a \sum-like symbol for exponents I need a symbol behaving like $\sum$ and $\prod$  but for exponentiation. The best I got is  Is it possible to do better? Ideally, should look like $\sum$ or $\prod$ but with capital Epsilon instead Sigma or Pi.
How to create my own math operator with limits? How can i write my own math operator with limits? I want it to look like:  \sum\limits_{e=1}^{m} but with a capital A (if possible bigger than the normal text) instead of the sum.  Thanks for the help!
I want to work on a small app that will use Telegram from within Ubuntu but wanted to first know if there was already a work in progress for this since I noticed that, for example, pidgin has support for WhatsApp. With this in mind, is there a messenger app that has support (even basic support) for Telegram from within Ubuntu. integral of $\int_{0}^{1}\frac{\ln(x^{2}+1)}{x+1}dx$ using contour integration? I have an interest in contour integration. I am not that good at it, but I enjoy learning what I can about it.  Here is a version of a rational log integral rarely encountered.  $\displaystyle \int_{0}^{1}\frac{\ln(x^{2}+1)}{x+1}dx=\frac{3}{4}\ln^{2}(2)-\frac{{\pi}^{2}}{48}$  I can do this using real methods (via double integral and substitution). I can post my workings if anyone would be interested.  My question is, can this be evaluated using contour integration due to the limits being $[0,1]$ instead of $[0,\infty)$?.  Contours may not be the most efficient way to go about it, but what is the course of action when the limits are 0 to 1 instead of 0 to infinity?. Clean install Windows 8.1 or Windows 8 from OEM key I am studying elementary Algebraic Topology recently. I have seen that a topological space is identified with a group. We are telling the group as Fundamental Group. So every topological space $X$ and for any $x \epsilon X$ there is a fundamental group $\pi_1 (X,x)$. I have a question about the converse. If we consider any arbitrary group $G$, then does there exist a topological space $X$ and an element $x\epsilon X$ such that $\pi_1 (X,x)=G$? All internal links on Stack Exchange sites should be protocol-relative In preparation for the eventual deployment of full HTTPS support on Stack Exchange, and also to make the currently available "alpha" HTTPS support more usable, all links from Stack Exchange sites to other Stack Exchange sites should be .  Currently, at least the following places still feature links with explicit http: protocol prefixes:   the page footer, the "Hot Network Questions" and "Community Bulletin" modules in the sidebar,  (the site switcher menu is OK, though),   and, of course,   lots and lots of user-supplied links in post and comment content.   I've posted this feature request with the intent to provide a single central place for tracking these issues, rather than having them scattered across multiple meta threads.  If you find more places on SE where protocol-relative links should be used, please report them below.  I fully expect this request, in its full sense, to be treated as  for the time being; however, these issues do need to be fixed at some point before our HTTPS support is ready for "prime time".  Ps. Yes, the next release of  (v1.10) is going to include a general client-side fix for most of these issues.  In the mean time, the  plugin effectively provides the same functionality, and much more besides. When & how did Yoda come to know about the Rule of Two? At the very end of Star Wars Episode I: The Phantom Menace, Mace Windu and Yoda had this conversation:     Mace Windu: There is no doubt. The mysterious warrior was a Sith.   Yoda: Always two there are....no more...no less. A master and an   apprentice.   When did he come to know about the secret ? And, how? Any evidence from ? What can I do if a package is not available on the newest version of Ubuntu (18.04) but is available on older versions? Immediately, his insides started writhing as though he'd just swallowed live snakes -- doubled up, he wondered whether he was going to be sick -- then a burning sensation spread rapidly form his stomach to the very ends of his fingers and toes -- next, bringing him gasping to all fours, came to a horrible melting feeling, as the skin all over his body bubbled like hot wax -- and before their eyes, his hands began to grow, the fingers thickened, the knuckles were bulging like bolts -- his shoulders stretched painfully and a prickling on his forehead told him that his hair was creeping down toward his eyebrows -- his robes ripped as his chest expanded like a barrel bursting its hoops -- his feet were agony in shoes four sizes too small      Harry potter and the chamber of secrets   It is the description of the feeling of drinking Polyjuice Potion, which makes someone into a different person, from the point of view of Harry Potter turning into Gregory Goyle.  And I don't understand what 'bring him gasping to all fours' means, especially 'four'. Does four here mean number 4? Does a Grapple or Shove count as an attack for the Mobile feat? The  feat enables you to not get opportunity attacks from creatures you try to attack.  Does it still apply if the attack you made was a Grapple or Shove ? The "Satellite Paradox": Twin paradox in orbiting satellites I want to simply eliminate the effect of acceleration, which is the cornerstone in resolving the traditional twin paradox, through the following thought experiment: Assume twins $A$ &amp; $B$ are located in the same orbital height, far away from the surface of a massive planet, on a long concrete column at rest WRT the planet. A rapid explosion that happens between the twins makes them orbit the earth with a high velocity, say, $0.6 \ c$, in the same orbital path but in different directions. According to relativity, since the orbiting satellites are completely inertial frames, each twin attributes a variable time dilation to the other one, and each twin expects the other one to be younger. Nonetheless, these twins are automatically reunited after traveling half of the orbit's circumference without being affected by additional accelerations. Which twin is younger in this case? Indeed, If each twin sees the other's clock as running slow all along the way, how can the clocks agree when they meet? For this configuration:  The acceleration due to the explosion does not affect the twins' clock rates since it occurs abruptly in the same place on the column where the twins are located back-to-back. The clocks have been synchronized just before the explosion.  