Question:     How does one set the tags numbering according to the related section or subsection? E.g. If it is the section 3.4 I would like to be able to label an equation as    \documentclass{article} \usepackage{amsmath, amsfonts, amssymb}  \begin{document} $$(s_1 \circ \varphi^{-1}_1)^*\boldsymbol \omega =\mathrm{Im} \left(\frac{\bar q}{1+|q|^2}dq\right) \tag{3.4.1} $$ \end{document}   Unfortunately I haven't been able to do so yet, and I would like to know if it is possible. If so, could anyone show how?
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?
Upgrading from Yosemite to El Capitan, but not Sierra We have an older iMac (Model A1311, Mid 2011). It has been running Yosemite. We have run into some of the WIFI issues associated with Yosemite.   Is it possible to upgrade to El Capitan but not Sierra?   El Cap has been out longer. Its my wife's computer, its older, and I really don't want to be debugging Sierra until a few  more "dot" releases come out. How to check if a column exists in a SQL Server table? I need to add a specific column if it does not exist. I have something like the following, but it always returns false:  IF EXISTS(SELECT *           FROM   INFORMATION_SCHEMA.COLUMNS           WHERE  TABLE_NAME = 'myTableName'                  AND COLUMN_NAME = 'myColumnName')    How can I check if a column exists in a table of the SQL Server database? Window title in bottom of Activities overview is not visible when opening multiple windows How do I create a file of size 10M, format it with ext3 filesystem and then mount it in /media/fuse?  I tried with  mkfs -t ext3 file   then to mount it  mount -t ext3 file /media/fuse   It didn't work because it said that file wasn't a block device. Can anybody help me? Can I SSH into a specific directory? How to connect to Android through SSH over 3G/4G public IP? I'd like to make commands I've typed (input) into terminal stand out from all the output.   For example:  imac:~ buster$ chmod -R g-w myfolder  imac:~ buster$ cd myfolder imac:myfolder buster$ ls -l total 0 drwxr-xr-x   9 root  admin   306 Apr 20  2010 bin drwxr-xr-x   7 root  admin   238 Apr 20  2010 include drwxr-xr-x  73 root  admin  2482 May 18 17:16 lib drwxr-xr-x   6 root  admin   204 Apr 20  2010 man imac:myfolder buster$ echo Go Giants! Go Giants!  bold jumps to mind but I'd accept a color or even highlighting the whole line...   I'm sure there's a way to do this but it's not obvious to me...  thanks! If $f:U\to V$ is holomorphic and $f'(z)\neq 0$ for all $z\in U$, then$f$ is locally bijective. I am trying to solve the following problem:     Let $f:U\to V$ be a holomorphic function such that $f'(z)\neq 0$ for all $z\in U$. Show that for all $z_0\in U$, there exists a disc $D_\varepsilon(z_0)\subseteq U$ such that $f:D_\varepsilon(z_0)\to f(D_\varepsilon(z_0))$ is bijective.   Atempt:  I am trying to use Rouche's Theorem, but I am stuck on a particular step. Let $z_0\in U$. Since $f'(z_0)\neq 0$, there is a disc $D_r(z_0)\subseteq U$ such that $$f(z)=f(z_0)+(z-z_0)h(z),\quad\forall z\in D_r(z_0)$$ where $h$ is holomorphic on $D_r(z_0)$ and $h(z)\neq 0$ for all $z\in D_r(z_0)$.   Let $0&lt;\varepsilon&lt;r$ to be defined later and fix $w\in D_\varepsilon(z_0)$. To show that $f$ is injective in $D_\varepsilon(z_0)$ is to show that the function $f(z)-f(w)$ has exactly one zero in $D_\varepsilon(z_0)$. But $$F(z):=(z-z_0)h(z)$$ has exactly one zero in $D_\varepsilon(z_0)$, so we might want to apply Rouche's Theorem with $F$ and $$G(z):=f(z)-f(w)-(z-z_0)h(z)=f(z_0)-f(w)=-(w-z_0)h(w)$$ to conclude that $F$ and $F+G$ have the same number of zeros and hence $f$ is injective. But that means that we need to find $0&lt;\varepsilon&lt;r$ such that $|G(z)|&lt;|F(z)|$ on $\partial D_\varepsilon(z_0)$. That is, $$|w-z_0||h(w)|&lt;|z-z_0||h(z)|$$ for all $w\in D_\varepsilon(z_0)$ and $z\in\partial D_\varepsilon(z_0)$.  Can we find such $\varepsilon&gt;0$?  It seems intuitive since if we expand $h$ in a power series at $z_0$, $h(z)=\sum_{n=0}^\infty a_n(z-z_0)^n$, then $$|w-z_0||h(w)| = |w-z_0|\sum_{n=0}^\infty a_n|w-z_0|^n &lt; |z-z_0|\sum_{n=0}^\infty a_n|z-z_0|^n.$$ for $w\in D_\varepsilon(z_0)$ and $z\in\partial D_\varepsilon(z_0)$. But this is of course not a proof. Chrome and IE 11 are fine, I'm only able to reproduce this in Firefox. Using version 27.0.1 on Windows 7. Meta as well as all the other sites are affected.        I can still see the hover effect, but the image is gone. I see this in Firebug:        The image doesn't show up in the Network tab. I am able to see the image by visiting  which goes to   I've done Ctrl-F5, I've cleared the cache and I've tried Private Browsing. Possibly related to  ? The Complete Rate-Limiting Guide I noticed that I can only perform certain actions such as commenting a finite number of times in a given period of time. Obviously, rate limiting is in place to prevent accidental misuse or intentional abuse of certain features.  