About the use of Newtonian Relations for the movement of stars in the Galaxy
Relativity and Galaxy Rotation Speed
Code working in jsFiddle but not in browser Why don't the White Walkers take the sea route to Westeros Show that the function $g(x) = x^2 \sin(\frac{1}{x}) ,(g(0) = 0)$ is everywhere differentiable and that $g′(0) = 0$ Why does a proof of $\exists f: X\to Y$ injection $\iff \exists g: Y \to X$ surjection requires the axiom of choice? Why does a proof of $\exists f: X\to Y$ injection $\iff \exists g: Y \to X$ surjection requires the axiom of choice?  This question is answered here:   I'm not interested in a proof itself of this theorem, I want to know why this requires the Axiom of Choice. It is company policy for admins to login to the servers via a personal username, and then run sudo -i to become root.  Upon running sudo -i, sudo will create an environmental variable called SUDO_USER, which contains the original user's username.  Is there a way to log ALL commands within syslog with something akin to the following syntax:  ${TIME/DATE STAMP}: [${REAL_USER}|${SUDO_USER}]: ${CMD}   An example entry would be:  Sat Jan 19 22:28:46 CST 2013: [root|ksoviero]: yum install random-pkg   Obviously it doesn't have to be exactly the above syntax, it just has to include a minimum of the real user (eg. root), the sudo user (eg. ksoviero), and the full command that was run (eg. yum install random-pkg).  I've already tried snoopy, but it did not include the SUDO_USER variable. How does the British-Irish Visa Scheme (BIVS) work? I am an Indian citizen and have applied for the Standard Visitor visa to the UK, and wish to travel to Ireland by using the BIVS scheme.    Do I need to fill up a separate application for BIVS endorsement or is it handed out automatically?  Also, If I enter the UK, and then travel to Ireland, can I re-enter the UK again? How to compile self-referencing functions (to perform recursive a task) I am a computer scientist, and one of my professors today used the symbol $\propto$. I tried to search that using google, but it returns no results, and I do not even know its name.  So, I would like to ask, what does the operator $\propto$ mean? What is its name, and how is it used? What is batch size in neural network? I'm using Python Keras package for neural network. This is the . Is batch_size equals to number of test samples? From Wikipedia we have  information:     However, in other cases, evaluating the sum-gradient may require   expensive evaluations of the gradients from all summand functions.   When the training set is enormous and no simple formulas exist,   evaluating the sums of gradients becomes very expensive, because   evaluating the gradient requires evaluating all the summand functions'   gradients. To economize on the computational cost at every iteration,   stochastic gradient descent samples a subset of summand functions at   every step. This is very effective in the case of large-scale machine   learning problems.   Above information is describing test data? Is this same as batch_size in keras (Number of samples per gradient update)? Any subgroup of index $p$ in a $p$-group is normal. Looking for a basic PostGIS viewer to use as basis for own application I'm looking for a rather basic PostGIS viewer. It should be possible to pan, zoom and retrieve coordinate information on mouse click. No need to support coordinate transformations. It should introduce as little further dependencies as possible. Preferably written in C++. I have a shapefile with contours and their heights.   Is it possible to make a DEM from contours in QGIS without using GRASS?   I found  but the answer is for ArcGIS Desktop. How to get apache to send a 404 based on no matching VirtualHost section (based on ServerName) being found? I am rebuilding an old server.  Only one of the five old sites need to go live and all five of the old sites point to the same IP address.  Unfortunately any time a request is made for one of the old sites via their own unique domain names they are passed the pages from the one site that I'm trying to make live.  I would just like the old sites to display a 404 instead of the one site that I'm actually trying to make live.  