Automatically download missing packages in texstudio
How do I update my TeX distribution?
Linear transformation of a binomial random variable? Let $X$ be a binomial random variable with parameters $n$ and $p$. Next, let: $$ Y = aX + b $$ I know that: $$ \mathbb{E}[Y] = \mathbb{E}[aX+b] = a\mathbb{E}[X] + b = anp + b \\ \text{Var}(Y) = \text{Var}(aX+b) = a^2 \text{Var}(X) = a^2np(1-p) $$ But how is $Y$ distributed? How do you cite a Github repository? How do defenders of libertarian freewill reconcile it with constraints imposed by the laws of physics? If apostrophe + s is the acceptable way of denoting a genitive in English, is it possible that possessive pronouns, such as hers, ours and yours, started life as possessive adjectives with apostrophe + s?  E.g. her's, our's, your's, their's? Perhaps, even his' ? Its and my obviously stick out from this tempting pattern.  Is there any evidence that this might be the case, or is the 's completely unrelated? Proving that the set of limit points of a set is closed Recently the cranks on my bike started to creak. I checked with my usual "bike-bible" . They recommended dis-assemble, lubricate, re-assemble.  So I did that.  Remove cranks. Remove spindle. Clean. Lubricate. Reassemble.  No, the creak is still there.  (To find out the source-area of the sound I had a friend riding the bike slowly while I ran alongside listening. And the sound where coming from the area of the bottom bracket/cranks. I am happy no neighbor saw me...)   For each revelation of the cranks there are two creak-noises.  If I, when on the bike, push down with both feet I hear a noise. Turn 180 degrees without pressure, push down again and there is the noise again. If I am "too soft", low pressure there are no sound. Since I have clips I have tried to only work with one foot to keep a constant load during a revelation, there where no detectable sound then.  Anyone have any idea what is wrong on the bike? And how I should fix it?  /Leif How can I get the page title? Vertical uniform circular motion.. can it really be uniform? This is the picture in my mind:    For centripetal force, I learned that: $T-mg\cos\theta= \frac{mv^2}{r}$  In vertical circular motion, the velocity is naturally going to decrease as kinetic energy is converted to potential energy as the particle moves up the circle- and thus resulting into a non-uniform circular motion.  However, I was told that if tension changes accordingly, the velocity will remain constant(as from the equation). What I do not get about this part of the explanation is that which force will balance mgsinθ (tangential force in the diagram  )? I came up some definitions I have sort of difficulty to distinguish. In parentheses are my questions.   $\dfrac {x}{0}$ is Impossible (  If it's impossible it can't have neither infinite solutions or even one. Nevertheless, both $1.$ and $2.$ are divided by zero, but only $2. $ has infinite solutions so as $1.$ has none solution, how and why ?) $\dfrac {0}{0}$ is Undefined and has infinite solutions. (How come one be Undefined and yet has infinite solutions ?) $\dfrac {0}{x}$ and $x \ne 0$, it's okay for me, no problem, but if someone else wants to add something about it, feel free to do it. What does role db_owner allow I have been trying to troubleshoot a login that is not able to view certain tables in a SQL Server 2012 database. In doing so I find I don't quite understand what membership in the db_owner role allows. I can understand the other roles such as db_datareader and db_datawriter but I remain confused as to what db_owner allows. Inverse Green's Function identity in derivation of Hedin's equations I'm trying to work through a derivation of Hedin's Equations in Effect of Interaction on One-Electron States by Hedin and Lundqvist (1969) and I've come across an identity that is given without much explanation that I'd like to understand.   We start with an equation of motion with single particle Green's functions G:   $\left[ i\frac{\partial}{\partial t_1} - h(1) - \phi(1) - V_H(1)\right] G(1,2) - i\int v(1^{+},3) \frac{\delta G(1,2)}{\delta \phi(3)} d3 = \delta(1,2)$  where $1=(x_1,t_1)$, $h$ is the one-electron kinetic energy and ion interaction, $\phi$ is a small perturbing field that is set to zero at the end, $V_H$ is the Hartree potential, and $v$ is the Coulomb interaction.  