How to help so I can improve on my documentation and reapply
UK visa refusal on V 4.2 a + c (and sometimes 'e')
Theoretically if I were able to build some sort of device that let me sit 1 foot away from the surface of the Sun (or any star for that matter) without being vaporized, would a star produce any sort of audible sound at that distance?   From my understanding, sound waves need a medium to propagate through (air, water, etc).   Does this mean that all stars are completely silent (in the audible spectrum of frequencies at least) as they fuse  hydrogen into helium?   I know stars emit radio, xray, infrared, ultraviolet electromagnetic waves, but how about audible (20 Hz to 20Khz) frequencies?   For some reason it seems like this process would produce some sort of sound. How do I make animations a steady speed? When I make an animation, it always starts out slow, then speeds up, then slows down at the end.  I cannot figure out how to fix this. Exporting multi layered Illustrator to Photoshop I got a stomach flu or I got the stomach flu or I got stomach flu? When I googled stomach flu, there were many questions and statements like      How do you get the stomach flu?    Or     Difference between a stomach flu and food poisoning    Or      Six facts about stomach flu   When do you use the, a or nothing? And which should I use for a sentence like "I got a stomach flu from someone" ? I heard using 'could' is for politeness. When I request something, should I say "Can you please" or "Could you please"? Does the latter sound over-polite and pretentious? When an account is deleted, the username in the user's posts and comments is changed to a generic user&lt;userID&gt;. But the username stays the same on close and delete notifications on posts the user had voted to close / delete1. I think it shouldn't, especially for users who used their real name as their username, if they chose to distance themselves from the site and remove their accounts, it makes sense that they wouldn't really want their name plastered on close and delete notifications.   A perhaps easy way to avoid the actual username remaining visible would be to change it to the generic user&lt;userID&gt; (or anything generic enough, like "anonymous") prior to deletion, and wait a bit for the generic username to propagate all over the site. If I'm not horribly misreading , this was part of the process in the old days.   This could be automated or added as a suggestion to the .  Glaring example can be seen , where the deleted user also posted a comment where their name is properly anonymized:        1 I've seen it on close notifications and self deleted answers. I'm not sure it happens on deleted questions, or deleted answers that aren't self deletions, and I don't have a way to verify it - other than stumbling on them accidentally Opening Chromium on Ubuntu VPS Ubuntu noob here. I recently got a VPS running Ubuntu, and decided to install Chromium, my preferred browser, on it. After installation completed, I got a message stating that I cannot open Chromium with root privileges. How would I go about opening Chromium? Does set difference distribute over set intersection? I am asked to prove that, if $A, B$ and $C$ are sets, then $$A-(B\cap C)=(A-B)\cap(A-C).$$  However, I think that either I have made an error in my working, or the wording of the problem contains a typographical error.    My working so far is as follows: $$\begin{align}x\in(A-(B\cap C)) &amp;\iff (x\in A)\wedge(x\not\in(B\cap C))\\ &amp;\iff(x\in A)\wedge((x\not\in B)\vee(x\not\in C))\\ &amp;\iff((x\in A)\wedge(x\not\in B))\vee((x\in A)\wedge(x\not\in C))\\ &amp;\iff(x\in(A-B))\vee(x\in(A-C))\\ &amp;\iff x\in((A-B)\cup(A-C)) \end{align}$$  First line to second line: by De Morgan's Law. Second line to third line: by distributivity of set intersection over set union. Third line to fourth line: by definitions of intersection and set difference.   If my working is correct, then I have shown that $$A-(B\cap C)=(A-B)\cup(A-C).$$ Am I correct? Something that confuses me, but has never caused any problems... the recommended way to dispatch an event is as follows:  public event EventHandler SomeEvent; ... {     ....     if(SomeEvent!=null)SomeEvent(); }   In a multi-threaded environment, how does this code guarantee that another thread will not alter the invocation list of SomeEvent between the check for null and the invocation of the event? When I right click anywhere I get an option to add a new file with a specified extension. I would like to add some custom files into this menu, so I can right click and create a new PHP file for instance.  