Sur l'existence des opérateurs d'onde pour l'équation de Wigner dans les espaces L2,pExistence of wave operators for the Wigner equation in L2,p spaces

Basing on the formalism established by Markovich, we show the completeness of wave operators for the Wigner equation in L². In the second part, using estimations proved by Castella and Perthame on the one hand, and the L^p→L^q estimations for the Schrödinger group on the other hand, we prove the existence of the wave operators in L^2,p spaces. To cite this article: H. Emamirad, P. Rogeon, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 811–816.     

Equations for Transition from Grahame–Parsons Model to Alekseev–Popov–Kolotyrkin Model

Equations are derived, which allow one to determine the electrode's surface coverage with adsorbate, charge, differential capacitance, and interfacial tension within the framework of a phenomenological model, for which the Grahame–Parsons and Alekseev–Popov–Kolotyrkin models are the limiting cases.     

Simulation of Wave Focusing in Cavities

Simulation results are presented for the focusing of shock waves in conical and wedge-shaped cavities. Results are reported for plane waves and explosion waves. The distribution of parameters in the focusing zone is found to depend on the specific conditions.     

Interacting Spin 0 Fields with Torsion via Duffin-Kemmer-Petiau Theory

Here we study the behaviour of the spin 0 sector of the DKP field in spaces with torsion. First we show that in a Riemann-Cartan manifold the DKP field presents an interaction with torsion when minimal coupling is performed, contrary to the behaviour of the KG field, a result that breaks the usual equivalence between the DKP and the KG fields.Next we analyse the case of the Teleparallel Equivalent of General Relativity (Weitzenböck manifold), showing that in this case there is a perfect agreement between KG and DKP fields. The origins of both results are also discussed.On leave from     

Numerical treatment of an asset price model with non-stochastic uncertainty

In contrast to stochastic differential equation models used for the calculation of the term structure of interest rates, we develop an approach based on linear dynamical systems under non-stochastic uncertainty with perturbations. The uncertainty is described in terms of known feasible sets of varying parameters. Observations are used in order to estimate these parameters by minimizing the maximum of the absolute value of measurement errors, which leads to a linear or nonlinear semi-infinite programming problem. A regularized logarithmic barrier method for solving (ill-posed) convex semi-infinite programming problems is suggested. In this method a multi-step proximal regularization is coupled with an adaptive discretization strategy in the framework of an interior point approach. A special deleting rule permits one to use only a part of the constraints of the discretized problems. Convergence of the method and its stability with respect to data perturbations in the cone of convexC ¹-functions are studied. On the basis of the solutions of the semi-infinite programming problems a technical trading system for future contracts of the German DAX is suggested and developed. Supported by the Stiftung Rheinland/Pfalz für Innovation, No. 8312-386261/307.     

Analysis of the structure of an amorphous sediment obtained upon decomposition of potassium oxofluroniobate in water

An amorphous sediment was prepared by the decomposition of potassium oxofluoroniobate K_{2 ? x} Nb₄O₃(O, F)₃F in water. For this sediment, the atomic radial distribution function was analyzed with the use of a fragment model, which allows one to interpret expanded coordination spheres as being formed by first several strongest diffusion maxima. These spheres carry the most reliable information on the structure. It is shown that the amorphous sediment consists of the randomly packed Nb(O,F)₆-octahedra with interatomic distances close to those observed in the ordered region in the N-Nb₂O₅ structure. During decomposition in water, the initial K_{2 ? x} Nb₄O₃(O, F)₃F phase loses KF-layers, whereas Nb₆ clusters with metal bonds are destroyed.     

On the possibility of a radical decrease in the strength of many-body interactions in the organic metal α-(BETS)<Subscript>2</Subscript> KHg(SCN)<Subscript>4</Subscript>

Behavior of the de Haas-van Alphen (dHvA) oscillations depending on the angle between the magnetic field direction and the perpendicular to conducting layers in the quasi-two-dimensional organic metal α-(BETS)₂ KHg(SCN)₄ was studied in detail. The angular dependence of the dHvA oscillation amplitude exhibits a series of minima (at ±43.2°, ±64.6°, and ±72.0°) related to the “zero spin” effect, through which it is possible to estimate the splitting factor. An analysis of this value suggests that many-body interactions in the compound studied are either absent or at least radically weakened.     

Application of hydroacoustic radiators for the generation of seismic waves

To excite seismic waves with a high coherence, powerful hydroacoustic radiators placed in a natural reservoir were used. Theoretical estimates and the test data demonstrate a high efficiency of the proposed method of seismic wave excitation. The calculations are in good agreement with the results of measurements. The results of phasing the radiation with the use of two monopole sources separated by a quarter-wave distance are presented. It is shown that the use of the proposed scheme of excitation makes it possible to control the radiation pattern while obtaining a high coherence of seismic waves.     

Current and shot noise in two capacitively coupled single electron transistors with an atomic sized spacer

The currents and their fluctuations in two capacitively coupled single electron transistors are determined in the limit of sequential tunnelling. Our considerations are restricted to the case when the islands (dots) of the transistors are atomic-sized, which means each of them has only one single electronic level available for the tunnelling processes. The Coulomb interactions of accumulated charges on the both single electron transistors lead to the effect of the negative differential resistance. An enhancement of the current shot-noise was also found. Spectral decomposition analysis indicated the two main contributions to the shot-noise: low- and high-frequency fluctuations. It was found that the low frequency fluctuations (polarization noise) are responsible for a strong enhancement of the current noise. Received 9 October 2001 / Received in final form 8 March 2002 Published online 9 July 2002