How to run FFMPEG commands from android
How to run ffmpeg from command line in android
Dynamic Paint not showing in rendered image The limit of a convergent Gaussian random variable sequence is still a Gaussian random variable I'm trying to prove this conclusion but have some problems with one of the steps.  Assume $X_1,\ldots,X_n,\ldots$ is a sequence of Gaussian random variables, converging almost surely to $X$, prove that $X$ is Gaussian.  We use characteristics function here. Since $|\phi_{X_n}(t)|\leq 1$, by dominated convergent theorem, we have for any $t$  $$ \lim_{n\rightarrow\infty}e^{it\mu_n-t^2\sigma_n^2/2}=\lim_{n\rightarrow \infty}\phi_{X_n}(t) = \lim_{n\rightarrow \infty}\mathbb{E}\left[e^{itX_n}\right] = \mathbb{E}\left[e^{itX}\right] = \phi_X(t) $$  this is the step that I cannot figure out: $e^{it\mu_n-t^2\sigma_n^2/2}$ converges for any $t$ if and only if $\mu_n$ and $\sigma_n$ converges.   Let $\mu=\lim_n \mu_n$, and $\sigma=\lim_n\sigma_n$, then $\phi_X(t)=e^{it\mu-t^2\sigma^2/2}$, which proves that $X$ is a Gaussian random variable.  Why can we get that $\mu_n$ and $\sigma_n$ converge? This looks intuitive for me, but I cannot make a rigorous prove. How to vertically align an image inside a div Weird syslog order Have you ever seen wrong order in /var/log/syslog ? I think that it causes only crontab.  Jun 28 22:20:01 alex CRON[2327]: (root) CMD (something &gt; /dev/null) Jun 28 22:21:01 alex CRON[2700]: (root) CMD (something &gt; /dev/null) Jun 21 03:49:01 alex CRON[2753]: (root) CMD (something &gt; /dev/null) Jun 28 22:23:01 alex CRON[2754]: (root) CMD (something &gt; /dev/null) Jun 27 05:08:01 alex CRON[2813]: (root) CMD (something &gt; /dev/null) Jun 26 00:19:01 alex CRON[2816]: (root) CMD (something &gt; /dev/null) Jun 28 22:25:01 alex CRON[2816]: (munin) CMD (if [ -x /usr/bin/munin-cron ]; then /usr/bin/munin-cron; fi) Jun 28 22:25:01 alex CRON[2821]: (root) CMD (something &gt; /dev/null) Jun 28 22:27:01 alex CRON[3225]: (root) CMD (something &gt; /dev/null) Jun 28 22:28:01 alex CRON[3240]: (root) CMD (something &gt; /dev/null) Jun 28 22:30:01 alex CRON[3290]: (root) CMD (something &gt; /dev/null) Jun 26 12:03:01 alex CRON[3291]: message repeated 2 times: [ (root) CMD (something &gt; /dev/null)] Jun 28 22:30:01 alex CRON[3291]: (munin) CMD (if [ -x /usr/bin/munin-cron ]; then /usr/bin/munin-cron; fi) Jun 28 22:31:01 alex CRON[3659]: (root) CMD (something &gt; /dev/null) Jun 28 22:32:01 alex CRON[3754]: (root) CMD (something &gt; /dev/null) Jun 16 06:41:01 alex CRON[3846]: (root) CMD (something &gt; /dev/null) Jun 28 22:35:58 alex cron[909]: (CRON) INFO (pidfile fd = 3) Jun 28 22:35:58 alex cron[944]: (CRON) STARTUP (fork ok) Jun 28 22:35:58 alex cron[944]: (CRON) INFO (Running @reboot jobs) Jun 28 22:36:01 alex CRON[1428]: (root) CMD (something &gt; /dev/null) Jun 28 22:37:01 alex CRON[3050]: (root) CMD (something &gt; /dev/null) Jun 28 22:38:01 alex CRON[3082]: (root) CMD (something &gt; /dev/null) Jun 28 22:39:01 alex CRON[3114]: (root) CMD (something &gt; /dev/null)   As you can see, there is bad time order between lines. It is just crontab error, or there is some problem with system clock, or something?  I am running the latest Ubuntu 14.04 kernel:  Linux alex 3.13.0-30-generic #54-Ubuntu SMP Mon Jun 9 22:45:01 UTC 2014 x86_64 x86_64 x86_64 GNU/Linux Let $F$ be a field, let $\omega$ be a primitive $n$th root of unity in an algebraic closure of $F$. If $a$ in $F$ is not an $m$th power in $F(\omega)$ for any $m\gt 1$ that divides $n$, how to show that $x^n -a$ is irreducible over $F$? Difference between a space and a "wave" symbol (tilde/"~")? Can anyone explain how one would convert one voltage range to another? I'm going to need to convert a range of -10 to +10 volts into a range of 0 to +5 volts. How would this be accomplished? Thanks!   Let me say  something more. Inside of a torpedo there are gyroscopes. This gyroscope give -10 volts when the torpedo have 180 degrees of deviation to the west and 10 volts when the deviation is to the east. This signal is DC, so i need to change this range a range: 0 to 5 v DC . Thanks I am playing a bit around with Qgis 2.14.6 to understand how it deals with distance measurement.  I took a line-shapefile that I saved in 3 different coordinate systems (4326, 32642 and a national one that doesn't exist in Qgis yet).  Using 32642 and the national one, the length is quite similar (6442m vs. 6428m)  But using 4326 (unprojected WGS84), I get 8057m  In all cases, I just used the Field Calculator and introduced $length.  I was already positively surprised that the result using 4326 was in meters and not in degrees.  To calculate the distance on the dataset in 4326, I assume that Qgis does some kind of re-projection in the background. Does anyone know which one?   