How to convert photos from heic into jpg?
How to convert a HEIF/HEIC image to JPEG in El Capitan?
How to enable touchpad? Yesterday, suddenly my touchpad on my MSI Laptop started to not respond. In other words, in Login screen, touchpad is working as expected. However, in Desktop screen, after I have logged in, touchpad is not working.  How can I enable touchpad in Desktop? Is it possible to cross the Wagan border by car? I was planning a trip by car when I found something a bit weird in :if you try to cross from Lahore to India, it tells that you have to 6457 km detour.  Is it possible to cross this border driving? If not, is there another way to cross without having to make more than 6000 km? Why is having a 2 stage flip-flop desirable? Are there advantages of having a master-slave compared to a one stage JK flip flop? I have a graph. This is my code.    \documentclass[10pt]{article}     \usepackage{pgf,tikz}     \usetikzlibrary{arrows,patterns}     \pagestyle{empty}      \definecolor{ttqqcc}{rgb}{0.2,0,0.8}     \definecolor{ffqqtt}{rgb}{1,0,0.2}     \definecolor{ttqqff}{rgb}{0.2,0,1}     \definecolor{uququq}{rgb}{0.25,0.25,0.25}      \begin{document}      \begin{tikzpicture}[line cap=round,line join=round,&gt;=triangle 45,x=1.0cm,y=1.0cm]      \draw[-&gt;] (-3.63,0) -- (3.67,0);     \foreach \x in {-3,-2,-1,1,2,3}       \draw[shift={(\x,0)}] (0pt,2pt) -- (0pt,-2pt)          node[below] {\footnotesize $\x$};     \draw[color=black] (3.48,0.07) node [anchor=south west] { $x$};      \draw[-&gt;] (0,-1.93) -- (0,5.57);     \foreach \y in {-1,1,2,3,4,5}       \draw[shift={(0,\y)}] (2pt,0pt) -- (-2pt,0pt)          node[left] {\footnotesize $\y$};     \draw[color=black] (0.06,5.19) node [anchor=west] { $y$};      \draw (0pt,-10pt) node[right] {\footnotesize $0$};      \clip(-3.63,-1.93) rectangle (3.67,5.57);     \draw[pattern color=ffqqtt,pattern=north east lines,fill opacity=0.1, smooth,samples=50,domain=0:1.0]      plot(\x,{\x^4-4*\x^2+3}) -- (1,0) -- (0,0) -- cycle;     \draw[pattern color=ttqqcc,pattern=crosshatch,fill opacity=0.1, smooth,samples=50,domain=1.0:1.7320508075688772]      plot(\x,{\x^4-4*\x^2+3}) -- (1.73,0) -- (1,0) -- cycle;      \begin{scope}[xscale=-1]     \draw[pattern color=ffqqtt,pattern=north east lines,fill opacity=0.1, smooth,samples=50,domain=0:1.0]        plot(\x,{\x^4-4*\x^2+3}) -- (1,0) -- (0,0) -- cycle;     \draw[pattern color=ttqqcc,pattern=crosshatch,fill opacity=0.1, smooth,samples=50,domain=1.0:1.7320508075688772]        plot(\x,{\x^4-4*\x^2+3}) -- (1.73,0) -- (1,0) -- cycle;     \end{scope}      \draw[smooth,samples=100,domain=-3.6342419080068153:3.665758091993186] plot(\x,{(\x)^4-4*(\x)^2+3});      \fill [color=uququq] (-1.73,0) circle (1.5pt);      \fill [color=uququq] (-1,0) circle (1.5pt);      \fill [color=uququq] (1,0) circle (1.5pt);      \fill [color=uququq] (1.73,0) circle (1.5pt);      \end{tikzpicture}     \end{document}   When I see the DVI output DVI, I have    And if I look at the PDF file, I have Shell's process group ID = foreground job's process group ID? I decisively conclude that Shell's process group ID = foreground job process group ID from the 2 sources below. When a background job is selected to run in the foreground, is it the shell's process group ID that changes to the foreground job's process group ID or the reverse?  1.     To facilitate the implementation of the user interface to job control, the operating system maintains the notion of a current terminal process group ID. Members of this process group (processes whose process group ID is equal to the current terminal process group ID) receive keyboard-generated signals such as SIGINT. These processes are said to be in the foreground. Background processes are those whose process group ID differs from the terminal’s; such processes are immune to keyboard-generated signals.    2.        Addition:  $sleep 3000 &amp; $sleep 2000 &amp; $ps xao pid,ppid,pgid,sid,tty,comm | grep tty  PID     PPID    PGID    SID     TTY     COMMAND 1153    1135    1153    1153    tty1    bash 1173    1153    1173    1153    tty1    sleep 1189    1153    1189    1153    tty1    sleep 1219    1153    1219    1153    tty1    ps 1220    1153    1219    1153    tty1    grep What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a linear algebra problem (with eigenvectors)? I've read a lot about PCA, including various tutorials and questions (such as , , , and ).   The geometric problem that PCA is trying to optimize is clear to me: PCA tries to find the first principal component by minimizing the reconstruction (projection) error, which simultaneously maximizes the variance of the projected data.    