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Find Documents in MongoDB whose with an array field is a subset of a query array By $A\oplus B$ we denote the symmectric difference of two sets. The definition is $A\oplus B =(A\setminus B) \cup (B\setminus A)$. Now I hope to show that $A\oplus (B\oplus C) = (A\oplus B)\oplus C$. I remember that there's an elegant proof, but I forget its detail. (The first step is to show $A\oplus (A\oplus B) = B$, and maybe applying this formula, we can obtain associativity.) How can I run a Minecraft Server on multiple CPU cores? I am working on setting up a Minecraft server on a machine I have at home. This particular machine has two quad-core CPUs running at 2.0Ghz so I would like to take advantage of the number of cores and run a server with 4 or 6 of the cores. My server of choice is CraftBukkit, the latest version of which is craftbukkit-1.4.7-R1.0 and launched with a start-up script of:  "C:\Program Files\Java\jre7\bin\java.exe" -Xms1G -Xmx8G -jar craftbukkit-1.4.7-R1.0.jar"   The  says:     Minecraft servers, as of 1.1.0, can use multiple cores, so now they will not sit idle.   but does not really expand on this.  My questions, then:   Is it possible to set the number of cores the server uses? How do I do it - via start-up options, or other methods? Is it really worth it and would it make that much of a difference with a lot of players? Clean URLs and php extension on nginx I've looked at dozens of other questions and references on the web - and by all my calculations, my setup should work, but it doesn't.  I have nginx installation with php-fpm.  If I try to access a .php file, it runs correctly and I get the correct results.  I got this in my config file:  location ~ \.php$ {     try_files $uri =404;     fastcgi_pass unix:/var/run/php5-fpm.sock;     include fastcgi_params;     fastcgi_param SCRIPT_FILENAME  $document_root$fastcgi_script_name; }   Now, I want to setup my web app so that /somedir/file automatically executes /somdir/file.php while still displaying /somdir/file in the browser's address bar.  So I modified my config to contain the following:  location / {     try_files $uri $uri/ $uri.php?query_string }   This kind of works, that is, the server does access the .php file.  Yet, instead of executing it using the existing location ~ \.php$ block above, it simply spits the php source code as the download into the browser.  If I append the .php manually to the requested URL, then the php is executed.  It feels as if once the server matches try_files to $uri.php, it then does not do another pass at locations to see that what it needs to do with the php files.  I tried putting the php block above and below the location /, but it makes no difference.  How can I get the php to be executed? What is the cause of gravitional force of attraction? Ok,this is a silly question. But for quite long I have been thinking about this. What is gravitation all about?? My book directly writes since force of gravitation is directly proportional to the masses and inversly proportional to the square of the distance ie. $$F = G\frac{M_1 . M_2}{r^2}$$ . So is this gravitation all about? What is the cause of it? The book then says     We are not in the scope in classical approach so as to discuss the cause of this. However,as a matter of fact that if there are more than one mass,then there is gravitation as it is their fundamental property.( Cause of gravitation can be attributed to exchange of non-classical particles between the masses) .    Then it ended the talkings. What are those non-classical particles? Why and how are they exchanged? So far I have studied physics , I never found such weird phenomenon like this. I want to know what is the cause of gravitation and what is the cause of exchange of those so-called non-classical particles? And how do they do it? Is there a way to bypass resistance/immunity to fire damage? I want to use fire-based spells for thematic reasons and a lot of things have immunity to it.   Is there a feat or class feature I could use to bypass/reduce those? For example, is there something that ignores fire resistance and reduces fire immunity to just resistance?   I know the easy way around it is just to pick another damage type spell but I really want to roleplay a pyromancer/firebender-type character. Why does the Prime Directive not apply to Rubicun III? In a first season episode of Star Trek: The Next Generation the Enterprise visits a planet named Rubicun III where () the Edo live.  It is often mentioned in Star Trek that the Prime Directive requires that pre-Warp civilisations be ignored until they discover Warp mechanics. But this planet and civilisation appears to be exempt from that status. Why? Prove that $L(V,W)$ forms a vector space Let $V$ and $W$ be vector spaces over a field $F$. Let $L(V,W) = \{T:V\to W : T \text{ is linear} \}$, that is, $L(V,W)$ is the collection of all linear functions from $V$ to $W$. For $S,T \in L(V,W)$ and $a \in F$, define new functions $(S+T):V \to W$ and $ aT :V \to W$ by $(S+T)(x) = S(x)+T(x)$ ; $(aT)(x) = a(T(x))$.   Prove that $S+T$ belongs to $L(V,W)$ and $aT$ belongs to $L(V,W)$. GPG can't check signature I have already proved Triangle Inequality $\lVert v+w\rVert \le \lVert v \rVert+\lVert w \rVert$ in vector space $\mathbb{R}^n$. However, I'm having difficulties proving the Reverse Triangle Inequality in the vector space.  