How to vertically center align a cell in a table?
How do I vertically center a single cell within a table?
Order of finite fields is $p^n$ Let $F$ be a finite field. How do I prove that the order of $F$ is always of order $p^n$ where $p$ is prime? How do I diagnose the source of focus problem in a camera? Probably a novice question, but how do I correctly diagnose from a photo for what reason that camera wasn't able to focus properly?  It can be any 1 of the following   Unsteady hand Lens issue Metering Re-Calibration required in camera or ...   Is there a set of unsaid protocols that needs to be followed by a photographer?  Goal is to get a sharp and crisp image prior to editing.  [PS: I own a Nikon D5200.] How to stop fluid inflow? I have fluid simulation with an inflow object. I want the inflow to go for 2 seconds, then have the inflow stop (so no more fluid is added) but keep the simulation going  (so the existing fluid sloshes around).  However, I do not see any way to set start and ending values on my inflow object.  How do I stop inflow at a certain frame/time in my simulation? Transforming Differential Equation to a Kummer's Equation I'm trying to transform an equation of the form $$ yw^{\prime\prime}(y) - [b - ay] w^\prime(y) - [d + ey]w(y) = 0 $$ into the form of a Kummer's or confluent hypergeometric differential equation: $$ y w^{\prime\prime}(y) + [f - y] w^\prime(y) + g w(y)  = 0 $$ I know it may have something to do with merging two of the singularities of the original equation, and maybe doing something with $y$, making it $\frac{y}{b}$ and taking b to infinity, but I don't know and can't find the details for this process, and for my equation specifically. There's not too much difference between the two but just enough so that I can't get it. Thanks in advance for any help! Accessing my Windows 7 files from my Ubuntu account I have just installed Ubuntu on my computer and I have windows 7 as my other operating system. is there a way that I can access my windows 7 files from my Ubuntu installation? Is there a way to change the restrictions passcode on an iPhone without restoring the phone? I haven't forgotten the passocde; I just want to change it. Conditional Expectation of Composite Function Preliminaries  Let $(\Omega, \mathcal{G}, \mathbb{P})$ be a complete probability space.  Let $D$ be a complete, separable, metrizable topological space with Borel $\sigma$-algebra $\mathcal{B}(D)$ (such as $D = \mathbb{R}^q$ with $\sigma$-algebra $\mathcal{B}(D) = \mathcal{B}(\mathbb{R}^d)$).  Let $\mathbb{R}$ be equipped with its canonical Borel $\sigma$-algebra $\mathcal{B}(\mathbb{R})$.  Let $g: \Omega \times D \rightarrow \mathbb{R}$ be a bounded $(\mathcal{G} \otimes \mathcal{B}(D) ) / \mathcal{B}(\mathbb{R})$-measurable function.  Let $\Pi: \Omega \rightarrow D$ be a $\mathcal{G}/\mathcal{B}(D)$-measurable random variable.  Let $H : \Omega \rightarrow \mathbb{R}$ be a $\mathcal{G}/\mathcal{B}(\mathbb{R})$-measurable random variable, defined by $$ H(\omega) := g(\omega, \Pi(\omega)).$$ Note, that, since $g$ is bounded, we have $H \in \mathcal{L}^2(\Omega, \mathcal{G}, \mathbb{P})$.  Let $j: D \rightarrow \mathcal{L}^2(\Omega, \mathcal{G}, \mathbb{P}) $ be defined by $$ j(\pi)(\omega) := g(\omega, \pi)  $$  For all $\pi \in D$, let $j(\pi)$ be independent of $\Pi$.  Question  I am interested in the conditional expectation $$\mathbb{E}[H \mid \Pi] :\Omega \rightarrow \mathbb{R}$$ of $H$ with respect to $\Pi$. More specifically, I suspect that (a $\mathbb{P}$-unique version of) this condititional expectation is given by  $$ \mathbb{E}[H \mid \Pi] (\omega) = \mathbb{E}[j(\Pi(\omega))], \quad (\dagger)  $$ whereby $\mathbb{E}[j(\Pi(\omega))]$ can of course also be written as $$\mathbb{E}[j(\Pi(\omega))] = \int_{\Omega} j(\Pi(\omega))(\tilde{\omega}) d\mathbb{P}(\tilde{\omega}) . $$  How can I prove, that $(\dagger)$ is the case? I have tried, tracking the definition of conditional expectation and using Fubini, but with little success so far.  Thanks for any advice! Proof of this result related to Fibonacci numbers: $\begin{pmatrix}1&1\\1&0\end{pmatrix}^n=\begin{pmatrix}F_{n+1}&F_n\\F_n&F_{n-1}\end{pmatrix}$? $$\begin{pmatrix}1&amp;1\\1&amp;0\end{pmatrix}^n=\begin{pmatrix}F_{n+1}&amp;F_n\\F_n&amp;F_{n-1}\end{pmatrix}$$  Somebody has any idea how to go about proving this result? I know a proof by mathematical induction, but that, in my opinion, will be a verification of this result only. I tried to find through the net, but in vain, if someone has some link or pointer to its proof, please provide, I'll appreciate that.  