Comptes Rendus de l'Académie des Sciences - Series I - Mathematics最新文献

One shows the existence of a smooth projective curve over $\text{F}{}_2$ and of representations of the arithmetic fundamental group of X⊗k with values in $\text{SL}{}_2\text{(k[[t]])}$, with k suitable finite field of characteristic 2, such that the image of the geometric fundamental group is infinite. This gives a negative answer to a question of A.J. de Jong.

We have introduced in a previous Note a variant of the Schwarz algorithm without overlap for wave propagation. We present here a nonconforming finite volume discretization of the algorithm and analyze the convergence of the discrete algorithm.

In [2] Chern proved, through methods of differential geometry, the Baum–Bott theorem in the non-degenerate case, that is, for one-dimensional holomorphic foliations whose singular set consists of isolated points and such that, in a neighborhood of such a point, any vector field defining the foliation has linear part with non-zero eigenvalues at the point in question. In this Note we show that, by slightly modifying Chern's proof, we can prove Baum–Bott's result as stated in [1], hence without the “non-degenerate” assumption.

Dans [2] Chern a démontré, en n'utilisant que des méthodes de géometrie différentielle, le théorème de Baum–Bott dans le cas non dégénérée, c'est-à-dire, pour les feuilletages holomorphes de dimension un avec points singuliers isolées et tells que, au voisinage d'un tel point, un champ définissant le feuilletage admet une partie linéaire avec toutes ses valeurs propres non nulles au point en question. Le but de cette Note est de montrer que la preuve donnée par Chern peut être un peu modifiée, de façon a obtenir le résultat de Baum–Bott dans [1], où l'hypothèse «non dégénérée » n'intervient pas.

As it is well known in K-theory, stabilization of matrices enables them to commute “up to homotopy”. The purpose of this short paper is to describe an analogous philosophy for cochains on a space. It is in fact a direct application of a paper of Henri Cartan [1], together with a new idea of stabilization for cochains, similar to matrices. The application below may be also deduced from a paper of J. Halperin and J. Stasheff [2] by a quite different method. This paper is part of a joint project with P. Baum about the cohomology of homogeneous spaces. Since it has some independent interest, it might be useful to present it on its own right.

We prove that the convex envelope of a differentiable, or C^1,α-function f is C¹, or C^1,α respectively, provided only that the function satisfies the very mild growth condition that f(x) tends to +∞ if |x| does so.

This Note presents a composition condition which yields vanishing of all the obstructions to a center displayed in Françoise's algorithm for the computation of higher order Melnikov functions [6,9]. We discuss some examples and the relation with the composition condition of Alwash and Lloyd [1,2].

We consider two thin linearly elastic cylindrical shells, bonded to each other. The thickness of each shell is 2ε, ε being small. The adhesive material is assumed to be a linearized Saint-Venant Kirchhoff material, with Lamé constants of order ε^q with q>0 as in [1,2]. This material then constitutes a cylindrical shell with a thickness ε^r with r>1. The upper shell is loaded with a volumic density of order ε². We consider the case q=3+r. We then establish the convergence, in appropriate spaces, of the scaled displacements and scaled stress tensors when ε goes to zero. The limit displacement satisfies a flexural model which involve the shear and the normal stress of the adhesive part. These stresses depend on the jump of the tangential and normal displacements of the bonded shells.

In this Note, we study a two-level Schrödinger–Bloch system: first we introduce a nondimensional form of the system in which a small parameter appears. Then we prove an existence theorem and an asymptotic result. Finally, we propose an efficient numerical scheme that is uniform with respect to the small parameter.

We will introduce two notions of compatibility between pseudo-Riemannian metric and Poisson structure using the notion of contravariant connection introduced in [1], we will study some properties of manifold endowed with such compatible structures and we will give some examples.

We construct a distribution on $\text{R}{}^2$, invariant under the linear action on $\text{R}{}^2$ of the group $\text{Γ=}\text{SL}\text{(2,}\text{Z}\text{)}$, whose decomposition into homogeneous terms depends on all non-holomorphic modular forms for the group Γ, and which plays a major role in the automorphic Weyl calculus.