Solution of Single Linear equation
How to find solutions of linear Diophantine ax + by = c?
What is "it" in the following sentence: It is clear that Bob likes doughnuts Product of an exponential function of IDD variables if $x_i$ are IID  continuous random variables, with $E[x_i]=μ$, is the following correct?   $E\left[\prod_{i=1}^n(1+⍺\space x_i)^i\right] = \prod_{i=1}^nE\left[(1+⍺\space x_i)^i\right] =  \prod_{i=1}^n(1+⍺\space E\left[x_i\right])^i = (1+⍺\space μ)^n$  thanks! If $L_i/K$ are Galois extensions of number fields, $i=1,\ldots,n$, and $L=L_1\cdots L_n$ is the compositum. Then it's true that a prime $\mathfrak{p}$ of $K$ splits in $L$ if and only if it splits in all of $L_i$. Does this also hold if the $L_i$ are not Galois extensions of $K$?  The proof that I know regarding the compositum uses the fact that the $L_i/K$ are Galois, so is this true in the more general setting and how would one prove it? Why MOSFET source is indicated with arrow ? Does an Animagus's animal form change along with their Patronus? In the two examples shown of an Animagus capable of casting a corporeal Patronus (Minerva McGonagall and James Potter) both had the same animal as their Patronus and as their Animagus animal.  Now, it is also shown that extreme circumstances can change one's Patronus. I think the only example of this was Tonks, which turned from a jackrabbit into a wolf in response for her love of Lupin.  If Tonks (or any other wizard who had their Patronus change) had been an animagus, would her animagus have changed as well? Is $\mathbb{R}$ a subset of $\mathbb{R}^2$? Is it correct to say that $\mathbb{R}$ is a subset of $\mathbb{R}^2$? Or, put more generally, given $n,m\in\mathbb{N}$, $n&lt;m$, is $\mathbb{R}^n$ a subset of $\mathbb{R}^m$?  Also, strictly related to that: what is then the "relationship" between the set $\{(x,0)\in\mathbb{R}^2,x\in\mathbb{R}\}\subset\mathbb{R}^2$ and $\mathbb{R}$? Do they coincide (I would say no)? As vector spaces, do they have the same dimension (I would say yes)?  If you could give me a reference book for this kind of stuff, I would really appreciate it.  Thank you very much in advance.  (Please correct the tags if they are not appropriate) I am trying to install Ubuntu 14.04 on FakeRAID along Win7.  Win 7 has been already installed, and dmraid is running.  During the installation I choose to manually partition, this is the structure:  \dev\mapper\isw_gchdghhd_Volume0 \dev\mapper\isw_gchdghhd_Volume0Op1 - NTFS Win7 loader \dev\mapper\isw_gchdghhd_Volume0Op2 - NTFS Win7 partition \dev\mapper\isw_gchdghhd_Volume0Op3 - swap \dev\mapper\isw_gchdghhd_Volume0Op5 - ext4 mounted as \ \dev\mapper\isw_gchdghhd_Volume0Op6 - ext4 mounted as \home   There is another sequence similar to above marked as "linear".  I choose \dev\mapper\isw_gchdghhd_Volume0 as boot device.  When immediately after the installation begins, an error with question marks pops up, and the installation stops. How can an ordered pair be expressed as a set? How to prove that a nilpotent operator has a basis representation that is strictly upper triangular? Usually in the morning I brush my teeth after breakfast. But my dentist told me that it's better not brush them right after eating food, because eating makes them soft.  So now I brush my teeth before breakfast. Is this the correct procedure?  PS. Just found , the author has the same opinion.  Just want to get a additional confirmation. Can mobs go through doors? I was wondering if mobs can go through doors or not. It's the difference between me just putting up a door to my house, or putting up dirt instead. Cool Text Highlighting in LaTeX LaTeX has soul. ConTeXt, of course, , where you can put sweet hightligher under your text for free!    In the pictured example, you can see highlights that not only highlight, but that do it with cool edges that look so good, you can smell fumes! The fearless author says he'll show how that was done in another post; this one shows only how to lay down a straight, yellow box. But, it is possible to do word-wrapped highlighting with cool-shapped boxes within ConTeXt, presumably.  The trouble for me is that getting into the ConTeXt world is steep climb right now, given the state of documentation and the flux of changes, so I need to continue with LaTeX. But the real problem is that now I can't live without the Organic-Looking Highlights of Awesomeness in that picture!  As I said, Non-Organic-Looking Highlights of the Ordinary are easy with the soul package:  \hl{Some awesome text that word wraps fine.}   It just taunts me on the page with its straight lines. So, if I sacrifice word wrapping, I can use PGF/TiKz and create the following macro:  \newcommand\hl[1]{%     \tikz[baseline,%       decoration={random steps,amplitude=1pt,segment length=15pt},%       outer sep=-15pt, inner sep = 0pt%     ]%    \node[decorate,rectangle,fill=navcolor,anchor=text]{#1\xspace};% }%   Which creates something like this:    Now, my color is too dark and my randomness needs adjusting, but you see that a similar effect could be achieved.  