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# R

## Action effects on visual perception of distances: A multilevel Bayesian meta-analysis

Previous studies have suggested that action constraints influence visual perception of distances. For instance, the greater the effort to cover a distance, the longer people perceive this distance to be. The present multilevel Bayesian meta-analysis …

## An introduction to Bayesian multilevel models using brms: A case study of gender effects on vowel variability in standard Indonesian

Bayesian multilevel models are increasingly used to overcome the limitations of frequentist approaches in the analysis of complex structured data. This paper introduces Bayesian multilevel modelling for the specific analysis of speech data, using the …

## What does a Bayes factor look like?

An attempt to illustrate what a Bayes factor looks like, using GIFs.

## Visualising within-subject effects and stochastic dominance with (augmented) modified Brinley plots

Why can’t we be more idiographic in our research? It is the individual organism that is the principle unit of analysis in the science of psychology (Barlow & Nock, 2009).

## Checking the asumption of independence in binomial trials using posterior predictive checking

As put by Gelman et al. (2013, page 148): 'because a probability model can fail to reflect the process that generated the data in any number of ways, posterior predictive *p*-values can be computed for a variety of test quantities in order to evaluate more than one possible model failure'.

## Using R to make sense of the generalised linear model

What is the difference between the errors and the residuals? What does it mean for a model to *predict* something? What is a link function? In the current post, we use four R functions (viz., the predict, fitted, residuals and simulate functions) to illustrate the mechanisms and assumptions of the generalised linear model.

## Three methods for computing the intra-class correlation in multilevel logistic regression

In the current post, we present and compare three methods of obtaning an estimation of the ICC in multilevel logistic regression models.

## Experimental absenteeism and logistic regression, part II

This post continues our exploration of the logistic regression model by extending it to a multilevel logistic regression model, using the brms package.

## Experimental absenteeism and logistic regression, part I

This post aims to assess the average probability of participant presence in psychological experiments and, in the meantime, to introduce Bayesian logistic regression using R and the rethinking package.

## On power and the 'match point situation'

In this post I will argue that the "match point situation" (i.e., the situation in which your entire life is dictated by chance only), is an everyday' situation for the researcher who uses *Null Hypothesis Significance Testing* (NHST) without controlling power.


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# How good are interior point methods? Klee-Minty cubes tighten iteration-complexity bounds.

By refining a variant of the Klee-Minty example that forces the central path to visit all the vertices of the Klee-Minty n-cube, we exhibit a nearly worst-case example for path-following interior point methods. Namely, while the theoretical iteration-complexity upper bound is O(2^{n}n^{\frac{5}{2}}), we prove that solving this n-dimensional linear optimization problem requires at least $2^n-1$ iterations.

## Citation

AdvOL-Report #2004/20 Advanced Optimization Laboratory, Department of Computing and Software, McMaster University, Hamilton, Ontario, Canada, December 2004.

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# $L^p$ Fourier transformation on non-unimodular locally compact groups

Document Type: Original Article

Author

Abstract

Let $G$ be a locally compact group with modular function $\Delta$ and left regular representation $\lambda$. We define the $L^p$ Fourier transform of a function $f \in L^p(G)$, $1\le p \le 2$, to be essentially the operator $\lambda(f)\Delta^{\frac{1}{q}}$ on $L^2(G)$ (where $\frac{1}{p}+\frac{1}{q}=1$) and show that a generalized Hausdorff--Young theorem holds. To do this, we first treat in detail the spatial $L^p$ spaces $L^p(\psi_0)$, $1 \le p \le \infty$, associated with the von Neumann algebra $M=\lambda(G)^{\prime\prime}$ on $L^2(G)$ and the canonical  weight $\psi_0$ on its commutant. In particular, we discuss isometric isomorphisms of $L^2(\psi_0)$ onto $L^2(G)$ and of $L^1(\psi_0)$ onto the Fourier algebra $A(G)$. Also, we give a characterization of positive definite functions belonging to $A(G)$ among all continuous positive definite functions.

Keywords

### History

• Receive Date: 19 August 2017
• Revise Date: 19 September 2017
• Accept Date: 19 September 2017


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# Tag Info

## Hot answers tagged auxiliary-files

37

Solution to use Texstudio and output the build (temporary) files into a seperate folder using biber: Put a new Folder with YourName into the same directory as your main .tex file. Options -> Configure -> Commands -> PdfLaTeX for MiKTeX add -aux-directory=YourName. If you use TeX Live use -output-directory YourName. Result looks something like this: ...

25

How does LaTeX implement UTF-8? The Unicode character é is encoded as two byte in UTF-8, precisely <C3><A9> (I'll use throughout this to denote bytes, also when they are character tokens for TeX). When \usepackage[utf8]{inputenc} is loaded, the byte <C3> is made active and defined to look for the following byte, because <C3> in UTF-8 ...

25

Without a minimal working example (MWE) this is just guessing, but if your document has defined acronyms or glossary entries within the document environment and you upgraded to version 4.0, an extra write is required. The reason for this is as follows: Version 3.07¹ and below wrote the name, description and symbol fields to the external glossary files (in ...

22

It depends on how paranoid your settings in texmf.cnf are. Mine (default texlive 2014) says: % Allow TeX \openin, \openout, or \input on filenames starting with .' % (e.g., .rhosts) or outside the current tree (e.g., /etc/passwd)? % a (any) : any file can be opened. % r (restricted) : disallow opening "dotfiles". % p (paranoid) : as r' and ...

21

With the help of When is the aux file read and written? and Barbara Beetons kind assistance I was able to determine what goes wrong and how to prevent it. This is the problem: Normally I then don't work with the TeX engine on the console, but simply correct my error and restart. This is what I should have done on the console: Type ?+Return to get an ...

21

There are certainly several ways to implement a data transport mechanism between runs. The LaTeX one attempts to be rather economically with resources. There are a number of tasks that it caters for: TOC-type files are only generated if the document asks for a TOC. This only becomes clear somewhere within the document (i.e., not automatically available at \...

18

Some further extension you might encounter depending on what packages you are using: .soc - package changes .fdb_latexmk - compile tool latexmk .fls - running latex with \$ latex -recorder .spl - documentclass elsarticle (Elsevier journals) .auxlock - tikzlibrary external .xwm - package xwatermark .tdo - package todonotes

18

You can use the draft mode: -draftmode Sets \pdfdraftmode so pdfTeX doesn't write a PDF and doesn't read any included images, thus speeding up execution. Arara also supports it, here's an example for TeXworks: % arara: pdflatex: { draft : yes } I use the following snippet to compile a large document with hundreds of pages and ...

18

I have the same problem. According to the bug report, it seems to be related to a change in the way TeXstudio saves a file. What can you do? Two options: a) Give up the cloud ... and simply work outside your Dropbox, as the OP suggested. You can still manually copy files into the Dropbox to back them up or share them. b) Downgrade TeXstudio and keep the ...

17

Adding to the nice answer by Christian, I'd like to mention some subtler aspects of writing in the .aux file. LaTeX defines a file handle for this, which is \@auxout, and provides the function \protected@write for “safe” writing in files. This function differs from ordinary \write in three main aspects: robust commands or \protected ones are written out ...

17

16

Although there is already an answer to this question, I think it is wrong. TeXShop users are always complaining about this problem and hardly any other people are complaining. I've been a TeXShop fan almost since the first edition but this is its most annoying feature. It happens to me all the time in TeXShop and almost never in any other program I use, ...

16

First of all, an interesting remark: it's quite surprising and amusing that this fact went unnoticed for virtually every single release of arara. I blame Nicola, of course: once she found this major issue, apparently the universe captured an unbalanced force and decided to go ballistic. :) As retaliation, Nicola is now part of the official arara team. ♥ ...

16

As mentioned in the comments, you should run biber to compile your bib file as you have used biber as the backend. \usepackage[style=authoryear,backend=biber]{biblatex} Here are the commands to compile your myFile.tex and your .bib files: pdflatex myFile biber myFile pdflatex myFile

16

LaTeX has always done that (and it's not really documented why) however I think it has two purposes. As egreg mentioned in comments it means that if the operating system does not allow file writing at that point you get an error at the start of the document not at some unpredictable place later where latex needs the aux file. By writing something you ensure ...

15

There is @paulo's awesome arara (The cool TeX automation tool) without which I can't imagine working anymore. It has a predefined clean directive that allows to specify which files should be seleted after compilation. The following file called test.tex would be compiled twice and then the aux and the toc file would be removed: % arara: pdflatex % arara: ...

13

This is a working but basic answer; it's somewhat involved. Also, I am not a programmer by any definition, nor an Os X expert. Surely there are better ways to achieve the same effect. At the end of the answer, there's a link where you can download a copy of the app described in the post. Background In Os X, any directory with an extension can be a "...

13

12

This is a nice example of what I term "impossible document", i.e., a document those content any layout specifications do not have a valid representation. This kind of problem can happen whenever content presentation depends on content placement. This particular case the placement of the figure resulted in a reference string of different length (which when ...

