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What's the best way to write subsequences?  $x_n_i$ gives an error, while $x_{n_{i}}$ works, but it just looks like $x_{ni}$ (the i isn't lowered enough below the n)... Prevent windows from going into sleep when my program is running? I have installed Ubuntu 12.04-64 bit on my Lenovo IdeaPad laptop, and the wired Ethernet (LAN) connection doesn't work.  Running the lspci -vv | grep Atheros command from the terminal shows me I have the AR8161 Gigabit Ethernet controller:  02:00.0 Ethernet controller: Atheros Communications Inc. AR8161 Gigabit Ethernet (rev 08)   This looks like a new product whose drivers are not built into Ubuntu.  How do I install drivers to get the AR8161 working? Computing the Galois group of polynomials $x^n-a \in \mathbb{Q}[x]$ I have some problems with this exercise. I don't know if it can be done. Consider the polynomial $ x^n - a \in \mathbb{Q} $ Can I compute the Galois group of this over $\mathbb{Q}$? Maybe having a nice "basis.  The splitting field is given by $\mathbb{Q}(\zeta_n,\alpha)$ , where $\zeta_n$ is a primitive root of unity , and $\alpha$ is some number such that $\alpha^n = a $. Well first of all, I want a $\underline{"good basis"}$ for the splitting field. In the sense that the minimal polynomials, of the adjoined elements, are different (in this case the computation of the galois group is very simple).  For example one easy case, it's when $a&gt;0$, then $(a)^{\frac{1}{n}} \in \mathbb{R}$ , so clearly the minimal polynomial of $(a)^{\frac{1}{n}} , \zeta_n$ are distincs, and I'm done. If $n$ is odd then , it's also easy, since one root it's also real, for example $x^3-3 $, the real root is $ \root 3 \of { - 3}  =  - \root 3 \of 3  $ , so I can consider the splitting field as $\mathbb{Q}(-\root 3 \of 3 , \zeta_3 )=\mathbb{Q}(\root 3 \of 3 , \zeta_3 )$. The difficult case is when $n$ is even and $a&lt;0$ , for example  $x^8+20$ or $x^4+20$ in some cases as in the second, there are particular cases since there exist algorithms for the Galois group of quartics, but in general. It can be done?  $\underline{Remark}$ I'm searching a $\underline{"good basis"}$ for the splitting field. In the sense that the minimal polynomials, of the adjoined elements, are different since in this case the computation of the galois group is very simple. AutoHotkey Equivalent for OS X? Is there an equivalent product/method for AutoHotkey. For those that don't know, its a product that allows you to program your mouse movements and keyboard. This allows me to "macro" certain functions on programs instead of having to do it manually. In the old days they used to call them keyboard stuffers. But that is only half of the solution as I need a "mouse movement" stuffer as well.  Is there such a beast? Why less temperature at high altitude Why there is always cold at high altitudes. e.g. at peak of mountains. Also as we go high from sea level, temperature starts decreasing. Why is it? Ubuntu 16.04 VIM without python support! Although Ubuntu 16.04 release notes mention that:  The default VIM package has been built against python3 instead of python2.  Yet after I installed vim with the following command:  sudo apt-get install vim   And checked:  vim --version   It showed:  -python -python3   Is it a bug? How do I get vim with Python support? Typesetting 144...4 with "n times" under the 4's is easy, but what about \sqrt{144...4}? Inspired by  on the math StackExchange, suppose you want to typeset the square root of the number 144...4, that is, 1 followed by n 4's. If you write $\sqrt{1\underbrace{44\ldots4}_{n\ \text{times}}}$, as in the current version of the question, you get a huge radical sign that reaches down to match the "n times" text below the number. Is there an elegant way to typeset this so that the radical sign looks like it would with $\sqrt{144\ldots4}$, but also keeping the underset text in the right place? Is there a way to condition output on a given date? I'd like to be able to print text that varies depending on whether the date matches a given date string  For example  suppose there was a command   \iftoday#1#2#3   which printed #2 if \today matched the string in #1 and #3 otherwise.  So a sample of my proposed usage would be:     \iftoday{February 3, 2016}{There's no garbage today}{Please put out the garbage}    I've tried various commands like pdftexcmd's strcmp, to no avail.    I suspect the problem may have to do with matching the string generated by \today.    