Défaut d'exactitude des modéles¶de Néron toriques sur un corps local

Let R be a complete discrete valuation ring with mixed characteristic. Denote by K its field of fractions and by k its residue field. Let 0 →A ^K →B ^K →C ^K → 0 be an exact sequence of abelian varieties over K and consider the corresponding complex of Nérons models 0 →A→B→C→ 0, over R. We assume that the identity component B _k ⁰ of the special fibre B _k of B is a torus and we study the defect of exactmess at B in this last sequence.

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Re?u: 4 décembre 1997/ Version revisée: 15 décembre 1997     

High order linear initial-value problems and Schauder bases

In this paper we approximate the solution of a linear initial-value problem, making use of a Schauder basis for certain Banach space associated with such a differential problem. In addition, we apply that results in order to calculate numerically the response from a structure modelled by a three degree-of-freedom mass–damper–spring system.     

FULL DISCRETE NONLINEAR GALERKIN METHOD FOR THE NAVIER-STOKES EQUATIONS

This paper deals with the inertial manifold and the approximate inertial manifold concepts of the Navier-Stokes equations with nonhomogeneous boundary conditions and inertial algorithm. Furtheremore, we provide the error estimates of the approximate solutions of the Navier-Stokes Equations.     

On the condition number of matrices arising in the tikhonov regularization method

In this work, we consider the regularization method for linear ill-posed problems. For operators and approximating subspaces satisfying certain conditions and for a specific form of the regularization parameter, upper and lower bounds are given for the condition number of the corresponding discrete problem.     

Exact groups and Fell bundles

Kirchberg and Wasserman's Theorem, according to which a group is exact if and only if its reduced C*-algebra is exact, is extended to the context of Fell bundles. Received: 31 December 2000 / Revised version: 7 August 2001 / Published online: 4 April 2002     

Rational approximation in the complex plane using a τ-method and computer algebra

Numerous versions of the Lanczos τ-methods have been extensively used to produce polynomial approximations for functions verifying a linear differential equation with polynomial coefficients. In the case of an initial-value problem, an adapted τ-method based on Chebyshev series and the use of symbolic computation lead to a rational approximation of the solution on a region of the complex plane. Numerical examples show that the simplicity of the method does not prevent a high accuracy of results. This revised version was published online in June 2006 with corrections to the Cover Date.     

Optimal Domains for <Emphasis Type="Italic">L</Emphasis><Superscript>0</Superscript>-valued Operators Via Stochastic Measures

We study extension of operators T: E→ L⁰([0, 1]), where E is an F–function space and L⁰([0, 1]) the space of measurable functions with the topology of convergence in measure, to domains larger than E, and we study the properties of such domains. The main tool is the integration of scalar functions with respect to stochastic measures and the corresponding spaces of integrable functions. Partially supported by D.G.I. #MTM2006-13000-C03-01 (Spain).     

Existence for a degenerate diffusion problem with a nonlinear operator

We study a degenerate nonlinear variational inequality which can be reduced to a multivalued inclusion by an appropriate change of the unknown function. We establish existence, uniqueness and regularity results. An application arising in the theory of water diffusion in porous media is discussed as an example.      

Continuity of the Restriction of C 0-Semigroups to Invariant Banach Subspaces

A linear semigroup in a Banach space induces a linear semigroup on a Banach space that can be continuously embedded in the former such that its image is invariant. This restriction need not be strongly continuous, although the original semigroup is strongly continuous. We show that norm or weak compactness of partial orbits is a necessary and sufficient condition for strong continuity of the restriction of a C₀-semigroup. We then show that if the embedded Banach space is reflexive and the norms of the restricted semigroup operators are bounded near the initial time, then the restricted semigroup is strongly continuous.