Adaptive parentheses at equations Is there a command that adapts automatically the size of the parentheses at the terms of the equations?  For example, in my ocasion I used \Big( but it's seems not enough.  I think could be more bigger.
Big Parenthesis in an Equation I have an equation contained inside \[...\], which automatically makes a \sum with sub- and superscripts turn big--so that the summation sign looks awkward inside parenthesis.  Any idea how to make the parenthesis completely enclose the whole summation?  \documentclass{article} \begin{document} We have: \[ \sum_{i=1}^n i = (\sum_{i=1}^{n-1} i) + n = \frac{(n-1)(n)}{2} + n = \frac{n(n+1)}{2} \] \end{document}
Two finite abelian groups with the same number of elements of any order are isomorphic Suppose $G, H$ are finite abelian groups with the same number of elements of any given order. Show they are isomorphic.   Since finite abelian groups are isomorphic if and only if their Sylow subgroups are, we may restrict our attention to the case where $G, H$, are $p$-groups, but I can't quite make it past there... Changing Screen Brightness Through Keyboard Functions on My Notebook I've installed Ubuntu 16.04 on my Asus X555LJ.  But I don't know how to install drivers or how to enable function keys to controls screen backlight brightness. Looking for a book, wormhole, space ship Crash landing From what I remember of the book:   A spaceship goes through a wormhole (I think) and crash lands on a planet They salvage what they can from the ship and build a castle on a mountain, cutting the stone with the lasers from the crashed ship The crew develop some sort of powers, the captain (She) seems to develop some sort of Precognition The planet's inhabitants where men rule and women are second class citizens Some women escape to the crew's castle so they can be equal citizens After they build the castle the crew fight the inhabitants the that came to attack them   What is the name of this book? Oxford Comma Conventions According to the Wikipedia page for the , "Use of the comma is consistent with conventional practice" and "Use of the comma is inconsistent with conventional practice." Did the Oxford Comma come before its omission, or was the Oxford Comma traditionally omitted?  It makes logical sense that every item in a list would be separated in the same way: by a comma. If the Oxford Comma is conventionally correct, when and why did people begin to omit it? Building a graph from OSM? I spent days looking in all questions here and trying tutorials. I need to build a graph for a region (It will be my input in simulation) I downloaded Postgresql and Postgis and osm2pgsql. Now i can load .osm files into a database. I want to have a complete database with roads ids so i can generate a table of edges and nodes then build my graph  nodes = intersections and edges = roads for a city using python.  Please any detailed help with steps.I saw a lot of keywords (Postgresql/postgis, Networkx, QGIS ..) but i couldn't manage to assemble a good tutorial  I am a very beginner. Back when the first discussion about deleted questions came up, I  building an official unofficial read-only archive for good deleted SE content.  I had a plan to build something like this:    Each link would point to a 1:1 scraped StackOverflow (or other SE network) deleted question (of course with a big fat disclaimer to the top, historical data, legal stuff, yada yada yada - and of course after asking Stack Exchange for permission, seeing as this would go far beyond what the CC license allows.)   I also registered a domain name that would (IMO) suit nicely, overflown.org.  However, when thinking about it, I realized doing this properly is a lot of work. You would have to:   build a scraper that can use a 10k+er's OpenID to fetch the deleted question (using the API or the data dump is for wusses. If we go through all this trouble, we want a historical document of what the site looked like "back then", right?) edit the page's DOM to remove dynamic elements, remove the "deleted" CSS classes, remove all the voting abilities from the buttons, and add the "this is historical data" disclaimer fetch - this is the biggest part and applies even if you use the API or data dump - all linked image resources (even those from imgur - even images used only in deleted questions could be purged one day), store them, and link them fetch all associated CSS style sheets and store them intelligently - preferably in a way that you don't fetch a copy of each file for each page (as normal page scrapers do), but also in a way that doesn't break if SE update their style sheets   long story short, I won't be in a position to build this any time in the foreseeable future - with old work, new work, and studying, I really have enough on my plate already.  