How to make \mid longer?
variable-sized "such that" pipe
I'm an elected diamond moderator on one site, and a user of several others. I think it would be extremely helpful for our flagging process if users had the option to enter freeform text explaining their flag on types of flags other than the "in need of moderator attention" flag.  An example of when this is relevant: Sometimes posts have had rude/abusive flags, but the rude/abusive part might be difficult to notice, or it might be a single word or sentence buried somewhere in the middle of the post. Users have to choose between "flag it as rude with no explanation" or "flag it as misc and explain what's going on". Often they'll pick the first because of course it seems like what they should do (e.g. they know the system has special handling attached to rude/abusive flags) but it means they can't explain what's going on to us, so we have to reach out directly in private to find out.  Sometimes it also helps to be able to explain why a comment is no longer needed, because past experience tells me the "no longer needed" flag on its own might be declined on a particular site -- so I pick the custom reason instead of "no longer needed" just so I can provide explanation.  I'd prefer users be able to understand they can pick the appropriate reason and be able to attach any explanation they deem necessary to further direct moderators to the issue. If not for all kinds of flags, then at least for spam or rude/abusive flags. Manually change filetype icons in Windows 7 I'm trying to find the dialog tab in Windows 7 that allows a user to change the icon used for a particular file type.  In Windows XP it would be under the Folder Options properties dialog.    Where is it on Windows 7?  I only want to change the icon of a specific filetype, to anything I want but this tab is no longer present in Folder Options of Windows 7. What happens to Bruce Banner when Hulk loses a tooth? In Age Of Ultron we witnessed Hulk lose a tooth.   My question is: Has Bruce Banner lost a tooth as well? Directory index forbidden by Options directive What are good advanced LaTeX books? I've been using LaTeX for about 3 months, and I'm hooked. My background is programming, so for the basic, google is sufficient. I did some research on amazon.com and found these two books with many positive feedback:    However, most of people said they are more like references than a real book. And if they really are, then I think I'd rather look up at CTAN. What I'm looking for is a book that can teach me how to program in LaTeX, for example:   Write my own package   Create animation  Create and using macro in LaTeX ....   I know there are many options around, however to pick the right one is not an easy task. Any advice or suggestion would be greatly appreciated. Thank you. Proof of the formula $1+x+x^2+x^3+ \cdots +x^n =\frac{x^{n+1}-1}{x-1}$ Possible Duplicate:          Proof to the formula  $$1+x+x^2+x^3+\cdots+x^n = \frac{x^{n+1}-1}{x-1}.$$ Spring's SecurityContextHolder.getContext().getAuthentication() returns null after RedirectView is used in HTTPS/SSL Stateful bash function What is the correct name to use with /give for Lapis Lazuli? In Minecraft, when cheats are enabled you can give yourself items using the command /give [user] [item] [count], e.g. /give user45623 dirt 32. What is the item name to use for Lapis Lazuli? I've tried lapis_lazuli, lapis, lazuli, dye4, and dye_4, but it's none of those. In which ways did scanning Nero's ship enhance/change Starfleet technology? I've heard the explanation that the Enterprise from 2009's Star Trek looked so much more advanced was because data gathered from the Kelvin initially scanning Nero's ship when it first appeared enabled them to upgrade their tech. I'm wondering if they've ever detailed exactly what technologies were advanced or enhanced or discovered. Undefined reference to static class member Can anyone explain why following code won't compile? At least on g++ 4.2.4.  And more interesting, why it will compile when I cast MEMBER to int?  #include &lt;vector&gt;  class Foo {   public:       static const int MEMBER = 1;   };  int main(){       vector&lt;int&gt; v;       v.push_back( Foo::MEMBER );       // undefined reference to `Foo::MEMBER'     v.push_back( (int) Foo::MEMBER ); // OK       return 0; } If $X$ is distributed $N(\mu_X, \sigma^2_X)$, $Y$ is distributed $N(\mu_Y, \sigma^2_Y)$ and $Z = X + Y$, I know that $Z$ is distributed $N(\mu_X + \mu_Y, \sigma^2_X + \sigma^2_Y)$ if X and Y are independent.  