12

As said by others, it's not really a great idea to (automatically) remove .aux, .log and similar files. Some of them provide important info in case things go wrong (for example .log), others are needed for things to actually work when you compile your document multiple times (.aux, .toc etc.). Deleting them can break things. However, if this is related to a ...

12

Update for Overleaf version 2: the menu has changed. If you need any additional files, you can find them in the compiler panel under "Logs and output files" and "other logs & files".

12

No, the .fls file should not be version controlled because it is a build artefact. That file is automatically generated when running LaTeX with the -recorder option and contains the full filesystem paths of all included files. That also means that the contents of this file depend on the installation directory of your TeX distribution and is therefore ...

11

ConTeXt MkIV related files: User-Input Files .tex: For content and typesetting instructions. .cld: For ConTeXt Lua Documents .xml: For XML data (related: .xhtml) Macro package files .mkiv: Code for MkIV .mkvi: Code for MkIV written with named variables \def\macro#{val1}#{val2} rather than \def\macro#1#2, etc.) .lua: Lua code for MkIV .lfg: Goodies for ...

11

morewrites – Always room for a new write stream The package aims to solve the error “No room for a new \write”, which occurs when the user or when the user’s packages have ’allocated too many streams using \newwrite (TeX has a fixed maximum number – 16 – [of] such streams built-in to its code). The package hooks into TeX primitive ...

11

10

You can use environment variable TEXMFOUTPUT to specify output directory for bibtex files. In your case, you can create makefile like: all: mkdir out -p pdflatex -output-directory out parent.tex TEXMFOUTPUT="out:" bibtex out/parent pdflatex -output-directory out parent.tex pdflatex -output-directory out parent.tex Consider more ...

10

Only a subset of the TeX language is available, if text is written to a file. The expandable machinery is working, but assignments and other unexpandable stuff is not. In this case \plural can be made expandable: \documentclass{article} \immediate\newwrite\txtfile \immediate\openout\txtfile=\jobname.txt \makeatletter \newcommand*{\plural}[1]{% \ifnum#1=...

Only top voted, non community-wiki answers of a minimum length are eligible


text:
# Laravel 4 Filters in Controllers

Filtering in Laravel 4 is extremely easy. In case you don’t know what I’m talking about, a filter in Laravel is used on a particular route or set of routes to prevent certain people or actions from happening on a particular route. Laravel ships with a few simple but powerful filters to get you started.

These include a filter to make sure a user is logged in and a one for protecting against CSRF attacks.

Typically, you would add these filters in your routes.php or filters.php. However, I feel that separating this code into another file away from the controller that it is protecting is cumbersome. I would rather put these filters in my controller so I can see at a glance what filters I have on certain routes. This can easily be done through the constructor of the controller. Let’s check it out.

Let’s pretend we have a resource controller that has a store method for storing a post into the database. We want to make sure this route is protected from CSRF attacks and should only be accessed by AJAX. This means we will need a filter for CSRF and for AJAX. The CSRF one comes with Laravel. Let’s build one for AJAX. Insert the following code into routes.php:

<?php
Route::filter('ajax', function()
{
if (!Request::ajax()) App::abort(404);
});

Then we need to add these two filters to our controller through its constructor.

<?php
class PostController extends BaseController {

public function __construct()
{
// Exit if not ajax
$this->beforeFilter('ajax', array('only' => 'store')); // Exit if not a valid _token$this->beforeFilter('csrf', array('only' => 'store'));
}

public function store()
{
// Store like a boss
}

}

This will now execute those two filters every time the store() method is called. If you wanted to make sure these filters were used on every call to this controller, then just omit the array passed as the second parameter to the beforeFilter() method.

That’s it! As you can see, putting your filters in your controllers instead of in different files allows you to keep all logic in your controllers.


text: Speaker : 蕭欽玉(Chin-Yu Hsiao)(本所) Szego kernel asymptotics for high power of CR line bundles and Kodaira embedding theorems on CR manifolds 2014-03-28 (Fri) 10:30 - 12:00 Seminar Room 617, Institute of Mathematics (NTU Campus) In this talk, I will report my recent work(arXiv:1401.6647). Let $L^k$ be the $k$-th power of a CR line bundle over a CR manifold $X$. Give $q$, let $[]^{(q)}_{b,k}$ be the Kohn Laplacian for $(0,q)$ forms with values in $L^k$. We show that a certain microlocal conjugation of the spectral function of $[]^{(q)}_{b,k}$ admits an asymptotic expansion in $k$ and we show further that the associated Szego kernel admits a full asymptotic expansion in $k$ if $[]^{(q)}_{b,k}$ has small spectral gap. By using these asymptotics, we establish almost Kodaira embedding theorems on CR manifolds and Kodaira embedding theorems on CR manifolds with transversal CR $S^1$ actions.


text:
for Journals by Title or ISSN for Articles by Keywords help

Publisher: Cambridge University Press   (Total: 367 journals)

 Combinatorics, Probability and Computing   Journal Prestige (SJR): 1.013   Citation Impact (citeScore): 35   Number of Followers: 4           Hybrid journal (It can contain Open Access articles)    ISSN (Print) 0963-5483 - ISSN (Online) 1469-2163    Published by Cambridge University Press  [367 journals]
• Ramsey Goodness of Bounded Degree Trees
• Authors: IGOR BALLA; ALEXEY POKROVSKIY, BENNY SUDAKOV
Pages: 289 - 309
Abstract: Given a pair of graphs G and H, the Ramsey number R(G, H) is the smallest N such that every red–blue colouring of the edges of the complete graph KN contains a red copy of G or a blue copy of H. If a graph G is connected, it is well known and easy to show that R(G, H) ≥ (|G|−1)(χ(H)−1)+σ(H), where χ(H) is the chromatic number of H and σ(H) is the size of the smallest colour class in a χ(H)-colouring of H. A graph G is called H-good if R(G, H) = (|G|−1)(χ(H)−1)+σ(H). The notion of Ramsey goodness was introduced by Burr and Erdős in 1983 and has been extensively studied since then.In this paper we show that if n≥ Ω(|H| log4 |H|) then every n-vertex bounded degree tree T is H-good. The dependency between n and |H| is tight up to log factors. This substantially improves a result of Erdős, Faudree, Rousseau, and Schelp from 1985, who proved that n-vertex bounded degree trees are H-good when n ≥ Ω(|H|4).
PubDate: 2018-05-01T00:00:00.000Z
DOI: 10.1017/S0963548317000554
Issue No: Vol. 27, No. 3 (2018)

• On Zeros of a Polynomial in a Finite Grid
• Authors: ANURAG BISHNOI; PETE L. CLARK, ADITYA POTUKUCHI, JOHN R. SCHMITT
Pages: 310 - 333
Abstract: A 1993 result of Alon and Füredi gives a sharp upper bound on the number of zeros of a multivariate polynomial over an integral domain in a finite grid, in terms of the degree of the polynomial. This result was recently generalized to polynomials over an arbitrary commutative ring, assuming a certain ‘Condition (D)’ on the grid which holds vacuously when the ring is a domain. In the first half of this paper we give a further generalized Alon–Füredi theorem which provides a sharp upper bound when the degrees of the polynomial in each variable are also taken into account. This yields in particular a new proof of Alon–Füredi. We then discuss the relationship between Alon–Füredi and results of DeMillo–Lipton, Schwartz and Zippel. A direct coding theoretic interpretation of Alon–Füredi theorem and its generalization in terms of Reed–Muller-type affine variety codes is shown, which gives us the minimum Hamming distance of these codes. Then we apply the Alon–Füredi theorem to quickly recover – and sometimes strengthen – old and new results in finite geometry, including the Jamison–Brouwer–Schrijver bound on affine blocking sets. We end with a discussion of multiplicity enhancements.
PubDate: 2018-05-01T00:00:00.000Z
DOI: 10.1017/S0963548317000566
Issue No: Vol. 27, No. 3 (2018)

• On Quantitative Noise Stability and Influences for Discrete and Continuous
Models
• Authors: RAPHAËL BOUYRIE
Pages: 334 - 357
Abstract: Keller and Kindler recently established a quantitative version of the famous Benjamini–Kalai–Schramm theorem on the noise sensitivity of Boolean functions. Their result was extended to the continuous Gaussian setting by Keller, Mossel and Sen by means of a Central Limit Theorem argument. In this work we present a unified approach to these results, in both discrete and continuous settings. The proof relies on semigroup decompositions together with a suitable cut-off argument, allowing for the efficient use of the classical hypercontractivity tool behind these results. It extends to further models of interest such as families of log-concave measures and Cayley and Schreier graphs. In particular we obtain a quantitative version of the Benjamini–Kalai–Schramm theorem for the slices of the Boolean cube.
PubDate: 2018-05-01T00:00:00.000Z
DOI: 10.1017/S0963548318000044
Issue No: Vol. 27, No. 3 (2018)

