Cross-referencing with label inside document
Why does an environment's label have to appear after the caption?
find $\sum_{k=2}^{\infty}\frac{1}{k^2-1}$ Find all real numbers $x$ for which $$10^x+11^x+12^x = 13^x+14^x.$$   I thought about taking the logarithm of both sides, but didn't see how that would help. How can we make the equation simpler? Given $\int_0^{\infty}e^{-x^2}dx = \frac{\sqrt{\pi}}{2}$, evaluate $\int_0^{\infty}e^{-a^2x^2-\frac{b^2}{x^2}}dx $ Given $$\int_0^{\infty}e^{-x^2}dx = \frac{\sqrt{\pi}}{2}$$ evaluate:   $$\int_0^{\infty}e^{-a^2x^2-\frac{b^2}{x^2}}dx. $$   I can find that  $$\left(ax+\frac{b}{x}\right)^2 = a^2x^2+2ab+\frac{b^2}{x^2}$$  therefore: $$\int_0^{\infty}e^{-a^2x^2-\frac{b^2}{x^2}}dx = e^{2ab}\int_0^{\infty}e^{-\left(ax+\frac{b}{x}\right)^2}dx$$  but I can't find any clue then. I have a C++ library that provides various classes for managing data.  I have the source code for the library.  I want to extend the C++ API to support C function calls so that the library can be used with C code and C++ code at the same time.  I'm using GNU tool chain (gcc, glibc, etc), so language and architecture support are not an issue.  Are there any reasons why this is technically not possible?  Are there any gotcha's that I need to watch out for?  Are there resources, example code and/or documentation available regarding this?    Some other things that I have found out:   Use the following to wrap your C++ headers that need to be used by C code.     #ifdef __cplusplus extern "C" {   #endif   //   // Code goes here ...   //   #ifdef __cplusplus   } // extern "C"   #endif    Keep "real" C++ interfaces in separate header files that are not included by C.  Think  here.  Using #ifndef __cplusplus #error stuff helps here to detect any craziness. Careful of C++ identifiers as names in C code Enums varying in size between C and C++ compilers.  Probably not an issue if you're using GNU tool chain, but still, be careful. For structs follow the following form so that C does not get confused.  typedef struct X { ... } X  Then use pointers for passing around C++ objects, they just have to be declared in C as struct X where X is the C++ object.   All of this is courtesy of a friend who's a wizard at C++. Say I have a code to draw a flow chart, I want now a arrow from node 3 to node 1, how can I do that?  1&lt;--| |   | 2   | |   | 3----   MWE  \documentclass[class=article,border=0pt]{standalone}  \usepackage{tikz} \usetikzlibrary{shapes,arrows}  % Define block styles \tikzset{     block/.style={rectangle, draw, line width=0.5mm, black, text width=5em, text centered,                   rounded corners, minimum height=2em},     line/.style={draw, -latex} }% &lt;- if you insist in using this in the document add this % here. \begin{document} \begin{tikzpicture}[node distance = 1cm, auto]     % Place nodes     \node [block] (BLOCK1) {a};     \node [block, below of=BLOCK1] (BLOCK2) {b};     \node [block, below of=BLOCK2, node distance=1cm] (BLOCK3) {c};     % Draw edges     \path [line] (BLOCK1) -- (BLOCK2);     \path [line] (BLOCK2) -- (BLOCK3); \end{tikzpicture} \end{document} Prove that $\int f\ d\lambda = \int_{a}^{b} f(x)\ dx,$ for any $f \in \mathcal R[a,b].$ Theorem $:$ Let $f : [a,b] \longrightarrow \Bbb R$ be a Riemann integrable function. Then $f \in L_1[a,b]$ and $$\int f\ d\lambda = \int_{a}^{b} f(x)\ dx.$$  The proof given in my book is as follows $:$     At the fag end of the proof $f$ has been proved to be measurable which uses the completeness of the measure space $\left ([a,b], \mathcal L \cap [a,b], \lambda |_{[a,b]} \right ).$ Then it has been stated that $f \leq \Phi_n,$ $\forall$ $n$ and hence $f \in L_1[a,b]$ since $\Phi_n \in L_1[a,b]$ by the proposition $5.4.3 \ $(i) which states the following $:$  Let $f \in \Bbb L$ and $g \in L_1[a,b].$ If $|f(x)| \leq g(x)$ for a.e. $x(\mu).$ Then $f \in L_1[a,b].$  I don't know how to use this proposition to claim that $f \in L_1[a,b].$ Also I don't understand the way dominated convergence theorem used here. What I know about dominated convergence theorem is as follows $:$  Let $(X, \mathcal S, \mu)$ be a complete measure space. Let $g \in L_1(X)$ and $\{f_n \}_{n \geq 1}$ be a sequence in $\Bbb L$ such that $|f_n(x)| \leq g(x)$ a.e. $x(\mu).$ Let $f_n(x) \to f(x)$ as $n \to \infty$ a.e. $x (\mu).$ Then $f \in L_1(X)$ and $$\int f\ d\mu = \lim\limits_{n \to \infty} \int f_n\ d\mu.$$  From here how to conclude that $$\Psi_n\ \bigg\uparrow\ f \implies \int f\ d\lambda = \lim\limits_{n \to \infty} \int \Psi_n\ d\lambda.