User ivan meir - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T17:28:36Z http://mathoverflow.net/feeds/user/7113 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/23113/is-there-any-geometry-where-the-triangle-inquality-fails/97383#97383 Answer by Ivan Meir for Is there any geometry where the triangle inquality fails? Ivan Meir 2012-05-19T09:44:28Z 2012-05-19T09:44:28Z <p>The reverse triangle inequality|x+y|>|x|+|y| holds in the Minkowski Space of Special Relativity for two timelike vectors in the same direction. So geometries that deny the triangle inequality in some signficant way can be very important I guess.</p> http://mathoverflow.net/questions/18100/theorems-with-unexpected-conclusions/29730#29730 Answer by Ivan Meir for Theorems with unexpected conclusions Ivan Meir 2010-06-27T20:18:19Z 2010-06-27T20:18:19Z <p>How about the Cook-Levin theorem - boolean satisfiability is NP complete. Though the consequence that "if there exists a polynomial time algorithm for boolean satisfiability then all problems in NP can be solved in polynomial time" may fit the bill better!</p> <p>I mean what does boolean satifiability have to do with finding hamiltonians on graphs or finding shortest roots in networks?!</p> <p>Ivan</p> http://mathoverflow.net/questions/5892/what-is-convolution-intuitively/29729#29729 Answer by Ivan Meir for What is convolution intuitively? Ivan Meir 2010-06-27T20:00:09Z 2010-06-27T20:00:09Z <p>If you convolve an image with a discrete matrix of values - so like a function that is zero outside a few pixles then you can create almost an unlimited number of filtering effects around each point. Fof example you can do some kind of averaging or weighted integration - which looks like blurring as Professor Tao mentions if you use a matrix whose values drop off smoothly, radially from the centre - a bump. You can also compute directional derivatives, look for edges, circles, blobs, steps - basically anything you like. </p> <p>The interpretation in terms of multiplication of Fourier coeficients is interesting and makes applications of the above in reality fast, especially if the filter is fixed, because you can use the Fast Fourier Transform on both images but you only need to update one of them. However I a not sure how intuitive it is!</p> <p>I'm not sure I have added much additional information but I hope this helps anyway,</p> <p>Ivan</p> http://mathoverflow.net/questions/18100/theorems-with-unexpected-conclusions/29730#29730 Comment by Ivan Meir Ivan Meir 2010-06-28T02:22:53Z 2010-06-28T02:22:53Z I think that if you knew NP completness existed already then you might guess that SAT is NP complete, however the really surprising thing is that there are so many different and varied NP complete problems. I also think that one has to bear in mind the fact that with hindsight many ideas look more obvious than they were at the time!