Le complete formel d'un espace analytique le long d'un sous-espace: Un theoreme de comparaison

We prove here a theorem, which generalizes Grauert's comparison theorem ([4], Hauptsatz IIa; cf. also Knorr [7], Vergleichssatz) and which is an analogue of a Grothéndieck's result in Algebraic Geometry ([6], Chap. III., 4.1.5). The proof makes essential use of a coherence theorem for sheaves of polynomials: Let X,Y be complex spaces, : XY a proper holomorphic map and T=(T₁,...,T_N) a system of indeterminates. Then, for everyO _X[T] graded sheafm, all direct image sheaves R^q_* m areY[T]-coherent. The proof is as in [2].

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Diese Arbeit entstand während eines Aufenthalts des Verfassers am Fachbereich Mathematik der Universität Regensburg als Stipendiat der Alexander-von-Humboldt-Stiftung.     

Sur le probleme de la rotation d'un corps solide autour d'un point fixe

Sans résumé Ce mémoire est le résumé d'un travail auquel l'Académie des Sciences de Paris, dans sa séance solennelle du 24 décembre 1888, a décerné le prix Bordin élevé de 3000 à 5000 franes     

Sur l'invariant deSmale d'un plongement

Sans résumé Pendant la préparation du présent article, l'auteur a été titulaire d'une bourse de la National Science Foundation, numéro N.S.F.-G 5863.     

Sur l'anneau d'un groupe hyperbolique

Using remarkable properties of the length fonction in hyperbolic spaces, one proves the unique factorization property for certain hyperbolic groups. In particular these groups have no zero divisors in their group rings.     

Sur l'identification d'un processus de branchement surcritique

We unify, under a one parameter family, the most common estimators of the mean and the variance of the offspring distribution for a supercritical one-type branching process. We give the rate for the almost-sure convergence, and the asymptotic normality for each one of these estimators. We select, within this family, the “best” estimators for the mean, the variance, and the pair (mean, variance). The asymptotic independence for the standardized estimation errors is also established. To cite this article: K. Hamza, F. Maâouia, C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Sur la construction d'un corps de Hilbert

We are concerned with the following: If k is a quadratic field and N a cyclic unramified extension of degree qⁿ over k, q a prime number, determine N explicitely via a primitive element , i.e., N=k(), in the spirit of Helmut Hasse [3]. We propose a method which determines these extensions, once we are able to specify the arithmetic of a certain field . To explicit our method, we construct the Hilbert fields of (226) and (646).     

Image inverse d'un D-module and Newton Polygon)

We show that, under conditions about the microcharacteristic variety of a coherent -module, the Cauchy problem is well-posed in the spaces of formal power series with Gevrey growth. We deduce that the filtration of the Irregularity Sheaf of a holonomic -module, which we defined in a previous work, is preserved under inverse image if some rather general geometric conditions are fullfilled.     

Fonction L unité d'un groupe de Barsotti-Tate

The purpose of this article is to give a cohomological formula for the unit-root part of the L-function associated to a Barsotti-Tate group G on a scheme S over a field of characteristic p when G extends to some compactification of S. This is an analogue of a part of a conjecture of Katz according to wich the L-function of an F-crystal should be expressed in terms of the p-adic etale sheaf corresponding to the unit-root part of the crystal. In order to carry out this project, we use the technics of [E-LS II] wich require in our case an extension of the Dieudonné crystalline theory ([B-B-M]) to “crystal of level mG” in the sense of Berthelot. We show that the unit-root L-function of the Dieudonné crystal associated to G can be expressed in terms of the syntomic cohomology of the Ext group of G by the constant sheaf.

Received: 24 March 1997 / Revised version: 6 January 1998     

Factorisation dans un Ordre Non Maximal d'un Corps Quadratique

Let O_f be an order of index f in a quadratic field. We denote A_f the set of elements of O_f whose norm is relatively prime to f. An element v ∈ A_f is called k-prime if for x, y ∈ A_f, v|xy implies v|x^k or v|y^k where k is the exponent of the group O_f. We prove that the k-th powers of the elements of A_f have a unique representation as a product of elements which are irreductible and k-prime. One criteria for resolution of some diophantine equations is an illustration from it.     

La Couronne d'un Cône Symétrique

The crown of a Riemannian symmetric space of non compact type is a domain in its complexification with the following remarkable property: All eigenfunctions of the invariant differential operators have a holomorphic extension to the crown, and this domain is maximal for this property. We explain how it follows from recent results by Krötz and Stanton, and by Barchini. Furthermore we describe the geometry of the crown of a symmetric cone, and finally we give several realizations of the crown of the real hyperbolic space.     

La valeur d'un entier classique en \lambda\mu-calcul

In this paper, we present three methods to give the value of a classical integer in -calculus. The first method is an external method and gives the value and the false part of a normal classical integer. The second method uses a new reduction rule and gives as result the corresponding Church integer. The third method is the M. Parigot's method which uses the J.L. Krivine's storage operators.

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Re?u le 4 Septembre 1995     

Representations approchees d'un groupe dans une algebre de banach

Let T be a continuous map from a compact group G to the group of invertible bounded linear operators on a Hilbert space H, the latter being endowed with the norm topology. If the norms T(gh)-T(g)T(h) are small enough (g,h G), we show that T is a small perturbation of some norm continuous representation of G on H.     

Temps d'arrÊt d'un système dynamique

Summary The most general positive integer-valued random variable v such that for a given bijective measure preserving transformation , the transformation ^v is still bijective and measure preserving is shown to be a (generally infinite) superposition of return times.

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Equipe de Recherche n 1 «< Processus stochastiques et applications»> dépendant de la section n 2 «Théories Physiques et Probabilités» associée au C.N.R.S.     

Sur les plus grands facteurs premiers d'un entier

Let and, for each integern such that (n)k, denote byP _k (n) itsk ^th largest prime factor. Further, given a set of primesQ of positive density <1 satisfying a certain regularity condition, defineP(n, Q), as the largest prime divisor ofn belonging toQ, assuming thatP(n,Q)=+ if no such prime factor exists. We provide estimates of , fork2, and of . We also study the median value of the functionP(n,Q) and that of the functionP _k (n) for eachk1.     

Atomes conditionnels d'un espace de probabilité

Sans résumé Présenté par A. Rényi     

Equation de Choquet-Deny sur le dual d'un groupe compact

Résumé On étudie les solutions de l'équation de convolution *= où et sont respectivement un poids et un état sur l'algèbre de von Neumann d'un groupe compactG, la convolution * étant déterminée par la structure d'algèbre de Hopf de cette algèbre de von Neumann.

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Summary We study the solutions of the convolution equation *= where and are a weight and a state on the von Neumann algebra of a compact group, and the convolution is given by the Hopf algebra structure of this von Neumann algebra.

     

Une formule pour calculer la distribution du maximum d'un processus stochastique

We give a formula for the distribution of the supremum on an interval of a random process with a real parameter. Our method is based on the number of crossings of a level. Two procedures are described: 1) for processes having C^∞ paths; 2) for processes having only continuous paths. The example of stationary Gaussian processes is considered.     

Evaluation de l'incertitude sur la solution d'un système lineaire

The evaluation of the accuracy of solutions of linear algebraic systems by numerical method is not easily accomplished on account of the finite precision of computer arithmetic.In this paper, we present a numerical method which determines for each variablex _i , the numberC _i of exact significant figures.