Group commutator relations and the neutral element.
Presentation $\langle x,y,z\mid xyx^{-1}y^{-2},yzy^{-1}z^{-2},zxz^{-1}x^{-2}\rangle$ of group equal to trivial group
Read Gif Images using WebView android How to solve $x^3=-1$? How to solve $x^3=-1$? I got following:  $x^3=-1$   $x=(-1)^{\frac{1}{3}}$  $x=\frac{(-1)^{\frac{1}{2}}}{(-1)^{\frac{1}{6}}}=\frac{i}{(-1)^{\frac{1}{6}}}$... Is the set of real matrices diagonalizable in $\mathcal M_n(C)$ dense in the set of all companion matrices? SELECT DISTINCT on multiple columns Supposing we have a table with four columns (a,b,c,d) of the same data type.  Is it possible to select all distinct values within the data in the columns and return them as a single column or do I have to create a function to achieve this? How do I re-position the displayed image on my laptop? I want to re-position the display on my ASUS K53SM laptop's screen because I somehow managed to damage some portion of it (and I don't want to spend on this laptop for the time being).  Please refer the following image:    I changed the resolution from 1366x768 to 1280*768 to avoid the bad portion of the screen, but the screen is now centered and the right portion of my screen is now rendered useless.  What I want to do is, set a custom resolution of my laptop and re-position it in a way that is utilizes all the working area of my screen.  How do I re-position the displayed image on my laptop? Double Factorial: Number of possibilities to partition a set of $2n$ items into $n$ pairs I know that the partition of $2n$ items into $n$ pairs has something to do with double factorial, but I am not sure how many possibilities we exactly have.   We can choose such a partition into pairs by first choosing $n$ elements to be in one half and the remaining $n$ in the other half, which gives ${{2n} \choose n}$ possibilities. Then we can take a permutation of both sets and match them accordingly.   This gives $${{2n} \choose n} n! n!=\frac{(2n)! n! n!}{n! n!}=(2n)!$$ possibilities. But with this we overcount, since we do not want the pairs to be ordered. Each of the $n$ pairs is counted twice, wherefore we have to divide by 2 for every pair, hence $\frac{(2n)!}{2^n}$?   Well, another possiblity to do that is just to iteratively pick $2$ elements among the remaining ones, which gives ${{2n} \choose 2} {{2n-2} \choose 2} \dotsb {4 \choose 2}$  I am not sure, but I do not think that this is the same and also, I do not see the connection to double factorial. Would be very glad if you could help me with these 3 possiblities.   Thank you. Could not load file or assembly 'System.Web.Mvc' My new ASP.NET MVC Web Application works on my development workstation, but does not run on my web server...    Server Error in '/' Application.    Configuration Error  Description: An error occurred during the processing of a configuration file required to service this request. Please review the specific error details below and modify your configuration file appropriately.     Parser Error Message: Could not load file or assembly 'System.Web.Mvc, Version=1.0.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35' or one of its dependencies. The system cannot find the file specified.    Source Error:    Line 44:         &lt;add assembly="System.Web.Abstractions, Version=3.5.0.0, Culture=neutral, PublicKeyToken=31BF3856AD364E35"/&gt; Line 45:         &lt;add assembly="System.Web.Routing, Version=3.5.0.0, Culture=neutral, PublicKeyToken=31BF3856AD364E35"/&gt; Line 46:         &lt;add assembly="System.Web.Mvc, Version=1.0.0.0, Culture=neutral, PublicKeyToken=31BF3856AD364E35"/&gt; Line 47:         &lt;add assembly="System.Data.DataSetExtensions, Version=3.5.0.0, Culture=neutral, PublicKeyToken=B77A5C561934E089"/&gt; Line 48:         &lt;add assembly="System.Xml.Linq, Version=3.5.0.0, Culture=neutral, PublicKeyToken=B77A5C561934E089"/&gt;   Source File: C:\inetpub\www.example.org\web.config    Line: 46    Assembly Load Trace: The following information can be helpful to determine why the assembly 'System.Web.Mvc, Version=1.0.