Why is there sometimes a semicolon before an anonymous function?
What does the leading semicolon in JavaScript libraries do?
polytopes as inequalities sistem solutions in R3 (x-y-z) cartesian space i'm here to ask if there's a TikZ/pgf support to draw areas resulting from a system of linear inequalities, into a xyz cartesian space. i found examples of my needs for xy plan at , but i also need to draw some 3d polytopes.  the problem is coordinate system as i found in pgfmanual.pdf seems not suited for R3: only (,) support but i need something like (,,).  As an example, i need to do drawings like this:    but i also need to get a colored surface with a 50% transparent color.  The system which generated that polytope is quite simple and is a linear programming problem:  x_1 + x_2 + x_3 &lt;= 4 x_1             &lt;= 2             x_3 &lt;= 3     3*x_2 + x_3 &lt;= 6 x_1             >= 0       x_2       >= 0             x_3 >= 0    Can you advise me some url/article/doc which can help me, or make me some example to lead me to learn how to reach my target?  Thank you for your attention I made a huge project, wanted to reduce file size from 1.3GB to below 1GB. Compressing did not help. I removed objects from scene. Also textures. I then realized, the file size even was the same when I delete ALL objects. Why?  Download of sample:   Before deleting all: 1.2GB, after: 1.1GB. What is the difference between .pem, .csr, .key and .crt and other such file extensions? I'm new to SSL / TLS and I want to work with the OpenSSL toolkit.  I don't know what .pem and .csr stands for?  I do know that .key is the private key and .crt is the public key. The Frobenius Coin Problem I am asked to prove that:       For integers $n, x,y &gt; 0$, where $x,y$ are relatively prime,        every $n \ge (x-1) (y-1)$ can be expressed as $xa + yb$, with nonnegative integers $a,b \ge0$.   How should I approach this? I have very limited knowledge in number theory. I imported the coordinates from an Excel table. They show as single points as intended. Now I want to add columns to the attribute table, but I'm not able to edit it. I wanted to import the following columns from Excel as well, but that doesn't seem to work either.  Sorry for the noob-question, but I couldn't find anything relating the theme through google and such.  Ok, with pictures then: I want to use that to add columns with information to these       You see, the small pensil thingy is greyed out, so I can't edit anything in this layer and I can't add any information to my points.  If I try Ale suggestion I get this error: Show $a\Bbb Z+b\Bbb Z = \gcd(a,b)\Bbb Z$ if $A$ subset of $B$ then $P(B)-P(A)=P(B\setminus A)\ge 0$ Let $P$ be a probability measure on $(\Omega, \mathscr{F})$, If $a,b,\in\mathscr{F}$ and $A\subset B$, then $P(B)-P(A)=P(B\setminus A)\ge 0$.  So far I have:  $A\subset B \implies B\setminus A = B\cap A^c = \emptyset$ as $A$ and $B^c$ are disjoint. Since $A\cup (B\setminus A)=A\cup (B\cap A^c)=(A\cup B)\cap (A\cup A^c)=B\cap\Omega = B$  Then for $A,B\in \mathscr{F}\implies P(A\cup (B\setminus A))=P(A)+P(B\setminus A) = P(B)$ by countable additivity.  Rearranging, $P(B)-P(A)=P(B\setminus A) \ge 0$. Intuituive reason why Fermats last theorem holds I am unsure of whether it is normal, but to me, intuitively Fermats last theorem should not hold.  If anyone intuitively believed it to be correct, why?     Can someone explain so I understand somewhat why FLT holds without reading a massive and complex proof? What is Java's answer to WPF? I'm mostly a .Net person at the moment, but I've been playing with Java some lately-- exploring what's out there.  Now I'm looking for the Java equivalent for WPF.  I know I could find an OpenGL library or two out there, but that's not really as rich or simple as the WPF system. I need to write a Java Comparator class that compares Strings, however with one twist.  If the two strings it is comparing are the same at the beginning and end of the string are the same, and the middle part that differs is an integer, then compare based on the numeric values of those integers.  For example, I want the following strings to end up in order they're shown:   aaa bbb 3 ccc bbb 12 ccc ccc 11 ddd eee 3 ddd jpeg2000 eee eee 12 ddd jpeg2000 eee   As you can see, there might be other integers in the string, so I can't just use regular expressions to break out any integer.  I'm thinking of just walking the strings from the beginning until I find a bit that doesn't match, then walking in from the end until I find a bit that doesn't match, and then comparing the bit in the middle to the regular expression "[0-9]+", and if it compares, then doing a numeric comparison, otherwise doing a lexical comparison.  Is there a better way?  Update I don't think I can guarantee that the other numbers in the string, the ones that may match, don't have spaces around them, or that the ones that differ do have spaces. How can I enable Ctrl+Alt+Backspace? Ctrl+Alt+← can usually be set to restart X, however I can't find the option to allow this (it is disabled by default).  I have looked in System-&gt;Preferences-&gt;Keyboard and System-&gt;Preferences-&gt;Keyboard Shortcuts but I can't find an option to enable it.  