Binomial Coefficient Even or Odd?
$C(n,p)$: even or odd?
Folding a cube (animation) I'm trying to fold a cube with an animation. I've tried inverse kinetics with no luck. Here are some images that explain what I'm trying to do. I'm trying to make this so that    when the upper bone is pushed down, the box is folded to the ground. when the upper bone is pulled up, it unfolds the box. parsing a date string from FTPClient.getModificationTime() I have a Linux instance that I set up some time ago.  When I fire it up and log in as root there are some environment variables that I set up but I can't remember or find where they came from.     I've checked ~/.bash_profile, /etc/.bash_rc, and all the startup scripts.  I've run find and grep to no avail.   I feel like I must be forgetting to look in some place obvious. Is there a trick for figuring this out? $ not defined using jQuery in WordPress I know that jQuery is loaded, because I can switch out the $ for 'jQuery' and everything behaves as expected, but this will be a messy script if I can't fix this  This script:  jQuery(document).ready(function(){     $("ul.vimeo_desc_feed li a").click(function(){         alert($(this).attr('href'));         return false;     }) });   Produces the error $ is not a function  This script:  jQuery(document).ready(function(){     jQuery("ul.vimeo_desc_feed li a").click(function(){         alert(jQuery(this).attr('href'));         return false;     }) });   works fine. Given $y_n=(1+\frac{1}{n})^{n+1}$ show that $\lbrace y_n \rbrace$ is a decreasing sequence Given  $$ y_n=\left(1+\frac{1}{n}\right)^{n+1}\hspace{-6mm},\qquad n \in \mathbb{N}, \quad n \geq 1. $$ Show that $\lbrace y_n \rbrace$ is a decreasing sequence. Anyone can help ?  I consider the ratio $\frac{y_{n+1}}{y_n}$ but I got stuck. Ubuntu 16.04.1 has appeared as .rar file. How do I burn it to a disk to use to install Ubuntu? I am interested in using Ubuntu for the fist time, so I went to the Ubuntu download page (), to get the download file. When the file downloaded he file, it appeared in WinRAR, so I cannot burn the file to a DVD. Can anybody point me in the right direction as to how to burn this file to a DVD when the file appears as a WinRAR file? Any help would be great appreciated. Thanks :) Proof that a Combination is an integer From its definition a combination $\binom{n}{k}$, is the number of distinct subsets of size $k$ from a set of $n$ elements.  This is clearly an integer, however I was curious as to why the expression  $$\frac{n!}{k!(n-k)!}$$ always evaluates to an integer.  So far I figured:  $n!$, is clearly divisible by $k!$, and $(n-k)!$, individually, but I could not seem to make the jump to proof that that $n!$ is divisible by their product. E.g.: If your Gmail ID is abc.xyz@gmail.com, it considers this the same as abcxyz@gmail.com.  Why is this so? $e^A$, where $A= \begin{bmatrix} 0 & \omega \\ -\omega& 0 \end{bmatrix}$ $\omega&gt;0$, Then Compute the matrix:          $e^A$,     where $A= \begin{bmatrix} 0 &amp; \omega \\ -\omega&amp; 0 \end{bmatrix}$      I have never seen any problem like this. So Please help me solving this. Any link for theoretical reading is welcome. MCMC in a frequentist setting I have been trying to get a sense of the different problems in frequentist settings where MCMC is used. I am familiar that MCMC (or Monte Carlo) is used in fitting GLMMs and in maybe Monte Carlo EM algorithms. Are there more frequentist problems where MCMC is used? There are three ways I know to pronounce the -ed at the end of an adjective:   /t/ as in cracked. /d/ as in lined. /ɪd/ as in naked   I realise naked is a special case because, as , it comes for Old English nacod, so the suffix isn't added.   shows the pattern of pronunciation of -ed in all other cases. However it doesn't explain why  ends with /ɪd/ (or /id/ or /əd/ depending on the dialect).   that wicked comes from OE wicca, so the d wasn't already there.  Why do we pronounce wicked as /ˈwɪkɪd/ and not /ˈwɪkt/? Get e-mail addresses from Gmail messages received How do I put an image texture on a material in Cycles? Formatting Keyboard Shortcuts for Comments Does $A$ a UFD imply that  $A[T]$ is also a UFD? I'm trying to prove that $A$ a UFD implies that $A[T]$ is a UFD.   The only thing I am sure I could try to use is Gauss's lemma.  Also, how can we deduce that the polynomial rings $\mathbb{Z}[x_1,\ldots,x_n]$ and $k[x_1,\ldots,x_n]$ are UFDs? Does priority matter in Magic? Is there proof that the DSA construction, also used by ECDSA, is secure assuming that discrete logarithms in the relevant group representation are difficult? Are there any research careers except professorship for a person holding PhD in pure mathematics? MySQL GUI Tools A friend of mine, native EN speaker, told me that the following is correct written like this:      We met on the 1st of June.   Is that really true? I cannot see any reference that these are used in written text.