Edit multiple layers
Resize multiple layers around their respective anchor points
For holomorphic functions, if $\{f_n\}\to f$ uniformly on compact sets, then the same is true for the derivatives. Let $\Omega$ be an open subset in $\mathbb{C}$. Let $\{f_n\}$ be a sequence of holomorphic functions on $\Omega$ such that $f_n\to f$ pointwise and converges uniformly on any compact subset $K\subseteq \Omega$. Then by Cauchy Theorem and Morera Theorem, $f$ is holomorphic. Let $f_n$ and $f'$ be the derivatives of $f_n$ and $f$ respectively. Prove that $f_n'\to f'$ uniformly on any compact subset $K\subseteq \Omega$.   How to prove? Event button as a module or as user program? Is it pythonic for a function to return multiple values? In python, you can have a function return multiple values.  Here's a contrived example:  def divide(x, y):     quotient = x/y     remainder = x % y     return quotient, remainder    (q, r) = divide(22, 7)   This seems very useful, but it looks like it can also be abused ("Well..function X already computes what we need as an intermediate value.  Let's have X return that value also").  When should you draw the line and define a different method? Is char *envp[] as a third argument to main() portable Theme Image Style for image located in module directory Prove $2^k+1$ divisible by 3 for odd K Using tikzcd in newcommand (for inline arrows) I’m using tikz-cd for diagrams, and have a medium-sized diagram that I want to re-use several times.  However, when I try using a definition like:  \newcommand{\myarrow}{$\begin{tikzcd} A \ar{r} &amp; B \end{tikzcd}$   I get an error:  ERROR: Package pgfbasematrix Error: Single ampersand used with wrong catcode.   Is it possible to put a tikz-cd diagram into a defined command somehow? Why do shields in Star Trek "wear out"? Elsevier actions following US sanctions on Iran Referencing without captions appearing but keeping numbering Let There Be Light Story Identification I am looking to identify a story that I read around 2001 (it is probably much older).  Someone showed me the story on pages printed from the internet, and it was attributed to Isaac Asimov (although I cannot state that is the true author).    The story is told in glimpses at different points of time in the future.  In each glimpse, humans are asking a more and more "intelligent" computer how to prevent the universe from collapsing into a singularity in the future, and the computer states it needs more computational power and resources to solve this problem.  At some point, man becomes one with the computer, and the computer exists in hyperspace (or subspace?).    In the final glimpse, it is the end of time and the universe is collapsing into a singularity.  At the instant the universe reaches the singularity, the computer figures out how to prevent it and says "Let there be light" and the universe begins to expand again.  Is anyone familiar with this story? Why does the integral of the surface area of a sphere equal it's volume?   $$\int{4\pi r^2 \ \mathrm{d}r =\frac{4}{3}\pi r^3}$$  I don't quite understand why the relationship between surface area and volume is this way. Is this true for any other shapes? Let $X_n$ be iid random variables with $P(X_n=(-1)^kk)=\dfrac{C}{k^2\log k}$ for all $k\geq 2$. Here $C$ is just a constant so that the sum of probabilities is $1$. Find constant $\mu$ such that $S_n/n\to \mu$ in probability where $S_n=\sum_{k=1}^nX_k$.   Here $E(X_n)=\infty$. I'm a bit lost after this. In general how does one find constants like this? I would like to enable the root account on my Ubuntu installation.  I realize the security implications of this. Do any open-source .Net libraries (commercially usable) exist for reading/writing LiDAR data? I have a few LiDAR point data (.las files) with me. I would like to read the X,Y and Z from it using .Net. I found , which is in C++ and I am not sure if it can be used commercially after reading the licensing information. Has anyone found any good ones? Metric $d(x,y)=\frac{|x-y|}{\sqrt{1+x^2}\sqrt{1+y^2}}$ on $\mathbb{R}$ When you have a link from lets say twitter that is t.co/foo that links back to your website how does that effect SEO and how do the major search engines handle Shortened URLs? How do I remove code duplication between similar const and non-const member functions? Preview Breaks with Invalid Tag Name [tag:+] In the formatted preview for Questions &amp; Answers, typing a tag link with an invalid tag name "crashes" the preview. As soon as you type the following the preview stops updating and an error can be observed in the Javascript console.   [tag:+]   Observed in Safari 7 and Chrome 31.   seems related to the business rule of not allowing certain characters in tags, but it sounds like a different bug. How can one show that a möbius transformation maps the unit circle to some axis? Suppose I have the möbius transformation f(z) = $\frac{1+z}{1-z}$ and I want to show that it will map the unit circle (excluding the point 1) to the imaginary axis.  Would it help to express my unit circle in polar form?     Here's what I did: f(e$^{i\theta}$) = $\frac{1+e^{i\theta}}{1-e^{i\theta}}$  But I'm not sure where to go from this step.