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.     

Thermal and kinetic study of the ferroelectric phase transition in deuterated triglycine selenate

The specific heat and the enthalpy variation of a highly deuterated crystal of ferroelectric triglycine selenate have been measured around its first-order phase transition using the technique square modulated differential thermal analysis (SMDTA). The low temperature variation rate has allowed analyzing the kinetics of the phase transition. Due to an internal crack in the sample, the transition is carried out in two steps and an intermediate region where the transition is blocked and both phases coexist without transformation has been found. The latent heat on cooling (L _c=1.32±0.02 J g^–1) is higher than on heating (L _h=1.08±0.02 J g^–1) due to the thermal hysteresis and the great difference between the specific heat in both phases. Nevertheless, the enthalpy balance is fulfilled on heating and on cooling.     

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.     

Analysis of the 5p6p configuration of Xe V

The spectrum of four times ionized Xenon (XeV), has been observed in the 500–6800 Å range and 84 new lines have been identified as transitions between levels of 5s5p ³, 5s ²5p5d, 5s ²5p6s, 5s ²5p ², and 5s ²5p6p configurations. Nine new levels belonging to the configuration 5p6p have been determined. The results of this analysis are supported by Hartree-Fock calculations. The configurations are interpreted by fitting the theoretical energy parameters to the observed levels using least-squares techniques.     

Cylindrical Gaussian-Hermite modes in rectangular waveguide resonators

Approximate solutions to the wave equation inside a rectangular metallic waveguide has been obtained in terms of cylindrical Gaussian-Hermite functions.E _mn ^π modes propagate with negligible straight guide losses in the far-infrared region. A new type of low-loss optical resonator suitable for FEL operation at long wavelengths is presented here.     

Effect of Sintering Temperature on the Corrosion and Wear Behavior of Protective SiO2-Based Sol-Gel Coatings

Sol-gel hybrid organic-inorganic and inorganic SiO₂-based protective coatings with and without added 3 m glass particles were developed and tested for their corrosion and wear behavior of an stainless steel substrate (AISI316L). The corrosion resistance greatly increases by incorporating glass particles in the sols. The incorporation of particles in the coatings allows the synthesis of thicker crack-free coatings. On the other hand, the corrosion resistance increases for coatings with a higher organic content obtained at lower sintering temperature. These coatings are also highly stable in saline aqueous solutions. However, the wear resistance is badly affected by the hybrid character of the SiO₂ matrix. The optimum coating process in terms of corrosion and wear resistance, appears to be a hybrid system with a dense SiO₂ network achieved at intermediate sintering temperatures.     

Determination of seven selected antipsychotic drugs in human plasma using microextraction in packed sorbent and gas chromatography–tandem mass spectrometry

A method using microextraction by packed sorbent (MEPS) and gas chromatography–tandem mass spectrometry (GC-MS/MS) is described for the determination of seven antipsychotic drugs in human plasma. The studied compounds were chlorpromazine (CPZ), haloperidol (HAL), cyamemazine, quetiapine, clozapine, olanzapine (OLZ), and levomepromazine; promazine, protriptyline, and deuterated CPZ were used as internal standards. The validation parameters included selectivity, linearity and limits of detection and quantitation, intra- and interday precision and trueness, recovery, and stability and were studied according to internationally accepted guidelines. The method was found to be linear between the lower limit of quantitation and 1000 ng/mL, except for OLZ and HAL (200 ng/mL), with determination coefficients higher than 0.99 for all analytes, and extraction efficiencies ranged from 62 to 92 %. Intra- and interday precision ranged from 0.24 to 10.67 %, while trueness was within a ±15 % interval from the nominal concentration for all analytes at all studied levels. MEPS has shown to be a rapid procedure for the determination of the selected antipsychotic drugs in human plasma, allowing reducing the handling time and the costs of analysis. Furthermore, GC-MS/MS has demonstrated to be a powerful tool for the simultaneous quantitation of the studied compounds, enabling obtaining adequate selectivity and sensitivity using a sample volume of as low as 0.25 mL.