When searching for answers on , I noticed a weird little framed box pop up in the results list:    The box turns out to be a MathJax box, and the code being displayed happens to be Perl code; apparently the $ sigils in the Perl code snippet are somehow interpreted as MathJax delimiters in Markdown, even though the code fragment is nested inside a code block. It therefore seems that the truncated preview text is insufficiently escaped.
When searching on a site with  enabled (), I saw some  rendering issues: (and currently it's also in the )        Even though the LaTeX rendering is fine when opening the :        The LaTeX code is:  $f(n) = \begin{cases} 0,  &amp; \text{$ \omega&lt;0, \omega=1, \omega&gt;3 $} \\[2ex] -\omega + 1,  &amp; \text{$ 0\le\omega&lt;1 $} \\[2ex] \omega^2 - 1,  &amp; \text{$ 1&lt; \omega \le 2 $} \\[2ex] 3 \omega,  &amp; \text{$2 &lt; \omega \le 3 $} \end{cases}$
Delete commits from a branch in Git I read that this is because the mean and variance completely specify a normal distribution. However, e.g. for a Poisson distribution the mean, variance and third moment can all be expressed with the same parameter lambda. Is this not what it means to 'completely specify' a distribution?  What is an example of two Poisson distributions having the same mean, variance and different higher moments? If we treated weak stationary as if it was strict stationarity, what would happen when we try to do time series analysis? I was hoping someone could give an overview as to how the Lie groups $SO(3)$ and $SU(2)$ and their representations can be applied to describe particle physics?  The application of Lie groups and their representations is an enormous field, with vast implications for physics with respect to such things as unification, but I what specifically made these groups of physical importance and why there study is useful.  I have just started studying these two groups in particular, but from a mathematical perspective, I'd very much appreciate understanding some sort of physical motivation. In Quantum Mechanics we usually consider operator-valued functions: these are functions that take in real numbers and gives back operators on the Hilbert space of the quantum system.  There are several examples of these. One of them is when we work with the Heisenberg picture, where we need to consider functions $\alpha : \mathbb{R}\to \mathcal{L}(\mathcal{H})$ such that $\alpha(t)$ is the operator at time $t$.  Another example is when we deal with exponentiation of operators, like when building the time evolution operator:  $$U(t,t_0)=\exp\left(-i\frac{H}{\hbar}(t-t_0)\right),$$  Here, the $\exp$ is usually understood as being defined via the eigenvalues of $H$.  The point is, the idea of a function $\alpha : \mathbb{R}\to \mathcal{L}(\mathcal{H})$ appears quite often in Quantum Mechanics, and sometimes one needs to differentiate these. In practice we do it formally, using all the properties we would expect, but I'm curious about how one would properly define this.  If we were dealing with bounded operators, then we could use the operator norm, which is available for this kind of operator, and define the derivative as we can usually we do when there's some norm around.  The point is that in Quantum Mechanics most of the time operators are unbounded.  So in the general case, how can one define the derivative of one operator-valued function? I have two passports/nationalities. How do I use them when I travel? I am a citizen of two different countries, and have two passports.  How should I use my passports when traveling? How to install TP-LINK T2UH Wireless adapter Driver (Ralink mt7610u) I've come across some strange interaction between overlay specification and \pause. Basically I have an itemize and after some text(or block). I want to step through the itemize and after that show the text/block.  I've tried to put a simple \pause between the itemize and the text, but in this way two slides are created, both with the full itemize and no text.  If I don't put the \pause the text is visible from the start(which I don't want).  