Prove that $F$ is locally constant iff the associated étale space over $X$ is a covering.
A locally constant sheaf on a locally connected space is a covering space; Proof?
Is the Ohm's law violated here? And also why is electricity generated at 11,000 V in India? Load a resource contained in a jar In my application I load resources in this manner:  WinProcessor.class.getResource("repository").toString();   and this gives me:  file:/root/app/repository   (and I replace "file:" with empty string)   This works fine when I run my application from the IDE, but when I run the jar of my application:  java -jar app.jar   The path becomes:  jar:/root/app.jar!/repository   is there any way to solve this problem?  I'll use the "repository" dir name in order to create this:  ConfigurationContext ctx = (ConfigurationContext) ConfigurationContextFactory.createConfigurationContextFromFileSystem(repositoryString, null);   In the same manner, I'll get one file name (instead of a dir) and I'll use it this way:  System.setProperty("javax.net.ssl.trustStore", fileNameString) This is sort of a follow-up to a feature request that resulted in obscuring spam / offensive content from 10K-visible answers:   Suggest the same to be done for questions. As of now, spam questions (, ) preserve their titles and content. Suggest to revise the titles to something like     This question was marked as spam or offensive and is therefore not shown   And the text to something like:     This question was marked as spam or offensive and is therefore not shown - you can see the revision history for details".   Where "the revision history" links to the question revision history.    For those interested, here is a link to screen shots of how spam shines through my flagging summary page and is displayed to me when I click the link to one of deleted questions: .  For the sake of precision, flagger having less than 10K rep would see only upper screen shot - the one that lists question titles ("Call giRℒs blah blah &lt;phone number&gt;") - in their  page. "There is a plethora..." or "There are a plethora..."? I've made a roughness 0 glass pane, when I'm in lookdev mode it's reflecting a background that I didn't put there. I know I could just ignore it, but I'd rather be able to see what it'll mostly look like when I'm in the later stages. I also just want to know how on Earth I managed to set this background without realising it  Reflection completely ignores any objects I put in front of it. If I placed this glass inside my house, it would still just reflect trees (This is the point where I felt I couldn't ignore it - reflections are going to play a big part in my project and I don't want to be in render mode all the time)  The nodes are the default glass BSDF, except I set roughness to 0  The glass is set to 20mm thick, if that makes a difference  The background moves with my perspective and moves when I relocate the glass  I have a few HDRI's on my PC, but none look remotely like this   Also, I'm using cycles as I find Evee buggy as hell Could it be that Goldbach conjecture is undecidable? The result closest to Goldbach conjecture is Chen's theorem [Sci. Sinica 16 157–176], the proposition ``1+2''. It is natural to ask if it is likely that under our arithmetic axioms the Goldbach conjecture is an undecidable proposition. Write18: capturing shell (script) output as command/variable? Let's say I compile the following file with pdflatex -shell-escape test.tex:   \documentclass{minimal}  \begin{document}  File listing is:  \immediate\write18{ls /usr}  \end{document}   This will send the output of the command ls /usr to report/log of pdflatex (primarily to stdout).   There are then two cases I'd like to utilize:    The output of ls /usr being included directly in the document (LaTeX stream). The output of ls /usr becoming the contents of a \newcommand (by this I mean, that I'd like the script to be executed when the \newcommand is executed first - and upon subsequent calls to the new command, the shell code should not be executed anew).    I have read through , but I'm not sure if this "pipe input" can be applied to \newcommand.   I have also read through  - and it seems that Tex' file I/O should be used; but I'm quite disliking the fact that I'd still have to redirect the script output (actually, in this case, the ls /usr output) to a file, and then read it in, to have it as contents of a command.   So, is there an easier way to achieve what I'd want (hopefully, illustrated through an example based on the above code)?     EDIT: Ehm, I should have asked one more question earlier :) I'll try with an edit here, although it will probably get missed .. :)   I originally asked for a \newcommand that will execute shell code only upon its definition (i.e., in a sense it is "cached"); and the answer from @egreg does exactly that. But then - would it be possible to have a different \newcommand definition, such that each time this newcommand is called, the shell command is executed anew? I.e. executing something like \@@input|"cat tempfile" (which cannot be executed as such), where tempfile changes between calls? Is there a difference between single and double quotes in Java? Is there a difference between single and double quotes in Java? Pagination broken when merging search results with additional WP_Query On the search results page (search.php) I would like to perform an additional WP_Query to keep a specific order of search result types e.g. search results from authors should always be shown before the other results -  The first few pages should hold the author results, the other results should be shown on all the following pages only (not mixed on each page).  