Sur les courbes irramifiées

Sans résuméPrésenté par G. Alexits     

Réflexion entre deux diffusions conjuguées

We observed, in a previous work, that Brownian motion reflected on an independent time-reversed Brownian motion is again Brownian motion. We present the generalisation of this result to pairs of conjugate diffusions (which are also dual, in the sense of Siegmund). To cite this article: F. Soucaliuc, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 1119–1124.     

Linéarisation et maillage des surfaces paramétrées

We propose a methodology to simplify the parameterization of a surface composed of parametric patches, typically encountered in CAD (computer aided design) environments. This new parameterization is defined via the construction of an adaptive triangulation, called support, of each patch. The adaptation is governed by the control of the gap between the initial parameterization of the patch and that of the support. This support is used to generate the mesh of the CAD surface using an indirect approach, in which the mesh is generated via the parametric domains. The support makes it possible to disconnect the mesher from the CAD system, and in this sense it constitutes a universal tool for meshing such surfaces. An application example is given to show the pertinency of our methodology.     

Algèbres de Sobolev Généralisées

We examine the structure of a generalized Sobolev spaces. We also exhibit a class of locally uniformlyA-convex algebras, the unitization of which are not the same type.

     

Diffusions réfléchies réversibles dégénérées

On a domain D in ^d, for a smooth enough probability density and a diffusion matrix which can degenerate, we construct the law Q ^s of a (x)d -symmetric reflecting process in D with matrix . Therefore, we use the associated Dirichlet form and a sequence of approximating processes already used by Pardoux and R. Williams in [23]. Under mild conditions on the boundary ofD (finite Minkowski content), we prove that Q ^s is the law of a semi-martingale and provide its decomposition. Comparing with the decomposition in additive functionals, we conclude that the process is reflected in the conormal direction ^* n where n denotes Chen's normal (cf [10]), that is, the reflection direction of the Brownian motion in Kuramochi compactification.     

Homologies associées aux variétés de Poisson

In this article, we obtain results on the cyclic homology of Poisson manifolds as defined by Kassel. In particular, we compute the cyclic homology of any symplectic variety. We also show that there exists a family of new operators of the type of the S operator of Connes, defined on the cyclic homology of a Poisson manifold, and describe the associated exact triangles associated to these new operators.

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Received February 23, 1998 / Published online July 20, 2000     

Catégories dérivées et variétés de Deligne-Lusztig

Sans résumé     

Sur les équations fonctionnelles aux itérées

Summary We study solutions of functional equationsP(f ^[10] ,,f ^[s] ) = 0, whereP is a non zero polynomial ins + 1 variables andf ^[k] denotes thekth iterate of a functionf. We deal with three distinct cases: first,f is an entire function of a complex variable, we show then thatf is a polynomial. Second, we also prove thatf is a polynomial if it is an entire function of ap-adic variable. Third, we considerf a formal power series with coefficients in a number fieldK; subject to some apparently natural restrictions onf and onP, we find thatf is an algebraic power series over the ring of polynomials inK[x].

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Sur les équations fonctionnelles aux itérées

     

Strates scindées pour un groupe réductif p-adique

We introduce, for a reductive p-adic group, a notion of split fundamental stratum of positive level playing the expected part in the type theory of Bushnell and Kutzko. In particular, we prove that a smooth representation containing such a stratum cannot be supercuspidal. The idea consists in deforming the stratum so that the Abelian character associated with the deformed stratum will be contained in the representation and will verify a “good” intertwining formula.     

Processus d'Antoniadis-Carmona et le principe de déviations modérées

We prove that the uniform moderate deviations principle is satisfied by the empirical measures associated to the Antoniadis-Carmona processes.     

Opérateurs de projection en théorie des primitives aréolaires bornées

Résumé On donne des propriétés générales des primitives aréolaires bornées et l'on met en évidence dans leur représentation intégralé deux opérateurs de projection: C de Cauchy et T de Pompeiu. à. M. Enrico Bompiani pour son Jubilé scientifique.     

Equations de Cahn-Hilliard généralisées dans un milieu déform able

We consider in this Note models of generalized Cahn—Hilliard equations that take into account the effects of internal microforces and introduced by M. Gurtin in [6] coupled with the Navier equation of linear elasticity (under the small deformations assumption) for which we obtain the existence and uniqueness of weak solutions. When the deformations are infinitesimal and when the displacement gradient is small, in which case we can neglect the evolutive term in the Navier equation, we can furthermore prove the existence of finite-dimensional attractors by noting that the variational formulation can be uncoupled. It is important to note here that these results cannot in general be obtained for the coupled (classical) Cahn—Hilliard equations.     

Répartition de Suites et Équations Fonctionnelles Associées

LetX be a compact metric space, a probability measure onX, T a measure preserving transformation ofX into itself. Furthermore, letZ be a compact abelian group, andS the skew-product defined onX×Z by the formula:S(x,z)=(T x,z+(x)) where is some map fromX toZ. It is known that under the hypothesis of unique ergodicity for the triple (X, ,T) and some suitable conditions of continuity onT and , the triple (X×Z,m,S) wherem is the product measure of by the Haar measure onZ is uniquely ergodic if and only if an associated functional equation has no non trivial solution.—We introduce here a generalization of unique ergodicity (which appears quite naturally when studying well distributed sequences) and prove about it the same kind of results.