Mathematics

  2010 MAR 9 - (VerticalNews.com) -- According to recent research from Toulouse, France, "To an oriented link in a solid torus we associate a trace graph in a thickened torus in such a way that links are isotopic if and only if their trace graphs can be related by moves of finitely many standard types."

  "The key ingredient is a study of codimension 2 singularities of link diagrams," wrote T. Fiedler and colleagues, University of Toulouse ...read more

  2010 MAR 9 - (VerticalNews.com) -- According to a study from Aubiere, France, "Let K be a complete ultrametric algebraically closed field. We investigate several properties of sequences (a(n))(n is an element of N) in a disk d(0, R-) with regards to bounded analytic functions in that disk: sequences of uniqueness (when f(a(n)) = 0 for all n is an element of N implies f = 0), identity sequences (when lim(n -> + infinity) f (a(n)) = 0 implies f = 0) and analytic boundaries (when limsup(n ->infinity)vertical bar f(a(n))vertical bar = parallel to f parallel to). ...read more

  2010 MAR 9 - (VerticalNews.com) -- "We deal with existence and uniqueness of the solution to the fully nonlinear equation -F(D(2)u) + /u/(s-1)u = f(x) in R-n, where s> 1 and f satisifes only local integrability conditions. This result is well known when, instead of the fully nonlinear elliptic operator F, the Laplacian or a divergence-form operator is considered," investigators in Paris, France report.

  "Our existence results use the Alexandroff-Bakelman-Pucci inequality since we cannot use any variational formulation. For radially symmetric f, and in the particular case where F is a maximal Pucci operator we can prove our results under fewer integrability assumptions, taking advantage of an appropriate variational formulation," wrote M.J. Esteban and colleagues, University of Paris ...read more