon some quantitative characteristic of the node. Edges are handled in a fairly standard way, but may be colored or have a width or weight which encodes an interesting value. In creating a hive plot, one maps network parameters to the plot, and thus the process can be readily tuned to meet one's needs. The mappable parameters are listed in Table \ref{Mapping}, and the mapping is limited only by one's creativity and the particular knowledge domain. Thus ecologists have their own measures of food webs, social network analysts have various measures describing interconnectedness etc. An essential point is that mapping network parameters in this way results in a reproducible plot. Krzywinski has an excellent paper detailing the features and virtues of hive plots and is a must-read.\cite{Krzywinski2011} He notes the following virtues of hive plots: • Hive plots are rational in that only the structural properties of the network determine the layout. • Hive plots are flexible and can be tuned to show interesting features. • Hive plots are predictable since they arise from rules that map network features to plot features. • Hive plots are robust to changes in the underlying network. • Hive plots of different networks can be compared. • Hive plots are transparent and practical. • Plots of networks are generally complex and require some investment to understand. Complexity plots well in a hive plot and details can be inspected. \begin{table} \begin{center} \begin{tabular}{\|l\|} \hline \emph{mappable hive plot parameters}\ \hline \hline Axis to which a node is assigned\ Radius of a node\ Color of a node\ Size of a node\ \hline Color of an edge\ Width or weight of an edge\ \hline \end{tabular} \end{center} \caption{Hive plot features that can be mapped to network parameters.\label{Mapping}} \end{table} Inspired by the examples given by Kryzwinski in his materials on the web, I created the R package FuncMap in December 2010.\cite{Hanson2011} This single function package maps the function calls made by an R package into 3 types: sources, which are functions that make only outgoing calls, sinks, which take only incoming calls, and managers, which do both. HiveR takes things quite a bit further. HiveR is a fresh implementation of hive plots in R, not a port of the original Perl version. As such, it does some things differently, and not all features are implemented (and they may or may not be in the future). HiveR will draw 2D hive plots with 2-6 axes in a style close to the original. However, HiveR adds value by making 3D, interactive plots possible when there are 4-6 axes. These 3D plots were inspired by the ideas of VSEPR theory in chemistry: the axes of these 3D plots are arranged with tetrahedral, trigonal bipyramidal or octahedral geometries for 4-6 axes respectively (see Figure \ref{VSEPR} and wikipedia/VSEPR). The specifics of 3D hive plots will be discussed in a later section. # HiveR Features ## Internal Representation of Hive Data HiveR stores the information needed to create a hive plot in a HivePlotData object which is an S3 class. As an S3 class, this structure can be easily extended by the user to store additional information (though using that information as part of a hive plot would require more work). Utilities are provided to summarize, troubleshoot and check the integrity of these objects (functions sumHPD and chkHPD respectively). The structure and content of a HivePlotData object is shown in Table \ref{Struc}. \begin{small} \begin{table} \begin{center} \begin{xtabular}{\| p{0.15\textwidth} p{0.2\textwidth} \| p{0.15\textwidth} \| p{0.35\textwidth} \|} \hline \$nodes & & & \ & \$id & int & identifier \ & \$lab & chr & label \ & \$axis & int & axis \ & \$radius & num & radius \ & \$size & num & size \ & \$color & chr & color \ \hline \$edges & & & \ & \$id1 & int & 1st node id \ & \$id2 & int & 2nd node id \ & \$weight & num & width \ & \$color & chr & color \ \hline \$type & & chr & 2D or 3D plot \ \hline \$desc & & chr & description \ \hline \$axis.cols & & chr & axis colors \ \hline - attr & & chr & "HivePlotData" \ \hline \end{xtabular} \end{center} \caption{The structure of a HivePlotData object.\label{Struc}} \end{table} \end{small} ## Generation of Random Network Data Sets HiveR has the ability to generate random network data sets using function ranHiveData. These are primarily useful for testing and demonstrations. A data set has a type, either 2D or 3D. Type 2D may have 2-6 axes and is plotted in a 2D window using grid graphics which are extremely fast. Type 3D applies to 4-6 axes only and these hive plots are drawn in 3D using rgl and are interactive. When using ranHiveData you can specify which type you desire. ## Built-in Data Sets HiveR contains two related 2D type data sets, Safari and Arroyo. These are plant-pollinator data sets which give the number of visits for each plant-pollinator pair. Data for the E. coli gene regulatory network is also included; it is derived from the RegulonDB.\cite{Gama2010} Each of these data sets are used in the examples below. Finally, there is a data set called HEC which is derived from the hair and eye color data set. ## Importing Real Data Sets There are three functions for importing data into HiveR: dot2HPD, adj2HPD and edge2HPD. The function dot2HPD will import files in .dot format and convert them to HivePlotData objects (see wikipedia/DOT_language). This is done with the aid of two external files. One contains information about how to map node labels to HivePlotData properties. The other contains information about mapping edge properties. This approach gives one a lot of flexibility to process the same graph into various hive plots. This process is demonstrated later for the E. coli data set. Currently, only a very small set of the .dot standard is implemented and one should not expect any particular .dot file to process correctly. The function adj2HPD will import an adjacency matrix, and edge2HPD will import an edge list. For these functions the initially created HivePlotData object will almost certainly need a fair amount of manipulation before it can be plotted. ## Modifying HivePlotData Sets Function mineHPD has several options for extracting information from within an existing HivePlotData object and converting it to a modifed HivePlotData object. Additional options are readily incorporated. For the current selection, check the help page (?mineHPD). This function will be used extensively in the examples that follow. In addition, function manipAxis can also be used to modify a HivePlotData object by scaling or inverting axes. This can be done on the fly (as the plot is created) or the HivePlotData object can be permanently modified. ## Making Hive Plots In a hive plot, because the position of the node along an axis (the radius) is quantitative, the nodes can be plotted at their absolute value (native units), normalized to run between 0\ldots1, plotted by rank or by a combination of ranking and norming. Some aspects of the plot that depend upon these options are shown in Table \ref{Method}. These different ways of plotting the same data often look dramatically different, and for a particular data set, some methods of plotting may provide more insight. Functions plotHive and plot3dHive have an argument method which controls node plotting on the fly; function manipAxis is used in the background and can also be called independently if desired. \begin{small} \begin{table} \begin{center} \begin{flushleft} \begin{xtabular}{\| p{0.15\linewidth} \| p{0.22\linewidth} \| p{0.22\linewidth} \| p{0.28\linewidth} \|} \hline \emph{method} & \emph{axis length} & \emph{center hole (2D)} & \emph{node behavior} \ \hline \hline native & $f(units)$ & asymmetric & nodes may overlap\ \hline ranked & $\propto rank(nodes)$ & circular & nodes evenly spaced \& don't overlap \ \hline normed & all equal & circular & nodes may overlap\ \hline ranked \& normed & all equal & circular & nodes evenly spaced \& don't overlap \ \hline \end{xtabular} \end{flushleft} \end{center} \caption{Comparison of methods for adjusting the radii of nodes during plotting.\label{Method}} \end{table} \end{small} # A Simple Example Using a Plant-Pollinator Network HiveR contains the built-in data sets, Safari and Arroyo which provide a useful demonstration of HiveR.^[Be warned: I am not an ecologist and these data sets and plots are merely a demonstration of HiveR.] These are plant-pollinator data sets which were derived from Vasquez and Simberloff.\cite{Vazquez2003} These describe two-trophic level systems that consist of almost exactly the same suite of plants and pollinators. Safari is based upon observations of an undisturbed area, while Arroyo is from a nearby location grazed by cattle. The original data is composed of plant-pollinator pairs and a count of visits during a fixed observation period for each pair. Figures \ref{fig:PPNA} and \ref{fig:PPN4} show two means of plotting Safari using package bipartite.^[Actually in this case we are using the data set Safariland from package bipartite; Safari was derived from Safariland.] Figure \ref{fig:PPNA} is a simple diagram giving plant-pollinator visits as a gray-plot heat map (plants are on the vertical axis). There are two parameters encoded here: the pairings and the number of visits (arguably, the dimensions of the matrix give the number of species involved as well). Figure \ref{fig:PPN4} displays plants across the bottom and pollinators across the top. The width of the connecting bands in the middle encodes the number of visits for a given plant-pollinator pair. The width of the top or bottom panel for a species is the total number of visits in which that species participates. Thus there are three parameters shown in this figure: the pairings, the total visits for a single species, and visits between a given pair. This second plot makes it pretty clear that four plant-pollinator pairs have by far the largest number of visits (these are the large gray-filled bands in the middle of the diagram). data(Safariland) r."} visweb(Safariland) r.", fig.width = 5, fig.height = 5} plotweb(Safariland, text.rot = 90, adj.high = 0, adj.low = 1, y.lim = c(0, 2), labsize = 0.8) Another approach to presenting this network graphically would be to use function gplot in the social network analysis package sna. gplot is flexible and has many options. Figure \ref{fig:PPN5} shows one possible display of Safari, plotted with mode = circle. In this plot, plant nodes are colored green and insect nodes red. The width of the edges is proportional to the number of visits between a pair of species. Figure \ref{fig:PPN6} shows the same data using the Fruchterman-Reingold algorithm, one which shows that there are actually two networks present (and which is not apparent from the the other plots). Edge width here is the same as before, but because the high traffic node pairs are close to each other, the connecting, wide edge looks a bit odd and is easy to miss (clearly, one could experiment to improve this detail). r (mode = circle).", warning = FALSE, fig.height = 5, fig.width = 5} gplot(Safariland, gmode = "graph", edge.lwd = 0.05, vertex.col = c(rep("green", 9), rep("red", 27)), mode = "circle") r (mode = Fruchterman-Reingold).", warning = FALSE, fig.height = 5, fig.width = 5} gplot(Safariland, gmode = "graph", edge.lwd = 0.05, vertex.col = c(rep("green", 9), rep("red", 27))) For a network of this size and complexity, any or some combination of these plots would probably be sufficient to answer many questions. However, we proceed to plot the data as a hive plot to demonstration some of the features of hive plots. Figure \ref{fig:PPN2} shows Safari and Arroyo displayed together in a hive panel, which facilitates direct comparison of the two networks. In these plots, plants are on one axis, and pollinators are on the other. Each organism was assigned a radius on its axis based by calculating \|d'\| using function dfun in package bipartite. \|d'\| is an index of specialization; higher values mean the plant or pollinator is more specialized. Edge weights were assigned proportional to the square roots greater numbers of visits, and the color-coding is comparable for each figure. Thus both the edge color and the edge weight encode the same information. It would of course be possible to encode an additional variables by changing either edge color or weight, or node size. These plots show a rich amount of information not available from the more standard plots and show that the networks are fundamentally different: • The degree of specialization with each network is different. This can be seen in the different radii for the nodes in each plot, as well as in the Arroyo panel where the plant axis begins at a lower value. • A greater number of visits (wider, redder edges) occur between more specialized species (nodes at larger radii) in Safari than Arroyo. • The huge number of visits encoded in red in Safari (the ungrazed site) is missing in Arroyo. data(Safari) Safari$nodes$size <- 0.5 data(Arroyo) Arroyo$nodes$size <- 0.5 vplayout <- function(x, y) viewport(layout.pos.row = x, layout.pos.col = y) # grid.newpage() pushViewport(viewport(layout = grid.layout(2, 1))) # pushViewport(vplayout(1, 1)) # upper plot plotHive(Safari, ch = 0.1, axLabs = c("plants", "pollinators"), axLab.pos = c(0.15, 0.15), rot = c(-90, 90), np = FALSE, axLab.gpar = gpar(fontsize = 16, col = "white")) grid.text("Safari (undisturbed)", x = 0.5, y = 0.95, default.units = "npc", gp = gpar(fontsize = 20, col = "white")) popViewport(2) # pushViewport(vplayout(2, 1)) # lower plot plotHive(Arroyo, ch = 0.1, axLabs = c("plants", "pollinators"), axLab.pos = c(0.15, 0.15), rot = c(-90, 90), np = FALSE, axLab.gpar = gpar(fontsize = 16, col = "white")) grid.text("Arroyo (disturbed)", x = 0.5, y = 0.95, default.units = "npc", gp = gpar(fontsize = 20, col = "white")) # Some Things to Keep in Mind Now that we have seen a simple hive plot, it's a good time to review some aspects to keep in mind as you wrap your head around the concept and we move to more complicated plots. Hive plots are radially-arranged parallel coordinate plots, and as with any parallel coordinate plot, the order of the axes is critical.\cite{Wegman1990} In creating a hive plot, assigning the nodes to axes is the hardest task, as no jumping or crossing of axes is allowed (due to bad aesthetics). As a result, you can't make this assignment without thinking about the edges at the same time. This initial mapping process often forces one to reconceputalize one's data, which in turns leads to new insights. By the way, there is no guarantee that any data set can be made into a hive plot, but there are certainly a number of data sets that will give a very useful hive plot after some thought. For 2D hive plots with 2 or 3 axes, there is no possibility of edges crossing an axis. However, for 4-6 axes, you must guard against this: Edges should go 1 $\rightarrow$ 2, 2 $\rightarrow$ 3, \ldots 5 $\rightarrow$ 6, but not 1 $\rightarrow$ 5 for example. For 3D hive plots, no edges can start and end on the same axis (there is no way to place these edges properly in 3D space). For 4 axes, all axes are adjacent and hence jumping is not an issue. But for 5 or 6 axes, you must guard against this manually. Note that the different axis systems in 3D have different numbers of adjacent axes: • Tetrahedron: 6 adjacent axis pairs, edge crossings are impossible • Trigonal bipyramid: 9 adjacent axis pairs.^[And the pairs are not equivalent: see Figure \ref{VSEPR}.] • Octahedron: 12 adjacent axis pairs The mapping of nodes to axes is limited only by your creativity and the knowledge domain you work in. For some ideas about how to assign the radius, see table 1 in Krzywinski.\cite{Krzywinski2011} Hive plots are almost agnostic with respect to directed graphs. Most functions don't use any information related to the direction of an edge. However, some of the options in mineHPD can take into account directionality by using the first node id as a starting point and the second node id as an ending point (HPD$edges$id1 and HPD$edges$id2). With 2D hive plots, which are drawn using grid graphics, the nodes "on top" are the last drawn nodes. You may wish to sort the nodes before drawing to get a certain effect -- the same is true for edges.^[While the last thing drawn is on top, they are not strictly drawn in the order given. See the code for plotHive for details. This is an open issue related to how grid.curve handles its curvature argument.] # The E. coli Gene Regulatory Network The E. coli gene regulatory network, based upon the RegulonDB,\cite{Gama2010} is an excellent example for showing how one can import and process a .dot file to create a hive plot. In this case we will read in a .dot file describing nodes and edges. A portion of this file is shown in Table \ref{DOT}. The .dot file will be processed using an external file to map the edge annotations to hive plot features. Node annotations in the .dot file can be similarly processed, but this particular example contains no node annotations so there's nothing to process. Table \ref{EI} shows the contents of the edge instruction file. tmp <- readLines("network_tf_gene.parsed.dot")[1595:1605] # format = "latex" is needed to keep caption in margin # booktabs = TRUE gives better formatting of the table kable(tmp, caption = "Portion of a DOT file.\\label{DOT}", format = "latex", booktabs = TRUE) tab <- read.csv(file = "EdgeInst.csv") kable(tab, caption = "Contents of edge instruction file.