I have started with   $$\lVert v \rVert^2=v \cdot v-w\cdot w+w\cdot w \le \lVert v-w \rVert+\lVert w \rVert^2$$ $$\lVert w \rVert^2=w \cdot w-v\cdot v+v\cdot v \le \lVert w-v \rVert+\lVert v \rVert^2$$  based on the Triangle Inequality but I don't know if it is correct. If this is right, I think I can go on with proving it the same way I would the normal Reverse Triangle Inequality. How to use GROUP BY to concatenate strings in SQL Server? How do I get:  id       Name       Value 1          A          4 1          B          8 2          C          9   to  id          Column 1          A:4, B:8 2          C:9 Some months ago, I linked to  in the CSS chat room and  in case anybody who cared happened to drop by:  In case anybody else noticed that  questions are now highlighted a little differently, I'm actively investigating this; here's the meta thread  It was unpinned quite some time ago by one of the other room owners. I don't need it anymore anyway since the issue has been . I notice, however, that it's still visible in the starred list, with the only regular (not pinned) star being my own:  When I try to click on the star to unstar it, chat thinks I'm trying to do otherwise and simply tells me I can't star my own messages. I can easily delete this message, but I'd very much like to unstar it instead, thankyouverymuch. Why couldn't Voldemort view the prophecy without Harry's help? This is something I've been curious about since starting this whole 'meta' thing a couple years back.     Let's say a user posts a feature request.   Under what circumstances is the feature-request read by staff? If staff decline to do anything (I'd guess it's some sort of triage), under what circumstances is the feature-request reevaluated by staff?     Let's say a user posts a bug.    Under what circumstances is the bug tested? What generally determines whether a verified bug is actionable? (And/or what are the criterion for deciding what to do?)     For both of the above, would it be possible to see a general-but-relatively-detailed flow for what happens to these questions? How do you access the matched groups in a JavaScript regular expression? I want to match a portion of a string using a  and then access that parenthesized substring:  var myString = "something format_abc"; // I want "abc"  var arr = /(?:^|\s)format_(.*?)(?:\s|$)/.exec(myString);  console.log(arr);     // Prints: [" format_abc", "abc"] .. so far so good. console.log(arr[1]);  // Prints: undefined  (???) console.log(arr[0]);  // Prints: format_undefined (!!!)   What am I doing wrong?    I've discovered that there was nothing wrong with the regular expression code above: the actual string which I was testing against was this:  "date format_%A"   Reporting that "%A" is undefined seems a very strange behaviour, but it is not directly related to this question, so I've opened a new one, .    The issue was that console.log takes its parameters like a printf statement, and since the string I was logging ("%A") had a special value, it was trying to find the value of the next parameter. What does `mv ./*` without specifying destination do? I accidentally forgot to specify destination before hitting the Return key. Where does mv ./* without specifying destination move the files and directories under current directory to? Is there a single word that describes both Witches and Wizards? In the Harry Potter world, there's the term "muggle" for people with no magical abilities, "muggle-born" for those with magical abilities who's parents are muggles and "squib" for those with no magical abilities who's parents are magical.  But is there any collective term for all magical people (as opposed to wizards for males and witches for females)?  I don't recall seeing any word that refers to all men and women and children with magical abilities, and it's the only group left without noun or collective noun to describe them. What circumstances can cause a question or answer to be deleted, and what does that actually mean?    How can a post be deleted? When can't I delete my own post? Can I still see my post even after it's deleted? Can I see a list of my deleted posts? How can I undelete one of my posts? What does deletion mean for a post? How do votes to delete work? What are the criteria for deletion? What else should I know about deleted posts? If I flag my question with a request to delete it, what will happen?       For more information, see the articles about  and  in the . A switch that is only ON if the reference voltage is matched -+ 0.1 volts Im a beginnerish will electronic and im looking for a switch that is only ON if the reference voltage is matched -+ 0.25 volts. So if i have a reference of 2.7v to match and i feed the switch a 2.75v the switch would be ON. But if i feed it  2.5v or 2.85v the switch would is OFF.   This might be a simple google search, but i am lacking the correct terminology. I'd like to be able to select a region (either with a graphical utility or command line) and be able to switch one block type with another, e.g. change all cobblestone in the region to stone. Does a program/mod exist that can do this?