My trouble is that I don't understand TeX enough to dig into the Soul package and add the TiKz/PGF goodness that it so sorely needs. So, I leave it to you guys. Anyone want to tackle this?   Or is it yet another piece of fruit, just a touch out of reach, that shall have to wait until ConTeXt settles down? cant install or remove anything on 18.04 cause of DPKG error How to create a file system as a non root user? I'd like to create a filesystem image as a non-root user, the problem I'm facing is that the way I'm currently doing it, it needs a mount and as a non-root can't do a mount.  This is what I'm now doing:  #!/bin/sh  IMG="app.ext4" LBL="PIHU_APP" MNT="/mnt/PIHU_APP" APP="/home/buildroot/board/arctura/PIHU_APP/application"  #64MB: dd if=/dev/zero of=$IMG bs=4096 count=16384  mkfs.ext4 $IMG e2label $IMG $LBL  mkdir -p $MNT mount -o loop $IMG $MNT cp -r $APP $MNT sync umount $MNT   I have full root access, so I can setup/prepare anything, but the script will be executed from a non-root account.  However, I have a feeling there may be a better way that might not even need mounting, but I'm not sure.. K out of N encryption I am searching for [free] software that can produce nice looking graphical models, e.g.     Any suggestions would be appreciated. How to identify a downvoting stalker Possible Duplicate:          Yeah I got a deranged stalker that keeps downvoting me.  Anyone know how going about identifying such individuals?  (I just got 4 all at the same time just after making a new post).      that was the question I originally asked. Please tell me, what is so wrong with it ? Are static class instances unique to a request or a server in ASP.NET? On an ASP.NET website, are static classes unique to each web request, or are they instantiated whenever needed and GCed whenever the GC decides to disposed of them?  The reason I ask is because I've written some static classes before in C# and the behavior is different than I would have expected. I would have expected static classes to be unique to each request, but it doesn't seem like that is the case.  If they are not unique to each request, is there a way to allow them to be?  UPDATE: The answer driis gave me was exactly what I needed. I was already using a singleton class, however it was using a static instance and therefore was being shared between requests even if the users were different which in this case was a bad thing. Using HttpContext.Current.Items solves my problem perfectly. For anyone who stumbles upon this question in the future, here is my implementation, simplified and shortened so that it easy to understand the pattern:  using System.Collections; using System.Web;  public class GloballyAccessibleClass {     private GloballyAccessibleClass() { }      public static GloballyAccessibleClass Instance     {         get         {             IDictionary items = HttpContext.Current.Items;             if(!items.Contains("TheInstance"))             {                 items["TheInstance"] = new GloballyAccessibleClass();             }             return items["TheInstance"] as GloballyAccessibleClass;         }     } } Is it possible to scale up an image to increase the the pixel density? I have taken a picture whose resolution is less. I can resize the image easily (i.e I can scale to higher resolution) but the image quality goes for a toss, which is true because the image might not have enough pixels to scale properly.   Is resizing a means of increasing the resolution of the image ? Is it possible to increase the pixel density of the image and then resize, so that quality of the image is not affected much?   I mainly use GIMP and Picasa. How can I bootstrap? How can I bootstrap Drupal 8 from an external script?  This an example script from the .  require_once __DIR__ . '/vendor/autoload.php'; use PhpAmqpLib\Connection\AMQPStreamConnection;  $connection = new AMQPStreamConnection('localhost', 5672, 'guest', 'guest'); $channel = $connection-&gt;channel(); $channel-&gt;queue_declare('task_queue', false, true, false, false); echo " [*] Waiting for messages. To exit press CTRL+C\n"; $callback = function ($msg) {   echo ' [x] Received ', $msg-&gt;body, "\n";   sleep(substr_count($msg-&gt;body, '.'));   echo " [x] Done\n";   $msg-&gt;delivery_info['channel']-&gt;basic_ack($msg-&gt;delivery_info['delivery_tag']); };  $channel-&gt;basic_qos(null, 1, null); $channel-&gt;basic_consume('task_queue', '', false, false, false, false, $callback);  while (count($channel-&gt;callbacks)) {   $channel-&gt;wait(); }  $channel-&gt;close(); $connection-&gt;close();   Within a worker script like this, I need to be able to create nodes.  How can I bootstrap Drupal 8 in this script?  ? and  bootstraps passing a fake request to the kernel, which to me looks like a work-around.  In Drupal 7 you could do something like this, apparently.  // Bootstrap Drupal. include_once './includes/bootstrap.inc'; drupal_bootstrap(DRUPAL_BOOTSTRAP_FULL);