Asymptotic Behavior of Sobolev-Type Orthogonal Polynomials on a Rectifiable Jordan Curve or Arc

Our object of study is the asymptotic behavior of the sequence of polynomials orthogonal with respect to the discrete Sobolev inner product <formula> \langle f, g \rangle = ∈t_{E} f(ξ) \overline{g(ξ)} ρ(ξ) |d ξ|+ f(Z) A g(Z)^H, </formula> where E is a rectifiable Jordan curve or arc in the complex plane f(Z) = (f(z_1), \ldots, f^{(l_1)}(z_1) , \ldots , f(z_m) , \ldots ,f^{(l_m)}(z_m)), A is an M \times M Hermitian matrix, M l ₁ + ⋅s + l _m + m , |d ξ| denotes the arc length measure, ρ is a nonnegative function on E , and z _i ∈Ω, i=1,2,\ldots,m , where Ω is the exterior region to E . July 23, 1999. Dates revised: September 11, 2000 and February 16, 2001. Date accepted: February 26, 2001.     

The nonlinear effects of quantum electrodynamics at high energies

In this paper we considere ⁺ e ^? scattering with intermediate photon-photon scattering as a possibility for getting information about the nonlinear effects of quantum electrodynamics (QED) at high energies. This process is a higher-order correction to double bremsstrahlung. However, these two processes have quite different behaviour with the photon-photon scattering angle. Here we calculate the unpolarized differential cross section of thee ⁺ e ^? scattering with intermediate γγ scattering and also the interference terms with the double bremsstrahlung. Moreover, we show that the sum of these two contributions predominates over the contribution of the double bremsstrahlung for sufficiently large scattering angles of the photons. This result enables us to extract the differential cross section of the γγ scattering. Through extrapolation to different kinematical conditions we can get the cross sections for nearly real photon-photon scattering, photon splitting and Delbrück scattering. As a quantitative example we use the result for a test of the electron propagator in a gauge-invariant way with the usual minimal interaction. We give also numerical examples of this test, which will improve the present values of the testing parameters.     

The phase composition of tin-nickel electrodeposited alloys

It was studied the tin phase composition of the electrodeposited alloys produced at different temperatures and current densities from an acid chloride/fluoride electrolyte and an acid chloride bath. Mössbauer spectra were consistent with a Ni₃Sn₄ intermetallic compound, dissolved tin, and a Cu?Sn intermetallic compound formed at the interface of the copper substrate.     

Optical properties of F.I.R. metallic grids: Reflection phase shift measurements

Utilization of metallic grids stacks for F.I.R filters needs a good knowledge of optical properties of each grid. We study here an experimental method in order to determine the wave's change of phase by reflection on a wire grid. We use a Perot-Fabry interferometer constituted by these grids.     

Oscillatory kinetics and mechanism of the chromate catalyzed decomposition of hydrogen peroxide

Oscillatory change of pH occurs during the chromate-catalyzed decomposition of hydrogen peroxide in a weakly acidic medium at elevated temperature and at high initial concentration of hydrogen peroxide. In a closed system, there are only two or three periods, but sustained oscillation occurs in a CSTR. In a CSTR bistability is also found. In closed systems the temperature exhibits a great maximum (up to 15°C increase), in a CSTR sustained oscillation occurs at a constant stationary temperature.