On Periodic Solutions of Degenerate Singularly Perturbed Linear Systems with Multiple Elementary Divisor

We establish sufficient conditions for the existence and uniqueness of a periodic solution of a system of linear differential equations with a small parameter and a degenerate matrix of coefficients of derivatives in the case of a multiple spectrum of a boundary matrix pencil. We construct asymptotics of this solution.     

Inequalities for the Moments and Distribution of the Ladder Height of a Random Walk

We obtain upper bounds for the tail distribution of the first nonnegative sum of a random walk and for the moments of the overshoot over an arbitrary nonnegative level if the expectation of jumps is positive and close to zero. In addition, we find an estimate for the expectation of the first ladder epoch.     

Complete ideals and singularities of space curves

We consider complete ideals supported on finite sequences of infinitely near points, in regular local rings with dimensions greater than two. We study properties of factorizations in Lipman special *-simple complete ideals. We relate it to a type of proximity, linear proximity, of the points, and give conditions in order to have unique factorization. Several examples are presented. Received: 2 February 2000 / in final form: 14 March 2001 / Published online: 18 January 2002     

Temperature Stresses in a Piecewise-Homogeneous Cylindrical Shell Caused by the Presence of a Longitudinal Crack

By using the method of generalized conjugation problems, we propose a numerical scheme for investigation of the redistribution of temperature stresses in a piecewise-homogeneous cylindrical shell caused by a longitudinal crack. This scheme is based on systems of integral equations (some of them are singular) to determine the unknown jumps of integral characteristics of the disturbed temperature field and displacements and their derivatives on the line of a crack and on the interface as well as the derivatives of these integral characteristics with respect to the longitudinal coordinate at the interface.     

An interior–exterior Schwarz algorithm and its convergenceUn algorithme de Schwarz intérieur–extérieur et sa convergence

In this work we study the solution of Laplace's equation in a domain with holes by an iteration consisting of splitting the problem in an exterior one, around the holes, plus an interior problem in the unholed domain. We show the existence of a decomposition of the solution when the exterior problem is represented by means of a single-layer protential. Also, for the three-dimensional case and with some adjustments for the two-dimensional case, we prove convergence of the method by writing the iteration as a Jacobi iteration for an operator equation and studying the spectrum of the iteration operator. To cite this article: R. Celorrio et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 923–926.