Image des opérateurs d?entrelacements normalisés et pôles des séries d?Eisenstein

This paper is about the pole of some Eisenstein series for classical groups over a number field. In a previous paper, we have shown how to normalize intertwining operators in such a way that they are holomorphic for positive parameters. Here we show that the image of such operators is (in the interesting cases) either 0 or an irreducible representation. This enables us to compute explicitly the residue of the Eisenstein series obtained from square integrable cohomological representations. At the end of the paper we give necessary and sufficient conditions in terms of Arthur?s data in order that a square integrable cohomological representation is cuspidal; the conditions are not totally satisfactory and we explain what we expect when Arthur?s results will be fully available.     

Surgénérateurs ; l'état des matériaux aux hautes irradiations, hautes puissances locales et températures, leurs gradients et propriétés mécaniques adaptées aux contraintes qui en résultent

The motivations to realize nuclear breeder reactors are developed in the present context of a strong growth in electronuclear power stations in many countries, using mostly moderated and water cooled reactors.The past studies can be of a substantial profit in France and, to a lesser degree, in other countries of the EU. However, to use fully the 238 uranium isotope, the materials for these breeders must withstand much harder radiation than those for water reactors. The power densities and thermal gradients will also be much more intense. The mechanical stresses, both static and dynamic, will be large and will act on materials with altered mechanical properties. Fuel elements will have to be produced with materials already irradiated several times and therefore showing such alterations.A field of studies concerning materials and their mechanical behavior in new and severe conditions is sketched here, both in construction and working conditions, together with proposed necessary instrumentation and research orientations.     

Direct simulation of the motion of neutrally buoyant balls in a three-dimensional Poiseuille flow

In a previous article the authors introduced a Lagrange multiplier based fictitious domain method. Their goal in the present article is to apply a generalization of the above method to: (i) the numerical simulation of the motion of neutrally buoyant particles in a three-dimensional Poiseuille flow; (ii) study – via direct numerical simulations – the migration of neutrally buoyant balls in the tube Poiseuille flow of an incompressible Newtonian viscous fluid. Simulations made with one and several particles show that, as expected, the Segré–Silberberg effect takes place. To cite this article: T.-W. Pan, R. Glowinski, C. R. Mecanique 333 (2005).     

Réflexivité d’une extension d’un opérateur normal par un opérateur nilpotent

Let T be an extension of a one to one normal operator A by a nilpotent operator N. In this paper we calculate the defect of reflexivity of T. We give a necessary and sufficient condition to insure the reflexivity of such extensions. In particular, it is shown that T is reflexive when N is reflexive.     

Comportement des noyaux de la chaleur des opérateurs de Schrödinger et applications à certaines équations paraboliques semi-linéaires

We consider general Schrödinger operators on domains of Riemannian manifolds with possibly exponential volume growth. We prove sharp large time Gaussian upper bounds. These bounds are then used to prove new Lp-Lp estimates for the corresponding semigroups. Applications to semi-linear parabolic equations are given.     

Problèmes elliptiques à frontière libre axi-symétriques: Estimation du diamètre de la section au moyen de la capacité

Résumé Le but de cet article est d'estimer la capacité d'un pétit segment [a(1–), a(1+)]×{z=0} du démi-plan := {x = (r, z)|r > 0, z } de ² par rapport à la capacité définie par la norme . Ce résultat est ensuite utilisé pour estimer le diamètre de la surface libre de certains problèmes elliptiques non linéaires.     

Large time behavior for nonlinear higher order convection–diffusion equations

We study the large time asymptotic behavior, in L^p (1p∞), of higher derivatives D^γu(t) of solutions of the nonlinear equation

(1)

where the integers n and θ are bigger than or equal to 1, a is a constant vector in with . The function ψ is a nonlinearity such that and ψ(0)=0, and is a higher order elliptic operator with nonsmooth bounded measurable coefficients on . We also establish faster decay when .     

Equations différentielles invariantes sur les groupes et algèbres de Lie réductifs II

Dans un article précédent, nous avons démontré que si D est un opérateur différentiel bi-invariant sur un groupe réductif G vérifiant la condition de Benabdallah-Rouvière, alors on peut résoudre l’équation différentielle Du=v dans l'espace des distributions G-invariantes (par automorphismes intérieurs) d'ordre fini; nous allons montrer ici que, sous la même hypothèse, on peut résoudre cette équation dans l'espace de toutes les distributions G-invariantes. D'autre part, nous donnons un exemple dans qui montre que les équations différentielles invariantes dans les algèbres de Lie réductives ne sont pas toujours résolubles dans l'espace des fonctions indéfiniment différentiables invariantes.