Of course, if somebody else in the community feels like giving this a try, cool! But what I was really thinking is - maybe this is something Stack Exchange should build after all?   I know Jeff's  on these questions is used to be     @system I did think about a sweet place for them, in the bitbucket. – Jeff Atwood♦ Dec 29 '10 at 1:54   but come on. Think about it:     Future deletion discussions and changes in on-topicness policy would become way more relaxed because the popular and loved stuff has a place to go. A site for "overflown" questions could be curated by selected community members, who decide whether a contribution deserves to be archived or not.  A separate domain name (I'm happy to donate overflown.org for the purpose if desired) and the separate site design would create enough distance to the Stack Exchange network: it would be crystal clear that this read-only archive is for historical purposes only, and the existence of a question there does not mean you can ask something similar on one of the live sites. The pages would be 1:1 scrapes of what the site looked like at the time of the scraping, making it a general historical archive as well. These questions traditionally drive a lot of traffic. The possibility of continuing to show ads in the usual places would allow Stack Exchange to take advantage of that traffic without endangering content quality on the SE network. Hosting an archive like this is a job for a business, not us regular joes. A private project hosted by some community member can go down once they forget to pay a bill, or decide they want to password protect their private blog or photo album. The ideal place to host a site like this is at a company with professional admins that intends to stay online for a long time.    How about it? $_SERVER["REMOTE_ADDR"] gives server IP rather than visitor IP How do I fill arrays in Java? I know how to do it normally, but I could swear that you could fill out out like a[0] = {0,0,0,0}; How do you do it that way? I did try Google, but I didn't get anything helpful. Read integers from external data file to document programming code in LaTeX I am attempting to document my MATLAB programming code in LaTeX. For  this, I use the mcode package, which defines the MATLAB lstlisting  environment. With the commands  \newcommand{\mfileMain}{main.m} \newcommand{\mfileMainFirstNumber}{\mfileMainFirstLine} \newcommand{\mfileMainFirstLine}{26} \newcommand{\mfileMainLastLine}{33} \lstinputlisting[firstnumber=\mfileMainFirstNumber,                  firstline=\mfileMainFirstLine,                  lastline=\mfileMainLastLine]{\mfileMain}   I set the firstnumber, firstline and lastline parameters and use  them to import a piece of MATLAB code into the LaTeX document with  \lstinputlisting. However, when I add some code before the  \mfileMainFirstLine, in this case 26, the code is shifted and the  documentation is ruined. To fix this, I would have to update the line  numbers.  I am trying to fix this issue by adding 'tracers' to my MATLAB  program. I use the commands  filename=['lstinputlisting_line_numbers_' mfilename '.txt']; fileID=fopen(filename,'w');   to create a text file in which I store the line numbers for which the  code is documented using the command  dbstack_eval=dbstack;fprintf(fileID,[num2str(dbstack_eval.line+1) '\n']);   . This results in a text file lstinputlisting_line_numbers_.txt with  content for instance like  53 62 75 91   in case I want to document four parts of the MATLAB program main.m.  What I want to do from here is simply use this line number data in the  \lstinputlisting commands. Perhaps it is possible to store the line  numbers in the \newcommands{}{}, or perhaps there is a better, more  elegant way of doing it. In this way, the line numbers would update  automatically in case I add new lines of code. Consequently, my LaTeX  document would still be okay, saving me a lot of time not having to  update the line numbers myself.  