Thanks a lot! $-1$ is a quadratic residue modulo $p$ if and only if $p\equiv 1\pmod{4}$ I came across this problem and I believe Lagrange's theorem is the key to its solution.  The question is:     Let $p$ be an odd prime. Prove that there is some integer $x$ such that $x^2 \equiv −1 \pmod p$ if and only if $p \equiv 1 \pmod 4$.   I appreciate any help.  Thanks. I played 1st and 2nd edition AD&amp;D a lot back in the day. But when 3rd edition came out, I dropped out of the hobby. Partly I just couldn't be bothered to re-learn the rules. The conversion systems, previews and material for 3rd edition I was seeing in Dragon and Dungeon magazines made it look like a very major change.  I recently picked up the new 5th edition starter set on a whim. Obviously the starter set rules are very stripped down in comparison to the full rules, but nevertheless, I was amazed by how comfortable and familiar the system felt. The only thing that felt like a truly radical change was the way things like thief skills and the like were now handled with a d20 instead of a percentage system.  There's plenty of information online (and here) comparing editions of the game in an incremental manner. But I'd be interested in a breakdown of how 2nd and 5th edition compare directly, specifically looking at whether there are broad areas of similarity. Can "Mr", "Mrs", etc. be used with a first name? Is it correct to use Mr/Mrs with a first name? Logical volume is not mounted but is in use. Please close all applications using this device (eg iscsi) What is the purpose of /home on a Mac? On Linux, (which I am used to), /home is the place where home folders live.  On a Mac, home is some kind of crazy mutant:  $ mount /dev/disk1 on / (hfs, local, journaled) devfs on /dev (devfs, local, nobrowse) map -hosts on /net (autofs, nosuid, automounted, nobrowse) map auto_home on /home (autofs, automounted, nobrowse)   Other than to be non-conformist, is there some purpose to this auto_home mount point?  Considering how it mucks up things that come right out of the box, there must be some wonderful thing that it accomplishes, but I can't figure out what that would be..... Logging in as the same user multiple times in Remote Desktop Windows Server 2008 Quick question: I have a situation where I need to let multiple people on different PCs log into one server 2008 machine as administrator simultaneously over remote desktop. I have the CALs for it, it's just not set up correctly. When one user tries to log in, it boots the other out. What I need is to present to them a different session, just each as logged in as admin. Sorry for the slightly rambling post, I'm new here. Thanks! Converting case of all values in all fields of table using ArcPy & Python? In , someone suggested in a  that I should not cast the result of malloc. i.e., I should do this: int *sieve = malloc(sizeof(int) * length);  rather than: int *sieve = (int *) malloc(sizeof(int) * length);  Why would this be the case? I have a register \count0=&lt;some-value&gt; and need to get the letter of the alphabet on the index of \count0. That is, if it is 1, I need an A, if 2, a B, etc.  Is this possible?  I'm reluctant sharing an MWE as it seems to overcomplicate things a bit:  \begin{tikzpicture} \node[regular polygon, regular polygon sides=7, minimum size=5cm] (A) {}; \foreach \i in {1,...,7}{     \count0=8     \advance\count0 by -\i     \node[circle, label=above:\scriptsize\the\count0, fill=black, minimum size=4pt, inner sep=0pt] (\the\count0) at (A.corner \i) {}; } \end{tikzpicture}   With the tikz package and the shapes.geometric tikz library.  This draws seven nodes labelled 1 .. 7 on a circle. I need to have A .. G instead of 1 .. 7. Nonconstant polynomials do not generate maximal ideals in $\mathbb Z[x]$ Let $f$ be a nonconstant element of ring $\mathbb Z[x]$. Prove that $\langle f \rangle$ is not maximal in $\mathbb Z[x]$.   Let us assume $\langle f \rangle$ is maximal. Then $\mathbb Z[x] / \langle f \rangle$ would be a field. Let $a \in \mathbb{Z}$. Then $a + \langle f \rangle$ is a nonzero element of this field, hence a unit. Let $g + \langle f \rangle$ be its inverse. Then $a g - 1 \in \langle f \rangle$, hence $ag(x)-1 = f(x)h(x)$ for some $h \in Z[x]$, hence $ag(0) + f(0)h(0) = 1$, thus $(a,f(0))=1$ for all $a \in \Bbb Z$, contradiction, hence the proof.  Is my argument correct? Is there any other method? List of Ubuntu Versions with Corresponding Linux Kernel Version Is there a list of Ubuntu versions with default corresponding Linux kernel versions somewhere?  I would specifically like to know the most recent version of Ubuntu that still used Linux Kernel 2.x. What is the difference between "likelihood" and "probability"?