I wish to insert a black boundary box around a graph. I have searched through the forum but I couldn't find a way to do so. The image attached is how my graph looks like.   Below is my document code:   \documentclass[11pt]{article} \usepackage{graphicx} \usepackage{float} \usepackage{grffile} \begin{document} \begin{figure}[H] \centering \includegraphics[height = 3in]{/Users/kusha/Desktop/graphs/kden_2011.pdf} \caption{Kernel density curves of male and female wages in 2011} \label{fig:kden_2011} \end{figure} \end{document}
I use \includegraphics command to insert image to the document. But how can I add a border around this image w/o any margin between border lines and image? It seems to be very easy, but I can't find it in the documentation.
What really goes on in a vacuum? I've been told that a vacuum isn't actually empty space, rather that it consists of antiparticle pairs spontaneously materialising then quickly annihilating, which leads me to a few questions.  Firstly, is this true? And secondly, if so, where do these particles come from?... (do the particles even have to come from anywhere?) Practical uses for the "internal" keyword in C# Could you please explain what the practical usage is for the internal keyword in C#?  I know that the internal modifier limits access to the current assembly, but when and in which circumstance should I use it? What exactly fries the chip when you invert power supply? By accident, I recently removed some videos from my phone. I tried to restoring them with Recuva and TuneUp Utilities and the results were "undf" files.  I tried to open with VLC, Media Player Classic and other video players to no avail. Where/how do I find out the codec for these files?   I would really love to be able to watch these videos again. I've connected a USB to Serial bridge dongle, and running dmesg | grep tty outputted the following:  [    0.000000] console [tty0] enabled [603199.380677] usb 2-2: cp210x converter now attached to ttyUSB0   So now I'm trying to write to it as per  by running the following:  cat hello.txt &gt; /dev/ttyUSB0   and   sudo cat hello.txt &gt; /dev/ttyUSB0   But both result in the following error:  bash: /dev/ttyUSB0: Permission denied   What am I doing wrong?  Thanks Inline elements shifting when made bold on hover I created a horizontal menu using a HTML lists and CSS. Everything works as it should except when you hover over the links. You see, I created a bold hover state for the links, and now the menu links shift because of the bold size difference.  I encounter the same problem as . However, the post does not have proper solution. I've searched everywhere for a solution and can't find one. Surely I can't be the only one trying to do this.  Does anyone have any ideas?  P.S: I don't know the width of the text in menu items so I cannot just set the width of the li items.    .nav { margin: 0; padding: 0; } .nav li {      list-style: none;      display: inline;      border-left: #ffffff 1px solid;  } .nav li a:link, .nav li a:visited {      text-decoration: none;      color: #000;      margin-left: 8px;      margin-right: 5px;  } .nav li a:hover{      text-decoration: none;      font-weight: bold;  } .nav li.first { border: none; } &lt;ul class="nav"&gt;     &lt;li class="first"&gt;&lt;a href="#"&gt;item 0&lt;/a&gt;&lt;/li&gt;     &lt;li&gt;&lt;a href="#"&gt;item 1&lt;/a&gt;&lt;/li&gt;     &lt;li&gt;&lt;a href="#"&gt;item 2&lt;/a&gt;&lt;/li&gt;     &lt;li&gt;&lt;a href="#"&gt;item 3&lt;/a&gt;&lt;/li&gt;     &lt;li&gt;&lt;a href="#"&gt;item 4&lt;/a&gt;&lt;/li&gt; &lt;/ul&gt; We can prove that there is no integer $n&gt;1$ such that $2^n-1\mid 3^n-1$. This leads to the following question:     Is it true that for every pair of primes $p&lt;q$ there are only finitely many integers $n$ such that $p^n-1\mid q^n-1$? Are there two primes $p&lt;q$ and an integer $n&gt;p+q$ such that $p^n-1\mid q^n-1$?Is it true that if $n&gt;6$ then $2^n-1\nmid 5^n-1$?   Edit: Here are some examples: \begin{array}{ll} 2^{36}-1\mid 41^{36}-1, &amp;3^{12}-1\mid 97^{12}-1,\\ 5^{6}-1\mid 37^{6}-1, &amp;7^{4}-1\mid 151^{4}-1. \end{array}  Now I prove there is no integer $n&gt;1$ such that $2^n-1\mid 3^n-1.$  Proof: Denote $A=2^n-1$ and $B=3^n-1$. If $n$ is even then $3$ divides $A$ but not $B$, a contradiction.  If $n$ is odd then $A\equiv -5\pmod {12}$. Since every prime greater than $3$ is $\equiv \pm1,\pm5 \pmod {12}$, some prime factor $p$ of $A$ must be congruent to $\pm5 \pmod {12}$. As $p \mid B$, we have $3^{n+1}\equiv 3 \pmod p$. Since $n+1$ is even, we get $(\frac{3}{p})=1$, a contradiction again. Images broken on a Stack Overflow blog post On the  blog post, nearly all the images are broken. I assume this is because they are all hosted on stackoverflow.blog/wp-content/uploads/ rather than zgab33vy595fw5zq-zippykid.netdna-ssl.com/wp-content/uploads/, and they got destroyed in the removal of Blog Overflow. I looked around at a few other blog posts, and this post seems to be the only one having an issue. I hope it is alright to ask something like this here, I am having trouble keeping up with all the special cases and my book is being kind of vague.  I know how to do the standard method of finding diagonal matrices, but I know that triangular matrices are special and my book makes a connection, but it is hard to tell what it is.  Thanks. Because of  I'd like to prevent apt-get upgrade and Update Manager from updating the "libgtk2.0-0" package.   How can this be achieved? I installed Ubuntu (twice actually) onto the same drive. I wanted to 'try again' since one of them didn't install correctly and the other installed differently, but it worked.   