The traditional gamma factor, attributed to one twin from the viewpoint of the other, is variable because the resultant velocity of one twin complying with the relativistic velocity addition is a variable measured from the viewpoint of the other one. However, whether or not the corresponding time dilation is varying, each twin anticipates the other one to be younger. There is no breaking of symmetry!  The $g$-field of the planet has nothing to do with orbiting satellites since they are inertial, and thus GR corrections are not inserted. (Remember the GPS settings!) I'm trying to watch for any new output of a log file. Another script (not under my control) is deleting the file then creating a new one with the same name. Using tail -f doesn't work because the file is being deleted. How do you do a deep copy of an object in .NET? I have run out of space on my WinXP virtual machine, which I only gave 10 GB space for when I created it.  Is there an easy way to increase it to, say, 20 GB?  I can't see any obvious option in VirtualBox settings.    The suggestion below gives this error  wim@wim-ubuntu:/media/data/winxp_vm$ VBoxManage modifyhd wim.vdi --resize 20000 VBoxManage: error: Cannot register the hard disk '/media/data/winxp_vm/wim.vdi' {46284957-2c09-4e70-8a49-bfbe0f7f681d} because a hard disk '/home/wim/VirtualBox VMs/winxp_vm/wim.vdi' with UUID {46284957-2c09-4e70-8a49-bfbe0f7f681d} already exists VBoxManage: error: Details: code NS_ERROR_INVALID_ARG (0x80070057), component VirtualBox, interface IVirtualBox, callee nsISupports Context: "OpenMedium(Bstr(pszFilenameOrUuid).raw(), enmDevType, AccessMode_ReadWrite, fForceNewUuidOnOpen, pMedium.asOutParam())" at line 210 of file VBoxManageDisk.cpp     Removing the .vdi from VirtualBox before calling VBoxManage command, then adding it back in, was successful.  But now I can't boot the virtual machine, I get this worrying screen:    By the way, it says FATAL: Could not read from the boot medium!  System halted.    The vdi must be reattached to the VM after VBoxManage command.  Further, the partition will need to be resized from WITHIN windows, because you will have this empty space:    I was able to resize the partition easily using a bit of freeware called . If $a_0+\frac{a_1}{2}+\dots + \frac{a_n}{n+1}=0$ then $a_nx^n+\dots + a_0$ has a root in $[0,1]$ Let $P(x)=a_nx^n+a_{n-1}x^{n-1}+\dots +a_0$ be a real polynomial such that $a_0+\frac{a_1}{2}+\frac{a_2}{3}+\dots + \frac{a_n}{n+1}=0$.  Show that $P$ has a root in $[0,1]$. I would like proof verification and alternative proofs.  My solution:      notice that the antiderivative of $P(x)$ is $\frac{a_nx^{n+1}}{n+1}+\frac{a_{n-1}x^n}{n}+\dots + \frac{a_1x^2}{2}+a_0x+C$. From here $\int_{0}^1P(x)dx=a_0+\frac{a_1}{2}+\frac{a_2}{3}+\dots + \frac{a_n}{n+1}=0$. If $P$ had no roots then $P$ would be a strictly positive(or negative) continuous function, so its integral would be strictly positive ( or negative), a contradiction. Documents with typical LaTeX errors I am giving a LaTeX course and have the idea to let the students find and solve problems within a few documents. Basically they shall learn how to create minimal examples and read error messages.  However, currently I have no document with 'typical' errors around.  If someone has such examples from him- or herself or within this forum I would like to have the code or link. It does not matter if its short or long. It should just be enough to let the students play with it for some minutes. How to prove this sequent using natural deduction? How do I prove $$S\rightarrow \exists xP(x) \vdash \exists x(S\rightarrow P(x))$$ using natural deduction? Just an alignment of which axioms or rules that one could use would be much appreciated. Can't reach wi-fi signal on Ubuntu, but can do it on other OS/devices (ath9k) I have two laptops, both running Ubuntu 13.10, as well as a different OS (Windows 7), dual boot on both.  My wi-fi router is on my bedroom and I want to get the wi-fi signal from the living room. I can reach the wi-fi signal from both pcs when running windows, with a relative good signal, but can't reach it on both of them when running Ubuntu, can't even connect to it.  Is there something that I can do to amplify the wi-fi signal? What's the significance of conditional and absolute convergence? I know how to find if a series is conditional or absolute convergence by taking the absolute value and seeing if that absolute sum converges (then the original sum is absolute). If the absolute diverges but the original converges, then that's conditional.   But my question is: is there a significance? Is absolute convergence series bigger than absolute? Does a series being absolute or conditional affect rate of convergence, or radius? Does it affect symmetry?   Looking at Google, I only found tests on how to find if it's absolute or conditional. But I want to find meaning or significance. Or at least more mathematical properties. Using the uncertainty principle to estimate the ground state energy of hydrogen I have been reading through this  of the ground state energy of hydrogen  and others like it. In this one it says it is using the uncertainty principal but then proceeded to use the following: $$pr=\hbar$$ But why is it not using: $$pr=\frac{\hbar}{2}$$ which is more in line with the uncertainty principle and what comes earlier in the derivation. Some questions on abelian category Let  $f: C \longrightarrow D$ be a morphism in an abelian category $\mathfrak{A}$ with kernel and cokernel both zero. How can I show that it is an isomorphism? I am not able to find it's inverse.   Let $g: C \longrightarrow D$ be a morphism in the abelian category $\mathfrak{A}$. Let $i: K \hookrightarrow C$ be the kernel of $g$. How can I prove that the induced map $\text{coker}\ i \rightarrow D$ is a monic?   I don't want to use Mitchell's embedding theorem.