On composition of some general fractional integral operators

In the present paper we derive three interesting expressions for the composition of two most general fractional integral oprators whose kernels involve the product of a general class of polynomials and a multivariableH-function. By suitably specializing the coefficients and the parameters in these functions we can get a large number of (new and known) interesting expressions for the composition of fractional integral operators involving classical orthogonal polynomials and simpler special functions (involving one or more variables) which occur rather frequently in problems of mathematical physics. We have mentioned here two special cases of the first composition formula. The first involves product of a general class of polynomials and the Fox’sH-functions and is of interest in itself. The findings of Buschman [1] and Erdélyi [4] follow as simple special cases of this composition formula. The second special case involves product of the Jacobi polynomials, the Hermite polynomials and the product of two multivariableH-functions. The present study unifies and extends a large number of results lying scattered in the lierature. Its findings are general and deep.     

Scaling probability, key to the equilibrium statistical volume distribution in foams

The equilibrium statistical volume distribution in foams, which has been previously demonstrated to be the so-called log-normal, is accounted on probability grounds by a scaling law on the bubble's volume time-evolution. This law states that the conditional probability for a given bubble to have the volume v(t + Δt), he assumption that it was v(t), to depend solely on the relationship v(t + Δt)/v(t), and in particular, to be independent of the time t. The theoretical results, however, allow to go further. Indeed, since the time dependece of its parameters (expectation and variance) are given functions of time, only two parameters are necessary to describe completely the foam.     

Structure of fullerene-containing soot at different formation stages of arc discharge vaporization of graphite

Electron microscopy is used in a study of nanoclusters of the carbon soot deposited on a probe in different areas of arc discharge during graphite vaporization under conditions favorable for fullerene synthesis. It is found that the spatial network of soot nanoclusters consists of alternating regions of higher density or associates of carbon particles. Two types of nanoclusters have been identified with the correlation radii of the associates equal to 0.6–0.8 and 1.6–2.2 nm, respectively. Type I nanoclusters are dominant in the soot microparticles, and their structure shows practically no variations with increasing separation r of the soot collector from the discharge axis over the range of distances studied, r=1–9 cm. The effective radius R ₀ of the “elementary” particles making up the associates in the soot nanoclusters of Type I calculated with the use of scaling relationships is 0.15–0.17 nm and is close to the gas-kinetic radius of carbon atoms. Type II nanoclusters have been identified in soot collected at r>3 cm. Values of R ₀ calculated in this case are 0.6–0.9 nm and decrease with increasing r, which indicates the presence of fullerene molecules in these nanocluster associates.     

Features of evolution of the substructure in the creep of dispersion-hardened nickel

A study is made of the laws governing high-temperature creep and the evolution of the substructure in dispersion-hardened alloy Ni — 3 vol. % HfO₂ during its free annealing and creep. The polygonized substructure was formed in the alloy prior to annealing. An analysis is made of structural transformations at different structural levels and the mechanism of high-temperature creep in the alloy. Institute of the Physics of Strength and Materials Science, Siberian Branch of the Russian Academy of Sciences. All-Republic Engineering-Technical Center, Siberian Branch of the Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 83–89, March, 1998.     

Kinetic theory of the generation of magnetic fields in the radiation-dominated stage of expansion of the universe

The system of linearized Einstein and Maxwell equations and a kinetic equation with model collision integral for the cosmological plasma are used to calculate the magnetic field generated by solenoidal perturbations in the radiation-dominated stage of expansion of the universe. The magnetic field is generated by two effects — the Harrison effect and a new effect due to kinetic processes. The second effect contributes to the magnetic field if solenoidal gravitational perturbations exist from the very beginning of the radiation-dominated stage.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 122–126, January, 1992.     

Calculation of the spectra of potassium-like multicharged ions

The energy levels and oscillator strengths for dipole transitions between the levels of low-lying configurations are calculated for ions of the KI isoelectronic sequence. The calculations are based on the energy approach to the effective potential method with the most important polarization effects taken into account, including core polarization by the outer electron. The results, some of which are obtained here for the first time for potassium-like ions, can be useful in a number of related fields, such as laser physics, plasmas, and so on.Odessa Hydrometeorological Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 3–9, November, 1992.     

Time machine in MTT world

Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 33, No. 1, pp. 205–207, January–February, 1992.     

Monitoring environmental electromagnetic fields. 1. Remote-sensing methods

This paper discusses monitoring electromagnetic fields (natural and artificial) in the atmosphere. Methods are described for remote sensing of the atmosphere and surface in order to examine static and alternating electromagnetic-energy fluxes in the biosphere.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 69–79, December, 1991.     

Effect of plasma treatment of the dielectric on electroforming of a thin-film MIM system

It was found that when a thin dielectric film is exposed to the plasma of a low-voltage gas discharge, channels with elevated conductivity form in the film and these channels significantly facilitate the subsequent electroforming of the MIM system. It is concluded from the experimental data that even in the case of metallic electrodes highly conducting channels are formed in the dielectric by electronic processes occurring under the conditions of a strong electric field and not by diffusion of the electrode material.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 94–98, October, 1991.