$$ Please help me in this regard. Thanks in advance. Problem with option border of class standalone I tested a MWE given in question . Following the documentation (page 9) I used the class option border={left right bottom top} with left=right=top=0pt and bottom=20pt (20pt only to show the effect here).  With the version 2012/09/15 v1.1b of standalone and the following MWE I get no 20 pt margin at the bottom of my picture.  What is the problem?  MWE:  \documentclass[% % border=1pt   border={0pt 0pt 20pt 0pt} %left right bottom top ]{standalone}% http://ctan.org/pkg/standalone \begin{document} $2^5 = x_5 \times y^8$ \end{document} How to encrypt individual folders? Is there a term for solving a sub-sub problem of a problem so far removed from the main problem the link is not clear? In some situations, trying to solve a problem uncovers another problem. Attempts to fix that uncover yet another. A few more rounds and one can be doing something seemingly completely unrelated to the main problem. Is there an expression for that? Dealing with a whole bunch of two-line config files, I'd like a way to exclude any files that have a different number of lines.  So, something like:  mv * destdir only if file contains exactly two lines   Or:  wc -l * | grep '^ *2' | xargs mv {} destdir   Except that neither of those is actual working code.  While writing this I realized I do have a way to do this, which is ugly as heck, and I've included it below as an answer.  Is there an easy/clean way to do this? Is Responsive Design good for web based software? According to WolframAlpha,  but I don't know how I can prove it. How should I deal with becoming discouraged as a graduate student? I am a third year (starting fourth year in the fall) PhD student in mathematics. I've passed all qualifying exams and am currently doing research. As far as I can tell, I am not doing poorly. I have the good fortune of having a great advisor, being in a very supportive department, and having friends and family who genuinely care about my success.   The fact is research is hard. It appears to consist primarily of staring at a problem for days and days and days without getting anywhere. Sometimes, rarely, I do figure something out and that feels wonderful, but the overwhelming majority of my time appears to be spent banging my head against a mostly figurative wall. I am not complaining about the material being hard, and I am not averse to putting in hard work, but I get frequently discouraged when I realize the vast volumes of mathematics that I yet know nothing about (and probably never will). It's very hard to quantify progress - in particular, there are too few tangible returns after too many hours worked. I find myself thinking along the lines of "Oh, if only someone actually smart were thinking about this problem they would have solved it in moments" and so on.   I've talked about this to some number of people; here is some advice I have received:   Take a day off. Putting in hours upon hours of trying things doesn't magically lead to a solution, particularly if the brain is tired and just wants to sleep. Have a hobby. Since math research doesn't exactly provide instant gratification, a hobby might provide some instead.  Talk to other graduate students. Realize that many graduate students go through this.   I'm interested to know how other folks have dealt with being discouraged as a graduate student. Does it get better with time and experience? Is this a sign that research is not for me and that I should seriously consider a life outside academia? What are some practices for getting a name change so that people can find me more easily? For a similar thing, , where Jay Wacker managed to get people to call him by the name Jay even though he didn't need to get a legal name change. I'm not sure how to go about this though.  The main problem with me is that I have such a frustratingly common name that a lot of people cannot find me when they google me. So many of them simply don't notice the middle initial that I always use in between my first and last names, and this could actually become a major issue in academia, since people have little time and are prone to giving up quickly if they want to look for me (or for my papers) and can't find me at all (I know this having seen how several academics use the Internet and how they look for people's names). This, in turn, could easily ruin my citation count in the future (it's not just that - it's helpful to others when I have a less common name so that they can more easily locate my stuff). I already know at least several people who specifically told me that they tried to find my email but that they couldn't find it (and this isn't limited to just them - there are many, many more - including long-lost friends who have wanted to talk to me for a long time, but who couldn't find me due to said ultra-common name). Of course, people can go through the respective university directories, but how many people really do that? From my observations (when I've seen people look for someone else), very very few do it. Hell, there are even several people at my OWN university who share the same exact first+last name as me.  