How to turn variable name into string in JS?
Variable name as a string in Javascript
How can I prove the IFF condition for this group of matrices? I'm tasked with showing that matrix $A$ commutes with every $2\times2$ matrix if and only if $A = \begin{bmatrix}a &amp; 0\\0 &amp; a\end{bmatrix}$ for some a.  I was able to prove in the first direction, assuming that $A = \begin{bmatrix}a &amp; 0\\0 &amp; a\end{bmatrix}$, by just multiplying the matrix by $\begin{bmatrix}a &amp; b\\c &amp; d\end{bmatrix}$ in AB = BA format, and showing how AB does equal BA.  $$ (=&gt;)$$  $$\begin{bmatrix}a &amp; 0\\0 &amp; a\end{bmatrix}\begin{bmatrix}a &amp; b\\c &amp; d\end{bmatrix} = \begin{bmatrix}a &amp; b\\c &amp; d\end{bmatrix}\begin{bmatrix}a &amp; 0\\0 &amp; a\end{bmatrix}$$  $$\begin{bmatrix}a^2 &amp; ab\\ac &amp; ad\end{bmatrix} = \begin{bmatrix}a^2 &amp; ab\\ac &amp; ad\end{bmatrix}$$  But now I have to prove in the other direction, assuming that A already does commute with every $2\times 2$ matrix, and I'm not particularly sure how I can do that. Somehow, I have to show that if A commutes with $\begin{bmatrix}a &amp; b\\c &amp; d\end{bmatrix}$, then A will be $\begin{bmatrix}a &amp; 0\\0 &amp; a\end{bmatrix}$, and I don't know how I can carry that out.   Where can I start? Ideas are appreciated. Can I live in the UK for a long time through repeat visits? I had recently entered the UK without a visa to be with my partner, from 21 July 2016 until 16 December 2016. I hope to return on the 9th of January. We don't meet the income requirement for a Spouse visa. I recently applied to university, and got in, and was intending to return to the UK on a student visa, but my university did not tell me about maintenance fees and my loan wasn't large enough to cover it all, so my visa would have been denied.  Now, I am hoping to attend university in the next semester, and therefore return to the US to apply for that visa. Do you think that if I try to return to the UK without a visa, I will be turned away?  I won't be working or studying during this time, however, I'm afraid that they'll consider it living in the UK illegally; I don't have a criminal record or anything like that. Mathematics Ph.D program foreign language requirement I will soon be attending a Ph.D program in mathematics. I do not know how common this practice is, but the department has a requirement that graduate students must learn a foreign language and be able to read and write mathematics in that language. The three choices are French, German, or Russian. I personally have no preference on which to learn, but I was wondering if there were other reasons that would make one language more advantageous over the others in terms of a general mathematical career. Thanks in advance in any response. Why can the entropy of an isolated system increase? How to enclosure a text block into big square brackets? everybody.  I need to enclosure a text block into big square brackets.  Something like this (I need to replicate it, more or less):   I've read that it could be possible with tikz but I don't know anything about that package.  Even, I found a code that reproduce something similar but with braces in this post:  The code is this:  \documentclass{article} \usepackage{lipsum} \usepackage[many]{tcolorbox} \usetikzlibrary{decorations.pathreplacing}  \newtcolorbox{rightbrace}{%     enhanced jigsaw,      breakable, % allow page breaks     frame hidden, % hide the default frame     overlay={%         \draw [             fill=none, % fill paper             decoration={brace,amplitude=0.5em},             decorate,             ultra thick,             gray,         ]         % right line         (frame.north east)--(frame.south east);     },     % paragraph skips obeyed within tcolorbox     parbox=false, }  \begin{document}  \begin{itemize}     \item First line           \begin{rightbrace}             \item Second line              \item Third line, which is quite long and seemingly tedious in the extreme             \item Fourth line, which isn't as long as the third            \end{rightbrace}     \item Fifth line \end{itemize}  \begin{rightbrace}     \lipsum[1] \end{rightbrace} \lipsum[2]  \end{document}   How could I put the square brackets around a block of text? (Using tikz, tcolobox or whatever package then can be useful for it).  Thanks for your help. What is the earliest work considered to be Science Fiction? I'm developing a site using Drupal 8 beta-14. I've created a view block of different terms and now I want to display it using code. How can I display it programatically?  I used to do it in Drupal 7 using this code but I'm confused about Drupal 8.  $block = module_invoke('block', 'block_view', '4'); $text_block = render($block['content']); reformat date to have month in words Currently my text file looks like this..  