But what would happen if X and Y were not independent, i.e. $(X, Y) \approx N\big( (\begin{smallmatrix} \mu_X\\\mu_Y \end{smallmatrix}) , (\begin{smallmatrix} \sigma^2_X &amp;&amp; \sigma_{X,Y}\\ \sigma_{X,Y} &amp;&amp; \sigma^2_Y \end{smallmatrix}) \big) $  Would this affect how the sum $Z$ is distributed? What can I do when getting “This question body does not meet our quality standards”? Proof of Heron's Formula for the area of a triangle Let $a,b,c$ be the lengths of the sides of a triangle. The area is given by Heron's formula: $$A = \sqrt{p(p-a)(p-b)(p-c)},$$ where $p$ is half the perimeter, or $p=\frac{a+b+c}{2}$.  Could you please provide the proof of this formula? Thank you in advance. Construction of Dirichlet distribution with Gamma distribution Let $X_1,\dots,X_{k+1}$ be mutually independent random variables, each having a gamma distribution with parameters $\alpha_i,i=1,2,\dots,k+1$ show that $Y_i=\frac{X_i}{X_1+\cdots+X_{k+1}},i=1,\dots,k$, have a joint ditribution as $\text{Dirichlet}(\alpha_1,\alpha_2,\dots,\alpha_k;\alpha_{k+1})$   Joint pdf of $(X_1,\dots,X_{k+1})=\frac{e^{-\sum_{i=1}^{k+1}x_i}x_1^{\alpha_1-1}\dots x_{k+1}^{\alpha_{k+1}-1}}{\Gamma(\alpha_1)\Gamma(\alpha_2)\dots \Gamma(\alpha_{k+1})}$.Then to find joint pdf of $(Y_1,\dots,Y_{k+1})$ I can not find jacobian i.e.$J(\frac{x_1,\dots,x_{k+1}}{y_1,\dots,y_{k+1}})$ Here's an example:  Double d = (1/3); System.out.println(d);   This returns 0, not 0.33333... as it should.  Does anyone know? Is it wrong to ask the same question elsewhere? I just posted a question to  and afterward realized that it might not be answered very quickly due to how specific it was. So I also posted it on the   I plan to update both the SU and Ubuntu posts with the final answer I end up using, but I can't help but feel users from both places might not like that I've posted to both.  So my question is: Is it frowned upon to post the same question elsewhere and link to it? Composition of a harmonic function with a holomorphic function is still harmonic If $f$ is a harmonic function in a domain $D \subset \mathbb{C}$, and $g$ is a conformal mapping of a domain $D_0$ onto $D$, is $f \circ g$ harmonic in $D_0$?   I noticed this question while reading several pdf of lecture notes, and I'm having trouble figuring it out. Can anyone help?  Thank you so much! I was pondering a bit more about  question regarding being able to &quot;omit&quot; the base case in a proof by strong induction due to vacuous truth. The post states:  Strong induction proves a sequence of statements $P(0), P(1), …$ by proving the implication &quot;If $P(m)$ is true for all nonnegative integers $m$ less than $n$, then $P(n)$ is true.&quot; for every nonnegative integer $n$. There is no need for a separate base case, because the $n=0$ instance of the implication is the base case, vacuously.  However, if we consider $n=0$, we would have that the statement is vacuously true, which I would take to mean that the implication is true regardless of the validity of $P(0)$. However, clearly it's necessary for $P(0)$ to hold for an induction proof to be valid. So I'm confused on how, by omitting the base case, $n=0$ isn't just a tautology, making the implication true regardless of whether $P(0)$ actually holds. MPPT charging a li-ion battery I just designed this MPPT solar charge controller which outputs 4.2 V regulated via MPPT, it uses the SPV1040 IC. This will be used on a satellite with 4 side panels, each with 8 solar cells in parallel outputting 2.6 V at approximately 122 Ma. Each panel will have this exact circuit and all the outputs will be connected in parallel to a 3.7 V lithium ion camera battery.  When active only 1 solar panel will be active and the other MPPT circuits will be offline or providing a very low amount of current. How should I connect the 4.2v to the battery, just directly or using some sort of controller to stop charging at 4.2v? Keep in mind the battery will always have a load and it will charge for around 50m in a 90m cycle due to being eclipsed. I would obviously like the battery to last as long as possible so I am not sure what are the implications of constantly having a battery connected to 4.2 V during 50m. Thanks.   The schematic was made based off a simulation made using the ST Edesignsuite directly from the provider.  Excuse my previous question about this, wasn't properly worded.