What is the difference between auto hosted, provider hosted and sharepoint hosted app?
Differences between hosting options for SharePoint apps
Why is the Yang-Mills gauge group assumed compact and semi-simple? What is the motivation for including the compactness and semi-simplicity assumptions on the groups that one gauges to obtain Yang-Mills theories?  I'd think that these hypotheses lead to physically "nice" theories in some way, but I've never, even from a computational perspective. really given these assumptions much thought. Computing matrices of linear transformation under different basis Came across a problem in my textbook and I am having trouble with it, the book provides an answer but no workings. Looking to get an explanation of what is going on  help I prepare for an exam. If we let $T : \mathbb R^2 \to \mathbb R^2$ be a linear transformation. Consdider two bases $V$ and $W$ of the vector space $\mathbb R^2$, where $V=\{v_1,v_2\}$ with $ v_1 =  \begin{bmatrix} -2 \\1   \end{bmatrix}$ and  $ v_2 =  \begin{bmatrix} 1 \\1   \end{bmatrix}$ and where $W = \{w_1,w_2\}$ with  $ w_1 =  \begin{bmatrix} -1 \\4   \end{bmatrix}$ and  $ w_2 =  \begin{bmatrix} 0 \\1   \end{bmatrix}$. Suppose that  $ A =  \begin{bmatrix} 1&amp;2   \\-1 &amp;4    \end{bmatrix}$ is the matrix of $T$ under basis $W$. I need to find the matrix $B$ the matrix of $T$ under basis $V$.  The solution is:   $ B = P^{-1}AP$ = $   \begin{bmatrix} -30&amp;22   \\-48 &amp; 35    \end{bmatrix} $  But I don't know why. What countries allow me to pass their borders visa-free?  Am I allowed to visit and work in EU and Schengen countries? Creating unnumbered chapters/sections (plus adding them to the ToC and/or header) Prove $\operatorname{rank}(AB) = \operatorname{rank}(B)$ I am given the info that A is an invertible  m by m matrix and B is a m by n matrix. By solving for the null space $ABx=0$, I get $A^{-1}ABx=A^{-1}0$, therefore $Bx=0$. I concluded that the null spaces of A and AB must be equivalent, and therefore the nullity(AB) = nullity(B) = some number p. Therefore rank(AB) = n-p = rank(B)   (because both AB and B are m by n matrices).   Is this proof valid, specifically the null space step? I just installed Oracle's Java version 7u7 on my Mac (running OSX Mountain Lion). However, when I run java -version it still displays the old version (6u29).    How do I fix this? Do I even need to fix this? What version will browsers (Firefox) use in this case? And what version will be used when I run Java applications directly?  I've seen  but this doesn't work in my situation (probably because this question is about the JRE and the other question about the JDK). In my case the Java Preferences app only displays Java 6 versions (32 bit and 64 bit).    Update:   which java points to /usr/bin/java /usr/bin/java is a symlink to /System/Library/Frameworks/JavaVM.framework/Versions/Current/Commands/java /System/Library/Frameworks/JavaVM.framework/Versions/ only contains the folder A (awesome version name) - which Current points to. Limiting range of value types in C++ Remove a part of a list of names I have some files and each files have distinct name but all of them have the same "-statement" at the end like this:  flower-statement.mp3 leave-statement.mp3  ball-statement.mp3 goal-statement.mp3   So I want to remove this: -statement  Is that possible? Is there any online resource that can tell me what visa rules are for passport holders of a specific country? When thinking about travelling, I often have to think about a place to visit, and then look up visa rules for that particular country. This can be a fairly painful process because official government sites can often be hard to find, and advice on (say) guidebooks or Wikitravel tends to be generic.  Is there any resource where I can enter my nationality/residency, and then look up a list of visa rules for various countries? How is the amplitude of light related to number of photons? If you increase the number of photons leaving a light source you increase the brightness/intensity, so it could be said that intensity is directly proportional to number of photons. However intensity is directly proportional to amplitude squared, so this leads me to wonder that if you increase the amplitude of a light wave, are you just creating more photons rather than affecting each individual photon in some way? Are these solutions of $2 = x^{x^{x^{\:\cdot^{\:\cdot^{\:\cdot}}}}}$ correct? Facebook must have changed something again because I cannot find out how to view the list of subscribers.  