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).     

A Scanning Electron Microscopy study of water in soil

Cold stage Scanning Electron Microscopy (SEM) with a rapid cooling technique makes it possible to investigate the water phase within unsaturated porous media. It is thought that this technique preserves the main features of the micromorphology of the water menisci as it exists in the liquid phase in soils. Saddle-shaped elements, as well as pendular rings of water, were observed with concave and convex curvatures of the water-air interface. The hydraulic conductivity of an unsaturated soil may be inferred from SEM photographs. Observations of isolated water menisci indicate the existence of an immobile water domain. The surface geometry of the water menisci was analyzed quantitatively and surface tension and capillary pressure were determined.     

Improvement of the properties of polyarylate reinforced with liquid crystalline polymers

Blends of polyarylate of bisphenol A, PAr, with two commercial main chain liquid crystalline polymers, Vectra A950 and Vectra B950, are studied. From dynamic viscoelastic measurements it is deduced that both systems (PAr/Vectra A950 and PAr/Vectra B950) are immiscible and scanning electron microscopy (SEM) micrographs show the presence of spherical domains of the liquid crystalline polymer when PAr constitutes the matrix. Extrusion capillary measurements reveal that, under conditions of temperature and shear rate similar to those of processing, the viscosity is reduced to approximately 10% of its value when the content of liquid crystalline polymer is only 20%. This great improvement of the rheological properties is observed in both PAr/Vectra A950 and PAr/Vectra B950 blends. The effect of draw ratio on Young's modulus for different compositions is also analyzed, pointing out the reinforcing action of both liquid crystalline polymers on polyarylate: for instance, 20% of Vectra B950 in the blend gives rise to a 700% increase of the modulus of fibres prepared at a draw ratio of 50. SEM of the extrudates reveals that the spherical domains are elongated at the entrance of the capillary giving rise to a microfibrillar morphology which is related to the excellent rheological and mechanical properties of the blends.     

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.     

Photodynamic activity of dibiotinylated aluminum sulfophthalocyanine in vitro and in vivo

The photodynamic activity of dibiotinylated aluminum sulfophthalocyanine was studied in vitro and in vivo. Dibiotinylated aluminum sulfophthalocyanine provided enhanced phototoxic action on OAT-75 cell monolayers as compared with the parent drug. Photodynamic therapy of mice with Ehrlich carcinoma using dibiotinylated aluminum sulfophthalocyanine (0.25 mg/kg) resulted in enhanced inhibition of tumor growth, pronounced vascular damage (thrombosis and destruction of vascular walls) and eventual tumor necrosis.     

Alkylation of nitroaromatics with tetraalkylborate ion via electrochemical oxidation

Aromatic nucleophilic substitution reaction (S(N)Ar) is one of the most thoroughly studied reactions. Alkylation of nitroaromatics with Grignard reagents via chemical oxidation of the sigma(H)-complexes is the most general method to introduce an alkyl group into a nitroaromatic compound. This approach has considerable drawbacks, especially when more than one nitro group are present in the aromatic ring. In this article, we present an electrochemical approach, which offers a new very selective methodology for obtaining alkyl polynitroaromatic compounds. Different strategies based on the use of tetralkylborate anion as nucleophiles are used so as to increase efficiency and to reduce the drawbacks associated with this reaction. A wide list of dinitro- and trinitro-aromatic compounds are studied, the range of yields obtained being from fair (40%) to excellent (85%). The key to improvement in the process is the use of electrochemical techniques for the oxidation of the mixture sigma(H)-complexes/tetrabutylborate ion. The electroactive character of the nucleophile, which can be oxidized to an alkyl radical, means that the S(N)Ar of the hydrogen polar mechanism is not the only mechanism operating during the electroxidation process, since the hydrogen radical S(N)Ar mechanism is running at the same time. Electrochemical mechanistic studies allow the participation of each mechanism in the global product yield obtained to be quantified.