numbering equations sectionwise I have align environments in each section of my TeX file and I use \numberthis\label to label the last equation in the align environment. But this labels or numbers the equations in the order they are in the file. Can I have a sectionwise numbering of the equations in the align environments? For example, the last equations of the 1st and 2nd align environments(assuming I have only got 'align' environments) in section A to be labeled as A.1 and A.2?  MWE-  \documentclass[english,aps,amsmath,amssymb]{revtex4-1}  \newcommand\numberthis{\addtocounter{equation}{1}\tag{\theequation}} \begin{document}    \section{section1}   \begin{align*}   x&amp;= 1\\    &amp;= 21313\numberthis\label{eqn}  \end{align*}  \begin{align*}  x&amp;=    1\\   &amp;=    2324\numberthis\label{eqn}  \end{align*}    \section{section2}   \begin{align*}   x&amp;=   1\\    &amp;=   34\numberthis\label{eqn}  \end{align*}   \begin{align*}  x&amp;=    2\\   &amp;=    345\numberthis\label{eqn}  \end{align*}    \end{document}   In this example, I have 4 equations and they get numbered from 1 to 4. I want to keep using the align environment and \numberthis command. And want to have numbering based on section like 1.1 and 1.2 (or A.1 and A.2) for the equations in the first section. How do I change the scope of numbering with \numberthis?
Continuous v. per-chapter/section numbering of figures, tables, and other document elements Some document elements (e.g., figures in the book class) are numbered per chapter (figure 1.1, 1.2, 2.1, ...). How can I achieve continuous numbering (figure 1, 2, 3, ...)?  And vice versa: Some document elements (e.g., figures in the article class) are numbered continuously. How can I achieve per-section numbering?  \documentclass{book}% for "vice versa" variant, replace `book` with `article`  \begin{document}  \chapter{foo}% for "vice versa" variant, replace `\chapter` with `\section`  \begin{figure} \centering \rule{1cm}{1cm}% placeholder for graphic \caption{A figure} \end{figure}  \end{document}   Bonus question: Is it possible to adjust the numbering of the sectioning headings themselves? Can I, e.g., switch from per-chapter to continuous numbering of sections in the book class?
Convert list of ints to one number? I have a list of integers that I would like to convert to one number like:  numList = [1, 2, 3] num = magic(numList)  print num, type(num) &gt;&gt;&gt; 123, &lt;type 'int'&gt;   What is the best way to implement the magic function?  EDIT  I did find , but it seems like there has to be a better way. Exporting symbols rather than points in .dxf I have a map I've made in QGIS which is points from a .csv file. These have then be turned into different symbols based on what they represent and then the sizes of said symbols based on values in the .csv.  I need to export this as a .dxf to use in AutoCAD so it basically looks the same as it does in QGIS. However, when I do so it just exports as single dots (points). Is there a way I can export them as the symbols as I can see in QGIS? A Regular Tetrahedron is a cool Polyhedron. A regular tetrahedron has this property:  For any two of its vertices exists a third vertex, which forms a regular triangle with these 2 vertices.(It doesn't necessarily have to be a face of it).  Are there any other polyhedrons that have the same property?  I think there isn't such a polyhedron. But not sure how to prove it. I've tried proving that there isn't an irregular tetrahedron with this property, assuming that there is a pair of unequal sides.   Current answers are a little confused with the conditions of the problem. In League of Legends, there are a number of effects which revive a champion upon death.  The item  is the most well-known and widely used of these.  I was wondering, however, whether its effect would come before or after other revive effects?  I have two examples.  First, Zilean's ultimate  will provide a champion with a Guardian Angel -like buff for a limited time.  If a champion has this buff in addition to a Guardian Angel, which effect will happen first?  Second, Anivia's passive  allows her to come back to life if her egg is not destroyed after she is killed.  If she has a Guardian Angel, will her passive be triggered before or after it? How does this compare to  and ?  It seems like in one case it is more beneficial to have Guardian Angel's precedence be greater, and in the other it is more beneficial to have it be less.  In the first scenario, if the Guardian Angel was triggered first, then Zilean would have a good chance of simply wasting his ultimate.  On the other hand, if it is triggered after these revival effects, then Anivia could not get the full benefit of her passive.  Is there a set order of precedence, or does each revival effect have their own unique "priority level" that is explicitly detailed for each ability? What is the regular expression to match strings (in this case, file names) that start with 'Run' and have a filename extension of '.py'?  The regular expression should match any of the following:  RunFoo.py RunBar.py Run42.py   It should not match:  myRunFoo.py RunBar.py1 Run42.txt   The SQL equivalent of what I am looking for is ... LIKE 'Run%.py' .... How do I use variables in a sed command? Wrapper for package managers There are a lot of language-specific package managers like cpan for perl, cabal for haskell etc. When we want to install some software, it can sometimes be installed from a corresponding repo, with installation instruction just like (say, ) npm install yaxy or cpan something or cabal install something.   