2008 NOV 24 - (VerticalNews.com) -- According to recent research published in the Journal of Theoretical Probability, "l Let S be the multiplicative semigroup of q x q matrices with positive entries such that every row and every column contains a strictly positive element."

  "Denote by (X-n) n>= 1 a sequence of independent identically distributed random variables in S and by X-(n) = X-n...X-1, n>= 1, the associated left random walk on S. We assume that (Xn) n>= 1 satisfies the contraction property [GRAPHICS] where S is the subset of all matrices which have strictly positive entries," wrote H. Hennion and colleagues, University of Rennes ...read more

  2008 NOV 24 - (VerticalNews.com) -- 'Let K be a field of characteristic not equal 2 such that every finite separable extension of K is cyclic. Let A be an abelian variety over K. If K is infinite, then A(K) is Zariski-dense in A. If K is not locally finite, the rank of A over K is infinite.'

  This article was prepared by Journal of Mathematics editors from staff and other reports. Copyright 2008, Journal of Mathematics via VerticalNews.com ...read more

  2008 NOV 24 - (VerticalNews.com) -- According to a study from the United States, "This paper defines and studies permutation representations on the equivariant cohomology of Schubert varieties, as representations both over C and over C[t(1), t(2)..., t(n)]."

  "We show these group actions are the same as an action of simple transpositions studied geometrically by M. Brion, and give topological meaning to the divided difference operators of Berstein-Gelfand-Gelfand, Demazure, Kostant-Kumar, and others. We analyze these representations using the combinatorial approach to equivariant cohomology introduced by Goresky-Kottwitz-MacPherson," wrote J.S. Tymoczko and colleagues, University of Iowa ...read more