• Linear Turán Numbers of Linear Cycles and Cycle-Complete Ramsey
Numbers
• Authors: CLAYTON COLLIER-CARTAINO; NATHAN GRABER, TAO JIANG
Pages: 358 - 386
Abstract: An r-uniform hypergraph is called an r-graph. A hypergraph is linear if every two edges intersect in at most one vertex. Given a linear r-graph H and a positive integer n, the linear Turán number exL(n,H) is the maximum number of edges in a linear r-graph G that does not contain H as a subgraph. For each ℓ ≥ 3, let Crℓ denote the r-uniform linear cycle of length ℓ, which is an r-graph with edges e1, . . ., eℓ such that, for all i ∈ [ℓ−1], |ei ∩ ei+1|=1, |eℓ ∩ e1|=1 and ei ∩ ej = ∅ for all other pairs {i,j}, i ≠ j. For all r ≥ 3 and ℓ ≥ 3, we show that there exists a positive constant c = cr,ℓ, depending only r and ℓ, such that exL(n,Crℓ) ≤ cn1+1/⌊ℓ/2⌋. This answers a question of Kostochka, Mubayi and Verstraëte [30]. For even ℓ, our result extends the result of Bondy and Simonovits [7] on the Turán numbers of even cycles to linear hypergraphs.Using our results on linear Turán numbers, we also obtain bounds on the cycle-complete hypergraph Ramsey numbers. We show that there are positive constants a = am,r and b = bm,r, depending only on m and r, such that $$R(C^r_{2m}, K^r_t)\leq a \Bigl(\frac{t}{\ln t}\Bigr)^{{m}/{(m-1)}}\quad\text{and}\quadR(C^r_{2m+1}, K^r_t)\leq b t^{{m}/{(m-1)}}.$$
PubDate: 2018-05-01T00:00:00.000Z
DOI: 10.1017/S0963548317000530
Issue No: Vol. 27, No. 3 (2018)

• A Sharp Dirac–Erdős Type Bound for Large Graphs
• Authors: H. A. KIERSTEAD; A. V. KOSTOCHKA, A. McCONVEY
Pages: 387 - 397
Abstract: Let k ⩾ 3 be an integer, hk(G) be the number of vertices of degree at least 2k in a graph G, and ℓk(G) be the number of vertices of degree at most 2k − 2 in G. Dirac and Erdős proved in 1963 that if hk(G) − ℓk(G) ⩾ k2 + 2k − 4, then G contains k vertex-disjoint cycles. For each k ⩾ 2, they also showed an infinite sequence of graphs Gk(n) with hk(Gk(n)) − ℓk(Gk(n)) = 2k − 1 such that Gk(n) does not have k disjoint cycles. Recently, the authors proved that, for k ⩾ 2, a bound of 3k is sufficient to guarantee the existence of k disjoint cycles, and presented for every k a graph G0(k) with hk(G0(k)) − ℓk(G0(k)) = 3k − 1 and no k disjoint cycles. The goal of this paper is to refine and sharpen this result. We show that the Dirac–Erdős construction is optimal in the sense that for every k ⩾ 2, there are only finitely many graphs G with hk(G) − ℓk(G) ⩾ 2k but no k disjoint cycles. In particular, every graph G with |V(G)| ⩾ 19k and hk(G) − ℓk(G) ⩾ 2k contains k disjoint cycles.
PubDate: 2018-05-01T00:00:00.000Z
DOI: 10.1017/S0963548318000020
Issue No: Vol. 27, No. 3 (2018)

• Density of Real Zeros of the Tutte Polynomial
• Authors: SEONGMIN OK; THOMAS J. PERRETT
Pages: 398 - 410
Abstract: The Tutte polynomial of a graph is a two-variable polynomial whose zeros and evaluations encode many interesting properties of the graph. In this article we investigate the real zeros of the Tutte polynomials of graphs, and show that they form a dense subset of certain regions of the plane. This is the first density result for the real zeros of the Tutte polynomial in a region of positive volume. Our result almost confirms a conjecture of Jackson and Sokal except for one region which is related to an open problem on flow polynomials.
PubDate: 2018-05-01T00:00:00.000Z
DOI: 10.1017/S0963548318000019
Issue No: Vol. 27, No. 3 (2018)

• On Lipschitz Bijections Between Boolean Functions
• Authors: SHRAVAS RAO; IGOR SHINKAR
Pages: 411 - 426
Abstract: Given two functions f,g : {0,1}n → {0,1}, a mapping ψ : {0,1}n → {0,1}n is said to be a mapping from f to g if it is a bijection and f(z) = g(ψ(z)) for every z ∈ {0,1}n. In this paper we study Lipschitz mappings between Boolean functions.Our first result gives a construction of a C-Lipschitz mapping from the Majority function to the Dictator function for some universal constant C. On the other hand, there is no n/2-Lipschitz mapping in the other direction, namely from the Dictator function to the Majority function. This answers an open problem posed by Daniel Varga in the paper of Benjamini, Cohen and Shinkar (FOCS 2014 [1]).We also show a mapping from Dictator to XOR that is 3-local, 2-Lipschitz, and its inverse is O(log(n))-Lipschitz, where by L-local mapping we mean that each output bit of the mapping depends on at most L input bits.Next, we consider the problem of finding functions such that any mapping between them must have large average stretch, where the average stretch of a mapping φ is defined as $${\sf avgstretch}(\phi) = {\mathbb E}_{x,i}[{\sf dist}(\phi(x),\phi(x+e_i)].$$ We show that any mapping φ from XOR to Majority must satisfy avgStretch(φ) ≥ c $\sqrt{n}$ for some absolute constant c > 0. In some sense, this gives a ‘function analogue’ to the question of Benjamini, Cohen and Shinkar (FOCS 2014 [1]), who asked whether there exists a set A ⊆ {0,1}n of density 0.5 such that any bijection from {0,1}n−1 to A has large average stretch.Finally, we show that for a random balanced function f: {0,1}n → {0,1}n, with high probability there is a mapping φ from Dictator to f such that both φ and φ−1 have constant average stretch. In particular, this implies that one cannot obtain lower bounds on average stretch by taking uniformly random functions.
PubDate: 2018-05-01T00:00:00.000Z
DOI: 10.1017/S0963548317000578
Issue No: Vol. 27, No. 3 (2018)

• Robust Tverberg and Colourful Carathéodory Results via Random Choice
• Authors: PABLO SOBERÓN
Pages: 427 - 440
Abstract: We use the probabilistic method to obtain versions of the colourful Carathéodory theorem and Tverberg's theorem with tolerance.In particular, we give bounds for the smallest integer N = N(t,d,r) such that for any N points in ℝd, there is a partition of them into r parts for which the following condition holds: after removing any t points from the set, the convex hulls of what is left in each part intersect.We prove a bound N = rt + O( $\sqrt{t}$ ) for fixed r,d which is polynomial in each parameters. Our bounds extend to colourful versions of Tverberg's theorem, as well as Reay-type variations of this theorem.
PubDate: 2018-05-01T00:00:00.000Z
DOI: 10.1017/S0963548317000591
Issue No: Vol. 27, No. 3 (2018)

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text:
# Tag Info

19

With version 2.5 of the microtype package, available on CTAN since 13 March 2013, the simple answer to my question is "use microtype". Thanks, Herbert and Joseph, for telling me that this can be done with the microtype package. I did know that microtype can do margin kerning, but I had always thought that this is only about punctuation. In reality, one ...

18

This could be related to a bug with negative protrusion values that I reported a year ago and which is obviously still open. Which luatex version are you using?

17

microtype has an optional argument that you can allow to shift the characters more to the right, e.g. [factor=1300] \documentclass{article} \usepackage[T1]{fontenc} \usepackage{lmodern,picture} \usepackage{microtype} \textwidth=3.85cm \begin{document} \itshape\noindent\makebox(0,0){\put(\textwidth,-2cm){\line(0,-1){80}}}% This is a small text. If jam is ...

16

Your analysis is correct. A couple of years ago, the pdftex team has been discussing whether pdftex should indeed try harder. No clear conclusion transpired except that it would probably be too difficult to get it right in all cases, hence the issue was postponed for later consideration ... maybe too late for pdftex now, and to be passed on to luatex. ...

15

I'd regard this as a bug in csquotes. You can solve it by putting the following code into your preamble, but I can't say if this breaks other things. \makeatletter \def\csq@qclose@ii#1{% \ifdim\lastkern=\csq@omitmarker #1\csq@eqgroup \else \csq@addkern@close \ifodd\csq@qlevel \csq@thequote@oclose \let\csq@kernchar@i\csq@thequote@...

15

I don't think it is reasonable to expect a full list to be created and maintained here. I think it is better to explain how to figure out whether fonts have this support so that users can determine the current answer for a specific font for themselves. If nothing else, this will enable people to check whether an answer here is still correct. Thérèse is ...

12

You can change the default factor like this (5 is not a sensible value but shows the effect quite good: \documentclass[a4paper, 12pt, oneside, article]{memoir} \usepackage{fontspec} \defaultfontfeatures{Ligatures=TeX} \newfontfeature{Microtype}{protrusion=default;expansion=default;} \directlua{fonts.protrusions.setups.default.factor=5} \setmainfont[...