These package managers have slightly different syntaxes, they all need root privileges and/or custom setup, or (in case of Yaxy) just a newer version of interpreter (nodejs packaged by Ubuntu was too old to run it).  Is there a wrapper for different package managers that unifies/automates setup for different package managers?  Edit: what I want is a way to execute installation command like that npm install yaxy and make it working without manual installing system npm+nodejs, getting non-functional executable, finding the simplest way to install fresher nodejs on my system, reinstalling... Variables are often adjusted (e.g. standardised) before making a model - when is this a good idea, and when is it a bad one? In what circumstances would you want to, or not want to scale or standardize a variable prior to model fitting?  And what are the advantages / disadvantages of scaling a variable? Why separation of variables works in PDEs? "Open With" dialog ignores my selection I am running Windows 7 x64. I have a file type that I want to associate with Microsoft Access 2003.  I right-click on the file and select Open With->Choose Default program. In the "Open With" dialog, I select the browse button. I choose Program Files (x86)\Microsoft Office\Office11\msaccess.exe and press "Open".  I end up back at the "Open With" dialog, but nothing has changed. Access is not listed as a program to use to open the file with. The original program (Adobe Acrobat) that is associated with this program is still selected.  Any tips on getting this association to work? Lesser-known integration tricks I am currently studying for the GRE math subject test, which heavily tests calculus. I've reviewed most of the basic calculus techniques (integration by parts, trig substitutions, etc.) I am now looking for a list or reference for some lesser-known tricks or clever substitutions that are useful in integration. For example, I learned of this trick   $$\int_a^b f(x) \, dx = \int_a^b f(a + b -x) \, dx$$  in the question    I am especially interested in tricks that can be used without an excessive amount of computation, as I believe (or hope?) that these will be what  is useful for the GRE. Find All Solutions to System of Congruence $$ \begin{cases} x\equiv 2 \pmod{3}\\ x\equiv 1 \pmod{4}\\ x\equiv 3 \pmod{5} \end{cases} $$  $ n_1=3\\ n_2=4\\ n_3=5\\ N=n_1 * n_2 * n_3 =60\\ m_1 = 60/3 = 20\\ m_2 = 60/4 = 15\\ m_3 = 60/5 = 12\\ gcd(20,3)=1=-20*1+3*7\\ gcd(15,4)=1=-15*1+4*4\\ gcd(12,5)=1=12*3-5*7\\ x=-20*2-15*1+12*3\equiv -19 \equiv 41 \pmod{60}\\ $  The above is what I've tried so far. Can someone tell me where I'm going wrong? It's my first time doing this and looking at the explanation and examples for the Chinese Remainder Theorem makes my head want to explode. Proving an entire, complex function with below bounded modulus is constant. How would I show that an entire function $f$ with the property $|f(z)| \geq 1$ must be constant?    I'm aware of Liouville's theorem, just not sure how to apply it here. When should I use a unique constraint instead of a unique index? When I want a column to have distinct values, I can either use a constraint  create table t1( id int primary key, code varchar(10) unique NULL ); go   or I can use a unique index  create table t2( id int primary key, code varchar(10) NULL ); go  create unique index I_t2 on t2(code);   Columns with unique constraints seem to be good candidates for unique indexes.  Are there any known reasons to use unique constraints and not to use unique indexes instead? Proving that $f(x)$ is less than or equal to $1+\pi/4$ Suppose $f$ is a real valued differentiable function defined on $[1,\infty)$ with $f(1)=1$. Suppose also that $f$ satisfies $$f'(x)=\frac{1}{x^2+f^2(x)}.$$ The question is to prove that $f(x) \leq 1+\pi/4$ for every $x \geq 1$    I tried to solve the differential equation but could not bring it in some known form. I examined the derivative of $\tan^{-1}x$ which looks similar to that  in the question. However I could not get any idea with that. Any help shall be highly appreciated. Thanks. Allow only alphanumeric characters for a UITextField win 10 home how to rename my home directory and account login I had Windows 8 installed on my system, which I screwed up, and now I run Ubuntu 12.04. While installing, Ubuntu used all the 461 GB of HDD space (one partition).   Now I want to make a new partition of maybe 100 GB or so, in order to install Windows 7 alongside Ubuntu (with a dual-boot). But I can't even get a partition done. I can't change the partition in GParted either - the option is disabled. How do I get horizontal lines to the left and right of a heading in Microsoft word? In Word 2007 I want to put a heading in the center of a line with a horizontal line to the left and to the right of the text.  The line must not cross through the text. I have tried using autoshapes and lines - but then the lines move each time I press Enter or &larr; Backspace and I have to put them in place again manually.  At Borders and Shading there is an "Insert horizontal line" option, but this gives me a solid line from the left to the right of the page and I cannot insert text anywhere on it or in it.    The final product should look something like this:     -------------------------  Heading ------------------------- I need to run a query like:  SELECT p.id, p.name,         (SELECT name            FROM sites s           WHERE s.id = p.site_id) AS site_list   FROM publications p   But I'd like the sub-select to return a comma separated list, instead of a column of data.  Is this even possible, and if so, how?