most recent 30 from http://mathoverflow.net 2013-05-21T10:36:45Z http://mathoverflow.net/feeds/user/8684 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/82323/getting-nervous-refereeing-a-paper/82337#82337 Jay Kangel 2011-12-01T01:33:42Z 2011-12-01T01:33:42Z

<p>This is really a comment but I don't have enough reputation points for that. It is a little more specific than Joël's.</p> <p>It's a small world. How many papers are out there where the author defines some type of supremum of a set of elements in a group? Perhaps you have disguised the actual mathematical structure.</p>

http://mathoverflow.net/questions/72281/does-convex-continuous-mapping-have-a-unique-fixed-point/72283#72283 Jay Kangel 2011-08-07T12:09:32Z 2011-08-07T12:09:32Z

<p>As to the specific question in the next to last paragraph, the identity function is convex. Except for the zero dimensional case there are many fixed points.</p>

http://mathoverflow.net/questions/20386/mathematics-as-a-hobby/56480#56480 Jay Kangel 2011-02-24T02:40:19Z 2011-02-24T02:40:19Z

<p>If you want to try to do some research it may be best to pick a field that is not popular with professional mathematicians. You may also want to try to pick something that has not been worked on for some time. I chose convex structures and the result is:</p> <p><a href="http://www.ams.org/meetings/sectional/1058-52-28.pdf" rel="nofollow">http://www.ams.org/meetings/sectional/1058-52-28.pdf</a> </p>

http://mathoverflow.net/questions/3134/whats-your-favorite-equation-formula-identity-or-inequality/36289#36289 Jay Kangel 2010-08-21T16:05:00Z 2010-08-21T16:05:00Z

<p>My favorite equation is</p> <p>$$\frac{16}{64} = \frac{1}{4}.$$</p> <p>What makes this equation interesting is that canceling the $6$'s yields the correct answer. I realized this in, perhaps, third grade. This was the great rebellion of my youth. Sometime later I generalized this to finding solutions to</p> <p>$$\frac{pa +b}{pb + c} = \frac{a}{c}.$$</p> <p>where $p$ is an integer greater than $1$. We require that $a$, $b$, and $c$ are integers between $1$ and $p - 1$, inclusive. Say a solution is trivial if $a = b = c$. Then $p$ is prime if and only if all solutions are trivial. On can also prove that if $p$ is an even integer greater than $2$ then $p - 1$ is prime if and only if every nontrivial solution $(a,b,c)$ has $b = p - 1$.</p> <p>The key to these results is that if $(a, b, c)$ is a nontrivial solution then the greatest common divisor of $c$ and $p$ is greater than $1$ and the greatest common divisor of $b$ and $p - 1$ is also greater than $1$.</p> <p>Two other interesting facts are (i) if $(a, b, c)$ is a nontrivial solution then $2a \leq c &lt; b$ and (2) the number of nontrivial solutions is odd if and only if $p$ is the square of an even integer. To prove the latter item it is useful to note that if $(a, b, c)$ is a nontrivial solution then so is $(b - c, b, b - a)$.</p> <p>For what it is worth I call this demented division.</p>

http://mathoverflow.net/questions/53036/books-you-would-like-to-read-if-somebody-would-just-write-them/53091#53091 Jay Kangel 2012-06-09T00:46:52Z 2012-06-09T00:46:52Z

The book <a href="http://www.amazon.com/Frames-Locales-Topology-Frontiers-Mathematics/dp/303480153X/ref=sr_1_1?s=books&amp;ie=UTF8&amp;qid=1339202318&amp;sr=1-1&amp;keywords=Frames+and+Locales" rel="nofollow">amazon.com/&hellip;</a> by Picado and Pultr is a general topology book written in the language of locales. Against your wishes this book does mention topologies. Much of this material is to point out differences between topologies and locales. Since the likely audience for this book will likely have some knowledge of topology I don't think one can expect the authors to do otherwise.