11

It is my understanding that margin kerning does work but that font expansion doesn't. This is one of the reasons why I'm currently using pdflatex and not XeLaTeX: OpenType support in XeTeX is very good because of the fontspec package, but XeTeX is not fully compatible with microtype. You don't explain why you need XeTeX, so I'll explain some possible ...

10

Personally, I think using the Latin Modern fonts with microtype seems to be a better approach \documentclass{article} \usepackage[T1]{fontenc} \usepackage{lmodern,microtype} \textwidth=3.85cm \begin{document} \it\noindent This is a small text. If jam is what you like, two fingers up, or whatever. Under certain conditions you see that the left and right ...

10

First, let us make it work with hyperref. hyperref redefines \@footnotemark itself, so instead of overwriting it, we just patch it with the etoolbox package. \usepackage{etoolbox} ... \makeatletter \newcommand*\new@makefnmark{\hbox{\@textsuperscript{\normalfont \microtypecontext{protrusion=footnote}\@thefnmark}}} \patchcmd{\@footnotemark} {\@...

10

This is indeed (as @yun suspected in his/her first comment to the question) again the bug in luatex with negative protrusion values. The relevant difference between version 2.4 and 2.5 of microtype is not in the package itself but in the configuration file for Latin Modern Roman, which now specifies also negative values for the italics font (which was ...

10

The definition of \thinspace is % latex.ltx, line 1315: \def\thinspace{\kern .16667em } so it's a kern; since it's not followed by glue it's not a feasible line break point. You probably want \hspace{.16667em} instead of it; then \allowbreak is not needed. On the other hand, \ignorespaces does nothing at all where you place it, because its only action ...

9

This is how you can extend or alter existing settings: Make sure that the settings you want to change are already loaded; in the preamble, this isn't guaranteed to be the case, so you need \LoadMicrotypeFile. Create new settings that load the default settings by way of the load key. If you want set protrusion for any glyph to zero, you explicitly have to ...

9

Let me first expand on the possible ways of how to specify characters in microtype's settings: For pdftex, the following input methods are allowed: a character (like A) within the (7-bit) ASCII range you may also use 8-bit (eg., Ä), and UTF-8 characters (eg., …), if the glyph is defined in the input encoding. to remain portable, you may use text ...

8

As @Thorsten mentioned, the problem is that microtype is unable to associate your protrusion settings properly with the footnote. This is because you only specify the font type via the incorrect size - \footnotesize in this case. The warning produced by pdfTeX is Package microtype Warning: I cannot find a protrusion list for font (microtype) ...

7

The point of hanging punctuation is not that you notice it, but rather that you don't notice it (as with most aspects of typography), i.e., the idea is to get the margin more uniform not to have letters stick out into the margin. As an example of use inthe TeX world: The LaTeX Companion makes use of it and you can examine a sample chapter at http://latex-...

7

The example in the TeXbook is obsolete since all current engines support margin kerning without any tricks. For plain XeTeX: \XeTeXprotrudechars=2 \font\rm="TeX Gyre Pagella"\relax \rm \rpcode\font\XeTeXcharglyph\hyphenchar\font=250 \hsize=20mm a a a a a a a a a abbabbabb aabbabbabb abbabb \bye \XeTeXprotrudechars=2 activates protrusion, the \rpcode line ...

7

You can try installing the current beta of the microtype package. Its support of XeTeX is incomplete but protrusion (and hence hanging hyphenation) already works and despite its beta status I haven’t (so far) experienced any difficulties with it.

7

This is indeed, as @egreg has said in the comments, by design (margin kerning is lost after \unhboxing or \unhcopying). But there are two commands that come as remedy: \leftmarginkern and \rightmarginkern allow access to the the respective kerns of an hbox. So to adapt your sample code, the following will reinsert margin kerning: \showboxdepth=20 \...

7

You can define a command that prints an emdash after a small kern (zero is not sufficient, but 1sp is the least nonzero length in TeX and goes unnoticed): \documentclass{article} \usepackage{etoolbox,microtype,showframe} \setlength{\textwidth}{7cm} \newrobustcmd{\npemdash}{% \mbox{\kern1sp ---}% } \begin{document} Let's push the emdash to the next ...

6

This is for lualatex: \documentclass{article} \usepackage{fontspec} \setmainfont[RawFeature={protrusion=default}]{TeX Gyre Pagella} \pdfprotrudechars2 % 1 if you don't want to change line breaking \begin{document} \input{knuth} \end{document}

6

This seems to be fixed in the current 0.80 release This is LuaTeX, Version beta-0.80.0 (TeX Live 2015) (rev 5238) restricted \write18 enabled. (./gg384.tex---- looking at table char 50 table: 0x60106f270 depth = 0 used = false width = 327681 expansion_factor = 333 ...

6

The sticking into the left margin of the second line comes from the character protrusion feature. Very likely package microtype is loaded. The protrusion of the first line is prevented by \begin{flushleft}, which adds an invisible empty box at the very beginning of the paragraph. This can be seen by \showlists with \showboxbreadth=\maxdimen\showboxdepth=\...

6

It is possible to temporarily disable microtype, here an example: \documentclass[12pt,oneside]{report} \usepackage{lmodern} \usepackage[T1]{fontenc} \usepackage[showframe]{geometry} \usepackage[activate,verbose=true]{microtype} \begin{document} \begingroup \microtypesetup{activate=false}% \noindent Disable protrusion from microtype for just one word ...

5

The inner code of \section prevents that the protrusion can work (it inserts a box with a skip and a \noindent). The \protrudeleft command from the question you linked to imho can't work here, as it implicitly assumes that it is used in vertical mode. You can get the protrusion with the following code. Attention This is not a "general" code. It assumes ...

5

I fiddled.... I have no idea what I am doing. If this breaks your document horribly, you get to keep all the itsy-bitsy pieces for yourself. I accept no responsibility if the code collaborates with your cat to order courier delivery of new tin-openers or dials out for pizza when bored. Caveat emptor... The basic problem, I think, is the definition of the ...

4

My bad, punctuation is not hanged at the beginning of a paragraph with an indentation, and this is normal. MWE : \documentclass{article} \usepackage{geometry} % Only for convinency, to show the margin. \geometry{a5paper,showframe} % Small paper, we show the frames. \usepackage{csquotes} % For the command \enquote, automatically in ...

4

I presently load microtype with protrusion adjustments as follows. Perhaps someone is interested in using my values, especially for Times (ptm), which imho has too much protrusion. Please note that my selection of adjustments is not an attempt at being exhaustive. \usepackage[verbose=silent]{microtype} \LoadMicrotypeFile{ptm} \SetProtrusion [ ...

4

See this question. The protrusion is only disabled for the first character of the paragraph, due to the \item (which is hidden in the case of quote and adjustwidth). The answers to that question give some possible solutions, or for simply increasing the margins you can use TeX primitives: {\leftskip 1em\rightskip 1em% `So'' the quotes to the left in this ...

4

I use LuaTeX for the most part, but fall back on XeTeX if a document requires bidi. Use TLContrib (see latex-alive.tumblr.com/post/1303450459 for concise instructions) to get the latest version of microtype. It supports protrusion in XeTeX, though not the other microtypographic features. Protrusion is already enough to fix the worst eyesores. And if you ...

Only top voted, non community-wiki answers of a minimum length are eligible


text:
# Resources tagged with: Interactivities

Filter by: Content type:
Age range:
Challenge level:

### There are 94 results

Broad Topics > Physical and Digital Manipulatives > Interactivities

### Inside Out

##### Age 14 to 16 Challenge Level:

There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you. . . .

### Excel Interactive Resource: Fraction Multiplication

##### Age 11 to 16 Challenge Level:

Use Excel to explore multiplication of fractions.

### Excel Interactive Resource: the up and Down Game

##### Age 11 to 16 Challenge Level:

Use an interactive Excel spreadsheet to explore number in this exciting game!

### Excel Interactive Resource: Interactive Division

##### Age 11 to 16 Challenge Level:

Use an Excel to investigate division. Explore the relationships between the process elements using an interactive spreadsheet.

### Tilting Triangles

##### Age 14 to 16 Challenge Level:

A right-angled isosceles triangle is rotated about the centre point of a square. What can you say about the area of the part of the square covered by the triangle as it rotates?

### Teddy Town

##### Age 5 to 14 Challenge Level:

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

### 3D Treasure Hunt

##### Age 14 to 18 Challenge Level:

Some treasure has been hidden in a three-dimensional grid! Can you work out a strategy to find it as efficiently as possible?

### Jam

##### Age 14 to 16 Challenge Level:

To avoid losing think of another very well known game where the patterns of play are similar.

### Icosian Game

##### Age 11 to 14 Challenge Level:

This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.

### Sliding Puzzle

##### Age 11 to 16 Challenge Level:

The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.

