It's simplier to show what I'd like to do
How do I put big brackets under different parts of an equation so that I can write, e.g., text specific to these parts? For example: f =  x^3 +  2     |___|  |__|        |     |    text 1  text 2
Inverse of this $3\times 3$ matrix using the Cayley–Hamilton theorem Find the inverse of the matrix $$\begin{pmatrix} -1 &amp; 2&amp; 0 \\ 1&amp; 1 &amp;0 \\ 2 &amp; -1&amp; 2 \end{pmatrix}$$ using the Cayley–Hamilton theorem.  Thanks! How can I delete an account on a specific site? My account has 20 (!) sites associated to it.  I only use it for 3-5 sites.  To reduce clutter, I would like to delete my profiles that I do not use much.  I have went through , but when I enter the profile URL as:  http://russian.stackexchange.com/users/5772/alex   it gives the error message:     oops! this isn't a link to a valid profile   What procedure do I go through to delete my profile only on certain sites? Dubai (UAE) visa requirements when staying in the airport for a French citizen? Which function ($f$) is continuous nowhere but $|f(x)|$ is continuous everywhere? Which function ($f$) is continuous nowhere but $|f(x)|$ is continuous everywhere?   I found this question , the question seems much interesting but for obvious reason it is closed there, I was wondering how to derive such a function? How do I get an animated gif to work in WPF? What control type should I use - Image, MediaElement, etc.? Length of a JavaScript object I have a JavaScript object. Is there a built-in or accepted best practice way to get the length of this object? const myObject = new Object(); myObject[&quot;firstname&quot;] = &quot;Gareth&quot;; myObject[&quot;lastname&quot;] = &quot;Simpson&quot;; myObject[&quot;age&quot;] = 21; In PHP you can just use $_POST for POST and $_GET for GET (Query string) variables. What's the equivalent in Python? A deck of 52 cards is shuffled, and we deal a bridge of 13 cards. Let $X$ be the number of aces and $Y$ be the number of spades. Show that $X$, $Y$ are uncorrelated.  Here is what I did:  $Cov(X,Y) = E[XY]-E[X]E[Y]$   uncorrelated means $Cov(X,Y) = 0$, hence  $E[XY]=E[X]E[Y]$   $E[X] =  \sum_{k=0}^{k=4} k \frac{\dbinom{4}{k} \dbinom{48}{13-k}}{\dbinom{52}{13}} $   $E[Y] =  \sum_{k=0}^{k=13} k \frac{\dbinom{13}{k} \dbinom{39}{13-k}}{\dbinom{52}{13}} $   Are the summations above correct? and how do I calculate $E[XY]$? Is there an easy way to attach source in Eclipse? I'm a big fan of the way Visual Studio will give you the comment documentation / parameter names when completing code that you have written and ALSO code that you are referencing (various libraries/assemblies).  Is there an easy way to get inline javadoc/parameter names in Eclipse when doing code complete or hovering over methods? Via plugin? Via some setting? It's extremely annoying to use a lot of libraries (as happens often in Java) and then have to go to the website or local javadoc location to lookup information when you have it in the source jars right there! How to distinguish gift from payment for the service? If somebody gives me reasonable advise or share important to me information.   Being attentive I would like to make a little gift or give some little (&lt;100$) amount of money (cash/wire/online) for that   How it would be classified by IRS?   Which obligations originate with this matter for me and my party?  How to do this in a most comfortable way to my party? Getting a FILE* from a std::fstream Is there a (cross-platform) way to get a C FILE* handle from a C++ std::fstream ?  The reason I ask is because my C++ library accepts fstreams and in one particular function I'd like to use a C library that accepts a FILE*. I've been working with Corel Draw previously and now i use Illustrator more.Still getting used to some of their features though. I want to insert an image into a circle I've drawn but i don't know how to go about it.It is called power clipping in Corel. Any answers would be appreciated. What gifts would be welcome for a Swedish host family? How to run Visual Studio post-build events for debug build only How can I limit my post-build events to running only for one type of build?  I'm using the events to copy DLL files to a local IIS virtual directory, but I don't want this happening on the build server in release mode. Find all continuous functions satisfying $\int_0^xf=(f(x))^2+C$ for some constant $C \neq 0$. Find all continuous functions $f$ satisfying   $$\int_0^xf=(f(x))^2+C$$ for some constant $C \neq 0$, assuming that $f$ has at most one $0$.  I have a question about the solution to this problem. It says that   Clearly $f^2$ is differentiable everywhere, its derivative at $x$ is $f(x)$ (I'm assuming that this is because the left hand side is differentiable, the right hand side must be differentiable as well). So $f$ is differentiable at $x$ whenever $f(x) \neq 0$, and  $$f(x)=2f(x)f'(x),$$ so $f'(x) = \frac{1}{2}$ at such points. Thus, $f= \frac{1}{2}x+b$ for some $b$ on any interval where it is non-zero; if $f$ has a zero, this gives two possible solutions, with two possible values of $b$, but since $f$ is assumed continuous, they must be the same. So we need $$\int_0^x(\frac{1}{2}t+b)dt=(\frac{1}{2}x+b)^2+C$$  so we must have $b=\sqrt{-C}$ or $-\sqrt{-C}$, leading to two solutions for $C \lt 0$.  I don't understand the bolded statements. First, how does the differentiability of $f^2$ guarantee that $f$ is differentiable, and why only at $x$ where $f(x) \neq 0$?  Next, why are there two possible solutions if $f$ has a zero, but since $f$ is continuous they must be the same?  Finally, does the last statement mean that if $C \gt 0$, then there is no solution, since we're restricted to real numbers here?  I would appreciate it if anyone answers my questions. Do images uploaded to imgur.com have any backup? Fast way of copying IMAP to IMAP on CentOS I'm trying to copy of IMAP emails from one server to my new server but after Googling for hours and trying several tools, nothing is working. Is there a tool that actually works?  I am copying hundreds of thousands of emails so using a email client is out of the question, I tried it, and at the rate of a email per 2 seconds, it would take a few weeks or months!  www.linux-france.org/prj/imapsync/ is commonly mentioned, however, the tool is no longer available.  I tried www.athensfbc.com/imap_tools/ which just hangs and does nothing.  Any migration tools that work? Split a file by line and have control over resulting files extension This is solely a reference request. I have heard a few versions of the following theorem:     If the joint moment generating function $\mathbb{E}[e^{uX+vY}] = \mathbb{E}[e^{uX}]\mathbb{E}[e^{vY}]$ whenever the expectations are finite, then $X,Y$ are independent.   And there is a similar version for characteristic functions. Could anyone provide me a serious reference which proves one or both of these theorems? Analogue of spherical coordinates in $n$-dimensions What's the analogue to spherical coordinates in $n$-dimensions? For example, for $n=2$ the analogue are polar coordinates $r,\theta$, which are related to the Cartesian coordinates $x_1,x_2$ by  $$x_1=r \cos  \theta$$ $$x_2=r \sin  \theta$$  For $n=3$, the analogue would be the ordinary spherical coordinates $r,\theta ,\varphi$, related to the Cartesian coordinates $x_1,x_2,x_3$ by  $$x_1=r \sin  \theta  \cos  \varphi$$ $$x_2=r \sin  \theta  \sin  \varphi$$ $$x_3=r \cos  \theta$$  So these are my questions: Is there an analogue, or several, to spherical coordinates in $n$-dimensions for $n&gt;3$? If there are such analogues, what are they and how are they related to the Cartesian coordinates? Thanks.