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35' could not be loaded.     WRN: Assembly binding logging is turned OFF. To enable assembly bind failure logging, set the registry value [HKLM\Software\Microsoft\Fusion!EnableLog] (DWORD) to 1. Note: There is some performance penalty associated with assembly bind failure logging. To turn this feature off, remove the registry value [HKLM\Software\Microsoft\Fusion!EnableLog].     Version Information: Microsoft .NET Framework Version:2.0.50727.3053; ASP.NET Version:2.0.50727.3053    Do I need to install the AspNetMVCBeta-setup.msi on the server?  Or is there a different installer for servers? I have an application in C# (2.0 running on XP embedded) that is communicating with a 'watchdog' that is implemented as a Windows Service. When the device boots, this service typically takes some time to start. I'd like to check, from my code, if the service is running. How can I accomplish this? Fermat primes relation to $2^n+1$ If $2^n+1$ is prime how to show that  $n$ must be a power of $2$  Being at elementary level I am at a loss what to begin with? Calendar.getInstance(TimeZone.getTimeZone("UTC")) is not returning UTC time How to translate and rotate the heading of landscaped pages? Beamer: Blackboard theme and overlays I am currently preparing my beamer presentation for my PhD defense.  I took the example at the url  to get a black board style presentation.  This template includes a short script which uses a random-generator to randomly scatter dust-trails on the black background to mimic chalk traces (see MWE below).  The thing is that parallel to that, I am also using overlays to uncover my slide layout by layout. The script is executed each time I am using a layout command which slows down the compilation quite substantially. I am not so familiar with control statements in latex, so here is my question:  How can-I modify this script for the background to be refreshed only when the slide is over, and not after each layout command?  Remarks:  1) I am using the Augie font, but I didn't included it in the MWE so that it can be compiled more easily  2) In case, it should make a difference I am also using the \begin{textblock*} \end{textblock*} environment from the textpos package to position text on the slide.  Here is my MWE:   \documentclass[10pt,mathserif]{beamer}  \usepackage[francais,english]{babel} \usepackage[utf8] {inputenc} %for ISOlatin1 (8859-1) sources \usepackage[T1] {fontenc}      %for polices DC 8bits   %%%Fancy fonts %\usepackage{emerald} %\usepackage{eulervm} %%%  %%Extra packages \usepackage{amsmath} \usepackage{amsfonts} \usepackage{tikz} \usetikzlibrary{arrows,shapes} \usepackage[absolute,overlay]{textpos}    %set text colors for different objects \setbeamercolor{frametitle}{fg=white} \setbeamercolor{structure}{fg=white} \setbeamercolor{normal text}{fg=white} \setbeamercolor{alerted text}{fg=white} \setbeamercolor{example text}{fg=white}   %%Black background \setbeamercolor{background canvas}{bg=black}    %%%%%%%%%%%%%%%%%%%%%% %%%%%Script: Random Dust Trails%%%%%%%%%%%%%%% \pgfmathsetseed{\number\pdfrandomseed} % seed for random generator \setbeamertemplate{background}{     \begin{tikzpicture}         \useasboundingbox (0,0) rectangle (\the\paperwidth, \the\paperheight);        \foreach \i in {1,...,30} {             \pgfmathsetmacro{\x}{random(0,10000)/5000-1}%             \pgfmathsetmacro{\y}{random(0,10000)/10000-0.1}%             \pgfmathsetmacro{\r}{random(0,10000)/1000-5}%             \rotatebox{\r}{                 \pgftext[at=\pgfpoint{\x\paperwidth}{\y\paperheight}, left, base]{\includegraphics[width=\textwidth]{paintstroke.png}}             }         };      \end{tikzpicture} } %%%%%%%%%%%%%%%%%%%%%%  %%No navigation bar \setbeamertemplate{navigation symbols}{}  \begin{document}      \begin{frame}          \begin{itemize}             \item&lt;1-&gt; bla slide 1             \item&lt;2-&gt; blu slide 1             \item&lt;3-&gt; blub slide 1         \end{itemize}      \end{frame}  %%I want the background to be refreshed with the Dust Trails script only at the end of the frame          \begin{frame}          \begin{itemize}             \item&lt;1-&gt; bla slide 2             \item&lt;2-&gt; blu slide 2             \item&lt;3-&gt; blub slide 2         \end{itemize}      \end{frame}  \end{document}   This is my first post, so please be kind if I did something illegal on the formatting of the message ;-).  Thanks in advance,  Yannick "How big of a problem" vs. "how big a problem" Quite a few phrases in English are constructed like so:     How [adjective] a [noun]...?   This is the question form of the construction, which is often answered with the negative:     Not that [adjective] a [noun].   or the positive:     Quite [adjective] a [noun].   However, from time to time I'll hear the word 'of' inserted before the 'a', e.g.:     Not that [adjective] of a [noun].   This usually sounds wrong to me, with the exception of the case where the adjective 'much' is used.  So, this sounds fine to my ear:     Not that much of a problem.   whereas this doesn't:     Not that loud of a noise.   Why is it that 'much' should be used with 'of', and other adjectives not?  Is it because 'much' is seen as measuring a quantity (of something), whereas other adjectives that may be used in this construction are seen as measuring the quality of a whole thing? Rsync filter: copying one pattern only Is the function strcpy always dangerous? I am using nginx/0.7.68, running on CentOS, with the following configuration:  server {     listen       80;     server_name ***;     index index.html index.htm index.php default.html default.htm default.php;      location / {             root   /***;             proxy_pass   http://***:8888;             index  index.html index.htm;     }     # where *** is my variables   The proxy_pass is to a DNS record whose IP changes frequently. Nginx caches the outdated IP address, resulting in a request to the wrong IP address.  How can I stop nginx from caching the IP address, when it is outdated? Is there a problem with Beamer in the latest MiKTeX update? This is about MiKTeX Revision 2.9.6360.  Immediately after the latest MiKTeX update, my Beamer files stopped compiling.  When i tried to compile a file that had been working fine I got a Package installation popup saying:  tex\latex\beamer\beamerbasemodes.sty  Is missing.  It is part of the following package  beamer   So i clicked to have it installed.  All that achieved is that i got an error message  ! LaTeX error: File 'beamerbasemodes.sty' not found   I repeated this a few times with minor changes to the file, and then went to the MiKTeX Package Manager to see what parts of Beamer are installed.  It said none were.  Either the update had removed Beamer, or the attempt to install beamerbasemodes on the fly had done it.  So I reinstalled it by hand.  In fact i did this several times in various ways.  It made one difference.  Sometimes the problem package was identified as  translator.sty  In case it would help, I ran Update FNDB and restarted my machine.  Each time I installed Beamer, the Package Manager then reported that Beamer was installed.    But when I tried to compile the file, the same things happened all over.   And when i went back to the MiKTeX Package Manager it reported Beamer is not installed.   Is Beamer now out of date?  