What are the correct plural forms of "penis"?
How do you decline nouns borrowed from languages with several categories for declining nouns (or none at all)?
System.Windows.Threading.Dispatcher and WinForms? Single quote within double quotes and the Bash reference manual In section 3.1.2.3  titled Double Quotes, the Bash manual says:      Enclosing characters in double quotes (‘"’) preserves the literal   value of all characters within the quotes, with the exception of ‘$’,   ‘`’, ‘\’, and, when history expansion is enabled, ‘!’.   At the moment I am concerned with the single quote(').  It's special meaning, described in the preceding section, section 3.1.2.2 is:     Enclosing characters in single quotes (') preserves the literal   value of each character within the quotes. A single quote may not   occur between single quotes, even when preceded by a backslash.   Combining the two expositions,    echo "'$a'"   where variable a is not defined (hence $a = null string), should print $a on the screen, as '', having it's special meaning inside, would shield $ from the special interpretation. Instead, it prints ''. Why so? How to add a class to a given element? Is a business card necessary for a graduate student? I know some PhD students have their own business cards, but I don't know if it is a standard practice for PhD students to have their own business cards. I think a business card can be useful for networking in conference or collaborating with some industrial partners. So, is are business cards necessary for a PhD student or other graduate students attending conferences?   PS: in case it is field-specific, I would like to know the different practices in different fields What's the typical microclimate in the aircraft passenger cabin? I would like to know the physical meaning of the , if there is any? I've used it in thermodynamics and classical mechanics and it seemed only a change of coordinates? Format a number with optional decimal places in Excel I have numbers in cells in Excel. I want the numbers formatted so that if they have decimal places they show to a maximum of two, and if they have no decimal places it doesn't show any.  For example.    15 should be formatted as 15, NOT 15.00 14.3453453 should be formatted as 14.35 12.1 should be formatted as 12.1  0 should be formatted as 0   The closest custom format code I've come up with is 0.##. Unfortunately this formats 15.00 as 15. (note the extra decimal point).  To further complicate the issue, the spreadsheet is a result of an export from SQL Server Reporting Services. So no macros are possible. Oh well, it looks like 0.## is my best bet, and they can just live with the extra period. How to generate a 2D array data structure in tikz? I need to illustrate a 2D array data structure in my document. This is a picture I found on the internet. I want something similar.    I also want to show the memory layout in the illustration. Something like this:   Can someone help me with drawing them in Tikz? Thanks in advance.  MWE  \documentclass{article} \usepackage[utf8]{inputenc} \usepackage{tikz} \usetikzlibrary{matrix,backgrounds}  \begin{document} \begin{tikzpicture}[font=\ttfamily, array/.style={matrix of nodes,nodes={draw, minimum size=7mm, fill=green!30},column sep=-\pgflinewidth, row sep=0.5mm, nodes in empty cells, row 1/.style={nodes={draw=none, fill=none, minimum size=5mm}}, row 1 column 1/.style={nodes={draw}}}]  \matrix[array] (array) { 0 &amp; 1 &amp; 2 &amp; 3 &amp; 4 &amp; 5 &amp; 6 &amp; 7 &amp; 8 &amp; 9\\   &amp;   &amp;   &amp;   &amp;   &amp;   &amp;   &amp;   &amp;   &amp;  \\}; \node[draw, fill=gray, minimum size=4mm] at (array-2-9) (box) {};  \begin{scope}[on background layer] \fill[green!10] (array-1-1.north west) rectangle (array-1-10.south east); \end{scope}  \draw (array-1-1.north)--++(90:3mm) node [above] (first) {First index}; \draw (array-1-10.east)--++(0:3mm) node [right]{Indices}; \node [align=center, anchor=south] at (array-2-9.north west|-first.south) (8) {Element\\ (at index 8)}; \draw (8)--(box); % \end{tikzpicture} \\ \begin{tikzpicture}[font=\ttfamily, array/.style={matrix of nodes,nodes={draw, minimum size=7mm, fill=red!30},column sep=-\pgflinewidth, row sep=0.5mm, nodes in empty cells, row 1/.style={nodes={draw=none, fill=none, minimum size=5mm}}, row 1 column 