Compiling a recursive function
How to compile self-referencing functions (to perform recursive a task)
I am drawing a 3D array like the attached picture, which actually describes a multidimensional array. However, I can not put the name of the axis and take the value from the matrix like the attached picture.  This is the code that I have:  \documentclass[margin=5mm]{standalone} \usepackage{tikz} \usetikzlibrary{matrix,calc}  \begin{document} \begin{tikzpicture}[every node/.style={anchor=north east,fill=white,minimum width=1.4cm,minimum height=7mm}] \matrix (mA) [draw,matrix of math nodes] { (1,1,3) &amp; (1,1,3) &amp; (1,1,3) &amp; (1,1,3) \\ (1,1,3) &amp; (1,1,3) &amp; (1,1,3) &amp; (1,1,3) \\ (1,1,3) &amp; (1,1,3) &amp; (1,1,3) &amp; (1,1,3) \\ (1,1,3) &amp; (1,1,3) &amp; (1,1,3) &amp; (1,1,3) \\ };  \matrix (mB) [draw,matrix of math nodes] at ($(mA.south west)+(1.5,0.7)$) { (1,1,3) &amp; (1,1,3) &amp; (1,1,3) &amp; (1,1,3) \\ (1,1,3) &amp; (1,1,3) &amp; (1,1,3) &amp; (1,1,3) \\ (1,1,3) &amp; (1,1,3) &amp; (1,1,3) &amp; (1,1,3) \\ (1,1,3) &amp; (1,1,3) &amp; (1,1,3) &amp; (1,1,3) \\ };  \matrix (mC) [draw,matrix of math nodes] at ($(mB.south west)+(1.5,0.7)$) { (1,1,3) &amp; (1,1,3) &amp; (1,1,3) &amp; (1,1,3) \\ (1,1,3) &amp; (1,1,3) &amp; (1,1,3) &amp; (1,1,3) \\ (1,1,3) &amp; (1,1,3) &amp; (1,1,3) &amp; (1,1,3) \\ (1,1,3) &amp; (1,1,3) &amp; (1,1,3) &amp; (1,1,3) \\ };  \draw[dashed](mA.north east)--(mC.north east); \draw[dashed](mA.north west)--(mC.north west); \draw[dashed](mA.south east)--(mC.south east); \end{tikzpicture}   \end{document} A simple inequality for floor function In Einstein's General Relativity, do the space-time dimensions curve? In Einstein's General Relativity, do the space-time dimensions curve according to the positions of stars, planets, and masses? Suppose $A$ and $B$ are similar matrices. Show that $A$ and $B$ have the same eigenvalues with the same geometric multiplicities.      Similar matrices: Suppose $A$ and $B$ are $n\times n$ matrices over $\mathbb R$ or $\mathbb C$. We say $A$ and $B$ are similar, or that $A$ is similar to $B$, if there exists a matrix $P$ such that $B = P^{-1}AP$. 100 apples are/is considered as a large number of apples Brown sugar instead of white sugar Find the least value of $ \sec^6 x +\csc^6 x + \sec^6 x\csc^6 x$ Find the least value of $$ \sec^6 x +\csc^6 x + \sec^6 x\csc^6 x$$ I tried AM greater than equal to GM But that's for finding maximum value.  This can probably be solved with calculus but I don't know for some reason I can't find the answer . Which is $80$. Where can I travel for prolonged periods of time while legally working remotely for a company in my home country? I found several questions about inbound travelers to the US in this scenario, but little about other countries: I work for a company in my home country (USA) who are open to me working remotely while traveling.   Which countries allow me to legally work remotely for a company in my home country (USA) while traveling in their country? The work has absolutely no connection to the destination country, it would take place identically entirely within the USA if I weren't traveling. I looked at similar questions and wanted to post a more specific one.  If I wanted one of my accounts on the network to no longer be associated to my global account, could an administrator do it manually? I mean, even if they could, would they?  It's a matter of professionalism. I don't want one of my accounts on the network to be visible from my other accounts. I just want that to be under a separate email that's not one of the OpenIDs associated with my global account.  I realize this would have been easier to do when I joined that site, but it's too late now, and only now have I realized that I don't really want that account showing up.  So can it be done by an administrator? I don't want to wait weeks and weeks for a response by using the contact form (funny, I've waited two with this post)... In Leibniz notation, the 2nd derivative is written as $$\dfrac{\mathrm d^2y}{\mathrm dx^2}\ ?$$  Why is the location of the $2$ in different places in the $\mathrm dy/\mathrm dx$ terms? As you know, we can enable the spell checker on single line text boxes in the following way:    We have to enable it every time for checking words.  How can we enable it forever, so it doesn't need to be enabled each time? The question is:     Are there square matrices $A,B$ over $\mathbb{C}$ s.t. $A^2+B^2=AB$ and $BA-AB$ is non-singular?   