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).     

The 3-D FEL pulse propagation equation: An analytical treatment in the low-gain and small-signal regime

Summary In this paper we show that the transverse mode evolution of a FEL operating with short pulses can be treated, in the small-signal and low-gain regime, using a relatively simple mathematical technique leading to a potentially fast numerical algorithm. We also point out that analytical solutions can be obtained for the cases where the slippage length is small compared to the longitudinal bunch length.     

Synthesis and Inclusion Properties of the Host Compound 1,3-Dihydro-1,1,3,3-tetraphenylisobenzofuran. X-Ray Crystal Structures of the Free Host and of an Inclusion Compound with 1,4-Dioxane

A novel host molecule, 1, suitable for crystalline lattice-type inclusion, has been synthesized, and its cocrystal formation ability has been investigated. Host 1 proved to be of potential use for organic solvent separation and retrieval, and a promising auxiliary for solidification of certain odorous substances. The crystal structures of the solvent-free host 1, and its complex with 1,4-dioxane (1 : 1), have been determined by single crystal X-ray diffraction. The structure of 1 (guest-free) is triclinic, P , with a = 9.452(2), b = 10.359(3), c = 13.116(3) Å, = 101.80(2), = 106.53(1) and = 104.32(1)°. The spacious, propeller-like molecules are held together by weak van der Waals' forces. The dioxane inclusion compound is monoclinic, P21/a, with a = 15.050(1), b = 8.641(1) and c = 20.658(1) Å, and = 94.56(1)°, and contains two crystallographically independent guest molecules, both located around symmetry centres. The molecular packing seems to be governed by C—H···O type bonds (C···O = 3.31 and 3.48 Å) from the host to the dioxane oxygens.     

Electrochemical oxidation of aliphatic amines and their attachment to carbon and metal surfaces

The electrochemical oxidation of aliphatic amines (primary, secondary, and tertiary) has been investigated by cyclic voltammetry and preparative electrolysis. The oxidation mechanisms have been established, and the lifetimes of the radical cations have been measured for secondary and tertiary amines. These results have been put in parallel with the attachment of amines to glassy carbon, Au, and Pt electrodes by cyclic voltammetry, X-ray photoelectron spectroscopy (XPS), and infrared reflection-absorption spectroscopy (IRRAS). It is then possible to show that it is not the radical cation but the radical obtained after the deprotonation which reacts with the electrode surface. XPS results also point to the existence of a covalent bond between Au or Pt and the organic moiety.