A minimum working example could look like the following. The LaTeX file  main.tex would have the content  \documentclass[a4paper]{article} \usepackage[framed,numbered]{mcode}  % Data for the 'lstinputlisting' environments. \newcommand{\mfileMain}{main.m} \newcommand{\mfileMainFirstNumberA}{\mfileMainFirstLineA} \newcommand{\mfileMainFirstLineA}{WHAT SHOULD I PUT HERE?} \newcommand{\mfileMainLastLineA}{WHAT SHOULD I PUT HERE?} \newcommand{\mfileMainFirstNumberB}{\mfileMainFirstLineB} \newcommand{\mfileMainFirstLineB}{WHAT SHOULD I PUT HERE?} \newcommand{\mfileMainLastLineB}{WHAT SHOULD I PUT HERE?}  \begin{document}     In the code     \lstinputlisting[firstnumber=\mfileMainFirstNumberA,                      firstline=\mfileMainFirstLineA,                      lastline=\mfileMainLastLineA]{\mfileMain}     we calculate the ....       And in the code     \lstinputlisting[firstnumber=\mfileMainFirstNumberB,                      firstline=\mfileMainFirstLineB,                      lastline=\mfileMainLastLineB]{\mfileMain}     we calculate the..... \end{document}   . The MATLAB file main.m would have the content  %% Line number output.  filename=['lstinputlisting_line_numbers_' mfilename '.txt']; fileID=fopen(filename,'w');  dbstack_eval=dbstack;fprintf(fileID,[num2str(dbstack_eval.line+1) '\n']);     %% Input to be specified by user.  alpha=10; % PDE parameter. x_s=0; % Starting coordinate. x_e=1; % End coordinate. N_n=1e2+1; % (N)umber of (n)odes. N_ip=2; % (N)umber of (i)ntegration (p)oints.  dbstack_eval=dbstack;fprintf(fileID,[num2str(dbstack_eval.line+1) '\n']);     fclose(fileID); % Close the file 'fileID'. Fantasy book where a young prince becomes a mage Regarding the recalc in question rep increase what happens due to the cap? When the recalc runs what happens regarding rep capping on particular days? Say I earned 200 solely from questions on one day, will I earn a further 200 when the recalc runs or will I earn zero?  On a similar note if I got no rep from a question upvote on a day will the recalc give me 10, 5 or 0 rep? I read a book a while ago in which a device is invented which opens up "tunnels" back through time. These tunnels cannot be traveled through, but can be used to view what happened in the past. I believe it starts out narrating the invention of the device, then skips ahead to after it is widely in use. There is another device created, a cloak of sorts,  which hides the user from the view of someone using the tunnel device. Does this ring a bell with anyone? Arrangements of a,a,a,b,b,b,c,c,c in which no three consecutive letters are the same Q: How many arrangements of a,a,a,b,b,b,c,c,c are there such that  $\hspace{5mm}$ (i). no three consecutive letters are the same?  $\hspace{5mm}$ (ii). no two consecutive letters are the same?  A:(i). 1314. ${\hspace{5mm}}$ (ii). 174.  I thought of using the General Principle of Inclusion and Exclusion along with letting $p_i$ denote a property that.. , and doing so, I will evaluate $E(0)$, which gives us the number of arrangements without any of the properties.   How do I go about doing that? I am trying to use the method stated above in solving this question, but I am unable to generalize the properties $p_i$. How to disable all caches in safari 11? Why KL divergence is non-negative? Why is KL divergence non-negative?  From the perspective of information theory, I have such an intuitive understanding:  Say there are two ensembles $A$ and $B$ which are composed of the same set of elements labeled by $x$. $p(x)$ and $q(x)$ are different probability distributions over ensemble $A$ and $B$ respectively.   From the perspective of information theory, $\log_{2}(P(x))$ is the least amount of bits that required for recording an element $x$ for ensemble $A$. So that the expectation $$\sum_{x \in  ensemble}-p(x)\ln(p(x))$$ can be interpreted as at least how many bits that we need for recording an element in $A$ on average.   Since this formula puts a lower bound on the bits that we need on average, so that for a different ensemble $B$ which brings about a different probability distribution $q(x)$, the bound that it gives for each element $x$ will surely not bit that is given by $p(x)$, which means taking the expectation, $$\sum_{x\in ensemble}-p(x)\ln(q(x))$$ this average length will surely be greater than the former one, which leads to $$\sum_{x\in ensemble }p(x)\frac{\ln(p(x))}{\ln(q(x))} &gt; 0$$  I don't put $\ge$ here since $p(x)$ and $q(x)$ are different.  