### Cushion Ball Interactivity

##### Age 14 to 16 Challenge Level:

The interactive diagram has two labelled points, A and B. It is designed to be used with the problem "Cushion Ball"

### Changing Places

##### Age 14 to 16 Challenge Level:

Place a red counter in the top left corner of a 4x4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves. . . .

### The Triangle Game

##### Age 11 to 16 Challenge Level:

Can you discover whether this is a fair game?

### Square It

##### Age 11 to 16 Challenge Level:

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

### Excel Interactive Resource: Number Grid Functions

##### Age 11 to 16 Challenge Level:

Use Excel to investigate the effect of translations around a number grid.

### Nine Colours

##### Age 11 to 16 Challenge Level:

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

### Excel Interactive Resource: Equivalent Fraction Bars

##### Age 11 to 16 Challenge Level:

A simple file for the Interactive whiteboard or PC screen, demonstrating equivalent fractions.

### Excel Interactive Resource: Fraction Addition & Fraction Subtraction

##### Age 11 to 16 Challenge Level:

Use Excel to practise adding and subtracting fractions.

### Just Rolling Round

##### Age 14 to 16 Challenge Level:

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

### Drips

##### Age 7 to 14 Challenge Level:

An animation that helps you understand the game of Nim.

### Excel Interactive Resource: Long Multiplication

##### Age 11 to 16 Challenge Level:

Use an Excel spreadsheet to explore long multiplication.

### Excel Interactive Resource: Haitch

##### Age 11 to 16 Challenge Level:

An Excel spreadsheet with an investigation.

### Excel Interactive Resource: Multiples Chain

##### Age 11 to 16 Challenge Level:

Use an interactive Excel spreadsheet to investigate factors and multiples.

### Countdown Fractions

##### Age 11 to 16 Challenge Level:

Here is a chance to play a fractions version of the classic Countdown Game.

### Have You Got It?

##### Age 11 to 14 Challenge Level:

Can you explain the strategy for winning this game with any target?

### Estimating Angles

##### Age 7 to 14 Challenge Level:

How good are you at estimating angles?

### A Tilted Square

##### Age 14 to 16 Challenge Level:

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?

### Disappearing Square

##### Age 11 to 14 Challenge Level:

Do you know how to find the area of a triangle? You can count the squares. What happens if we turn the triangle on end? Press the button and see. Try counting the number of units in the triangle now. . . .

### Colour in the Square

##### Age 7 to 16 Challenge Level:

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

### Fractions and Percentages Card Game

##### Age 11 to 16 Challenge Level:

Can you find the pairs that represent the same amount of money?

### White Box

##### Age 7 to 18 Challenge Level:

This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.

### Factor Lines

##### Age 7 to 14 Challenge Level:

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

### Got It

##### Age 7 to 14 Challenge Level:

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

### Mixed up Mixture

##### Age 14 to 16 Challenge Level:

Can you fill in the mixed up numbers in this dilution calculation?

### Number Pyramids

##### Age 11 to 14 Challenge Level:

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

### Got a Strategy for Last Biscuit?

##### Age 11 to 16 Challenge Level:

Can you beat the computer in the challenging strategy game?

### Rollin' Rollin' Rollin'

##### Age 11 to 14 Challenge Level:

Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?

### Spot the Card

##### Age 14 to 16 Challenge Level:

It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?

### Guesswork

##### Age 14 to 16 Challenge Level:

Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.

### Konigsberg Plus

##### Age 11 to 14 Challenge Level:

Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.

### Partitioning Revisited

##### Age 11 to 14 Challenge Level:

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4

### Stars

##### Age 11 to 14 Challenge Level:

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

### Picturing Triangular Numbers

##### Age 11 to 14 Challenge Level:

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

### Interactive Number Patterns

##### Age 14 to 16 Challenge Level:

How good are you at finding the formula for a number pattern ?

### More Number Pyramids

##### Age 11 to 14 Challenge Level:

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

### Power Crazy

##### Age 11 to 14 Challenge Level:

What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?

### Factors and Multiples Game

##### Age 7 to 16 Challenge Level:

A game in which players take it in turns to choose a number. Can you block your opponent?

### Treasure Hunt

##### Age 7 to 14 Challenge Level:

Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

### Substitution Cipher

##### Age 11 to 14 Challenge Level:

Find the frequency distribution for ordinary English, and use it to help you crack the code.

### First Connect Three

##### Age 7 to 14 Challenge Level:

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?


text:
+0

# help Algebra

0
40
1

If 4x = 3y, what is the value of (2x + y)/(3x - y)?

Dec 27, 2021

### 1+0 Answers

#1
+13015
+1

If 4x = 3y, what is the value of (2x + y)/(3x - y)?

Hello Guest!

$$4x = 3y\\ y=\frac{4x}{3}\\ \color{blue}(2x + y)/(3x - y)\\ =(2x+\frac{4x}{3})/(3x-\frac{4x}{3})\\ =\dfrac{6x+4x}{9x-4x}\\ \color{blue}=2$$

If 4x = 3y,  is  (2x + y) / (3x - y) = 2

!

Dec 27, 2021


text:
# Kanipic U4 cis camtueitrnghJ_ Ieicu AOr nrthema meralonot "L5nan 3sonacankc Icart lo Icat Ir @um n anthcpufhd devuban C 3

###### Question:

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text:
Blinking an LED is all fine and dandy, but it doesn't make for any pretty effects. A breathing LED, now that is something pretty to gaze upon.

But how can we do that? A microcontroller only knows two states, HIGH and LOW, how can we get a state in between these two values?

The trick is to switch your output so quickly that your eyes cannot detect this change. This is what happens when you switch on a light from an AC current. The light is actually blinking so rapidly that you can't see the difference between dark and lit conditions. This is what we'll rely on when changing the perceived brightness of our light.

The lit and non-lit timings are constant in overhead lights, so you don't detect a difference in brightness. However if we increase the time by which it is lit by just a little, it will seem brighter to us. By modifying the ratio when the LED is on and when it is off, also known as the duty-cycle, the LED can be made to appear dimmer or brighter. This method is known as Pulse Width Modulation (PWM).

On the microcontroller, on any pin, 0 corresponds to LOW and 255 corresponds to HIGH. Any value in-between scales accordingly. In order to build a breathing LED, all we have to do is to change some features in our programming and wire our LED differently.

#### Programming

Let's start by redefining our pin. Some pins are capable of PWM and others are not. Select the pin that is capable of PWM, sometimes indicated with a wavy symbol ~ and then define it in setup as follows:

analogPin(D1,OUTPUT);

If you've previously defined this pin as a digitalPin you'll have to change it. Digital signals are HIGH and LOW signals, or 1 and 0. Analog signal on the other hand have a gradient of values. This stems from the historical context whereby scales were used to make measurements before they were replaced by computers which used this sort of fast-changing HIGH and LOW signals to make measurements.

Similarly, since we defined the output as analog, we can write an analog value to the pin:

analogWrite(D1,0);

However, we want to modify this over time, so we'll use a counter for the intensity of our light and a multiplier to make it go up and down. These are constants and we can define them outside of setup:

int count = 0;
int increment = 1;

And we want to increment it in the loop function:

count = count + increment;

But if we reach 255 we want to decrease it and if we are at 0 we want to increase the count:

if (count == 255 && increment == 1)
{
increment = -1;
}
if (count == 0 && increment == -1)
{
increment = 1;
}

Finally we want to set a delay so that it is a slow increase and decrease of the signal:

delay(300);

Now having all the pieces, can you put it together into a sketch?

#### Sketch

int count = 0;
int increment = 1;

void setup ()
{
analogPin(D1,OUTPUT);
}

void loop()
{
if (count == 255 && increment == 1)
{
increment = -1;
}
if (count == 0 && increment == -1)
{
increment = 1;
}
analogWrite(D1,count);
count = count + increment;
delay(300);
}

Note that this is not the most efficient means by which you can program this behaviour. However it is easier to follow. If you have some programming experience and have an alternative solution, use it by all means.

#### Hardware

Reconnect the positive lead to the LED to the pin you defined in your program.

#### FAQ

• Help my LED is blinking not breathing!
Did you connect it to a PWM pin? Refer to the chip capabilities page to determine which pin is capable of PWM output.

#### What you learned

1. What is PWM and how it works.
2. The difference between analog and digital.
3. How to use analogWrite.


text:
# How to solve for the implied stock lending rate given equity options prices?

When market makers price options on hard-to-borrow equities, they include the cost to borrow the underlying equity that their broker is going to charge them to sell the security short to hedge. I'm trying to back-out this cost. I'm guessing it is similar to implied volatility but I'm solving for the interest rate. Can anyone point me in the right direction?

-
Sorry for not being clear. See my edits. –  unclepaul84 Sep 2 '11 at 14:00

The cost of the hedge does not appear directly in the price for any one option, but rather will appear as an apparent violation of put-call parity. However, due to differing demand for puts and calls, this merely widens the arbitrage bounds ordinarily set by put-call parity, but does not imply a single implied borrow rate. In other words, the borrow rate is an input to establishing the put-call parity bounds. One can reverse the relationship to obtain a lower limit on the borrow rate, but an upper limit cannot be inferred.

