How to Have Selected Faces Emit Smoke
How can I control where smoke and fire are emitted from?
Indefinite integral of $ \int \frac{x^3}{\sqrt{x^2+1}} \,\text{d}x$. Can you please provide any sort of hint or suggestion on how to find the following indefinite integral?  $$\int\frac{x^3}{\sqrt{x^2+1}}\text{d}x$$  I tried substituting everything but it didn't work. I also tried trigonometric substitution but I couldn't find any valid trigonometric identity for $ \sqrt{\cos^2(x)+1} $ or $ \sqrt{\sin^2(x)+1} $. Isn't $HOME supposed to be the location of the user's home directory? I'm having trouble with a web application I'm writing: The web application, which runs as user nobody, needs to launch an inkscape process to manipulate some SVG files. Because this runs as user nobody, there is no home directory. What I am doing is creating a temporary directory under /tmp and trying to set that as the home directory via export HOME=/tmp/someUniqueId. I then set a few things in that "temporary" home directory, like a symlink .fonts to the folder for the font files to use.  I know this works for finding the ~/.fonts directory. But when I launch Inkscape, all I get is a message that Inkscape could not create the .inkscape directory:    Doesn't $HOME set the location of my home directory? Why is Inkscape still trying to access / as my home directory? How to loop over the lines of a file? Accessing class members on a NULL pointer I was experimenting with C++ and found the below code as very strange.   class Foo{ public:     virtual void say_virtual_hi(){         std::cout &lt;&lt; "Virtual Hi";     }      void say_hi()     {         std::cout &lt;&lt; "Hi";     } };  int main(int argc, char** argv) {     Foo* foo = 0;     foo-&gt;say_hi(); // works well     foo-&gt;say_virtual_hi(); // will crash the app     return 0; }   I know that the virtual method call crashes because it requires a vtable lookup and can only work with valid objects.   I have the following questions    How does the non virtual method say_hi work on a NULL pointer? Where does the object foo get allocated?   Any thoughts? How to convert a currency string to a double with jQuery or Javascript? PrintWriter and PrintStream never throw IOExceptions Some days ago I realized that  (as well as ) never throw an IOException when writing, flushing or closing.  Instead it sets an internal flag (trouble=true) when an error occurs. It's not possible to get the exact exception, but only if there was some exception ().  My question is: why would one want to have such behavior? Isn't that bad API design? The bikeshed problem and Stack Exchange In short, :     If you go before the Board of   Directors and ask for 1.5 billion   dollars to build a nuclear reactor, no   one will review or discuss the details   of the plant. They will assume that   experts have been over every inch of   the plans, and not want to look   foolish by asking a silly question.      However, if you ask the same group to   approve a 30 dollar expenditure for   lumber with which to build a bikeshed   (presumably a British term for the   smallest possible building) then be   prepared for a 45 minute discussion   about all aspects of the bikeshed,   including the color of the paint. The   explanation for this is that everyone   can grasp the scale of a bikeshed.   To transform this problem to Stack Overflow terms, questions that are trivial such as "How to convert a C string to a QString or "What is the difference between . and ->" get a lot more views, answers and votes than real questions of the form "How do I frob this widget" that bother real professionals. Fewer views mean less possible votes for good answers and hence less incentive for people to answer.  How can Stack Exchange solve this problem? Sum : $\sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)^3}$ Prove that : $$\sum_{k=0}^{\infty} \frac{(-1)^{k}}{(2k+1)^3}=\frac{\pi^3}{32}.$$    I think this is known (see ), I appreciate any hint or link for the solution (or the full solution). Chaining the Imperius curse What would happen if a wizard w successfully casts the Imperius curse on a equally powerful wizard a and then order him to cast the same curse back on w?  Follow-up questions.  It is established that casting the curse can be done .  What would happen in the case of a chain of casts that would hit back the original wizard? w-&gt;a-&gt;b-&gt;c-&gt;w  The original wizard could rather command the last wizard c, in the chain, to curse his first target instead. w-&gt;a-&gt;b-&gt;c-&gt;a wich would create a loop of a-&gt;b-&gt;c-&gt;a...  In what kind of limbo would wizards a, b and c exist in?  ( for the sake of simplicity, we can assume that every curse target is not very good at resisting the curse ) I have hundreds of figures with filenames containing "#" to include using \includegraphics, I've tried packages like grffile or currfile, but none of them work. Can anyone suggest a real solution so that I don't need to change hundreds of file names? Thanks.  