In Academia, this is even a bigger problem because the vast majority of your connections will be people who only vaguely recognize/know you, so they may know most of the search clues. Even a "full name" + university won't solve all the problems, because I may switch universities and people may only remember the old university that I was in. I'm also very very interdisciplinary, so I want to be searchable to people outside my field as well.  And even if I fix the issue for Google with a massive SEO operation or whatever (that may even be impossible for my ridiculously common name), it's still not going to fix the problem for all of the other ways that people use search.  I'm currently transitioning between undergrad and grad school, so now may be the perfect time for a name change? But I don't know what to do. Is it better for me to change my first name or my last name? The problem is that a citation like "Chen 2011" is going to produce so many entries that no one will ever find them, even though they frequently do google things like that (and I simply cannot prevent people from googling something like that). Chen is so frustratingly common that even a "Chen and Name2 2011" paper could come from some random medical paper rather than from something I wrote.  As an additional complication, the % of Chinese people using the English Internet is exponentially rising, and I can only expect the problem to get worse in the future because of that (and not just for my first name, but even variants of my first name too). The most common way to refer to non-immediate family? I have several entries in my list of references that include of the order of 40 authors. Is there a way to make bibtex automatically reduce these lists to e.g. the first name + "et al."?  I don't want to edit the BibTeX entries manually and I cannot use biblatex. If at all possible I would also make as little changes as possible to the bibliography style.  There are similar questions, but none of those had a concise answer:       natbib e.g. seems to change only the reference within the text, but not the entry in the bibliography.  EDIT: I am using \bibliographystyle{unsrt} as style definition. Using ArcPy to Switch Layout Templates? Using ArcMap 10.1, since there is not a way to control portrait or landscape of the layout view through python, is there a way to switch layout templates without opening a new mxd through python?   Since there is a change layout template button it would be nice to have a python function to do the same. From what time I've spent with threads in Java, I've found these two ways to write threads:  With implements Runnable:  public class MyRunnable implements Runnable {     public void run() {         //Code     } } //Started with a "new Thread(new MyRunnable()).start()" call   Or, with extends Thread:  public class MyThread extends Thread {     public MyThread() {         super("MyThread");     }     public void run() {         //Code     } } //Started with a "new MyThread().start()" call   Is there any significant difference in these two blocks of code ? Why do electrons not fully fill up all the orbitals sequentially? Why do electrons not fully fill up all the orbitals sequentially? By this I mean: why don't the electrons fully take up the previous orbit first and then move onto the next orbit? Take calcium for example, it's electron config is 2, 8, 8, 2. Why isn't it 2, 8, 10? Why does another orbit need to be created when there are still many spots to fill up?  (I know that this is a chemistry question in a physics forum, but I really could not find a chemistry or even a broader science type forum here ) How to know if Google Sheets IMPORTDATA, IMPORTFEED, IMPORTHTML or IMPORTXML functions are able to get data from a resource hosted on a website? Google Sheets has several import functions   IMPORTDATA IMPORTFEED IMPORTHTML IMPORTXML   Sometimes the above functions returns errors like #N/A Imported content is empty and would like to be sure that there isn't a problem with the resource content to be imported.  How do I know if these functions are able to get the content that I looking to import?  I know that there also exist IMPORTRANGE but that function only is able to import content from Google Sheets spreadsheets