1/.style={nodes={draw}}}]  \matrix[array] (array) {  &amp;  &amp;  &amp;  &amp;  &amp;  &amp;  &amp;  &amp;  &amp; \\  &amp;   &amp;   &amp;   &amp;   &amp;   &amp;   &amp;   &amp;   &amp;  \\}; % \end{tikzpicture} \\ \begin{tikzpicture}[font=\ttfamily, array/.style={matrix of nodes,nodes={draw, minimum size=7mm, fill=blue!30},column sep=-\pgflinewidth, row sep=0.5mm, nodes in empty cells, row 1/.style={nodes={draw=none, fill=none, minimum size=5mm}}, row 1 column 1/.style={nodes={draw}}}]  \matrix[array] (array) {  &amp;  &amp;  &amp;  &amp;  &amp;  &amp;  &amp;  &amp;  &amp; \\  &amp;   &amp;   &amp;   &amp;   &amp;   &amp;   &amp;   &amp;   &amp;  \\}; % \end{tikzpicture} \end{document} I'm just starting to learn linear algebra and I understand Gaussion elimination but I don't understand this proof:    Is the heart of this the fact that all the while when I've been row-reducing matrices to reduced row-echelon form... I've actually been multiplying a matrix by a series of a elementary matrices?  What does the notation $[A\ \ 0]$ mean?  How is the equation $A = E_1^{-1}...E_k^{-1}$ arrived at? Prove that if $\lim_{n \to \infty}z_{n}=A$ then:  $$\lim_{n \to \infty}\frac{z_{1}+z_{2}+\cdots + z_{n}}{n}=A$$ I was thinking spliting it in: $$(z_{1}+z_{2}+\cdots+z_{N-1})+(z_{N}+z_{N+1}+\cdots+z_{n})$$ where $N$ is value of $n$ for which $|A-z_{n}|&lt;\epsilon$ then taking the limit of this sum devided by $n$ , and noting that the second sum is as close as you wish to $nA$ while the first is as close as you wish to $0$. Not sure if this helps.... Show that $\left| \frac{1}{x}-\frac{1}{z} \right| \le \left|\frac{1}{x} - \frac{1}{y} \right| + \left|\frac{1}{y} - \frac{1}{z} \right|$. I'm trying to prove that  $$ \left| \frac{1}{x}-\frac{1}{y} \right| $$  is a metric on $X = \mathbb R^+$.  The properties of non-negativity and symmetry are obvious (do I actually even need to prove them?), but the tricky one is, as usual the inequality property, i.e.  $$ d(x,z) \le d(x,y) + d(y,z) \text{ for any } z \in X. $$  So, ok, I have that  $$ d(x,z) \le d(x,y) + d(y,z) \\ \iff \left| \frac{1}{x}-\frac{1}{z} \right| \le \left|\frac{1}{x} - \frac{1}{y} \right| + \left|\frac{1}{y} - \frac{1}{z} \right| \\ \iff \left| \frac{1}{x} \right|- \left| \frac{1}{z} \right| \le \left| \frac{1}{x}-\frac{1}{z} \right| \le \left|\frac{1}{x} - \frac{1}{y} \right| + \left|\frac{1}{y} - \frac{1}{z} \right| $$  ...and that's about as far as I've gotten–which is to say, not very far. I also tried multiplying both sides by $ \left| \frac{1}{x}-\frac{1}{z} \right| $, but that wasn't very fruitful. If someone could point me in the right direction, it'd be greatly appreciated. Thanks. How can I compile this successfully? I have to use algpseudocode package to improve my paper look like more professional   But I can't compile successfully.  \usepackage{amsmath} \usepackage{algorithm} \usepackage[noend]{algpseudocode}  \makeatletter \def\BState{\State\hskip-\ALG@thistlm} \makeatother  \begin{document} \begin{algorithm} \caption{AIP}\label{euclid} \begin{algorithmic}[1] \Procedure{MyProcedure}{} \State $\textit{locationAgent} \gets \text{position of }\textit{{agent}}$ \State $\textit{locationMD} \gets \text{position of }\textit{{MD}}$ \If {\textit{distance(eNB,$agent_i$)}}&gt;$\delta$ \BState \emph{loop}: \State $j \gets \textit{patlen}$ \If {$\textit{string}(i) = \textit{path}(j)$}\Return TURE \State $j \gets j-1$. \State $i \gets i-1$. \State \textbf{goto} \emph{loop}. \State \textbf{close}; \EndIf \State $i \gets i+\max(\textit{delta}_1(\textit{string}(i)),\textit{delta}_2(j))$. \State \textbf{goto} loop \EndProcedure Get Absolute Position of element within the window in wpf I would like to get the absolute position of an element in relation to the window/root element when it is double clicked. The element's relative position within it's parent is all I can seem to get to, and what I'm trying to get to is the point relative to the window.  I've seen solutions of how to get a the point of an element on the screen, but not in the window. How to sort text in sqlite3 with specified locale? Sqlite3 by default sorts only by ascii letters. I tried to look in google, but the only thing I found were informations about collations. Sqlite3 has only NOCASE, RTRIM and BIARY collations. How to add support for a specific locale? (I'm using it in Rails application) birthday problem - expected number of collisions There are many descriptions of the "birthday problem" on this site — the problem of finding the probability that in a group of $n$ people there will be any (= at least 2) sharing a birthday.  