Convergence d'un schéma itératif explicite

An iterative method which deals with the computation of solutions of variational equations by the finite element method is presented in this paper. The computation, in some cases, can be done explicitly for each element. We apply this method for a nodal scheme to solve a diffusion problem and we give convergence results.     

Résolution d'équations intégrales d'un type particulier

Summary A method is outlined here in order to find out continous solutions with definite parity, of linear homogeneous integral equations having a kernelK (x,y) which is a homogeneous function in some infinite domain of thex, y-plane.     

Homogénéisation d'un problème de capillarité

We study the behavior of the height of a liquid contained in a vertical cylindrical tube where are immerged a periodic distribution (period ɛ) of cylindrical fibers with radius r < ɛ and whose material-liquid coefficient is λ. It is showed that the homogenized problem depends on the limit of λr/ɛ² as (ɛ, λ, r) → (0,0, 0). The second problem is when the border is made of two alternate periodic bands, the first of length r being incrusted in the second of length ɛ − r. Here, the homogenized problem depends on the limit of r/ɛ as (, r) → (0, 0). For this, we use epi-convergence techniques.     

Support d'un processus de réflexion

Summary Let D be a regular open set in ⁿ. We describe in this paper the support of ¯D-valued diffusion processes with Reflecting Boundary Condition, generalizing the results of Stroock and Varadhan obtained when D = Ø.     

Propriétés et applications d'un circuit flipflop ultra-rapide

Sans résumé     

Performances d'un amplificateur différentiel à transistors

Sans résumé     

Homogénéisation d'un matériau périodique faiblement perturbé aléatoirement

We present in this Note an approach aiming at computing the first-order homogenized behaviour of a medium consisting of a randomly perturbed periodic reference material. The approach, which proves to be very efficient from a computational point of view, is rigorously founded in a certain class of settings and has been successfully numerically tested for more general settings.     

Automorphismes des extensions algébriques d'un corps

Sans résumé     

Sur les petites déviations d'un processus de Lévy

Nous caractérisons les processus de Lévy sur partant de 0 qui peuvent être approchés par la fonction nulle pour la topologie localement uniforme. Ceci nous permet de déterminer le support d'un processus de Lévy quelconque dans l'espace de Skorohod, et de retrouver un théorème de Tortrat sur le support des lois indéfiniment divisibles.     

Comment agit le câble tracteur d'un téléphérique

Summary Many studies, and even official regulations use the name balance cable to describe one of the two ends of the traction cable of a telpher.This definition implies that the end of the cable referred to as balance cable plays a minor part in the efficient running of the telpher.The author shows this interpretation is not justified, in the sense that the two ends of the cable are mechanically equivalent and indispensable to the system. The article shows also that the counter-balance cannot be used as a device adjusting stress during operation, this effect being obtained only through the action of the driving pulley.     

Stabilisation frontière d'un système d'élasticité

We prove in this Note the global existence, uniqueness and stabilization of an elasticity system with nonlinear boundary damping. This work extends results obtained by Alabau and Komornik in [1]     

Résolution mathématique d'équations décrivant l'évolution d'une surface d'un matériau contraint

We consider a cristal structure, constituted by an elastic substrate and a film with a small thickness. The lattice parameters between the film and the substrate are not the same; consequently, a strain appears in the structure. This strain generates morphologies(see [1,2]).The difficulty consists in finding the profile of the film-vapor surface at any time, which depends on the elastic displacement of the structure. To this end, a physical model, detailed in [2], consists in solving a coupled system of partial derivative equations. The unknowns are the elastic displacement of the structure and the profile of the evolution surface. The elastic displacement solves the linearized elasticity equations posed over the domain occupied by the structure. The boundary of this domain depends on the evolution surface. The second equation is the evolution equation, depending on the elastic displacement by a term of the surface energy. This model is greatly simplified in order to obtain a decoupled two-dimensional model: the map of the film-vapor surface solves a non-linear partial derivatives equation, which is independent of the displacement of the structure.In this Note, we give some results of the existence and uniqueness of a solution for this model under some assumptions about the first derivative of the map.     

Sur une propriété caractéristique d'un produit de droites

Sans résumé     

Stratifications et ensemble de non-cohérence d'un espace analytique réel

Sans résuméL'auteur est associé au groupe G.N.S.A.G.A. du C.N.R.     

Caractérisation des moments d'inertie d'un système matériel

We characterize those real-valued functions on the set of subspaces of a euclidian affine space that represent the moments of inertia of some suitable solid body. Moreover, we find the lowest number of point masses that can be used to obtain such a solid body. To cite this article: P. Barbaroux, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 1067–1070.