David   Webb    Box 34 Rural Route 2    Nixa    MO  65714   (417)555-1478   555-66-7788 09-13-1970 Martha  Kent    1122 North Hwy 5    Smallville  KS  66789   (785)555-2322   343-55-8845 04-17-1965 Edward  Nygma   443 W. Broadway Gotham City NJ  12458   (212)743-3537   785-48-5524 08-08-1987 O'Reilly    Baba    123 Torch Ln    Joplin  MO  64801   (417)222-1234   456-65-3211 12-13-1999 Martin Bob  44 Boss Rd  Joplin  MO  64801   (417)888-4565   456-98-1111 01-01-2007   the dates are in the 9th field and I want to display them as January 7, 2017 instead of 01-07-2017 for example.  How should I do that? If using options please explain what they do briefly. Doing this in bash. Needing to put it in a script and output to a new file to preserve original. When I apply a glossy shader to the material of my text, the text becomes just black. Why?    I have lamp and everything, but the problem persists. The text is red before I add the glossy shader.  I'm using Cycles render.   Thanks! To turn off my system, I can use one of these three commands:  sudo halt   Or:  sudo poweroff   Or:  sudo shutdown -h now   What are the differences between these commands, or are they all just aliases of each other? Is this a correct demonstration for why elements above untriseptium cannot exist? With the confirmation that elements 113, 115, 117, and 118 are indeed fundamental elements that are now to be named on the periodic table, the next question is: what is the highest atomic number possible for an element? Feynman had a go at this years ago, and he derived (according to my limited understanding) that above element-137 (informally denoted 'Feynmanium') the electrons in the nearest orbit about the nucleus would be traveling at a velocity greater than the speed of light. (Note I am considering the Bohr model of the atom in this question.) I wished to demonstrate to my friends why this is and I came up with the following explanation.  According to Bohr's quantum condition, the angular momentum of an electron about the nucleus is given by $$ L=m_evr_n=n\hslash \implies r_n=\frac{n\hslash}{m_ev},$$ where $m_e$ is the mass of the electron, $v$ its velocity, $n$ an integer, and $r_n$ the radius of the $n$th possible orbit. Because we are concerned with the nearest orbit to the nucleus, $n=1$; and thus $$r=\frac{\hslash}{m_ev}.$$   Now, according to Coulomb's law, if the electron orbits about the nucleus the centripetal motion can be described by $$\frac{Ze^2}{4\pi\epsilon_or}=m_ev^2, $$ where $Z$ denotes the number of protons in the nucleus (the atomic number), and $e$ the elementary charge. Solving for $Z$ and substituting in $r$ from above yields $$Z=\frac{4\pi\epsilon_o \hslash v}{e^2}. $$ But what is $v$? Well, the maximum velocity an electron could ever have is the speed of light, and we wish to find the atomic number associated with an orbiting electron traveling at this speed, so we set $v=c$ and obtain our final result of $$Z=\frac{4\pi\epsilon_o\hslash c}{e^2}\approx 137.521,$$ which implies that for $Z&gt;137$, the electrons at a position of $n=1$ in the Bohr model would have a velocity $&gt;c$; and thus the highest atomic number achievable on the periodic table is 137.  Again, I just want to make sure this is a correct method for deriving element-137 before presenting. Perhaps one could explain how relativity plays a role here. I know Feynman used the Dirac equation to get this result...so could anyone (subsequently of course) expatiate on this in a simplistic manner? Thanks! In other words, how to prove:  For all real constants $a$ and $b$ such that $a &gt; 1$, $$\lim_{n\to\infty}\frac{n^b}{a^n} = 0$$  I know the definition of limit but I feel that it's not enough to prove this theorem. Ubuntu halts after few seconds of starting and nothing works command, virtual terminal, GUI I'm buying a bus ticket to get to Boston 23 hours before my flight to ensure I reach my departure airport on time.  If I didn't arrange bus transport well in advance, what legal remedies would I have if a delayed bus caused me to miss my flight? Integration of exponential and square root function Legality of using names in a game? Why is foo.hasOwnProperty('__proto__') equal to false? Question: Best way to derive an ellipse formula when given bunch of points (say 60 points which when connected draws an ellipse)?  Background: Using R Momocs library function  which returns confidence ellipse coordinates. Would be nice to abstract those points into a formula.  You can see my ellipse points in the image below;    Any suggestions much appreciated, Thanks Entity Framework and SQL Server View Where can I safely store my stuff? I'd like to find a place to store stuff while I'm out adventuring, without spending 5000 on a house (at least, until I can afford that...). Where can I safely store items without worrying about them disappearing?   There are two possible places that come to mind,  (to which I have the key and was told I could stay), and the small bedroom given to me at the  (which I was told was mine, despite seeing J'zaro sitting in it later). Can I store items safely in either of these places?