I would normally work with [greek,russian,frenchb,english]{babel} which requires [utf]{inputenc} and am getting problems with some of the tkz-base macros. The error messages are incoherent so I hope the MWE below will do the talking by uncommenting either one or the other of the babel invocations. Examples 3. and 4. are straight out of Alain Matthes' tkz-base Manual:  \documentclass{article} % RN. 3 Oct 2017 %======================= \usepackage{comment} % %\usepackage[utf8]{inputenc} %\usepackage[greek,russian,frenchb,english]{babel} %     OR even only: %\usepackage[frenchb,english]{babel} % \usepackage{tkz-base} \begin{document} 1.\\ \begin{tikzpicture} \tkzDrawSegment[color=red,thick]({0,0},{2,1}) \end{tikzpicture}  2.\\ \begin{tikzpicture} \tkzDrawSegments({0,0},{2,1} {0,1},{2,0}) \end{tikzpicture}  3.\\ \begin{tikzpicture}[scale=1] \tkzInit[xmax=6,ymax=6] \tkzGrid \tkzSetUpPoint[shape = circle,color = red,size = 8,fill = red!30] \tkzDefPoint(-1+1,-1+4){O} \tkzDefPoint({3*ln(exp(1))},{exp(1)}){A} \tkzDefPoint({4*sin(FPpi/6)},{4*cos(FPpi/6)}){B} \tkzDefPoint({4*sin(FPpi/3)},{4*cos(FPpi/3)}){B’} \tkzDefPoint(30:5){C} \tkzDefPoint[shift={(1,3)}](45:4){A’} \begin{scope}[shift=(A)] \tkzDefPoint(30:3){C’} \end{scope} \tkzDrawPoints[color=blue](O,B,C) \tkzDrawPoints[color=red,shape=cross out](B’,A,A’,C’) \tkzLabelPoints(A,O,B,B’,A’,C,C’) \end{tikzpicture}  4.\\ \begin{tikzpicture}[scale=1] \begin{scope}[rotate=30] \tkzDefPoint(2,3){A} \begin{scope}[shift=(A)] \tkzDefPoint(90:5){B} \tkzDefPoint(30:5){C} \end{scope} \end{scope} \tkzDrawSegments[color=blue](A,B B,C C,A) \tkzDrawPoints(A,B,C) \tkzLabelPoints[above](B,C) \tkzLabelPoints[below](A) \end{tikzpicture} \end{document}
In my preamble, you'll find:  \renewcommand{\baselinestretch}{1} \renewcommand{\familydefault}{\sfdefault} \usepackage[sfmath]{kpfonts} \usepackage[mathrmOrig]{sfmath} \usepackage{amsmath} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{animate} \usepackage{anysize} \usepackage{arcs} \usepackage{array} \usepackage[scale=0]{background} \usepackage{blindtext} \usepackage{calc} \usepackage{cancel} \usepackage{chngcntr} \usepackage{CJK} \usepackage{CJKspace} \usepackage{CJKpunct} \usepackage{colortbl} \usepackage{enumitem} \usepackage{epstopdf} \usepackage{etoolbox} \usepackage{fancybox} \usepackage{fancyhdr} \usepackage{float} \usepackage{framed} \usepackage{graphicx} \usepackage{hyphenat} \usepackage{ifthen} \usepackage{latexsym} \usepackage{lmodern} \usepackage{multicol} \usepackage{multirow} \usepackage{mwe} \usepackage{pgffor} \usepackage{rotating} \usepackage{tabularx} \usepackage{textcomp} \usepackage{tgheros,tgtermes,tgcursor} \usepackage{tikz} \usepackage{times} \usepackage{tipa} \usepackage{varwidth} \usepackage{wasysym} \usepackage{wboiboites} \usepackage[abs]{overpic} \usepackage[breaklinks,colorlinks=true,linkcolor=red,citecolor=red, urlcolor=blue]{hyperref} \usepackage[framemethod=TikZ]{mdframed} \usepackage[breakable, theorems, skins]{tcolorbox,empheq} \usepackage[default]{gillius} \usepackage[document]{ragged2e} \usepackage[latin1]{inputenc} \usepackage[spanish]{babel} \usepackage[T1]{fontenc} \usepackage[total={18.59cm,26.5cm},left=1.5cm,top=2.5cm]{geometry} \usetikzlibrary{matrix,arrows, positioning,shadows,shadings,backgrounds,calc, shapes, tikzmark} \usetikzlibrary{shadows.blur} \usetikzlibrary{shapes.symbols} \usetikzlibrary{patterns,fadings} \tcbuselibrary{skins,breakable,listings,theorems}    I'm trying to draw an arrow for X axis and Y axis.   \begin{tikzpicture} \draw[yellow!10, fill=blue!5](-1, -1) rectangle (7, 5); \draw[dotted] (-0.75,-0.75) grid (6.75,4.75); \node[below] at (-0.25,0){$O$}; \draw[-&gt;,black, thick] (-0.75,0)--(6.75,0); \end{tikzpicture}   But I get this error:    Additionally, if I remove -> from the options of \draw the tikz picture compiles normally.
