overuse of alignat environment
align vs equation
"Continuity" of stochastic integral wrt Brownian motion My Logitech G5 Laser mouse has 9 buttons but it's SetPoint software only allows 5 of them to be used as "mouse buttons" and the remaining 4 can only be assigned special windows functions (Forward, Back, Cruise Up, etc) or Keystroke Assignments.  Many of the games I play will take up to 10 "MOUSE BUTTON" inputs for in-game actions but wont recognize the remaining 4 buttons even when assigned keystroke assignments.  Is there a way to make these last 4 buttons "Generic Buttons" as well as buttons 3,4,and 5? (1 is left click and 2 is right click).  My other question is if the above is not possible, maybe I can use AutoHotkey to remap keystrokes as assigned by my SetPoint software to mouse button commands?  If so how? What, if anything should one do if a user's "about me" profile section contains extremely inflammatory terms (racist, etc.) I don't think anyone wants to be the thought police, and I'm particularly wary of censorship on a part of the site that is a user's personal self-statement, and is a little off the beaten path.  On the other hand, I'm also concerned that we may not want a site where clicking on a user to see their other posts would expose folks to racist or other bigoted terms that almost everyone would agree are inappropriate for civil discourse.    Don't forget the "be nice" rule".  Note that I don't want a "flag user" rule, which I know has been beaten to death already, and further think that swears and semi-inflammatory opinions, etc. should generally just be ignored - I'm only asking about terms that provoke serious emotions around racial, religious, ethnic, or sexual orientation issues.  What, if anything, is the appropriate response in such cases? php SimpleXML check if a child exists List comprehension rebinds names even after scope of comprehension. Is this right? Debian users have a kind of "wayback machine":  , which is really great.  There are regressions sometimes, and if I don't have local deb package with old version, I'm getting sad sometimes. Having a wayback machine like this is very helpful.  I can't find analogue of it for Ubuntu. Have I missed it? Subclassing tuple with multiple __init__ arguments As I understand, correct plural versions of passerby and attorney general become passersby and attorneys general.  But why?  With passerby, the the preposition "by" has been combined with the noun "passer" to become a one word noun "passerby".  So why shouldn't this be passerbys?  If I am an attorney general, and you are an attorney general, why are we not attorney generals?  As an American I have always heard it as attorneys general, however  suggests British English does use "attorney-generals" (as well as an interesting 2nd paragraph that further probes my question).  Are there hard rules to this topic?  Or merely generally accepted practices based on locale? Save all render passes to EXR image? I am having an issue with EXR file export that I did not encounter in previous versions of Blender. I used to be able to render a render layer with all its passes and get all the passes included with the render layer with the EXR export; the problem I am finding now is that I am not able to "pack" the passes with the EXR file (see graphic below). I am working with "standard" EXR, as I understand that the EXR multilayer is for multiple file handling (packing all the image files into a single container), but I may be wrong.    In the screenshot, the graphic is an EXR saved from the rendered layer; you can see in the screenshot how the "extra" passes from the render layer has been ignored by the graphic and only shows the standard image, z and alpha passes. I found this issue for the first time with Blender 2.71; and maybe with Cycles; in the past I have never had an issue with EXR export.  Am I missing something? I hope EXRs still work with Blender, I wouldn't know how to composite without such invaluable aid. Sorry if this question has already been answered somewhere; I have really searched the site for information on EXR but I could not find an answer to my issue. Reference for creative set criterion theorem Multiple Damage Resistance Similar questions to this have been asked, but I wasn't able to find one that answers this specifically.  Say that you have resistance to slashing damage as well as resistance to fire damage (no caveats to nonmagical damage or not).  