Update: 1. I'm using Windows. 2. When I compile it, it shows "Illegal parameter number in definition" When a user who approved an edit is removed, an incorrect "-2 reverted" event appears in reputation history I am aware that . But now there is an extraneous "reverted" event to go along with user removal:     Source: .   The edit was not reverted, it's . In any case, I should not lose 2 points twice for the total of -4. And indeed, my reputation only dropped from 131 to 129 despite what the history suggests.   So the line with "-2 reverted" is a bug.     A more extreme example:  got 21 "reverted" events on 2017-06-30, none of which should be there. His rep loss is 42, not 84 as the reputation history says. I wanted to try out different desktop environments so I installed XFCE, KDE, GNOME, etc on top of Unity in Ubuntu 12.04  After a while I decided that I didn't like those other DEs and would stick to Unity. So I changed my default DE to Unity by configuring gdm.  sudo dpkg-reconfigure gdm   Now I am able to choose my DE at login time and all of DEs are working properly.   But the strange thing is that my boot up screen says 'lubuntu', my login screen is KDE, and my desktop is Unity.   How and why is this happening? Why didn't my gdm configuration have any effect? Does login and boot up screen need to be configured separately from the DE?  There are other similar questions here but they are not the same as this one. I do not want to remove the other enviroments I'm quite happy with having a list of DEs to select from. I want to know how to set proper defaults. Condition for a tensor to be decomposable Using round function in QGIS expression? I created a grid of rectangular polygons with the Create Grid function, from the Vector Creation group of the Processing Toolbox in QGIS 3.4.2. The rectangles measure half a degree of longitude by half a degree of latitude.    When I want to label the polygons, I write an expression that rounds the values of latitude and longitude attributes to 2 decimal places, since the attributes created in the grid brings many decimal places.    But the round function rounds the values badly.    I know that I can create new attributes that express the coordinates with fewer decimal places and label the entities based on those attributes, but I was struck by the behavior of the function. I expected it to round to the nearest value.    Does anyone know what the problem is that the round function wrongly rounds off the decimal number?    Attached screenshots of Source Fields and the Attribute Table. what is wrong with this??? please,can anyone help?  \begin{equation} \label{probabilityy} P^{t}({E_{0})=P_{0}+(1-P_{0})P_{1}+ (1-P_{0})(1-P_{1})P_{2}+.......+P_{n}\Pi_{k_{0}}^{n-1}(1-P_{k}) \end{equation} How can I define a 3D version of the built-in VoronoiDiagram (VoronoiMesh in V10) function? Inner join vs Where Is there a difference in performance (in oracle) between  Select * from Table1 T1  Inner Join Table2 T2 On T1.ID = T2.ID   And  Select * from Table1 T1, Table2 T2  Where T1.ID = T2.ID   ? My hypothesis is that $\mathbb{R \times R}$,  the set of all pairs $(r_1, r_2)$, of real numbers is uncountable. I understand that the set of all pairs of natural numbers is countable. But could someone explain why the set of all pairs of real numbers uncountable? I am having trouble proving it using diagolization Claim: if $f$ is differentiable at $x = x_0$ then $f$ is continuous at $x = x_0$.   Please, see if I made some mistake in the proof below. I mention some theorems in the proof:   The condition to $f(x)$ be continuous at $x=x_0$ is $\lim\limits_{x\to x_0} f(x)=f(x_0)$.  (1) If $f(x)$ is differentiable at $x-x_0$, then $f'(x)=\lim\limits_{x\to x_0} \dfrac{f(x)-f(x_0)}{x-x_0}$ exists and the function is defined at $x=x_0$.   (2) Therefore, by the Limit Linearity Theorem, $\lim\limits_{x\to x_0} f(x)$ exists and we'll show it is equals $f(x_0)$.   (3) We'll do this by the Precise Limit Definion: given $ \epsilon&gt;0, \exists\delta|0&lt;|x-x_0|&lt;\delta$, then $0&lt;|f(x)-f(x_0)|&lt;\epsilon$. As this limit exists by (2), we can make $f(x)$ as close to  $f(x_0)$ as one wishes, therefore $\lim\limits_{x\to x_0} f(x)=f(x_0)$, what satisfies the condition for $f(x)$ be differentiable at  $x=x_0$. The end. Explicitly accept change for PPA 'Label' When I run apt-get update on my ubuntu 17.10 I receive the following error:  E: Repository 'http://ppa.launchpad.net/ondrej/php/ubuntu artful InRelease' changed its 'Label' value from '***** The main PPA for PHP (5.6, 7.0, 7.1) with many PECL extensions *****' to '***** The main PPA for supported PHP versions with many PECL extensions *****' N: This must be accepted explicitly before updates for this repository can be applied. See apt-secure(8) manpage for details."   The man page doesn't really point to a solution.  My question is, how do I explicitly accept the change?