Specific newcolumntype (for 'R') not working? Could someone kindly explain why the following works:  \documentclass{article} \usepackage{tabular} \newcolumntype{C}[1]{&gt;{\centering}m{#1}} \newcolumntype{L}[1]{&gt;{\centering}m{#1}} \begin{document} \begin{center}   \begin{tabular}{ | L{3cm} | C{3cm} | r | }     \hline     A &amp; B &amp; C \\ \hline     1 &amp; 1 &amp; 16384 \\     \hline   \end{tabular} \end{center} \end{document}   But if I try to include the following, it fails(?):  \newcolumntype{R}[1]{&gt;{\centering}m{#1}}   Many thanks
How to create fixed width table columns with text raggedright/centered/raggedleft? I would like to create a table with some columns' width specified, while the text in those columns should be centered both horizontally and vertically. I found out that  \usepackage{array} \begin{tabular}{| c | c | m{5cm} |}   vertically centers the text in the last column, but justifies it horizontally (like text in normal paragraphs).  Update: With Jake's method, it seems both \\ and \hline cause an error. How to fix it?
Which year does Spider-Man: Homecoming take place in? It seems like to deleted too much files by rm -r and now I have the error of "the system is running a low-graphic mode" in Ubuntu and I have to work in Windows because of that.  However I can load it in recovery mode. I need to copy the files from Downloads folder to a flash drive. Downloads folder has them as I can see by ls command.   When I plug in a flash drive, there will be some messages saying that everything is ok (as I understood) and it's plugged. But when I go to /media/my_name and do ls then I don't see anything. I don't see anything in /run/media/my_name either(I'm not sure if should though).  I can't connect to the Internet for some reason. Ubuntu was installed by wubi.exe file.  How do I save the content of my Downloads folder to a flash drive? The Frobenius Coin Problem I am asked to prove that:       For integers $n, x,y &gt; 0$, where $x,y$ are relatively prime,        every $n \ge (x-1) (y-1)$ can be expressed as $xa + yb$, with nonnegative integers $a,b \ge0$.   How should I approach this? I have very limited knowledge in number theory. Question about the Euclidean ring definition I recently came across the following definition for a euclidean ring:  There exists a function $g:R\to\Bbb N_0$ with the following properties:  1.) $\forall x,y \in R$ with $ y \neq 0$ there exist $q,r \in R$ with $x = qy + r$ where $r=0$ or $g(r) &lt; g(y)$.  2.) $\forall x,y\in R\setminus\{0\}$ we have $g(xy)\ge g(x)$  What I don't understand, is the point of the second requirement. I have seen definitions where this is not a requirement. What does 2.) achieve?   Thanks very much Would Gravitational Time Dilation still apply between two gravitational sources? As explained on , when an object is experiencing strong gravitational forces, time passes slower for it. If, in theory, you had two objects exerting the same amount of gravitational pressure on an object in opposite directions, effectively cancelling each other out, would they cancel out the time dilation, or would they compound, making the time dilation more prevalant? Show that  $A \setminus ( B \setminus C ) \equiv ( A \setminus B) \cup ( A \cap C )$  This is an exercise I was trying to do ( not homework ) and I got stuck as follows:  Working from $A \setminus ( B \setminus C )$:  $x \in A \wedge x \notin ( B \setminus C )$ $x \in A \wedge ((x \in B \wedge x \in C) \vee (x \notin B \wedge x \in C) \vee (x \notin B \wedge x \notin C) )$  At this point I'm not sure how to proceed.  Working from the other side $ ( A \setminus B) \cup ( A \cap C ) $:  $ x \in ( A \setminus B) \cup ( A \cap C ) $  $ x \in ( A \setminus B) \vee x \in ( A \cap C ) $  $ ( x \in A \wedge x \notin B ) \vee ( x \in A \wedge x \notin C ) $  $ x \in A \wedge (x \notin B \vee x \notin C ) $  $ x \in A \wedge x \notin ( B \cap C ) $  $ A \setminus ( B \cap C ) $  I could also use some formating tips like how display logical not and how to get the lines to display properly without blank lines inbetween. :-) Sarrus Rule with LaTeX Etiquette on sending a thank you e-mail to respondents who gave me helpful information With regards to Plymouth --  Are there alternative boot screens available?  