\\label{EI}", format = "latex", booktabs = TRUE) Here we go. First, read in the node and edge information and process it using the edge instruction file (this assumes your working directory is set to the folder with the relevant files). EC1 <- dot2HPD(file = "network_tf_gene.parsed.dot", node.inst = NULL, edge.inst = "EdgeInst.csv", desc = "E coli gene regulatory network (RegulonDB)", axis.cols = rep("grey", 3)) Before going on, we'll summarize what we've created. Next, we'll assign the node radius based upon the edge degree, then assign the nodes to axes based upon their role as source, manager or sink. Finally, there are some edges which start and end at the same radius on the same axis. These have zero length and cannot be drawn so they must be removed (these are transcription factors that regulate themselves in most cases). sumHPD(EC1) EC2 <- mineHPD(EC1, option = "rad <- tot.edge.count") sumHPD(EC2) EC3 <- mineHPD(EC2, option = "axis <- source.man.sink") sumHPD(EC3) EC4 <- mineHPD(EC3, option = "remove zero edge") sumHPD(EC4) Notice how the number of axes, radii and edges change through this process. Finally, we'll need to organize the edge list so that the edges which are repressors are drawn last (you could do this other ways, of course, but we need to know this in order to be able to interpret the plots). edges <- EC4$edges edgesR <- subset(edges, color == 'red') edgesG <- subset(edges, color == 'green') edgesO <- subset(edges, color == 'orange') edges <- rbind(edgesO, edgesG, edgesR) EC4$edges <- edges EC4$edges$weight <- 0.5 Now we're ready to plot! Figure \ref{fig:E_coli_2} is a hive panel showing this network with different scales for the nodes. Each plot takes about 10 seconds to draw. vplayout <- function(x, y) viewport(layout.pos.row = x, layout.pos.col = y) grid.newpage() pushViewport(viewport(layout = grid.layout(3, 1))) # pushViewport(vplayout(1, 1)) # upper plot plotHive(EC4, dr.nodes = FALSE, ch = 20, axLabs = c("source", "sink", "manager"), axLab.pos = c(40, 75, 35), axLab.gpar = gpar(fontsize = 6, col = "white", lwd = 2), arrow = c("degree", 150, 100, 180, 70), np = FALSE) grid.text("native units", x = 0.5, y = 0.05, default.units = "npc", gp = gpar(fontsize = 8, col = "white")) popViewport(2) # pushViewport(vplayout(2, 1)) # middle plot plotHive(EC4, dr.nodes = FALSE, method = "rank", ch = 100, #axLabs = c("source", "sink", "manager"), #axLab.pos = c(100, 125, 180), #axLab.gpar = gpar(fontsize = 10, col = "white"), np = FALSE) grid.text("ranked units", x = 0.5, y = 0.05, default.units = "npc", gp = gpar(fontsize = 8, col = "white")) popViewport(2) # pushViewport(vplayout(3, 1)) # lower plot plotHive(EC4, dr.nodes = FALSE, method = "norm", ch = 0.1, axLabs = c("source", "sink", "manager"), axLab.pos = c(0.1, 0.2, 0.2), axLab.gpar = gpar(fontsize = 6, col = "white"), np = FALSE) grid.text("normed units", x = 0.5, y = 0.05, default.units = "npc", gp = gpar(fontsize = 8, col = "white")) # 3D Hive Plots HiveR extends the original hive plot concept to 3 dimensions using the interactive graphics package rgl. One advantage to this is that 3D hive plots have more pairs of adjacent axes compared to the corresponding 2D hive plot, which cuts down on the possibility of edges crossing axes and makes assigning nodes to axes easier. The interactivity doesn't hurt either! We will demonstrate the process using a recent example of protein-protein interactions.\cite{Jager2012} This data set contains interaction data for HIV-human proteins, as well as some related human-human protein interactions. The strength of these interactions are quantified in terms of a MiST score which is derived from mass spectral data after some processing. Data for the interaction of two human cell lines with HIV are available (we'll just use one, but you could make the same plot with the interactions for the other cell line to compare the two).^[The plots here were created using data provided as supplementary material. A full script of the processing is available from the author.] Figure \ref{Jager1} is Figure 3 from the paper. We're going to focus on the portion of this network shown in Figure \ref{Jager2} to demonstrate the conceptual process of mapping data to a hive plot.^[Remember, this is just one of many ways one might map the raw data.] Figure \ref{Map2} (left) shows a small, idealized portion of this network for discussion. In this figure, a black dot represents a human protein that interacts with an HIV protein. Human protein D, for example, interacts with two different HIV proteins, PR and IN. However, human protein E interacts with only one HIV protein (PR), but interacts with another human protein F, which in turn interacts with HIV protein Pol. The blue edge between E and F indicates indirect communication between HIV proteins PR and Pol via the two human proteins. Figure \ref{Map2} (right) shows the process of mapping the connections and quantitative information into the hive plot. Each HIV protein node in the original diagram will become an axis in the hive plot.^[The replacement of nodes with axes is one way hive plots help us think about the data differently.] Because there are four of these, we will be making a tetrahedral hive plot with four axes. The human proteins which interact with two HIV proteins will become red edges in the hive plot (and they are red in these figures). Protein D for example will be plotted on the PR axis at a radius of 9 because that is the MiST score for this human protein interacting with this HIV protein. Protein D will also appear on axis IN, but at a radius of 6, because it interacts a bit more weakly with this HIV protein. This process is repeated for all the interactions. Human protein E, on the other hand, only interacts with one HIV protein. As a result, it appears only on the PR axis at a radius of 6. Don't forget that E interacts with F: F is plotted on axis Pol at a radius of 7 and then E and F are connected by a blue edge signalling the indirect interaction between HIV proteins PR and Pol. Other human proteins which interact with only one HIV protein are plotted on the appropriate axis with a radius corresponding to their MiST score. Finally, any human protein with 2 or more edges is plotted as a larger yellow node, while those with only one edge are plotted in green. Figure \ref{static} shows the resulting hive plot, using the original data for HIV interacting with HEK cells, drawn using native units. Red edges represent a human protein.^[Unlike the more standard network graphs where a protein would be a node rather than an edge.] Red edges with more or less constant radius are human proteins that interact fairly equally with the HIV proteins on each axis. There is one red edge which shows a strong interaction with one HIV protein (PR) and a weak interaction with the other (Pol) and hence does not have a near-constant radius. The complete lack of human proteins between axes IN and RT, IN and PR and PR and RT (i.e., no red edges) tells us that these three HIV proteins are relatively isolated. HIV protein Pol on the other hand is very central to this system as it participates in virtually all the edges, which is to say that it interacts with many human proteins. # Acknowledgements Naturally, I thank Martin Krzywinski for numerous helpful communications. I also appreciate helpful discussions on gene ontology concepts with my colleague Professor Chet Fornari. # Appendices ## Drawing 3D Spline Curves One of the challenges in developing HiveR was that there were no algorithms for drawing 3D spline curves available. Consequently, I wrote a set of functions that take 2 end points in 3D space, rotates them into a 2D space, computes a spline curve, and then rotates the curve back into the original 3D space. The process is thoroughly vetted and robust. A 3D spline is shown in Figure \ref{spline3D}. The main workhorse is the function rcsr. ## HiveR vs. Perl Original Version The original hive plot drawing program written by Krzywinski was written in Perl. There are now versions in Java and D3; see www.hiveplot.com. Listed below are some differences between HiveR and the original Perl version. • In the Perl original code one can clone an axis to show connections that would start and end on the same axis. In HiveR, one can simply add a new axis based upon some property of the system. Alternatively, for 2D hive plots, HiveR is able to show edges that start \& end on the same axis. • No segmentation of an axis is currently possible with HiveR • The Perl original code uses bezier curves to create the edges; HiveR uses splines with a single slightly off-center control point. ## Features For Consideration • Add the ability to subtract 2 hive plots and display the result. • Set up a mechanism to automatically permute the axes in 3D mode when the number of axes = 5 or 6 so that the best option can be selected. Might also be worth doing in 2D mode for 4-6 axes, except in this case it's not a question of how you display but how you import the data. Wegman\cite{Wegman1990} has a formula describing all possible combinations that would be needed. • More ways to import various formats are needed. ## Try the HiveR package in your browser Any scripts or data that you put into this service are public. 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https://en.wikipedia.org/wiki/Flyback_diode	# Flyback diode A simple circuit with an inductance and a flyback diode A flyback diode (sometimes called a snubber diode, commutating diode, freewheeling diode, suppressor diode, suppression diode, clamp diode or catch diode[1][not in citation given])[citation needed] is a diode used to eliminate flyback, which is the sudden voltage spike seen across an inductive load when its supply current is suddenly reduced or interrupted. ## Working principle In its most simplified form with a voltage source connected to an inductor with a switch, we have 2 states available. In the first steady-state, the switch has been closed for a long time such that the inductor has become fully energized and is behaving as though it were a short (Figure 1). Current is flowing "down" from the positive terminal of the voltage source to its negative terminal, through the inductor. When the switch is opened (Figure 2), the inductor will attempt to resist the sudden drop of current (dI/dt is large therefore V is large) by using its stored magnetic field energy to create its own voltage. An extremely large negative potential is created where there once was positive potential, and a positive potential is created where there was once negative potential. The switch, however, remains at the voltage of the power supply, but it is still in contact with the inductor pulling down a negative voltage. Since no connection is physically made to allow current to continue to flow (due to the switch being open), the large potential difference can cause electrons to "arc" across the air-gap of the open switch (or junction of a transistor). This is undesirable for the reasons mentioned above and must be prevented. A flyback diode solves this starvation-arc problem by allowing the inductor to draw current from itself (thus, "flyback") in a continuous loop until the energy is dissipated through losses in the wire, the diode and the resistor (Figure 3). When the switch is closed the diode is reverse-biased against the power supply and doesn't exist in the circuit for practical purposes. However, when the switch is opened, the diode becomes forward-biased relative to the inductor (instead of the power supply as before), allowing it to conduct current in a circular loop from the positive potential at the bottom of the inductor to the negative potential at the top (assuming the power supply was supplying positive voltage at the top of the inductor prior to the switch being opened). The voltage across the inductor will merely be a function of the forward voltage drop of the flyback diode. Total time for dissipation can vary, but it will usually last for a few milliseconds. Figure 1, Back EMF from a solenoid Figure 2, Back EMF filtered with a flyback diode In these images we observe classic signs of back EMF and its elimination through the use of a flyback diode (1N4007). The inductor in this case is a solenoid connected to a 24V DC power supply using 20 awg wire. Each waveform was taken using a digital oscilloscope set to trigger when the voltage across the inductor dipped below zero. In Figure 1 the voltage as measured across the switch bounces/spikes to around -300 V. In Figure 2, a flyback diode was added in antiparallel with the solenoid. Instead of spiking to -300 V, the flyback diode only allows approximately -1.4 V of potential to be built up (-1.4 V is a combination of the forward bias of the 1N4007 diode (1.1 V) and the foot of wiring separating the diode and the solenoid). The waveform in Figure 2 is much less bouncy than the waveform in Figure 1. In both cases, the total time for the solenoid to discharge is a few milliseconds. ## Design In an ideal flyback diode selection, one would seek a diode which has very large peak forward current capacity (to handle voltage transients without burning out the diode), low forward voltage drop, and a reverse breakdown voltage suited to the inductor's power supply. Depending on the application and equipment involved, some voltage surges can be upwards of 10 times the voltage of the power source, so it is critical not to underestimate the energy contained within an energized inductor. When used with a DC coil relay, a flyback diode can cause delayed drop-out of the contacts when power is removed, due to the continued circulation of current in the relay coil and diode. When rapid opening of the contacts is important, a low-value resistor can be placed in series with the diode to help dissipate the coil energy faster, at the expense of higher voltage at the switch. Schottky diodes are preferred in flyback diode applications for switching power converters, because they have the lowest forward drop (~0.2 V rather than >0.7 V for low currents) and are able to quickly respond to reverse bias (when the inductor is being re-energized). They therefore dissipate less energy while transferring energy from the inductor to a capacitor. When the flyback diode is used to simply dissipate the inductive energy, as with a solenoid or motor, cheap 1N4001 and 1N5400 silicon diodes are used instead. ## Induction at the opening of a contact According to Lenz's law, if the current through an inductance changes, this inductance induces a voltage so the current will go on flowing as long as there is energy in the magnetic field. If the current can only flow through the air, the voltage is therefore so high that the air conducts. That is why in mechanically-switched circuits, the near-instantaneous dissipation which occurs without a flyback diode is often observed as an arc across the opening mechanical contacts. Energy is dissipated in this arc primarily as intense heat which causes undesirable premature erosion of the contacts. Another way to dissipate energy is through electromagnetic radiation. Similarly, for non-mechanical solid state switching (i.e., a transistor), large voltage drops across an unactivated solid state switch can destroy the component in question (either instantaneously or through accelerated wear and tear). Some energy is also lost from the system as a whole and from the arc as a broad spectrum of electromagnetic radiation, in the form of radio waves and light. These radio waves can cause undesirable clicks and pops on nearby radio receivers. To minimise the antenna-like radiation of this electromagnetic energy from wires connected to the inductor, the flyback diode should be connected as physically close to the inductor as practicable. This approach also minimises those parts of the circuit that are subject to an unwanted high-voltage — a good engineering practice. ### Derivation The voltage at an inductor is, by the law of electromagnetic induction and the definition of inductance: ${\displaystyle V_{L}=-{d\Phi _{B} \over dt}=-L{dI \over dt}}$ If there is no flyback diode but only something with a great resistance (such as the air between two metal contacts), say, R2, we will approximate it as: ${\displaystyle V_{R_{2}}=R_{2}\cdot I}$ If we open the switch and ignore VCC and R1, we get: ${\displaystyle V_{L}=V_{R_{2}}}$ or ${\displaystyle -L{dI \over dt}=R_{2}\cdot I}$ which is a differential equation with the solution: ${\displaystyle I(t)=I_{0}\cdot e^{-{R_{2} \over L}t}}$ We observe that the current will decrease faster if the resistance is high, such as with air. Now if we open the switch with the diode in place, we only need to consider L1, R1 and D1. For I > 0, we can assume: ${\displaystyle V_{D}=\mathrm {constant} }$ so: ${\displaystyle V_{L}=V_{R_{1}}+V_{D}}$ which is: ${\displaystyle -L{dI \over dt}=R_{1}\cdot I+V_{D}}$ whose solution is: ${\displaystyle I(t)=(I_{0}+{1 \over R_{1}}V_{D})\cdot e^{-{R_{1} \over L}t}-{1 \over R_{1}}V_{D}}$ We can calculate the time it needs to switch off by determining for which t it is I(t) = 0. ${\displaystyle t={-L \over R_{1}}\cdot ln{\left({V_{D} \over {V_{D}+I_{0}{R_{1}}}}\right)}}$ ## Applications Flyback diodes are commonly used when inductive loads are switched off by semiconductor devices: in relay drivers, H-bridge motor drivers, and so on. A switched-mode power supply also exploits this effect, but the energy is not dissipated to heat and instead used to pump a packet of additional charge into a capacitor, in order to supply power to a load.	2016-10-25 07:28:11	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 10, "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": 0.5697072744369507, "perplexity": 1038.8502932385513}, "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-2016-44/segments/1476988719960.60/warc/CC-MAIN-20161020183839-00315-ip-10-171-6-4.ec2.internal.warc.gz"}
https://community.thunkable.com/t/how-to-fix-the-row-going-out-of-the-row-if-the-width-too-high/249839	# How to fix the row going out of the row if the width too high Hi there, How to fix whatever the row width is too long,it just increase inside the row not going out. thanks. Hi, What is the width of your row? 320 1 Like Anyone? Hi, Since it’s 320px, I assume you make the row long by blocks - Like when level = 5 , set width to width+100px. So, to prevent the length of row to extend screen, Add a repeat until loop, and set condition to row.width = 320px / or any. This will stop extend of row	2021-02-27 15:46:34	{"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": 0.8306480646133423, "perplexity": 4204.902983185795}, "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-2021-10/segments/1614178358976.37/warc/CC-MAIN-20210227144626-20210227174626-00435.warc.gz"}
