that appears above the captcha seems to be broken.    (You can also )  This appears to affect    , even though they use different images.       Note that if you view the image URL directly and accept the SSL warning, all the images may appear to start working for you - but restarting your browser will reveal broken images again.   I actually encounter this captcha quite frequently due to writing up my answers in an external editor, and then pasting them in as a new response. I just started noticing the broken image today.
Noticing that the "Human Verification" image did not show, I found that the src, , shows that sstatic.net is giving an SSL vertificate for *.stackexchange.com..
Adjusting space between array rows and columns \documentclass[english]{article} \usepackage[T1]{fontenc} \usepackage[latin9]{inputenc} \usepackage{babel} \begin{document} % ... \[ \begin{array}{ccccc} x(1) &amp; = &amp; \frac{x(0)}{1} &amp; = &amp; x(0)\\ x(2) &amp; = &amp; \frac{x(1)}{2} &amp; = &amp; \frac{x(0)}{2}\\ x(3) &amp; = &amp; \frac{x(2)}{3} &amp; = &amp; \frac{x(0)}{2.3}\\ x(4) &amp; = &amp; \frac{x(3)}{4} &amp; = &amp; \frac{x(0)}{4!}\\  &amp;  &amp;  &amp;  &amp; \vdots\\ x(n) &amp; = &amp; \frac{x(n-1)}{n} &amp; = &amp; \frac{x(0)}{n!} \end{array} \] % ... \end{document}   Because of the fractions in the array cells, array elements are vertically too close to each other, they are literally touching to each other. Also the horizontal spacing is too much as you see in the image (screen shot from the output PDF file).  How do I make these cell-spacings look better? "In" vs. "after" for future talk The class will be over in 10 minutes. The class will be over after 10 minutes.  I know the first is correct but why? I would like to configure Apache 2 running on Kubuntu to execute Perl CGI scripts. I've tried some steps that I came across by googling, but nothing seems to work.  What is the right way of achieving this? I can't seem to access instance members of the surrounding class from inside an enum, as I could from inside an inner class. Does that mean enums are static? Is there any access to the scope of the surrounding class's instance, or do I have to pass the instance into the enum's method where I need it?  public class Universe {     public final int theAnswer;      public enum Planet {         // ...         EARTH(...);         // ...          // ... constructor etc.          public int deepThought() {             // -&gt; "No enclosing instance of type 'Universe' is accessible in this scope"             return Universe.this.theAnswer;         }     }      public Universe(int locallyUniversalAnswer) {         this.theAnswer = locallyUniversalAnswer;     } } Cards entering the battlefield simultaneously and "Enter the Battlefield" effects How do we perform transverse measurements in a two level system? In quantum mechanics any two level system can be mapped onto effective spin variables. If the system is defined by two energy levels, $|E_1\rangle$ and $|E_2\rangle$, the Hamiltonian is  $$ H = \left(\begin{array}{cc} E_1 &amp; 0 \\ 0 &amp; E_2 \end{array}\right) \, .$$  This can be recast as  $$ H = \frac{E_1+E_2}{2} 1\!\!1 + \frac{E_1-E_2}{2} \sigma_3\, .$$  $1\!\!1$ is the identity operator and $\sigma_3$ is the third pauli matrix. This is very nice because we can now apply our knowledge and intuition of spin dynamics to any two level system.  My question is the following: for a real spin I can measure expectation values of $\sigma_{1,2}$ by physically rotating my system and align its $x$ or $y$ axis with my measuring apparatus. How do I do this (in the lab!) with a pseudo-spin system? Imagine I am looking at a cold atom and I want to know if the system is in an symmetric or anti-symmetric superposition of $|E_1\rangle$ and $|E_2\rangle$, how do I do it? How to prove that $\sum_{r=0}^n\binom{n}{r}2^r=3^n$ How do I enable auto-login in LightDM? I want user foo to auto-login using LightDM (which has been used by Ubuntu since version 11.10). How would I do that? Evaluating a sequence of complex numbers: $|z_n - z_m| < \frac1{1+ |n-m|}$ Let $\{z_n\}$ be sequence of complex numbers such that   $$ |z_n - z_m| &lt; \frac{1}{1+ |n-m|} $$ for all $n,m$  Given this information, can we compute $\lim_{n \to \infty} z_n $?  Attempt:  For sure the sequence is bounded since the RHS is always $\leq 1 $. IF $z_m = 0$, then we have   $$ |z_n | &lt; 1 $$ for all $n$. I claim that the limit is $1$. How can I prove this ? How can I automatically log out the guest account after a period of inactivity? As part of a kiosk system, I have set up a Guest account on a Mac OS X Snow Leopard computer. This account is cleared every time someone logs off the computer. However, plenty of people don't. Is there any way that I can automatically log out this guest account after a period of inactivity?  