How to install a new keyboard for my laptop
I just spilt coffee on my laptop, what should I do?
How is the /tmp directory cleaned up? Is it automatic? If so, how frequently is it cleaned up? Polynomial irreducible - maximal ideal I have a couple of ideals which I wonder if I correctly classify as maximal/prime ideal.  $I_1 = \langle 2x^2 + 9x -3\rangle$, $I_2 = \langle x - 1\rangle$  $\mathbf 1)$ Is $I_1$ a maximal ideal in $\mathbb{Q}[x]$?  Yes, since $I_1$ is irreducible with $p=3$ using Eisenstein's criterion, thus maximal ideal.  $\mathbf 2)$ Is $I_2$ a prime ideal in $\mathbb{Q}[x]$?  Yes, since $I_2$ is obviously irreducible, and thus a maximal ideal, and every maximal ideal is a prime ideal.  $\mathbf 3)$ Is $I_2$ a maximal ideal in $\mathbb{Z}[x]$?  Yes, $I_2$ is obviously irreducible, and thus a maximal ideal.  $\mathbf{Edit:}$ No, as it is not a field. $$ $$  Am I right in my conclusions?  Appreciate any help. Ubuntu 16.04 sftp and vscode ssh not working In a 2D top-down game, how can I create projectiles that have a height? $\lim_{n \rightarrow\infty} ~ x_{n+1} - x_n= c , c > 0$ . Then, is $\{x_n/n\}$ convergent? How to make a cross-module variable? Silverlight - how do I get the text of the selected item in a combobox How to reorder /etc/resolv.conf at load time I have a CentOS system that retrieves its upstream DNS servers via DHCP.  I want to run DNSMasq on this box and use it as a server to resolve some hostnames for development.  The problem is when my system starts, the upstream DNS servers are loaded into /etc/resolv.conf and THEN the DNS1 entry from my ifcfg-enp0s3 setup gets loaded.   That's a problem because when I query for the internal dev names, it tries to go out to the upstream DNS server instead of checking DNSMasq first.  I need the DNSMasq server to be at the TOP of the /etc/resolv.conf and the dhcp loaded ones at the bottom of the resolv.conf so that DNSMasq will work properly.  Any simple way to do that? Show that $u(x)=\ln\left(\ln\left(1+\frac{1}{|x|}\right)\right)$ is in $W^{1,n}(U)$, where $U=B(0,1)\subset\mathbb{R}^n$. The entire problem statement is:  Let $n&gt;1$ and let $U=B(0,1)\subset\mathbb{R}^n$. Show that $u:U\to\mathbb{R}$ given by  $$u(x)=\ln\left(\ln\left(1+\frac{1}{|x|}\right)\right)$$ is in $W^{1,n}(U).$  My attempt at the proof is as follows:  To show that $u\in W^{1,n}(U)$ it suffices to show that $|Du|\in L^{n}(U)$. Consider $$u_{x_i}=\frac{1}{\ln\left(1+\frac{1}{|x|}\right)}\frac{1}{1+\frac{1}{|x|}}|x|^{-2}\frac{x_i}{|x|},$$ which simplifies to, $$u_{x_i}=\frac{1}{\ln\left(1+\frac{1}{|x|}\right)}\frac{1}{1+\frac{1}{|x|}}\frac{x_i}{|x|^3}.$$ Thus, $$|Du|=\frac{1}{\ln\left(1+\frac{1}{|x|}\right)}\frac{1}{1+\frac{1}{|x|}}\frac{1}{|x|^2}$$ which can be manipulated to, $$|Du|=\frac{1}{\ln\left(1+\frac{1}{|x|}\right)}\frac{1}{1+|x|}\frac{1}{|x|}.$$  Moreover, since $U=B(0,1)$ we can bound the second term from above which gives, $$|Du|\leq\frac{1}{\ln\left(1+\frac{1}{|x|}\right)}\frac{1}{|x|}$$  Thus, we can instead show that $$\int_U\left(\frac{1}{\ln\left(1+\frac{1}{|x|}\right)}\frac{1}{|x|}\right)^n&lt;\infty.$$  Converting this into polar coordinates we have with $r=|x|$, $$\int_0^R\int_{\partial B(0,r)}\left(\frac{1}{\ln\left(1+\frac{1}{r}\right)}\frac{1}{r}\right)^n\,dSdr=\int_0^R\left(\frac{1}{\ln\left(1+\frac{1}{r}\right)}\frac{1}{r}\right)^n\int_{\partial B(0,r)}dSdr$$ Note that $\int_{\partial B(0,r)}\,dS=n\alpha(n)r^{n-1}$, which is the surface area of $B(0,r)$. Thus, we have then $$n\alpha(n)\int_0^R\left(\frac{1}{\ln\left(1+\frac{1}{r}\right)}\frac{1}{r}\right)^nr^{n-1}\,dr=n\alpha(n)\int_0^R\left(\frac{1}{\ln\left(1+\frac{1}{r}\right)}\right)^n\frac{1}{r}\,dr$$  And so this is where I get stuck in the problem, since I don't how I can evaluate that last integral to show it's finite.  