Yesterday I was filming a scene with my phone but suddenly the application crashed and when I try to open the m4v generated it says that is corrupted.  I have downloaded the video files (around 36MB) on my PC and I am trying to open and repair it. Can you suggest me a way to do it?  FFMPEG info  As suggested in comments I try check what FFMPEG says me about that file with this command  ffmpeg.exe -i VID_20120425_144739.m4v -c:v copy -c:a copy out.mp4 2&gt; log.txt   Here it is the result:  ffmpeg version N-40126-ga4b58fd Copyright (c) 2000-2012 the FFmpeg developers   built on Apr 26 2012 03:29:50 with gcc 4.6.3   configuration: --enable-gpl --enable-version3 --disable-w32threads --enable-runtime-cpudetect --enable-avisynth --enable-bzlib --enable-frei0r --enable-libass --enable-libcelt --enable-libopencore-amrnb --enable-libopencore-amrwb --enable-libfreetype --enable-libgsm --enable-libmp3lame --enable-libnut --enable-libopenjpeg --enable-librtmp --enable-libschroedinger --enable-libspeex --enable-libtheora --enable-libutvideo --enable-libvo-aacenc --enable-libvo-amrwbenc --enable-libvorbis --enable-libvpx --enable-libx264 --enable-libxavs --enable-libxvid --enable-zlib   libavutil      51. 47.100 / 51. 47.100   libavcodec     54. 15.100 / 54. 15.100   libavformat    54.  3.100 / 54.  3.100   libavdevice    53.  4.100 / 53.  4.100   libavfilter     2. 72.100 /  2. 72.100   libswscale      2.  1.100 /  2.  1.100   libswresample   0. 11.100 /  0. 11.100   libpostproc    52.  0.100 / 52.  0.100 [mov,mp4,m4a,3gp,3g2,mj2 @ 003fc940] moov atom not found VID_20120425_144739.m4v: Invalid data found when processing input   Latest two lines are displayed in red. Relation between confidence interval and testing statistical hypothesis for t-test It is well known that confidence intervals and testing statistical hypothesis are strongly related. My questions is focused on comparison of means for two groups based on a numerical variable. Let's assume that such hypothesis is tested using t-test. On the other side, one can compute confidence intervals for means of both groups. Is there any relation between overlapping of confidence intervals and the rejection of the null hypothesis that means are equal (in favor of the alternative that means differ - two-sided test)? For example, a test could reject the null hypothesis iff the confidence intervals do not overlap. How does LSTM prevent the vanishing gradient problem? LSTM was invented specifically to avoid the vanishing gradient problem. It is supposed to do that with the Constant Error Carousel (CEC), which on the diagram below (from ) correspond to the loop around cell.  (source: ) And I understand that that part can be seen as a sort of identity function, so the derivative is one and the gradient stays constant. What I don't understand is how it does not vanish due to the other activation functions ? The input, output and forget gates use a sigmoid, which derivative is at most 0.25, and g and h were traditionally tanh. How does backpropagating through those not make the gradient vanish ? Sending 2D arrays in Fortran with MPI_Gather Find all roots of $\,x^2\!\equiv x\pmod{\!900}$, i.e all idempotents in $\Bbb Z_{900}$ I need the idempotent elements of $Z_{900}$ $2^2\cdot 3^2\cdot 5^2=900$ Of course there's $$0 \pmod 4 \\ 0 \pmod 9 \\ 0 \pmod {25} \\ $$ and $$ 1 \pmod 4 \\ 1 \pmod 9 \\ 1 \pmod {25} \\ $$ I found the answers by making a C++ program to test all numbers, but I don't know how to quick solve on paper. This is the output of the program $(0, 0, 0) \rightarrow 0 \\ (1, 1, 1) \rightarrow 1 \\ (0, 0, 1) \rightarrow 576 \\ (0, 1, 0) \rightarrow 100 \\ (1, 0, 0) \rightarrow 225 \\ (1, 1, 0) \rightarrow 325 \\ (0, 1, 1) \rightarrow 676 \\ (1, 0, 1) \rightarrow 801 \\$ An irreducible $f\in \mathbb{Z}[x]$, whose image in every $(\mathbb{Z}/p\mathbb{Z})[x]$ has a root? Problem: Is there an irreducible $f\in \mathbb{Z}[x]$, whose image in every $(\mathbb{Z}/p\mathbb{Z})[x]$ has a root for $p$ prime? If there is, what is the minimal degree possible?   I can only prove that $x^2-c$ is impossible, by quadratic reciprocity and Chinese remainder theorem. Even the case of $a x^2 - c$ is unknown to me.  Meanwhile, if $f$ is not required  to be irreducible, but only have no root in $\mathbb{Z}$, then $(x^2-a)(x^2-b)(x^2-ab)$ is a solution for non-sqaure $a,b,ab$, since if both $a,b$ are not squares in $\mathbb{Z}/p\mathbb{Z}$, then $ab$ is a square. Yet I still don't know if this is of minimal degree.  Also, it is natural to pose generalizations   When $p$ is not necessarily prime (equivalently for all prime powers). When $p$ is odd prime. When $p$ represents sufficiently large primes (equivalently all but a finite number left). How do I run two isolated instances of firefox? For testing purposes, I want to install two different instances of firefox on ubuntu - so that they don't share cookies. (I want to simultaneously login with both instances as different users to our website).  