-

As 'sheegaon' suggested, you can solve for an implied interest rate -- which is not necessarily the cost of borrowing the underlying stock -- using put-call parity.

As you probably know, an implied volatility algorithm increases and decreases its implied volatility guess until the theoretical price and market prices of an option converge. Similarly, to imply options' interest rate and implied volatility, take a put and call pair with the same strike and expiration, and increase or decrease their interest rate and implied volatility inputs until put-call parity holds and the put and call theoretical and market prices converge. In building such algorithms, I take advantage of the property that puts have positive and calls have negative sensitivity to interest rates, while both calls and puts have positive sensitivity to implied volatility.

Note that put-call pairs of different strikes or expirations often imply different rates.

-

Please be aware when you back out implied interest rate for stocks with uncertain dividend payout.

-


text:
Javascript is required
1
JEE Main 2021 (Online) 18th March Morning Shift
Numerical
+4
-1
Two separate wires A and B are stretched by 2 mm and 4 mm respectively, when they are subjected to a force of 2 N. Assume that both the wires are made up of same material and the radius of wire B is 4 times that of the radius of wire A. The length of the wires A and B are in the ratio of a : b. Then a/b can be expressed as 1/x where x is _________.
2
JEE Main 2021 (Online) 16th March Evening Shift
Numerical
+4
-1
For an ideal heat engine, the temperature of the source is 127$$^\circ$$C. In order to have 60% efficiency the temperature of the sink should be ___________$$^\circ$$C. (Round off to the Nearest Integer)
3
JEE Main 2021 (Online) 26th February Evening Shift
Numerical
+4
-1
1 mole of rigid diatomic gas performs a work of $${Q \over 5}$$ when heat Q is supplied to it. The molar heat capacity of the gas during this transformation is $${xR \over 8}$$. The value of x is _________. [R = universal gas constant]
The volume V of a given mass of monoatomic gas changes with temperature T according to the relation $$V = K{T^{{2 \over 3}}}$$. The workdone when temperature changes by 90K will be xR. The value of x is _________. [R = universal gas constant]


text:
# Lesson 9Water Wheels and the Unit CirclePractice Understanding

State a negative angle of rotation that is coterminal with the given angle of rotation. (Coterminal angles share the same terminal side of an angle of rotation.) Sketch and label both angles.

### 1.

Given

Coterminal angle:

### 2.

Given

Coterminal angle:

### 3.

Given

Coterminal angle:

### 4.

Given

Coterminal angle:

### 5.

Given

Coterminal angle:

### 6.

What is the sum of a positive angle of rotation and the absolute value of its negative coterminal angle?

### 7.

Every angle has an infinite number of coterminal angles both positive and negative if the definition is extended to angles of rotation greater than . For example: an angle of is coterminal with angles of rotation measuring , , etc.

Given , name .

Given , name .

## Set

### 8.

Triangle is a right triangle. The length of one side is given. Fill in the values for the missing sides .

### 9.

Each point on the circle marks the end of a terminal ray in standard position. Label the measure of the angle of rotation at each position of the terminal ray. Angles will be in radians. Leave in your answer. (Each section is equal.)

### 10.

Use the values in #8 to write the exact coordinates of the points on the given circle. Be mindful of the numbers that are negative.

### 11.

Find the arc length, , from the point to each point around the circle. Record your answers as decimal approximations to the nearest thousandth.

Use your calculator to find the following values.

### 20.

In which quadrant(s) are sine and cosine both negative?

### 21.

Name an angle of rotation in radians where sine is equal to .

### 22.

Name an angle of rotation where cosine is equal to .

## Go

People in the 1950s and 1960s probably enjoyed music just as much as you do, but they didn’t have modern technology. They had vinyl records and phonographs. Vinyl records came in speeds. A record could be a , , or . These numbers referred to the rpms or revolutions per minute. means it would make in one minute.

### 23.

Calculate the angular speed of a , , and record in degrees per minute.

#### c.

Angular speed describes how fast something is turning. Linear speed describes how far it travels while it is turning. Linear speed depends on the circumference of a circle and the number of revolutions per minute.

Vinyl records were not the same size. A rpm record had a diameter of , a a diameter of , and a had a diameter of .

### 24.

#### a.

If a fly landed on the outer edge of a record, how far would it travel in ?

#### b.

How far if it was perched on the outside edge of a record?

#### c.

How far if it was perched on the outside edge of a record?


text:
# Problem: 2CO2(g) ⇌ 2CO(g) + O2(g)      Kc = 2.0 x 10-7If 2.0 mol of CO2 is placed in a 5.0 Liter container, and decomposes according to the above equation, calculate the concentration of O2 at equilibrium.A. 2.0 x 10-3 MB. 4.6 x 10-3 MC. 9.2 x 10-3 MD. 2.7 x 10-3 ME. 5.8 x 10-3 M

###### FREE Expert Solution

We are being asked to calculate the concentration of O2 at equilibrium:

2 CO2(g) ⇌ 2 CO(g) + O2(g)      Kc = 2.0 x 10-7

When dealing with equilibrium and Kc:

Kc → equilibrium units are in molarity
Kc is an equilibrium expression:

$\overline{){{\mathbf{K}}}_{{\mathbf{c}}}{\mathbf{=}}\frac{\mathbf{products}}{\mathbf{reactants}}}$

only aqueous and gaseous species are included in the equilibrium expression
▪ the coefficient of each compound in the reaction equation will be the exponent of the concentrations in the equilibrium expression

We're going to calculate for the final concentration of HI(g) using the following steps:

89% (288 ratings)
###### Problem Details

2CO2(g) ⇌ 2CO(g) + O2(g)      Kc = 2.0 x 10-7

If 2.0 mol of CO2 is placed in a 5.0 Liter container, and decomposes according to the above equation, calculate the concentration of O2 at equilibrium.

A. 2.0 x 10-3 M

B. 4.6 x 10-3 M

C. 9.2 x 10-3 M

D. 2.7 x 10-3 M

E. 5.8 x 10-3 M


text:
# Express the Laplacian of $u \ldots ∂$

Let $u=u(x,y)$. Now make the change of variables $x=x(r,θ)=r\cos θ$, $y=y(r,θ)=r\sin θ$. Express the Laplacian of $u$: $∂^2 u/∂x^2 + ∂^2 u/∂y^2$ in terms of derivatives of $u$ with respect to $r$ and $θ$ and everything should be in terms of $r$ and $θ$ with also the assumption that all partials are continuous.

-

It's a boring but standard application of the chain rule. For example, $$\frac{\partial u}{\partial x} = \frac{\partial u}{\partial r} \frac{\partial r}{\partial x}+\frac{\partial u}{\partial \theta} \frac{\partial \theta}{\partial x}.$$

A general, but complicated, approach to the Laplace operator in different coordinate systems is outlined here. Actually, $\mathbb{R}^n$ can be endowed with several riemannian metrics, and we get different expressions for the Laplace-Beltrami operator. When we use the flat metric, we get the standard Laplace operator. If we introduce curvilinear coordinates, then the expression changes.

-
...and the product rule, I think. And shouldn't one also ask whether the bottom line has an intuitive justification that might suggest other ways of proving it? – Michael Hardy May 6 '12 at 17:25
Once upon a time, I learned that there is a powerful formula in Riemannian geometry, and that this formula contains almost every reasonable change of variables: polar coordinates, cylindrical coordinates, etc. It uses the coefficients of the metric in local coordinates, but I'm an analyst and I can't remember the most general expression :-) – Siminore May 7 '12 at 9:27


text:
+1 vote
For a peridic square wave ,which one of the following statements is TRUE?

1). The fourieF series coefficients do not exist

2).The Fourier series coefficients exist but the reconstruction converges at most point.

I know the correct answer is 2). But I need some explanation.


text:
# Jacobi iteration to reduce the quadratic function

Given certain function $f(X)$ which is quadratic in $X\in\mathbb{R}^{n\times d}$,

$$\frac{1}{2}tr(X^TAX) - tr(Y^TBX)$$ for positive definite weighted Laplacian matrices $A, B\in\mathbb{R}^{n\times n}$, i.e. the diagonal elements are negative summation of the negative off-diagonal elements plus a constant for strict diagonal dominance: $A=\left(\begin{array}{ccccc} c_1+\sum a_{1s} & & & & \\ & \ddots & & -a_{ij} \\ & & \ddots & & \\ & -a_{ij} & & \ddots & \\ & & & & c_n+\sum a_{ns} \end{array}\right) \in\mathbb{R}^{n\times n},$

and an arbitrary $Y\in\mathbb{R}^{n\times d}$. In order to obtain its minimim, I set the gradient to $0$,

$$\nabla f(X) = AX-BY \tag 1$$

so, the solution to the following linear system

$$AX=BY \tag 2$$

with the unknown $X$ would give me the minimizer of $f(X)$. Since $A$ is strictly diagonally dominant, the system is solved by Jacobi iteration known to converge to exact solution in this case.