How can I do this? How do I get the path of the directory in which a  script is located, inside that script? I want to use a Bash script as a launcher for another application. I want to change the working directory to the one where the Bash script is located, so I can operate on the files in that directory, like so: $ ./application Is there an off/disable control anywhere? I realize that the INFO button toggles it off, but it comes right back on as soon as you tap the shutter, and that it a problem in low light situations where the LCD keeps blasting me in the eye. i Need a batch file to create a folder "test" in every removable device than i plug in my computer (pendrives and etc)  i am trying something like this  set "extDrive=" for /f %%D in ('wmic volume get driveLetter^ where drivertype=2 ) do set extDrive=%%D mkdir "%extDrive%\test"   Someone can tell me why this is not working ?? How tall is Supreme Leader Snoke? In Star Wars: The Force Awakens, we see Supreme Leader Snoke a few times dispensing orders to his subordinates.      However, we always see him communicating via hologram, and we've seen in previous Star Wars films that these holograms are often projected at a different size than the original person is.   So how tall is he really?  I don't think we ever got a good shot of him with something to give a sense of scale. Proving Invertibility and Eigenvalues If matrix $A$ is an $n\times n$ matrix such that $A^2 -A -2I=0$.  How can I show that $A$ is invertible and that $A^{-1} = \frac12(A-I)$? Also, how do I show that one of the eigenvalues of $A$ is $2$ or $ -1$? I appreciate any help on this question. Permanent xmodmap in Ubuntu 13.04 I cannot make xmodmap run on login in Ubuntu 13.04. I have searched around, including in askubuntu and all answers I found do not work.  I have a file named .Xmodmap in my home folder which contains the desired mappings. If I run it manually it works fine, so there is no error there. In order to make it run on startup, I have tried:     Using various .xinitrc containing one of the following commands:      xmodmap .Xmodmap xmodmap ~/.Xmodmap   /usr/bin/xmodmap /home/NAME/.Xmodmap if [ -s ~/.Xmodmap ]; then xmodmap ~/.Xmodmap fi  Using .Xresources instead of .xinitrc with the same variations. Setting it as a startup application.   None of the above works in Ubuntu 13.04 (64-bit). I also saw a few ideas about globally changing the keyboard mappings, but most of them were not applicable in Ubuntu 13.04 (i.e. the corresponding files did not exist where specified) and I prefer not to touch the global settings anyway. Calculation of $\lim_{n\to \infty}\prod_{r=1}^{n} \left(1+\frac{r}{n}\right)^{\frac{1}{n}}$ Calculation of  $\displaystyle \lim_{n\to \infty}\prod_{r=1}^{n} \left(1+\frac{r}{n}\right)^{\frac{1}{n}}$  $\bf{My\; Solution::}$  Let $y=\displaystyle \lim_{n\to \infty}\prod_{r=1}^{n} \left(1+\frac{r}{n}\right)^{\frac{1}{n}}$, Now taking $\log_{e}$ on both side  $\displaystyle \log_{e}(y) = \lim_{n\to \infty}\log_{e}\left(\prod_{r=1}^{n} \left(1+\frac{r}{n}\right)^{\frac{1}{n}}\right)=\lim_{n\to \infty}\frac{1}{n}\cdot \sum_{r=1}^{n}\log\left(1+\frac{r}{n}\right)$  Now Using Reinman Sum of Integral ...  $\displaystyle \log_{e}(y) = \lim_{n\to\infty}\frac{1}{n}\cdot \sum_{r=1}^{n}\log\left(1+\frac{r}{n}\right) = \int_{0}^{1}\ln(1+x)dx = \log_{e}(4)-\log_{e}(e) = \log_{e}\left(\frac{4}{e}\right)$  So $\displaystyle y =\lim_{n\to \infty}\prod_{r=1}^{n} \left(1+\frac{r}{n}\right)^{\frac{1}{n}} =\frac{4}{e}$  But how can i solve above question using Stirling Approximation,  May I ask for help?  Thank you in advance! I would like my JSON output in Ruby on Rails to be "pretty" or nicely formatted.   Right now, I call to_json and my JSON is all on one line.  At times this can be difficult to see if there is a problem in the JSON output stream.  Is there way to configure to make my JSON "pretty" or nicely formatted in Rails? Short circuit or disconnect to bypass a compressor Let $K$ be a field and $f \in K[x]$ a polynomial of degree $n&gt;0$. Assume that $E$ is an extension of $K$ such that $f$ can be expressed as a product of linear factors over $E$:  $$f(x)=\gamma (x-\alpha_1)(x-\alpha_2)\dots(x-\alpha_n).$$  I want to show that $\lvert K(\alpha_1,\dots,\alpha_2) : K \rvert$ is a divisor of $n!$. I also want to show that if $\lvert K(\alpha_1,\dots,\alpha_n): K \geq (n-1)!$ then $f$ is irreducible over $K$ or $f$ already has a root in $K$.  The problem has a hint. It says: "Use induction on $n=\deg f$. If $f=gh$ in $K[x]$ with $\deg g =r$ and $\deg h=n-r$, then $r!(n-r)!$ is a divisor of $n!$.  Any idea for solving this problem would be appreciated.