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).     

Nonlinear Amplitude-Phase Effects in Selective Reflection from a Resonance Gas

Selective reflection of a laser wave from a resonance gas is considered for arbitrary intensity, polarization, and angle of incidence on the interface. Variations of the reflection spectra nonlinear in the wave amplitude are studied taking into account the nonlinear increment of the optical phase upon reflection. The result of this increment is a quadrature component of the reflected wave shifted by a quarter period, which may be observed using the homodyning technique (optical mixing). The regularities studied are of interest both for spectroscopy and for nonlinear transformations in the quantum statistics of reflected light.     

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.     

Dynamics of non-equilibrium phase boundaries in a heat conducting non-linearly elastic medium

The phase transformation of the first kind in a non-linearly elastic heat conducting medium is simulated by the relationships on a strong discontinuity. A generalization of the Stefan formulation is given. An existence condition for stationary flow, analogous to the Gibbs phase equilibrium condition, is obtained for non-equilibrium phase boundaries. A pure dilatational phase transition in a compressible fluid and pure shear transformation of the twinning type in non-linearly elastic crystals are considered as model examples. The problem of the structure is solved for closure of the system of relationships on the shock.

A phase transformation ordinarily turns out to be localized in a narrow domain of space and it can be simulated in terms of the conditions on a strong discontinuity /1/. Formulation of the problem of the static equilibrium of liquid phases as well as of liquid and (non-linearly elastic) solid phases was given by Gibbs, who proposed a phase equilibrium criterion and formulated appropriate conditions on the shock; the extension of the Gibbs conditions to the case of the equilibrium of two solid phases is known in both the linear /2/ and non-linear /3/ theories of elasticity. The dynamic problem of the propagation of the equilibrium phase boundary is considered in the Stefan formulation as a rule, including the assumption about the continuity of the density (the strain tensor component) on the shock; the thermal problem is here separated from the mechanical one. Simulating the interphasal surface on the shock the temperature fields are merged by using the well-known Stefan conditions as well as the phase equilibrium condition that reduces to giving the temperature on the front.

The purpose of this paper is to extend the Stefan-Gibbs formulation to the case of the motion of a coherent isothermal phase boundary in a non-linearly elastic heat conducting medium and to derive the dynamic analogue of the phase equilibrium condition (and the Stefan conditions) with possible dissipation at the transformation front. Two dissipative mechanisms are examined, viscous and kinetic. The case of equilibrium phase boundaries was investigated in /4–6/.     

The thermodynamic properties of Ln2BaO4 (Ln = Sm, Dy, Ho)

The thermodynamic properties of the Ln₂BaO₄ phases (Ln = Dy, Ho, Sm) were studied by the electromotive force method with a fluoride electrolyte (890–1180 K), solution calorimetry in 1.07 N hydrochloric acid at 298.15 K, and differential scanning calorimetry (298–860 K). The experimental data were jointly processed, and the thermodynamic functions of the compounds over the temperature range 298–1200 K were calculated.     

226Ra in milk of the dairy cattle from the rural region of Pernambuco, Brazil

Summary Studies performed by the Brazilian Nuclear Corporation (NUCLEBRAS), in collaboration with the Geological Survey Company of Brazil (CPRM), identified high levels of natural uranium in the districts of Pedra and Venturosa, in the rural region of the state of Pernambuco (PE) - Brazil, where the maximum value found in rocks was 22,000 mg.     

Nature of π-Electronic Transitions in UV Spectra of Deoxyvasicinone and Its Derivatives

The principal types of electronic transitions in absorption spectra of deoxyvasicinone and its 6-amino- and 6-nitro-derivatives were determined by analyzing the electron-density distributions in excited states calculated using ZINDO/S.     

Indirect Oxidation of Organic Substances by Intermediates of the Oxygen Reduction

Results of two urgent and practically important directions of research on the indirect oxidation of organic compounds by highly reactive intermediates generated electrochemically from oxygen (HO₂ ^–, HO₂ ^·, HO^·) are considered and orderly arranged. The studies in question are the indirect synthesis and mineralization of organic toxicants in waste water.     

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.