I am trying to join the Quant Stack Exchange:   When I try to join it gives me an error "Oops" something went wrong. There are no further details, and it has been like for many attempts and in different browsers.  I have joined other Stack Exchanges with no problem. Also, I am attempting to join through a Facebook profile, which is how I have joined the other sites.
I look for similar questions to this one but my problem is different. I want to join this community:    so I click in     but I got this error:    but then, I found that the community is already in list of communities:    However, if I click on the community, I'm an anonymous member     and even I have the option to join again     but if I click on it, the problem starts again :( what can I do?
Why it's true? $\arcsin(x) +\arccos(x) = \frac{\pi}{2}$ The following identity is true for any given $x \in [-1,1]$: $$\arcsin(x) + \arccos(x) = \frac{\pi}{2}$$  But I don't know how to explain it. I understand that the derivative of the equation is a truth clause, but why would the following be true, intuitively?  $$\int^{x}_{C1}\frac{1\cdot dx}{\sqrt{1-x^{2}}} + \int^{x}_{C2}\frac{-1 \cdot dx}{\sqrt{1-x^{2}}} =\\  \arcsin(x) - \arcsin(C1) + \arccos(x) - \arccos(C2) = 0 \\  \text{while } \arcsin(C1) + \arccos(C2) = \frac{\pi}{2}$$  I can't find the right words to explain why this is true?    Edit #1 (25 Jan, 20:10 UTC): The following is a truth clause: $$ \begin{array}{ll} \frac{d}{dx}(\arcsin(x) + \arccos(x)) = \frac{d}{dx}\frac{\pi}{2} \\ \\ \frac{1}{\sqrt{1-x^{2}}} + \frac{-1}{\sqrt{1-x^{2}}} = 0 \end{array} $$  By integrating the last equation, using the limits $k$ (a constant) and $x$ (variable), I get the following:  $$ \begin{array}{ll} \int^x_k\frac{1}{\sqrt{1-x^{2}}}dx + \int^x_k\frac{-1}{\sqrt{1-x^{2}}}dx = \int^x_k0 \\ \\ \arcsin(x) - \arcsin(k) + \arccos(x) - \arccos(k) = m  \text{ (m is a constant)}\\ \\ \arcsin(x) + \arccos(x) = m + \arcsin(k) + \arccos(k) \\ \\ \text{Assuming that } A = m + \arcsin(k) + \arccos(k) = \frac{\pi}{2} \text{ ,for } x \in [-1,1] \end{array} $$ Using Calculus, why is that true for every $x \in [-1,1]$?    Edit #2:  A big mistake of mine was to think that $\int^x_k0 = m \text{ (m is const.)}$, but that isn't true for definite integrals.  Thus the equations from "Edit #1" should be as follows: $$ \begin{array}{ll} \int^x_k\frac{1}{\sqrt{1-x^{2}}}dx + \int^x_k\frac{-1}{\sqrt{1-x^{2}}}dx = \int^x_k0 \\ \\ \arcsin(x) - \arcsin(k) + \arccos(x) - \arccos(k) = 0\\ \\ \arcsin(x) + \arccos(x) = \arcsin(k) + \arccos(k) \\ \\ A = \arcsin(k) + \arccos(k) = \frac{\pi}{2} \text{ ,for } x \in [-1,1] \end{array} $$ Story identification: Old man has hacker neighbor who mysteriously dies Does anyone know this story? It was a novelette published with another one (I don't remember what it was) in . The premise was that the narrator is an old man whose neighbor, a hacker, dies under mysterious circumstances. A younger woman who is an expert in computer security is hired by the police to investigate what happened, and she has a fling with the narrator. After a while she dies as well, and the narrator realizes that it is an evil force that comes through electric lines is responsible for the killings. The title has interesting formatting in that it ends with a square (much like a command prompt cursor: [_] ) Saving image from PHP URL Easily measure elapsed time If someone else is booking international ticket for me using his credit or debit card, does he need to be present physically at the time of check-in?   Suppose I am coming back from Singapore to my home country and my ticket is booked by my friend for me, who lives in my home country. Do airlines in Singapore ask for the person to be present physically to check in? While I've done quite a bit of travel now and back myself to handle situations when it comes to border guards, sorting accommodation and / or transportation, one thing I still struggle to come to terms with is haggling in the markets, be it for food, clothing or other.    Image © Peter Morgan, 2014   What is the best way to go about this? I'm generally either worried I'll offend them, or that they're trying to rip me off anyway, so it's a weird combination of awkwardness inside my head ;) Dynamic trigger creation from managed package I have a requirement to create triggers dynamically after a managed package is installed. I have read that the tooling API can be used to create triggers dynamically however it cannot be used in production. Is it possible to create triggers from a managed package in an org? I want to be able to create the trigger based on some user inputs. My floating point number has extra digits when I print it "Reflexive only" verbs English can use a lot of verbs in a reflexive context. Even ones that usually are used intransitively.     I laugh myself silly.   However, it seems like there are very few – perhaps no – verbs that ONLY work in a reflexive context.  