This is my intuitive understanding, is there a purely mathematical way of proving KL divergence is non-negative? The problem can be stated as:  Given $p(x)$ and $q(x)$ are both positive over real line, and $\int_{-\infty}^{+\infty}p(x)dx = 1$, $\int_{-\infty}^{+\infty}q(x)dx = 1$.  Prove $$\int_{-\infty}^{+\infty}p(x)\ln\frac{p(x)}{q(x)}$$ is non-negative.  How can this be proved? Or can this be proved without extra conditions? Java Enum definition Kali Linux: apt update returns "Hash Sum mismatch" error I'm experiencing exactly the same issue as described in this question: . Before you mark this as a duplicate however, I have tried the solutions posted there, as well as on numerous other sites, including:  sudo apt-get clean sudo rm -rf /var/lib/apt/lists/* sudo apt-get update   Editing /etc/apt/sources.list with alternate official mirrors, such as  deb http://mirrors.ocf.berkeley.edu/kali kali-rolling main non-free contrib or deb https://http.kali.org/kali kali-rolling main non-free contrib  Everything worked after I first imported the VM. I ran sudo apt update and it found some ~650 packages to upgrade. I ran sudo apt upgrade and it encountered an error partway through. That error was solved using sudo apt --fix-broken install, but that is when this hash sum error began. Unfortunately due to hours of troubleshooting I no longer have the details of the earlier error, but I believe it was an error extracting a package due to corrupt data.  I've tried multiple official mirrors, but I get the same error. Additionally, when I downloaded the Packages.gz file  on my Windows machine (VM host) and computed the SHA256 hash, I got the exact hash that apt printed as the expected value. This led me to believe that the error was not with the mirror but with my VM.  The next thing I tried was wget https://mirrors.ocf.berkeley.edu/kali/dists/kali-rolling/main/binary-amd64/Packages.gz followed by sha256sum Packages.gz, which provided yet another different hash output.  To be clear, I have seen 3 different hashes for the same file:   The "correct" hash shown by apt as expected, which is the one that windows also produced after downloading the file using a browser The incorrect hash calculated by apt, which led to the error A different hash calculated by sha256sum after downloading the file using wget using the same URL as for the browser download   I should also note that I have only been referencing the SHA256 hash in each step. The other hash functions are also mismatched when I run sudo apt update, but the file size is the same. I had considered that downloads might be failing due to limited disk space (it is a VM after all) but I don't think that's the case.  What am I missing? Resize images in PHP without using third-party libraries? After Windows 10 Fall Creators Update, a svchost.exe instance is constantly using CPU time Since installing the Windows 10 Fall Creators Update, I have a svchost.exe process that is constantly using about 14​ % of CPU time:    This svchost.exe instance is responsible for hosting three services:    The CPU time is consumed by a thread inside that process that  cannot attribute to any of these three services:    Given that these three services are considered critical system services, it's hard to do anything about them. These services cannot be stopped or disabled by services.msc, and terminating the process triggers a bugcheck (CRITICAL_PROCESS_DIED). Disabling the Windows Defender Firewall through the settings UI does not reduce CPU usage.  I'm out of ideas. What could be causing this? How can I debug this further? Is there a workaround to stop these services?    Update: After some debugging with , we've isolated this to the Windows Defender Firewall service. Process Monitor shows that it's constantly accessing the registry:    A CSV export of a Process Monitor capture, filtered to that process, is available .  I’m still looking for a way to stop that behavior.    Update 2: Analysis with the Windows Performance Analyzer shows that most CPU time is consumed by code from rpcrt4.dll: Is it ever revealed what Crookshanks is? When Hermione first got her pet thing Crookshanks, there was a mention that it looked kinda like a cat, but wasn't.  Was it ever revealed what Crookshanks really was?