In Googling for this, I came upon this question:    However, it doesn't take me to my list os subscribers.  Where do I view this list now?  Please include a screenshot and highlight the link I need to click on.  This way, when Facebook changes their layout again, your screenshot will at least clue future inquirers in on this fact so they know they're not going crazy.  Edit  Here's what I see when I log into Facebook: Show that $\tan{(\pi/7)} \tan{(2\pi/7)}\tan{(3\pi/7)}=\sqrt{7}$ How do I check an iOS device's battery health? Point reflection over a line I'm having trouble understanding the solution presented below (It's from a textbook). I tried to get something similar, but to no avail. Help me find the way he derived those a,b,x2 and y2 expressions.   Point p is a point which we want to reflect (It's a simple structure with two integers x and y representing coordinates on a 2d plane); (x0,y0) and (x1,y1) are coordinates of endpoints of a line.  Expected result is a new point with reflected coordinates.   Point mirror(Point p, int x0, int y0, int x1, int y1) {     double dx,dy,a,b;    long x2,y2;    Point p1; //reflected point to be returned      dx  = (double) (x1 - x0);    dy  = (double (y1 - y0);     a   = (dx * dx - dy * dy) / (dx * dx + dy*dy);    b   = 2 * dx * dy / (dx*dx + dy*dy);     x2  = Math.round(a * (p.x - x0) + b*(p.y - y0) + x0);     y2  = Math.round(b * (p.x - x0) - a*(p.y - y0) + y0);     p1 = Point((int)x2,(int)y2);      return p1;  } What happened to the Grid at the end of Tron Legacy? Plot above desired region A get() like method for checking for Python attributes If I had a dictionary dict and I wanted to check for dict['key'] I could either do so in a try block (bleh!) or use the get() method, with False as a default value.  I'd like to do the same thing for object.attribute. That is, I already have object to return False if it hasn't been set, but then that gives me errors like     AttributeError: 'bool' object has no attribute 'attribute' Suppose there are two face down cards each with a positive real number and with one twice the other. Each card has value equal to its number. You are given one of the cards (with value $x$) and after you have seen it, the dealer offers you an opportunity to swap without anyone having looked at the other card.  If you choose to swap, your expected value should be the same, as you still have a $50\%$ chance of getting the higher card and $50\%$ of getting the lower card.  However, the other card has a $50\%$ chance of being $0.5x$ and a $50\%$ chance of being $2x$. If we keep the card, our expected value is $x$, while if we swap it, then our expected value is: $$0.5(0.5x)+0.5(2x)=1.25x$$ so it seems like it is better to swap. Can anyone explain this apparent contradiction? NFL overtime: after a field goal, clock runs out on second team's possession Under the NFL's current "modified sudden death" overtime rules, if the first team scores a field goal, the second team is entitled to one more possession.  What happens if the clock runs out during that possession?  Suppose the score is tied 20-20 at the end of the 4th quarter. Team A wins the overtime coin toss and receives the kickoff to begin overtime.  After a long slow drive, Team A scores a field goal to make the score 23-20.  Now they kick off to Team B.  Team B is not able to score, and the overtime period ends with Team B still in possession.  What happens?   is not very explicit on this point.  Article 4 (a) says:     There shall be a maximum of one 15-minute period, even if the second team has not had an opportunity to possess the ball or if its initial possession has not ended. If the score is tied at the end of the period, the game shall result in a tie.   I think this means that Team A wins, 23-20, but I am not completely sure.  Has this ever happened in a regular-season NFL game?