How do I make this dark colored overlay/filter effect and what are these effects called?
How to colorize an image as in the example?
I am trying to define a proof for  $A \cup B = B$ if and only if $A \subset B$  I started with:  $$A \cup B$$ $$x \in A \lor x \in B$$   but I am unsure on how to continue. Evaluating $\frac{1}{2\pi}\int_{0}^{2\pi}\frac{1}{1-2t\cos\theta +t^2}d\theta$ I need solve this integral, and I tried various methods of solving and did not get it. The integral is:   $$\frac{1}{2\pi}\int_{0}^{2\pi}\frac{1}{1-2t\cos\theta +t^2}d\theta,$$  where $t$ is a positive integer. How to run batch file without admin privillege? Why does $\tan^{-1}(1)+\tan^{-1}(2)+\tan^{-1}(3)=\pi$? Playing around on wolframalpha shows $\tan^{-1}(1)+\tan^{-1}(2)+\tan^{-1}(3)=\pi$. I know $\tan^{-1}(1)=\pi/4$, but how could you compute that $\tan^{-1}(2)+\tan^{-1}(3)=\frac{3}{4}\pi$ to get this result? Say I am logged into a remote system, how can I know what it's running? On most modern Linuxes (Linuces?), you have the lsb_release command:  $ lsb_release -ic     Distributor ID: LinuxMint Codename:       debian   Which as far as I can tell just gives the same info as /etc/lsb-release. What if that file is not present? I seem to recall that the lsb_release command is relatively new so what if I have to get the OS of an older system?  In any case, lsb stands for Linux Standard Base so I am assuming it won't work on non-Linux Unices. As far as I know, there is no way of getting this information from uname so how can I get this on systems that do not use lsb_release? Limiting number of lines in textarea I'm looking for a javascript that can limit the number of lines (by line I mean some text ended by user pressing enter on the keyboard) the user is able to enter in textarea. I've found some solutions but they simply don't work or behave really weird. The best solution would be a jquery plugin that can do the work - something like , but it should be able to limit text line count not character count. Custom Tools not Saving in Toolbar on Startup/ Normal.mxt? Finding $\int_0^\infty \frac{\cos(ax)-\cos(bx)}{x}dx$ I am practicing calculus section of GRE Math Subject test, and I can't figure out a way to do the following integral: $$\int_0^\infty \frac{\cos (ax) - \cos (bx)}{x}dx.$$  I absolutely have no clue how to do this. Can someone show me the solution explicitly? Thank you. Why does the new review page sometimes shows questions to vote to close without anybody having voted to close it? I was reviewing  for , and noticed that nobody voted to close it, even though the page reports a duplicate.      Why does this happen? What is the C# equivalent of friend? Possible Duplicate:          I'd like the private member variables of a class to be accessible to a Tester class without exposing them to other classes.   In C++ I'd just declare the Tester class as a friend, how do I do this in C#? Can someone give me an example? Gauss's law in a uniform charge distribution extending infinitely in all directions Let us assume the universe filled with positive charge. About a particular point, all the positive charged particles will be symmetrical. Now consider a sphere of radius $r &lt; \infty$ and apply Gauss law. According to Gauss law the electric flux through the sphere will be some finite value as it contains some positive charge. But by symmetry the electric field through the sphere and hence electric flux will be zero. This is a contradiction. How can I remap keyboard keys in windows 8.1? I'm looking for a simple utility which will modify registry and would not require running at startup. I tried sharpkeys but, it does not seem to work in windows 8.1. Any other suggestions? Or a simple how-to tutorial for windows 8.1?  Edit: Keytweak isn't working either. Actually I want to map an unused key to function key (fn) and neither sharpkeys nor keytweak detect the keystroke for that key.   Thanks Stars and pins are retained when chat messages are moved! In the chat system, stars and pins are retained when moved to another room. This is probably a bug. Here a picture:  When a room owner pins a message, they can move it to another room, and they cannot unpin it. However when a starred message is moved to another room, the user can unstar it in the room it was moved to. Conversation source:  * is irrelevant and does not have to do with this bug report. Many thanks to . strip last comma from get_the_category I am wondering whether there is any difference between a gerund acting as subject and an infinitive acting as a subject. Series of books featuring dragons, enchanted forests, magic swords, etc When I was younger I read a series of 3 or 4 books involving largely traditional mages/dragons/enchanted forests.  I'd like to buy it for some of my younger extended family members but I can't remember the name of it.  Here's what I remember from this:   I read the last book first, in which the son of a woman turned out to be largely one of the main characters in the other books takes an enchanted sword into a forest on a quest to do something. At one point in one of the earlier books the group was travelling through a swamp like area to get to a tower where a witch(or mage lived). There was a king (possibly the son's father) who was frozen in a castle during the last book. The evil mages/witches would melt (but not die) when some spell was cast on them. I read the series circa 1992 (estimated), comparable to the DragonLance series it was geared towards a younger audience (I don't remember any sex/brutal slayings of anyone). I believe in the first book the mother of the son in the last book runs away from home and becomes something of a maid to a dragon. I can't remember if there were evil dragons or not, I seem to remember that at least some of them were good (or at least largely neutral).   If I think of any other details I'll add them. ARIMA equation interpretation I'm trying to replicate ARIMA (1,0,1)(1,0,1) equation in excel as a formula but I am not able to understand the interpretation of white noise residual e(t) or u(t).If could help me understand the interpretation and how to derive it from raw data it'll be really great.  Thanks If i try to update node revision like this:  $node = node_revision_load(59); $node-&gt;set('publish_on', null); $node-&gt;save();   or simple save:  $node = node_revision_load(59); $node-&gt;save();   I have a PHP memory error, (i have 1gb allocated) Wrong posts number on Review section I loved the keyboard shortcuts in Windows 7 (i.e. Win + &larr; moves a window to the left side of the screen), but I'm not sure on what some of the new ones might be for Windows 8.  What are all of the NEW keyboard shortcuts that I can use while working in Windows 8?