http://physics.stackexchange.com/questions/66496/recent-planck-probe-results-how-unexpected	# Recent Planck probe results: how unexpected? The data from the Planck probe's observations are in, and according to the European Space Agency they show a "hemispheric asymmetry in the cosmic microwave background (CMB)". Quote: an asymmetry in the average temperatures on opposite hemispheres of the sky [...] with slightly higher average temperatures in the southern ecliptic hemisphere and slightly lower average temperatures in the northern ecliptic hemisphere. This runs counter to the prediction made by the standard model that the Universe should be broadly similar in any direction we look. How unexpected is this variance from the Standard Model and can it be quantified? How certain is it that the data are accurate? For the recent discovery of the Higgs boson at the LHC, a five sigma result was considered sufficient to make the announcement. What is the sigma for the reported hemispherical asymmetry? Yet the report of faster-than-light neutrinos, subsequently withdrawn due to equipment failures, was based on six sigma evidence. And in one of the backwaters of Wikipedia, we learn that: Some anomalies in the background radiation have been reported which are aligned with the plane of the solar system, which contradicts the Copernican principle by suggesting that the solar system's alignment is special.[10] Land and Magueijo dubbed this alignment the "axis of evil" owing to the implications for current models of the cosmos,[11] although several later studies have shown systematic errors in the collection of that data and the way it is processed.[12][13][14] Various studies of the CMB anisotropy data either confirm the Copernican principle,[15] model the alignments in a non-homogeneous universe still consistent with the principle,[16] or attempt to explain them as local phenomena.[17] Some of these alternate explanations were discussed by Copi, et. al., who looked at data from the Planck satellite to resolve whether the preferred direction and alignments were spurious.[18][19] (Wikipedia's main Planck probe article makes no mention of the hemispherical asymmetry.) When can we expect this controversy to be resolved, and are more outcomes possible than (1) the Planck probe data are found to be in error or (2) the Standard Model must undergo major revision? - The neutrino fiasco was caused by systematic error (a bad cable connection) being larger than statistical error (the six-sigma thing). The Planck (and COBE and WMAP) team have done their best to eliminate the systematic errors -- mostly related to subtraction of foregrounds. But the hemispheric asymmetry is actually the most sensitive to foreground errors. So I doubt that anyone will be much surprised if it eventually goes away with better models of foregrounds. Meanwhile, it's certainly worth thinking about models that could create such an asymmetry! – Mike May 30 '13 at 19:39 Hi Eugene, nice question I like this :-) – Dilaton May 30 '13 at 21:58 One of the Planck papers discusses these anomalies in detail: Planck 2013 results. XXIII. Isotropy and Statistics of the CMB. How unexpected is this variance from the Standard Model and can it be quantified? How certain is it that the data are accurate? For the recent discovery of the Higgs boson at the LHC, a five sigma result was considered sufficient to make the announcement. What is the sigma for the reported hemispherical asymmetry? The anomalies found by Planck were already seen in the WMAP data, so they confirm the existence of these features. I can't find the specific sigma for the hemispherical asymmetry, but most of the anomalies are reported to have a significance of ~$3\sigma$. That's enough to raise eyebrows in the astronomical world, although particle physicists would be less impressed :-) The question is if these anomalies are actually meaningful, and we can expect heated debates in the coming years between 'believers' and 'non-believers'. There are a few things to consider: • The CMB could be distorted by foreground objects, possibly by our local cluster, our own galaxy and even our solar system. • The CMB pervades the entire universe, but we can only observe a small part of it: we're seeing a cross-section in the form of a sphere, centred on us and with a certain radius (it took the photons 13.8 billion years to reach us). An observer in a different galaxy and/or at a different cosmic time would see a different part of the CMB. These effects are sometimes called cosmic variance. Basically, it means that what we observe may not be truly representative of the entire universe. Also, we're dealing with statistical data, and flukes happen. We're biased at seeing patterns, even though they may not mean anything. For example, if you throw a dice 100 times in a row, then all sorts of apparent patterns may occur. For instance, it could contain the sequence 666666. That specific sequence may seem unlikely and significant, but it is just as likely as any other specific sequence, like e.g. 202020 or 675439. When can we expect this controversy to be resolved The Planck team has yet to release the polarisation data (probably next year), which may shed some light on the situation. But I think these issues will entertain the cosmologists for quite a few years. A promising field of research is the mapping of the large-scale distribution of (dark) matter, using gravitational lensing. This would help calculating the Integrated Sachs–Wolfe effect (which is the gravitational redshift/blueshift of CMB photons as they pass through the potential well of galaxy clusters) more accurately. the Planck probe data are found to be in error The data is reliable (the Planck data agrees with WMAP), it's all about the interpretation. the Standard Model must undergo major revision? It is possible that the explanation lies in a slight deviation from the Standard Model (but no major revision); after all, the Standard Model is an idealisation. Our universe may not be exactly homogeneous or isotropic at large scales. The Planck team actually tried fitting a non-standard model, a so-called Bianchi Model, with mixed results (Planck 2013 results. XXVI. Background geometry and topology of the Universe). Some others get rather carried away, speculating about the influence of 'other universes'. As a final note, it is important to stress that, in the overall scheme, the impact of these anomalies is very small. The Standard Model fits the CMB almost perfectly, and is in agreement with studies of clusters of galaxies and supernovae. (Source: Planck 2013 results. I. Overview of products and scientific results, Fig 19) The fact that the Standard Model works so well and that the cosmological parameters are now known with such accuracy is a very remarkable feat. Thanks to the quality of the data and the success of the theories, cosmologists understand the overall picture with confidence, and can now focus on the details. P.S. All the Planck papers can be found here: Planck 2013 Results Papers. The most important one is Paper XVI, in which the cosmological parameters are discussed. - Your Answer is chock-full with apposite information, more than enough to merit the green check mark! I have only glanced through the two Planck papers on arXiv that you've linked to, will try to read them later. But that graph that you've included does not seem to be in either of them, would you mind telling me where it's from? I take it, then, that you don't place too much importance on the Copernican principle? It's not a "natural law" or basic postulate, so what is its significance for you? A "sanity check" of sorts, akin to Occam's razor, but nothing more? – Eugene Seidel May 31 '13 at 12:21 @EugeneSeidel The graph is from the first Planck paper. I've added the link, and a bit more, in my answer. As for the Copernican principle, I think it's a very good approximation. But the universe is clumpy on cluster-scales, and this will somewhat affect the light that we observe. The question is how much. Unfortunately we're stuck here on Earth, and can't know what the universe looks like at different locations... – Pulsar May 31 '13 at 18:04 This difference is tiny and it's very hard to put any sort of "sigma" confidence to the measurement because we only have one Universe to measure. The anisotropy is small enough that it's hard to say if its statistically significant. Everything I've read (sorry for some reason I can't find the sources right now) suggest that the Planck CMB measurement matches vanilla $\mathrm{\Lambda CDM}$ predictions well enough that nothing stands out as very surprising. -	2014-10-21 07:39:51	{"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": 0.6781006455421448, "perplexity": 848.2245362474896}, "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/1413507444209.14/warc/CC-MAIN-20141017005724-00097-ip-10-16-133-185.ec2.internal.warc.gz"}
https://blogs.mathworks.com/loren/2018/03/06/the-matlab-online-live-editor-challenge/	# The MATLAB Online Live Editor Challenge8 Posted by Loren Shure, Today I’d like to introduce a guest blogger, David Garrison, who is a MATLAB Product Manager here at MathWorks. Dave will talk about an exciting new contest for students and faculty where you can win a cash prize by showing us what you can create using the Live Editor in MATLAB Online. ### Contents #### Show off your live script and win! Hello everyone. Loren has been kind enough to let me use her blog to tell you about the MATLAB Online Live Editor Challenge. The challenge is open to students and faculty of any college, university, or degree-granting institution. It's an opportunity for students to win up to $750 and for faculty to win up to$1000. Simply show us how you would use the Live Editor in MATLAB Online to create a live script on a topic of interest to you. For students, pick a topic you've learned about in a class or from a research project or pick a concept in science, engineering, math or anything else that interests you.. For faculty, select a topic in your area and show us how you would teach that topic using a live script. You can work individually or in teams and submit as many entries as you want. We’ll judge each entry on things like presentation clarity, topic uniqueness, creativity, and effective use of Live Editor features. If your entry is a winner, we'll feature your live script on our website and you'll receive a cash prize. #### MATLAB Online For the challenge you'll be using MATLAB Online to create and share your live script. With MATLAB Online, you can use the latest version of MATLAB in your a web browser without installing, configuring, or managing any software. You can check your eligibility to use MATLAB Online here. Here's an example live script that I wrote in MATLAB Online for estimating sunrise and sunset times. #### How to Enter To enter the MATLAB Online Live Editor Challenge, follow these three easy steps. 1. Submit an entry form. Don't forget to do that because we can't consider your entry without it. 2. Use the Live Editor in MATLAB Online to create an original live script on a topic of your choice. 3. Put your live script and any supporting files in a folder in MATLAB Online, then share that folder with [email protected]. That's all you have to do. The deadline for entries is June 29, 2018 (7 a.m. ET). For complete details and contest rules, go to www.mathworks.com/academia/student-challenge/matlab-online-live-editor-challenge. Good luck! We look forward to seeing what you create with the Live Editor in MATLAB Online. #### Any Questions? If you have any questions about the MATLAB Online Live Editor Challenge, please let us know here. Get the MATLAB code Published with MATLAB® R2017b Michael McCann replied on : 1 of 8 Can postdocs enter? David Garrison replied on : 2 of 8 Yes, postdocs can enter. Please enter as a faculty member and show us a live script you would use to teach a topic in your area. Royi Avital replied on : 3 of 8 In order to fit students Live Editor must be improved in 2 things: 1. Have support for MarkDown. 2. Have support to write Inline Math using $LaTeX Code$ and Display Math using $$LaTeX Code$$. This matches Jupyter and will make things easier for most. Currently it takes too much time to write Math using the wizard. David Garrison replied on : 4 of 8 You can add equations using LaTeX. From the Insert tab, select the Equation dropdown. You have two options — enter your equation as LaTeX or use the interactive equation editor. Royi Avital replied on : 5 of 8 David, I know what you suggested and this is exactly the issue with Live Editor. What’s needed is a smoother user experience using $…$ and $$…$$ escapes as in Jupyter. Or at least make is also valid. This box is just unneeded extra clicks. Jupyter is perfect, just Copy & Paste. David Garrison replied on : 6 of 8 OK. Thank you for your feedback. Royi Avital replied on : 7 of 8 It seems the comment masks out some of the text. I meant I want to use something like that for Display Math: $$LaTeX Code$$ And something like that for Inline Math: Inline Math $LaTeX Code$. I hope this time it will work and will be displayed correctly. Royi Avital replied on : 8 of 8 It seems the comment masks out some of the text. I meant I want to use something like that for Display Math: $$LaTeX Code$$ And something like that for Inline Math: Inline Math $LaTeX Code$. I hope this time it will work and will be displayed correctly.	2018-03-17 12:10:42	{"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": 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": 0.1773061603307724, "perplexity": 2441.2146095906605}, "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-2018-13/segments/1521257645069.15/warc/CC-MAIN-20180317120247-20180317140247-00002.warc.gz"}
https://naturalfossil.com/are-electric-forces-and-magnetic-forces-related	# Are electric forces and magnetic forces related? Date created: Mon, Feb 8, 2021 9:36 PM Content FAQ Those who are looking for an answer to the question «Are electric forces and magnetic forces related?» often ask the following questions: ### 👉 How are magnetic forces and electric forces related? F (vector) = qE (vector) The resulting force vector is in the same direction as the field vector (for positive charges). A magnetic field generates a force ONLY on a MOVING charge, and ONLY if the... ### 👉 How are electric and magnetic forces related? The ideology of the magnetic forces and electric forces are the hot topics in various sorts of fields including the mechanics, electromagnetic, electrostatics, magnetostatic and different areas related to physics. Both of these forces are attractive in nature and it is not an easy task to differentiate between them. For this intention, the Difference between Magnetic Force and Electric Force is presented here. Every magnet has specific area around it in which you can check its force within ... ### 👉 Explain how electric and magnetic forces are related? A magnetic force is a force felt from a nearby magnet, or electric current (a moving charge). An example of an electric current would be electricity moving through a wire. Both magnets and electric... This is the main cause that the magnetic and electric forces are related to each other. In every situation where both the magnetic and electric forces are associated with each other is known as the electromagnetic field where both of them move at right angles to each other while working independently. Long range forces are forces that act over a long distance, like electric forces, magnetic forces, or gravity.Long range forces are forces that act over a long distance, like electric forces ... Both magnetic and electric force oscillate at right angles to one another. In magnetic force, electromagnetic field absorbs VARS (Inductive); conversely, in an electric force, electromagnetic field generates VARS (capacitive). Magnetic force is produced and found around a moving electric charge, and a magnet whereas electric force is produced due to the presence of voltage and can easily found around the wires and appliances where the voltage is present. Magnetic force measured in milliGauss ... Difference Between Magnetic Force and Electric Force • Electric forces can be produced by either stationary or moving electric charges, whereas magnetic forces can be... • Magnetic force on a moving charge is always normal to the direction of the movement and the magnetic field whereas the... The Lorentz Force was introduced by Hendrik Antoon Lorentz in 1895. In an electric field a charged particle will always bear a force because of this field. However, charged particles in a magnetic field will only feel a force due to the magnetic field if it is moving relative to this field. We've handpicked 20 related questions for you, similar to «Are electric forces and magnetic forces related?» so you can surely find the answer! ### How are magnetic and electric forces similar? Both magnetic and electric force oscillate at right angles to one another. In magnetic force, electromagnetic field absorbs VARS (Inductive); conversely, in an electric force, electromagnetic field generates VARS (capacitive). Magnetic force is produced and found around a moving electric charge, and a magnet whereas electric force is produced due to the presence of voltage and can easily found around the wires and appliances where the voltage is present. Magnetic force measured in milliGauss ... ### Do objects without electric charge feel magnetic forces? So just like mass, electric charge is another intrinsic property particles can have. A particle of non-zero charge, or a point charge, will always form an electric field around it. So how are magnetic fields formed? From my understanding so far, magnetic fields are formed when the charges are in motion. ### What affects the strength of electric and magnetic forces? Correct answer - What factors affect the strength of electric and a magnetic force? Pls explain ### What is the difference between electric and magnetic forces? Direction of Forces: Electric force does work on a rest or moving charge BUT the magnetic force does only work on moving charge. ### What is true of electric charges and magnetic forces? August 6, 2021 Posted by Madhu. The key difference between electric field and magnetic field is that electric field describes the area around the charged particles, whereas magnetic field describes the area around a magnet where the poles of the magnet show the force of attraction or repulsion. The term electric field was introduced by Michel ... ### Why are the electric and magnetic forces still unified? The