Extrait d'une lettre

Sans résumé     

Endomorphisme de bascule et courbure areolaire d'une sous-variete d'une variete riemannienne

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Equivalence d'une couronne de barres de combustible et d'une surface active

Sans résuméSubside N^o 4353 du Fonds national suisse de la recherche scientifique.     

Anneaux hexaphiques d'une variable

This paper follows up «Anneaux polynômiaux à deux variable», this Rendiconti, Tomo 28 (1979), pp. 80–90.     

Caractérisation du module d'une fonction additive à l'aide d'une équation fonctionnelle

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Essai d'une bibliographie de la représentation analytique d'une fonction monogène

Sans résumé La bibliographie suivante a été élaborée sur la demande de M. Mittag-Leffler. La Rédaction.     

Carre symetrique d'une forme primitive

A direct proof is given for the functionnal equation satisfied by the primitive symmetric square attached to a newform of any level. The method uses technics of modular forms theory and is based on a carefully study of minimal forms and Atkin-Lehner operators on twisted forms. The root number is explicit thanks to some properties of Gauss sums averaes analogous to Barnes Lemma.     

Preuve d'une conjecture de Brieskorn

In this paper we prove the following conjecture of Brieskorn: The complex of (holomorphic) differential forms of an isolated hypersurface singularity of dimension n>1 is exact in degree n–1.     

Perturbation d'une matrice hermitienne ou normale

Summary Given a hermitian (normal) matrixA with known eigenelements, we study the behavior of these elements under a hermitian perturbationH. With a symmetric 2×2 matrix, the problem is explicit (algebraic equation of 2nd degree), and we try, in the case of ann×n hermitian matrix, to obtain upper bounds which are as close as possible of exact results forn=2. The results are collected in § I. They state in a unified manner some results of Davis [2], Gavurin [4], Golub [5], Kato-Temple [7], Ortega [3], Wilkinson [8] and others.In § II, we apply this theory to produce error bounds for eigenelements computed by theQR and Jacobi methods. The given error bounds are realistic and easy to compute during the algorithms. When the separation distance between eigenvalues ofA approaches zero, the problem of computing eigenelements ofA+H is ill-conditionned with respect to the eigenvalues, the eigenvectors being orthogonal. The precision then obtained is given.

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Perturbation d'une matrice hermitienne ou normale

     

Autour d'une conjecture de Serge Lang

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Extensions completes d'une theorie forcing complete

We give two examples of a universal theoryT such that the forcing companionT ^F (as defined by A. Robinson for infinite forcing) has some model which is not the elementary equivalent of a generic model ofT. Our examples answer in a negative way a question posed by E. Fisher and A. Robinson. In the first example, forT ^F, there is an extensionT′ which is complete and forcing comcomplete (that is, (T′) ^F=T′) not generated by a generic model ofT. In the second exampleT ^F has a complete extensionT′ which is not forcing complete.      

Semi-centre de l'algèbre enveloppante d'une sous-algèbre parabolique d'une algèbre de Lie semi-simple

Our aim is to describe the semicentre of the enveloping algebra of a parabolic subalgebra p of a semisimple finite dimensional complex Lie algebra g. Whilst [F. Fauquant-Millet, A. Joseph, Transformation Groups 6 (2) (2001) 125-142] describes explicitly the semicentre of the quantized enveloping algebra associated to p, specialization at q=1 gives only part of the required classical semicentre, even when p is a Borel. Similarly the graded of a polynomial subalgebra of the Hopf dual of the enveloping algebra of g, associated to the Kostant filtration, gives a lower bound on the required semicentre. Then by a method developed from [A. Joseph, Amer. J. Math. 99 (6) (1977) 1151-1165; J. Algebra 48 (1977) 241-289] we obtain an upper bound. Finally when g is a product of simple Lie algebras of type An or Cn we show that these bounds coincide and conclude that in this case the semicentre of the enveloping algebra of p is a polynomial algebra.