Suppose $(a,b)=1$. If $a$ divides $c$ and $b$ divides $c$ prove that $ab$ divides $c$
Prove: If $a\mid m$ and $b\mid m$ and $\gcd(a,b)=1$ then $ab\mid m$
I'm trying to install a service using InstallUtil.exe but invoked through Process.Start. Here's the code:  ProcessStartInfo startInfo = new ProcessStartInfo (m_strInstallUtil, strExePath); System.Diagnostics.Process.Start (startInfo);   where m_strInstallUtil is the fully qualified path and exe to "InstallUtil.exe" and strExePath is the fully qualified path/name to my service.  Running the command line syntax from an elevated command prompt works; running from my app (using the above code) does not. I assume I'm dealing with some process elevation issue, so how would I run my process in an elevated state? Do I need to look at ShellExecute for this?  This is all on Windows Vista. I am running the process in the VS2008 debugger elevated to admin privilege.  I also tried setting startInfo.Verb = "runas"; but it didn't seem to solve the problem. Tiling problem: 100 by 100 grid and 1 by 8 pieces Has user testing found that the "three horizontal bars" for main menu on mobile is commonly understood? "Three horizontal lines" aka "hamburger icon" seems to be becoming a convention for the "main menu" button, especially on mobile sites:    Has anyone done any user testing of this convention, or got any A/B testing results? (i.e. is there an increase in bounce rate compared to using the word "Menu"?)  I did some quick user testing with wireframes featuring this icon for the main menu. 3 out of 6 people got it and used it. The others did not.  One person in particular had a lot of trouble "getting back to the top" (i.e. restarting their navigation from the top level of the site) as they didn't know about the convention, or that the logo would link to the home page.  I guess it will be different for different demographics - users of Facebook on mobile probably know it.  Anyone got any findings they can share? If a Continuous function $f(x)$ satisfies $f(x) = f(2x)$, for all real $x$, then does $f(x)$ necessarily have to be constant function? If so, how do you prove it? If not any counter examples? Why is my query suddenly slower than it was yesterday? [Salutations]  (check one)  [ ] Well trained professional, [ ] Casual reader, [ ] Hapless wanderer,   I have a (check all that apply)  [ ] query [ ] stored procedure [ ] database thing maybe     that was running fine (if applicable)   [ ] yesterday [ ] in recent memory [ ] at some point    but is suddenly slower now.  I've already checked to make sure it's not being blocked, and that it's not the victim of some long running maintenance task, report, or other out of band process.  What is the problem, what should I do, and what information can I provide to get some help?  [*Insert appropriate closing remarks*] Schengen Business visa without a business invitation letter What should I do if a user posts sensitive information as part of a question or answer? I've observed several incidents where users inadvertently posted detailed, sensitive information. For example, a Server Fault user who posted a question with working login credentials to his actual production server, or the Stack Overflow user who posted actual medical records as example data for his question.   What should be the procedure for handling such cases? Distribution of Dark Matter around galaxies It is well-known that measurements of the velocity profile in galaxies are not compatible with Newtonian laws. A way to circumvent the problem is to assume that galaxies are surrounded by a spherical halo of Dark Matter. The density of mass of this Dark Matter can then be computed from the velocity profile with Newton's laws.   My question is the following: the formation of a galaxy involves essentially only the gravitational interaction. According to Newton (and General Relativity too), the trajectory of a particle does not depend on its mass. As a consequence, I do not understand how usual matter and Dark Matter could have followed different trajectories leading to such different mass distributions nowadays. Can somebody explain this (apparent) paradox ? When $\min_{x \in X,y \in Y} f(x,y) = \min_{x \in X} \min_{y \in Y} f(x,y)$? Grep: unexpected results when searching for words in heading from man page I'm running into weird behavior when trying to grep a man page on macOS. For example, the Bash man page clearly has an occurrence of the string NAME:  $ man bash | head -5 | tail -1 NAME   And if I grep for name I do get results, but if I grep for NAME I don't:  $ man bash | grep 'NAME' $ man bash | grep NAME   I've tried other uppercase words that I know are in there, and searching for SHELL yields nothing whereas searching for BASH yields results.  