Unified Force of Nature: 1-The Electric & Magnetic Forces Mahmoud E. Yousif Physics Department - The University of Nairobi, P.O.BOX 30197 Nairobi-Kenya Corresponding Author: Mahmoud E. Yousif ... ### How are electric forces and charge related? Scott S. May 16, 2014. The force between to point charges is calculated by Coulomb's Law: F = kQ1Q2 r2 where Q1 and Q2 are the two charges in coulombs, k is the … ### How are electric forces and distance related? Electric forces are inversely proportional to the square of the distance from the source of the force. Wow, what does that mean? In math it looks like this. Electric Force = #(k_e\|q_1*q_2\|)/(r^2)# ### How are electric and magnetic forces different from one another? The electric force acts between all charged particles, whether or not they're moving. The magnetic force acts between moving charged particles. This means that every charged particle gives off an electric field, whether or not it's moving. Moving charged particles (like those in electric current) give off magnetic fields. ### How are electric and magnetic forces different than gravitational force? The key difference between gravitational force and magnetic force is that gravitational force acts on all the things that have a mass whereas magnetic force acts on things having iron or an electric charge on them. Both gravitational force and magnetic force describe the attraction between two things due to different reasons. ### What applications do electric and magnetic forces have in transportation? What applications do electric and magnetic forces have in transportation. This repulsing force is what causes propulsion in a system designed to take advantage of the phenomenon. Electric forces are the forces that occur due to electric charges whereas magnetic forces are the forces that occur due to magnetic dipoles. A door catch is a simple device that uses the magnetic force of attraction ... ### What are the two causes of electric and magnetic forces? mainly positive and negative charges ### What factors affect the strength of electric and magnetic forces? Ask questions about data to determine the factors that affect the strength of electric and magnetic forces. This lesson focuses on these aspects of NGSS Three Dimensional Learning: Science & Engineering Practices Plan and ... ### When did coloumb establish laws of electric and magnetic forces? Coulomb developed his law as an outgrowth of his attempt to investigate the law of electrical repulsions as stated by Joseph Priestley of England. To this end he invented sensitive apparatus to measure the electrical forces involved in Priestley’s law and published his findings in 1785–89. ### How are electric and magnetic fields related? a simple relation to relate electric and magnetic field in an electromagnetic field is by using a simple relation of E=cB where c is the speed of light because electromagnetic wave travels by speed c. you can obtain this relation by using fact that product of permittivity of free space and permeability is 1/c2 . ### How magnetic field and electric current related? Their derivatives produce the Jefimenko's Equations for electric and magnetic fields relating the current feild values to past charge and current distribution values. They resolve our questions above by implying that electromagnetic information travels at light speed and the various relations deduced above regarding the electric and magnetic fields do not actually violate causation. ### Who discovered electric and magnetic fields related? In 1820, the Danish scientist Hans Christian Oersted discovered the magnetic effect of electric current. He performed a simple experiment which established the relationship between electricity and magnetism. ### What is the way in which electric and magnetic forces interact? A magnetic interaction is when magnets find a way to unite; interact with each other. How are magnetic poles and electric charges similar? Please note that for most practical forces, electric and ... So the magnetic field is perpendicular to both the direction of propagation and the electric field. It's also worth noting $\|\vec{k}/\omega\|=1/c$.	2021-12-01 09:10:34	{"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": 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": 0.7261717915534973, "perplexity": 504.6530784219203}, "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-2021-49/segments/1637964359976.94/warc/CC-MAIN-20211201083001-20211201113001-00116.warc.gz"}
https://barnfinds.com/parked-since-73-1957-chevrolet-bel-air/	# Parked Since ’73: 1957 Chevrolet Bel Air You are looking at what the seller claims is a 4,883 (actual) mile survivor! The 1957 Chevrolet Bel Air has to be one of the most iconic classic cars in history. Even most non-car people know about a ’57 Chevy. This one looks like a true survivor and has apparently been in storage since 1973. It can be found here on eBay with a current bid of over $30,000 and was supposedly owned by the same family from 1957 to 2019. Now being sold by MFD Classic Motors – Classic Car Paddocks in Traverse City, MI, the car is seeing very strong bidding. Take a look at this car and let us know what your impression is. The interior is really bright and the upholstery, dash, and door panels look awesome. The rear seat looks like it hasn’t been sat on at all and the floor and the underside of the dash look like they are brand new. With regard to the interior, this car needs nothing but maybe a light cleaning. The engine compartment is probably the biggest drawback to this car. You can see it has clearly sat for a while and needs a freshening up to match the rest of the package. The engine is a 283 2-barrel and the seller says the oil is old but clean. The seller cleaned out the fuel line and added fresh gas. It now fires up and runs well although the radiator has some leaks and the water pump is noisy. The car was repainted at some point and in this photo, you can see some discoloration to the finish, especially behind the rear wheel openings. The seller thinks that the clear coat is turning color. Hopefully a cut and buff will take care of that, but the new owner had a better plan on a re-spray if you are going to win any shows. Here you can see the stark contrast between the exterior color and the door frame. I fear a cut and buff will probably not be enough to bring back the luster of the body, but since the car has apparently been repainted once there’s really no problem with doing it again. In fact, if the buyer chooses the same paint color, the prep work won’t be too bad and the car can probably be re-sprayed with only minor disassembly. If this was your car, would you repaint it? ## WANT ADS WANTED 1968-72 Chevrolet Nova Looking for a survivor rough around the edges original car for a sleeper project!! Contact WANTED 1968 Dodge Charger running or not Contact WANTED 1970 or 1071 Ford Torino squire wagon Looking for nice car ready to drive. Might consider rust free car to build. Contact WANTED 1969 Plymouth Roadrunner Looking for parts for this project. Especially seats Contact WANTED 1960-1965 Ford Ranchero Looking for period-correct cap or topper. Protect-O-Plate was the main brand, but open to any brand Contact ### Comments 1. art Old oil but looks clean? Radiator leaks? Water pump failing? How cheap can one get? Also, maybe spring$20 and find a window crank for the drivers door? Buyer are letting sellers get away with a lot these days. Car is otherwise nice looking but inspection vital based on this info…yikes. 22 • al i agree although this is a nice looking car i fear that its going to be an onion once you start unpeeling it . i think this one is better left to a true car rebuilder as its going to need a lot of work to become roadworthy,. anything mechanical thats sits still is not a good outcome. defintely not one i would jump at right away wihout some very close examination 1 • lyle zurflu Looks like a lot of work! All new rubber, lines flushed and replaced, paint job (all paint jobs require base and clear unless you use 1 stage paint), brake job, rust removal, etc 1 2. JOHN Member I’d just add a wheel/tire package and rive it! Almost too nice to mess with, and you are right, that interior is BRIGHT!!! 2 • JOHN Member Are those courtesy door lights original? Not a 57 expert by any means, but don’t remember seeing them before. Also, speaking of lights, the underhood look to be later GM, or is that design that old? • Joanne / Fred Alexander Door Lights are Not original – – – in all the 57 Chevys I’ve seen , appraised, bought /sold have never seen these – – • Fred Alexander Door Lights are Not original – – – in all the 57 Chevys I’ve seen , appraised, bought /sold have never seen these – – 3. Socaljoe So the car was 16 years old and already had a repaint when parked and I’m supposed to believe the miles are original? I call BS 34 • SusanOliver Yes, and what is this about clear coat? If it has been in storage since 1973, were we even using clear coat then? I think not. Besides, who wants a 57 when you can have a 56? 16 • ken tillyUK Member 11 • MrMustang I’d much rather have a 57 over a 56 but I’m a Mustang guy, what do I know about Chebys? 3 • Roger 58 Chev would be my choice. 2 3 4. Classic Steel I think its a sweet ride needing a run through on engine with new hoses, radiator to shop to boil out and flush and clean / or find chrome breather. I am aways a fan of no post tri fives👍👀 The ask is probably close on being a one owner and a good body to boot is rare in my book. My first car in late 78 was a 55 Chevy two door hardtop with a 327 340 horsepower, headers with caps, Holley carb, four speed with inline shifter That was jet black with buckets. The 12 bolt pushed the chrome reverses with caps to light up and spin to get traction 1/4 runs late nights in the country 🏁 5 5. Doc Needs a full refurbishment. Best part is the selling dealer cheaping it out will not meet reserve unless some buyer is that dumb to over pay. Be smarter to find one in the $30k-$50k value done 5 6. FordGuy1972 Member I find the poor state of the engine compartment to be surprising for such a claimed low-mileage car. That and the state of the exterior finish. I can only attribute these issues to either poor storage conditions or the low mileage claim is bogus. Like SusanOliver, I never heard of clear coat paint back in the early ’70s; clear coat didn’t come along until the late ’80s. The finish is a mess; maybe you can clean it up with good cutting compounds or fine sandpaper but you might be looking at a re-paint. The winning bidder will pay a quite a bit for this ’57 Chevy at the auction’s end. He/she had better be prepared to spend even more money to correct the finish, address mechanical issues, replace the tires and clean up under the hood. 12 • Chuck I’m also a bit skeptical about that mileage claim. I bought a brand new 1973 VW 412 sedan with a factory applied clear-coat paint job. I know that Porsche, Audi and Mercedes also had factory clear-coat then, maybe others did too. So, yeah. There was clear-coat in ’73. 1 7. 86_Vette_Convertible Have to agree on the missing window crank missing, why wouldn’t you replace it? The trunk script looks to be laying in the trunk, bent. How do you bend that taking it off and why was it taken off in the first place? Third item is what is that cable that looks to be cut off on the drivers door? There’s also surface rust where the seals contact on the trunk and doors. If the radiator leaks, why would you dump in stop leak instead of fixing the radiator and water pump if both need replacing and trying to sell the car for top $$? It’s a good looking car overall but still will take work and$$ to make it into a show car IMO. I suspect there will be more work and cost than many will think about, even things like original tires? Does that mean it needs to be trailered for now to it’s next home? Whether it’s worth the asking $$or not depends on the pockets of whoever is thinking about buying it. 6 • Bellingham Fred The missing window crank has reappeared in a later picture. That cut off cable seems to me to be the wiring for the after market courtesy lights. I looked at all the pix on eBay including the ones at the bottom from the dealership. That wiring is on both doors and it appears to be a short waiting to happen. 1 8. Del To many small things wrong for this amount of coin. Fix it up first. 7 9. Johnmloghry Member Do not drive this car any distance without first servicing/replacing water pump, radiator and all hoses lest you want to scorch the engine. Also make sure the brakes are working properly, This car should be shipped to new location before going through it attending all needed safe operating areas. Good luck to the new owner. God bless America 3 • Dickie F And I believe a 50s car needs a lot larger cooling system, when it arrives in 2019. A upgrade is required. 3 10. Johnmloghry Member Nice car but needs lots of attention to detail. It’s not a buy and drive car at this point. God bless America 2 11. Bob McK Member I would believe that the mileage is 104,883. That would make this a nice car. If it only has 4,883 miles on it, this car is rough. 6 12. skibum2 So many experts have no idea about the odometer do they…Oh well…and as for clear coat, I was using that when I painted cars in the early 70’s…..After owning over a hundred tri five chevys I have to say this is a nice one.. however I am done restoring cars as it has gotten too expensive for a old school mechanic…good luck to the new owner.. 3 13. jimmy the orphan That engine bay didn’t get to looking like that in less than 5k miles. This is a nice 57′ but why did it ever need to be repainted? Its not worth what’s been bid on it. I have enough tri5’s now. There’s to many sellers trying to hide to much so they can try to get to much. There’s still some of us old boomers around to say ” Hey wait a minute ” Later……………………JIMMY 2 14. TheotherScottie Over 100? 15. Car Nut Tacoma Lovely looking car! It’s awesome to see an original survivor. It may not be a show car, but so what? Cars like these were meant to be driven. Repaint it if you wish. But as long as everything works like it should, drive it! Enjoy it! That’s why I’m not a fan of the 30k price. I like to be able to have someone inspect the car before I buy. 1 16. Jay E. The speedos are so easy to unhook, the mileage could be anything. I’m with Fordguy. Why would it need a repaint at 4K? Even iof it needed a repaint, why was the inside of the trunk painted, and why has that clearcoat “faded” Seems mis represented to me. I’d far prefer a 57 over a 56, and this “no post” is the best version. Don’t think it will go for much more, although it is awfully nice. Repainting it will be expensive and replacing every 60 year old bushing, weatherstrip and seal is tedious. 4 • JOHN Member We used to disconnect the speedometer cable when we drove the family car… even my older sister’s knew how! 1 • shanahan My brother’s friend made old cars feel young. For 20. he’s knock off as many miles as you wanted. 4k, no way. 1 17. JET That’s exactly what a car should look like after sitting for forty some years. 18. Bob Mulhall This car looks like a well maintained 105,000 mi car …..A total repaint is in order and pull the drivetrain and start over..20,000 + 20,000 restoration would = a 40,000 Chevy,,just my thoughts….. 1 19. moosie BOGUS CAR, 20. Al “The Brake master cyclinder was full of crystalized fluid, which has been cleaned out and new fluid added. The brakes are now working.” that should read the brakes are working for now !!!!! that cars going to need some serious looking at before it can be driven on the road 21. Joanne / Fred Alexander Mileage claim doubtful unless documented. regardless you’ll pour another 15K – 20K into this car to meet its potential as a low miler one owner. It is a nice vehicle but the Tredalvac brake booster most likely needs rebuild – — “Cleaned” the master cylinder = = that’ll have to go – – – dents on top of radiator from a mechanic pounding it eith his fist to pur nuts and bolts on when servicing or repairing?? Radiator, heater core new tires window crank (good luck finding a good used one – – – or NOS that matches, Speedo cable needs lubricating – – -this I’d do before ever going on the road – – – I apprenticed on these plus my 57 Pontiac Laurentian Sport Coupe (2Dr HT) that I had owned for 40 years — in Canada the Pontiacs were a Chevy a\in Pontiac clothes. Anyway trust this ole mechanic – -there’ll be lots to do and$$\$ to spend over the purchase price – -but if you have deep pockets go for it (if it can be documented ) Niff said for now. 2 22. Norman Wrensch Of course the oil is clean, after sitting all those years the crap settled to the bottom of the pan. And looking at the engine compartment it looks like 104K. Which on these old girls that is engine rebuild time. Before the mid 80’s- 90’s you would be dam lucky if you made it to 100k without rebuilding an engine. My first 57 only had 80K when I bought it and it needed rebuilding. 1 23. TimM Another low mileage car that needs everything!!! I say Bull to that!!! Why repaint a car with such low mileage on it!!! Was it sitting outside for the passed 50 years!!! Why not fix everything and sell a good running driving car!!! 1	2021-07-23 19:42:13	{"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": 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": 0.19006261229515076, "perplexity": 3927.8639441951987}, "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/1627046150000.59/warc/CC-MAIN-20210723175111-20210723205111-00714.warc.gz"}
https://web2.0calc.com/questions/halp-me-asap	+0 # HALP ME ASAP!!! 0 51 2 I need help ASAP!!! Assuming that $y\neq 1/2, $simplify the expression $\dfrac{12y^3-6y^2}{2y-1}. $ Aug 6, 2020 #1 +1035 +5 Tried it already? Now, here is how I did it: What can you do to 12y^3-6y^2 to make it easier to divide? (cough factoring out a 6? cough) So, after I factored out a 6, I got 6(2y^3-y^2)/(2y-1). This was easy to divide, and I got 6y^2, which is 6y^2 OR If you were smart enough to see if right after factoring, you could multiply the bottom by 6. This is 12y-6. Now, the difference between the top and the bottom? y^2. So, you still end up with 6y^2 :) Aug 6, 2020 edited by ilorty Aug 6, 2020 #2 +21953 +2 Hint: 12y3 - 6y2 = 6y2(2y - 1) Aug 6, 2020	2020-09-25 01:01:08	{"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": 0.9712105989456177, "perplexity": 4408.443544946384}, "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/1600400221382.33/warc/CC-MAIN-20200924230319-20200925020319-00127.warc.gz"}