From $A^2+B^2=AB$ one could obtain $A^3+B^3=0$. Can we get something from this?  Edit:  $$A^2+B^2=AB\implies\\ A(A^2+B^2)=A^2B \implies\\ A^3+AB^2=A^2B \implies \\ A^3+(A^2+B^2)B=A^2B \implies \\  A^3+A^2B+B^3=A^2B \implies \\ A^3+B^3=0 $$ Magic quotes in PHP According to the , in order to make code more portable, they recommend using something like the following for escaping data:  if (!get_magic_quotes_gpc()) {     $lastname = addslashes($_POST['lastname']); } else {     $lastname = $_POST['lastname']; }   I have other validation checks that I will be performing, but how secure is the above strictly in terms of escaping data? I also saw that magic quotes will be deprecated in PHP 6. How will that affect the above code? I would prefer not to have to rely on a database-specific escaping function like mysql_real_escape_string(). Why does speed of light have to be constant? My question is not about why speed of light has a particular constant value which has been sufficiently addressed in other questions on SE already. I want to know whether the fact that speed of light has to be constant is a consequence of other fundamental laws of Universe, or is it just a fundamental law itself.  My motivation for asking this question is thinking about Special Theory of Relativity. One way of understanding why time dilation and length contraction happen is to look at it from the perspective of constancy of speed of light. Alice who is on the moving source of light and Bob, a fixed observer see the speed of light as constant. In order for Alice to see the speed of light as a constant value, time slows down and length expands (in forward direction) thus keeping the speed constant.   In the  I'm doing, the Professor tells that this constancy of speed of light could be more generally referred to as, "Principle of wave constancy". That is, the speed of any wave is a property of the medium (and thus it remains constant). So, the speed of a wave in water, for example, remains constant even if the source of the waves (say a paddle keeps moving). Frequency and wavelength may change but the speed remains constant. In a similar fashion, light is an electromagnetic wave and thus its speed is constant. And the constant speed is defined by the medium (which happens to be vaccum i.e., no medium for light).   My questions are twofold now -    Is the above reasoning correct to explain why speed of light is constant? (i.e., thinking of it as constancy of any wave in general) Theoretically, could there be other waves that could travel through vaccum at a different speed? If yes, time dilation and length contraction will have to be different.   I'd appreciate it if the answer is kept non-technical (essential math is okay). More importantly, I request you to try and explain without using General Theory of Relativity. Because I'm thinking how the scientific understanding by 1905 had already knew that speed of light has to be constant. How do I install an individual package on a Linux system? Each number in a subset $S\subseteq \{1,\ldots,2n\}$ does not divide another one. Then $\max |S|$? This problem comes from a seemingly innocuous question from a professor during a lesson for a Math Olympiad course. [A part of this question is really a classic of number theory/combinatorics]  Problem: Let $S$ be a a non-empty subset of $\{1,2,\ldots,2n\}$. It is clear that if $|S|$ is "enough large" then, independently from the choice of $S$, there are for sure some distinct $a,b \in S$ such that $a$ divides $b$.  Then, what is the maximal $k$ such that, for some $S$ with cardinality $k$, if $a,b$ are distinct members of $S$ then $a$ does not divide $b$?  [Ps. I know the solution] After reading some articles on blender speed, I see that using CUDA enabled GPU computing will be of help in rendering.   I am trying to stitch a shirt on human .obj file. For that I bake 60 frames for it to fall on the human correctly. It takes about 20 seconds for the bake. I'd want to host it real time.  youtube link of the same :   Can I use GPU computing to reduce the bake time just like rendering time ? Image of the tensor product of strict maps of Banach spaces Node for setting render colour, regardless of lighting I'm trying to make a material node setup to set final render colors, regardless of lighting conditions. Is such a setup possible? How to let `dpkg -i` install dependencies for me?