As an example:   Site 1 (192.168.0.1) [www.first.com] Site 2 (192.168.0.1) [www.second.com] Site 3 (192.168.0.1) [www.third.com]   I want to move site 1 live again.  So I turned on apache on the machine with the IP address of 192.168.0.1, with all of site 1's files in the /var/www directory.  When I browse to 192.168.0.1 or www.first.com I correctly see site 1. When I browse to www.second.com and www.third.com I also receive site 1 which is the problem.  Is there a way I can 404 any request which comes in without www.first.com?  Here is my sites-available:  NameVirtualHost *:80  LogFormat "%h %l %u %t \"%r\" %&gt;s %b" common  &lt;Files ~ "^\.ht"&gt;     Order allow,deny     Deny from all     Satisfy All &lt;/Files&gt;  &lt;Directory /&gt;   Order Deny,Allow   Deny from all   Options None   AllowOverride None   Options None &lt;/Directory&gt;  &lt;Directory /var/www&gt;   Order Allow,Deny   Allow from all &lt;/Directory&gt;  &lt;VirtualHost *:80&gt;         ServerName first.com         ServerAlias www.first.com         DocumentRoot /var/www         ErrorLog /var/log/first.com.err         CustomLog /var/log/first.com.log common &lt;/VirtualHost&gt;  &lt;VirtualHost _default_:*&gt;         ServerName unknown         DocumentRoot /var/www_404 &lt;/VirtualHost&gt; How to show similar display of codes of different programming languages in LaTeX I am very new to LaTeX and I am writing my thesis. In a chapter, I want to show my codes, which are in Mathematica.   I use the listings package as follows:  \documentclass{article}   \usepackage{listings}   \begin{document}   \lstset{language=Mathematica}    \begin{lstlisting}   Do[i^j,{i,1,10},{j,1,10}]   \end{lstlisting}    \end{document}   However, the output is much different to what the code looks like in the Mathematica IDE (even if I use other languages in \lstset{language=&lt;name&gt;}):    I read some questions on the site but, in some of them, the font or color of the codes were not the same. Could you please help me to display something like the picture below in LaTeX?  If it is important, I am using the BiDi package. Does separation of variables in PDEs give a general solution? When a partial differential equation is solved using the separation of variables method, is the produced solution the most general one that satisfies the equation or have we lost some forms of the solution because of the assumption that it is in the form of separated variables? My Area51 account crossed 200 rep today, but still other accounts don't reflect the change in reputation. When will the changes be applied? or is there no association bonus for Area51 account? "Accountsd wants to use the 'iCloud' keychain" I, too, am suddenly getting this message.  I don't see a Keychain First Aid option in Keychain, and the two Login Keychain Settings were already unlocked.  Any other ideas for what the error message is all about, and what I should do about it? Unintentional Lies and Misinformation Polynomials, prove exercise question about question There is a polynomial P with integer coefficients and with pairwise different integers $a,b,c$ . Prove that it is not possible for $P(a) = b$, $P(b)=c$, $P(c) = a$  First off I don't understand "pairwise different" part - what does it mean ,can you show me this as an equation? After that I'd like to get a hint in case I don't make it. + I'd prefer to have hints/answers written more algebraically without $\sum$ etc. (It helps me get better understanding what's going on under the hood) I'm having difficulty solving an exercise in my course.  The question is:      Prove that $n!\geq 2^n$.   We have to do this by induction. I started like this:   The lowest natural number where the assumption is correct is $4$ as: $4! \geq 2^4 \iff 24 \ge 16$. The assumption is: $n! \ge 2^n$.   Now proof for $(n+1)$ which brings me to: $(n+1)! \ge 2^{(n+1)}$  I think I can rewrite it somehow like this:  $$ {(n+1)} \times {n!}  \stackrel{\text{(definition of factorial)}}{\ge} 2^n \times 2 $$  $$ (n+1) \times 2^n \ge 2^n \times 2 $$  Then I think I can eliminate the $2^n$ and have something like this: $n+1 \ge 2$, or $n \ge 1$.  But I think I'm wrong here some where and was hoping somebody has some advice on this. How can I prove the above assumption?  Any help would be appreciated, kind regards.