Exporting A4 size
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I get the following error when I try to typeset a beamer document.  kpathsea: Running mktexpk --mfmode / --bdpi 600 --mag 0+525/600 --dpi 525 mathkerncmssi8 gsftopk: fatal: map file `cid-base.map' not found. mktexpk: don't know how to create bitmap font for mathkerncmssi8. mktexpk: perhaps mathkerncmssi8 is missing from the map file. kpathsea: Appending font creation commands to missfont.log.  ) !pdfTeX error: pdflatex (file mathkerncmssi8): Font mathkerncmssi8 at 525 not found  ==&gt; Fatal error occurred, no output PDF file produced!   But if I remove sansmathaccent.sty from the TeX Live tree, the document typesets fine. Here is a minimal working example.  \documentclass[10pt]{beamer}  \begin{document}  \begin{frame}{A very short beamer document}  $e^{i\pi}+1=0$  \end{frame}  \end{document} Let $a_1=1$ and $a_n=n(a_{n-1}+1)$ for $n=2,3,\dots$. Define $$P_n=\left(1+\frac{1}{a_1}\right)\left(1+\frac{1}{a_2}\right)\dots\left(1+\frac{1}{a_n}\right)$$Find $$\lim_{n \to \infty}P_n$$   Trial: $$1+\frac{1}{a_n}=1+\frac{1}{n(a_{n-1}+1)}\;.$$ But I can't simplyfy.Please help. Get list of all tables in Oracle? How do I query an Oracle database to display the names of all tables in it? Visualization for Euclidean Algorithm How do you photograph rain? What are recommended settings for my Nikon Coolpix P1 to best portray rain?  Here's what I got. No retouching was applied.   The picture I took when the rain was heavy with the automatic settings:  The picture I took with the "Sports" program; by then, however, the rain was not as hard. Ugh, ugly gray strip at the bottom, that was the flat surface I put my camera on to get a stable picture.   My main problem is that the actual rain and hailstorm is very hard to see in the picture. The overall effect is, instead, of fog.    Follow-up from the thread, courtesy of more rain, now with less hailstorm and more thunder.  The feedback amounted to flash and faster shutter. I took a few photos and I'm having some trouble to reconstruct what I did to get each result. Two representative results:   Fast shutter, with some guest starring:I'm talking about that horrible building obviously. Faster shutter and flash:Kinda difficult to say those pictures were taken sixty seconds of each other. :)   I'm not sure, however, that either of this is really an improvement of the original results. I'm doing some exercises on Apostol's calculus, on the floor function. Now, he doesn't give an explicit definition of $[x]$, so I'm going with this one:     DEFINITION Given  $x\in \Bbb R$, the integer part of $x$ is the unique $z\in \Bbb Z$ such that $$z\leq x &lt; z+1$$ and we denote it by $[x]$.   Now he asks to prove some basic things about it, such as: if $n\in \Bbb Z$, then $[x+n]=[x]+n$  So I proved it like this: Let $z=[x+n]$ and $z'=[x]$. Then we have that  $$z\leq x+n&lt;z+1$$  $$z'\leq x&lt;z'+1$$  Then $$z'+n\leq x+n&lt;z'+n+1$$  But since $z'$ is an integer, so is $z'+n$. Since $z$ is unique, it must be that $z'+n=z$.  However, this doesn't seem to get me anywhere to prove that  $$\left[ {2x} \right] = \left[ x \right] + \left[ {x + \frac{1}{2}} \right]$$  in and in general that   $$\left[ {nx} \right] = \sum\limits_{k = 0}^{n - 1} {\left[ {x + \frac{k}{n}} \right]} $$  Obviously one could do an informal proof thinking about "the carries", but that's not the idea, let alone how tedious it would be. Maybe there is some easier or clearer characterization of $[x]$ in terms of $x$ to work this out.  Another property is $$[-x]=\begin{cases}-[x]\text{ ; if }x\in \Bbb Z \cr-[x]-1 \text{ ; otherwise}\end{cases}$$  I argue: if $x\in\Bbb Z$, it is clear $[x]=x$. Then $-[x]=-x$, and $-[x]\in \Bbb Z$ so $[-[x]]=-[x]=[-x]$. For the other, I guess one could say:  $$n \leqslant x &lt; n + 1 \Rightarrow  - n - 1 &lt; x \leqslant -n$$  and since $x$ is not an integer, this should be the same as $$ - n - 1 \leqslant -x &lt; -n$$  $$ - n - 1 \leqslant -x &lt; (-n-1)+1$$  So $[-x]=-[x]-1$ Aufbau principle in modern quantum theory A new version of Ubuntu has been released. I still can't find it on ubuntu.com. Where can it be downloaded from, or is it the only way to install it using update-manager to upgrade an existing installation? example of compact operator Let $E=l^p=\left\{x=\left(x_n\right): x_n\in\mathbb{R}, \sum_{1}^{\infty}\left|x_n\right|^p&lt;\infty\right\}$ with $1\le p&lt;\infty$, $\left\|x\right\|_E=\left(\sum_{1}^{\infty}\left|x_n\right|^p\right)^{1/p}.