Where else is rate limiting applied on Stack Exchange sites, and what are the limits? Let $x_{1},x_{2},\cdots,x_{n}$ be real numbers. Show that     $$\sum_{i,j=1}^{n}|x_{i}+x_{j}|\ge n\sum_{i=1}^{n}|x_{i}|.$$   I think this problem may be solved using nice methods, but I can't find them yet; I know this may be of use: $$|a|+|b|\ge |a+b|.$$ But I can't make it work. Thank you everyone. What does the term "BODMAS" mean? What is BODMAS and why is it useful in programming? Precision of Coulomb's law Up to which precision has the coulomb law proven to be true? I.e.  if you have two electrons in a vacuum chamber, 5 meters appart, have the third order terms been ruled out? Are there any theoretical limits to measure the precision ( Planck's constant?). Obviously there are practical limitations ( imperfect vacuum, cosmic rays, vacuum fluctuation). Still, does anyone know what was the smallest amount ever correctly predicted by that law?    Edit : Summary  On the high end of the energy spectrum a precision of 10^-16 has been shown ( 42 years ago )  For electron point charges at large distances the law might brake down due to practical reasons.  For moving particles QED gives a correction to the law: How can I get file extensions with JavaScript? See code:   var file1 = "50.xsl"; var file2 = "30.doc"; getFileExtension(file1); //returns xsl getFileExtension(file2); //returns doc  function getFileExtension(filename) {     /*TODO*/ } Where can I download Windows 7 (legally from Microsoft)? I just bought a serial for Windows 7 on-line from the Microsoft store (the most painful shopping experience EVER!). I selected that I wanted to download my version of Windows 7 after purchase. After payment, I have listed a Product Key but no download link in sight.   Where do I download my Windows 7 ISO to burn to disk?  Note: I'm not a Technet or MSDN subscriber. Calling Non-Static Method In Static Method In Java How do I determine the size of my array in C? What would happen if two wizards made each other a Horcrux? Would they be invincible? How would you kill one of them? How to replace a string on the 5th line of multiple text files? I want to replace the 5th line of multiple text files (file1.txt,file2.txt,file3.txt,file4.txt) with the string " Good Morning " using a single terminal command.  All the text files are located on my ~/Desktop.  Note: My desktop consists of 6 .txt files.I want to apply the change to above mentioned 4 text files only. What is the role of NS records at the apex of a DNS domain? $ORIGIN example.com. ; not necessary, using this to self-document  $TTL 3600 @        IN     SOA   ns1.example.com. admin.example.com. (                       1970010100 7200 1800 1209600 300)  @        IN     NS   ns1.example.com. @        IN     NS   ns2.example.com.  @        IN     A    198.51.100.1 ns1      IN     A    198.51.100.2 ns2      IN     A    198.51.100.3  sub1     IN     NS   ns1.example.edu.  sub2     IN     NS   ns1.sub2 ns1.sub2 IN     A    203.0.113.1 ; inline glue record   The role of a NS record beneath the apex of a domain is well-understood; they exist to delegate authority for a subdomain to another nameserver. Examples of this above would include the NS records for sub1 and sub2. These allow the nameserver to hand out referrals for portions of the domain that it does not consider itself authoritative for.  The purpose of the NS records at the apex of a domain, ns1 and ns2 in this case, seem to be less understood by the internet at large. My understanding (which may not be holistic) is as follows:   They are not used by caching DNS servers in order to determine the authoritative servers for the domain. This is handled by , which is defined at the registrar level. The registrar never uses this information to generate the glue records. They  used to delegate authority for the entire domain to other nameservers. Trying to do so with software such as ISC BIND will not result in the "expected" referral behavior at all, as the nameserver will continue to consider itself authoritative for the zone. They are not used by the nameserver to determine whether it should return authoritative responses (AA flag set) or not; that behavior is defined by whether the software is told to be a master or a slave for the zone. Most nameserver software will quite happily serve apex NS records that disagree with the information contained by the upstream glue records, which will in turn cause well-known DNS validation websites to generate warnings for the domain.   With this being the case, what are we left with? Why are we defining this information if it doesn't appear to be consumed by caching DNS servers on the internet at large?