global $wp_query; //holds the results of the initial search query  $authorposts = $wp_query-&gt;posts;     $query = new WP_Query( 'year=2012&amp;monthnum=12&amp;day=12' ); $otherposts = $query-&gt;posts;  $wp_query-&gt;posts = array_merge( $authorposts, $otherposts  ); $wp_query-&gt;post_count = count( $wp_query-&gt;posts );  if ( have_posts() ) : while ( have_posts() ) : the_post(); ?&gt;   //show results loop...   The problems appear with the behaviour of pagination - while the $authorposts seem to paginate correctly i.e. correct page numbers for author posts and pagination works as only those where existent. But the $otherposts on the other hand are shown at the bottom of each page, right under the author posts. And they are the same on every page! Also the page count reflects the count of the first query only.  I have also tried to merge with the plus operator:  $wp_query-&gt;posts = $authorposts + $otherposts;   but in this scenario the $otherposts don't show up at all and the page count stays the same (page count for author posts).  All the examples with similar goals using two separate queries I've seen looked quite the same -  So I'm wondering if the my way of extending the original search query results with that additional WP_Query is sufficient or if I'm missing some $wp_query fields to be populated (correctly)? What's the correct way doing this?  Update: It should be noted that I'm using the WP-PageNavi plugin to paginate but this should not be relevant in the first place as the first page is already rendered wrong. And it's also initialized with the query object: wp_pagenavi( array( 'query' =&gt; $wp_query )); Is my MAC address public when browsing the Internet? What are the differences between a bridge camera and a DSLR? What  are the differences between a bridge camera and a DSLR? Opposite of "trendy" without a negative meaning I am looking for an opposite to the word trendy without giving a meaning that those who adopted the trend are old-fashioned in hindsight. For example,     Service Oriented Architecture is the trend as of now. But what is trendy in 2014 can become ______ in 2015.   So in 2015, the trend becomes widespread to the extent that it is no longer trendy, but not necessarily old-fashioned.  Edit: I am currently thinking of using mainstream. But still any other thoughts are welcome! Please add the ability to fold blocks of code in questions and answers It would be great to have the option to fold code snippets, entire questions and answer posts on a user basis and allow defining some generic foldable regions within the question/answer editor.  Non generic folding info could be stored in cookies perhaps to move the storage/processing requirement to the client side.  Definable folding can take any free and safe HTML tag or other multi character trick (&lt;>Fold this&lt;>) Why is ScreenToWorldPoint always giving same coordinates with mouse position? Whenever I use ScreenToWorldPoint(Input.mousePosition) and display the output in console this always gives me the same coordinates. MyCode: Vector3 screenToWorld;  void Update() {     screenToWorld = Camera.main.ScreenToWorldPoint(Input.mousePosition);     Debug.Log(screenToWorld); } $G$ a group s.t. every non-identity element has order 2. If $G$ is finite, prove $|G| = 2^n$ and $G \simeq C_2 \times C_2 \times\cdots\times C_2$ Let $G$ be a group s.t. every non-identity element has order 2. If $G$ is finite, prove $|G| = 2^n$ and $G \simeq C_2 \times C_2 \times\cdots\times C_2$  I know G is abelian since $ab = (ab)^{-1} = b^{-1} a^{-1} = ba$ for all non-trivial $a,b \in G$ so I have several questions remaining:    How do I prove $|G| = 2^n$? I'd like to say we use induction to prove this but I'm at a loss as to where I would start. Why is $G \simeq C_2 \times C_2 \times\cdots\times C_2$?   I've read several answers to question similar to this yet unfortunately most of them involve Galois Fields and vector spaces, both concepts I'm unfamiliar with. I'd greatly appreciate an intuitive proof. Evaluating $\int_{I^n} \left( \min_{1\le i \le n}x_i \right)^{\alpha}\,\, dx$ Let $\alpha \in \mathbb R$ and let's call $I:=[0,1]$. Evaluate   $$  \int_{I^n} \left( \min_{1\le i \le n}x_i \right)^{\alpha}\,\, dx.  $$   Well, the case $n=1$ is easy and the integral equals $\frac{1}{\alpha+1}$, for every $\mathbb R \ni \alpha \ne - 1$.  I've done also the case $n=2$ and, if I'm not wrong, it's $\displaystyle \frac{2}{(\alpha+1)(\alpha+2)}$.  My big problem is that I cannot understand how to deal with the general case. Any ideas?   Thanks in advance. Why marinade meat with acid or enzymes? How to remove enamel from wire? What causes this green background in ls output? Short story about a crew finding an ancient alien ship filled with tons of artifacts from their society