https://upcommons.upc.edu/browse?authority=aa057981-5119-4cff-80a6-73081eb441fc;orcid:0000-0003-1572-8486;drac:179542;gauss:1001857&type=author	Now showing items 1-20 of 26 • A geometric approach to dense Cayley digraphs of finite Abelian groups (Elsevier, 2016) Conference report Open Access We give a method for constructing infinite families of dense (or eventually likely dense) Cayley digraphs of finite Abelian groups. The diameter of the digraphs is obtained by means of the related {\em minimum distance ... • A geometric approach to dense Cayley digraphs of finite Abelian groups (2016) Article Open Access We give a method for constructing infinite families of dense (or eventually likely dense) Cayley digraphs of finite Abelian groups. The diameter of the digraphs is obtained by means of the related minimum distance diagrams. ... • A preliminary model for optimal load distribution in heterogeneous smart environments (2019) Conference report Restricted access - publisher's policy Smart cities are becoming popular and, with them, a plethora of resources is emerging turning into a massive concentration of computing devices. In such environments, the deployment of a smart resources management system ... • Abelian Cayley digraphs with asymptotically large order for any given degree (2016-04-29) Article Open Access Abelian Cayley digraphs can be constructed by using a generalization to Z(n) of the concept of congruence in Z. Here we use this approach to present a family of such digraphs, which, for every fixed value of the degree, ... • An algorithm to compute the primitive elements of an embedding dimension three numerical semigroups (2014) Article Open Access We give an algorithm to compute the set of primitive elements for an embedding dimension three numerical semigroups. We show how we use this procedure in the study of the construction of L-shapes and the tame degree of the ... • Aprenentatge de càlcul (Edicions UPC, 2002) Book Conté: 1. Successions, continuïtat i derivació. 2. Integració i sèries. • Clasificación de 3-semigrupos numéricos mediante L-formas Conference report Restricted access - publisher's policy Un semigrupo num erico generado por tres elementos tiene asociadas una o dos teselaciones peri odicas del plano generadas por una baldosa en forma de L. Se conocen algunas propiedades combinatorias del semigrupo en t ... • Classification of numerical 3-semigroups by means of L-shapes (2014-06-01) Article Open Access We recall L-shapes, which are minimal distance diagrams, related to weighted 2-Cayley digraphs, and we give the number and the relation between minimal distance diagrams related to the same digraph. On the other hand, we ... • Computing denumerants in numerical 3-semigroups (2018) Article Open Access As far as we know, usual computer algebra packages can not compute denumerants for almost medium (about a hundred digits) or almost medium-large (about a thousand digits) input data in a reasonably time cost on an ordinary ... • Control – 1A de Matemàtica Discreta [Curs 2019-2020] - Q2 (Universitat Politècnica de Catalunya, 2020-03-30) Exam • Control – 1B de Matemàtica Discreta [Curs 2019-2020] - Q2 (Universitat Politècnica de Catalunya, 2020-03-30) Exam • Denumerants of 3-numerical semigroups (2014) Article Open Access Denumerants of numerical semigroups are known to be difficult to obtain, even with small embedding dimension of the semigroups. In this work we give some results on denumerants of 3-semigroups S=<a,b,c>S=<a,b,c>. Closed ... • Examen de Teoria de Grafs - MATD [Curs 20202021] - Q2 (Universitat Politècnica de Catalunya, 2021-03-26) Exam • Factorization and catenary degree in 3-generated numerical semigroups (2009-08-01) Article Restricted access - publisher's policy Given a numerical semigroup S(A), generated by A = {a,b,N} ⊂ N with 0 < a < b < N and gcd(a,b,N) = 1, we give a parameterization of the set F(m;A) = {(x, y, z) ∈ $N^3$ \| xa + yb + zN = m} for any m ∈ S(A). We also give the ... • Familias infinitas de digrafos de Cayley de grado 2 óptimos sobre grupos abelianos finitos Conference report Restricted access - publisher's policy Sea GN un grupo abeliano finito de orden N. Para cada conjunto de generadores f, g = GN, consideremos el digrafo de Cayley Cay(GN, {f, g}). Seg´un sea GN c´ıclico o no c´ıclico, podemos obtener un di´ametro ´optimo ... • MATEMÀTICA DISCRETA (Examen 1r quadrimestre) [Curs 2019-2020] (Universitat Politècnica de Catalunya, 2019-11-06) Exam • MATEMÀTICA DISCRETA (Examen final - 1r quadrimestre) [Curs 2019-2020] (Universitat Politècnica de Catalunya, 2020-01-13) Exam • MATEMÀTICA DISCRETA (Examen final - 1r quadrimestre) [Curs 2020-2021] (Universitat Politècnica de Catalunya, 2021-01-15) Exam	2021-04-19 10:20:03	{"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": 0.83022141456604, "perplexity": 7965.4660012444165}, "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-2021-17/segments/1618038879305.68/warc/CC-MAIN-20210419080654-20210419110654-00073.warc.gz"}
https://www.gamedev.net/forums/topic/681377-engine-design-v03-classes-and-systems-thoughts/	# Engine design v0.3, classes and systems. thoughts? This topic is 763 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic. ## Recommended Posts Hi all, Last half year I've been learning D3D11 and I've now decided not to refactor my existing D3D9 engine, but instead develop a new one from scratch (reusing modules/ components where possible). But before I run off and start creating classes, I've made a high over design as a guideline, with the systems and classes I'd like to use. I really like to hear your thoughts on this approach and design. Any input is appreciated, better now then further in the development process. Side note; the design is a guideline and will be a 'living document' as I progress through development. ? Edited by cozzie ##### Share on other sites It's a pretty picture, but at the level-of-detail you've shown it looks basically like any other generic engine high-level architecture. ##### Share on other sites I'm not going to point out the problems in your design but I encourage you to search here on the forums about "game engine architecture". It is also recommended that you read Jason Gregory's Game Engine Architecture book to understand the details of each game engine system. Roughly speaking, for your first game engine I recommend a source tree that looks like this: External (Dependencies) imgui PhysX ... Tools ModelConverter ModelEditor ... Engine Core Allocation File Math Platform Win32 Linux iOS Standard Template ... Rendering GpuDevice.h GpuContext.h OpenGL OpenGL_Device.cpp OpenGL_Context.cpp D3D11 D3D11_Device.cpp D3D11_Context.cpp ... Animation ... Physics ... Audio ... Game Object ... Game_1 Game_2 Game_3 ... Each module (e.g. Core, Rendering, etc.) being a static library that gets linked into the game. If you're really organized then you might consider using UML's Class Diagrams instead of paint sketches to model the relationship between each system. Edited by Irlan Robson ##### Share on other sites Agreed, drop the useless C in front of every class. You will just kill that key that much sooner, what did that key ever do to you? Plus, every decent editor has intellisense these days. Forget setters and getters, I prefer my code to read like English. class Window { public: // ... // Why do you need Get/Set, it's pretty explicit this way: void Title(const std::string& text); std::string Title() const; }; ##### Share on other sites Thanks for the valuable input; - as for the prefixes, this is and will always be a matter of taste. I'll take it in consideration :wink: @Josh: thanks, this is a good thing, because I've made it myself based on own insights and the d3d9 engine I've created before this. Regarding high-level, I fully agree; maybe I will make a separate dependencies overview, because combining both will definately not make it better readable. @Irlan: thanks, this helps in defining the systems and what will belong where. I'll definately go for LIB's per system. This also helps readability of the projects further on. I'll also have to create a smooth build proces, because there will never be a moment that a system/ LIB is final :) I'll think about the UML's, I did this once before, when I made a game with my d3d9 engine, this helped in that specific case. @Mike: I'm not sure that I can read your example better then a Set/ Get function, but I understand the point, maybe it's a matter of getting used too. ##### Share on other sites Separating out classes based on API like D3dSkybox and D3dLight is something I'd avoid. For example what does D3dLight have that CLight doesn't? It's a structure that has a position+/orientation, colour, type etc. In terms of interfacing with D3D, all you'll be doing is setting some constants or other buffer type - that can be abstracted efficiently at a much lower level. Abstracting buffers and entire blobs of data (buffer + state) makes porting to other platforms much easier too (and fits well with modern rendering APIs). T ##### Share on other sites Thanks, that's a good thing to think about. For some classes for me this sounds easier then others. For example, where would you store a mesh's vtx buffer? In my case it's the Cd3dMesh class, because CMesh is API/ platform independent and just an IO/ data thing. version 0.2: ##### Share on other sites Why are you making platform dependent lights, skyboxes, and etc? What is the different between a model drawn in directx and a model draw in vulkan? There isn't one. The whole point of a model is to hold vertex buffers and index buffers, so just make platform specific vertex and index buffers. The same with everything else under CSceneManager. But in reality, you will spend years if you keep trying to make the perfect uml diagram for an engine. You don't know what you need until you need it. 1. 1 2. 2 3. 3 Rutin 18 4. 4 JoeJ 14 5. 5 • 14 • 10 • 23 • 9 • 32 • ### Forum Statistics • Total Topics 632630 • Total Posts 3007525 • ### Who's Online (See full list) There are no registered users currently online ×	2018-09-24 05:43:38	{"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": 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": 0.2096647471189499, "perplexity": 3565.5007047992}, "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/1537267160145.76/warc/CC-MAIN-20180924050917-20180924071317-00199.warc.gz"}
https://ftp.aimsciences.org/article/doi/10.3934/dcds.2005.12.115	Advanced Search Article Contents Article Contents # A one-parameter family of analytic Markov maps with an intermittency transition • In this paper we introduce and study a one-parameter family of piecewise analytic interval maps having the tent map and the Farey map as extrema. Among other things, we construct a Hilbert space of analytic functions left invariant by the Perron-Frobenius operator of all these maps and study the transition between discrete and continuous spectrum when approaching the intermittent situation. Mathematics Subject Classification: 58F20, 58F25, 11F72, 11M26. Citation: ## Article Metrics HTML views() PDF downloads(62) Cited by(0) ## Other Articles By Authors • on this site • on Google Scholar ### Catalog / DownLoad: Full-Size Img PowerPoint	2023-03-26 08:54:02	{"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": 0, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.6767551898956299, "perplexity": 2131.0431565419485}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "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-2023-14/segments/1679296945440.67/warc/CC-MAIN-20230326075911-20230326105911-00727.warc.gz"}
http://cms.math.ca/cjm/kw/Salem%20numbers	Salem Numbers and Pisot Numbers via Interlacing We present a general construction of Salem numbers via rational functions whose zeros and poles mostly lie on the unit circle and satisfy an interlacing condition. This extends and unifies earlier work. We then consider the obvious'' limit points of the set of Salem numbers produced by our theorems and show that these are all Pisot numbers, in support of a conjecture of Boyd. We then show that all Pisot numbers arise in this way. Combining this with a theorem of Boyd, we produce all Salem numbers via an interlacing construction. Keywords:Salem numbers, Pisot numbersCategory:11R06	2015-07-06 13:36:16	{"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": 0.6501356363296509, "perplexity": 569.320382593138}, "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-2015-27/segments/1435375098464.55/warc/CC-MAIN-20150627031818-00096-ip-10-179-60-89.ec2.internal.warc.gz"}
https://socratic.org/questions/56e085237c014915a104e55d	# Question 4e55d Mar 10, 2016 ${\text{270 ppm Al}}^{3 +}$ #### Explanation: The first thing to do here is convert your values to liters and grams, respectively. This will make the calculations a lot easier as we go. So, to convert gallons to liters and pounds to kilograms, use the following conversion factors $\text{1 gal " ~~ " 3.7854 L"" }$ and $\text{ " "1 kg " ~~ " 2.2046 lbs}$ To go from kilograms to Grams, use the conversion factor $\text{1 kg" = 10^3"g}$ So, you will have 660 color(red)(cancel(color(black)("gal"))) * "3.7854 L"/(1color(red)(cancel(color(black)("gal")))) = "2498.4 L" 9.4color(red)(cancel(color(black)("lbs"))) * (1color(red)(cancel(color(black)("kg"))))/(2.2046color(red)(cancel(color(black)("lbs")))) * (10^3"g")/(1color(red)(cancel(color(black)("kg")))) = "4263.8 g" Now, the problem wants you to find the concentration of aluminium cations, ${\text{Al}}^{3 +}$, expressed in parts per million, ppm. In order to find the concentration of a solute in ppm, you must essentially figure out how many grams of that solute you get in ${10}^{6}$ grams of solvent. $\textcolor{b l u e}{\| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \text{ppm" = "grams of solute"/"grams of solvent} \times {10}^{6} \textcolor{w h i t e}{\frac{a}{a}} \|}}}$ So, if you have $\text{1 g}$ of solute in ${10}^{6}$ grams of solvent, you have a $\text{1 ppm}$ concentration. Now, aluminium sulfate, "Al"_color(red)(2)("SO"_4)_3, contains $\textcolor{red}{2}$ aluminium cations. In order to find how much aluminium you get per $\text{100 g}$ of aluminium sulfate, calculate the compound's percent composition. To do that, use the molar mass of aluminium and the molar mass of aluminium sulfate ${\text{For Al: " " " " " " "M_M = "26.98 g mol}}^{- 1}$ ${\text{For Al"_2("SO"_4)_3:" " M_M = "342.15 g mol}}^{- 1}$ So, the percent composition of aluminium sulfate is (color(red)(2) xx 26.98 color(red)(cancel(color(black)("g mol"^(-1)))))/(342.15color(red)(cancel(color(black)("g mol"^(-1))))) xx 100 = "15.77% Al" This means that $\text{100 g}$ of aluminium sulfate will contain $\text{15.77 g}$ of aluminium, i.e. aluminium cations. In your case, the sample of aluminium sulfate will contain 4263.8color(red)(cancel(color(black)("g Al"_2("SO"_4)_3))) * overbrace("15.77 g Al"^(3+)/(100color(red)(cancel(color(black)("g Al"_2("SO"_4)_3)))))^(color(purple)("15.77% Al")) = "672.4 g Al"^(3+) To get the mass of solvent, which in your case is water, use water's density. If no information is provided, you can assume it to be equal to ${\text{1.0 g mL}}^{- 1}$. Remember that $\text{1 L" = 10^3"mL}$, so 2498.4color(red)(cancel(color(black)("L"))) * (10^3color(red)(cancel(color(black)("mL"))))/(1color(red)(cancel(color(black)("L")))) * overbrace("1 g"/(1color(red)(cancel(color(black)("mL")))))^(color(purple)("water's density")) = 2.4984 * 10^6"g" So, you know how many grams of aluminium cations you have and how many grams of water you have, which means that you can now find the concentration in ppm $\text{ppm" = (672.4 color(red)(cancel(color(black)("g"))))/(2.4984 * color(blue)(cancel(color(black)(10^6)))color(red)(cancel(color(black)("g")))) * color(blue)(cancel(color(black)(10^6))) ="269.13 ppm}$ Rounded to two sig figs, the answer will be "ppm Al"^(3+) = color(green)(\|bar(ul(color(white)(a/a)"270 ppm"color(white)(a/a)\|)))#	2022-01-21 13:55:46	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 26, "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": 0.6592889428138733, "perplexity": 3933.059237817788}, "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/1642320303385.49/warc/CC-MAIN-20220121131830-20220121161830-00630.warc.gz"}
