Quelques considérations à propos de l'équation fonctionnelle de Binet-Cauchy

Sans résumé     

Use of wavelets in potential scattering problems

Application of the Daubechies compact support wavelets to problems of nonrelativistic potential scattering described by integral Lippmann-Schwinger equation is discussed. Structure of wavelet representation of various physical operators is investigated. It is shown that for a special class of potentials wavelets enable sparse approximation of the kernel of the Lippmann-Schwinger equation. Constraints for such potentials are derived. This paper is dedicated to Prof. J. Bičák on the occasion of his 60th birthday.     

On the cases of Kirchhoff and Chaplygin of the Kirchhoff equations

It is proven that the completely integrable general Kirchhoff case of the Kirchhoff equations for B ?? 0 is not an algebraic complete integrable system. Similar analytic behavior of the general solution of the Chaplygin case is detected. Four-dimensional analogues of the Kirchhoff and the Chaplygin cases are defined on e(4) with the standard Lie-Poisson bracket.     

Solitons generated by self-organization in bismuth germanium oxide single crystals during the interaction with laser beam

We present here the experimental, theoretical, and numerical investigations of Kerr solitons generated by self-organization in black and yellow high quality bismuth germanium oxide (Bi₁₂GeO₂₀) single crystals. A picosecond laser beam of increasing power induces competing cubic and quintic nonlinearities. The numerical evolution of two-dimensional complex cubic-quintic nonlinear Schrödinger equation with measured values of nonlinearities shows the compensation of diffraction by competing cubic and quintic nonlinearities of opposite sign, i.e., the self-generation and stable propagation of solitons. Experiments as well as numerical simulations show higher nonlinearity in the black Bi₁₂GeO₂₀ than in the more transparent yellow one.     

Characterization of Gaseous Plasma Sustained in Mixtures of HMDSO and O2 in an Industrial-Scale Reactor

Optical emission spectroscopy and mass spectrometry was used to characterize gaseous plasma in an industrial reactor of volume 5 m³ during deposition of protective coatings. Plasma was created in mixtures of hexamethyldisiloxane (HMDSO) and oxygen at the powers between 1 and 8 kW. The plasma density was somehow below 10¹⁴ m^?3. The flows of both gases were varied up to 200 sccm while the effective pumping speed was adjusted by changing the roots pump rotation speed between 250 and 4000 rpm. At such conditions the HMDSO was only partially dissociated to fragments. The behaviour of optical emission lines and mass ion currents was well correlated indicating that even one single technique was sufficient to monitor the behaviour of plasma at various discharge conditions. The optical emission spectroscopy as a simple and economic method is therefore suitable for controlling key processing parameters in such a plasma reactor.