Sur les racines d'une équation fondamentale

Sans résumé Les théorèmes I et II de la présente note ont été déjà publiés dans un mémoire portant ce même titre et communiqué à l'académie des sciences à Stockholm le 14 nov. 1900.     

Équation homologique et cycles asymptotiques d'une singularité nœud-col

Let a germ of holomorphic vector field Z be given and assume that is an isolated degenerate-resonnant singular point for Z (one and only one non-zero eigenvalue). Such a vector field acts as a derivative over the space of holomorphic germs at the origin of the complex plane. We obtain the solutions of the homological equation Z·F=G by integrating G along some asymptotic paths tangent to the complex trajectories of Z and ending at the singularity; this locate the obstructions to solve such an equation in the period of G along asymptotic cycles. The Borel transform is thus extended to the foliated setting and this geometrical approach helps us in the study of the conjugacy problem. For instance we find without expense of computation the obstructions obtained previously by P.M. Elizarov for the Poincaré-Dulac models. This approach of the caracteristics method in the singular setting will lead us, in a further print, to describe the analytical classification of germs of degenerate-resonnant vector fields.     

Sur les solutions d'une équation fonctionnelle,III

Sans résumé

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

Sans résumé     

La solution d'une équation fonctionnelle à l'aide de la théorie des distributions

Sans résumé Présenté par B. Sz.-Nagy     

Les constantes locales de l'équation fonctionnelle de la fonctionL d'Artin d'une représentation orthogonale

Sans résuméA Jean-Pierre Serre en témoignage d'admiration     

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.     

L'espace des sélections d'une dendrite

We prove that the selection space of a nondegenerate dendrite is homeomorphic to ?².     

Sur le principe de superposition et l'équation de Riccati

In this Note we study the conditions under which a system of ordinary differential equations admits a nonlinear superposition of the solutions, and also the linearization of such systems. A particular study is established for the Riccati equation. To cite this article: S. Rezzag et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Estimations uniformes pour l'équation de Yamabe en dimensions 5 et 6

We give some a priori estimates for Yamabe equation on Riemannian manifold in dimensions 5 and 6. In dimension 5 we present an inequality of type sup×inf. In dimension 6, we have an estimate if we assume that the infima of the solutions are uniformly bounded below by some positive constant.     

Interprétation bijective d'une récurrence des nombres de Motzkin

The purpose of this note is to give a combinatorial proof of the three-term linear recurrence for Motzkin numbers. The present work is inspired by Rémy's combinatorial proof of the linear recurrence for Catalan numbers (RAIRO Inform. Theor. 19(2) (1985) 179) and the more recent proof given by Foata and Zeilberger (J. Combin. Theory Ser. A 80(2) (1997) 380) for Schröder numbers (Z. Math. Phys. 15 (1870) 361).