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.     

Lemmes de décomposition appliqués à des inégalités de type Hardy–Sobolev

Decomposition (or concentration-compactness) lemmas have already shown their efficience in order to show existence of minimizers or ground state solutions. The aim of this paper is to apply new version of these lemmas to minimisation problems involving Hardy–Sobolev type inequalities on a specific class of unbounded domains. More precisely, we shall find ground state solution for the following quotient, where value of real numbers ,b,q and are given.

Construction de surfaces algébriques dont le diviseur de Severi est supérieur à l'unité

Sans résuméAu Prof.van der Waerden, pour son 60^e anniversaire     

Processus empirique de fonctionnelles de champs gaussiens à longue mémoire

We study the asymptotic behaviour of the doubly indexed empirical process of stationary Gaussian subordinated random fields with long-range dependence. Contrary to the situation chosen in the pre-existing papers, the long memory is not necessarily isotropic. In all the investigated cases, the limiting process is degenerated insofar as it has the form $f(x)Z(t)$ where f is the marginal density and Z a random field. To cite this article: F. Lavancier, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Sur les formules de quadrature numérique à nombre minimal de noeuds d'intégration

Résumè Cet article a pour objet la recherche, à partir de la théorie des polynômes orthogonaux, de conditions permettant l'obtention de formules de quadrature numérique sur des domaines de ⁿ, avec fonction poids, à nombre minimal de noeuds et exactes sur les espacesQ _k de polynômes de degré k par rapport à chacune de leurn variables. Ces résultats, complétés par des exemples numériques originaux dans ², adaptent à ces espacesQ _k ceux démontréq par H.J. Schmid [14] dans le cadre des espacesP _k de polynômes.

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About Cubature formulas with a minimal number of knots

Summary In this paper we search, from the orthogonal polynomial theory, for conditions which allow to obtain cubature formulas on sets of ⁿ, with weight function. which have a minimal number of knots and which are exact on the spaceQ _k of all polynomials of degree k with respect to each variablex _i, 1in.These results, completed by original numerical examples in ², adapt to the spacesQ _k those proved by H.J. Schmid [14] in the case of polynomial spacesP _k.

     

Une correspondance de modules pour les blocs à groupes de défaut abéliens

Let b be a block of a finite group G with an abelian defect group P and an inertial quotient E. Let us denote by L the semi-direct product of P and E. If E is cyclic and acts freely on P−{1}, we prove that the stable categories of Gb- and L-modules are equivalent, as a consequence of a more general result, without any hypothesis on E, about partial covering exomorphisms relating Gb with a suitable twisted group algebra _*

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à Jacques Tits à l'aube de sa sexagénie     

Représentation de Weil associée à une représentation d'une algèbre de Jordan

In the present Note we construct the Weil representation of the Kantor-Koecher-Tits Lie algebra g associated to a simple real Jordan algebra V. Afterwards we introduce a family of integral operators intertwining the Weil representation with the infinitesimal representations of the degenerate principal series of the conformai group of a Jordan algebra V. We apply this result to the case conformal group SL(2r, ℝ).     

Principes de grandes déviations pour l’estimateur à noyau de la densité de probabilité

We establish pointwise and uniform large deviations principles for nonparametric kernel density estimators. The estimates are based on sequences of independent and identically distributed real random variables.     

Sections hyperplanes à singularités simples et exemples de variations de structure de Hodge

On construit des variétés projectives lisses complexes de dimension 3 à 6 munies de variations de structure de Hodge, en généralisant une construction que J. Carlson et C. Simpson avaient effectuée en dimension 2. Ensuite, on étudie quelques unes de leurs propriétés, en particulier leurs groupes de cohomologie.     

Intégration de multifonctions par rapport à une mesure paramétrée

We investigate some properties of the integral, with respect to a parametrized probability, of a multifunction whose values are compact (nonconvex) subsets of a Banach space. We obtain an approximation of the closure of the Aumann's integral of a multifunction with values in a separable Banach space by the Aumann's integral of multifunctions with values in finite dimensional spaces.     

Classification de certains feuilletages associés à un cusp

We study singularities of foliations given by R. Moussu closely related to a conjecture of R. Thom. We give their analytic classification and prove their topological rigidity.

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Notations , ,F 0 - H 0, III - H ₁,H _p I - H-cusp,H _r -cusp I-3 - H _p I-3, III-2 - -cusp II-1 - _r -cusp III-1     

Réunion de printemps de la société suisse de physique à lucerne le 5 mai 1962

Ohne Zusammenfassung

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Réunion de printemps de la société suisse de physique à lucerne le 5 mai 1962Compte rendu des communications de physique et de mathématiques appliquées

     

Prolongement Méromorphe des séries de Dirichlet à Support dans un sous-Ensemble semi-algébrique de Rn

We consider the Dirichlet series Z(P,A;s) = P^–s(m) (s C) where P R[X₁ ,..., X_n] and A is an open semi-algebraic subset of Rⁿ. We will say that Z(P,A;s) exists if this multiple series is absolutely convergent. In this paper we study the existence and several properties of meromorphic continuations of such series, under certain assumption on P and A. As an application, we show the existence of a finite asymptotic expansion of the counting function with support in A: N_p(A,t):= m A Zⁿ | P(m) t} when t +.     

Distance de Hellinger-Kakutani des lois correspondant à deux processus à accroissements indépendants

Summary In this paper we calculate Hellinger integrals of order for the distribution laws of processes with independent increments. We consider the problems of absolute continuity, mutual singularity and contiguity in further applications. By using Hellinger processes the above problems can be treated in a new systematic manner.

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Distance de Hellinger-Kakutani des lois correspondant à deux processus à accroissements indépendants

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Les auteurs tiennet à remercier J.Jacod et les referees: leurs remarques ont permis d'améliorer la première version de ce texte.