Is it possible to run several virtual machines each with independent mouse+keyboard on a single PC?
Dedicated mouse and keyboard for a virtual machine, is it possible?
LaTeX template for typesetting a novel Proof that every finite dimensional normed vector space is complete Can you read my proof and tell me if it's correct? Thanks.  Let $V$ be a vector space over a complete topological field say $\mathbb R$ (or $\mathbb C$) with $\dim(V) = n$, base $e_i$ and norm $\|\cdot\|$. Let $v_k$ be a Cauchy sequence w.r.t. $\|\cdot\|$. Since any two norms on a finite dimensional space are equivalent, $\|\cdot\|$ is equivalent to the $l^1$-norm $\|\cdot\|_1$ which means that for some constant $C$, $\varepsilon &gt; 0$, $k,j$ large enough, $$ \varepsilon &gt; \|v_j - v_k\| \geq C \|v_j - v_k\|_1 e_i= C \sum_{i=1}^n |v_{ji} - v_{ki}| \geq |v_{ji} - v_{ki}|$$ for each $1 \leq i \leq n$. Hence $v_{ki}$ is a Cauchy sequence in $\mathbb R$ (or $\mathbb C$) for each $i$. $\mathbb R$ (or $\mathbb C$) is complete hence $v_i = \lim_{k \to \infty} v_{ki} $ is in $\mathbb R$ (or $\Bbb C$) for each $i$. Let $v = (v_1, \dots , v_n) = \sum_i v_i e_i$. Then $v$ is in $V$ and $\|v_k - v\| \to 0$:  Let $\varepsilon &gt; 0$. Then $$ \|v_k - v\| \leq C \|v_k - v\|_1 = C \sum_{i=1}^n |v_{ki} - v_i| \leq C^{'}n \varepsilon$$  for $k$ large enough. There are no book recommendations for Astrophysics here. I will write my own answer, but I am also interested in what are others' views on the question (I will NOT mark my own answer as the best one). How to prefix post permalinks with /blog/ - without affecting custom post types? I have several custom post types, which are properly structured as /%post_type%/%postname%/, however I wish to have the same effect for regular blog entries: /blog/%postname%/  If I prepend the permalink structure with /blog/ it affects the custom post types as well, so currently my permalink structure is simply /%postname%/  Which is the recommended way of doing this? I had a solution involving some rewrites, but the permalink shown in the post editor area does not reflect it. I can already scroll left and right with two-finger swiping, however, in Windows I can use the same gestures to go forward and back in browsers and such. Is this possible in Ubuntu? Multiple "order by" in LINQ Prove that $T(n) = T(n/3) + T2n/3) + 5n$ is $O(n log n)$ By default  indents with a hard tab character. How do I change it to spaces? I would like to grant the  app write access to external storage in Marshmallow.  The app does not request it explicitly (unlike other apps that seem to use the Storage Access Framework to do so).    In the app permissions screen, there is no permission listed for external storage, only for 'storage' (which seems to mean internal storage).  So there does not seem to be any direct way to grant this permission.   My phone is rooted and I could just run Syncthing as root - but this option creates many problems and sometimes results in the app hanging indefinitely.    Is there any other way around this problem? There are two directories shown by 'ls'.  Normally directories anywhere are blue on black background.  But the first one is blue on green and impossible to read.  Why is this?  How to make it blue on black, or at least something light on something dark?  This is on Ubuntu 12.04, using bash in Gnome Terminal.  In Konsole, the blue is slightly darker, and possible to read, though could be way better. The relationship between the eigenvalues of matrices $XY$ and $YX$ If $X \in \mathbb{C}^{m \times n}$ and $Y \in \mathbb{C}^{n \times m}$ ($m \geq n$), how to prove the following?  $$\sigma (XY) = \sigma(YX) \cup \underbrace{\left \{ 0, ..., 0 \right \}}_{m-n}$$  Here, $\sigma$ denotes the set of eigenvalues/spectrum. What is the correct form in the following sentences, "both" and "both of them"?      a) "Both of them are unique."      b) "Both are unique."   If "both" by itself already contains "both of them", so I can conclude that the first option is not correct. Isn't it? I was trying to prove this inequality using induction, but couldn't do.  Question: Suppose $a$ and $b$ are real numbers with $0 &lt; b &lt; a$. Prove that if $n$ is a positive integer, then:  $$a^n-b^n \leq na^{n-1}(a-b)$$ 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. Book about actress forced to disguise alien murderer I read this book once when I was in middle school. A girl solves a murder or a mystery on a spaceship. It was a thin paperback books.   All I can remember is that there was an alien, and there was a movie star or actress or famous makeup artist on the ship traveling with another woman. By the end of the book the murderer was the woman the actress was traveling with who forced her to use her makeup skills to disguise her, and she was really some kind of alien. A square with side $a$ is given. What is the average distance between two uniformly-distributed random points inside the square?  For more general "rectangle" case, see . The proof found there is fairly complex, and I am looking for a simpler proof for this special case. I expect it could be significantly simpler.  See also . Stop PDFs from displaying inside Google Chrome When I click on a PDF link in Chrome, it opens automatically inside the browser window. How can I get it to download instead and open with an external viewer?  Update: I implemented djhowell's solution but Chrome still seems to be handling PDF files differently from regular files. When I click a PDF link it opens in Adobe Reader, but normally files download to a folder first.  I also find it weird that this is controlled by Reader and not Chrome. Are there not any file-type controls in Chrome anywhere? How does one create a custom application launcher for Wine installed apps? I was wondering what the cardinality of the set of all real sequences is. A random search through this site says that it is equal to the cardinality of the real numbers. This is very surprising to me, since the cardinality of all rational sequences is the same as the cardinality of reals, and it seemed fairly intuitive to me that if cardinality of a set $A$ is strictly greater than the cardinality of the set $B$, then cardinality of $A^{\mathbb{N}}$ should be strictly greater than cardinality of $B^{\mathbb{N}}$. It turns out to be false.  Some technical answers have appeared in this forum elsewhere but I do not understand them. As I am not an expert in this topic, could some one explain me in simple terms why this is happening?  Also is the cardinality of all functions from reals to reals also the same as the cardinality of reals? Is there a definition of  and proper explanation of it?  It is said "Electric charge is the physical property of matter that causes it to experience a force when close to other electrically charged matter."  How is it though that matter can get charged?  Defining charge as the property of feeling a force with other charged matter seems circular.  What is charge?  Is there a non-circular definition / explanation?