They then insert the identity  $\frac{\delta G(1,2)}{\delta\phi(3)} = -\int G(1,4) \frac{\delta G^{-1}(4,5)}{\delta\phi(3)} G(5,2) d(4,5)$  which is then used to define the self energy  $\Sigma(1,2) =  -i \int v(1^+,3) G(1,4)\frac{\delta G^{-1}(4,2)}{\delta\phi(3)} d(3,4)$.  I know this identity is related to the definition of the inverse Green's function  $ \int G(1,3) G^{-1}(3,2) d(3) = \delta(1,2)$  but I can't figure out how to get from this definition to the identity that is inserted into the equation of motion. Any ideas?  Thank you! Multiple Apple Developer Accounts A new Victorian-set British novel begins sentences containing h-dropping with lower-case e's, as in " 'e took my money, 'e did." This seems incorrect but I'm at a loss to find the rule. Is $0$ a natural number? Is there a consensus in the mathematical community, or some accepted authority, to determine whether zero should be classified as a natural number?  It seems as though formerly $0$ was considered in the set of natural numbers, but now it seems more common to see definitions saying that the natural numbers are precisely the positive integers. Why can't we see images reflected on a piece of paper? Crossfading Video AND Audio with ffmpeg This Super User answer  has got me so far, but now that I have tried many solutions and seen every SO link out there, it's time to ask you all for help.  I am trying to crossfade 2 videos that are 10 seconds each in ts format with audio and video at the same time.   The steps are:   Add complex filter black screen Fade out video 1 after 9 seconds, with 1 second fade duration Fade in video 2 at 9 seconds, with 1 second fade duration Trim black filter output to 19 seconds   This works fine for just video alone, but when I attempt to add audio, I can't get past this error message:     Output pad "default" with type audio of the filter instance "Parsed_asetpts_4" of asetpts not connected to any destination   It appears I'm not connecting the audio output properly. I think I need to alter the [over] lines to include audio. But how do I do this?  `ffmpeg -i vid1.ts -i vid2.ts -f lavfi -i color=black -filter_complex \ "[0:v]format=pix_fmts=yuva420p,\ fade=t=out:st=9:d=1:alpha=1,setpts=PTS-STARTPTS[v0];\ [0:a]\ afade=t=out:st=9:d=1,asetpts=PTS-STARTPTS[a0];\ [1:v]format=pix_fmts=yuva420p,\ fade=t=in:st=0:d=1:alpha=1,setpts=PTS-STARTPTS+9/TB[v1];\ [1:a]\ afade=t=in:st=0:d=1,asetpts=PTS-STARTPTS+9/TB[a1];\ [a0][a1]amix=inputs=2;\  [2:v]scale=720x406,trim=duration=19[over];\ [over][v0]overlay[over1];\ [over1][v1]overlay=format=yuv420[outv]" -vcodec libx264 -y -map [outv] final.ts` Where can I find good ConTeXt documentation If I write the following class:  public class Example {        int j;       int k;        public Example(int j, int k) {            j = j;            k = k;       }        public static void main(String[] args) {            Example exm = new Example(1,2);            System.out.println(exm.j);            System.out.println(exm.k);       }  }   The program compiles, but when I run the program, the main method will print out two 0s. I know that in order to say that I want to initialize the instance variables in the constructor I have to write:  this.j = j; this.k = k;   But if I don't write it, then which variable is evaluated (or considered) in the constructor (on the left and on the write hand side of the expressions)? Is is the argument or the instance variable? Does it make a difference?  Are there other cases where the use of this is obligatory? Problem 20-9 in Lee's Introduction to Smooth Manifolds (2nd Ed.) asks to prove that for a Lie group $G$, and for $X, Y\in \text{Lie}(G)=\mathfrak g$, there is $\epsilon&gt;0$ and a smooth map $Z:(-\epsilon, \epsilon)\to \mathfrak g$ such that   $$(\exp tX)(\exp tY) = \exp\left(t(X+Y) + \frac{1}{2}t^2[X, Y] + t^3 Z(t)\right)$$   What we want to show is that the first and second term in the Taylor expansion of $\exp^{-1}\left((\exp tX)(\exp tY)\right)$ are $t(X+Y)$ and $\frac{1}{2}t^2[X, Y]$ respectively.  Calculating the first term is easy since we just need to differentiate $\exp^{-1}((\exp tX)(\exp tY))$ with respect to $t$ at $t=0$ once, and this gives the desired result.  But for the second term we need to take the second derivative at which I am stuck. The meaning of Bit-wise NOT in Python