I've already found a simple work-around: instead of using itemize[&lt;+-&gt;] I can specify the slides on the items(e.g item&lt;1-&gt;, ...item&lt;2-&gt;,... \pause), but I don't like this solution for some reasons:   I have to type more than before I have to hard-code the slide numbers This is solution is not robust. Modification on the item order, removal or addition of new items would break it. I think there has to be some better solution.   So, how should I do?  By the way, a minimal example:  \documentclass{beamer}  \usepackage[utf8]{inputenc} \usepackage{default}  \begin{document}  \begin{frame}     \begin{itemize}[&lt;+-&gt;]         \item A         \item B         \item C     \end{itemize}      \pause  % double pause here      Some text. \end{frame}  \end{document} Can I talk to the blue alpaca? Reese's boyfriend seems to constantly be asleep. When I try and talk to him, she warns me that he's been hard at work all night, but I can't actually enter the shop at night.   Is there any way to talk to him or any benefit for doing so? I've tried to talk to him daily for a week (thinking it was something akin to talking to Sable) but I've had no luck. Trying to come in after-hours doesn't work. is $f$ constant or dilation $f:\mathbb{R}^3\to\mathbb{R}, f(rx)=r^{\alpha}f(x)$ for some $\alpha&gt;0$, $\forall x\in\mathbb{R}$, for any $r\in\mathbb{R}$, could any one tell me which of the following is true?  $1.$ If $f(x)=f(y)$ whenever $||x||=||y||=\beta&gt;0$, then $f(x)=\beta ||x||^{\alpha}$  $2.$ If $f(x)=f(y)$ whenever $||x||=||y||=1$, then $f(x)= ||x||^{\alpha}$  $3.$ If $f(x)=f(y)$ whenever $||x||=||y||=1$, then $f(x)=c||x||^{\alpha}$ for some constant $c$  $4.$ If $f(x)=f(y)$ whenever $||x||=||y||$, then $f(x)$ must be a constant function. Thank you. $AB-BA$ is a nilpotent matrix if it commutes with $A$ I saw this in a  and am putting it here for posterity.  Problem: Let $A$ and $B$ by square matrices and set $C=AB-BA$. If $AC=CA$, prove $C$ is nilpotent. How can I iterate over an enum? A proof by strong induction that $a_n\le3^n$ where $a_n=a_{n-1}+a_{n-2}+a_{n-3}$ I am not sure whether this is right. Can anyone verify, whether this proof is valid? Thanks!        Define a sequence $\{a_n\}_{n\ge0}$ as follows:   $$a_0=1,\qquad,a_1=3,\qquad,a_2=9,\qquad,a_n=a_{n-1}+a_{n-2}+a_{n-3}\text{ for }n\ge3.$$   Prove that for any positive integer $n$, $a_n\le3^n$.        Proof. Let $P(n)$: $a_n\le 3^n$, $n$ is a non-negative integer.      (i) Base case:         Consider when $n=0$. LHS$=a_0=1$, RHS=$3^0=1$ $\therefore$ LHS$\le$RHS, then $P(0)$ holds.   Consider when $n=1$. LHS$=a_1=3$, RHS=$3^1=3$ $\therefore$ LHS$\le$RHS, then $P(1)$ holds.   Consider when $n=1$. LHS$=a_2=9$, RHS=$3^2=9$ $\therefore$ LHS$\le$RHS, then $P(2)$ holds.         (ii) Inductive case:   Assume $P(i)$ is true for $0 \le i \le k$, $k\ge2$.      (iii) Inductive conclusion: Consider $n=k+1$.   $$ \begin{align*} \mathrm{LHS}=a_{k+1}&amp;=a_k+a_{k-1}+a_{k-2} \qquad\text{(by definition, since $k\ge 2$)}\\                     &amp;\le 3^k+3^{k-1}+3^{k-2} \qquad\text{(by Induction Hypothesis)}\\                     &amp;=3^k(3^{-1}+3^{-2}+3^{-3})\\                     &amp;=3^k\left(\frac13+\frac19+\frac1{27}\right)\\                     &amp;=\frac{13}{27} 3^k\\                     &amp;\le 3^{k+1} = \mathrm{RHS} \end{align*} $$   Therefore, by the Principle of Strong Induction, $P(n)$ is true for all non-negative positive integers $n$. HashSet vs. List performance It's clear that a search performance of the generic HashSet&lt;T&gt; class is higher than of the generic List&lt;T&gt; class. Just compare the hash-based key with the linear approach in the List&lt;T&gt; class.  However calculating a hash key may itself take some CPU cycles, so for a small amount of items the linear search can be a real alternative to the HashSet&lt;T&gt;.  My question: where is the break-even?  To simplify the scenario (and to be fair) let's assume that the List&lt;T&gt; class uses the element's Equals() method to identify an item. Protect Google Spreadsheet formatting while allowing changes to data I would like to protect the formatting of a cell (or a range of cells) in a Google Spreadsheet, but still allow changing the data in that (or those) cell(s).  