Convergence de modèles moléculaires vers des modèles de mécanique des milieux continus

The work we present here is focused on the justification of continuum mechanics as a natural asymptotic of molecular theories when the interatomic distance goes to zero. We give a sound theoretical ground to existing models, and derive and next study (apparently) new ones.     

Classes de Chern des intersections complètes locales

We prove, for (strong) local complete intersections with isolated singularities, a formula expressing the Chern—Schwartz—MacPherson class in terms of the Chern class of the virtual tangent bundle and the Milnor numbers at the singular points.     

Systoles des surfaces plates singulières de genre deux

The extremal metrics for the isosystolic problem on surfaces of genus two are studied in this paper. We show that, contrary to E. Calabis conjecture in genus three, no flat metric with conical singularities is extremal for this problem in genus two.in final form: 28 August 2003     

Dimension de Hochschild des algèbres graduées

It is a basic fact that the global dimension of a connected $\mathbb{N}$-graded algebra coincides with the projective dimension of the trivial module. This result is recovered by proving that the Hochschild dimension is equal to the projective dimension of the trivial module. Thus the result becomes more natural with bimodules entering into the picture. To cite this article: R. Berger, C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Un modèle de Rotenberg avec des vitesses de maturité nulles

The Note [1] is devoted to the study of the Rotenberg's [8] model describing the growth of cell population when the maturation velocity belongs to a, b, with 0 < a < b < ∞. In this Note we bring new techniques for treating the case 0 = a < b < ∞.     

Espace des modules de certains polyèdres projectifs miroirs

A projective mirror polyhedron is a projective polyhedron endowed with reflections across its faces. We construct an explicit diffeomorphism between the moduli space of a mirror projective polyhedron with fixed dihedral angles in (0,\fracp2]{(0,\frac{\pi}{2}]}, and the union of n copies of \mathbbR^d{\mathbb{R}^{d}}, when the polyhedron has the combinatorics of an ecimahedron, an infinite class of combinatorial polyhedra we introduce here. Moreover, the integers n and d can be computed explicitly in terms of the combinatorics and the fixed dihedral angles.     

Sur le problème de descente des formes quadratiques

In this paper, we give some positive answers to a conjecture of B. Kahn on a descent problem for quadratic forms [9].     

Hypercontractivité pour des systèmes de spins de portée infinie

Résumé Nous considérons un système de spins sur ^d . Nous prouvons l'équivalence entre premièrement une condition faible de mélange deuxièmement le contrôle du trou dans le spectre et troisièmement celui de la constante de Sobolev logarithmique pour des potentiels de Gibbs de portée non nécessairement finie. Nous en tirons des conséquences sur la vitesse de convergence des semi-groupes dansL ² et sur la décroissance des corrélations: il n'y a pas de régime intermédiaire entre un taux algébrique ent ^–2d (resp. |j-k|^–2d) et un taux exponentiel. Les résultats généraux sont montrés pour des spins à valeur dans une variété riemannienne compacte ou dans un espace fini.

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Summary We consider a spin system on ^d . We prove the equivalence between first a weak mixing condition, secondly the controle of spectral gap and thirdly the controle of logarithmic Sobolev constants for non necessarily finite range Gibbs potentials. Hence we draw consequences concerning theL ² decay to equilibrium and the correlations decay: there is no transitory rate between an algebraic decay ast ^–2d (resp. |j-k|^–2d)and exponential decay. The general results are obtained for both continuous and discrete compact spins.

This article was processed by the authors using the LATEX style filepljour Im from Springer-Verlag     

Sur la Classification des Nilalgèbres Commutatives de Nilindice 3

We give some structure results and recursive-like methods for constructions and classifications of commutative nilalgebras of nilindex 3.     

Stabilisation frontière de problèmes de Ventcel

We study Ventcel's problems for the wave equation and the isotropic linear elastodynamic system. The boundary observability and the exact controlabillity were established in [3]. We prove the energy decay for the elastodynamic system with stationary Ventcel's conditions. We also give a boundary feedback leading to arbitrarily large energy decay rates for the elastodynamic system with evolutive Ventcel's conditions. A spectral study proves, finally, that the “natural” feedback is not sufficient for the exponential decay in the case of the wave equation with Ventcel's conditions.