Proving that the groups $S_3$ and $D_6$ are isomorphic
Proof that $S_3$ isomorphic to $D_3$
How to find all the tables in MySQL with specific column names in them? Mapping/texturing inside of a box I'm trying to replace the content of a box in a video, I have used the tracking system to match the movement of the video box with the interior of the one rendered in Blender, but I am running trough what seems a simple thing but I can't manage to get done.   I want the outside faces of the box to be invisible while hiding the inside of the box where the front wall of the box hides it, and the inside of the box to be rendered where visible. To do that I thought it would be as simple as making the face normals point to the inside of the box and giving a color only to the faces where normals are pointing to. But I can't manage to get that, am I going the wrong road? How can I achieve my goal? Creating polygon from hole in QGIS? dimension of a subspace spanned by two subspaces If $M$ and $ N$ be the subspaces of a vector space $V$ then prove that  $(\dim M) + (\dim N) = (\dim M+N) + (\dim M \cap N)$. How does Cooper get out of the black hole? In the movie Interstellar,  Cooper (played by ) enters a black hole and sends a message to Murph (his daughter). Later, he is found by rangers, but I don't understand how he gets out of the black hole?  As far as I know, nothing can get out of a black hole, as it has extremely high gravity. How can I create Light Streaks in Cycles? Create hexagonal mesh on 3D Parametric Plot and 3D spheres? Traces of all positive powers of a matrix are zero implies it is nilpotent Let $A$ be an $n\times n$ complex nilpotent matrix. Then we know that because all eigenvalues of $A$ must be $0$, it follows that $\text{tr}(A^n)=0$ for all positive integers $n$.  What I would like to show is the converse, that is,      if $\text{tr}(A^n)=0$ for all positive integers $n$, then $A$ is nilpotent.   I tried to show that $0$ must be an eigenvalue of $A$, then try to show that all other eigenvalues must be equal to 0. However, I am stuck at the point where I need to show that $\det(A)=0$.  May I know of the approach to show that $A$ is nilpotent? The stress tensor can be written as: $$\sigma_{ij}=-p \delta_{ij}+\sigma'_{ij}\label{1}\tag{1}$$ where $\sigma_{ij}'$ is called the extra stress tensor.   From what I understand pressure is pressure is force per unit area, so that the force acting on the surface $d\vec A$ is given by:  $$\vec F=-p d\vec A\label{2}\tag{2}$$ (This has the effect that the force on an infinitesimally thin surface due to a continuous pressure is zero). However, $\sigma_{ij}$ represent the force in the $i$ direction on a surface with normal in the $\hat e_j$ direction. So the force acting on a surface $d \vec A$ must be: $$F_i=\sigma_{ij}dA_j\label{3}\tag{3}$$ Equations (2) and (3) clearly do not agree (even if we look soley at the force in the $d\vec A$ direction they don't agree). So my question is what is the exact meaning of pressure in expression (1) and why do we not have: $$\sigma_{ii}=-p$$ Direct link for PDF files in SkyDrive/OneDrive I want to make a direct link to a document at SkyDrive, so that I'll see only the PDF at the browser, not any of the SkyDrive chrome.  For example, if you click , you will go automatically to the PDF file.  Is there any way to do this? Can I start and stop a tile floor job? I am tiling my bathroom floor and don't soon have a full day to dedicate to the job. Is it ok to lay down a few tiles each day and come back to the job when I have time? I would only lay mortar for the tiles I have time to lay each day.    My concern is that the mortar wouldn't properly "join" to the previously laid sections of tile and cause an inferior result, but I'm not really basing this concern on any facts. That is what I'm hoping to learn with this question. Why can't I travel onwards if my bag wasn't going to make the flight? I was flying KLM from the UK to the USA with a short layover in Amsterdam.  Because of delays in the UK, I almost missed my flight.  The flight attendant told me my bag wasn't going to make it, but if I walk fast, my gate is just two over.  When I got to the gate, they had already closed the doors, but the counter was opened - I mentioned that my bag was not going to make it, but that's okay.  She said, "hold on," got onto her walkie-talkie, and said,  "Yep, that's what I thought: you can't fly if your bag's not going."  I originally thought that it might be a security concern, but that doesn't really make any sense.  Why can't I travel if my luggage doesn't make the connection?  EDIT: I should clarify that I have no beef with KLM - they treated my overnight in Amsterdam professionally and helpfully; I'm just curious what the reason would be. In the begining of "" episode (Star Trek Next Generation 6x16) an Yridian tells Worf, that he has a certain information,      that Worf's father is still alive (apparently not killed in ) and is held in a prison camp on Carraya IV.   Yridian is an information broker and agrees to reveal details (i.e. location) only for a price.      Worf agrees.   How or with what Worf would pay for this? There is no economic factor inside the Federation (no money is being used) and I don't recall anything, Worf would have on board Enterprise, that would have enough value for an information this kind. Possible point location algorithm I need to calculate possible point location based on its speed and some other factors. For example, there is a man in the middle of the forest and I need to calculate his possible location at some time periods. There are few facts about his movement:   His speed differs at certain periods of time - it can be raining, or it can be super hot - speed lowers / increases; Some objects in space - swamps, rocks - can lower his speed as well; At some time periods the man does not move at all.   So, here is the question - is there any algorithm that can calculate possible location of the man based on following parameters? The output should be a polygon for every given time_period.  {   time_periods: [{     from: 2012-12-12T20:00:00,     to: 2012-12-12T22:00:00,     speed: 5   }, {}],   objects: [{     geodata: POLYGON(...),     speed_modifier: 0.5   }, {}] }   Generated polygons will be visualized on the map afterwards. Got less output with print0 option on find? I have read the man page and other references, but I am still confused by the behavior of find with -print0 option.  -print0      This primary always evaluates to true.  It prints the pathname of              the current file to standard output, followed by an ASCII NUL              character (character code 0).   First command:  $ find /some/path/ -iname "*intro*jpeg" -o -iname "*intro*jpg" 2&gt; /dev/null /some/path//asdf199Intro-5kqlw.jpeg /some/path/199intro-2jjaj.JPEG /some/path/199intro-3.jpg /some/path/wuer199intro-4.JPG /some/path/xbzf199INTRO-1.jpg   Second command:  $ find /some/path/ -iname "*intro*jpeg" -o -iname "*intro*jpg" 2&gt; /dev/null -print0 /some/path/136intro-3.jpg/some/path/wuer136intro-4.JPG/some/path/xbzf136INTRO-1.jpg   I can see that the the filenames from the second command are null character separated, but why do I get 3 output as opposed to 5 above? Will a PCI Express x16 3.0 card work in a PCI Express x16 slot? I have a motherboard with a PCIexpress x16 slot.  I want to purchase a card called AMD Radeon HD 7770, which uses PCIe version 3.0.  Is that backwards compatible? Are there any concrete rules that say which words (parts of speech) in a title should start with a capital letter? What would be a correct capitalization for the title of this question? What happens to waves when they hit smaller apertures than their wavelenghts? How permanent magnets work?Are they working with motion of electrons? Why does my grep expression need to use $'string' to match tab characters?