Are there any? Add Point to Plot3D Proving that, $|f'(x)-f'(y)|\le k|x-y| \implies (f'(x))^2< 2 kf(x) $ Let $f:\Bbb R\to (0,\infty)$ be a differentiable function such that for some constant $k$ we have, $$|f'(x)-f'(y)|\le k|x-y|$$   for all $x,y \in\Bbb R.$ Then prove that, $$(f'(x))^2&lt;2 kf(x).$$   Due to lack of arguments I could not proof this inequality. But rather I proved that is true for the particular function,   $$f(x) =\cos^2(x)+1\implies f'(x) = -\sin(2x).$$ And we readily have,$$|\sin(2x)-\sin(2y)| = \left|\int_{2x}^{2y}\cos t dt\right|\le 2|x-y|$$ as well   $$(f'(x))^2 = 4 \sin^2 x\cos^2x &lt; 4(\cos^2x +1) = 4f(x).$$  It is also true for the function $x\mapsto \sin^2x +1.$   From these example I don't see how to prove the general case. Any hint will be welcome. What is the best way to remove accents (normalize) in a Python unicode string? I have a Unicode string in Python, and I would like to remove all the accents (diacritics). I found on the web an elegant way to do this (in Java):  convert the Unicode string to its long normalized form (with a separate character for letters and diacritics) remove all the characters whose Unicode type is &quot;diacritic&quot;.  Do I need to install a library such as pyICU or is this possible with just the Python standard library?  And what about python 3? Important note: I would like to avoid code with an explicit mapping from accented characters to their non-accented counterpart. Small Caps and Bold Face I can't seem to have both the small caps and boldface styles on a line:  \huge\sc\bf Hello   This will generate bold text, and if the \sc is placed after, it will generate small caps text but not bolded. They seem to override each other, so is there any way to apply them both? Why are all of Mr. Shirley's gifts the same? Whey I try to run the program Layout Editor (available on ) on Ubuntu 14.04.1 64-bit LTS I get the following output in the terminal:  $ layout layout: /usr/lib/x86_64-linux-gnu/libstdc++.so.6: version `GLIBCXX_3.4.20' not found (required by layout)   I tried the command strings on /usr/lib/x86_64-linux-gnu/libstdc++.so.6 as following and here is the input and the output:  $ strings /usr/lib/x86_64-linux-gnu/libstdc++.so.6 | grep GLIBCXX GLIBCXX_3.4 GLIBCXX_3.4.1 GLIBCXX_3.4.2 GLIBCXX_3.4.3 GLIBCXX_3.4.4 GLIBCXX_3.4.5 GLIBCXX_3.4.6 GLIBCXX_3.4.7 GLIBCXX_3.4.8 GLIBCXX_3.4.9 GLIBCXX_3.4.10 GLIBCXX_3.4.11 GLIBCXX_3.4.12 GLIBCXX_3.4.13 GLIBCXX_3.4.14 GLIBCXX_3.4.15 GLIBCXX_3.4.16 GLIBCXX_3.4.17 GLIBCXX_3.4.18 GLIBCXX_3.4.19 GLIBCXX_DEBUG_MESSAGE_LENGTH   How can I resolve this issue I somehow guess that it is related with GCC but cannot figure out how to fix the problem. Furthermore, I have tried a PPA as suggested on  and there is a similar question for an older version of Ubuntu at . However, after I ran sudo update I get numerous warnings and the list I obtained with the strings command did not have new entries after installing gcc 4.9, so I purged the PPA() with ppa-purge. Any help, suggestions on how to proceed are greatly appreciated. What's the difference between mobile and desktop processors? How is $ \cos (\alpha / \beta) $ expressed in terms of $\cos \alpha $ and $ \cos \beta $? If it is possible to express  $ \cos n \alpha $ in terms of $ \cos \alpha $  as a power series for integer $n$ ...  I like to see an expression for the quotient angle that obviously tallies when $ (\alpha , \beta) $ are swapped.  EDIT1:  Something like:  $$ \cos (\alpha - \beta)= \cos \alpha \cos \beta  + \sin \alpha  \sin \beta $$  EDIT2:  Like to know why $ \cos ( \alpha / \beta )$ cannot be expressed in terms of $ \cos \alpha, \cos \beta $, but  $ \cos ( \alpha + \beta) $  can be expressed in terms of  $\cos \alpha $ and $ \cos \beta. $ I've recently updated from Debian 'jessie' to Debian 'stretch', and have started having a problem with numbers being formatted backwards when using the bidi package in conjunction with the mathspec package.  Here's a MWE:  \documentclass{article} \usepackage{mathspec} \usepackage{bidi} \begin{document} Per 2.7.1 of the RFC. \end{document}   On Debian 'jessie', when built with xelatex, this produces "Per 2.7.1 of the RFC."  But on 'stretch' this gives "Per 1.7.2 of the RFC."    Any suggestions of how to fix this? Why exactly can't a single resistor be used for many parallel LEDs? I'm self-studying Guillemin and Pollack, but I'm stuck on Problem 3 of section 2. It says that if $V$ is a vector subspace of $\mathbb{R}^N$, then $T_x(V)=V$ if $x\in V$.  If $x\in V$, then since $V$ is a manifold, there is a local parametrization $\phi: U\to V$ where $U$ is open in $\mathbb{R}^k$. Without loss of generality, we can require $\phi(0)=x$. Then $T_x(V)$ is defined to be the image of $d\phi_0$ on $\mathbb{R}^k$.   An arbitrary element of $T_x(V)$ looks like $$ d\phi_0(v)=\lim_{t\to 0}\frac{\phi(0+tv)-\phi(0)}{t}=\lim_{t\to 0}\frac{\phi(tv)-x}{t} $$  but this doesn't seem very useful to show $T_x(V)=V$. What is the right approach?