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).     

Monotone Nonincreasing Random Fields on Partially Ordered Sets. I

For an arbitrary poset H and measure ρ on H × _R (where _R is the real axis), we construct a monotone decreasing stochastic field η_ρ and compute its finite-dimensional distributions. In the case where H is a Λ-semilattice and the measure ρ satisfies additional conditions, we compute various characteristics of the field η_ρ such as the expectation of the field value at a point, variance of the field value at a point, and correlation function of the field. The described construction of random fields gives a new method for constructing positive definite functions on posets. Bibliography: 6 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 301, 2003, pp. 92–143.     

Thermal conductivity of crystalline chrysotile asbestos

The thermal conductivity of crystalline chrysotile asbestos made up of hollow tubular Mg₃Si₂O₅(OH)₄ filaments is measured in the range 5–300 K. The paper discusses the possibility of using this material in studies of the thermal conductivity of thin filaments of metals and semiconductors incorporated into the channels of crystalline chrysotile asbestos tubes.     

Beryllium (boron) clustering quest in relativistic multifragmentation (BECQUEREL Project)

A physical program of irradiation of emulsions in beams of relativistic nuclei named the BECQUEREL Project is reviewed. It is destined to study in detail the processes of relativistic fragmentation of light radioactive and stable nuclei. The expected results would make it possible to answer some topical questions concerning the cluster structure of light nuclei. Owing to the best spatial resolution, the nuclear emulsions would enable one to obtain unique and evident results. The most important irradiations will be performed in the secondary beams of He, Be, B, C, and N radioactive nuclei formed on the basis of JINR Nuclotron beams of stable nuclei. We present results on the charged state topology of relativistic fragmentation of the ¹⁰B nucleus at low energy-momentum transfers as the first step of the research.     

Group Representation of Relativistic Quantum Crystal Optics

A group representation of radiation propagation in an anisotropic medium is developed. The system of wave equations for electromagnetic potentials, obtained from the Maxwell equations with account for the constitutive equations, has been factorized. It is shown that the linear differential operator of the factorized system is orthogonal in transparent crystals and unitary in gyrotropic ones and is represented through the momentum operator. On the basis of the commutation relations for the components of this operator, the eigenvalue problem has been solved and the expression for the change in the radiant energy in the crystal in the form of spherical waves has been obtained. The dependences of the ray and phase velocities and the polarization vectors of waves on the birefringence anisotropy and gyrotropy as well as on the angular momentum, displacement current, and bound charge determining them have been analyzed. It has been established that in the general case of gyrotropic crystals where the nonreciprocity phenomenon takes place and in magnetoelectrics Maxwell equations are represented in a form similar to the Dirac equations and the electromagnetic radiation is correctly described by means of bispinors and is quantized as fermions.     

Synthesis and properties of the nanocomposite of zink oxide and poly(amic acid)

The composite comprised of zinc oxide quantum dots and poly(amic acid) (PAAc) was prepared and studied by X-rays diffraction, X-ray photoelectron spectroscopy, light scattering, UV absorbance and UV fluorescence. The UV absorbance of the ZnO/PAAc composite was found to be much larger than that of its components taken separately. The fluorescence of the ZnO/PAAc composite was found to be shifted to longer wavelengthes in comparison with pure ZnO. The presence of the dopant dodecylbenzenesulfonic acid was found to affect the observed fluorescence.     

Electric Instability in <Emphasis Type="Italic">n</Emphasis>-CdTe:In Layers with <Emphasis Type="Italic">S</Emphasis>-Shaped Voltage-Current Characteristics

A switching of the S-type in the 20–200 μm thick polycrystalline n-CdTe:In layers with resistance of 10³–10⁶ Ω·cm is studied. The electric instability in the layers is found to be due to the electron-thermal breakdown mechanism. The dependence of the switching threshold parameters on the intensity of exposure can be used for fabrication of infrared-radiation controlled electric switches on the basis of n-CdTe:In layers. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 28–30, June, 2005.     

Anionic iron(II) alkoxides as initiators for the controlled ring‐opening polymerization of lactide

Hetero‐bimetallic Fe(II) alkoxide/aryloxides were evaluated as initiators for the ring‐opening polymerization of rac‐lactide. [(THF)NaFe(O^tBu)₃]₂ ( 1 ) and [(THF)₄Na₂Fe(2,6‐diisopropylphenolate)₄] ( 2 ) (THF = tetrahydrofuran) both polymerized lactide efficiently at room temperature, with complex 1 affording better control over the molecular weight parameters of the resultant polymer. At conversions below 70%, a linear increase in molecular weight with conversion was observed, indicative of a well‐controlled polymerization process. Complex 2 is the first example of a dianionic Fe(II) alkoxide and has been structurally characterized to reveal a distorted square planar FeO₄ array in which both Na counterions bridge two aryloxide ligands and are further complexed by two THF ligands. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3798–3803, 2003     

Elastic scattering of slow positrons on atoms

The results of calculations of the elastic scattering cross section of positrons on noble gas and alkali atoms are presented. The calculations are performed within the one-electron Hartree-Fock approximation with multielectron correlations in the so-called random phase approximation with exchange taken into account. Virtual positronium formation is taken into account and proved to be very important. Arguments are presented that the positron polarization potential is repulsive for alkali atoms. The results obtained are in a reasonable agreement with experiment and with some previously reported calculations.