$ Let $\left(\lambda_n\right)$ is a bounded sequence in $\mathbb{R}$ and consider the operator $T$ defined by $$T(x)=\left(\lambda_1x_x,\ldots,\lambda_nx_n,\ldots\right)$$ where $x\in l^p$. Prove that $T$ is a compact operator from $E$ to $E$ iff $\lambda_n\rightarrow 0$.  Can anyone give me some hints to solve this problem? Thank you! Which story is true at end of the movie "Life of Pi"? At the end of the movie  Pi tells us two stories. One with the tiger (unrealistic) and one without the tiger (realistic).  I believe that he was metaphorically referring himself as the tiger who enters the forest (world) after being rescued.  Is my thinking correct? can you explain me the ending?  At the end did Irfan Khan (older Pi/narrator) say that "even God chose the first story"? Does it mean that the first story was indeed real? During iPhone update to iOS 10.3.1, I was asked for my password using the correct machine name for my Mac mini. To be clear, the request was not for my iCloud password, my actual local user account password for macOS. This can also happen in the other direction - setting up a Mac may ask for verification for you to enter your iPhone / iPad passcode (and not your iCloud password)  I could not find any information about this kind of access. I was thinking it was security for iCloud and possibly related to two step authorization or two factor authorization. This is the first time I can think of that I entered a desktop password outside of that actual desktop.  I don't have a screen shot but I recall an implication that some files in my Mac are encrypted and need my password. '... need to enter the password for .'   Are there settings I can I control this assuming it's a legitimate part of iCloud setup process or iOS setup process? Could someone please explain? I couldn't find anything on the internet, everything talks about how to go about it in some way, but nothing says exactly what it is.   Also, what is a fully trusted assembly and how do they differ from one another?  I have a MS certification exam and this is the only topic that I just don't understand.  EDIT: Thanks guys. Now I have a better understanding of security in .NET. I was able to pass my certification exam. Why is the last digit of $n^5$ equal to the last digit of $n$? I was wondering why the last digit of $n^5$ is that of $n$? What's the proof and logic behind the statement? I have no idea where to start. Can someone please provide a simple proof or some general ideas about how I can figure out the proof myself? Thanks. I'm trying to install Windows 7 with a 4GB flash drive, but my error that comes up is that my hard drive I'm trying to install on is in ext4. I need to format it to read NTFS. I can't seem to find any topics on how to format an active hard drive. I found a topic that explains how to move Ubuntu to a new drive, but it's a bit confusing to me. Simplify result of $\int_0^{\infty} \frac{1}{1+x^n}dx$ It is quite easy to show that (by using residue theorem) $$\int_0^{\infty} \frac{1}{1+x^n}dx = \frac{2 \pi i^{1+2/n}}{n(e^{2 \pi i / n} - 1)} $$ for $$n \ge 2$$  Is there any possibility to simplify $$\frac{2 \pi i^{1+2/n}}{n(e^{2 \pi i / n} - 1)}$$ or it is best result?  Thanks in advance! How to find max of amount of opportunity related to account? I have a below requirement : I need to find maximum amount on related opportunities and to display on account. Ex: suppose I have account A1 and A1 have 5 opportunities with amount o1=>100 o2=>500 o3=>300 o4=>1000 o5=>50 on my account i should have max_opportunity_amount =1000.  I have written below trigger ,but  I am not sure what to do further  trigger maxOppAmountonAcc on Opportunity(after insert){      map&lt;id,Opportunity&gt; oppMap = new map&lt;id,Opportunity&gt; ();     set&lt;Id&gt; oppId = new set&lt;Id&gt;();     for(Opportunity o : Trigger.new)     {         oppMap.put(o.accountId,o);         oppId.add(o.id);     }       List&lt;Account&gt; accList = new List&lt;Account&gt;();      for(Account a : [Select id ,MaxOppAmount__c,(select id,max(amount)  from opportunities) from Account where id in : oppMap.keyset()])     {      }  } A does the same B as does C Power set equivalency of Axiom of Choice How do I disable search-as-you-type text in Ubuntu 17.10 and later? I cannot find enable-interactive-search in    gsettings set org.gnome.nautilus.preferences enable-interactive-search true.     I searched using    gsettings list-recursively | grep search     and    gsettings list-recursively | grep interactive     but no such option.  Can you help me disable this in Ubuntu 17.10 and later? Git ignore file for Xcode projects Which files should I include in .gitignore when using Git in conjunction with Xcode?