Mathematics

  2010 MAR 23 - (VerticalNews.com) -- "In this note, we study the convergence of the Levenberg-Marquardt regularization scheme for nonlinear ill-posed problems," investigators in Dusseldorf, Germany report.

  "We consider the case that the initial error satisfies a source condition. Our main result shows that if the regularization parameter does not grow too fast (not faster than a geometric sequence), then the scheme converges with optimal convergence rates," wrote M. Hochbruck and colleagues, University of Dusseldorf ...read more

  2010 MAR 23 - (VerticalNews.com) -- "In this article, we analyze an Euler implicit-mixed finite element scheme for a porous media solute transport model. The transporting flux is not assumed given, but obtained by solving numerically the Richards equation, a model for subsurface fluid flow," scientists writing in the journal Numerical Methods for Partial Differential Equations report.

  "We prove the convergence of the scheme by estimating the error in terms of the discretization parameters. In doing so we take into account the numerical error Occurring in the approximation of the fluid flow," wrote F.A. Radu and colleagues ...read more

  2010 MAR 23 - (VerticalNews.com) -- According to recent research from Graz, Austria, "The main goal of this paper is to determine the Poisson boundary of lamplighter random walks over a general class of discrete groups Gamma endowed with a ''rich'' boundary. The starting point is the Strip Criterion of identification of the Poisson boundary for random walks on discrete groups due to Kaimanovich (Ann. Math. 152: 659-692, 2000)."

  "A geometrical method for constructing the strip as a subset of the lamplighter group Z(2) (sic) Gamma starting with a ''smaller'' strip in the group Gamma is developed. Then, this method is applied to several classes of base groups Gamma: groups with infinitely many ends, hyperbolic groups in the sense of Gromov, and Euclidean lattices," wrote E. Sava and colleagues, Graz University ...read more