Showing papers in "Comptes Rendus Mathematique in 2002"

TL;DR: Although this method is not specifically designed for topology optimization, it can easily handle topology changes for a very large class of objective functions and its cost is moderate since the shape is captured on a fixed Eulerian mesh.

TL;DR: Cioranescu et al. as discussed by the authors proposed a novel approach to periodic homogenization based on an unfolding method, which leads to a fixed domain problem without singularly oscillating coefficients.

TL;DR: In this paper, the authors introduce new concentration inequalities for functions on product spaces, which allow to obtain a Bennett type deviation bound for empirical processes indexed by upper bounded functions, which is an improvement on Rio's version (6) of Talagrand's inequality (7) for equidistributed variables.

TL;DR: Cirstea and Radulescu as mentioned in this paper studied the uniqueness of positive solutions blowing-up on ∂Ω, in a general setting that arises in probability theory, and showed that positive solutions can blow-up in a smooth bounded domain.

TL;DR: Gosse and Toscani as discussed by the authors proposed a well-balanced numerical scheme for the one-dimensional Goldstein-Taylor system which is endowed with all the stability properties inherent to the continuous problem and works in both rarefied and diffusive regimes.

TL;DR: In this article, Lagrangian reduced-basis methods for single-parameter symmetric coercive elliptic partial differential equations were considered and it was shown that, for a logarithmic-(quasi-)uniform distribution of sample points, the reducedbasis approximation converges exponentially to the exact solution uniformly in parameter space.

TL;DR: Maday and Turinici as discussed by the authors proposed a time discretization for partial differential evolution equations that allows for parallel implementations, and they reported a first numerical implementation that reveals a large interest.

TL;DR: Acerbi et al. as discussed by the authors report on some regularity results for weak solutions to systems modelling electrorheological fluids in the stationary case, as proposed in [8].

TL;DR: Bardos et al. as discussed by the authors derived the weak coupling limit of the N -body linear Schrodinger equation with Coulomb potential, and derived the time-dependent Schroff-Poisson equation as the weak-coupling limit.

TL;DR: Coquel et al. as discussed by the authors proposed closure laws for interfacial pressure and interfacial velocity within the frame work of two-pressure two-phase flow models to ensure positivity of void fractions, mass fractions and internal energies when investigating field by field waves in the Riemann problem.

TL;DR: Friesecke et al. as discussed by the authors showed that nonlinear plate theory arises as a Γ-limit of three-dimensional nonlinear elasticity and showed that the L 2 distance of ∇v from a single rotation is bounded by a multiple of the L2 distance from the set SO(3) of all rotations.

TL;DR: This Note proposes to develop and analyze reduced basis methods for simulating hierarchical flow systems, which is of relevance for studying flows in a network of pipes, an example being a set of arteries or veins.

TL;DR: Golse as mentioned in this paper proved the hydrodynamic limits of the Boltzmann or BGK equations to the incompressible Euler or Navier-Stokes equations in space dimension 1.

TL;DR: In this article, Klainerman and Rodnianski proposed a rough solution to the Einstein vacuum equations expressed relative to wave coordinates, which takes advantage of the specific structure of the Einstein equations.

TL;DR: Martinez and Sordoni as discussed by the authors constructed a general reduction scheme for the study of the quantum propagator of molecular Schrodinger operators with smooth potentials, which is made up of infinitely small error terms with respect to the inverse square root of the mass of the nuclei, depending on the C ∞ (resp. analytic) smoothness of the interactions.

TL;DR: Friesecke et al. as discussed by the authors showed that the Foppl-von Karman theory arises as a low energy Γ-limit of three-dimensional nonlinear elasticity.

TL;DR: In this article, Paparoditis et al. define a local block-resampling procedure and give an example of its applicability for time series that are not stationary.

TL;DR: Corvaja and Zannier as mentioned in this paper presented a proof of Siegel's theorem on integral points on affine curves, through the Schmidt subspace theorem, rather than Roth's theorem.

TL;DR: Feyel and Ustunel as discussed by the authors showed that the Wasserstein distance between ν 1 and ν 2 is invertible on the support of ν 3.

TL;DR: In this paper, the authors introduced the notions of lower and upper singular dimensions of Sobolev space, and showed that both are equal to N−kp, where k is the number of singular sets.

TL;DR: Nekhoroshev et al. as discussed by the authors introduced fractional monodromy for a class of integrable fibrations which naturally arise for classical nonlinear oscillator systems with resonance.

TL;DR: Del Pino et al. as discussed by the authors studied the asymptotic behavior of nonnegative solutions to Δ p u m using an entropy estimate based on a sub-family of the Gagliardo-Nirenberg inequalities.

TL;DR: Deligne et al. as mentioned in this paper describe groups from the perspective of dual pairs, and their representations from the action of the dual pair on an exceptional Lie algebra, and the subgroups which occur form a Magic Triangle, which extends Freudenthal's Magic Square of Lie algebras.

TL;DR: In this article, a synthetic method to differentiate with respect to a parameter par-tial differential equations in divergence form with shocks is presented, and applied to three problems: the Burgers equation, the shallow water equations and Euler equations for fluids.

TL;DR: Neut et al. as discussed by the authors used the methode d'equivalence de Cartan for deciding the equivalence of deux objects de nature geometrique sous l'action of a pseudo-groupe de diffeomorphismes locaux.

TL;DR: Giordano and Pestov as discussed by the authors showed that a von Neumann algebra is approximately finite-dimensional if and only if its unitary group with the strong topology is the product of an extremely amenable group with a compact group.

TL;DR: Ramis et al. as discussed by the authors propose a notion asymptotique, a caractere q-Gevrey, which is an extension of the notion of fonction theta of Jacobi.

TL;DR: In this article, a smooth counting function of the scaled zeros of the Riemann zeta function is considered and the first few moments tend to the Gaussian moments, with the exact number depending on the statistic considered.

TL;DR: For the classical inviscid water wave problem under the influence of gravity, described by the Euler equation with a free surface over a flat bottom, the authors construct periodic traveling waves with vorticity.

TL;DR: Bourgain et al. as discussed by the authors proposed a frontiere Lipschitzienne frontiere with a frontier frontiere frontiere in R d, d⩾2 and showed that it is possible to find a solution u ∈ C 0 ( Ω )∩ W 1,d (Ω) de l'equation divu=f dans Ω verifiant de plus u=0 sur ∂Ω and l'estimee ‖u ǫ L ∞ +ǫ W 1,d �