how to get the value of an element in the url after #?
Can I read the hash portion of the URL on my server-side application (PHP, Ruby, Python, etc.)?
Reason for Subject-Verb Inversion: Only in cases where A is B, shall the Company do X Are there any guarantees in JLS about order of execution static initialization blocks? Suppose $G$ has odd order, show the function $f:G\rightarrow G$ defined by $f(x)=x^2$ is injective. This proposition is easily provable if we assume $G$ is Abelian, but I don't know how to start this without the assumption of being Abelian. Probability of a painted cube being reassembled into itself Suppose 27 cubes are stacked together, suspended in the air, to form a larger cube.  The cube is then painted on all the exposed surfaces and dried.  The smaller cubes are then randomly permuted in both spatial position and spatial orientation to form another large cube.  What is the probability that new larger cube is identical to the original?  This is not homework, it was passed on by a friend who found it somewhere on the internet, and they do not remember where. How to make /sbin/shutdown, /sbin/reboot etc. require sudo again in 16.04? For whatever reason, we do no longer need to be root (or using sudo) to run /sbin/shutdown, /sbin/reboot etc.  This seems to be because those executables are now symlinks to /bin/systemctl which handles everything as normal user.  However, what if I want shutdown and reboot to require root authentication again? How can I achieve this? How to take a site offline using Drush? Prove that the natural map $\alpha : \text{Hom}(X,\text{Spec} A) \rightarrow \text{Hom}(A,\Gamma(X,\mathcal{O}_X))$ is an isomorphism This is question 2.4 in Hartshorne. Let $A$ be a ring and $(X,\mathcal{O}_X)$ a scheme. We have the associated map of sheaves $f^\#: \mathcal{O}_{\text{Spec } A} \rightarrow f_* \mathcal{O}_X$. Taking global sections  we obtain a homomorphism $A \rightarrow \Gamma(X,\mathcal{O}_X)$. Thus there is a natural map $\alpha : \text{Hom}(X,\text{Spec} A) \rightarrow \text{Hom}(A,\Gamma(X,\mathcal{O}_X))$. Show $\alpha$ is bijective.  I figure we need to start off with the fact that we can cover $X$ with affine open $U_i$, and that a homomorphism $A \rightarrow \Gamma(X,\mathcal{O}_X)$ induces a morphism of schemes from each $U_i$ to $\text{Spec} A$ and some how glue them together. But I have no idea how to show that the induced morphisms agree on intersections. How does this work? Bootstrap 3 - Why is row class is wider than its container? How does one change the Attribute table view on QGIS 3? An initial answer says to use the Switch to Table view button but I can't seem to find this button. Book about space alien cats I read a book when I was young, it was about space alien cats. I believe the title was Quzzles, but I really don't know. The book was stolen from me before I was finished. I don't know much else about it. Non academic career options for PhD in Math I am thinking of getting my M.S. in Computer Science. I chose C.S. because I enjoy programming and because its a solid choice, career wise.  Low unemployment, good pay, all that jazz.  But my real passions has always been math and lately I have been thinking about swapping and going for my graduate degree in Math. If I went the math route I would probably go full PhD (since I don't think there is much you can do with just a Masters in math).  But as much as I love math, I can't see myself being a math teacher. I would want to work in research or industry, applying math to solve real world problems.    What kind of non-academic jobs are there for someone with a PhD in math (or what is the best resource to see what jobs are out there)? How can we get the command line of a running application? Why can't we see light travelling from point A to B? Let's say we have a cloud of dust which is a lightyear across and someone shoots a beam of light from point A to B , why it is not possible for an observer far far away to see the light while it travels through the cloud at the speed of light? Improve the editing flow with predefined options for "Edit Summary" The characteristic and minimal polynomial of a companion matrix of a monic polynomial $f \in \mathbb F\left[x\right]$ in $1$ variable $x$ over a field $\mathbb F$ plays an important role in understanding the structure of finite dimensional $\mathbb F[x]$-modules.  