However, I'm interested if only $a$ $single$ iteration of Jacobi method on some arbitrary initialization $X_0$ would yield result $X_1$ that satisfies $f(X_1)<f(X_0)$.

Note that I tried many books on Jacobi method, but I was unable to make the connection with the optimization problem. The Jacobi method is known to yield "progressive better results" to the linear system, but I'm not sure what this implies precisely, and what implications it might have on the above optimization attempt. On one place I found that the Jacobi iterands $\{X_0, X_1, \dots, X_{k-1}, X_{k}\}$ satisfy

$$\lVert X-X_k\rVert_2 < \lVert X-X_{k-1} \rVert_2 \tag 3$$

where $X$ is the true solution to (2). Does the proof on the convergence of Jacobi actually imply (3)? And, if so, does that imply progressively lower values of $f(X_k)$, $k\in\{0, 1, \dots, \}$?

One way I tried is $f(X_1)-f(X_0)<0$, with the replacement as in Jacobi $$X_1=D^{-1}(BY-RX_0)$$

with the splitting $A=D+R$, where $D=diag(A)$, but was unable to regroup the terms.

I would appreciate if the answers would contain supporting references, so that I might explore the connection more deeply.

• If there is a way to state that, given $$f(x)=\frac{1}{2}x^TAx -b^TX$$ the value of $f(x_1)-f(x_0)<0$, where $x_1=D^{-1}(b-Rx_0)$, and the splitting $A=D+R$, as above, perhaps that could somehow be translated to the actual problem. If it helps, assume diagonal entries of $A$ are the only positive entries. Well, the intuitions tells that each Jacobi iteration should decrease the function value, but the problem is to state it formaly. Mar 1, 2012 at 12:23

Your conjecture is true. Let us define $\Delta x_k = x_{k+1}-x_k$, $x=A\backslash b$, $e_k=x-x_k$. By the definition of iteration, $\Delta x_k = D^{-1}Ae_k$. So $$f(x_{k+1}) - f(x_k) \\ = x_k^TA\Delta x_k + \frac{1}{2}\Delta x_k^TA\Delta x_k - (Ax)^T \Delta x_k\\ = -e_k^TA\Delta x_k + \frac{1}{2}\Delta x_k^T A \Delta x_k\\ = \frac{1}{2}e_k^T A D^{-1}AD^{-1} A e_k - e_k^T A D^{-1}A e_k = \frac{1}{2}v_k^T D^{-1/2}AD^{-1/2} v_k-v_k^Tv_k = v_k^T(\frac{1}{2}D^{-1/2}AD^{-1/2}-I)v_k.$$ Then, from convergence condition of Jacobi iteration that the spectra of $I-D^{-1}A$ is less than one, you can deduce your conjecture. To this end, we note that

1. $\frac{1}{2}D^{-1/2}AD^{-1/2}-I$ is symmetric so its definiteness is equivalent to its spectra lies on one side of zero.

2. $D^{-1/2}AD^{-1/2}$ have the same spectra with $D^{-1}A$ from the fact spectra is invariant under commutation.

3. The spectra of $D^{-1}A$ lies in $(0,2)$.

• Thanks. I guess your implying that the matrix withing the brackets of the last line is negative semi-definite. How to prove that? Mar 1, 2012 at 15:38
• I have added more hints. Hope it helps. Mar 1, 2012 at 15:51
• Yes, thanks. Just a reference on 2. would be appreciated; you're not implying $D^{-1/2}AD^{-1/2}=D^{-1}A$ ? Mar 1, 2012 at 16:19
• No, the two matrices are not equal. But their spectra coincide. You can prove it by the following argument: if $ABx=\lambda x$, then $BA(Bx)=\lambda (Bx)$. Mar 1, 2012 at 16:49
• Is the spectra from 3. covering $(0, 2)$? Mar 2, 2012 at 12:21


text:
# mcrl2/pbes/find.h¶

Include file:

#include "mcrl2/pbes/find.h"

Search functions of the pbes library.

## Classes¶

• mcrl2::pbes_system::detail::find_propositional_variables_traverser

## Functions¶

void mcrl2::pbes_system::find_all_variables(const T &x, OutputIterator o)

Returns all variables that occur in an object.

Parameters:

• x an object containing variables
• o an output iterator to which all variables occurring in x are written.

Returns: All variables that occur in the term x

std::set<data::variable> mcrl2::pbes_system::find_all_variables(const T &x)

Returns all variables that occur in an object.

Parameters:

• x an object containing variables

Returns: All variables that occur in the object x

void mcrl2::pbes_system::find_free_variables(const T &x, OutputIterator o)

Returns all variables that occur in an object.

Parameters:

• x an object containing variables
• o an output iterator to which all variables occurring in x are added.

Returns: All free variables that occur in the object x

std::set<data::variable> mcrl2::pbes_system::find_free_variables(const T &x)

Returns all variables that occur in an object.

Parameters:

• x an object containing variables

Returns: All free variables that occur in the object x

void mcrl2::pbes_system::find_free_variables_with_bound(const T &x, OutputIterator o, const VariableContainer &bound)

Returns all variables that occur in an object.

Parameters:

• x an object containing variables
• o an output iterator to which all variables occurring in x are written.
• bound a container of variables

Returns: All free variables that occur in the object x

std::set<data::variable> mcrl2::pbes_system::find_free_variables_with_bound(const T &x, VariableContainer const &bound)

Returns all variables that occur in an object.

Parameters:

• x an object containing variables
• bound a bound a container of variables

Returns: All free variables that occur in the object x

void mcrl2::pbes_system::find_function_symbols(const T &x, OutputIterator o)

Returns all function symbols that occur in an object.

Parameters:

• x an object containing function symbols
• o an output iterator to which all function symbols occurring in x are written.

Returns: All function symbols that occur in the term x

std::set<data::function_symbol> mcrl2::pbes_system::find_function_symbols(const T &x)

Returns all function symbols that occur in an object.

Parameters:

• x an object containing function symbols

Returns: All function symbols that occur in the object x

void mcrl2::pbes_system::find_identifiers(const T &x, OutputIterator o)

Returns all identifiers that occur in an object.

Parameters:

• x an object containing identifiers
• o an output iterator to which all identifiers occurring in x are written.

Returns: All identifiers that occur in the term x

std::set<core::identifier_string> mcrl2::pbes_system::find_identifiers(const T &x)

Returns all identifiers that occur in an object.

Parameters:

• x an object containing identifiers

Returns: All identifiers that occur in the object x

void mcrl2::pbes_system::find_propositional_variable_instantiations(Container const &container, OutputIterator o)

Returns all data variables that occur in a range of expressions.

Parameters:

• container a container with expressions
• o an output iterator to which all data variables occurring in t are added.

Returns: All data variables that occur in the term t

std::set<propositional_variable_instantiation> mcrl2::pbes_system::find_propositional_variable_instantiations(Container const &container)

Returns all data variables that occur in a range of expressions.

Parameters:

• container a container with expressions

Returns: All data variables that occur in the term t

void mcrl2::pbes_system::find_sort_expressions(const T &x, OutputIterator o)

Returns all sort expressions that occur in an object.

Parameters:

• x an object containing sort expressions
• o an output iterator to which all sort expressions occurring in x are written.

Returns: All sort expressions that occur in the term x

std::set<data::sort_expression> mcrl2::pbes_system::find_sort_expressions(const T &x)

Returns all sort expressions that occur in an object.

Parameters:

• x an object containing sort expressions

Returns: All sort expressions that occur in the object x

bool mcrl2::pbes_system::search_variable(const T &x, const data::variable &v)

Returns true if the term has a given variable as subterm.

Parameters:

• x an expression
• v a variable

Returns: True if v occurs in x.

## Functions¶

find_propositional_variables_traverser<Traverser, OutputIterator> mcrl2::pbes_system::detail::make_find_propositional_variables_traverser(OutputIterator out)


text:
June 19, 2017

The Geometric McKay Correspondence (Part 1)

Posted by John Baez

The ‘geometric McKay correspondence’, actually discovered by Patrick du Val in 1934, is a wonderful relation between the Platonic solids and the ADE Dynkin diagrams. In particular, it sets up a connection between two of my favorite things, the icosahedron:

and the $\mathrm{E}_8$ Dynkin diagram:

When I recently gave a talk on this topic, I realized I didn’t understand it as well as I’d like. Since then I’ve been making progress with the help of this book:

• Alexander Kirillov Jr., Quiver Representations and Quiver Varieties, AMS, Providence, Rhode Island, 2016.

I now think I glimpse a way forward to a very concrete and vivid understanding of the relation between the icosahedron and E8. It’s really just a matter of taking the ideas in this book and working them out concretely in this case. But it takes some thought, at least for me. I’d like to enlist your help.

