User andrew homan - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T02:15:08Z http://mathoverflow.net/feeds/user/96 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/50082/approximate-algorithms-for-poissons-equation-pde/55553#55553 Answer by Andrew Homan for Approximate Algorithms for Poisson's Equation (PDE) Andrew Homan 2011-02-15T21:22:16Z 2011-02-15T21:22:16Z <p>You can modify the method <a href="http://www.everything2.com/title/Brownian+motion+solves+a+PDE?lastnode_id=124" rel="nofollow">described here</a> for the Laplace equation to work for Poisson.</p> http://mathoverflow.net/questions/39866/are-local-noetherian-rings-with-principal-maximal-ideal-pir Are local, Noetherian rings with principal maximal ideal PIR? Andrew Homan 2010-09-24T15:02:44Z 2010-09-24T15:02:44Z <p>A question asked by a friend. I believe it's false, but lack a decisive counterexample.</p> <p><a href="http://mathoverflow.net/questions/36611/is-a-valuation-domain-pid-when-its-maximal-ideal-is-principal" rel="nofollow">This question</a> shows that it is true for valuation rings, but I know too little about them.</p> <p>In the wider context, a solution to this problem would provide another proof that Artinian local rings whose maximal ideal is principal are principal ideal rings by shifting from Artinianness to Noetherianness instead of exploiting the nilpotence of the maximal ideal.</p> <p>I'm tagging this commutative-rings because those are the only ones I really care about, but a noncommutative example would be just as decisive.</p> http://mathoverflow.net/questions/16010/do-separable-and-normal-have-topological-meanings-for-fields Do separable and normal have topological meanings for fields? Andrew Homan 2010-02-22T01:34:50Z 2010-02-22T02:21:28Z <p>The terminology would suggest that a separable field extension is so because the resulting field extension has some sort of separable topology, and that a normal extension corresponds to one with a normal topology.</p> <p>I imagine this is true, or else they wouldn't have named them in such a way.</p> <p>Also, I'm not sure what subfield this falls under, so if you could suggest additional tags, that would be great as well.</p> http://mathoverflow.net/questions/8756/examples-of-algebraic-closures-of-finite-index Examples of algebraic closures of finite index Andrew Homan 2009-12-13T14:33:03Z 2010-01-07T14:57:19Z <p>So there are easy examples for algebraic closures that have index two and infinite index: $\mathbb{C}$ over $\mathbb{R}$ and the algebraic numbers over $\mathbb{Q}$. What about the other indices?</p> <p>EDIT: Of course $\overline{\mathbb{Q}} \neq \mathbb{C}$. I don't know what I was thinking.</p> http://mathoverflow.net/questions/71287/tanh-version-of-a-fourier-transform Comment by Andrew Homan Andrew Homan 2011-07-26T06:07:23Z 2011-07-26T06:07:23Z Yes. I don't have a reference for the inversion formula for the X-ray transform, but one should be able to follow the procedure for the Radon transform given here: <a href="http://wwwmath.uni-muenster.de/num/inst/natterer/Preprints/2000/natterer/paper.pdf" rel="nofollow">wwwmath.uni-muenster.de/num/inst/natterer/&hellip;</a> http://mathoverflow.net/questions/71287/tanh-version-of-a-fourier-transform Comment by Andrew Homan Andrew Homan 2011-07-26T06:02:59Z 2011-07-26T06:02:59Z It looks like an attenuated (or weighted) X-ray transform. http://mathoverflow.net/questions/51913/pde-two-dimensional-inhomogeneous/51939#51939 Comment by Andrew Homan Andrew Homan 2011-01-13T22:31:51Z 2011-01-13T22:31:51Z &quot;No boundary conditions&quot; is also a sort of boundary condition, as far as Green's functions are concerned. Typically these are the easiest situations to calculate Green's functions for. http://mathoverflow.net/questions/39866/are-local-noetherian-rings-with-principal-maximal-ideal-pir Comment by Andrew Homan Andrew Homan 2010-09-24T16:43:21Z 2010-09-24T16:43:21Z Oops. Well, I'm still a commutative algebra noob. Thanks for the references! http://mathoverflow.net/questions/16010/do-separable-and-normal-have-topological-meanings-for-fields/16015#16015 Comment by Andrew Homan Andrew Homan 2010-02-22T02:55:01Z 2010-02-22T02:55:01Z So there really is no connection. Hmph. http://mathoverflow.net/questions/16010/do-separable-and-normal-have-topological-meanings-for-fields Comment by Andrew Homan Andrew Homan 2010-02-22T02:53:47Z 2010-02-22T02:53:47Z Then I misunderstood your comment. After reading it I thought there still was some connection, and mining the link for information came back with nothing, so I was still in a state of confusion. Simply saying &quot;This is incorrect.&quot; answers my question better. http://mathoverflow.net/questions/8756/examples-of-algebraic-closures-of-finite-index/8759#8759 Comment by Andrew Homan Andrew Homan 2009-12-13T22:08:19Z 2009-12-13T22:08:19Z I wish I could upvote your original reference. I love digging up old German math articles.