how to auto populate with conditions
How to auto populate with conditions?
Encrypting as3 flash .swf Evaluate the sum $\sum_{k=1}^n {n \choose k-1} {n \choose k}$ Evaluate the summation of: $$ \sum_{k=1}^n {n \choose k-1} {n \choose k} $$ I have been trying to solve this problem by translating C(n, k-1) into C(n, k), because I know that: $$ \sum_{k=1}^n {n \choose k}^2={2n \choose n} $$ However, I haven't been having any luck. Am I on the right track? What am I doing wrong? "Back" and "Install Now" buttons grayed out in 14.04 installer The "Back" and "Install Now" buttons are grayed out in the 14.04 installer. How do I restore them? Why is the covariant derivative of the metric tensor zero? Why rationalize the denominator? In grade school we learn to rationalize denominators of fractions when possible. We are taught that $\frac{\sqrt{2}}{2}$ is simpler than $\frac{1}{\sqrt{2}}$.  says that "there is a bias against roots in the denominator of a fraction". But such fractions are well-defined and I'm failing to see anything wrong with $\frac{1}{\sqrt{2}}$ - in fact, IMO it is simpler than $\frac{\sqrt{2}}{2}$ because 1 is simpler than 2 (or similarly, because the former can trivially be rewritten without a fraction).  So why does this bias against roots in the denominator exist and what is its justification? The only reason I can think of is that the bias is a relic of a time before the reals were understood well enough for mathematicians to be comfortable dividing by irrationals, but I have been unable to find a source to corroborate or contradict this guess. I learned recently that when an object moves with a velocity comparable to the velocity of light the (relativistic) mass changes. How does this alteration take place? A new search engine for Stack Exchange Opacity Mask With Multiple Images (Illustrator CS5) I am trying to do an opacity mask and it is driving me crazy.  Bascially I have a layer of ice. It's four different pictures of ice overlapping each other so it looks like a whole bunch of ice. I want to have it fade in from both sides (left and right) until it is completely opaque in the middle.  I've select all of the pictures and chosen 'Make Opacity Mask' from the Transparency Panel and it disappears but then I don't know how to manipulate the opacity.   In the Transparency panel it doesn't show a picture of what I'm working with so I can't simply click next to it to create the opacity mask like I've seen in tutorials.  I've also tried to overlay a rectangle over the objects, choose them all then try 'Make Opacity Mask' but that didn't work either. Any ideas? Thanks. My significant other and I finish our master degrees at the same time and thus we are applying for PhD programmes at the same time. One major factor of accepting a potential offer would be if we could study at the same university, so I feel that mentioning a two-body problem would be advantageous for both, us and the admission committee. But where do I mention this? Is a line in the statement of purpose suitable here?     If you admit me, please also consider admitting my significant other Jane Roe.   Some additional information: We both do research in computer science. While I do research in natural language processing my partner does research in computer vision. include svg images with the svg package Sort arrays of primitive types in descending order English equivalent of the expression “a longer arm than résumé” How to Sort a 2D array? How do I rename a domain and preserve SEO? As part of graduating from Area51 and becoming a full fledged site we sometimes change domain names from http://topic.stackexchange.com to http://example.com. Aside from the obvious 301 redirect rules to support existing urls transparently, are there other techniques that would aid in the preservation of SEO? When do we use "at" and "in" with "arrive" talking about place, not time? Mathematical Induction Question About A Basis Step When I entered the value $$\frac{1}{i}$$ in my calculator, I received the answer as $-i$ whereas I was expecting the answer as $i^{-1}$. Even google calculator shows the same answer (Click  to check it out).  Is there a fault in my calculator or $\frac{1}{i}$ really equals $-i$? If it does then how? Warning: mysql_fetch_* expects parameter 1 to be resource, boolean given error Proof of upper-tail inequality for standard normal distribution $X \sim \mathcal{N}(0,1)$, then to show that for $x &gt; 0$, $$ \mathbb{P}(X&gt;x) \leq \frac{\exp(-x^2/2)}{x \sqrt{2 \pi}} \&gt;. $$ How to remove specific elements in a numpy array