It is an important fact that the characteristic polynomial and the minimal polynomial of $C(f)$ are both equal to $f$. This can be seen quite easily by induction on the degree of $f$.  Does anyone know a different proof of this fact? I would love to see a graph theoretic proof or a non inductive algebraic proof, but I would be happy with anything that makes it seem like more than a coincidence! A relative of mine has received a multiple-entry UK visa for 2 years. Is there a particular limit on how many months in total per year she can stay in UK? The way I understand the current rule is that such visitors can enter UK as many times as they want as long as they do not stay for longer than 6 months per single visit. However, does this mean that if she stayed with us for 5 months and went back home for 1-2 months, she could come and stay for another 5 months? I heard that it is advisable to spend only 180 day per calendar year in UK and not more, but I could not find that rule in any official UK Home Office documents. Thanks in advance for any info about this. $r$ primitive root of prime $p$, where $p \equiv 1 \mod 4$: prove $-r$ is also a primitive root question is as follows:  Let $p$ be a prime with $p \equiv  1 \mod 4$, and $r$ be a primitive root of $p$.  Prove that $-r$ is also a primitive root of $p$.  I have shown that $-r^{\phi(p)} \equiv 1 \mod p$.  What I am having trouble showing, however, is that the order of $-r$ modulo $p$ is not some number (dividing $\phi(p)$ that is LESS than ($\phi(p)$).  By way of contradiction, I've shown that the order of $-r$ cannot be an EVEN number less than $\phi(p)$.  But my methodology does not work for the hypothetical possibility of an ODD order that is less than $\phi(p)$.  Any and all help appreciated.  Happy to show methodology for any of the parts I have managed to do, if requested. Questions with mathjax don't fit in the box This bug is intermittent, only showing up on some answers, but not others.  Sometimes, posts that have mathjax equations expand the math, but don't resize the text box, cutting off some text on the bottom.  Note that this is on the IOS public beta, so that may partially have caused the problem.     App Version: 1.5.3.5 Device: iPhone 5s (GSM) OS Version: Version 10.0 (Build 14A5322e) Keyboard shortcut to focus on (idle) terminal I would like to know, if there is possible to use keyboard shortcut to focus on first idle (non working) terminal window in unity (13.10)? Something like Ctr+Alt+T, but before opening the new instance of terminal, searching for any idle instance? If $a$ and $b$ commute and $\text{gcd}\left(\text{ord}(a),\text{ord}(b)\right)=1$, then $\text{ord}(ab)=\text{ord}(a)\text{ord}(b)$. Prove if $\operatorname{ord}(a)=m$, $\operatorname{ord}(b)=n$, and $\operatorname{gcd}(m,n)=1$, then $\operatorname{ord}(ab)=mn$.   I was reading this and was thinking how this proof would look like. I tried to do it and am not sure if this is correct. Here is what I did:  If $a$ and $b$ commute then $(ab)^{mn} = a^{mn} * b^{mn} = (a^m)^n * (b^n)^m = 1 * 1 = 1.$ So $ord(ab) | mn$.  Now, take $k = \operatorname{ord}(ab) = m^\prime * n^\prime$ where m' is relatively prime with $n$ and $n'$ is relatively prime with $m$. By the result above $m' | m$ and $n' | n$. Now we have $((ab)^k)^{m/m'} = 1$ since $(ab)^k=1$. But on the other hand, by the commutativity:  $$((ab)^k)^(m/m') =$$  $$((ab)^(m' * n'))^(m/m') =$$  $$ a^{n'm} * b^{n'm} = $$  $$(a^m)^{n'} * b^{n'm'}=$$  $$b^{n'm'} = 1$$  This implies that $n' * m'$ is divisible by $n$. But $m'$ is relatively prime with $n$, so we must have $n' = n.$ By symmetry, $m' = m$. So $ord(ab) = mn$.  Just to say this again, I want to prove if $a$ and $b$ commute and $m$ and $n$ are relatively prime then   $$ord(ab)=mn.$$   The comments are vague. I guess this must be the answer then and there probably is not another way to do this.