How can I multiply a column by a variable and write out?
Use a shell variable in awk
"I didn't realize it was him." Prove that if $d \mid n \in \mathbb{N}$, then $\varphi(d) \mid \varphi(n)$. I want to prove that if $d \mid n \in \mathbb{N}$, then $\varphi(d) \mid \varphi(n)$.  It's given that $d \mid n$, so we know that $n = dm$, for some $m \in \mathbb{Z}$. Now, I want to show that $\varphi(d) \mid \varphi(n)$, i.e. that $\varphi(n) = k\varphi(d)$, for some $k \in \mathbb{Z}$. Drawing a blank of where to go from here. Create line heatmap with QGIS I have loaded my bike tours as .gpx files into QGIS.    It already looks quite nice but I was wondering if it might be possible to create something similar to the strava heatmap with tools of QGIS.     I have tried to generate points along the lines and use kernel density but it just does not look nice as a raster layer.  Any suggestions? Control 220V AC line using MCU Find all rings $R$ satisfying $\mathbb Z \subset R \subset \mathbb Z[\frac {1}{2}]$ Find all rings $R$ satisfying $\mathbb Z \subset R \subset \mathbb Z[\frac {1}{2}]$.   Solution: Let $f \in R$. Then $f= \frac {m}{2^n}$ for some integers $m,n$.  Since $2^{n-1} \in R$, hence $\frac {m}{2} \in R$. Hence one gets that $ \frac {1}{2} \in R$, so $R=\mathbb Z[\frac {1}{2}]$, so there is no ring $R$ satisfying given conditions.     What are the other possible solutions of this problem?    P.S: You can give a solution using any theorem from commutative algebra also. 408 Request Time-outs still continues I'm frequently getting 408 Request Time-out errors  when browsing through Stack Overflow and Meta. I used to get this four or five times a day before, but now it has become very frequent. I've read  in which Kyle Brandt ♦ says:     We send our web logs to SQL so we can query them. It turns out that we have a bug that prevents 408s from being logged to SQL. [...] I will do more extensive research when our 408s are part of queryable logs (should be a week or two [...]).   My internet connection is somewhat stable and I haven't experienced this issue on other sites before. I don't think it's a browser-specific issue as it is reproducible on latest versions of Google Chrome and Firefox (on Ubuntu 13.10). However, it is specific to Stack Overflow and Meta. I'm unable to reproduce this on other SE sites.  Am I the only one facing this issue? Could it be something wrong with the regional CDN or something like that? Could someone please take a look at this issue? ()  This appears when I try to close-vote questions, too: Prove $X$ is compact iff for each family $\{ F_\alpha\}_{\alpha\in I}$ of closed subsets of $X$ with the FIP, we have $\cap F_\alpha\neq\varnothing$. I'm reading Intro to Topology from Mendelson.  The entire problem statement is,  Prove that $X$ is compact if and only if for each family $\lbrace F_\alpha\rbrace_{\alpha\in I}$ of closed subsets of $X$ that has the finite intersection property, we have $\bigcap_{\alpha\in I} F_\alpha\neq\varnothing$.  My attempt at the proof is as follows:  First assume that $X$ is compact. For the sake of contradiction, suppose that there exists a family $\{ F_\alpha\}_{\alpha\in I}$ of closed subsets of $X$ with FIP such that $\bigcap_{\alpha\in I} F_\alpha=\varnothing$. Since $X$ is compact if $\lbrace F_\alpha\rbrace_{\alpha\in I}$ any family of closed sets such that $\bigcap_{\alpha\in I} F_\alpha=\varnothing$, then there exists a finite set of indices $\lbrace \alpha_1,\dots,\alpha_n\rbrace$ such that $\bigcap\limits_{i=1}^n F_{\alpha_i}=\varnothing$. Yet, since $\lbrace F_\alpha\rbrace_{\alpha\in I}$ has the finite intersection property, for every finite index of $J\subset I$, $\bigcap\limits_{\alpha\in I} F_\alpha\neq\varnothing$.  Suppose now that $X$ is not compact, that is, there exists an open cover $\lbrace U_\alpha\rbrace_{\alpha\in I}$ of $X$ with no finite subcover. Consider the set $F_\alpha=C(U_\alpha).$ Then $\lbrace F_\alpha\rbrace_{\alpha\in I}$ is a collection of closed subsets of $X$ with the finite intersection property and were $\bigcap_{\alpha\in I} F_\alpha=\varnothing.