I have installed ffmpeg by following   Now, ffmpeg works if I cd to bin and execute it with ./ffmpeg  I wonder if I could execute ffmpeg just by typing ffmpeg in a terminal from anywhere.
How do I add a directory to the $PATH in Ubuntu and make the changes permanent?
What is the "Templates" folder in the home directory for? For as long as I can remember, every time I install Ubuntu there is a folder in the home directory called "Templates." I've always just deleted it, but I'm curious: what's it supposed to be used for, and why is it in the default install? Does Wolfram Mathworld make a mistake describing a discrete probability distribution with a probability density function? Question:   Prove that a norm is always non-negative.   Assume that the norm is negative.   Define: $f: \mathbb{R}^{n}\rightarrow \mathbb{R}^{-}_{0}$  $v \mapsto \left ( \vec{v} \right )f=\left \| \vec{v} \right \|$  $\left ( \vec{u}+\vec{v} \right )f=\left \| \vec{u}+\vec{v} \right \| \in \mathbb{R}^{-}_{0}$ and  $\left ( \vec{u} \right )f=\left \| \vec{u} \right \|,\left ( \vec{v} \right )f=\left \| \vec{v} \right \|=\left \| \vec{v} \right \| \in \mathbb{R}^{-}_{0}$  At this point I am unable to progress further.  Any help is appreciated. Let $P(X)$ denote the power set of $X$ (the set of all subsets of $X$) with a partial order given by inclusion.  If $F: P(X) \to  P(X)$ is monotone (order preserving), then $F$ has a fixed point.  How are we going to prove that without using the term (complete lattice)?! Intuition on proof of Cauchy Schwarz inequality To prove Cauchy Schwarz inequality for two vectors $x$ and $y$ we take the inner product of $w$ and $w$ where $w=y-kx$ where $k=\frac{(x,y)}{|x|^2}$ ($(x,y)$ is the inner product of $x$ and $y$) and use the fact that $(w,w) \ge0$ . I want to know the intuition behind this selection. I know that if we assume this we will be able to prove the theorem, but the intuition is not clear to me. How to prove $\sum\limits_{r=0}^n \frac{(-1)^r}{r+1}\binom{n}{r} = \frac1{n+1}$? Other than the general inductive method,how could we show that $$\sum_{r=0}^n \frac{(-1)^r}{r+1}\binom{n}{r} = \frac1{n+1}$$  Apart from induction, I tried with  to check the validity, but I can't think of an easy (manual) alternative.  Please suggest an intuitive/easy method. Can I publish without affiliation? Set horizontal width on custom listings environment I want to create a custom listings environment and want to set its width as something like 90% of textwidth, centred.  Per an  for algorithms, the first thing I tried was to embed the listing in a minipage environment. However, . I found a way to still make standard environment work, but it requires to use the escape command every time before ending the environment.  The second thing I tried was this latter command, but as far as I can see, it doesn't offer a feature to set the width of the listing or centre it.  \documentclass{article} \usepackage{listings} \usepackage{lipsum}   \lstnewenvironment{queryl} %% APPROACH 1  {\lstset{frame=shadowbox,escapechar=`}}  {}  \newenvironment{query} %% APPROACH 2  {\begin{minipage}{4cm}\centering\begin{queryl}}  {\end{queryl}\end{minipage}}   \begin{document} %% APPROACH 1 Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis. \begin{queryl} begin { do nothing } end ; \end{queryl} Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis.  %% APPROACH 2 Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis.  \begin{query} begin { do nothing } end ;`%&lt;- needs escape-to-LaTeX character to work \end{query}  Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis. \end{document}     One can note that for the first environment, the frame extends beyond the width of the text. Also, puzzlingly the minipage environment doesn't seem to want to centre and swallows space (though I guess I could perhaps at least get that to work with tinkering).  In any case, does anyone have any ideas on how to set a width for a custom listings environment and centre it without requiring use of the escape character each time to end the environment? A certain element which makes functionals positive Suppose $X$ is a possibly non-separable Banach space and let $X^*$ be its dual. Also, let $(f_n)_{n=1}^\infty$ be a sequence of [EDIT: linearly independent] norm-one functionals in $X^*$. Does there exist an element $x\in X$ such that $f_n(x) \in (0,\infty)$ for all $n$? Run a program without administrative privileges in Windows 7 My account in Windows 7 is an administrator account. When I open the Run box (WinKey + R), I am warned, "This task will be created with administrative privileges."    Is there any way to run programs as myself, but without administrative privileges when logged in as an administrator? How to create two partitions? Proving that, $|f'(x)-f'(y)|\le k|x-y| \implies (f'(x))^2< 2 kf(x) $ Let $f:\Bbb R\to (0,\infty)$ be a differentiable function such that for some constant $k$ we have, $$|f'(x)-f'(y)|\le k|x-y|$$   for all $x,y \in\Bbb R.$ Then prove that, $$(f'(x))^2&lt;2 kf(x).$$   Due to lack of arguments I could not proof this inequality. But rather I proved that is true for the particular function,   $$f(x) =\cos^2(x)+1\implies f'(x) = -\sin(2x).$$ And we readily have,$$|\sin(2x)-\sin(2y)| = \left|\int_{2x}^{2y}\cos t dt\right|\le 2|x-y|$$ as well   $$(f'(x))^2 = 4 \sin^2 x\cos^2x &lt; 4(\cos^2x +1) = 4f(x).$$  It is also true for the function $x\mapsto \sin^2x +1.$   From these example I don't see how to prove the general case. Any hint will be welcome. Explicitly finding the sum of $\arctan(1/(n^2+n+1))$ This is from a GRE prep book, so I know the solution and process but I thought it was an interesting question: Explicitly evaluate $$\sum_{n=1}^{m}\arctan\left({\frac{1}{{n^2+n+1}}}\right).$$ If $n$ vectors are linearly independent, is their span $\mathbb{R}^n$? Have $n$ vectors in $\mathbb{R}^n$.  If the $n$ vectors are linearly independent, can we conclude that their span is $\mathbb{R}^n$? Invisible space when trying to remove file (but exclude all files in a list)? I'm trying to accomplish a simple task using the excellent post : I would like to remove all files from a folder except those listed in a .txt file contained in the folder. The syntax works fine, but for some reason all files are removed - basically the script is saying that there are no correspondences between the filenames in the folder and those in the .txt file - but I can see that there are!   I thought maybe there might be some invisible white space after my file names that I cannot see (in the folder or the .txt file). But I don't think so...Is there another solution that I am not thinking of? How to know whether Lagrange multipliers gives maximum or minimum? Key to get help about current function Where can I find historical data on flights, specifically Delta international flights?  I need to find out about cancellations, diversions and any other flight data pertaining on particular route at a given time.  This source has to be official and stand up to legal scrutiny. Why is fundamental group insufficient to classify manifolds? (Re?)Install Ubuntu on a Dell laptop that had Ubuntu preinstalled