Consider two random variables $X$ and $Y$ with $X = f(Y)$ for $f$ deterministic. Suppose that $X$ is bivariate, $X = \{ X_1, X_2 \}$. How would you notate the function that, given $y \in Y$ returns the first element $x_1$ of $f(y) = x = [x_1, x_2]$?
Say $\mathbf{x} \in \mathbb{R}^n$, what is the common notation to extract the first component as an operation?  Something like $\mathcal{P}_j = \mathbf{x}_j$? $\mathbf{x}_j$ is the j-th component.   I need this because I have a function $f(\mathbf{x}) \approx \mathbf{x}$, so I need something like $\mathcal{P}f(\mathbf{x}) \approx \mathbf{x}_j$ since my metric is defined for a single component of $\mathbf{x}_j$.
I'm working with some code that widely uses the idiom of returning a pointer to a static local variable.  eg:  char* const GetString() {   static char sTest[5];   strcpy(sTest, "Test");   return sTest; }   Am I right in thinking that this is safe?  PS, I know that this would be a better way of doing the same thing:  char* const GetString() {   return "Test"; }   Edit: Apologies, the function signature should of course be:  const char* GetString(); What are the meaning and possible origin of "word!" and "word up"? Short story about humans serving as hosts to the larval stage of insects I read this story in a sci-fi paperback magazine probably in the 1970s or 1980s, but it might have been published much earlier.  It begins with a conversation between two young men (brothers?), the older of whom, it eventually transpires, has taken the place of the younger in serving as a host to insect-type creatures.  The insect-types are the main form of life on the planet, and use the human interlopers/colonizers as hosts for the larval stages of their    young. Must have pre-dated the &quot;Alien&quot; movies because when I read it the idea of humans serving as larval hosts was new to me. Don't remember how the story ends -- whether the emergence of the larva kills the human host. How do I share samba via Open VPN? Is that possible? I have configured open VPN in my home so that it can be accessible from my office easily.  Now I want to share samba via my open VPN. How can I share samba over open VPN between Ubuntu and Windows?  Home public IP: HHH.OOO.MMM.EEE Home desktop IP: 192.168.10.10 Office public IP: OOO:FFF:III:CCC Office Windows desktop IP: 192.168.1.10 Fancyhdr does not apply same header/footer on chapter and non-chapter pages Update: this is a lengthy post, you can     Note: The quick language list refers to the list in the screenshot below, accessible throught the shortcut Win + Space bar  I have two languages for windows spell check in my system, English (United States) and French (Switzerland), but despite both languages being properly configured with "Swiss French" input keyboard, US Keyboard input keeps appearing on this list:    Here's the settings for English (United States) language, you can see the only input is "Swiss French":    Same for Français (Suisse), the only input is "Swiss French":    In the Control Panel, both are also set as Swiss French:    All my settings are set to use "language list":     Here's a few things that I already tried:   I already managed to remove it by some language configuration gymnastics, by adding and removing languages, it always eventually comes back I have already done this:  There's no mention of US Keyboard in my registry settings either:     Please help, I'm desperate, this is my third computer with Windows 10 and they all do the same thing. How to learn physics effectively and efficiently Are there any galois fields which consist of product of two primes, as in $\mathrm{GF}(2\cdot 3) = \mathrm{GF}(6)$? How does Motherboard and CPU affect RAM choice? I am seeking advice on which memory to use with my motherboard and CPU. Below are my components and some relevant information extracted from their official websites.   NOTE: Although this is a very specific case, a general answer is equally good for me — and also alot more useful for everyone else!  CPU: AMD Phenom II X4 810   ASUS M4A785TD-V EVO listed as one of many  motherboards.   Motherboard: ASUS M4A785TD-V EVO   4 x DIMM, Max. 16 GB, DDR3 1800(O.C.)*/1600(O.C.)/1333/1066/800 ECC,Non-ECC,Un-buffered Memory Dual Channel memory architecture (Complete list of specs: ).   NOTE II: I wouldn't want to do any overclocking as I have no experience with that. So I think the 1333 MHz is the most appropriate. Since the higher frequencies are marked with "O.C."  Questions:   How can I be certain that a specific RAM will work well (or not work) together with my CPU and motherboard? (The Qualified Vendor List is a good starting point, but it's a bit limited and sometimes a bit outdated). Is it true that choice of memory is not independent of the processor? How?    I'm worried I'll be missing something essential when buying my next RAM chips :) Is exon order always preserved in splicing? Are there any cases in which the splicing machinery constructs an mRNA in which the exons are not in the 5' -> 3' genomic order? I'm interested any such cases, whether they involve constitutive or alternative splicing. I am trying to follow Blender Guru's beginner tutorial. He went to the Compositor tab and was using it to Denoise an image but when I got there, no nodes show up. Can you guys help? What was Tauriel doing during the events of The Lord of the Rings movies? [Yes, The Hobbit movies are nonsense. But how could I call myself a fantasy fan if I didn't demand my nonsense be as logical as possible?]  Tauriel is presented as a highly-skilled fighter and a combatant for the side of good. Despite this, she apparently did nothing during Sauron's war on the free peoples.  Was she somehow     still mourning Killi, after all these decades?   Was she dead? Or is there another reason she didn't participate? Is the notorious $n^2 + n + 41$ prime generator the last of its type? Find and Replace Inside a Text File from a Bash Command Stack Exchange doesn't allow me to answer protected questions because I gave away earned rep in bounties I noticed that I can't answer protected questions. I don't want to actually, but it says:        It was , but I also didn't have an ability to answer other protected questions.  I earned 270 reputation points + 100 reputation point bonus. Then I  350 reputation points as a bounty. Then I earned 59 reputation points. Today I started another bounty (50 reputation points), etc – I offered 4 bounties with total 500 rep.  Despite the fact I started from the association bonus, I must have an ability to answer protected questions, as I earned reputation points here. But offered them as bounties.    I now have enough reputation points, but I would like it to be fixed, because I like offering bounties very much.  I would like system to check for my bounties when it checks if I can answer protected question. Should we have a tag for significant points in time? I am studying for an exam and I am having trouble with this practice question:  In this question, we consider finite bit strings that do not contain $00$. Examples of such bitstrings are $0101010101$ and $11110111$. For any integer $n\geq 2$, let $B_n$ be the number of bitstrings of length $n$ that do not contain $00$.   Determine $B_2$ and $B_3$. Prove that $B_n = B_{n-1} + B_{n-2}$ for each $n\geq 4$. For each $n\geq 2$, express $B_n$ in terms of a Fibonacci number.   Any help is greatly appreciated An integrable and periodic function $f(x)$ satisfies $\int_{0}^{T}f(x)dx=\int_{a}^{a+T}f(x)dx$. I want to prove:     For an integrable function $f(x)$ and periodic with period $T$, for every $a \in \mathbb{R}$, $$\int_{0}^{T}f(x)\;dx=\int_{a}^{a+T}f(x)\;dx.$$   I tried to change the values and define $y=a+x$ so that $dy=dx$ and the limits of the integrals are as we want, but I'm not sure how to use the fact that $f(x)$ is periodic.  Thanks a lot! Using Fermats prime numbers to prove that there is infinitely many prime numbers Why do both cron and systemd execute automatic upgrades?