Audio Visualization with Background Image
Can Blender render pngs with the background transparent?
Induced metric on a null hypersurface Can all fundamental forces be fictitious forces? After reading many questions, like   and , I wonder:   Is it possible to consider the other fundamental forces too, the electroweak interaction and the strong interaction or ultimately the unification of these, to be fictitious forces like gravity in the framework of general relativity?   If we want a final unification of all fundamental forces, hasn't this feature of gravity to become a feature of the other forces as well? Any group of index 2 is normal I'm trying to understand the proof that any group of index $2$ is normal.   Let $G$ be a group and $H$ a subgroup of index $2$.  I understand that if $x\in H$ then $xH=H=Hx$ since $H$ is a subgroup. However, I don't understand why if $x\in G\setminus H$ then $xH=G\setminus H.$  I know there are other proofs of this on this site but none of them specifically address this question. I have an external HDD and I kind of messed up the file permissions but when fixing it I thought it is ok bc with my username I can access the files perfectly fine. Now that I use this with two PC (actually ATM I don't have access to my other PC) I can't access these files.  The problem is this directory has hundreds of folders with no permission for "everyone". I would like to give it the default permissions including have all access for the user "everyone". How do I do that via command line for these hundreds of folders? How to install Gnome 3 without breaking Unity? I tried installing gnome 3 , but it broke Unity and I had to reinstall Natty from scratch.  Does anyone know if there is a way to install Gnome 3 without breaking Unity? Best way to center a  on a page vertically and horizontally? Violation of linearity assumption in Logistic Regression I built a logistic model with 7 continuous independent variable and 8 categorical (dummy) variables in R. I tested for the linearity assumption using the Box Tidwell test and all my variables show high significance.  I am wondering now, if the assumption is violated what it would mean for the coefficient estimates and if I still can run the model with caution.   I read about the approach of using regression splines but I am confused how I would determine those and interpret the model then. Escaping both forward slash and back slash with sed There should be infinitely many primes of the form $5+6n$. How do you prove it? The same should be true for $7+6n$. Where can I find delay/cancelation statistics for a given airline route? My flight got canceled yesterday and I am currently waiting for the delayed next flight.   Is there any website that keeps records of airlines being delayed/canceled? I would like to know my chances. I did find some sites through google (flightaware, flightstats), but they focus on us flights only and I am currently in the azores. How to understand a volatility based ETF like VXX The ETF VXX is based on the volatility index VIX. If volatility goes up, VIX goes up and VXX goes up. Similar thing for the downside. Now when I buy an ETF like SPY, I can conceptually understand that I am buying a small portion of each of the underlying companies. So if an underlying company stock makes a move, the ETF SPY makes a move in  the same direction.  But when I buy VXX, what exactly is the underlying? It is VIX. I am unable to grasp the concept of 'volatility' as the underlying. I can visualise only stocks and commodities as the underlying because in my understanding, the unerlying needs to be something physical (let us say stocks are physical commodities for this example).  Can someone explain the concept of 'volatility' as the underlying?  Is the word 'underlying' even appropriate in this case or is the word 'underlying' only to be used for derivative products? Finding the limit of $\frac {n}{\sqrt[n]{n!}}$ I'm trying to find  $$\lim_{n\to\infty}\frac{n}{\sqrt[n]{n!}} .$$   I tried couple of methods: Stolz, Squeeze, D'Alambert  Thanks!  Edit: I can't use Stirling. After upgrading to 12.04 from 10.04, can't login to PHPMYADMIN Check if url has domain name and not an ip Any $B \subset \{10,11,...,99\}$, with $|B| =10$ has two subsets such that $\sum_{a \in B_1} a = \sum_{b \in B_2} b$ Let there be $B \subset \{10,11,...,99\}$, with $|B| =10$. I need to prove, using the pigeonhole principle, that there are at least two disjoint subsets of $B$ (and none empty) where the sums of their elements are identical. I.e. $\exists B_1 \ne \varnothing, B_2 \ne \varnothing$ such that $B_1 \bigcup B_2 = B$, $B_1 \bigcap B_2 =\varnothing$ and $$\sum_{a \in B_1} a = \sum_{b \in B_2} b$$ I have a 64-bit machine that has Windows 7 32-bit and Ubuntu 32-bit installed as a dual boot setup. Can I run 64-bit software on top of these 32-bit OSes, or are they a "bottleneck" limiting the true capability of the underlying hardware? The website I'm working is allegedly going to have a massive hit rate soon after launch. The client is talking about the possibility  of around 2500 hits per second over a day or so.   Ignoring the fact that this hit rate is probably wild client optimism and apart from getting the largest servers possible, what is the best way that Drupal should be configured to support a large hit rate.  I've read Scaling the , ,  and many other pages, but what I'm looking for is real experience of doing this, what works, what doesn't, and what to expect. Would it be possible to create a wand more powerful than the Elder Wand? I have been researching the meaning of positive semi-definite property of correlation or covariance matrices.   I am looking for any information on   Definition of positive semi-definiteness; Its important properties, practical implications; The consequence of having negative determinant, impact on multivariate analysis or simulation results etc. Suppose $f:\mathbb{R}\to\mathbb{R}$ is Borel measurable. I want to show that $\displaystyle \int_a^b f(x)\mathrm dx=0$ for all $-\infty&lt;a&lt;b&lt;\infty$ with $a$ and $b$ rational implies that $f=0$ a.e. I'm really not sure how to approach this problem; any help would be welcome.