Where can I change this setting? I was wondering if there is a viable place on Stack Exchange to ask economics-related questions.  Questions I'd have in particular could be equation-based or theoretical.  I suppose the equation-based questions could possibly fit into mathematics but I haven't checked their FAQ. Does scaling lead to weak convergence to the null function? Let $f\in L^p(\mathbb{R}^d)$, with $1&lt;p&lt;\infty$. Is it true that    $$\lambda^{\frac{d}{p}}f(\lambda x ) \rightharpoonup 0\quad \text{ weakly in }L^p\text{ as }\lambda\to+\infty?$$   One has the easy case for $f\in L^{p-\epsilon}\cap L^p$. This condition allows the use of Hölder's inequality as follows (here $\frac{1}{p}+\frac{1}{p'}=1$ and $\phi$ is a continuous function with compact support):  $$\begin{split}\left\lvert \int_{\mathbb{R}^d} \lambda^{\frac{d}{p}} f(\lambda x)\phi(x)\, dx\right\rvert&amp; \le \lambda^{\frac{d}{p}}\lVert f(\lambda x)\rVert_{L^{p-\epsilon}}\lVert \phi\rVert_{L^{(p-\epsilon)'}} \\  &amp;= \lambda ^{\frac{d}{p}- \frac{d}{p-\epsilon} } \lVert f\rVert_{L^{p-\epsilon}}\lVert\phi\rVert_{L^{(p-\epsilon)'}}\to 0. \end{split} $$ But what happens if that condition is removed? I carried out an explicit check on the standard example of a function $f$ that belongs to $L^2(\mathbb{R})$ and does not belong to $L^{2-\epsilon}(\mathbb{R})$ for any $\epsilon &gt; 0$, namely  $$f(x)=\begin{cases} 0 , &amp; x&lt;2 \\ \frac{1}{\sqrt{x}\log x}, &amp; x \ge 2\end{cases}.$$ Taking $\phi=\chi_{[a, b]}$ with $2&lt;a&lt;b$ one has  $$\left \lvert \int_{\mathbb{R}} \lambda^{\frac{1}{2}}f(\lambda x)\phi(x)\, dx \right\rvert  = \dfrac{  \int_{\lambda a }^{\lambda b} \frac{dy}{\sqrt{y}\log(y)} } {\lambda^{\frac{1}{2}}}, $$ and an application of l'Hôpital's rule shows that the right hand side tends to $0$ as $\lambda \to \infty$. This implies weak convergence to $0$ by a standard density argument.   This seems to point towards an affirmative answer to the question in the gray box. Implementation of "show" for function Autosegmental Representation in tikz-qtree This is what I want to achieve    and this:    But all I've been able to make with tikz-qtree is the following:  \documentclass[12pt,a4]{article} \usepackage[utf8]{inputenc} \usepackage{tipa,tikz,tikz-qtree} \begin{document}  \begin{tikzpicture} [baseline] \tikzset{frontier/.style={distance from root=90pt}} \Tree [.$\sigma$ [.O [ p ] ] [.R [.$\mu$ a ] [.$\mu$ : ] ] ] \end{tikzpicture} \begin{tikzpicture} [baseline] \tikzset{frontier/.style={distance from root=90pt}} \Tree [.$\sigma$ [.O [ p ] ] [.R [.$\mu$ a ]  ] ] \end{tikzpicture}   And this:  \begin{tikzpicture}[baseline] \tikzset{frontier/.style={distance from root=90pt}} \Tree [.$\sigma$ [.O [ l ] ] [.R [.$\mu$ a ] [.$\mu$ l ] ] ] \end{tikzpicture} \begin{tikzpicture} [baseline] \tikzset{frontier/.style={distance from root=90pt}} \Tree [.$\sigma$ [.O [ : ] ] [.R [.$\mu$ a ] [ l ] ] ] \end{tikzpicture} \end{document}   Which renders:    and    The important part here is the linking from the leaves to more than one parent (it would be nice if I had the option of making the line dashed too). Now, pst-asr doesn't quite achieve what I want it to. It's important that I have the moras ('mu's). (Also it's a pstricks package, which means I must typeset it in DVIPSPDF.) I have tried a bit of the forest-package (especially forest-GP1), but I can't make that work as I want either. Lastly, some have recommended xyling, but I find that package very difficult to use.  Any recommendations?  Thanks. What is the difference between using a colon and a semi-colon to join two sentences? I've seen a few questions on this site relating to semi-colons, which I believe I correctly understand, but what I'm not as clear about is colons.  For example:     The man ate the apple; it tasted good.   Is this not correctly also written as:     The man ate the apple: it tasted good.   In this case, what is the difference between the two sentences? Running out of cards in Exploding Kittens In the Exploding Kittens game, the rules say     You won't ever run out of cards in the Draw Pile, so there is never any need for a reshuffle.   In every game I've played all the cards end up on the discard pile fairly quickly and there is nothing left in the draw pile, so we have to reuse them.  Is this meant to happen? Are we doing something wrong? Find and replace text within multiple files What changes with Kerberos authentication in IPv6 when everyone has a public IPv6 Address? How should Kerberos authentication be set up with IPv6?     What implications are there when client devices each use a public, globally routeable IPv6 IP address?  What changes when setup this way instead of using a NAT as was the norm with IPv4? Someone told me I need a ticket out of Thailand in order to enter.  I am traveling to Thailand, on March 18th. I have a Ticket from Bangkok to Sweden booked for June 4th.   I will be staying in Thailand for 2 weeks when I arrive there, then traveling around Cambodia, Laos and Vietnam until June 4th when I leave.   With that ticket out of Thailand, will I be able to get in and get a (30 day) Visa-On-Arrival (or not because the ticket out is not within the first 30 days). Or do I need to show proof that I am leaving within 2 weeks of being there at first?