I am wondering how to find instead the expected number of people sharing a birthday in a group of $n$ people. I remember that expectation means the weighted sum of the probabilities of each outcome:  $$E[X]=\sum_{i=0}^{n-1}x_ip_i$$  And here $x$ must mean the number of collisions involving $i+1$ people, which is $n\choose i$. All $n$ people born on different days means no collisions, $i=0$; two people born on the same day means $n$ collisions, $i=1$; all $n$ people born on the same day means $n$ collisions, $i=n-1$.  Since the probabilities of three or more people with the same birthday are vanishingly small compared to two people with the same birthday, and decreases faster than $x$ increases, is it correct to say that this expectation can be approximated by  $$E[X]\approx {n\choose 0}p_{no\ collisions}+{n\choose 1}p_{one\ collision}$$  This doesn't look right to me and I'd appreciate some guidance.    Sorry - edited to change ${n\choose 1}$ to ${n\choose 0}$ in second equation. Sloppy of me. Where does the curve $x^y = y^x$ intersect itself? This problem is quite easily solved by using logarithms and derivative and forming the function $f(x,y) = x^y - y^x$, however there are assertions that this problem can be solved without using either of the two. I can not see how one would proceed to solve this problem in the absence of logarithmic manipulation and differentiation. Can anyone shed some light on this? How to make the taskbar blink my application like Messenger does when a new message arrive? Is there an API call in .NET or a native DLL that I can use to create similar behaviour as Windows Live Messenger when a response comes from someone I chat with? I read a book a while ago in which a device is invented which opens up "tunnels" back through time. These tunnels cannot be traveled through, but can be used to view what happened in the past. I believe it starts out narrating the invention of the device, then skips ahead to after it is widely in use. There is another device created, a cloak of sorts,  which hides the user from the view of someone using the tunnel device. Does this ring a bell with anyone? I have never used Ubuntu or any other Linux OS before last Friday. For all I know, I might have installed Ubuntu wrong and be missing a component. I would prefer if you use simplest terminology possible, but I'm OK with doing a bit of googling if need be. I just installed Steam for Ubuntu 16.04 but it won't open when I click on it in the launcher. The icon flashes for a few seconds, stops and then nothing happens. I looked in the system monitor and steam shows up there but ending the process and trying again does nothing. I heard trying to open apps that aren't working through the terminal tells you what the error is so I tried that and I got this:  Running Steam on ubuntu 16.04 64-bit STEAM_RUNTIME is enabled automatically Installing breakpad exception handler for appid(steam)/version(0) libGL error: unable to load driver: radeonsi_dri.so libGL error: driver pointer missing libGL error: failed to load driver: radeonsi libGL error: unable to load driver: swrast_dri.so libGL error: failed to load driver: swrast   Please help I just want to play CS:GO again. Is there a technical reason Android update story is so bad? Is there a technical reason why Android phones general lag a lot behind the stable released version of Android?    This applies to both new phones, for example a recent trip to the phone shop everything was 4.0 to 4.2.1, KitKat could not be seen. And also old phones, my girlfriend's iPhone 4 had an OTA update to the latest OS, this is a July 2010 phone, whilst a July 2010 Android is basically a paperweight.    Presumably Android itself doesn't concern itself with the actual hardware, and thus talks to the OS via abstractions? I guess then the handset maker just provides the drivers for the specific hardware, thus I can't see the issue with pushing OTA updates if the ABI remains stable (my phone doesn't grow new hardware features).