https://projecteuclid.org/euclid.ijm/1403534491	## Illinois Journal of Mathematics ### Analytic torsion on manifolds under locally compact group actions Guangxiang Su #### Abstract For a complete Riemannian manifold without boundary which a unimodular locally compact group properly cocompact acts on it, under some conditions, we define and study the analytic torsion on it by using the $G$-trace defined in ($L^{2}$-index formula for proper cocompact group actions, preprint). For a fiber bundle $\pi:M\to B$, if there is a unimodular locally compact group acts fiberwisely properly and cocompact on it, we define the torsion form for it, and show that the zero degree part of the torsion form is the analytic torsion. This can be viewed as an extension of the $L^{2}$-analytic torsion. #### Article information Source Illinois J. Math., Volume 57, Number 1 (2013), 171-193. Dates First available in Project Euclid: 23 June 2014 https://projecteuclid.org/euclid.ijm/1403534491 Digital Object Identifier doi:10.1215/ijm/1403534491 Mathematical Reviews number (MathSciNet) MR3224566 Zentralblatt MATH identifier 1300.58011 Subjects Primary: 58J52: Determinants and determinant bundles, analytic torsion #### Citation Su, Guangxiang. Analytic torsion on manifolds under locally compact group actions. Illinois J. Math. 57 (2013), no. 1, 171--193. doi:10.1215/ijm/1403534491. https://projecteuclid.org/euclid.ijm/1403534491 #### References • A. F. Atiyah, Elliptic operators, discrete groups and von Neumann algebras, Astérisque 32 (1976), 43–72. • N. Berline, E. Getzler and M. Vergne, Heat kernels and Dirac operators, Springer, Berlin, 2003. • J. M. Bismut and J. Lott, Flat vector bundles, direct images and higher real analytic torsion, J. Amer. Math. Soc. 8 (1995), 291–363. • M. Braverman, A. Carey, M. Farber and V. Mathai, $L^{2}$ torsion without the determinant class condition and extended $L^{2}$ cohomology, Commun. Contemp. Math. 7 (2005), 421–462. • D. Burghelea, L. Friedlander, T. Kappeler and P. McDonald, Analytic and Reidemeister torsion for representations in finite type Hilbert modules, Geom. Funct. Anal. 6 (1996), 751–859. • J. M. Bismut and W. Zhang, An extension of a theorem by Cheeger and Müller, Astérisque 205 (1992). • J. Cheeger, Analytic torsion and the heat equation, Ann. of Math. (2) 109 (1979), 259–332. • A. Carey and V. Mathai, $L^{2}$-torsion invariants, J. Funct. Anal. 110 (1992), 377–409. • G. Dong and M. Rothenberg, Analytic torsion forms for noncompact fiber bundles, MPIM preprint, 1997. • J. Heitsch and C. Lazarov, Spectral asymptotics of foliated manifolds, Illinois J. Math. 38 (1994), 653–678. • J. Heitsch and C. Lazarov, Riemann–Roch–Grothendieck and torsion for foliations, J. Geom. Anal. 12 (2002), 437–468. • J. Lott, Heat kernels on covering spaces andtopological invariants, J. Differential Geom. 35 (1992), 471–510. • V. Mathai, $L^{2}$-analytic torsion, J. Funct. Anal. 107 (1992), 369–386. • J. Milnor, Whitehead torsion, Bull. Amer. Math. Soc. (N.S.) 72 (1996), 358–426. • W. Müller, Analytic torsion and the R-torsion of Riemannian manifolds, Adv. Math. 28 (1978), 233–305. • W. Müller, Analytic torsion and the R-torsion for unimodular representations, J. Amer. Math. Soc. 6 (1993), 721–753. • D. Quillen, Determinants of Cauchy–Riemann operators over a Riemann surface, Funct. Anal. Appl. 19 (1985), 31–34. • D. B. Ray and I. M. Singer, $R$-torsion and the Laplacian on Riemannian manifolds, Adv. Math. 7 (1971), 145–210. • H. Wang, $L^{2}$-index formula for proper cocompact group actions, preprint, \arxivurlarXiv:1106.4542v3. • E. Witten, Supersymmetry and Morse theory, J. Differential Geom. 17 (1982), 661–692. • W. Zhang, An extended Cheeger–Müller theorem for covering spaces, Topology 44 (2005), 1093–1131.	2019-10-18 03:33:08	{"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": 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": 0.705195963382721, "perplexity": 1902.5813170153328}, "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-2019-43/segments/1570986677884.28/warc/CC-MAIN-20191018032611-20191018060111-00269.warc.gz"}
https://acroz.dev/2019/12/05/scala-implicit-classes/	# Implicit Classes in Scala Scala implicit classes allow you to augment the behaviour of existing objects with new functionality. This pattern, sometimes called “Pimp my library”, provides a useful method to implement expressive Scala code. ## Syntax To create an implicit class, add the implicit keyword before the class definition. Note that implicit classes have to be constructed inside other traits, classes or objects: object Implicits { implicit class DoubleListOps(values: List[Double]) { def mean: Double = values.sum / values.length } } When this implicit class is in scope, the methods it defines will can be called as if they were methods on values of the type it wraps. For example, in the example above, we can now call .mean on any List[Float]: scala> import Implicits._ import Implicits._ scala> val numbers = List(10.2, 12.1, 11.6) numbers: List[Double] = List(10.2, 12.1, 11.6) scala> numbers.mean res0: Double = 11.299999999999999 Implicit classes only work with one normal argument, but can take additional implicit arguments. For example, we can make the above ‘mean’ functionality generic to all numeric types: object Implicits { implicit class NumericListOps[A](values: List[A])( implicit num: Numeric[A] ) { def mean: Double = num.toDouble(values.sum) / values.length } } This can be used with any number type, for example with Ints: scala> import Implicits._ import Implicits._ scala> List(1, 2, 3).mean res0: Double = 2.0 ## Notes This pattern is sometimes called “Pimp my library” as it allows you to extend the functionality of objects implemented in libraries you have no control over! In fact, this is very similar to how Scala extends the String type from Java with additional functionality. I hope you have seen that implicit classes provide a useful tool for writing expressive and concise code in Scala. For more information, have a look at the scala docs.	2021-03-06 02:18:08	{"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": 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": 0.2257891744375229, "perplexity": 5533.793480685236}, "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-2021-10/segments/1614178374217.78/warc/CC-MAIN-20210306004859-20210306034859-00130.warc.gz"}
https://cracku.in/23-if-a-62n-35n-1-where-n-123-and-b-35n-1-where-n-123-x-cat-2018-slot-2-quantitative-aptitude	Question 23 # If A = {$$6^{2n} -35n - 1$$}, where $$n$$ = 1,2,3,... and B = {35($$n$$-1)}, where $$n$$ = 1,2,3,... then which of the following is true? Solution If we carefully observe set A, then we find that $$6^{2n} -35n - 1$$ is divisible by 35. So, set A contains multiples of 35. However, not all the multiples of 35 are there in set A, for different values of $$n$$. For $$n = 1$$, the value is 0, for $$n = 2$$, the value is 1225 which is the 35th multiple of 3. If we observe set B, it consists of all the multiples of 35 including 0. So, we can say that every member of set A will be in B while every member of set B will not necessarily be in set A. Hence, option A is the correct answer.	2022-08-19 08:44:07	{"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": 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": 0.8527171611785889, "perplexity": 182.68105832238874}, "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/1659882573630.12/warc/CC-MAIN-20220819070211-20220819100211-00321.warc.gz"}
http://www.maths.usyd.edu.au/s/scnitm/jormerod-StatisticsSeminar-Bondell	SMS scnews item created by John Ormerod at Fri 10 May 2013 1327 Type: Seminar Distribution: World Expiry: 18 May 2013 Calendar1: 17 May 2013 1400-1500 CalLoc1: Carslaw 373 Auth: [email protected] (assumed) Statistics Seminar: Bondell -- Consistent high-dimensional Bayesian variable selection via penalized credible regions For high-dimensional data, selection of predictors for regression is a challenging problem. Methods such as sure screening, forward selection, or penalization are commonly used. Instead, Bayesian variable selection methods place prior distributions over model space, along with priors on the parameters, or equivalently, a mixture prior with mass at zero for the parameters in the full model. Since exhaustive enumeration is not feasible, posterior model probabilities are often obtained via long MCMC runs. The chosen model can depend heavily on various choices for priors and also posterior thresholds. Alternatively, we propose a conjugate prior only on the full model parameters and to use sparse solutions within posterior credible regions to perform selection. These posterior credible regions often have closed form representations, and it is shown that these sparse solutions can be computed via existing algorithms. The approach is shown to outperform common methods in the high-dimensional setting, particularly under correlation. By searching for a sparse solution within a joint credible region, consistent model selection is established. Furthermore, it is shown that the simple use of marginal credible intervals can give consistent selection up to the case where the dimension grows exponentially in the sample size. If you are registered you may mark the scnews item as read. School members may try to .	2017-10-17 22:18:45	{"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": 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": 0.5264086127281189, "perplexity": 5085.218089432}, "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-2017-43/segments/1508187822513.17/warc/CC-MAIN-20171017215800-20171017235800-00158.warc.gz"}
https://docs.poliastro.space/en/stable/autoapi/poliastro/twobody/thrust/change_ecc_inc/index.html	# poliastro.twobody.thrust.change_ecc_inc¶ ## Module Contents¶ ### Functions¶ change_ecc_inc(ss_0, ecc_f, inc_f, f) Simultaneous eccentricity and inclination changes. Guidance law from the model. Thrust is aligned with an inertially fixed direction perpendicular to the semimajor axis of the orbit. poliastro.twobody.thrust.change_ecc_inc.change_ecc_inc(ss_0, ecc_f, inc_f, f) Simultaneous eccentricity and inclination changes. Guidance law from the model. Thrust is aligned with an inertially fixed direction perpendicular to the semimajor axis of the orbit. Parameters • ss_0 () – Initial orbit, containing all the information. • ecc_f (float) – Final eccentricity. • inc_f () – Final inclination. • f () – Magnitude of constant acceleration. Returns a_d, delta_V, t_f Return type tuple (function, , ) References • Pollard, J. E. “Simplified Analysis of Low-Thrust Orbital Maneuvers”, 2000.	2022-08-14 11:59:27	{"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": 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": 0.6284679770469666, "perplexity": 11985.568039642274}, "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/1659882572033.91/warc/CC-MAIN-20220814113403-20220814143403-00384.warc.gz"}
https://cs.stackexchange.com/tags/greedy-algorithms/new	# Tag Info 3 The formalized problem here is selecting the minimum number of points such that for each temperature interval $\ell_i\in L$ we have at least one point that covers it. Let each interval $\ell_i$ be represented by $(c_i, h_i)$ Order all $\ell_i\in L$ by their $h_i$. While there are still items that need fridges. Buy a fridge and set it to $h_1$. For every ... 0 What you describe is just an approximate algorithm for the Job Shop problem (which is also NP-complete, reduced from Partition -- split a set of integers in two so that both add to the same value, the problem you describe) that can be shown has an approximation ratio of 2. See for example this set of slides for a proof and hints at refinements that get ... 1 As Jeff Erickson says in his book, "greedy algorithms never work". (Except in the --rare-- cases where they do, and they offer simple, efficient approximations to many NP-hard search problems, see for instance Kun's "When Greedy Algorithms are Good Enough: Submodularity and the (1 – 1/e)-Approximation", check also Krause and Golovin's survey for more in-... 0 I'd start with the shortest temperature range, stash everything that fits in it into a refrigerator, rinse and repeat. But a temperature range may overlap several that don't overlap among themselves, among those that do overlap search for a temperature that hits most ranges. This heuristic sounds like it should give a good solution, but I'd first look if ... 2 Yes, this is NP-hard. Since neither the $a_i$ nor the $d_i$ depend on the solution, the problem is equivalent to the problem of minimizing the sum of the completion times of the requests, which is known in the scheduling literature as "$1\|r_i\|\sum C_i$" and is NP-hard. Reference: J.K. Lenstra, A.H.G. Rinnooy Kan, and P. Brucker. Complexity of machine ... 0 It doesn't matter in which order we place the guards, so we can assume that we place the guards in such an order that each guard covered the first artwork from the right that isn't covered yet (since there must be a guard covering that artwork). The guard can be placed anywhere from 5m to the left of the artwork to 5 to the right. Wherever we place him, ... 0 Let us prove your greedy algorithm is optimal in the sense of the least number of guards returned by simple reasoning. Consider all "closest artwork"s found by your greedy algorithm. The algorithm ensures that each neighboring pair of them is over 10 meters apart. So any two of them are over 10 meters apart, which means one guard can monitor at most one of ... 1 You can achieve this per induction over the position of the last artwork. Note that in the optimal strategy the guard must be put 5 meter ahead of the left most artwork and not exactly at it. In the induction step you have to consider an additional artwork and distinct two cases, whether it is covered by the last fixed guard or not. If it is, you do not ... 2 Brooks' theorem states that every connected graph $G$ with maximum degree $\Delta$ can be colored (in linear time) using at most $\Delta + 1$ colors. In fact, the graphs that require $\Delta + 1$ colors are precisely complete graphs and odd cycles. You state that we have a connected graph $G$ with an odd number of vertices and we want to color $G$ with $k$ ... Top 50 recent answers are included	2020-02-18 20:43:14	{"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": 0.750937819480896, "perplexity": 442.1386648069176}, "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/1581875143805.13/warc/CC-MAIN-20200218180919-20200218210919-00395.warc.gz"}
https://mathoverflow.net/questions/265560/line-bundles-and-cyclic-covers-of-curves	# Line bundles and Cyclic Covers of Curves Let $X \to Y$ be a cyclic etale cover of smooth projective geometrically connected curves over some field $k$. Then the map is classified by an element of the cohomology group $H^1_{et}(Y_{k_s}, \mu_n)$; in other words the data of the covering is equivalent to giving a line bundle on $Y$ together with a trivialization of its $n$-th power. It follows that the induced map on Picard schemes given by pullback is not injective. My question is: what can be said about the kernel? I am especially interested in the special case of a degree $2$ cover; i.e are there are any other elements in the kernel besides the trivial bundle and the bundle classified by the covering. This one is given explicitly by pushing forward the structure sheaf on $X$ and modding out by the structure sheaf on $Y$. Theorem. Let $X \to Y$ be an étale Galois cover with group $G$ of proper geometrically integral schemes over any field $k$. Then we have an exact sequence $$0 \to \operatorname{Hom}(G,k^\times) \to \operatorname{Pic}(Y) \to \operatorname{Pic}(X)^G.$$ In particular, the kernel has size at most $n = \|G^{\operatorname{ab}}\|$, with equality if and only if $n$ is invertible in $k$ and $\mu_r \subseteq k$, where $r$ is the exponent of $G^{\operatorname{ab}}$. Proof. An étale Galois cover with group $G$ is the same thing as a $G$-torsor, and we have a Hochschild–Serre spectral sequence (see e.g. Milne's Étale cohomology notes, Thm 14.9) $$E_2^{pq} = H^p(G,H^q(X,\mathbb G_m)) \Rightarrow H^{p+q}(Y,\mathbb G_m).$$ The exact sequence of low degree terms is $$0 \to H^1(G,\mathbb G_m(X)) \to H^1(Y,\mathbb G_m) \to H^1(X,\mathbb G_m)^G \to H^2(G,\mathbb G_m(X)) \to \ldots .$$ Since $X$ is proper and geometrically integral, the global sections of $\mathcal O_X$ are just the constants $k$, hence the global sections of $\mathbb G_m$ are just $k^\times$. This clearly has the trivial $G$-action, so $$H^1(G,\mathbb G_m(X)) = \operatorname{Hom}(G,k^\times).$$ This proves the first statement. The second statement follows since $$\operatorname{Hom}(G,k^\times) = \operatorname{Hom}(G^{\operatorname{ab}},k^\times),$$ and for any finite abelian group $G$ there is a noncanonical isomorphism $G^{(p')} \cong \operatorname{Hom}(G,\bar k^\times)$, where $(-)^{(p')}$ denotes the prime to $p$-part if $\operatorname{char} k = p > 0$ (and the entire group if $\operatorname{char} k = 0$). Since the group generated by the images of homomorphisms $G \to \bar k^\times$ is the subgroup $\mu_r$ for $r$ the exponent of $G$, we conclude that they are all realised over $k$ if and only if $\mu_r \subseteq k$. $\square$ Let me give an answer when $\mathrm{char} \, k=0$. In this situation the double cover $f \colon X \to Y$ is defined by a line bundle $\mathcal{L}$ such that $\mathcal{L}^{\otimes 2} = \mathcal{O}_Y$ and the trace map provides a splitting $$f _* \mathcal{O}_X = \mathcal{O}_Y \oplus \mathcal{L}^{-1}.$$ Assume now that $\mathcal{M}$ belongs to the kernel of $$f^* \colon \mathrm{Pic} \, Y \to \mathrm{Pic} \, X.$$ Then $f^* \mathcal{M} = \mathcal{O}_X$ so, by applying the functor $f_$ and the projection formula, we obtain $$f_ \mathcal{O}_X = f_* f^* \mathcal{M} = \mathcal{M} \otimes f_* \mathcal{O}_X = \mathcal{M} \oplus (\mathcal{M} \otimes \mathcal{L}^{-1}).$$ By the Krull-Schmidt theorem the decomposition of a vector bundle in a direct sum of indecomposable ones is unique up to permutation of the summands, so we get either $\mathcal{M} = \mathcal{O}_Y$ or $\mathcal{M}=\mathcal{L}$. Summing up, $\ker \, f^$ is the subgroup of order $2$ generated by $\mathcal{L}$. Exactly the same argument shows that if the étale cover is cyclic of degree $n$, then $\ker f^$ is cyclic of the same order.	2021-04-10 15:10:49	{"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": 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": 0.9817108511924744, "perplexity": 47.67542896325993}, "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-2021-17/segments/1618038057142.4/warc/CC-MAIN-20210410134715-20210410164715-00347.warc.gz"}
