Propriétés de l'EMV de rupture de processus de Poisson

This Note concerns the estimation of the parameter of the intensity of an inhomogeneous spatial Poisson process by the maximum likelihood method. We consider an intensity admitting a discontinuity along a closed curve depending of an unknown parameter. The established results show the consistency, the convergence in law and the convergence of the moments of the maximum likelihood estimator.     

Propriétés d'indépendance algébrique de valeurs de séries de Hecke–Mahler

Here we characterize in a complete and explicit way the relations of algebraic dependence over $\mathbb{Q}$ of complex values of Hecke–Mahler series at algebraic points of the multiplicative group ${\mathbb{G}}_{\mathrm{m}}^2(\mathbb{C})$. Our result contains previous results of Loxton and van der Poorten, Mahler, and Masser. To cite this article: F. Pellarin, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Sur une généralisation de la notion de V-variété

We consider a topological space which is locally isomorphic to the quotient of R^k by the action of a discrete group and we call it quasifold of dimension k. Quasifolds generalize manifolds and orbifolds and represent the natural framework for performing symplectic reduction with respect to the induced action of any Lie subgroup, compact or not, of a torus. We define quasitori, Hamiltonian actions of quasitori and the moment mapping for symplectic quasifolds, and we show that every simple convex polytope, rational or not, is the image of the moment mapping for the action of a quasitorus on a quasifold.     

L'influence de la géométrie de Bolyai-Lobatchevsky sur le développement de la géométrie

Sans résumé     

Généralisation de la notion de l'enveloppe

Sans résumé Présenté par G. Hajós     

L'influence de la géométrie de Bolyai-Lobatchevsky sur le développement de la méthode axiomatique

Sans résumé     

Intersection de sous-groupes et de sous-variétés I

We study the intersection of a subvariety X of an abelian variety A over with the union of all the algebraic subgroups of A of given dimension d. Our main result states that if we remove a suitable exceptional subset from X and if d is small enough then the intersection enjoys a Northcott-like property: the points of bounded height on it form a finite set. The condition on d involves only the dimension of X and the structure of A up to isogenies. We show how it can be weakened if we assume certain conjectures in the direction of an abelian version of Lehmer's problem. The theorem is especially meaningful when X is a curve since it is then possible to bound the height and hence to prove finiteness of the set under consideration. This generalises the result of E. Viada on powers of elliptic curves and is analogous to work of E. Bombieri, D. Masser and U. Zannier on tori, whose general strategy we follow.     

Sur une caractérisation de la répartition normale de probabilités

Sans résumé Présenté par A. Rényi     

Inégalités de concentration pour les processus empiriques de classes de parties

We propose new concentration inequalities for maxima of set-indexed empirical processes. Our approach is based either on entropy inequalities or on martingale methods. The improvements we get concern the rate function which is exactly the large deviations rate function of a binomial law in most of the cases. Received: 11 January 2000 / Revised version: 12 May 2000 / Published online: 14 December 2000     

Déformations de fibrés vectoriels sur les variétés de dimension 3

In the first part, we give some necessary conditions for a torsion free sheaf on a smooth threefold to be a reduced limit of vector bundles.In a second part of the article, we illustrate these results by reinterpreting a condition described by G. Ellingsrud and S.A. Strømme as a condition obtained in the first part. This enables us to identify, in a well known too big familly, the torsion free sheaves that are limit of vector bundles.     

Un modéle pseudo-tridimensionnel d'écoulement de fluides parfaits et généralisation de l'équation pour la fonction de courant

Résumé Dans une région des l'espace on considère l'écoulement d'un fluide et on fait l'hypothèse qu'il est pseudotridimensionnel, c'est-à-dire que son mouvement est stationnaire et qu'il existe un système de coordonnées curvilignes (y ¹,y ²,y ³) tel que les surfaces coordonnéesy ³=constante sont des surfaces de courant. Cette hypothèse entraîne l'existence d'une fonction de courant (y ¹,y ²,y ³). Si le fluide est parfait et barotrope on obtient que ³/ le long des lignes de courant oú ³ est la troisième composante contravariante du rotationnel de la vitesse et la densité de masse. Cette propriété permet de formuler une équation pour la fonction de courant, généralisant l'équation habituelle de la mécanique des fluides plans.

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Let us consider a flow motion in a given special domain. We make the assumption that the movement of the fluid is pseudo-tridimensional, i.e., the flow motion is steady and there exists a system of curvilinear coordinates (y ¹,y ²,y ³) such that stream surfaces are defined byy ³=constant. Under this assumption there exists a stream function .Whenever the fluid is perfect and barotropic, we show that ³/= constant on stream lines (where ³ is the 3rd contravariant component of the speed's curl and is the density).Using this property we are able to write an equation for the stream function, which embeds the usual equation for two-dimensional fluid movements.

     

Réduction de la conjecture de Hodge à une continuité

The obstructions, for a closed differential form on a projective manifold, to be cohomologous to an algebraic cycle with complex coefficients, are computed in terms of the Chow transformation. They can be expressed as an orthogonality condition, on the manifold itself, with families parametrized by the Grassmannian of currents which are completely determined. A parameter does not yield any obstruction if the associated projective subspace meets properly the manifold. The embedding of the manifold is degenerated, in view of applying the characterization of currents associated to algebraic cycles by the Chow transformation. We study the set of periods obtained when the parameter varies, in particular, we prove a continuity result, thanks to the constructibility of the Bernstein polynomial. When the cohomology class is rational, we conjecture that this set is connected.     

Espaces de Besov et estimations de Strichartz généralisées sur le groupe de Heisenberg

In this paper, we prove dispersive and Strichartz inequalities on the Heisenberg group. The proof involves the analysis of Besov-type spaces on the Heisenberg group.

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Le travail du troisième auteur est partiellement finacé par la NNSF de Chine.     

Décomposition de domaine pour un calcul hybride de l'équation de helmholtz

We prove an estimate for the Dirichlet-Neumann operator, and for the H¹ local norm for solutions of Helmholtz equation outside an obstacle without trapping rays. We give an algorithm solving Helmholtz equation outside a union of such obstacles. Convergence follows from this estimate. At each step of the resolution, only one obstacle is considered for itself; this defines a decomposition domain technique fitting this equation. One can use different numerical schemes, one at each step, adapted to the considered component of the obstacle; therefore, this algorithm is a hybrid computation. The results are given for two obstacles, and the generalization is straightforward