Shapefiles here if anyone wants to play around:   EDIT - adding more info after more tests  As you can see, now both my shapefile and the project are in EPSG:4326, so unprojected:    Here the rough measurement of my shapefile, with the Qgis measure tool:   When I use the field calculator, the preview gives me a value in degrees, while the result seems to be in meters:      This would mean that the function $length, like the measurement tool, always gives a result in meters, but using a very coarse approximation of the degrees => meters transformation:    Is this a bug? or should it really behave like this? I find it at best counter-intuitive (but maybe it's just me) and, at worse, completely misleading (it makes very little sense to use, everywhere on earth, the length of 1 degree at the Equator). Any input or opinion here? Should I open a bug report (at least for the inconsistency between the preview and the actual result)? PlotRange precision limit? Integral $\int^{ \pi /2}_{0} \ln (\sin x)\ dx$ $$\int^{ \pi /2}_{0} \ln (\sin x)\  dx$$  The answer is $- \frac{\pi}{2} \ln 2$.  I have changed it into $$\frac{1}{2} \int^{1}_{0} t d \ln t^{2}$$  But I didn't get the answer with it. I know blender can display both orthographic and perspective projection. But, when we look at a cube in blender's viewport, I'm unable to distinguish by eye, if the projection in the viewport is a one-point, a two-point or a three-point perspective. What does blender use, and is this something changeable? What is the title of a 80's (i believe?) movie where humans in the far future are going extinct, and are aquiring new humans by going back in time to todays world, kidnapping air travelers that are known to have died that day, from the flying passenger aircraft just before its crashing.  A key visual:    Inside a hangar, a time portal opened, and a tail of a (flying) passenger aircraft extruded into the hangar where a stairs provided access to the back door of the aircraft.  The kidnappers made sure the surviving passengers remain seated and would forget about the whole ordeal. Kidnapped humans got replaced by lookalike dummies, including things they had on them. They tried hard not to alter the timeline. I am totally stumped for what to do here, any help would be appreciated.   1) What happens if you apply the method of steepest descent to $f(x)=x_1^2+x_2^2+x_3^2$?  2)Lagrange multipliers method- Find the dimensions of the rectangular box open at the top of greatest internal volume, given the surface area of the five faces is $108 \, \mathbb{cm}^2$.  Thanks I am applying for a UK visa. Can I show 5 months worth of bank statements for the UK visa, or is 6 months a requirement, as its not mentioned on their website?  There are no appointment dates showing in April. Is there any time limit in which we have to book an appointment after paying the fee? Can I sync bookmarks between Firefox and Chromium? So, Firefox has turned so resource intensive that my netbook can't run it without making me want to pull my hair out. Thus, I have been trying Chromium with quite some success (I have managed to find proper equivalents for my firefox plugins), the only thing I'm lacking is my bookmarks, which are stored in my Firefox Sync account. Point is I don't want to use Google Bookmarks, mostly because of the whole thing with encryption.  Is there any way to use Firefox Sync with Chromium?, or is there any secure alternative? The (countably infinite) wedge sum of circles is quotient of  disjoint countable union of circles $\amalg S_i$, with points $x_i\in S_i$ identified to a single point, while the infinite earring H is the topological space defined by the union of circles in the Euclidean plane $\mathbb{R}^2$ with center $(1/n, 0)$ and radius $1/n$ for $n = 1, 2, 3, ...$. In the definition of countably infinite wedge sum of circles, it is not specified the size of circles, the points which to be identified to a single point etc. So we can take disjoint union of circles of radius $1/n$ and identify a point from each to a common single point to get the infinite earring. I couldn't understood the difference between these two topological spaces. Can one explain more precisely the difference between these two spaces? I want every new user from now on to have bash as their shell by default.    I know that to change your own shell to bash, you would use the command "chsh -s /bin/bash", but how do I automatically set all future users' shell to bash by default? Use of var keyword in C# Does there exist a holomorphic function with the following property? How do I connect Android devices to a WiFi AP and mobile data network simultaneously? When I turn WiFi on, my 3G connection shuts down, which is fine in most cases. However, I need to connect to a LAN at work that is not connected to the internet and I'd prefer not to lose my data connection when I connect to the work intranet. How can I keep both connections active? Ideally, I could limit this desired behavior to this one SSID because I want it to continue to operate with the default behavior for all other WiFi connections.  If that can't be done, prefer a solution that is easy to toggle on and off. I'm using a Samsung Galaxy Nexus (Verizon Wireless) on CyanogenMod 9.