Remote computer management
Keep processes running after SSH session disconnects
Is the closure of path-connected set path connected? set of almost complex structures on $\mathbb R^4$ as two disjoint spheres The set of almost complex structures on $\mathbb R^{2n}$ is given by $$ M_n = \frac{GL(2n,\mathbb R)}{GL(n,\mathbb C)} = \mathcal C_+ \sqcup \mathcal C_-,$$ taking into account that $\det = \pm 1$ gives two disjoint sets.  How do we show that $M_2=S^2 \sqcup S^2$? Moreover, I'm a bit confused by dimensions: how does $\dim_{\mathbb R}M_2=8$ relates with the latter decomposition?  This is exercise 1.2.1 from the book Complex geometry by Huybrechts. Why do we say that the Earth moves around the Sun? GPU Rendering causing strange lines When I render using my r9 390 graphics card, weird lines are appearing over the render. This problem has just started happening recently, as a few days ago I was rendering the same scene without the lines appearing. I don't believe I've changed any settings in Blender and the below scene is from a new file, so render settings should be default.   Rendering using my CPU is fine:   The only thing I can think that has changed is I recently updated my card to the latest drivers. Playing games with it is still fine and the card is quite new so I wouldn't think it's a problem with the card itself. Creating multiline strings in JavaScript How do I solve the following second order partial differential equation?  $4u_{xx}+5u_{xy}+u_{yy}+u_x+u_y=2$  I have classified the equation to be hyperbolic and changed variables to obtain the canonical form as $u_{\epsilon\nu}={1\over{3u_\nu}}-{8\over9}$ which I believe is correct but I am struggling to find the general solution? A step by step solution would be appreciated. Capturing a time in milliseconds How can I animate the Restrict Visibility property of an object? I've been trying to create an animation where an object blinks on and off.   For example, I have a Cube and I set a keyframe on it's Restrict Visibility icon (the "eye" icon) with I, then I toggle off that "eye" so my cube doesn't show in the Viewport and again I press I to record that keyframe. Then, when I preview the animation in the Viewport, I see my cube appears and then disappears like I want, but when I render it, the cube does not disappear at all.  What am I doing wrong? What are the zero divisors of $C[0,1]$? Suppose you have a ring $(C[0,1],+,\cdot,0,1)$ of continuous real valued functions on $[0,1]$, with addition defined as $(f+g)(x)=f(x)+g(x)$ and multiplication defined as $(fg)(x)=f(x)g(x)$. I'm curious what the zero divisors are.  My hunch is that the zero divisors are precisely the functions whose zero set contains an open interval. My thinking is that if $f$ is a function which is at least zero on an open interval $(a,b)$, then there exists some function which is nonzero on $(a,b)$, but zero everywhere else on $[0,1]\setminus(a,b)$. Conversely, if $f$ is not zero on any open interval, then every zero is isolated in a sense. But if $fg=0$ for some $g$, then $g$ is zero everywhere except these isolated points, but continuity would imply that it is also zero at the zeros of $f$, but then $g=0$, so $f$ is not a zero divisor.   I have a hard time stating this formally though, since I'm only studying algebra, and not analysis. Is this intuition correct, and if so, how could it be rigorously expressed? Can someone give me some example code that creates a surface with a transparent background in pygame? Free ornaments font I'm looking for a free ornaments font. I know about  and pifont. Where can I find more glyphs? Limit of $\lim_{n\rightarrow \infty} \sum^{n}_{i=1} \frac{1}{\sqrt {n^2 +i} }$ Does JPA support mapping to sql views? I'm currently using Eclipselink, but I know now days most JPA implementations have been pretty standardized. Is there a native way to map a JPA entity to a view? I am not looking to insert/update, but the question is really how to handle the @Id annotation. Every entity in the JPA world must have an ID field, but many of the views I have created do not conform to this. Is there native support for this in the JPA or do I need to use hacks to get it to work? I've searched a lot and found very little information about doing this. A Variation of the even-town odd-town problem I have a question that is highly similar to this one:  However, I'm not sure how to do this when fractional powers are involved. I understand that the answer involving the binomial theorem shows this for fractions too, but I'm not sure how to go through the mechanics of it all. For example, when trying to differentiate $\sqrt{ax+b}$, I get to   $$ \lim_{h \rightarrow 0}  \frac{\sqrt{a(x+h)+b} - \sqrt{ax+b}}{h} $$  then can't get the $h$ to cancel out. I think this involves algebraic manipulation of some sort, but can't figure it out.  