Posted at 9:30 PM UTC | Permalink | Followups (17)

June 10, 2017

Eliminating Binders for Easier Operational Semantics

Posted by John Baez

guest post by Mike Stay

Last year, my son’s math teacher introduced the kids to the concept of a function. One of the major points of confusion in the class was the idea that it didn’t matter whether he wrote $f(x) = x^2$ or $f(y) = y^2$, but it did matter whether he wrote $f(x) = x y$ or $f(x) = x z$. The function declaration binds some of the variables appearing on the right to the ones appearing on the left; the ones that don’t appear on the left are “free”. In a few years when he takes calculus, my son will learn about the quantifiers “for all” and “there exists” in the “epsilon-delta” definition of limit; quantifiers also bind variables in expressions.

Reasoning formally about languages with binders is hard:

“The problem of representing and reasoning about inductively-defined structures with binders is central to the PoplMark challenges. Representing binders has been recognized as crucial by the theorem proving community, and many different solutions to this problem have been proposed. In our (still limited) experience, none emerge as clear winners.” – Aydemir, Bohannon, Fairbairn, Foster, Pierce, Sewell, Vytiniotis, Washburn, Weirich, and Zdancewic, Mechanized metatheory for the masses: The PoplMark challenge. (2005)

The paper quoted above reviews around a dozen approaches in section 2.3, and takes pains to point out that their review is incomplete. However, recently Andrew Pitts and his students (particularly Murdoch Gabbay) developed the notion of a nominal set (introductory slides, book) that has largely solved this problem. Bengston and Barrow use a nominal datatype package in Isabell/HOL to formalize $\pi$-calculus, and Clouston defined nominal Lawvere theories. It’s my impression that pretty much everyone now agrees that using nominal sets to formally model binders is the way forward.

Sometimes, though, it’s useful to look backwards; old techniques can lead to new ways of looking at a problem. The earliest approach to the problem of formally modeling bound variables was to eliminate them.

Posted at 1:24 PM UTC | Permalink | Followups (9)

June 7, 2017

Enriched Lawvere Theories for Operational Semantics

Posted by John Baez

guest post by Mike Stay

Programs are an expression of programmer intent. We want the computer to do something for us, so we need to tell it what to do. We make mistakes, though, so we want to be able to check somehow that the program will do what we want. The idea of semantics for a programming language is that we assign some meaning to programs in such a way that we can reason about the behavior of a program. There are two main approaches to this: denotational semantics and operational semantics. I’ll discuss both below, but the post will focus for the most part on operational semantics.

There’s a long history of using 2-categories and related structures for term rewriting and operational semantics, but Greg Meredith and I are particularly fond of an approach using multisorted Lawvere theories enriched over the category of reflexive directed graphs, which we call Gph. Such enriched Lawvere theories are equal in power to, for instance, Sassone and Sobociński’s reactive systems, but in my opinion they have a cleaner categorical presentation. We wrote a paper on them:

Here I’ll just sketch the basic ideas.

Posted at 8:51 AM UTC | Permalink | Followups (21)


text:
# plotMD

0th

Percentile

##### Mean-Difference Plot of Expression Data

Creates a mean-difference plot (aka MA plot) with color coding for highlighted points.

Keywords
hplot
##### Usage
"plotMD"(object, column = 1, xlab = "Average log-expression", ylab = "Expression log-ratio (this sample vs others)", main = colnames(object)[column], status=NULL, ...)
"plotMD"(object, column = 1, array = NULL, xlab = "Average log-expression", ylab = "Expression log-ratio (this sample vs others)", main = colnames(object)[column], status=object$genes$Status, zero.weights = FALSE, ...)
"plotMD"(object, column = 1, array = NULL, xlab = "A", ylab = "M", main = colnames(object)[column], status=object$genes$Status, zero.weights = FALSE, ...)
"plotMD"(object, column = 1, array = NULL, xlab = "A", ylab = "M", main = colnames(object)[column], status=object$genes$Status, zero.weights = FALSE, ...)
"plotMD"(object, column = ncol(object), coef = NULL, xlab = "Average log-expression", ylab = "log-fold-change", main = colnames(object)[column], status=object$genes$Status, zero.weights = FALSE, ...)
##### Arguments
object
an RGList, MAList, EList, ExpressionSet or MArrayLM object. Alternatively a numeric matrix.
column
integer, column of object to be plotted.
array
alternative to column for microarray data objects. If specified, then column is ignored.
coef
alternative to column for fitted model objects. If specified, then column is ignored.
xlab
character string, label for x-axis
ylab
character string, label for y-axis
main
character string, title for plot
status
vector giving the control status of each spot on the array, of same length as the number of rows of object. If NULL, then all points are plotted in the default color, symbol and size.
zero.weights
logical, should spots with zero or negative weights be plotted?
...
other arguments are passed to plotWithHighlights.
##### Details

A mean-difference plot (MD-plot) is a plot of log-intensity ratios (differences) versus log-intensity averages (means). For two color data objects, a within-array MD-plot is produced with the M and A values computed from the two channels for the specified array. This is the same as a mean-difference plot (mdplot) with the red and green log2-intensities of the array providing the two columns.

For single channel data objects, a between-array MD-plot is produced. An articifial array is produced by averaging all the arrays other than the array specified. A mean-difference plot is then producing from the specified array and the artificial array. Note that this procedure reduces to an ordinary mean-difference plot when there are just two arrays total.

If object is an MArrayLM object, then the plot is an fitted model MD-plot in which the estimated coefficient is on the y-axis and the average A-value is on the x-axis.

The status vector can correspond to any grouping of the probes that is of interest. If object is a fitted model object, then status vector is often used to indicate statistically significance, so that differentially expressed points are highlighted. If object is a microarray data object, then status might distinguish control probes from regular probes so that different types of controls are highlighted.

The status can be included as the component object$genes$Status instead of being passed as an argument to plotMD.

See plotWithHighlights for how to set colors and graphics parameters for the highlighted and non-highlighted points.

##### Note

This function is an alternative to plotMA, which was one of the original functions of the limma package in 2002. The history of mean-difference plots and MA-plots is reviewed in Ritchie et al (2015).

##### References

Ritchie, ME, Phipson, B, Wu, D, Hu, Y, Law, CW, Shi, W, and Smyth, GK (2015). limma powers differential expression analyses for RNA-sequencing and microarray studies. Nucleic Acids Research Volume 43, e47. http://nar.oxfordjournals.org/content/43/7/e47

The driver function for plotMD is plotWithHighlights. See also mdplot for a very basic mean-difference plot function.

An overview of plot functions available in LIMMA is given in 09.Diagnostics.

##### Aliases
• plotMD
• plotMD.RGList
• plotMD.MAList
• plotMD.EListRaw
• plotMD.EList
• plotMD.MArrayLM
• plotMD.default
##### Examples
A <- runif(1000,4,16)
y <- A + matrix(rnorm(1000*3,sd=0.2),1000,3)
status <- rep(c(0,-1,1),c(950,40,10))
y[,1] <- y[,1] + status
plotMD(y, column=1, status=status, values=c(-1,1), hl.col=c("blue","red"))

MA <- new("MAList")
MA$A <- runif(300,4,16) MA$M <- rt(300,df=3)

# Spike-in values
MA$M[1:3] <- 0 MA$M[4:6] <- 3
MA$M[7:9] <- -3 status <- rep("Gene",300) status[1:3] <- "M=0" status[4:6] <- "M=3" status[7:9] <- "M=-3" values <- c("M=0","M=3","M=-3") hl.col <- c("blue","red","green") plotMD(MA,main="MA-Plot with 12 spiked-in points", status=status, values=values, hl.col=hl.col) # Same as above but setting graphical parameters as attributes attr(status,"values") <- values attr(status,"col") <- hl.col plotMD(MA, main="Mean-Difference Plot with 12 spiked-in points", status=status) # Same as above but passing status as part of object MA$genes$Status <- status plotMD(MA, main="Mean-Difference Plot with 12 spiked-in points") # Change settings for background points MA$genes\$Status <- status
plotMD(MA, bg.pch=1, bg.cex=0.5)

Documentation reproduced from package limma, version 3.28.14, License: GPL (>=2)

### Community examples

Looks like there are no examples yet.


text:
# Set Theory Seminar - Ralf Schindler (Munster), "Paradoxical" sets with no well-ordering of the reals

Title: "Paradoxical" sets with no well-ordering of the reals
Abstract: By a Hamel basis we mean a basis for the reals, R, construed as a vecor space over
the field of rationals. In 1905, G. Hamel constructed such a basis from a well-ordering
of R. In 1975, D. Pincus and K. Prikry asked "whether a Hamel basis exists in any
model in which R cannot be well ordered." About two years ago, we answered this positively
in a joint paper with M. Beriashvili, L. Wu, and L. Yu. In more recent joint
work, additionally with J. Brendle and F. Castiblanco we constructed a model of
ZF with a Luzin set, a Sierpiński set, a Burstin basis, and a Mazurkiewicz set,
but with no well-ordering of R. In joint work with V. Kanovei, we constructed such a model in which even all those "paradoxical" sets are projective.

## Date:

Wed, 27/03/2019 - 14:00 to 15:30

Ross 63