What's going on here?  Update: Thanks for all the answers! I thought it worth adding the context in which I ran into this. I wanted to write a bash function to wrap man and in cases where I've tried to look up the man page for a shell builtin, jump to the relevant section of the Bash man page. There might be a better way, but here's what I've got currently:  man () {   case "$(type -t "$1")" in     builtin)       local pattern="^ *$1"        if bashdoc_match "$pattern \+[-[]"; then         command man bash | less --pattern="$pattern +[-[]"       elif bashdoc_match "$pattern\b"; then         command man bash | less --pattern="$pattern[[:&gt;:]]"       else         command man bash       fi       ;;     keyword)       command man bash | less --hilite-search --pattern='^SHELL GRAMMAR$'       ;;     *)       command man "$@"       ;;   esac }  bashdoc_match() {   command man bash | col -b | grep -l "$1" &gt; /dev/null } Check which IPs or web-sites an app is communicating with? Usually they do it behind the scenes. So I'd love to know where apps are actually sending data and from whom they are actually getting responses. Replace Text Edit as the default text editor I've seen questions  which don't quite solve my problem.  I'd like to make Sublime Text 3 the default file viewer/editor for all files that currently use textedit.  Most of these files can be command+i'd, but the ones that have no extension cannot. They give all sorts of permissions errors such as the ones in this image   Is there any way to just never use textedit, and instead set sublime as the default editor for all files? Interpreting coefficient in a linear regression model with categorical variables I will give my examples with R calls. First a simple example of a linear regression with a dependent variable 'lifespan', and two continuous explanatory variables.  data.frame(height=runif(4000,160,200))-&gt;human.life human.life$weight=runif(4000,50,120) human.life$lifespan=sample(45:90,4000,replace=TRUE) summary(lm(lifespan~1+height+weight,data=human.life))  Call: lm(formula = lifespan ~ 1 + height + weight, data = human.life)  Residuals: Min       1Q   Median       3Q      Max  -23.0257 -11.9124  -0.0565  11.3755  23.8591   Coefficients:              Estimate Std. Error t value Pr(&gt;|t|)     (Intercept) 63.635709   3.486426  18.252   &lt;2e-16 *** height       0.007485   0.018665   0.401   0.6884     weight       0.024544   0.010428   2.354   0.0186 *   --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1   Residual standard error: 13.41 on 3997 degrees of freedom Multiple R-squared: 0.001425,   Adjusted R-squared: 0.0009257  F-statistic: 2.853 on 2 and 3997 DF,  p-value: 0.05781   In order to find the estimate of 'lifespan' when the value of 'weight' is 1, I add (Intercept)+height=63.64319  Now what if I have a similar data frame, but one where one of the explanatory variables is categorical?  data.frame(animal=rep(c("dog","fox","pig","wolf"),1000))-&gt;animal.life animal.life$weight=runif(4000,8,50) animal.life$lifespan=sample(1:10,replace=TRUE) summary(lm(lifespan~1+animal+weight,data=animal.life))  Call: lm(formula = lifespan ~ 1 + animal + weight, data = animal.life)  Residuals: Min      1Q  Median      3Q     Max  -4.7677 -2.7796 -0.1025  3.1972  4.3691   Coefficients:             Estimate Std. Error t value Pr(&gt;|t|)     (Intercept) 5.565556   0.145851  38.159  &lt; 2e-16 *** animalfox   0.806634   0.131198   6.148  8.6e-10 *** animalpig   0.010635   0.131259   0.081   0.9354     animalwolf  0.806650   0.131198   6.148  8.6e-10 *** weight      0.007946   0.003815   2.083   0.0373 *   --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1   Residual standard error: 2.933 on 3995 degrees of freedom Multiple R-squared: 0.01933,    Adjusted R-squared: 0.01835  F-statistic: 19.69 on 4 and 3995 DF,  p-value: 4.625e-16   In this case, to find the estimate of 'lifespan' when the value of 'weight' is 1, should I add each of the coefficients for 'animal' to the intercept: (Intercept)+animalfox+animalpig+animalwolf? Or what is the proper way to do this?  Thanks Sverre Is it time for Stack Exchange, Inc and the community to legally separate amicably? There's no need to  the  that have led to a lack of trust between  of  and . Suffice it to say that astoundingly they continue to assert that  and, instead of apologizing and reinstating Monica have demanded that she go through a process with no transparency, due process, or involvement from the community.   