Un theoreme sur les homomorphismes de schemas abeliens

Sans résumé À André Weil, pour son anniversaire     

Un theoreme sur les sommes amalgamees de groupes simpliciaux

In [1], D.M. Kan and R.F. Thurston prove two theorems on amalgamed sums of simplicial groups (cf corollaries 1 and 2 above) starting from a topological theorem of J.H.C. Whitehead. The proofs given in this paper are simplicial from the beginning; in the case where all groups are concentrated in dimension 0, one finds back J.H.C. Whitehead's theorem.     

Une méthode multipas implicite-explicite pour l'approximation des équations d'évolution paraboliques

Résumé Considérons une équation d'évolution parabolique linéaire associée à un opérateur linéaireA(t) dépendant du tempst. Nous développons dans cet article une méthode de discrétisation, basée sur les méthodes linéaires à pas multiples, traitant de manière implicite une partie de l'opérateurA(t) indépendante du temps, l'autre partie est traitée de manière explicite. Nous étudions la stabilité et la convergence de cette méthode.

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An implicit-explicit multistep method of the approximation of parabolic equations

Summary Let us consider a linear parabolic equation which is associated with a time dependent operatorA(t). In this paper, we present a method, which is founded on linear multistep methods, which discretize a time-independent part of the operatorA(t) in an implicit way, and the other part in an explicit way. We study stability and convergence for this method.

     

Un théorème de prolongement pour des fonctions analytiques

Sans résumé     

Un résultat de consistance pour des SVM fonctionnels par interpolation spline

This Note proposes a new methodology for function classification with Support Vector Machine (SVM). Rather than relying on projection on a truncated Hilbert basis as in our previous work, we use an implicit spline interpolation that allows us to compute SVM on the derivatives of the studied functions. To that end, we propose a kernel defined directly on the discretizations of the observed functions. We show that this method is universally consistent. To cite this article: N. Villa, F. Rossi, C. R. Acad. Sci. Paris, Ser. I 343 (2006).     

Un processus effectif de détermination des systoles pour les surfaces hyperboliques

We give an effective process to discribe explicitly the systols of an hyperbolic surface depending on his Fenchel-Nielsen coordinates.      

Preuve ≪Elementaire≫ du theoreme de Grothendieck-Lefschetz pour les hypersurfaces

Sans résumé     

Parcours dans les graphes: Un outil pour l'algorithmique des ensembles ordonnes

A finite poset can easily be represented by a directed acyclic graph. This work intends to make use of performant graph search methods as a tool for checking order properties. Semi-modular posets and semilattices are investigated here.An underlying idea consists in turning to account structural properties of the poset, and deriving effective algorithms. This purpose leads us to ‘good’ theoretic characterizations — that is, directly available from an algorithmic point of view — and especially a new one for modular lattices.     

Un algorithme de type Robin pour des problèmes de contact unilatéral

In this Note, we propose a Robin domain decomposition algorithm to approximate a frictionless unilateral problem between two elastic bodies. Indeed, this algorithm combines on the contact zone the Dirichlet and Neumann boundaries conditions (Robin boundary condition). The primary feature of this algorithm is the resolution of the same variational inequality on each sub-domain. To cite this article: M. Ipopa, T. Sassi, C. R. Acad. Sci. Paris, Ser. I 346 (2008).     

Application des inequations quasi-variationnelles a quelques problemes non lineaires de la physique des plasmas

This paper deals with some problems arising in plasma physics. The typical example is the following: where is the (neither local, nor monotone, nor continuous) operator: . Using a quasi-variational approach, we prove the existence of minimal and maximal solutions for a weak form of this problem, involving a multi-valued operator β. Various generalizations are treated.      

Un principe variationnel pour les empilements de cercles

Sans résuméOblatum 16-XI-1990     

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.