Is this use of en dash legitimate?
When should I use an em-dash, an en-dash, and a hyphen?
Novel about a guy who is possessed by the divine essence and the world ends? I read this novel back in the mid-80's but I'm pretty sure it was written in the 70's.  Strange things start to happen around a homeless man - like the laws of chance are changed.  The investigators discover that they can figure out what is going to happen next by interpreting the dreams/vision of the man.  One such dream is of a large body of water that is split into two pieces. Turns out that means that "C" (sea) - the speed of light has been halved.  The homeless man had become the embodiment of the creator essence. The creator was hiding, because it was tired of trying to keep the universe working and from the fight with is adversary - chaos.  At the end of the book, the creator allows the world to be destroyed and recreates it - except that planets are cubes and move in squares.  Yes - it was rather bizarre. Question involving discriminant of quadratic congruence in elementary number theory. Why isn't my Minecraft LAN server working? My LAN server won't let my cousin join me or me join my cousin. It won't show up on the multiplayer screen - it keeps saying "scanning for LAN servers" but it never finds it. I am at his house and we use different computers but it won't connect. How can I fix this? No more updates for Google Chrome 32-bit I am using Google Chrome 48.0 32-bit. Today when I launched Google Chrome, I got this message:    This computer will soon stop receiving Google Chrome updates because this Linux system will no longer be supported   I thought Ubuntu 14.04 is supported for five years, what's exactly happening here?  And on 64-bit Ubuntu, I get an error from Update Manager and apt-get update:  Failed to fetch http://dl.google.com/linux/chrome/deb/dists/stable/Release  Unable to find expected entry 'main/binary-i386/Packages' in Release file (Wrong sources.list entry or malformed file)   Some index files failed to download.   They have been ignored, or old ones used instead. Proving $a^2$ is even $\implies$ $a$ is even by contradiction For example, here are top five accounts in each site (this picture was taken when I was in Biology SE).    As you can see, all the badges are DNA, while Academia's badges should be hats, so on.  What do you think? Find full path of the Python interpreter? Conservation Of Angular Momentum of a falling stone I am currently stuck on the following question.   A stone is dropped from a stationary helicopter 500m above the ground, at the equator. How far from the point vertically below the helicopter does it land and in what direction? Solve this problem by conserving angular momentum.   My current interpretation is that when the stone falls in order to converse angular momentum the angular velocity must increase. This leads to the stone travelling to the east.   I equated the angular momentum at the start       L0=*(re+h)mVo  where re is radius of earth, h is the height above that, m is mass and Vo is inital velocity. To the angular momentum at any time  L=(re+h-1/2gt^2)m(Ve+Vo)  where the 1/2at^2 term comes from gravitational acceleration and Ve is the additional velocity.   I rearranged to find Ve and then integrated over the time it takes to fall the 500m in order to work out the extra distance the stone traveled. However, my answer is 1/2 what the answer should be. I have checked the maths and it seems to be fine. So I believe my set up is wrong. Any help would be appreciated. $\ker \phi = (x_1-a_1, ..., x_n-a_n)$ for a ring homomorphism $\phi: R[x_1, ..., x_n] \to R$ Let $R$ be a commutative ring, $a_1, ..., a_n$ its elements and  $\phi: R[x_1, ..., x_n] \to R$  defined by  $ \phi(f(x_1, ..., x_n)) = f(a_1, ... ,a_n)$  a ring homomorphism.  Prove: $\ker \phi = (x_1-a_1, ..., x_n-a_n)$  It is obvious that $(x_1 - a_1, ..., x_n -a_n) \subseteq \ker \phi$. I'm not sure how to prove the converse.  At this point I don't know any division algorithms for multivariable polynomials, only for the ones in $R[x]$(and the book from where I taken the exercise doesn't assume the reader to know something beyond basics of rings and ideals, and the division algorithm for $R[x]$). Though I know this could be solved for $i = 1$ by dividing by $x-a$:   Let $f(x) \in \ker \phi$, divide by $x-a: f(x) = q(x)(x-a) + r, f(a) = r = 0$, so $f(x) = q(x)(x-a) \in (x-a)$. Calculate all integer solutions $(x,y,z)\in\mathbb{Z}^3$ of the equation $x^2+y^2+z^2 = 2xyz$.   