https://www.maths.unsw.edu.au/seminars/fullarchive?term_node_tid_depth_3=266	# Full Seminar Archive Our regular seminar program covers a broad range of topics from applied mathematics, pure mathematics and statistics. All staff and students are welcome. This page has a complete list of past seminars and a list restricted by year can be accessed via the left-hand menu. Jianya Liu - Shandong University The behavior of the Mobius function is central in the theory of prime numbers. A surprising connection with the theory of dynamical systems was discovered in 2010 by P. Sarnak, who formulated the... Adam Harper - University of Warwick Random multiplicative functions $f(n)$ are a well studied random model for deterministic multiplicative functions like Dirichlet characters or the Mobius function. Arguably the first question ever... Jacob Tsimerman - University of Toronto (joint w/ Arul Shankar) We discuss a new method to bound 5-torsion in class groups of quadratic fields using the refined BSD conjecture for elliptic curves. The most natural “trivial” bound on the n-... Dragos Ghioca - University of British Columbia The Dynamical Mordell-Lang Conjecture predicts the structure of the intersection between a subvariety $V$ of a variety $X$ defined over a field $K$ of characteristic $0$ with the orbit of a point in... Jasmin Matz - University of Copenhagen Suppose $M$ is a closed Riemannian manifold with an orthonormal basis $B$of $L^2(M)$ consisting of Laplace eigenfunctions. A classical result ofShnirelman and others proves that if the geodesic flow... Jason Bell - University of Waterloo The degree of a dominant rational map $f:\mathbb{P}^n\to \mathbb{P}^n$ is the common degree of its homogeneous components. By considering iterates of $f$, one can form a sequence ${\rm deg}(f^n)$,... Gérald Tenenbaum - Université de Lorraine Let $\varrho$ be a complex number and let $f$ be a multiplicative arithmetic function whose Dirichlet series takes the form $\zeta(s)^\varrho G(s)$, where $\zeta(s)$ is the Riemann zeta function and... Jens Marklof - University of Bristol Take a point on the unit circle and rotate it N times by a fixed angle. The N points thus generated partition the circle into N intervals. A beautiful fact, first conjectured by Hugo Steinhaus in the... Gal Binyamini - Weizmann Institute of Science I will discuss "point counting" in two broad senses: counting the intersections between a trascendental variety and an algebraic one; and counting the number of algebraic points, as a function of... Jörg Brüdern - University of Göttingen We study arithmetic functions that are bounded in mean square, and simultaneously have a mean value over any arithmetic progression. A Besicovitch type norm makes the set of these functions a Banach...	2021-11-29 02:35:56	{"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": 0.6673622131347656, "perplexity": 606.4352310408656}, "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-2021-49/segments/1637964358685.55/warc/CC-MAIN-20211129014336-20211129044336-00405.warc.gz"}
https://www.esaral.com/q/if-two-straight-lines-intersect-each-other-then-prove-that-the-ray-opposite-the-bisector-of-one-23920/	If two straight lines intersect each other, then prove that the ray opposite the bisector of one Question: If two straight lines intersect each other, then prove that the ray opposite the bisector of one of the angles so formed bisects the vertically-opposite angle. Solution: Let $A B$ and $C D$ be the two lines intersecting at a point $O$ and let ray $O E$ bisect $\angle A O C$. Now, draw a ray $O F$ in the opposite direction of $O E$, such that $E O F$ is a straight line. Let $\angle C O E=1, \angle A O E=2, \angle B O F=3$ and $\angle D O F=4$. We know that vertically-opposite angles are equal. $\therefore \angle 1=\angle 4$ and $\angle 2=\angle 3$ But, $\angle 1=\angle 2 \quad[$ Since $O E$ bisects $\angle A O C]$ $\therefore \angle 4=\angle 3$ Hence, the ray opposite the bisector of one of the angles so formed bisects the vertically-opposite angle.	2022-10-06 17:16:36	{"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": 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": 0.8259515166282654, "perplexity": 303.6162773389989}, "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-2022-40/segments/1664030337853.66/warc/CC-MAIN-20221006155805-20221006185805-00594.warc.gz"}
https://www.scm.com/doc/ADF/Input/FDE.html	# FDE: Frozen Density Embedding¶ The Frozen-Density-Embedding (FDE) option invokes calculation of the effective embedding potential introduced by Wesolowski and Warshel [184] in order to take into account the effect of the environment on the electronic structure of an embedded system. The embedding potential (Eq. 3 in Ref. [240]) depends explicitly on electron densities corresponding to the embedded subsystem (e.g. a solvated molecule) and its environment (e.g. solvent). For a detailed review, see Ref. [205]. The ADF implementation of the method is described in detail in Ref. [185, 217]. A time-dependent linear-response generalization of this embedding scheme was derived in Ref. [186]. Its implementation in an approximate form, which assumes a localized response of the embedded system only (uncoupled FDE), is described in the supplementary material to Ref. [187]. For possible drawbacks and pitfalls in connection with this approximation, see Refs. [185, 190, 193]. The theory of coupled excited states for subsystems is described in Refs. [296,297], and extended for general response properties in Ref. [298]. This theory (subsystem TDDFT, coupled FDE) allows to treat the mutual response of several subsystems, including the ones that are considered environment. A generalization of the FDE scheme to the calculation of NMR shieldings has been given in Ref. [218], where also the approximations involved and possible problems are discussed. With the exception of interaction energies, the current implementation in ADF only allows the calculation of molecular properties that only depend on the electron density and of response properties using TDDFT. For an application to the calculation of several molecular properties in solution and a comparison to the DRF model also available in ADF, see Ref. [190]. For further applications of the ADF implementation, see Ref. [189] (weakly interacting complexes), Refs. [185, 190-192] (solvent effects), and Refs. [206-207] (other environment effects). To invoke a frozen-density embedding calculation, two additional specifications in the input are required. First, one or more frozen fragments have to be included in the FRAGMENTS block, and second, the block key FDE has to be included. In the simplest case, this input should look like this: FRAGMENTS ... FragType FragFile type=FDE ... END FDE PW91K end In the FRAGMENTS block, for any fragment it is possible to specify the option type=FDE to indicate that the density of this fragment is kept frozen. This density is imported from the file FragFile. The frozen fragments have to be included in addition to the usual, non-frozen fragments. The atoms of the frozen fragments have to be included in the ATOMS block. As with normal fragments, the fragment found in the file will be rotated and translated to its position specified in the ATOMS block. For more details on specifying fragments, see the section ‘fragment files’. In the FDE input block, the recommended PW91k (also known as GGA97) approximant is recommended for the non-additive kinetic energy (the default is the local density approximant). A recommended alternative is NDSD. For all other options the defaults will be used. Please note that throughout the FDE part of the documentation, the word “approximant” is used instead of the more usual “functional” to emphasize that the exact functional is not known, also in the case of the kinetic energy functional. In the literature one may encounter both words used interchangeably. By including more than one frozen fragment, it is possible to use a frozen fragment that is a superposition of the densities of isolated molecules (this was possible in the previous version of ADF using the DENSPREP option). For a discussion and tests of the use of such approximate environment densities, see Ref. [185]. There is no restriction on the use of symmetry in FDE calculations, and usually the correct symmetry will be detected automatically. However, in the preparation of frozen fragments that will be rotated and/or translated in the FDE calculation, one has to include the keyword NOSYMFIT for technical reasons. In the current implementation, only the electron density of the embedded (non-frozen) system is calculated. Therefore, with the exception of interaction energies, only properties that depend directly on the electron density (e.g. dipole moments) are available. In particular, the calculation of energy gradients is not implemented yet. All quantities given in the output refer (unless explicitly specified otherwise) to the non-frozen system only. To employ the extension of FDE to the calculation of NMR shieldings, the file TAPE10 has to be used in the FDE calculation (by including the option SAVE TAPE10), and subsequently the NMR shielding has to be calculated using the program NMR (not with EPR). The TDDFT extension of the FDE formalism allows the calculation of electronic excitation energies and polarizabilities. This extension is automatically activated if FDE is used in combination with the EXCITATIONS or the RESPONSE key. To allow the mutual response of several subsystems, see the section on [subsystem TDDFT]. ## Fragment-specific FDE options¶ For each frozen fragment, several additional options can be applied. To do this, the fragment specification is used as a subblock key by appending a & sign. The subblock is terminated with SubEnd. This subblock key looks, in the most general form, as follows: FRAGMENTS ... FragType FragFile type=FDE & {FDEOPTIONS [USEBASIS] [RELAX or FREEZEANDTHAW] [OPTIMIZE]} {FDEDENSTYPE [SCF \| SCFexact \| SCFfitted ]} {RELAXCYCLES n or FREEZEANDTHAWCYCLES n} {XC [LDA \| GGA ggapotx ggapotc \| MODEL SAOP]} SubEnd ... END FDEOPTIONS FDEOPTIONS USEBASIS If the USEBASIS option is specified, the basis functions of this frozen fragment will be included in the calculation of the embedded subsystem. This allows to expand the density of the embedded subsystem using not only atom-centered basis sets localized in the embedded subsystem but also the ones in the environment Ref. [238]. In large-scale simulations using the embedding potential, this option is recommended to be used in the preparation stage to investigate the basis set dependence of the results (chapter 5.3 in Ref. [205]). This option is also an indispensable element in the procedure introduced in Ref. [238] to test approximants to the kinetic-energy component of the embedding potential introduced by Wesolowski and Warshel. FDEOPTIONS RELAX or FREEZEANDTHAW If the RELAX option (or equivalent FREEZEANDTHAW option) is specified, the density of this frozen fragment will be relaxed in freeze-and-thaw cycles [Ref. 240], i.e., the embedded subsystem is frozen, while this fragment is thawed. This is repeated, until convergence is reached or until the maximum number of iterations has been performed. By relaxing frozen fragments, it is possible to improve a given approximate environment density by including the polarization of the environment due to the embedded system. This option is recommended to be used in the preparation stage of a large-scale numerical simulation. The freeze-and-thaw calculations lead to a pair of electron densities (embedded system and environment) that minimizes the total energy. As a consequence, the electron density of the environment derived from the freeze-and-thaw calculations can be used as a reference to verify the adequacy of the assumed electron density for the environment in a large-scale simulation. Due to technical restrictions, freeze-and-thaw is not possible if an open-shell (unrestricted) fragment is present. FDEOPTIONS USEBASIS RELAX or FDEOPTIONS USEBASIS FREEZEANDTHAW It is further possible to combine USEBASIS and RELAX or FREEZEANDTHAW. In this case, the basis functions of the non-frozen fragment will be included when the density of the fragment is relaxed. This allows fully relaxed calculations with supermolecular expansion of the electron density of each subsystem. This option is to be used to test approximants to the kinetic-energy component of the embedding potential introduced by Wesolowski and Warshel by means of the procedure introduced in [Ref. 238]. FDEOPTIONS OPTIMIZE If the key FDEOPTIONS OPTIMIZE is not specified, then only the active fragment is optimized in a Geometry Optimization run (the FDE fragments are not optimized). If you include FDEOPTIONS OPTIMIZE, then the corresponding FDE fragment will also be optimized. The OPTIMIZE key implicitly activates the option RELAX, which is necessary to evaluate the nuclear gradients of the respective fragment [Ref. 486]. The OPTIMIZE key only supports mono-molecular basis set expansions and can therefore NOT be combined with the USEBASIS option. For Geometry Optimizations the usage of the FULLGRID option is recommended. See the example Example: Geometry optimization ICW FDE/sSDFT. Note:: When performing geometry optimization ICW FDE one must: FDEDENSTYPE The FDEDENSTYPE option can be used to specify which density is read from the fragment file. The possible options are: FDEDENSTYPE SCF (or FDEDENSTYPE SCFexact) The exact density (not calculated using the fit functions) is used. This is the default. FDEDENSTYPE SCFfitted The fitted density is used. This is less accurate but can be significantly faster. RELAXCYCLES n or FREEZEANDTHAWCYCLES n This gives the maximum number of freeze-and-thaw cycles that are performed for this fragment. If the maximum number given in the FDE block is smaller, or if convergence is reached earlier, then fewer cycles are performed. For historical reasons, two equivalent keywords are available. XC The XC option can be used to select the exchange-correlation potential that is used for this fragment when it is relaxed. By default, the same potential as for the non-frozen system is used, but in some cases it might be preferable to use another approximation for certain fragments. An example is given in Ref. [189]. XC LDA This option selects LDA as exchange-correlation potential for relaxing this fragment. XC GGA ggapotx ggapotc This selects a GGA potential for relaxing this fragment. The GGA potential is specified by giving the name of the exchange potential, followed by the name of the correlation potential. The available potentials are listed in the documentation for the XC key. XC MODEL SAOP This selects the model potential SAOP for relaxing this fragment. ## Kinetic energy approximants¶ The approximants to the kinetic energy dependent component of the embedding potential are described here. FDE {approximants to the kinetic energy dependent component of the embedding potential} {CJCORR [rho_cutoff]} {GGAPOTXFD exchange approximant} {GGAPOTCFD correlation approximant} end approximants to the kinetic energy dependent component of the embedding potential Several approximants to the kinetic-energy-dependent component of the effective potential given in Eq. (21) of [Ref. 184] are available. None of them is applicable if the embedded system is covalently bound to its environment. The user is recommended to look at the numerical value of the TSNAD(LDA) parameter which is given in the units of energy and can be considered as a measure of the overlap. The following rule of thumb should be applied: if this parameter is smaller than the estimated interaction energy between the embedded subsystem and the environment, then the available approximants are most probably adequate. If it exceeds this limit, the results can be less reliable. Printing TSNAD(LDA) is not done by default, as it can be quite time-consuming. Its printing is switched on by including “EXTPRINTENERGY”, and “PRINTRHO2”, and “FULLGRID” in the FDE input block. If no kinetic energy approximant is specified, by default the local-density approximation (Thomas-Fermi approximant) is used. For an assessment of approximants for weakly overlapping pairs of densities see Refs. [238, 239, 188, 241]. Based on these studies, the use of PW91k (= GGA97) is recommended. APPROXIMANTS TO BE USED IN NORMAL APPLICATIONS THOMASFERMI (default) Local-density-approximation form of vt[rhoA,rhoB] [237] derived from Thomas-Fermi expression for Ts[rho] [194, 195]. GGA97 (or PW91K) Generalized-gradient-approximation form of vt[rhoA,rhoB] [239] derived from the Lembarki-Chermette [197] approximant to Ts[rho]. This approximant is currently the recommended one based on the numerical analysis of its accuracy [188, 239] and the fact that the used enhancement factor disappears at large reduced density gradients, i.e. where the second-order gradient-expansion approximation fails [238, 241]. NDSD Similarly to GGA97, the NDSD approximant is constructed by taking into account the asymptotic behavior of the functional vt[rhoA,rhoB] at small density gradients. In the construction of NDSD, the exact property of vt[rhoA,rhoB] at rho_A $$\rightarrow$$ 0 and for $$\int$$ rhoB = 2 given in Eq. A6 of Ref. [279] is also taken into account. The analysis of the accuracy of this potential [279] shows that NDSD is of the same or superior quality as GGA97. NDSD is, therefore, recommended as the successor of GGA97 to be used anywhere where the quality of the results depends directly on the accuracy of the potential vt[rhoA,rhoB], i.e., for obtaining electronic-structure-dependent properties. The analytical form of the corresponding approximant to the functional Tsnad [rho_A,rho_B]\$ exists (Eq. 23 in Ref. [279]). It is not possible, however, to obtain the analytical form of the corresponding parent functional for the kinetic energy Ts[rho]. To reflect this and the fact that, similarly to the GGA approximants to vt[rhoA,rhoB], the numerical values of only first- and second derivatives of density are needed, the label NDSD (Non-Decomposable Second Derivatives) is used. OBSOLETE APPROXIMANTS (can be used but GGA97 leads usually to a better embedding potential see [238, 239]) LLP91 Generalized-gradient-approximation form of vt[rhoA,rhoB] [238] derived from Lee-Lee-Parr [Ref. 198] approximant to Ts[rho]. PW86k Generalized-gradient-approximation form of vt[rhoA,rhoB] [238] derived from the Fuentealba-Reyes approximant to Ts[rho] [242]. THAKKAR92 Generalized-gradient-approximation form of vt[rhoA,rhoB] [239] derived from the Thakkar approximant to Ts[rho] [201]. APPROXIMANTS WHICH MIGHT BE USEFUL ONLY FOR THEORY DEVELOPMENT The accuracy of some of these approximants was investigated in detail [239, 238, 188, 241]. Each of them was shown to lead to a qualitatively incorrect embedding potential. They shouldn’t be used in practical applications. COULOMB Neglecting completely vt[rhoA,rhoB] (vt[rhoA,rhoB] equals zero) together with the exchange-correlation component of the embedding potential introduced by Wesolowski and Warshel. TF9W The approximant to vt[rhoA,rhoB] [184] derived from the second-order gradient expansion [242]] for Ts[rho]. WEIZ The approximant to vt[rhoA,rhoB] [241] derived from the von Weizsäcker approximant to Ts[rho] [186]. OL91A Generalized-gradient-approximation form of vt[rhoA,rhoB] [238] derived from the first Ou-Yang and Levy approximant to Ts[rho] [200]. OL91B Generalized-gradient-approximation form of vt[rhoA,rhoB] [239] derived from the second Ou-Yang and Levy approximant to Ts[rho] [200]. E00 Generalized-gradient-approximation form of