You are fighting someone who has a flaming greataxe (just an enchanted item) that deals 1d12+STR slashing damage, plus 1d6 fire damage on hit and they hit you.    How do you calculate the damage?   (1d12+1d6+STR)/2 (1d12/2) + (1d6/2) + STR (1d12+STR/2) + (1d6/2) something else? How can I require an optional Perl module if installed? I have Perl code which relies on Term::ReadKey to get the terminal width. My installation is missing this module, so I want to provide a default if the module isn't present rather than throw an exception. How can I conditionally use an optional module, without knowing ahead of time whether it is available. # but only if the module is installed and exists use Term::ReadKey; ...  How can I accomplish this? I have spent a whole day trying to solve the following problem. Please help if you know how to do this.  I am using natbib (\usepackage[sort&amp;compress,square,comma]{natbib}), and my current citation style looks like [1-4], [5, 8-9].  What is the easiest way to change the citation style to [1]-[4] and [5],[8]-[9]? What is the distinction between "among" and "amongst"? How to identify the process locking a file? pgfplots fillbetween with multiple curves I have a TikZ picture like this:  \begin{tikzpicture}   \begin{axis}[     axis lines=middle,     xmin=-0.5,xmax=3.5,ymin=-0.5,ymax=3.5   ]   \addplot[very thick,blue, samples=300, domain=0:3, name path=A] {sqrt(x)};    \addplot[very thick,yellow!70!red, samples=300, domain=0:3, name path=B] {9-3*x};    \addplot[very thick,red!90!teal, samples=300, domain=0:3, name path=C] {3};    \addplot[very thick,green!70!magenta, samples=300, domain=0:3, name path=D] coordinates{(1/9,-6) (1/9,6)};   \end{axis} \end{tikzpicture}     I’d like to fill the area enclosed by these four curves.  Similar questions have been answered using pgfplots’s fillbetween package, but it only seems to support filling between two curves. What are my options? Is there any reason to use this-> I am programming in C++ for many years, still I have doubt about one thing. In many places in other people code I see something like:  void Classx::memberfunction() {     this-&gt;doSomething(); }   If I need to import/use that code, I simply remove the this-> part, and I have never seen anything broken or having some side-effects.  void Classx::memberfunction() {     doSomething(); }   So, do you know of any reason to use such construct?  EDIT: Please note that I'm talking about member functions here, not variables. I understand it can be used when you want to make a distinction between a member variable and function parameter.  EDIT: apparent duplicate: Is gravity just electromagnetic attraction? Recently, I  was pondering over the thought that is most of the elementary particles have intrinsic magnetism, then can gravity be just a weaker form of electromagnetic attraction? But decided the idea was silly.    But I then googled it and found  article. Is this idea really compatible with other theories as the article mentions? Is there any chance of this proposition being true? Did English ever have a word for 'yes' for negative questions? The Germans have doch and the French have si as a word that means "yes" in response to a negative question, such as:     Don't you want some ice-cream?   Yes [I do]!   In English, we only have yes (as far as I know) and further clarification is required in order to be unambiguous.  Did we ever have such a word in English and, if so, what happened to it? If not, given the French and Germanic influences on English, any idea why not? Proof for two sequences producing the maximum value when sorted I am trying to improve my discrete Math skills by doing some proof exercises. But I am struggling to understand how to start proving the following hypothesis:  $$ S = {x}_1{y}_1 + {x}_2{y}_2 + \ldots + {x}_n{y}_n $$ Where ${x}_1,{x}_2\ldots{x}_n$ and ${y}_1,{y}_2\ldots{y}_n $ are ordering of two different sequences of positive real numbers, each containing n elements. S takes its maximum value when ${x}_1,{x}_2\ldots{x}_n$ and ${y}_1,{y}_2\ldots{y}_n $ are sorted in non decreasing order.  I was thinking that I should maybe use a proof by contradiction. Where the negation of the hypothesis is: S takes it minimum value over all ordering of the two sequences when both sequences are sorted into non increasing order.  However I am not sure my negation of the hypothesis is correct or how proceed from there. I do not want the complete proof because I am trying to learn how to do it myself but if some one can tell me how to make a start on this I would be grateful.