Starfleet... never bothered to check on our progress   -Khan, Star Trek II, the Wrath of Khan  I understand that the odds of the neighboring planet exploding and causing the other planet to shift into its orbit in such a way as to utterly destroy the climate on said neighbor is very very low. But it seems rather irresponsible to me not to at least pay them a visit.   At the end of Space Seed, it seems that this was a legitimate Federation punitive measure (given Kirk et al busted out the fancy uniforms) which to me made it seem like the Federation was somewhat obligated to ensure they didn't die down there.   What gives? Why didn't Starfleet, at the very least, do a drive by? (In canon, please)
In Star Trek II: The Wrath of Khan (the one from 1982, not the recent remake), Khan yells "This is Ceti Alpha V!" and they're all like this is a big surprise, we didn't know.  If they had previously charted the planet, wouldn't the computer have told them the planets weren't quite where they should be based on earlier visits? I mean, we can predict the next hundred transits of Venus, shouldn't 23rd century explorers be able to predict where the Ceti planets are less than twenty years after their first visit?
This might be a completely wrong question, but this is bothering me since many days ago. Given the mass (Sun) curves the space around it, gravitation is the result of such curved space (Correct me if I am wrong, source: A Documentary film). Given any point on a circle with center same as center of the mass, curvature in the space should be equal (Intuition).   Planets rotate around the Sun because of the curve in the space they should follow a circular path and the distance between planet and Sun should be at a distance.  Given the fact that earth has a elliptical orbit around the sun, and the distance between Earth and Sun varies according to position of the earth. Why do we have a elliptical orbit not a circular orbit. We currently have about 50 pages, each of which I want a user (eg, bob, rob, smith) to be able to edit only 1 page.  For example, bob &amp; smith each have their own page.  I do not want bob to be able to edit smith's page.  I want bob to ONLY be able to edit bob's page.  I don't care if he can see other pages. Looking through the user roles, I don't see a way to currently to do this- I only see how to allow restrict access on a global scale.  Are their any plugins to help restrict edit access per user, or roles restricted to editing specific pages and I can just add 1 user per role?  Or was there a way to do this with default settings I missed. Given $f = f(u(t), t)$, is it possible to find the following derivative? ($f$,$u \in \mathbb{R}^n$, $t \in \mathbb{R}$)  $$ \frac{\partial f}{\partial||u||^2_2} $$  I am aware of the following derivatives:  $$ \frac{\partial||x||^2_2}{\partial x} = \frac{\partial ||x^Tx||_2}{\partial x} = 2x $$  So I can invert it to give me (elementwise division in the RHS)  $$ \frac{\partial x}{\partial||x||^2_2} = \frac{1}{2x} $$  This step does feel like abuse of notation I find it hard to convince myself of its validity.  If it's right though, I could just apply the chain rule to find  $$ \frac{\partial f}{\partial u} \frac{\partial u}{\partial||u||^2_2} $$  However, knowing that both $f$ and $u$ are a function of $t$, I am somehow doubting my own reasoning. Or does that just mean that the derivative will still be a function of $t$ and I have nothing to worry about? Can anyone shed some light?  UPDATE: I'm now doubting the existence of  $$ \frac{\partial u}{\partial ||u||^2_2} $$  because $u = u(||u||_2^2)$ is not injective. Is the inversion step I did above legitimate? Is there another possible approach? How do I move clock to the right end of GNOME 3 Panel from the middle? Given a set $\mathcal{S}$ of size $n$, let a $k$-partition of $\mathcal{S}$ be a grouping into $k$ disjoint classes $$(S_1 ,S_2,...,S_k)$$   Where the $S_i$ do not necessarily contain the same number of elements.  Let $C(S_1, S_2, ... S_k)$ be the set of combinations which can be made by taking exactly one element of each class, (i.e. $C(S_1, S_2, ... S_k)$ is the Cartesian Product $S_1 \times S_2 \times ...\times S_k$). For a given $(n,k)$, what is the minimum number of k-partitions $N$ such that  $\bigcup\limits_{i=1}^{N} C(S_1^{(i)}, S_2^{(i)}, ...,S_3^{(i)}) = $ All Possible Combinations  Example:  for $n=4$ and $k=2$, $\mathcal{S} = \{1,2,3,4\}$ we can choose:  $$ S^{(1)} = \left\{\left\{ 1, 2\right\}, \left\{ 3, 4\right\}\right\}$$ $$ S^{(2)} = \left\{\left\{ 1, 3\right\}, \left\{ 2, 4\right\}\right\}$$  Then $$C_{1} = \left\{\left\{ 1, 3\right\} ,\left\{ 1, 4\right\},\left\{ 2, 3\right\},\left\{ 2, 4\right\}\right\}$$ $$C_{2} = \left\{\left\{ 1, 2\right\} ,\left\{ 1, 4\right\},\left\{ 2, 3\right\},\left\{ 3, 4\right\}\right\}$$  and $C_1 \cup C_2 =$ All possible combinations and $N=2$. What kind of lubrication should I use for a lock? I recently made the Yale lock on my front door much easier to open by spraying some WD-40 in there.  