vt[rhoA,rhoB] [263] derived from a kinetic energy functional by Ernzerhof [264] which represents the gradient expansion approximation up to the fourth order. P92 Generalized-gradient-approximation form of vt[rhoA,rhoB] [263] derived from a kinetic energy functional by Perdew [265] which represents the gradient expansion approximation up to the sixth order. LONG DISTANCE CORRECTIONS TO THE EFFECTIVE POTENTIAL CJCORR Option to switch on a long-distance correction. By default this option is not used. As was shown in Ref. [220], with the available approximate kinetic-energy approximants, the embedding potential has the wrong form in the limit of a large separation of the subsystems. In particular, it was shown that this can have serious consequences in the case of “supermolecular expansion of electron density of each subsystem” calculations (USEBASIS option). In Ref. [220], a correction is proposed that enforces the correct long-distance limit. (See also this reference for limitations of this correction.) CJCORR [rho_cutoff] This option switches on the long-distance correction. This option has to be used in combination with one of the above kinetic-energy approximants. By default, a density cut-off of 0.1 is employed. GGAPOTXFDGGAPOTCFD Option to specify the non-additive exchange-correlation approximant. By default, in the construction of the effective embedding potential the exchange-correlation approximant that was specified in the XC block is used. It is possible to specify a different approximant with the GGAPOTXFD and GGAPOTCFD options. This is particularly useful in combination with the use of model potentials like SAOP, that can not be used in the embedding potential because of their orbital dependence. (For a discussion, see Ref. [189].) GGAPOTXFD exchange approximant The exchange approximant is used in the construction of the embedding potential. The same exchange approximants as in the XC key are available. GGAPOTCFD correlation approximant The correlation approximant is used in the construction of the embedding potential. The same correlation approximants as in the XC key are available. ## General FDE options¶ In addition to the fragment-specific options and the kinetic energy approximants, there are also a number of options available in FDE calculations that will be described in the following. FDE {FULLGRID} {RELAXCYCLES n or FREEZEANDTHAWCYCLES n} {RELAXPOSTSCF or FREEZEANDTHAWPOSTSCF} {EXTPRINTENERGY} {PRINTRHO2} {ENERGY} {SDFTENERGY} {DIPOLE} end FULLGRID By default, FULLGRID is not used, and in FDE calculations the integration grid is generated as described in Ref. [185] by including only atoms of the frozen subsystem that are close to the embedded subsystem in the generation of the integration grid. The distance cutoff used is chosen automatically, based on the extent of the basis functions of the embedded subsystem. (It can also be chosen manually, see the option qpnear in the INTEGRATION key) This scheme results in an efficient and accurate integration grid. However, it is possible that the default integration scheme is not accurate enough. This can be the case for weakly interacting systems and when the distance between the frozen and the embedded system is large. It is therefore recommended to check the quality of the default integration grid by comparing to results obtained using the full supermolecular grid (FULLGRID option). If the subkey FULLGRID is included, all atoms of the frozen system are included in the generation of the integration grid. This results in the same grid that would be used in a supermolecular calculation of the combined frozen and embedded system. The integration grid generated by this option might be much larger than the default grid. This option should be used to check the quality of the default integration grid. RELAXCYCLES n or FREEZEANDTHAWCYCLES n Specifies the maximum number n of freeze-and-thaw iterations [Ref. 240] that are performed (for frozen fragments with the RELAX) option. If a smaller number of iterations is specified as a fragment-specific option, for this fragment this smaller number is used. Furthermore, if convergence is reached earlier, no more iterations will be performed. RELAXPOSTSCF or FREEZEANDTHAWPOSTSCF If this option is included, several post-SCF properties will be calculated after each freeze-and-thaw cycle [Ref. 240]. These are otherwise only calculated in the last cycle. EXTPRINTENERGYPRINTRHO2 If the options EXTPRINTENERGY and PRINTRHO2 are included (both are needed and should be listed on separate lines), several additional quantities will be printed, including TSNAD(LDA). In order to obtain meaningful numbers, also the FULLGRID keyword (see above) has to be used. ENERGY Option to switch on the calculation of the FDE energy as the sum of the energy E[rhoA] of the active, embedded system and the interaction energy Eint[rhoA,rhoB] of the embedded system with the frozen environment. This relies on the calculation of the total energy for the embedded system and all caveats and restrictions for total energy evaluations apply (see keyword TOTALENERGY). All energy contributions are evaluated on the grid of the active subsystem. Some contributions to the interaction energy Eint[rhoA,rhoB] require an accurate integration grid in the region of the environment. Thus, in pure embedding calculations (without fragment-specific option RELAX), an accurate calculation of the FDE energy requires a full supermolecular integration grid (FULLGRID option). Details on the implementation and the performance of kinetic energy functionals for interaction energies are documented in Ref. [263] The calculation of the full, variationally minimized subsystem DFT energy, that is, the sum of the energy of two subsystems E[rhoA] and E[rhoB] and their interaction energy Eint[rhoA,rhoB] in the framework of FDE, is invoked if then the fragment densities are relaxed in freeze-and-thaw cycles (option RELAXCYCLES and fragment-specific FDE option RELAX). In this case the supermolecular integration grid is not required. Instead, in each step of the freeze-and-thaw cycle, the critical energy terms are taken from the previous freeze-and-thaw step of the presently frozen fragment. The convergence of the energy contributions with the number of freeze-and-thaw iterations should be carefully monitored. Due to conceptual problems for the evaluation of the non-additive kinetic energy contribution, only two subsystems, that is, one frozen fragment, is supported for FDE energy calculations with freeze-and-thaw. SDFTENERGY This is a generalization of the original ENERGY implementation that allows for the evaluation of the FDE/sDFT total energy. Usage of a supermolecular integration grid is recommended (FULLGRID option), because of the non-additive kinetic and XC contributions. EXTPRINTENERGY can be combined with this option to print the subsystem DFT energy after each freeze-and-thaw cycle. For pure embedding calculations, the SDFTENERGY implementation reads the total energy from each frozen fragment’s TAPE21 file. The total energy of frozen fragments is not (re-)evaluated during FDE calculations. It is therefore mandatory to add the TOTALENERGY keyword to the preparatory isolated fragment calculations. DIPOLE The dipole of the supersystem is calculated as the sum of analytically integrated fragment dipole moments. Note that the dipole moment becomes origin dependent for charged (sub-)fragments. The current implementation does NOT take care of this. ## Frozen Density Embedding with External Orthogonality¶ An implementation of External Orthogonality (EO) into the FDE framework in ADF can be found in Ref. [384]. In this method in the fragment calculation one need to specify ghost atoms at the positions of the atoms in all the other fragments. Thus each fragment is calculated in the supermolecular basis. AOMat2File IgnoreOverlap FDE EXTERNALORTHO {factor} ... END EXTERNALORTHO Used to specify the use of external orthogonality (EO) in the FDE block, with an optional factor (default factor is 1e6). Note that the overlap region is defined by ghost atoms, and the general keyword IGNOREOVERLAP is necessary. Additionally, the general keyword AOMAT2FILE is required to save some important fragment AO matrices to TAPE21 for use in an EO calculation. it is recommended that one uses the STOFIT keyword for the STOFIT density fitting method. ## FDE and (localized) COSMO¶ COSMO solvation can be included in combination with FDE. This means that a COSMO cavity will be created that holds both the active and frozen fragments. For very large systems the solution of the COSMO equations can become the bottleneck of the calculation. A local COSMO variant, which exploits the subsystem nature of the underlying electronic description, is implemented in ADF, see Ref. [449]. This method, called LoCOSMO, is an approximation to regular COSMO for fragment-based electronic structure methods. If a given fragment is active (i.e. only its own density changes over the SCF cycles), the surface charges outside a given radius around this fragment will be kept fixed in magnitude (excluded from the COSMO optimization). However, no interactions are ignored by adding a corresponding constant term to the COSMO solution vector. SOLVATION .. CHARGED LoCosmo LoCosmoDist END LoCosmo LoCosmoDist If LoCosmo is included the local COSMO will be used in the calculation. LoCosmoDist is a cutoff radius (Angstrom), which must be specified by the user, if LoCOSMO is included. All surface charges within this radius from any atom of the active fragment are included in the active charge space. A sensible value for LoCosmoDist is 5.0 Angstrom. To be really useful, Freeze-and-Thaw cycles should be carried out with LoCOSMO. After each fragment calculation, the KF file LOCSURCH is written to disk. If present, this file will be automatically read in during the next (LoCOSMO) fragment calculation. This means that if the internal FT cycles are used by specifying RELAXCYCLES, the code creates and reads in the file in a fully automatic fashion. LOCSURCH is neither created nor read during a regular COSMO calculation. In case one calculates excitation energies with the EXCITATION block key, and LoCOSMO is specified, only the solvent response due to surface charges within the specified cutoff radius will be taken into account, see also Ref. [450]. It should be noted that in a regular (uncoupled) FDE TDDFT calculation, the response due to the frozen density is neglected. ## Subsystem TDDFT, coupled FDE¶ The linear-response subsystem TDDFT code implements the theory of coupled excited states for subsystems as described in Refs. [296,297]. This theory is based on the FDE extension to excited states [186], which is implemented in ADF in a local response approximation, i.e., neglecting the dynamic response of the environment [187]. The subsystem TDDFT code allows to treat the mutual response of several subsystems, including the ones that are considered environment. A more typical situation would be a system composed of several equivalent chromophores treated as individual subsystems. In this case, the local response approximation leads to uncoupled excited states of the subsystems (hence the acronym FDEu is employed often), while the subsystem TDDFT code couples the monomer excitations to obtain the excited states of the total system (often denoted as coupled frozen density embedding, FDEc). This can be related to excitonic couplings between the monomers [297]. The current implementation is restricted to NOSYM calculations and Singlet-Singlet excitations without frozen core approximation. It makes use of the ALDA kernel (including a Thomas-Fermi part for the contribution arising from the non-additive kinetic energy) for consistency with the uncoupled FDE implementation for excited states. Some features have not or not extensively been tested and should be used with great care, e.g., linear dependencies in the basis set. Details on the calculation of transition moments, oscillator and rotational strengths are described in Ref. [298]. Subsystem TDDFT (FDEc) calculations can be invoked with the SUBEXCI key. SUBEXCI input FDEc calculations on coupled excited states first require that an uncoupled FDE-TDDFT calculation has been performed for every subsystem that should be included in the coupled calculation, and that the corresponding TAPE21 files, in which the considered subsystems are “active”, have been saved (see the separate FDE input description). This means that it is not possible to use the information on frozen/inactive fragments from a TAPE21 file of a previous uncoupled FDE calculation, which contains all subsystems. Although it is technically possible to use TAPE21 files from non-FDE calculations on the separate subsystems, this would lead to results that are inconsistent with the subsystem TDDFT methodology from Ref. [296]. In any case, a previous TDDFT calculation for each subsystem that should be included in the coupling procedure is necessary. If that is not the case, the subsystem will still be considered in the calculation of the total electron density (needed in the setup of the exchange-correlation kernel), but will not be included in the coupling procedure. The first subsystem should always be one of the coupled subsystems. The input will then look like the corresponding input for an uncoupled FDE-TDDFT calculation, but in addition should contain the following block: SUBEXCI {LOWEST nlowest} {OPTSTATES list_of_optstates} {CTHRES coupling_threshold} {SFTHRES solutionfactor_threshold} {COUPLBLOCK} {TDA} {CICOUPL} END LOWEST nlowest The selection of the excited states to be coupled consists of two steps. First, a number of reference states are selected. As a default, the nlowest (default: 10) lowest excited states present on the fragment file for the first subsystem are considered. OPTSTATES list_of_optstates If the keyword OPTSTATES is given, only those excited states of the first subsystem are considered as reference states that are given in the list_of_optstates (numbers of states separated by blanks). CTHRES coupling_threshold Second, all excitations of all subsystems (present on the fragment TAPE21 files) with an excitation energy that differs by less than coupling_threshold (to be given in units of eV; default: 30 eV) from one of the reference states are selected to be included in the coupling. Note that additional excited states of system 1 may be included here. COUPLBLOCK If COUPLBLOCK is specified in the input, all couplings between all of these local excited states are included. Otherwise (default), the coupling_threshold is also applied to select pairs of states for which couplings are calculated. I.e., couplings are not calculated if the two particular states to be coupled differ in energy by more than coupling_threshold. SFTHRES solutionfactor_threshold To reduce the computational effort, it is possible to ignore the effect of orbital pairs with coefficients less than solutionfactor_threshold in the solution factors (TDDFT eigenvectors) of the underlying uncoupled calculation in the construction of the exact trial densities during the calculation of the coupling matrix elements. These orbital pair contributions are not ignored in the subsequent calculation of transition moments, oscillator, and rotational strengths. The default value of 0.00001 typically leads to a precision of the coupled excitation energies of about 0.0001 eV. TDA TDA specifies the use of the Tamm-Dancoff-Approximation (Tamm-Dancoff approximation) in the underlying uncoupled FDE-TDDFT calculations (Ref. [364]). Contrary to the full SUBEXCI-TDDFT variant, SUBEXCI-TDA allows for the usage of hybrid functionals in the underlying uncoupled FDE-TDDFT calculations. CICOUPL Within the Tamm-Dancoff Approximation, the couplings between localized excited states on different subsystems correspond directly to so-called exciton couplings (see Ref. [364]). The CICOUPL keyword, in conjunction with TDA, prints these exciton couplings. It is also possible to use CICOUPL with full FDEc-TDDFT. In that case, the excitonic couplings between monomers are reconstructed from an effective 2x2 CIS-like eigenvalue problem, as e.g. done in Ref. [297]. In addition, the input file may contain either an EXCITATION block or the keyword DIFFUSE. Both options lead to a slight adaption of the integration grid. Apart from this, the EXCITATION block will be ignored. The key ALLOW PARTIALSUPERFRAGS is currently necessary to be able to use subsystem information for only one subsystem from a TAPE21 file of a previous FDE calculation: ALLOW PARTIALSUPERFRAGS ## Restrictions and pitfalls¶ In the current implementation, only the electron density of the embedded system is calculated. Therefore, with the exception of interaction energies, only properties that depend directly on the electron density (e.g., dipole moments) are available. In addition, the TDDFT extension allows the calculation of electronic excitation energies and polarizabilities, and NMR shieldings can be calculated. Warning EVERYTHING ELSE IS NOT YET IMPLEMENTED. THE RESULTS OBTAINED FOR OTHER PROPERTIES MIGHT BE MEANINGLESS. Kinetic energy approximant: Although the effective embedding potential is derived from first principles using universal density approximants, the ADF implementation relies on approximations. Currently, two implemented approximations are recommended [188]: PW91k (also known as GGA97) which uses electron densities and the corresponding gradients to express the non-additive kinetic energy component of the embedding potential, or TF (Thomas-Fermi LDA approximant), which does not use gradients at all. Either approximation is applicable only in cases where the overlap between electron densities of the corresponding interactions is small. Note: so far, no approximation has been developed for the strong-overlap case - two subsystem linked by covalent bonds for instance.	2018-12-14 14:19:11	{"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": 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": 0.7419286966323853, "perplexity": 1710.4483283218945}, "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-2018-51/segments/1544376825916.52/warc/CC-MAIN-20181214140721-20181214162221-00448.warc.gz"}

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