Standing waves and Photons
What is the relation between electromagnetic wave and photon?
Can someone tell me how to get a closed form for  $$\sum_{k=1}^n k^p$$  For $p = 1$, it's just the classic $\frac{n(n+1)}2$.   What is it for $p &gt; 1$? How do I load an mp4 video with multiple audio tracks into blender? I've recently started using OBS multiplatform to record game play. I currently have it set to record sounds on 2 different tracks. The first for system sounds (like gamesound, mumble, etc.) and the second to record the mic.  I am able to switch between tracks when I play the unedited video using VLC, but when I load the mp4 into blender, I only get track 1.  Did I do something wrong, or does blender vse not support multiple tracks?  Blender after loading mp4:  VLC video information:   UPDATE  For now, it seems like the solution will be to use an external tool to get the second audio track and import it into blender afterwards. A  has been logged with the Blender bug reporting tool.  UPDATE 2  The bug report has been closed/archived with the gist being "not a bug". It has been added to the . If you are looking to have support for multiple audio tracks, I would suggest looking at other video editing software until Blender adds support for this feature. Should inner tube have excess length? I am moving from Malaysia to the US, and planning to bring my desktop computer with me. I plan to pack it in my checked-in luggage. Will the computer risk being damaged? Any precaution should I take to reduce this risk? Will there be any trouble with the airline or immigration about bringing computer? "When people do make changes" - which tense is this? Which tense are sentences like:   "When people do make changes good things happen" "Even if monkeys can play an important role, their actions can pose risk to the general public" Wordpress speed slow after .5 million single image post via wp-cli Quote environment with reference at the end right 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? Get Age of a person in MySQL Can I put a rack on a carbon road bike? I got a carbon-framed  recently but I also want to use it for commuting to and from work and I want a place to put my lock and other stuff on the bike. Is it possible to have a rack on this kinda bike. Say if $A$ is an $n \times  n$ matrix, why is it that if $A^{T}A$ is positive definite, the matrix $A$ is then invertible? All I know is $A^{T}A$ gives a symmetric matrix but what does $A^{T}A$ is positive definite tell or imply or hint about the matrix $A$ itself that leads to the fact that it will be invertible? Interaction of Invoke Duplicity and Misty Step What affects field upgrades in BF4? Best way to track onchange as-you-type in input type="text"? Ways to evaluate $\int \sec \theta \, \mathrm d \theta$ The standard approach for showing $\int \sec \theta \, \mathrm d \theta = \ln|\sec \theta + \tan \theta| + C$ is to multiply by $\dfrac{\sec \theta + \tan \theta}{\sec \theta + \tan \theta}$ and then do a substitution with $u = \sec \theta + \tan \theta$. I like the fact that this trick leads to a fast and clean derivation, but I also find it unsatisfying: It's not very intuitive, nor does it seem to have applicability to any integration problem other than $\int \csc \theta \,\mathrm d \theta$.  Does anyone know of another way to evaluate $\int \sec \theta \, \mathrm d \theta$? What is the best way to increase my reputation and privileges? Is there a way to check the size of the video memory? Specifically, is there one that works accurately for both integrated GPU's as well as PCI/AGP graphics cards?  