$  Thanks for any feedback! Adding PDF (especially GeoPDF) to ArcMap as data? I receive a lot of PDF maps (vector, image, with georeference and without) and I am having to convert them to an image file before I can add them to ArcMap and georeference.    I can't see any obvious out-of-the-box utility that would allow me to add and georeference a PDF directly without having to convert to an image file first.   Any ideas?  I would prefer to add a PDF to map directly without any prior "pdf to image" conversion "I saw one of my classmates who was/were?" Why is my ASCII art all wonky? Nothing looks right in the ASCII art.  It looks wrong and nothing is proportional, how do I fix this? I have tried fiddling with my font size, but nothing still looks right! How do I connect to a MSSQL database using Perl's DBI module in Windows? Billing Information Required for App Updates I'm trying to update 3 apps on my iPad and 3 things happen that never usually happen.   It asks me to sign in. It asks for my billing information. My card gets denied.   Now I know my card still works fine so that isn't the problem. The same thing happens when I try to install previously downloaded apps (that cloud button) or install new free apps.  I have no outstanding payments (is it even possible to have outstanding payments with Apple?) so why is this happening?  In case it's needed, I'm using an iPad Air running the latest version. 16GB Harddrive and Wi-Fi only.  I should also make it clear that "None" isn't an option for payment. Where does gravitational waves' energy go? Following the measurement of gravitational waves, many sources described them and explained they carry energy away. What I don't get is how this energy will get transfered back to anything else.  If the fabric of space-time itself is vibrating, it would seem to be in impossible for any physical object to gain this energy.    What am I missing?  How would one hypothetically get energy out of gravitational waves?  If impossible, does the universe end up with nothing but GW? How to correctly install Minecraft, including setting any needed packages or apps to install it and to troubleshoot the most common problems that Ubuntu users face when trying to use Minecraft.  I am trying to install and run Minecraft without first having to install the Oracle version of Java. I want to use the OpenJDK version that comes with Ubuntu and as a last resort, use the Oracle one.  I also want to know a list of problems related to Minecraft in Ubuntu and the possible solutions to them.  A step by step guide on how to install Minecraft would also help. Can I have a common account across the Stack Exchange family of sites? How to replace plain URLs with links? proof that on a compact manifold a vector field is complete I would like to know if my proof of the following statement is correct     If $M$ is a compact manifold, then every vector field $X$ over $M$ is complete.   Proof:  I take $p\in M$ and $(\gamma_p,I_p)$ a maximal integral curve through $p$. $I_p$ is open and non empty so if $I_p$ is closed, it is equal to $\mathbb{R}$.  So take $s\in \text{Adh}(I_p)$. There exists $t_i\rightarrow s, t_i\in I_p$. Define $q$ as $\text{lim}(\gamma_p(t_i))$ and take a maximal integral curve passing by $q$ as $(\gamma_q,I_q)$. Then since the vector fields are $C^\infty$, $\gamma_q(I_q)\cap\gamma_p(I_p)$ is nonempty (intuitively, this is clear but don't really know how to show it).  On the intersection, $\gamma_p$ and $\gamma_q$ coincide. So we can extend the maximal curve $\gamma_p$ to include $\gamma_q$. This implies that $q\in\gamma_p(I_p)$ and is actually equal to $\gamma_p(s)$  I think the main idea is there even though it probably lacks a bit of rigour. Show images related to features in QGIS? Say for example, if there's a point data with old trees, then when you use the identify tool, you can see the photograph of the tree  Or even one level further, the labels displaying these images right away without any clicking needed  I believe the term is file streaming? What is the electric charge of the Sun and its corona? I know that the Linux kernel supports TRIM as of version 2.6.33, so there should be TRIM support in ubuntu.  Is TRIM enabled by default or do I need to change some settings or install additional software for it to work? If so, how?