When I first read that, I immediately thought of something like linear regression; maybe you can solve it using gradient descent if needed.  However, then my mind was blown when I read that the optimization problem is solved by using linear algebra and finding eigenvectors and eigenvalues. I simply do not understand how this use of linear algebra comes into play.  So my question is: How can PCA turn from a geometric optimization problem to a linear algebra problem? Can someone provide an intuitive explanation?  I am not looking for an answer like  that says "When you solve the mathematical problem of PCA, it ends up being equivalent to finding the eigenvalues and eigenvectors of the covariance matrix." Please explain why eigenvectors come out to be the principal components and why the eigenvalues come out to be variance of the data projected onto them  I am a software engineer and not a mathematician, by the way.  Note: the figure above was taken and modified from . Combinatorial proof for Stirling number of 1st kind's generating function So I see this identity a lot but I can't find a detailed combinatorial proof for it.  $$n(n+1)...(n+k-1)=\sum_{j=0}^k \begin{bmatrix}k \\j \end{bmatrix}n^j$$ Can someone please help? "object-oriented" vs "object oriented" When should we use "object-oriented" and when "object oriented" when talking about programming?  An example:     Why should I start writing object oriented code?   I personally think that there should be a hyphen, because "oriented" connects to the word "object", but I am not sure. Show that $\sum_{n=1}^{\infty}(n^{3}\sin\left(\frac{1}{n}\right)-n^{2}+\frac{1}{6})$ converges Let $t\in \mathbb R$. Prove that $\displaystyle{\sum_{n=1}^{\infty}n^{3}\sin\left(\frac{1}{n}\right)-n^{2}+t}$ converges iff $t=\frac{1}{6}$.  While the $(\Rightarrow)$ direction was fairly easy (as $a_n$ should converge to $0$, forcing $t=\frac{1}{6}$), i'm facing some hard time trying to prove the second direction, that is $\displaystyle{\sum_{n=1}^{\infty}(n^{3}\sin\left(\frac{1}{n}\right)-n^{2}+\frac{1}{6})}$ converges. I did notice that $a_n=a_{-n}$ and tried to write this series as a Leibnitz series, but had no luck since the sequence doesn't decrease. I also tried to prove absolute convergence but then again, no luck. Thanks. When should I vote to delete a question? I've recently reached enough reputation on one of the sites to be able to cast delete votes. I am not sure when a question is supposed to be deleted as opposed to just remain closed.   What criteria should I use when deciding whether or not to cast my delete vote? Dark Mode for Stack Exchange sites Each Stack Exchange site should provide users the option of using a dark mode design/theme.  Why is this feature missing?  The major IDEs are already a letdown regarding dark color schemes. Correct tracked camera orientation I have been playing around with camera tracking and I'm happy enough with the tracking and alignment of the markers with the footage when viewed through the camera.    The problem is, when I am not looking through the camera I can see that the grid isn't aligned to the camera.    How do you correctly align the grid to this tracked camera? I have set a floor and two points for scale, also clicked setup tracking scene, but this just added cube and plane which were on the grid. FrameLabel and OverTilde Why can ECC key sizes be smaller than RSA keys for similar security? Difference between [NSMutableArray array] vs [[NSMutableArray alloc] init] How to add custom objects to the "add object" menu? Error when clipping raster in QGIS: "'ascii' codec can't encode character"? I have done it many times (clipping a raster with a polygon layer or by extension) but today I got an error for the first time and I don't know how to solve it. I am always using the same type of raster layers. When running the clipping tool I got the following message:  gdal_translate -of GTiff -ot Byte -projwin 410282.185971 4694950.41162 410783.882475 4694524.96815 -co COMPRESS=DEFLATE -co PREDICTOR=1 -co ZLEVEL=6 -co TFW=YES "C:/Users/FERRAN ALA/Desktop/Justificació Fontanals/QGIS/Topo 1_5000/bt5mv20sd0f283077st1r031.sid" "C:/Users/FERRAN ALA/Desktop/Justificació Fontanals/QGIS/background/image.tif"   GDAL command output:     'ascii' codec can't encode character u'\xf3' in position 201: ordinal not in range(128) See log for more details   Does anybody know what that is? I need help to calculate the  Fourier transform of this funcion  $$b(x) =\frac{1}{x^2 +a^2}\,,\qquad a &gt; 0$$ Thanks. How to use stars and bars for solving number of integral solutions to an equality? Finding the inverse of the arc length function