Thank you for any help or feedback! says:  Note that there is one axiom for every such predicate φ; thus, this is an axiom schema. To understand this axiom schema, note that the set B must be a subset of A. Thus, what the axiom schema is really saying is that, given a set A and a predicate P, we can find a subset B of A whose members are precisely the members of A that satisfy P. By the axiom of extensionality this set is unique  (Emphasis added) My question is why, by the axiom of extensionality, is this set unique? The Axiom of Extensionality is about set equality; what is the relation between the Axiom of Extensionality with uniqueness of this set? I have been playing with Ubuntu for a few weeks now, and I'd like to revert my computer back to it's original - factory - defaults.   On the computer I have a recovery partition (it's a netbook). I went through the process of recovery and everything seemed fine. However, when I restart the computer I'm presented with   grub rescue &gt;   Now, my understanding is that when I installed Ubuntu "side by side" it replaced the MBR or something like it, with GRUB.   I've read on a slew of forums, that I need to use a Windows Recovery Disk.   Here are my issues:   a) I don't have a recovery disk, I have a recovery partition - it's a netbook. b) I don't have an external cd drive.   What I do have is a USB key that has about 1gb of space on it.   Thanks in advance. Why taking components of a component of a vector is invalid? I have two submit buttons in a form. How do I determine which one was hit serverside? access parent object in javascript Sometimes I have asked a question which got no answers, but is answered in the comments to the question.  How should I handle these questions? I can't accept an answer, so it is never an accepted question.  For example this one:   (ok here the answer in the comments is from me, but nevertheless I also have others of them) Proof of a formula involving Euler's totient function: $\varphi (mn) = \varphi (m) \varphi (n) \cdot \frac{d}{\varphi (d)}$ The third formula on the  states that $$\varphi (mn) = \varphi (m) \varphi (n) \cdot \dfrac{d}{\varphi (d)} $$ where $d = \gcd(m,n)$.  How is this claim justified?  Would we have to use the Chinese Remainder Theorem, as they suggest for proving that $\varphi$ is multiplicative? How to avoid being prompted for a password by sudo? I know I can become root (super user) via the su command but I have to authorize it after entering the commands. Is there a way I can become root and authorize (with password) in one line Test of whole distribution for two samples How to detect if a function is called as constructor? Given a function:  function x(arg) { return 30; }   You can call it two ways:  result = x(4); result = new x(4);   The first returns 30, the second returns an object.  How can you detect which way the function was called inside the function itself?  Whatever your solution is, it must work with the following invocation as well:  var Z = new x();  Z.lolol = x;  Z.lolol();   All the solutions currently think the Z.lolol() is calling it as a constructor. I couldn't find much on the new Lucene-based search, and don't know much about the engine in general, so I'm asking this question.  Does anybody have a description of how search results are ranked?  Does the rank calculation include:   rep of post's author? views? unique referers? PageRank of referers? rank of questions that link to the post? whether a question is closed? vote count? answer count?