3 particles A,B and C are situated at the vertices of an equilateral triangle ABC of side d at t=0 .
Case of the 'mice problem' for $n=3$
How to configure idle period for auto locking screen I just installed a fresh Ubuntu 12.04 (Precise Pangolin).   I noticed that, there is no screensaver settings, which is fine. I like to control the period of time after which the blank screen is shown,which automatically locks the screen.  I do not want to enable screensaver. I only wish to be able to change the idle time period required to lock the screen automatically. It seems to me, it is by default around 10-15 minutes. Is there a technical reason Android update story is so bad? Is there a technical reason why Android phones general lag a lot behind the stable released version of Android?    This applies to both new phones, for example a recent trip to the phone shop everything was 4.0 to 4.2.1, KitKat could not be seen. And also old phones, my girlfriend's iPhone 4 had an OTA update to the latest OS, this is a July 2010 phone, whilst a July 2010 Android is basically a paperweight.    Presumably Android itself doesn't concern itself with the actual hardware, and thus talks to the OS via abstractions? I guess then the handset maker just provides the drivers for the specific hardware, thus I can't see the issue with pushing OTA updates if the ABI remains stable (my phone doesn't grow new hardware features). English (other than American English) has a clear differentiation between the two words. Both are about translocating something. In "bring" the something of somebody is moved to where the speaker is currently situated. "Take" is used to translocate something or somebody to a place that the speaker is not currently at.   You cannot “bring” your books to school if you are currently at home. You can only take them to school. Most of the time one can get the meaning from the context of the sentence but it can get very confusing when the other party is on the telephone and you do not know their location.   Why does American English not differentiate and when did it lose the differentiation? Remote start up a machine that is in the shut down state? Possible Duplicate:          May I know how can one remote start up a machine that is in a shut down state? In the sentence: "I didn't know she had a son,"   Can I say "I didn't know she has a son" instead, because he is a teenager now?  Or are both correct? Is there any way to automatically unwrap UV map proportionally to object or "world" size?  For example:  I've made two cubes, one is two times bigger than other (scale is applied). Then I unwrapped texture with Smart UV project which will try to span all faces on whole texture space(0 to 1) so bricks on left cube will be bigger than bricks on right cube.   But what I want to achieve is this:     In broader context:  When I import model from Archicad (in form of OBJ) all objects have UV's in some scale (so all bricks have the same size on every imported object). And when I want to create custom object in scene I have to manually scale UV's to adjust bricks size for every new object (instead of scaling to one constant parameter). How to find Mac admin password not reset Mac admin password What would happen if every person in the world gathered at a minimum possible area and jumped all at once? Would that have any effect on Earth? How do I scan for Wireless Access Points? How to open port via SSH tunnel? There is a system B with the following open servers: I have a web server listening on port 80 and a ssh server listening on 22. However, only port 22 is publicly available. Now, I would like to create some kind of tunnel, so that I can access B:80 from A. However, my client computer A that would like to connect to the system B is not publicly open, either.  So, all I have is a client computer A from where I would like to access the server B and, there, an open port 22. On A, no port is open or can be opened.  What (I think) I would need is to open locally (on A) some port that connects in some way through port 22 of B to port 80 on B.  Is this possibly without using any man-in-the-middle open servers with multiple ports? The real fastest gun in the west Are the questions in the about page taken from real posts? If not, who designs them?  Particularly, why does this specific answer have a date from before the question was asked? I am creating a type of adventure map. Once you enter the map, you step on some pressure plates that are supposed to seamlessly close the wall behind you. For some reason this command does not work when in a command block or just in text. Here is the command:  /fill -17 4 -109 -18 5 109 minecraft:light_gray_concrete   The output it gives me is "That position is not loaded". I am on a singleplayer superflat world in 1.14.3. Any help would be very appreciated! How to download all required Ubuntu drivers I know it existed as sort of a folder in Windows Explorer in at least Windows XP, but I just can't seem to find it in Windows 7...  How can I take a picture with my webcam in Windows 7 without using any 3rd party tools? How to get the current directory in a C program? I'm making a C program where I need to get the directory that the program is started from.  This program is written for UNIX computers. I've been looking at opendir() and telldir(), but telldir() returns a off_t (long int), so it really doesn't help me.   How can I get the current path in a string (char array)? I use the listings package for code listings and I turned the line numbers on. But they appear left of the paragraph. I want them inside the paragraph. In the documentation it looks just right. Here is my code:  \documentclass[12pt,a4paper]{scrartcl} \usepackage{listings} \lstset{numbers=left} \begin{document} \section{Test} Test \begin{lstlisting}     test() \end{lstlisting} \end{document} macOS Catalina: "App is damaged and can't be opened. You should move it to the trash." Experiencing a problem with several apps after installing macOS Catalina.  When the app is downloaded from the internet I get the error:     "APP NAME" is damaged and can't be opened. You should move it to the trash.   Any workarounds to bypass macOS gatekeeper for specific apps? Why is Ubuntu 14.04 so slow on my laptop? $A^A$ in category of graphs (reference is Lawvere/Schanuel, Session 31, Ex. 1)  I'm trying to calculate the exponential object $A^A$ and its evalution map $e \colon A \times A^A \to A$ in the category of graphs, where $A$ is the "arrow graph" (ie. one arrow and two dots).  In the following, $D$ is the graph with one dot and no arrows, $1$ is the terminal object in this category (graph with one dot and one arrow, the loop).  So far I have:   The points of $\mathbf{1}\to A^A$ correspond to the maps $A\to A$ (via two standard isomorphisms), and since $\mathbf{1}$ is the loop, and there is one map of graphs $A \to A$, there is one loop in $A^A$. The dots $D\to A^A$ correspond to the maps $A \times D \to A$, of which there are four, hence four dots in $A^A$. The arrows $A \to A^A$ correspond to the maps $A \times A \to A$, of which there are four, hence four arrows in $A^A$.   But I'm stuck on how to put these together to constitute $A^A$ and its evaluation map. Center of $D_6$ is $\mathbb{Z}_2$ The center of $D_6$ is isomorphic to $\mathbb{Z}_2$.   I have that $$D_6=\left&lt; a,b \mid a^6=b^2=e,\, ba=a^{-1}b\right&gt;$$ $$\Rightarrow D_6=\{e,a,a^2,a^3,a^4,a^5,b,ab,a^2b,a^3b,a^4b,a^5b\}.$$ My method for trying to do this has been just checking elements that could be candidates. I've widdled it down to that the only elements that commute with all of $D_6$ must be $\{e,a^3\}$ but I got there by finding a pair of elements that didn't commute for all other elements and I still haven't even shown that $a^3$ commutes with everything. For example, I have been trying to show now that $$a^3b=ba^3$$ and haven't gotten too far yet but if I had to answer a question like this on the exam, I feel it would be difficult, is there any kind of trick or hints other than brute force using the relations to get that $a^3$ commutes with everything?  For the solution once I have that the center of $D_6$ is what I think then as there is only one group of order $2$ up to isomorphism, it must be isomorphic to $\mathbb{Z}_2$.  Ideally a way that doesn't appeal to $D_6$ as symmetries of the hexagon if that seems possible.