While on screen it appears that \today returns February 3, 2016. I can't get it to match February 3, 2016 when I compare strings.  Obviously, I'd be perfectly happy if I could get this to work by represent today's date in any of the standard date formats.  Thanks very much in advance for any suggestions. I thought of this a while ago, but can't make up a proof or a counterexample. Does anyone know more about this?  $$\sqrt{a+b}  \le \sqrt a + \sqrt b , \forall a,b \in \mathbb R_+$$  Moreover, what happens with more variables? Say:  $$\sqrt{x_1+x_2+...+x_n} \le \sqrt x_1 +\sqrt x_2 + ... + \sqrt x_n $$  with $ x_i \in\mathbb R_+ \forall i \in \{1,2,...,n\} $  Or when $i = \mathbb N$  PS: I tried looking on the internet for this but I don't know how I would call this. Why does "unisex" mean both sexes? There are some places where men and women are segregated — for example public toilets and public swimming pool changing areas.  By this I mean, for example, that there are "Men's toilets" and "Ladies' toilets".  However, in some more cosmopolitan swimming baths, and other places, there are such things as unisex changing areas, or unisex toilets.  From my understanding uni- implies one, as in universe, unilateral or unicycle.  However when it comes to unisex, this means both sexes, so applies to two things.  How does uni- mean one in unisex? Does it mean one? Access denied for user 'root@localhost' (using password:NO) How to install pygments on windows 7 When I run LaTeX file its gives error as  "! Package minted Error: You must have pygmentize installed to use this package", you must have pygments installed. when I go through minted documentation minted itself required pygments, so Tex friend How do I install this pygment, I don't know the procedure to install. Please guid me or any link pygement.exe file Do I leave a revised question closed even though it falls out of scope for a different reason than the original closure reason? Abnormal PREEMPTIVE_OS_AUTHENTICATIONOPS Waits A uniformly continuous function maps bounded set to bounded sets I am trying to prove the following:  If $A\subset\mathbb R$ is bounded and $\,f:A\to \mathbb R\,$ is uniformly continuous, then $f[A]$ is bounded.  Could you check my proof?  Let $A \subseteq [-K,K]\subseteq \mathbb R$. Let $\varepsilon = 1$. If $f$ is uniformly continuous there is $\delta$ wuth $|x-y| &lt;\delta$ imply that $|f(x)-f(y)|&lt;1$ for all $x,y\in A$. Let $a \in A$. Then because $A$ is bounded there is a finite number of balls $B(a_n,\delta)$ that cover $A$. Let the number be $N$. Then $f(a)-N \le f(x) \le f(a) + N$ for all $x\in A$. It turns out that removing a virtual package with apt-get only remove the package itself,  leaving behind the real packages that were installed by it  So how do you remove a virtual package, along with all the real packages that it installs? How to prove wave nature of large object? Generalized Fresnel integral $\int_0^\infty \sin x^p \, {\rm d}x$ I am stuck at this question. Find a closed form (that may actually contain the Gamma function) of the integral  $$\int_0^\infty \sin (x^p)\, {\rm d}x$$  I am interested in a Laplace approach, double integral etc. For some weird reason I cannot get it to work.   I am confident that a closed form may actually exist since for the integral:  $$\int_0^\infty \cos x^a \, {\rm d}x = \frac{\pi \csc \frac{\pi}{2a}}{2a \Gamma(1-a)}$$  there exists a closed form with $\Gamma$ and can be actually be reduced further down till it no contains no $\Gamma$. But trying to apply the method of Laplace transform that I have seen for this one , I cannot get it to work for the above integral that I am interested in.   May I have a help? Cannot add custom launcher to Ubuntu Dock ('Add to Favorites' option does not show up) I have a custom .desktop file: [Desktop Entry] Type=Application Terminal=false Icon[en_US]=/home/alex/bin/idea-IC-173.4127.27/bin/idea.png Name[en_US]=IntelliJ Exec=/home/alex/bin/idea-IC-173.4127.27/bin/idea.sh Name=IntelliJ Icon=/home/alex/bin/idea-IC-173.4127.27/bin/idea.png  Output of ls -lha .local/share/applications/intellij.desktop: -rwx--x--x 1 alex alex 248 Dez 30 10:54 .local/share/applications/intellij.desktop  Answers posted to a previous question () don't work for me. I can find this launcher in Activities and I can double click on that file and IntelliJ will start. Nevertheless, I cannot add this launcher as a favorite to the dock. The option does not show up.