Un principe d'invariance relatif à un processus généralisant le mouvement brownien N-dimensionnel

We prove that the generalized random walks associated to a root system R in $\text{R}{}^{\mathrm{N}}$ and a nonnegative multiplicity function k defined on R, converge in distribution (if suitably normalized) to a Markov process with càdlàg trajectories and infinitesimal generator a differential-difference operator on $\text{R}{}^{\mathrm{N}}$ which generalizes the usual Laplacian. To cite this article: L. Gallardo, L. Godefroy, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Symetries isometriques applications a la dualite des espaces reticules

We show that ifE is a non-reflexive Banach lattice, there exists for everyn a dual of finite even order ofE which contins isometicallyl _n ^/l . We show that itE is a Banach lattice which is isometric to the dual of a Banach spaceX, then the order intervals are σ (E, X)-compact. We prove then that under various conditions, a Banach lattice which is a dual as a Banach space, is a dual as a Banach lattice. In particular, this is true when the predual ofE is unique.      

Overtone spectroscopy of some benzaldehyde derivatives

Overtone spectrum of o, m and p-nitrobenzaldehydes and p-chlorobenzaldehyde has been studied in 2000–12000 cm⁻¹ region. Vibrational frequencies and anharmonicity constants for aryl as well as alkyl CH stretch vibrations have been determined. We have also determined the internuclear distances for the aryl CH bond in the different molecules. The small variation observed in these distances is an indication of the substitution effect. It is observed that in the case of p-disubstituted benzens, the shift in aryl CH bond is proportional to sum of the Hammet σ of the substituents. However in the case of o-disubstituted benzenes it is only 80% of the para-substituted shift.     

Strong Subdifferentiability of Convex Functionals and Proximinality

Using strong subdifferentiability of convex functionals, we give a new sufficient condition for proximinality of closed subspaces of finite codimension in a Banach space. We apply this result to the Banach space K(l₂) of compact operators on l₂ and we show that a finite codimensional subspace Y of K(l₂) is strongly proximinal if and only if every linear form which vanishes on Y attains its norm.     

Ueber fractionirte Destillation

Ohne Zusammenfassung     

Propriété de Liouville et équation de Poisson pour le laplacien généralisé de Dunkl

Let Δ_k be the Dunkl generalized Laplacian associated to a root system R of $\text{R}{}^{\mathrm{N}}$ and a non-negative function k defined on R and invariant by the Weyl group. In this Note, we show that this differential-difference operator on $\text{R}{}^{\mathrm{N}}$ satisfies the Liouville property, then we solve the Poisson equation Δ_ku=?f by using a generalized Fourier analysis method. To cite this article: L. Gallardo, L. Godefroy, C. R. Acad. Sci. Paris, Ser. I 337 (2003).