What's the easiest way to change the boot screen? What level is a spell if you cast it without expending a spell slot? Is it possible to extend a tourist Schengen visa (12 more days)? My daughter applied at the Italian Consulate in Philadelphia, and they gave her two entries for 20 days (we thought it was for 20 days each entry). She was in Italy 12 days, then went to England for 1 week and flew to Venice to take a 10-day cruise. She couldn't make it because they said she has only 8 remaining days, but she still has a land tour already paid this week.  What can she do? Can she extend the Schengen visa for 12 more days? Right now, she is in Madrid, but next week she has to fly from Barcelona to Paris to start with the tour. What would happen if she decides to take the tour with the expired visa? She is a US permanent resident. Do all accepted students in top-tier engineering programs get invited to interview before getting admitted? The value of a, b and c for this integral Find out the value of $a, b$ and $c$, for which $$ \lim _{x\to 0}\:\:\frac{1}{x^5}\left(\int _0^x\:\left(a+b \cos\left(t\right)+c \cos\left(2t\right)\right)dt\right)=\frac{1}{5} $$  My first thought was to separate the integral into multiple ones because i thought that it is pretty clear that each integral is a common one and a,b,c are constants and can be taken out . After I solved the integral, that's where I had the problem. I couldn't do the limit of the result that I've got in order to find out the value of $a,b$ and $c$ . Countable additivity implies countable subadditivity? Suppose $\mu$ is a measure in a ring $R$ of a set $X$. So for any mutually disjoint subsets $A_1,A_2,\ldots$ such that $\sum_{i=1}^\infty A_i\in R$, we have that $\mu(\sum_{i=1}^\infty A_i) = \mu(A_1)+\mu(A_2)+\cdots$. (i.e. countable additivity)  I'm wondering: Does that imply countable subadditivity? I.e. for any subsets $A_1,A_2,\ldots$ such that $\sum_{i=1}^\infty A_i\in R$, is it always true that $\mu(\sum_{i=1}^\infty A_i)\le \mu(A_1)+\mu(A_2)+\cdots$?  I believe it should be true, because you can take the mutually disjoint subsets $A_1,A_2-A_1,A_3-(A_1\cup A_2),A_4-(A_1\cup A_2\cup A_3),\cdots$, each of which is in $R$ (because unions and differences of sets in $R$ are again in $R$), then apply countable additivity, then use monotonicity on the fact that $A_n-(A_1\cup\cdots\cup A_{n-1})\subseteq A_n$.  Is that right? I just want to make sure I didn't make any mistake in my logic. Using past tense when referencing a still-true fact In the sentence: "I didn't know she had a son,"   Can I say "I didn't know she has a son" instead, because he is a teenager now?  Or are both correct? How to view network traffic requested by a specific app? There are lots of discussion on how to see which app is requesting network connection. I have tried the following apps:  tcapturepacket wifi monitor connection tracker   However, none of them was useful. For example, for a short period of time, I uploaded a 30KB pcap file which can be viewed . Still I haven't find out which app is requesting connection and to where it is trying to connect.  I also tried to look at adb logcat, but didn't find useful information. Maybe something has been missed here. Any guess? Why can rm remove read-only files? When I'm in a phone call, I still get alerts for emails and texts. The noise will play and, if the phone is on Speaker, it will vibrate -- often leading the person I'm talking to wonder what that weird noise was.  Surely there must be a way to silence the phone while you're talking on it. It's very distracting to have beepings going off right next to your ear! What is the Physical Meaning of Commutation of Two Operators? I understand the mathematics of commutation relations and anti-commutation relations, but what does it physically mean for an observable (self-adjoint operator) to commute with another observable (self-adjoint operator) in quantum mechanics?   E.g. an operator $A$ with the Hamiltonian $H$? Rejecting a PhD offer after having accepted it. Advice?