http://www.web-frog.com/categories/maths/ en-gb Copyright 2003 Martin Sewell Mon, 15 Dec 2003 18:54:46 GMT http://backend.userland.com/rss Radio UserLand v8.0.8 martin@martinsewell.com martin@martinsewell.com rssUpdates 5 6 7 4 8 9 3 10 60 http://www.web-frog.com/categories/maths/2003/12/09.html#a451 <P>Let <I>k</I> be an integer such that <I>k</I> is larger than or equal to zero, and let <I>H</I> be the Hilbert number. In this paper, we use the method of describing functions to prove that in the Li&eacute;nard equation, the upper bound for <I>H</I>(2<I>k</I>+1) is <I>k</I>. By applying this method to any planar polynomial vector field, it is possible to completely solve the second part of Hilbert's 16th problem.</P> <UL> <LI><A href="http://www.mathematik.uni-bielefeld.de/~kersten/hilbert/16.html">Hilbert's original German text <I>Mathematische Probleme</I> 16</A> <LI><A href="http://news.bbc.co.uk/1/hi/sci/tech/3243736.stm">BBC NEWS | Science/Nature | Historic maths problem 'cracked'</A> <LI><A href="http://tesugen.com/2003/12/06/elin-oxenhielm-update">Elin Oxenhielm Update (Tesugen)</A> <LI><A href="http://slashdot.org/article.pl?sid=03/11/26/1942205">Slashdot | Swedish Student Partly Solves 16th Hilbert Problem</A> <LI><A href="http://www.unstruct.org/archives/000186.html">unstruct.org: Swede Solves 100 year old Math Puzzle</A> <LI><A href="http://www.math.su.se/~yishao/16thproblem.shtml">Yishao Zhou's Comments</A> <LI><A href="http://www.oxenhielm.com/">Elin Oxenhielm's Response</A> <LI><A href="http://www.nature.com/nsu/031208/031208-4.html">Mathematicians dispute proof of century-old problem: Mystery remains as journal withdraws paper.</A> </UL> http://www.web-frog.com/categories/maths/2003/12/09.html#a451 Tue, 09 Dec 2003 18:15:06 GMT http://radiocomments2.userland.com/comments?u=126057&amp;p=451&amp;link=http%3A%2F%2Fwww.web-frog.com%2F2003%2F12%2F09.html%23a451