Has the time has come for Stack Exchange, Inc to spin off the community and all the data needed to keep the sites running to a separate non-profit, who would then in turn license the software from the company?  What's in it for the community?   The community can practice self determination for issues from as basic as the number of moderators they have to as fundamental as the policies they enforce. If the company development continues to be unresponsive to the community's needs, the community would be able to develop its own open source software that would meet its needs. They can find their own funding model instead of having ads imposed on them.   What's in it for the company?   Community actions will no longer reflect on the company. Interaction with the community as a customer may come more naturally to current leadership than the present paradigm. They don't have to worry about paying for the community's operating expenses. They can focus on doing one thing well. Unable to 'apt-get dist-upgrade' due to appstreamcli database error I have created a USB stick with a persistent Ubuntu 16.04 (release version). I tried a couple of ways, using Startup Disk Creator and MultiSystem, but I get the same end result.  When I boot into the USB and do 'apt-get update', all is well.  When I try 'apt-get dist-upgrade' I get:     ** (appstreamcli:2761): CRITICAL **: Error while moving old database out of the way. AppStream cache update failed.   The only reference to this error message I can find is  but would appear to be fixed, at least fixed by the time the release version of Ubuntu 16.04.  Aside: I want to test Unity8, which includes installing software.  I don't have a spare computer, so I thought a persistent USB would do the trick.  Any takers? Blurring/Feathering a Procedural Pointiness Mask I'm trying to create a procedural mask to affect the sharp edges of my model using the Pointiness output from the Geometry node, leading to the eventual idea of using it to create customisable weathering effects, such as .  This is the base setup that I've got so far.   How is it possible to blur/feather the black edges of the mask so that they would essentially expand across the object until the whole object is rendered black?   I've had a look at both of the go-to texture blur methods suggested for cycles found  and  however these seem to rely on there being a vector input/output for the texture, which is not the case in my example.  The Procedural Cracks tutorial by CGMasters came closest to what I was trying to achieve with the 'Worn Edges' section of the , but I didn't have any success trying to convert it to my situation.  Any ideas would be massively appreciated! :)  EDIT: Not sure if it was clear enough from the description but I'm trying to steer clear of baking/UV-Unwrapping/the Works on this one... Purely procedural :)  UPDATE: I've made a couple of updates to the shader which has given me slightly better results, although it's still not quite there and the mask blur/expansion issue is still not successful.  This is what it now looks like:   The issue is now coming from the grey values of the mask 'leaking' out across the whole mesh and not stemming from the black values... if that makes sense? :P   In researching weathering effects in blender, I stumbled across , which is exactly what I want to achieve?  UPDATE 2: Still no luck achieving the desired effect in the gif, however I feel I'm slightly closer from adding another colour ramp node after the previous ones.    Does anyone have any more ideas?  UPDATE 3: Found a working solution, added an answer below if people are interested :) How to use Font as a variable? How can I automatically add some skeleton code when creating a new file with vim When creating a new file with vim, I would like to automatically add some skeleton code.  For example, when creating a new xml file, I would like to add the first line:    &lt;?xml version="1.0"?&gt;   Or when creating an html file, I would like to add:  &lt;!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"&gt; &lt;html&gt;   &lt;head&gt;     &lt;title&gt;&lt;/title&gt;   &lt;/head&gt;   &lt;body&gt;   &lt;/body&gt; &lt;/html&gt; Insert distinct data into Combobox List Zooming in to inspect texture details in 3D view clips some closer faces like shown in the image. It's not the camera view so changing camera settings doesn't help.   Where can the distance to the clipping plane be adjusted?