I was getting frustrated with the GRUB menu because it was really sloppy (There were two Windows options - one with the Windows bootloader to go into Ubuntu, and two different versions of Ubuntu from the first install for some reason and memtest, etc.).  In my attempts at getting rid Ubuntu to do a fresh installation, I went ahead and deleted the partitions that weren't swap or main via Windows 7. As I said, I am a noob.  Now, even though I though I completely got rid of Ubuntu, including the GRUB menu, when I boot my PC I am brought directly to GRUB Rescue. And from what I've found from other forums, GRUB rescue isn't even completely functional for me (it doesn't recognize any commands that it should support besides ls. It also returns unknown filesystem for any partition I try to view or boot.)  Is there any way that I can boot straight into Windows? I fear I may have gone about deleting those partitions in the wrong way. If so, what are my options? Screen resolution stuck at 1024x768 How to access a SQL Server database from other computer connected to the same workgroup? I have created a C# application which uses a SQL Server database. I have other computers connected to me and to each other in a workgroup. I have shared my C# application with others. When they open the application they get the error      A network related or instance-specific error occured while establishing a connection to SQL Server. the server was not found or was not accessible   But the application is working fine on my PC. The connection string I am using is   Data Source=ASHISHPC1\SQLEXPRESS;Initial Catalog=ACW;User ID=ash159;Password=ashish159   which is stored in a .config file.   The application is working fine on my PC. What must I do? I have enabled the TCP/IP in the server but the same error persists. Some change in connection string or something else? How does ssh run a command? I'm using Bash on both client and server. When running a command over SSH:   ssh &lt;host&gt; 'declare' gives a list of shell variables. ssh &lt;host&gt; 'mount' gives a list of mountpoints.   However, declare is a Bash builtin, while mount is an external command. How does SSH know which to run if there is a shell builtin and an external command with the same name on the server? Back transforming regression results when modeling log(y) I'm fitting a regression on the $\log(y)$.  Is it valid to back transform point estimates (and confidence/prediction intervals) by exponentiation?  I don't believe so, since $E[f(X)] \ne f(E[X])$ but wanted other's opinions.  My example below shows conflicts with back transforming (.239 vs .219).  set.seed(123)  a=-5 b=2  x=runif(100,0,1) y=exp(a*x+b+rnorm(100,0,.2)) # plot(x,y)  ### NLS Fit f &lt;- function(x,a,b) {exp(a*x+b)}  fit &lt;- nls(y ~ exp(a*x+b),  start = c(a=-10, b=15))  co=coef(fit) # curve(f(x=x, a=co[1], b=co[2]), add = TRUE,col=2,lwd=1.2)  predict(fit,newdata=data.frame(x=.7)) [1] 0.2393773  ### LM Fit # plot(x,log(y)) # abline(lm(log(y)~x),col=2) fit=lm(log(y)~x) temp=predict(fit,newdata=data.frame(x=.7),interval='prediction') exp(temp)         fit       lwr       upr 1 0.2199471 0.1492762 0.3240752 I am a Swedish citizen traveling to Kyrgyzstan via Russia. Do I need a transit visa while waiting for my flight iin 24 hours? Does the sign of scores or of loadings in PCA or FA have a meaning? May I reverse the sign? I performed principal component analysis (PCA) with R using two different functions (prcomp and princomp) and observed that the PCA scores differed in sign. How can it be?  Consider this:  set.seed(999) prcomp(data.frame(1:10,rnorm(10)))$x              PC1        PC2  [1,] -4.508620 -0.2567655  [2,] -3.373772 -1.1369417  [3,] -2.679669  1.0903445  [4,] -1.615837  0.7108631  [5,] -0.548879  0.3093389  [6,]  0.481756  0.1639112  [7,]  1.656178 -0.9952875  [8,]  2.560345 -0.2490548  [9,]  3.508442  0.1874520 [10,]  4.520055  0.1761397  set.seed(999) princomp(data.frame(1:10,rnorm(10)))$scores          Comp.1     Comp.2  [1,]  4.508620  0.2567655  [2,]  3.373772  1.1369417  [3,]  2.679669 -1.0903445  [4,]  1.615837 -0.7108631  [5,]  0.548879 -0.3093389  [6,] -0.481756 -0.1639112  [7,] -1.656178  0.9952875  [8,] -2.560345  0.2490548  [9,] -3.508442 -0.1874520 [10,] -4.520055 -0.1761397   Why do the signs (+/-) differ for the two analyses? If I was then using principal components PC1 and PC2 as predictors in a regression, i.e. lm(y ~ PC1 + PC2), this would completely change my understanding of the effect of the two variables on y depending on which method I used! How could I then say that PC1 has e.g. a positive effect on y and PC2 has e.g. a negative effect on y?    In addition: If the sign of PCA components is meaningless, is this true for factor analysis (FA) as well? Is it acceptable to flip (reverse) the sign of individual PCA/FA component scores (or of loadings, as a column of loading matrix)? How can I fix a mistake I made on my income tax filing? [US] How can I fix a mistake I made on my income tax filing? Is there a rule to understand how the group "Cha" has to be pronounced?  "Character" sounds with a hard first syllable, while "Charm" sound softer, but I don't find how to tell which sound to use before earing someone saying the word. It could be because of the double consonant "rm" vs "ra"? Or is it just a matter of knowing the rule for every single word?  EDIT: More specifically, let's talk about UK English pronunciation. In respect to a larger proof I need to prove that $(n-m) \mid (n^r - m^r) $ (where $\mid$ means divides, i.e., $a \mid b$ means that $b$ modulus $a$ = $0$). I have played around with this for a while now but to no avail and would be grateful if you could help me.