For example, I want to add a validation rule on a cell that says the cell has to contain a number between 1 and 10, and I would like others to be able to change the value in that cell, but not the validation rule itself.  How do I do that?  So far I was only able to completely protect the cell (content + formatting) or not at all (the user can change the content as well as the formatting).  To me this seems to be an important functionality when adding access rights to spreadsheets. Is it possible that it is completely missing from Google Spreadsheets? Usually I use beamer  with the Warsaw theme which puts theorems (and other things) in boxes. Now I switched my theme to Marburg but i still want to keep the boxes. How can one do that? En Dashes & Hyphens in Same Phrase Without recasting and in lieu of unsightly suspensive hyphenation, could these work? The en dash (which means "to") is used between the figures, and the hyphens are used in the compound modifier. To me, the examples below are concise and clear.  Do you agree that the examples below are 100% punctuated correctly--yes or no?  45–50-year-old men  10–20-mile radius  $45–$55-million-per-year industry  $100,000–$150,000-a-year savings  10–15-degree temperature difference  $2–$5-per-day service fees  45–75-cent-a-week raises  55–65-mph speed zone  15–20-ounce steaks  20%–40%-a-year tax increases Cartographic techniques for symbolizing routing data Some common problems with displaying routes created from street data, such as bus routes, include:   Routes may overlap themselves, such as when a route takes the same road in opposite directions Routes may overlap other routes that take the same street. Routes are often overly detailed, or "noisy", owing to their derivation from street data. Indicating a route's direction unambiguously without overloading it with arrows can be a challenge.   What are some techniques for dealing with these issues in order to create a practical and usable route map, such as this ? Do you know of any such public transport maps that were produced by automatic techniques rather than manual illustration/digitization?  Specifically I am using ArcGIS 10, but solutions involving other software are welcome as well.  One technique I have had some success with for dealing with 1) is using ArcMap's  with a negative offset -- assuming the lines are oriented in the direction of travel, this will offset the lines such that the right and left-hand sides are distinct and oriented as you would expect (at least for  countries, for left-hand traffic countries one would use a positive offset). However the result tends to be a bit wonky around turns, interchanges and and U-turns, and is inflexible when dealing with multiple routes.  Another possibility that I am not very familiar with but which seems promising is  -- however, I have not had much luck in finding examples of using representations for transportation maps and whether it might fit the bill. What licence is subscriber content provided under 4.0, 3.0 or them all? In the footer it says:     site design / logo © 2018 Stack Exchange Inc; user contributions licensed under  with . rev 2018.8.7.31273   However, in the footer under Company > Legal > '6. Content Permissions, Restrictions, and Creative Commons Licensing' it instead doesn't specify which CC BY-SA licence we're releasing our content under. It also links to the CC BY-SA 4.0 license:     The CC-BY-SA Creative Commons license terms are explained in further detail by , but you should be aware that all Public Content you contribute is available for public copy and redistribution, and all such Public Content must have appropriate attribution.   Since  if subscriber content is only provided under 4.0, where the footer says 3.0 it can cause users to break the licences.  The footer under Area 51 also mentions that content is licensed under CC BY-SA 2.5.  Since it's not defined which version of the license the content is provided under, I also interpret it to potentially mean all the versions.    What license is subscriber content licensed under? in a mountain climbing expeditions 5 men and 7 women are to walk in a mountain climbing expeditions 5 men and 7 women are to walk single file so that no 2 men are adjacent. How many ways are possible? Understanding the differential $dx$ when doing $u$-substitution