My Attempt:  We will calculate for $x,y,z&gt;0$. Then, using the AM-GM Inequality, we have  $$ \begin{cases} x^2+y^2\geq 2xy\\ y^2+z^2\geq 2yz\\ z^2+x^2\geq 2zx\\ \end{cases} $$  So $x^2+y^2+z^2\geq xy+yz+zx$. How can I solve for $(x,y,z)$ after this? (a) $S_k=\{A\subset\mathbb{N}: |A|=k\}$ for $k\in\mathbb{N}$  (b) $S = \bigcup_{k=1}^\infty S_k$   Work: For (a), I am not too sure about what approach I should use. I think finding a bijective function between the $S_k$ and $\mathbb{N}$ is hard to do . I also thought about using the Schroeder-Bernstein theorem and find injective functions $f:\mathbb{N}\rightarrow S_k$and $g:S_k\rightarrow\mathbb{N}$ in order to prove that $S_k$ and $\mathbb{N}$ are numerically equivalent. However, I have a hard time finding and proving these injective functions. I haven't really looked at (b) as I have yet to complete (a). How to get the last value of an ArrayList What graphics packages are there for creating graphics in LaTeX documents? Where to declare environment variables? What are correct places for:   Global environment variables meant to affect all users? User-specific environment variables? Why is my Mega Stone not in the location it should be? I upgraded my Mega Ring and have been looking for Mega Stones, and I found . However, the Mega Stone isn't in the place it's supposed to be, and I'm sure the location is right. Why isn't my Mega Stone here? What is a "year" in Westeros? Ubuntu 17.10 windows' menu in panel I installed the latest version of Ubuntu (17.10) , but the problem is, I can't find the menu bars of applications in the GNOME panel. For instance, the Chrome menu bar doesn't appear on the panel like in Ubuntu 17.04 and earlier versions. What TV movie had lost space cadets who piloted yellow tripod robots, and a squid bad guy? I'm trying to find a movie I watched on TV, probably in the 90s. I think it was a made-for-TV movie.  It was about a ship with an AI. The ship was crewed by young adults. I think they were cadets?   There was an accident (like a warp drive malfunction) and they end up in another part of space where they meet a female alien whose ship had been shot down.  I remember they had manned robots they would pilot and they took them to a planet to get upgraded and they are attacked by more manned robots. They had three legs and they were yellow, I think.  I also remember the baddie had a holo-projector or something like that which allowed him to change his appearance. He commanded a massive fleet and he worked for someone he spoke to in a video chat that looked like a squid. Bound states of the $V(x)=\pm \delta'^{(n)}(x)$ potential? The $\delta(x)$ Dirac delta is not the only "point-supported" potential that we can integrate; in principle all their derivatives $\delta', \delta'', ...$ exist also, do they?  If yes, can we look for bound states in any of these $\delta'^{(n)}(x)$ potentials? Are there explicit formulae for them (and for the scattering states)?  To be more precise, I am asking for explicit solutions of the 1D Schroedinger equation with point potential,  $$- {\hbar^2 \over 2m} \Psi_n''(x) + a \  \delta'^{(n)}(x) \Psi(x) \ = E_n \Psi_n(x) $$  I should add that I have read at least of three set of boundary conditions that are said to be particular solutions:   $\Psi'(0^+)-\Psi'(0^-)= A \Psi(0)$ with $\Psi(0)$ continuous, is the zero-th derivative case, the "delta potential". $\Psi(0^+)-\Psi(0^-)= B \Psi'(0)$ with $\Psi'(0)$ continuous, was called "the delta prime potential" by Holden. $\lambda \Psi'(0^+)=\Psi'(0^-)$ and $\Psi(0^+)=\lambda\Psi(0^-)$ simultaneusly, was called "the delta prime potential" by Kurasov   The zero-th derivative case, $V(x)=a \delta(x)$ is a typical textbook example, pretty nice because it only has a bound state, for negative $a$, and it acts as a kind of barrier for positive $a$. So it is interesting to ask for other values of $n$ and of course for the general case and if it offers more bound states or other properties. Is it even possible to consider $n$ beyond the first derivative?  Related questions  (If you recall a related question, feel free to suggest it in the comments, or even to edit directly if you have privileges for it)  For the delta prime, including velocity-dependent potentials, the question has been asked in   In the halfline $r&gt;0$, the delta is called "Fermi Pseudopotential". As of today I can not see questions about it, but  seems to be the same potential.  A general way of taking with boundaring conditions is via the theory of self-adjoint extensions of hermitian operators. This case is not very different of the "particle in 1D box", question  A general take was the question  A related but very exotic question is  because obviosly the point-supported interacctions have a peculiar scaling  Comments  Of course upgrading distributions to look as operators in $L^2$ is delicate, and it goes worse for derivatives of distributions when you consider its evaluation $&lt;\phi | \rho(x) \psi&gt;$. Consider the case $\rho(x) = \delta'(x) = \delta(x) {d\over dx}$. Should the derivative apply to $\psi$ only, or to the product $\phi^*\psi$? dpkg: error: dpkg status database is locked by another process I just wondered if somebody could tell me what this means:  E: dpkg was interrupted, you must manually run 'sudo dpkg --configure -a' to correct the problem. reidsr@ubuntu:~$ sudo dpkg --configure -a dpkg: error: dpkg status database is locked by another process reidsr@ubuntu:~$    How do I run sudo dpkg --configure -a  manually?