On the reconstruction of conductivity of bordered two-dimensional surface in R^3 from electrical currents measurements on its boundary

An electrical potential U on bordered surface X (in Euclidien three-dimensional space) with isotropic conductivity function sigma>0 satisfies equation d(sigma d^cU)=0, where d^c is real operator associated with complex (conforme) structure on X induced by Euclidien metric of three-dimensional space. This paper gives exact reconstruction of conductivity function sigma on X from Dirichlet-to-Neumann mapping (for aforementioned conductivity equation) on the boundary of X. This paper extends to the case of the Riemann surfaces the reconstruction schemes of R.Novikov (1988) and of A.Bukhgeim (2008) given for the case of domains in two-dimensional Euclidien space. The paper extends and corrects the statements of Henkin-Michel (2008), where the inverse boundary value problem on the Riemann surfaces was firstly considered

An Evolutionary Model with Interaction between Development and Adoption of New Technologies

We propose a difference-differential equation that reflects interactions between innovation and imitation processes to describe the evolution of the distribution curve of firms by efficiency levels. An explicit solution of this equation is obtained for arbitrary finite initial conditions. It is shown that this equation admits one-parametric family of logistic waves, and that arbitrary solution exponentially converges to one of the waves. This result explains two stylized empirical facts: the "logistic" shape of diffusion curves and the stable form of production capacities distribution by efficiency levels. Possible generalizations, modifications and applications are discussed.innovation; imitation; diffusion; logistic distribution; efficiency; wave solution; stability; Burgers equation

Cauchy-Pompeiu type formulas for d-bar on affine algebraic Riemann surfaces and some applications

We have obtained the explicit versions and precisions for the Hodge-Riemann decomposition of formes on affine algebraic curve V. The main application consists in the construction of Faddeev-Green function for Laplacian on V. Basing on this [HM](arXiv:0804.3951 and J.Geom.Anal., 2008,18), we extended from the case X in C to the case of bordered Riemann surface X in V the R.Novikov (1988) scheme for the effective reconstruction of conductivity function sigma on X through Dirichlet-to-Neumann mapping on bX for solutions of d(sigma d^cU)=0. In Sec.4 we give a correction of the paper [HM]