Or is this a problem on the new update?  Is there a simple fix i can use? When I ordered this TP-Link AC1300 Wireless Dual Band PCI-Express Adapter (Archer T6E), I looked into customers reviews and they said it worked fine with no drivers on Ubuntu. I didn't have a CD/DVD player on my desktop so I (on a laptop with a DVD drive) copied and pasted the DVD support disk content on to a USB drive and used that. But when I tried to run autorun.exe it puts up archive manager and says An error occurred while loading the archive Ubuntu verison- Ubuntu 16.04 LTS.  Output from: lspci -vnn  02:00.0 Ethernet controller [0200]: Realtek Semiconductor Co., Ltd. RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller [10ec:8168] (rev 11) Subsystem: ASRock Incorporation Motherboard (one of many) [1849:8168] Kernel driver in use: r8169  Kernel modules: r8169   I am fairly new to Ubuntu (1 month) and have learned alot (sudo commands) and now know that windows is overpriced and that ubuntu is better in most fields.  Thanks for the help. PCIe Bus error severity=Corrected I have a new HP Pavilion Gaming Notebook and a new installation of Ubuntu 16.04. When I press Ctrl + Alt + F1 I go start seeing the errors shown in the following image and it doesn't allow me to interact with the console:    I also see these errors for a while everytime I boot. I need to do Ctrl + Alt + F1 to access a non graphical terminal to install some Nvidia drivers. What's going on?  What's causing the problem seems to be: 00:1c.5 PCI bridge [0604]: Intel Corporation Sunrise Point-H PCI Express Root Port #6 [8086:a115] (rev f1)  jpiabrantes@joao:~$ lspci -nn 00:00.0 Host bridge [0600]: Intel Corporation Sky Lake Host Bridge/DRAM Registers [8086:1910] (rev 07) 00:01.0 PCI bridge [0604]: Intel Corporation Sky Lake PCIe Controller (x16) [8086:1901] (rev 07) 00:02.0 VGA compatible controller [0300]: Intel Corporation Skylake Integrated Graphics [8086:191b] (rev 06) 00:04.0 Signal processing controller [1180]: Intel Corporation Skylake Processor Thermal Subsystem [8086:1903] (rev 07) 00:14.0 USB controller [0c03]: Intel Corporation Sunrise Point-H USB 3.0 xHCI Controller [8086:a12f] (rev 31) 00:14.2 Signal processing controller [1180]: Intel Corporation Sunrise Point-H Thermal subsystem [8086:a131] (rev 31) 00:16.0 Communication controller [0780]: Intel Corporation Sunrise Point-H CSME HECI #1 [8086:a13a] (rev 31) 00:17.0 SATA controller [0106]: Intel Corporation Sunrise Point-H SATA Controller [AHCI mode] [8086:a103] (rev 31) 00:1c.0 PCI bridge [0604]: Intel Corporation Sunrise Point-H PCI Express Root Port #5 [8086:a114] (rev f1) 00:1c.5 PCI bridge [0604]: Intel Corporation Sunrise Point-H PCI Express Root Port #6 [8086:a115] (rev f1) 00:1c.6 PCI bridge [0604]: Intel Corporation Sunrise Point-H PCI Express Root Port #7 [8086:a116] (rev f1) 00:1f.0 ISA bridge [0601]: Intel Corporation Sunrise Point-H LPC Controller [8086:a14e] (rev 31) 00:1f.2 Memory controller [0580]: Intel Corporation Sunrise Point-H PMC [8086:a121] (rev 31) 00:1f.3 Audio device [0403]: Intel Corporation Sunrise Point-H HD Audio [8086:a170] (rev 31) 00:1f.4 SMBus [0c05]: Intel Corporation Sunrise Point-H SMBus [8086:a123] (rev 31) 01:00.0 3D controller [0302]: NVIDIA Corporation GM107M [GeForce GTX 950M] [10de:139a] (rev a2) 07:00.0 Unassigned class [ff00]: Realtek Semiconductor Co., Ltd. RTS522A PCI Express Card Reader [10ec:522a] (rev 01) 08:00.0 Network controller [0280]: Realtek Semiconductor Co., Ltd. RTL8723BE PCIe Wireless Network Adapter [10ec:b723] 09:00.0 Ethernet controller [0200]: Realtek Semiconductor Co., Ltd. RTL8101/2/6E PCI Express Fast/Gigabit Ethernet controller [10ec:8136] (rev 0a) Why don't Death Eaters always use Avada Kedavra? When the Death Eaters attacked Hogwarts, why did the Death Eaters not just use Avada Kedavra and kill everyone?