On reconstruction of objects from measurements of the diffracted field (*)

The aim of this paper is the shape restoration of a plane object from measurements of its diffracted field at a discrete and finite set of points. The plane sampling lattice is supposed: i) rectangular; ii)periodic.

The problem is approached as an interpolation one. A numerical algorithm for practical reconstructions is presented. A-priori limitations on the perimeter of the object and conditions on the samples lead to a-priori bounds able to estimate the precision of the reconstruction.     

Taylor Expansions of Distributions

Classical Taylor expansions of holomorphic functions in the complex plane are extended to distributions in Rⁿand in domains     

How Topological are Topological Groups?

Abstract

A Characterization of the category of topological groups is provided which does not refer to the category of topological spaces at all, but only to the category of uniform spaces. Similarly, the category of SIN-groups is characterized in a purely uniform way.     

EXTREMUM AGGREGATES OF MINIMAL 0-DOMINATING FUNCTIONS OF GRAPHS

Abstract

A 0-dominating function 0DF of a graph G = (V,E) is a function f: V → [0,1] such that Σ _xεN(v) f(x) ≥ 1 for each ν ε V with f(v) = 0. The aggregate of a 0DF f is defined by ag(f) = Σ_vεV f(v) and the infimum and supremum of the set of aggregates over all minimal 0DFs of a graph are denoted by γ₀ and Γ₀ respectively. We prove some properties of minimal 0DFs and determine γ₀ and Γ₀ for some classes of graphs.     

Probabilistic gradient approximation for a viscous scalar conservation law in space dimension d≥2

In this paper, we are interested in the solution of a viscous scalar conservation law. We remark that its first order spatial derivatives solve a system of partial differential equations presenting a nonlocal nonlinearity. We associate a nonlinear martingale problem with this system. After proving existence and uniqueness for the martingale problem, we obtain a propagation of chaos result for a system of interacting diffusion processes. We deduce that it is possible to approximate the solution of the viscous scalar conservation law thanks to the interacting diffusions     

A BARRIER BOUNDARY VALUE PROBLEM FOR PARABOLIC AND ELLIPTIC EQUATIONS

Barrier type boundary conditions are modeled for describing the substance diffusion in a medium when obstacles in the medium are considered. The existence of solutions of parabolic and elliptic differential equations with barrier boundary condition is presented in this paper.