A-integrability of sums of trigonometric series

We investigate sine and cosine series such that their coefficients tend to zero and some subsequences of the coefficients have bounded variation.     

On the possibility of using linear current generators for geophysical research

A procedure was developed to obtain analytical estimates of the operating modes of linear electric generators (LEGs) of the railgun type with current supply to active inductive loads. An analysis of the solutions obtained shows a low effectiveness of using generators of this type to power geophysical dipoles in electrical prospecting (the efficiency does not exceed 20%). Induction coil-type LEGs provide for much higher efficiency. Numerical modeling was performed of the operating modes of one design of such generators. Versions of nonlinear-inductance LEG circuits that produce quasirectangular load current pulses and are of interest for solving electrical prospecting problems were proposed and studied. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 5, pp. 175–184, September–October, 2006.     

Operations over scalar polynomials and their computer realization

In this paper, algorithms which realize some operations over scalar polynomials in one and two variables and their computer realization are suggested. The following operations are considered: 1) the computation of the GCD for given scalar polynomials and the decomposition of each polynomial into a product of two factors: the first factor is the GCD, and the second factors form a sequence of relatively prime polynomials; 2) the division of polynomials by their common divisor; 3) the decomposition of polynomials in two variables into irreducible factors; 4) the computation of the LCM for given scalar polynomials. Bibliography: 5 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 219, 1994, pp. 158–175. This work was supported by the Russian Foundation of Fundamental Research (grant 94-01-00919). Translated by V. N. Kublanovskaya.     

The scattered radiation spectrum of a laser and the measurement of the electron concentration in a pulse plasma

The scattered radiation spectrum obtained in probing a high-frequency (hf) pulse plasma with a laser beam is discussed. The presence of satellites is attributed to Raman scattering at plasma vibrations occasioned by electron drift. The procedure, and results of measuring the electron density on the basis of the intensity of scattered radiation are described. Preliminary calibration of the apparatus was carried out by comparison with Rayleigh scattering in air and in argon.In conclusion we should iike to thank Dr. R. A. Demirkhanov for his interest in our study and Dr. I. A. Akhiezer for his useful comments on the results.     

Synthesis and hydrodynamic and conformation properties of star-shaped polystyrene with calix[8]arene core

Properties of individual molecules of star-like polystyrene with calix[8]arene core in dilute chloroform solutions were studied using methods of static light scattering, translation diffusion, and viscometry. The solution behavior of the polymer investigated significantly differs from the properties of linear polymers. Star-like polystyrene macromolecules in solutions are characterized by compact structure—the hydrodynamic radius is not higher than 5.5?nm at M?=?125,000?g?mol^?1. The shape of star-like polystyrene macromolecules differs slightly from spherical.     

Structural and conformational properties of hyperbranched copolymers based on perfluorinated germanium hydrides

Two series of hyperbranched copolymers based on perfluorinated germanium hydrides of various topological structures are studied in dilute chloroform solutions by the methods of molecular hydrodynamics and optics. The first series is composed of copolymers with various molecular masses (from 2.3 × 10⁴ to 31 × 10⁴) that contain rigid linear chains between branching points and various amounts of branching points in cascades of the dendritic fragment, while the second series is comprised of copolymers that, at close branching degrees, on average, are characterized by a looser structure owing to a large amount of linear units at the periphery of macromolecules with M = (2.5 × 10⁴)?(23 × 10⁴). Macromolecules of the studied polymers have compact dimensions and a high density of the polymer substance; their shape asymmetry is low. In terms of these characteristics, they approach dendrimers. At a fixed molecular mass, the copolymers with a loose structure have higher dimensions of macromolecules and higher intrinsic viscosities.     

Isotope exchange between NO and H2O on a platinum-containing catalyst based on fiberglass

The dynamics of ¹⁸O isotope exchange between NO or H₂O and a catalyst and the dynamics of ¹⁸O label transfer from NO to H₂O have been studied under conditions of sorption-desorption equilibrium. The occurrence of a reaction of oxygen exchange between NO and water sorbed in the bulk of the catalyst was detected. This reaction occurs at platinum sites with the participation of acid sites of the glass matrix. The rate constants of the reaction of NO with platinum sites and the diffusion coefficients of water in the bulk of the glass matrix are evaluated.     

Solution of the partial eigenvalue problem for a regular matrix pencil

Algorithms are proposed for the solution of the partial eigenvalue problem for regular polynomial matrix pencils. Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 159, pp. 33–39, 1987.