How do I do that? I do it with Firefox &amp; Opera, but I prefer Firefox (because of firebug). I bought a Magic the Gathering display box today with cards from the new edition Innistrad. Unfortunately one of the cards in a booster pack was damaged. It is not just a simple scratch - one corner is bent and a small part of the card is missing. According to different trading platforms this card would be worth about 6 Dollars minimum in mint condition. So it is not really expensive but also not totally worthless.  What can I do about this? Can I obtain a replacement card from the producer (WotC) or from the store I bought it from? How can I prove that the card was damaged when I opened the booster pack? I am sure I am not the first person who got a damaged card from a booster pack. How are such issues usually handled? When I am in texture mode one of my objects looks like it is in solid mode. The model is textured like all other models in the scene, but it doesn't look like it is in texture mode.  Screenshot will explain better:      What this model looks like. What all models should look like in texture mode. How to keep VLC player in minimized mode? I'm using VLC media player which can play almost all kinds of audio and video formats. While listening to audio, I keep VLC in minimized mode and can work on other windows. But when I select to listen video songs mixing with audio songs, VLC is maximizing itself to play every video song in the playing list, which is really annoying in the middle of work.  So how can I keep always VLC player in minimized mode while playing a list of songs mixed with audio and video songs? Very strange error suddenly appeared running Biber If $|f(z)|\le |g(z)|$, can we say $f$ is constant? Let $f$ and $g$ be entire functions and $g(z)\neq 0$ for all $z\in \mathbb{C}$. If $|f(z)|\le |g(z)|$, can we say $f$ is constant?  Liouville theorem says that an entire bounded function is constant, but g is not given bounded here. So I think it should be false. What else can we say about $f$? How do I hide javascript code in a webpage? More than 1000 gallons of paint is/are sold each day Possible Duplicate:             Can anyone help me determine the correct verb in this sentence? I am not sure what to do. If it were not such a complex introductory phrase, it would be more obvious. The general consensus of my friends who are not professional writers is that the verb should be are.   To me the question is whether or not the subject is singular (i.e., “a large collective volume of paint”, perhaps in a tank) or plural (a lot of the individual gallon containers of paint).  If simplified to other options, it would be like these:   Paint is sold. Gallons of paint are sold. More paint is sold. More gallons of paint are sold. More than 1000 gallons of paint is sold. [emphasis on total volume] More than 1000 gallons of paint are sold. [emphasis on individual containers] I asked this question at stackoverflow and have been kindly redirected here.  I'd like to align some equations in Latex using the AMS packages. Each equation has two equal signs that need to be aligned. So something in the line of  A = B = C D = E = F   I've tried using the align-environment like this  \begin{align} A &amp;= B &amp;= C \\ D &amp;= E &amp;= F \end{align}   This works in principle (it aligns), however it adds ridiculously large spaces before the second equal sign in each line. But I just want the line to runs as if there was no additional alignment tab. Only when I replace for example "B" by "BBB" I want the equal sign before "F" to shift to right the exact amount of space.  Could anyone help me out on that one? It's kind of driving me crazy since I don't get the idea of that strange behavior and I just can't find any solution. Maybe alignat could help, but I don't really get how that environment works.  Cheers, Oliver Are actions and bonus actions interchangeable? Putting a piece of code in between two html tags in Solaris $6^{(n+2)} + 7^{(2n+1)}$ is divisible by $43$ for $n \ge 1$ Can I mill my opponent into defeat with Mindcrank and Duskmantle Guildmage? Okay the scenario I'm thinking of is as follows:   I control a ,  and 3 untapped lands (2 swamps, 1 Island to be perdantic). In my opponents turn he casts a burn spell to kill my duskmantle.   I activate his first ability in response.   The way I am hoping the following interactions will go is:   Duskmantles ability will hit the stack at the top and resolve The burn spell resolves dealing its damage to Duskmantle The burn spell card hits the graveyard and triggers the infinite loop for duskmantle and mindcrank killing my opponent Duskmantle perishes   Is this the way that the stack would pan out? Do I win in this situation regardless of the stack being correct or not above? (I am not fully familiar with how the stack really works in magic) You can see the cards from my deck . Who knows about the summation of this series: $$\sum\limits_{i=1}^{n}i^m $$  where $m$ is constant and $m\in \mathbb{N}$?  thanks