Perturbation des produits infinis et applications

Sans résumé Les auteurs remercient l'Institut de recherche d'été de la Société Mathématiques du Canada, le CNR, DIGES du Québec et la Fondation Fleischer pour leur appui. An erratum to this article is available at .     

Theories egalitaires dans les Langages sur types de graphes

Sans résumé Ce travail doit son origine et son développement, aux préoccupations de recherche qui animent le groupe de “Logique et théorie des catégories,” dirigé par le Professeur A. Preller à l'U.E.R. de Luminy (Université d'Aix-Marseille II). Presented by J. D. Monk.     

Sur la théorie locale des pseudogroupes de transformations continus infinis I

Sans résumé

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Re?u le 20 octobre 1995 / Version revisée re?ue le 29 mai 1996     

Produits infinis de resolvantes

This paper is concerned with the convergence of the sequence χ _n =(I+λ _n A)⁻¹χ _n−1 whereA is maximal monotone and λ _n >0. Various assumptions onA and λ _n are considered.      

Tournois infinis et critiques

Given a tournament T=(V,A), a subset X of V is an interval of T provided that for every a,b∈X and x∈V?X, (a,x)∈A if and only if (b,x)∈A. For example, ?, {x} (x∈V) and V are intervals of T, called trivial intervals. A tournament all the intervals of which are trivial is called indecomposable; otherwise, it is decomposable. An indecomposable tournament T=(V,A) is then said to be critical if for each x∈V, T(V?{x}) is decomposable and if there are x≠y∈V such that T(V?{x,y}) is indecomposable. We introduce the operation of expansion which allows us to describe a process of construction of critical and infinite tournaments. It follows that, for every critical and infinite tournament T=(V,A), there are x≠y∈V such that T and T(V?{x,y}) are isomorphic. To cite this article: I. Boudabbous, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Rotations et quasi-invariance sur l'espace des chemins

The purpose of this paper is to show by examples the role of rotations in the study of quasi-invariance on a nonflat Wiener space

     

Structure des cocycles markoviens sur l'espace de Fock

Summary We show that strongly continuous unitary Markov cocycles on Fock space are solutions of a quantum stochastic Schrödinger equation and give their explicit form through a decomposition of Fock space on the eigenspaces of the number operator. We also give necessary and sufficient conditions for a generalized Hamiltonian to be the generator of such a cocycle. This generalizes the work of Hudson and Parthasarathy in the norm-continuous case.     

Anneau des formes quasi-modulaires sur un groupe co-compact

We describe the additive structure of the graded ring ${\stackrel{?}{M}}_1(\Gamma )$ of quasimodular forms over any discrete and cocompact group $\Gamma ?\mathrm{PSL}(2,\mathbb{R})$. We show that this ring is not finitely generated. We calculate the exact number of new generators of weight k (even). This number is constant for k sufficiently large and equals ${\dim }_{\mathbb{C}}I/(I\cap {\stackrel{?}{I}}^2)$, where I and $\stackrel{?}{I}$ are the ideals of modular forms and quasimodular forms, respectively, over Γ of strictly positive weight. To cite this article: N. Ouled Azaiez, C. R. Acad. Sci. Paris, Ser. I 343 (2006).     

Essai sur les petites vibrations des astres fluides

Sans résumé     

Développments terminaux des graphes infinis III. Arbres maximaux sans rayon,cardinalité maximum des ensembles disjoints de rayons

A class of FELLER 's one-dimemsional continuous strong MARKOV processes generated by the generalized second order differential operator D_mD₈⁺ is considered. In the case of natural boundaries of the state space ?? and an identical road map s(x) = x, these diffusion processes are martingales. In a first part of this note some earlier results concerning the representation of such processes as weak solutions of stochastic differential equations are improved. The second part concerns with diffusions absolutely continuous with respect to a given one, determined by the generator D_mD. Such absolutely continuous diffusions on the line were first described analytically by S. OREY in terms of the corresponding speed measures and road maps. By the aid of the derived stochastic equations an explicit expression for the corresponding RADON -NIKODYM derivatives is possible. This allows a characterization of diffusions with non-identical scale functions by stochastic differential equations.     

Iterations sur des ensembles finis et automates cellulaires contractants

By using a Perron-Frobenius theory for Boolean matrices, contraction is defined for finite cellular automata. This notion ensures global convergence towards a unique fixed point (stable configuration), convergence of the Gauss-Seidel associated process, etc. This can be seen as a link between results of numerical algebra for systems of equations and the domain of finite iterations.