Many integrated GPU's have dynamically allocated memory, so the solution would hopefully return either the maximum available video memory or the currently allocated amount. For stand-alone NVidia or ATI cards it would obviously return the total amount of physical GPU RAM.  lspci -v does output memory figures, but I do not believe it is the video memory. I suspect the figure reported is some system memory allocation or block or channel size, but I don't know for sure. You can see in these  that lspci was wrong in 5 of the 6 tests:  ** ASUS EN210 PCIe - 1024 Mb ***   01:00.0 VGA compatible controller: nVidia Corporation GT218 [GeForce 210] (rev a2)         Subsystem: ASUSTeK Computer Inc. Device 8354         Memory at e3000000 (32-bit, non-prefetchable) [size=16M]         Memory at d0000000 (64-bit, prefetchable) [size=256M]         Memory at e0000000 (64-bit, prefetchable) [size=32M]  *** Galaxy 8400GS PCIe - 512 Mb ***   01:00.0 VGA compatible controller: nVidia Corporation G98 [GeForce 8400 GS] (rev a1)     Subsystem: nVidia Corporation Device 05cc     Region 0: Memory at e4000000 (32-bit, non-prefetchable) [size=16M]     Region 1: Memory at d0000000 (64-bit, prefetchable) [size=256M]     Region 3: Memory at e2000000 (64-bit, non-prefetchable) [size=32M]  *** VirtualBox VM - 10 Mb (headless server) ***   00:02.0 VGA compatible controller: InnoTek Systemberatung GmbH VirtualBox Graphics Adapter         Memory at e0000000 (32-bit, prefetchable) [size=16M]  *** VirtualBox VM - 128 Mb ***   00:02.0 VGA compatible controller: InnoTek Systemberatung GmbH VirtualBox Graphics Adapter (prog-if 00 [VGA Controller])         Memory at e0000000 (32-bit, prefetchable) [size=128M]  *** S3 Savage 4 AGP - unknown Mb (old lspci log), but I don't think they made these cards with 128Mb memory! ***   00:01.0 VGA compatible controller: S3 Inc. Savage 4 (rev 06) (prog-if 00 [VGA controller])     Subsystem: IBM Unknown device 01c5     Region 0: Memory at feb80000 (32-bit, non-prefetchable) [size=512K]     Region 1: Memory at f0000000 (32-bit, prefetchable) [size=128M]  *** NVIDIA Quadro FX 1800 integrated - 1024 Mb ***   01:00.0 VGA compatible controller: nVidia Corporation GT215 [Quadro FX 1800M] (rev a2) (prog-if 00 [VGA controller])     Subsystem: Dell Device 040c     Memory at e2000000 (32-bit, non-prefetchable) [size=16M]     Memory at d0000000 (64-bit, prefetchable) [size=256M]     Memory at e0000000 (64-bit, prefetchable) [size=32M] Why does it says "welcome back -user- click here to 'refresh page'" After logging into one Stack Exchange site, when I visit another SE site, it says to me, welcome back - user - click here to refresh - web page.   Isn't it possible to refresh the page using code &amp; without the user's interaction? Ubuntu 14.04.5/16.04 and newer on AMD graphics I have 14.04.5/16.04 or newer and an AMD GPU. I'm not getting the performance I want, and some programs say they need things like OpenCL.  I've heard about fglrx, but if I try to install it on my machine, it breaks and I have no GUI.  Is there anything I can do to get my AMD card working to its full potential? Almost sure convergence of the Poisson process Let $N = \{N(t) \}_{t\geq 0 }$ be a Poisson process. I already know that $N(t)- \lambda t$ is a martingale where $\mathbb{E} [ N(t) ] = \lambda t$.   I want to prove that $$ \frac{N(t)}{t} \rightarrow \lambda, \quad t \rightarrow \infty \quad \text{ a.s.}. $$  To prove this I received a hint that I should use the martingale law of large numbers which states that:  Theorem: (Martingale LLN)  Let $S= (S_n = \sum_{k=1}^n X_k)_{n=1,2,\ldots}$ be a martingale with respect to the filtration $(\mathcal{F}_n)_{n=1,2,\ldots}$. Then $\sum_{k=1}^n X_k/k$ converges almost surely on the set $\left\{ \sum_{k=1}^\infty k^{-2} \mathbb{E}\left[ X_k^2 \mid \mathcal{F}_{k-1} \right] &lt; \infty \right\}$. Hence $S_n/n \rightarrow 0$ a.s. on the same set.  Now to use this theorem I think I need to use Doob-Meyer to decompose $N(t)$ as the sum of a martingale and an increasing process. Which would be the martingale $M(t) = N(t) - \lambda t$ and increasing process $A(t) = \lambda t$. But how is $M(t)$ the sum of a martingale? And I do not know how this exactly relates to the thing I have to prove. Thanks for any help.