However, I just saw  on WD-40 not being a “true” lubricant, and wondered whether it was appropriate to use on Yale locks? I installed Android studio some time ago using the following suggested method:     To set up Android Studio on Linux:      Unpack the downloaded Tar file,   android-studio-ide--linux.zip, into an appropriate location   for your applications. To launch Android Studio, navigate to the   android-studio/bin/ directory in a terminal and execute studio.sh. You   may want to add android-studio/bin/ to your PATH environmental   variable so that you can start Android Studio from any directory.   Follow the links to install the SDK outside of the Android Studio   directories.   For whatever reason it has become corrupt and insists I must un-install and re-install. I can't for the life of me find how to un-install it however.  I didn't use apt-get so I can't do apt-get remove.  Does anyone have any suggestions? I have a vector file containing thousands of points. Where points are within x distance from each other, I wish to delete one of the points and keep the other (either by snapping to one point, or simply erasing one of the two points)  However, in Whitebox the vector cleaning tool only works with polygons and lines.  Is there some other way I can do this with my shapefiles? Disk Utility won't Unmount HD for formatting Run a command before & after ubuntu apt upgrade & unattended-upgrades Capitalization of "Theorem 1" in mathematics papers In many mathematics papers, I read sentences like:     With an appeal to Theorem 4.5 we get …   Is the capitalization of theorem in this case correct? If it is correct why do we capitalize the word? Does WaitForMultipleObjects() reset all auto-reset events? Prove that if a function's average is nondecreasing then the function is nondecreasing. Let $\omega:\mathbb{R}_+\to\mathbb{R}_+$ such that $\omega(0) = 0$ and $\xi(s) = \frac{1}{s}\int\limits_{0}^s \omega(t)dt$ is nondecreasing, i.e., $\forall s,s': s\leq s'$, $\xi(s)\leq \xi(s')$. Show that $\omega(t)$ is nondecreasing a.e., i.e. find a function $w(t)$ such that $w$ is nondecreasing and $\omega = w$ a.e.  I was able to show the reverse implication easily, that if $\omega$ is nondecreasing then $\xi$ is nondecreasing. This way seems more difficult. elementary row operation change the eigenvalue of a matrix How to create a shortcut that executes an xdotool command to simulate a key press? I'm trying to simulate a media key press using a custom shortcut.  So far, I've been able to achieve the simulation I need using the command:  xdotool key XF86AudioPlay   It works perfectly, it pauses or starts the music player every time it is run.  The problem comes when trying to run it as a shortcut.  First I tried to run an alias with a custom shortcut, but it did not work.  As explained on :     The commands run by keyboard bindings are not parsed via a shell. Your best bet is to create a directory bin in your homedir.   Next I created the suggested script and named it simplay:  #!/bin/sh xdotool key XF86AudioPlay   It is located inside a bin folder which is part of the PATH, this works fine and can be run from any location.  When trying to create the Custom Shortcut, I was unable to get it to execute, the configuration is the following:  Name: test Command: simplay  Shortcut: Ctrl+Alt+R   After searching a bit more I found another way to execute the shortcut:  gnome-terminal -e simplay   I tried it on a terminal and noticed that when executing it it would rapidly open a new terminal window, execute the child process, pausing the music and immediately close the window.  I changed the command on the shortcut and when hitting it I noticed the same behavior opening a terminal and immediately being closed but this time the child process did not pause the music, which makes me think that the script has been called on all my previous attempts but it is somehow not being able to execute.  How can I solve this problem according to your knowledge? Configure Postfix to use external MX servers for delivery of local mail if user is unknown What is the distribution of the sum of non i.i.d. gaussian variates? If $X$ is distributed $N(\mu_X, \sigma^2_X)$, $Y$ is distributed $N(\mu_Y, \sigma^2_Y)$ and $Z = X + Y$, I know that $Z$ is distributed $N(\mu_X + \mu_Y, \sigma^2_X + \sigma^2_Y)$ if X and Y are independent.  But what would happen if X and Y were not independent, i.e. $(X, Y) \approx N\big( (\begin{smallmatrix} \mu_X\\\mu_Y \end{smallmatrix}) , (\begin{smallmatrix} \sigma^2_X &amp;&amp; \sigma_{X,Y}\\ \sigma_{X,Y} &amp;&amp; \sigma^2_Y \end{smallmatrix}) \big) $  Would this affect how the sum $Z$ is distributed? Proving that the difference of the terms of a sequence, multiplied by $n$ converge $x^a - 1$ divides $x^b - 1$ if and only if $a$ divides $b$ Let $x &gt; 1$ and $a$, $b$ be positive integers. I know that $a$ divides $b$ implies that $x^a - 1$ divides $x^b - 1$. If $b = qa$, then  $$x^b - 1 = (x^a)^q - 1^q = (x^a - 1)((x^a)^{q-1} + \ldots + x^a + 1).$$  I'm interested in the converse of the statement. If $x^a - 1$ divides $x^b - 1$, does this imply that $a$ divides $b$? What is "superuser" and how do I get that privilege?