Thanks How are shorter power-plays counted in power play percentage? How can I re-enable backspace navigation in Chrome? Coupon collector's problem: mean and variance in number of coupons to be collected to complete a set (unequal probabilities) There are $n$ coupons in a collection. A collector has the ability to purchase a coupon, but can't choose the coupon he purchases. Instead, the coupon is revealed to be coupon $i$ with probability $p_i=\frac 1 n$. Let $N$ be the number of coupons he'll need to collect before he has at least one coupon of each type. Find the expected value and variance of $N$. Bonus: generalize to the case where the probability of collecting the $j$th coupon is $p_j$ with $\sum\limits_{j=1}^n p_j=1$  I recently came across this problem and came up with/ unearthed various methods to solve it. I'm intending this page as a wiki with various solutions. I'll be posting all the solutions I'm aware of (4 so far) over time.    EDIT: As mentioned in the comments, this question is different from the one people are saying it is a duplicate of since (for one thing) it includes an expression for the variance and it covers the general case where all coupons have unequal probabilities. The case of calculating the variance for the general case of coupons having unequal probabilities has not been covered anywhere on the site apart from , which this one intends to consolidate along with other approaches to solve this problem.    EDIT: Paper on the solutions on this page submitted to ArXiv: I want to clear a element from a vector using the erase method. But the problem here is that the element is not guaranteed to occur only once in the vector. It may be present multiple times and I need to clear all of them. My code is something like this:  void erase(std::vector&lt;int&gt;&amp; myNumbers_in, int number_in) {     std::vector&lt;int&gt;::iterator iter = myNumbers_in.begin();     std::vector&lt;int&gt;::iterator endIter = myNumbers_in.end();     for(; iter != endIter; ++iter)     {         if(*iter == number_in)         {             myNumbers_in.erase(iter);         }     } }  int main(int argc, char* argv[]) {     std::vector&lt;int&gt; myNmbers;     for(int i = 0; i &lt; 2; ++i)     {         myNmbers.push_back(i);         myNmbers.push_back(i);     }      erase(myNmbers, 1);      return 0; }   This code obviously crashes because I am changing the end of the vector while iterating through it. What is the best way to achieve this? I.e. is there any way to do this without iterating through the vector multiple times or creating one more copy of the vector? I see that there a number of questions (, , , , ) on best practices, none of them answer the issue I am going to talk about.  We all need to prepare large documents (or slides) from time-to-time. And once you have reached a certain number of pages, you find that compiling the whole document takes a substantial time, which you need to do to check that the part you have written is error free, specially if it contains a number of images.   To circumvent the situation, I have used the following practices over years to keep compile time at minimum.   Divide the document in to many chapters: The chapters are put in separate files. Only the one I am working one is uncommented.  \documentclass{book}  \begin{document}  %\input {chapterone.tex} \input {chaptertwo.tex} %\input {chapterthree.tex} %\input {chapterfour.tex}  \end{document}    The above technique can also be used for \include.   Keep a preamble replica of the main file in a temporary file (build file): I use this technique when I am preparing a presentation with many slides, say a hundred. Prepare a main file, copy it to another build file. Delete everything between  \begin{document} and \end{document} in the build file. Prepare a slide (or a group of slides) in the build file. Cut and paste the contents between \begin{document} and \end{document} in the build file to relevant location in the main file only when satisfied with the output (image locations, overfull boxes etc.)     We can hear your inputs about the best practices you practice when a you are preparing a document or presentation from scratch.    Now, I have failed to find a good answer in the case when you have finished the whole document or presentation and now you need tweaking the small things, may be edit a text here, add an image there. What will be your best practice?  Perhaps, again keeping only one chapter uncommented will be usable here. But what about large presentations? May be adding a \end{document} just after the point-of-change will be beneficial, but only if you can put that before midpoint of the file.  Commenting a part of the file will also work, but that is error-prone, at least for me.