I tried using the security preferences pane, but that just causes the confirm logout dialog to show up.  I have hacked around the /System/Library/User Templates/ folder, so I can set the screensaver, desktop background, &amp;c. If something like ScriptSaver can solve my problem, I will gladly use it. Irreducibility of an infinite sequence of polynomials I am trying to understand the Georgi chapter of tensor methods in $SU(3)$ representations, and I don't know how to resolve the tensor product of 2 matrices in a 2 heavy quark + 2 light antiquark system. Namely:  Let the tetraquark system be:           $QQ\bar q\bar{q}$  So, those $Q$ heavy quarks interact and can be understood in the $3\bigotimes 3$ representations for $SU(3)$, and $\bar q\bar q$ can be understood as the $\bar 3\bigotimes\bar 3=3\bigoplus\bar 6$ representations for $SU(3)$.  The interaction diagram for the $Q$ heavy quarks is shown in the following scheme, which is an analogy to the Feynman Diagram where a gluon is understood to be exchanged between upper and lower arrows:  $i'\xrightarrow{(T_{a})^{i'}_{i}}i ,  {}^iQ$  $j'\xrightarrow{(T_{a})^{j'}_{j}}j ,  {}^jQ$  So, as usuall we consider the elements of $3$ representation as $u^i$, and therefore the elements of $\bar 3$ representation as $v_{j}$.  I must understand how does the following expression transform:  $(T_{a})^{i'}_{i}(T_{a})^{j'}_{j}\cdot(1/2)\cdot (w^iv^j+w^jv^i)=\Xi\cdot(1/2)\cdot(w^{i'}v^{j'}+w^{j'}v^{i'})$  In other words, how can one give the correct value of $\Xi$?  Note1: $T_a$ is understood to be the $a-ith$ generator of the associated Lie Algebra, which come from the definition of the Gell-Mann Matrices.  $(T_{a})^{i}_{j}\propto(\lambda)_{ij}$, in matrix notation.  Note2: I understand the Young Tableaux and they are not intended to be used here, so please don't try to explain this situation through the tables.   Note3: I assume this is a purely solvable mathematical problem and doesn't need a deep insight into the physical concepts...  Also requesting information about how to understand the tensor products in these cases, since I have been checking many sources but the definitions seem not clear enough. Time taken for collision We have three particles at the vertices of equilateral triangle of side $d$. At $t=0$ they start moving in such away that at all instant of time each of them has a speed $v$ towards adjacent one. We have to find the time after which they will collide. I know that you can solve this by calculating from reference frame of any one particle, but I want a way to solve this by calculating the total distance traveled first in ground frame and then dividing by speed. Is there any shortcut/easy way to switch this system proxy settings? Let $K\subseteq \mathbb{R}^{n} \times \{ 0 \}\subseteq \mathbb{R}^{n+1} $ and $v=(0,0,\cdots,1) \in \mathbb{R}^{n+1}$.      For every $x \in K$,  let $$Lx=\left \{ tv+(1-t)x \; | \ t \in [0,1] \right \}$$      Define    $$ \text{Cone}(K)=\bigcup_{x \in K}Lx. $$   namely the union of all segments from $v$ to every point of $K$.      According to all definitions that I see on books, Cone is defined:       However the exercise I'm working on  asks to find under what circumstances  $$\text{Cone}(K)=\bigcup_{x \in K}Lx$$ is isomorphic to $(K \times [0,1]) /(K \times \{ 1 \})$ (quotient space).   For example if $$K=\{(1/n,0):n\in\mathbb{N}\} \cup (0,0)$$ I can see both of sets form the same graph but I'm still unable to derive a homeomorphism between these two objets. What is the easiest way to parse an INI File in C++? I'm trying to parse an INI file using C++. Any tips on what is the best way to achieve this? Should I use the Windows API tools for INI file processing (with which I am totally unfamiliar), an open-source solution or attempt to parse it manually? Geoserver ecw plugin problem I am trying to publish some ecw files with geoserver 2.7.2 on ubuntu 15.04 x64. I downloaded gdal plugin, gdal_data and native libraries for image-io 1.1.11 and set environment variables; GDAL_DATA, LD_LIBRARY_PATH.  I can see new store types when adding new one (ECW, EHdr, JP2ECW etc.). But when I try to save an ECW store with a valid ecw file which I tested with ArcMap, geoserver crashes with this error:    terminate called after throwing an instance of 'std::length_error'   what():  basic_string::_S_create Aborted (core dumped)  Do you have any idea about this problem? How to make traditional output for derivatives Where does "pay through the nose" originate? I found that every character has a "Personal Item" in his inventory after you start the game. My question is: What is the purpose of it? I mean yeah you could sell it for 100$ but that really is absolutely nothing. It also doesn't have any stats so what can I use it for?