User science.nest - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T19:57:27Z http://mathoverflow.net/feeds/user/13343 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/60810/simple-example-of-renormalization Simple example of renormalization science.nest 2011-04-06T12:39:02Z 2011-06-11T15:38:46Z <p>As far as I understand, the RG theory, or functional RG theory is a mathematical tool for moving in the "scale dimension". The tool can be used for calculation of Feigenbaums constant (e.g. <a href="http://mathworld.wolfram.com/FeigenbaumConstant.html" rel="nofollow">mentioned here</a>). Can the theory be given a simple example of how to move one "step" in the "scale dimension" ?</p> http://mathoverflow.net/questions/57062/probability-that-a-graph-g-does-not-contain-a-cycle Probability, that a graph G does not contain a cycle science.nest 2011-03-02T00:34:27Z 2011-04-24T14:46:08Z <p>Hello, given graph G, with vertices set V, n=|V|, and edge set E, k=|E|, what is the probability, that it does not contain any cycle C_l, for l>=3?</p> <p><strong>The requested clarification</strong>: My intention was to form the question in such a way, that there is no information about any distribution of the edges, and <em>n</em> and <em>k</em> are parameters. This lack of information should be in fact the information. You construct graphs in any possible ways, and you have to decide which constructs are more possible to occur and which are less expected. This probably implies the uniform distribution.</p> http://mathoverflow.net/questions/62058/wandering-sets-how-much-usable-are-they Wandering sets -- how much usable are they? science.nest 2011-04-17T22:15:39Z 2011-04-17T22:15:39Z <p>Knowing that a dynamical system has a wandering set implies that the system is dissipative. Is this the only information that wandering sets provide?</p> <p>Limit cycles, fixed points, strange attractors, repellers etc. do provide useful information about a dynamical system. Maybe wandering sets can also be used with similar "importance"?</p> http://mathoverflow.net/questions/61953/deeper-meanings-of-phase-space-any-books Deeper meanings of Phase Space -- any books? science.nest 2011-04-16T20:55:33Z 2011-04-17T02:37:35Z <p>I often think about the phase space with quite deep interpretations. For example, contraction of phase space means losing energy. But, some of the energy is easily restored (free energy?) while some other is hard to restore (enthalpy, internal energy). This is like dividing the phase space to flexible and rough?</p> <p>Are my insights correct or maybe they can be easily extended more?</p> <p><strong>Are there any books with such interpretation-like approach to phase space and dynamical systems?</strong></p> http://mathoverflow.net/questions/62058/wandering-sets-how-much-usable-are-they Comment by science.nest science.nest 2011-04-23T15:46:15Z 2011-04-23T15:46:15Z I see the question is closed. This is sad to me. IMO the way the question was asked is the standard way of approaching new topics. Richard Feynman would know how to answer such question. http://mathoverflow.net/questions/62058/wandering-sets-how-much-usable-are-they Comment by science.nest science.nest 2011-04-18T00:57:11Z 2011-04-18T00:57:11Z Bill thank you for your opinion. I hope that I will get some answer (few motto-words would be sufficient).