Normalization and averaging on compact lie groups in nonlinear mechanics

We consider the method of normal forms, the Bogolyubov averaging method, and the method of asymptotic decomposition proposed by Yu. A. Mitropol’skii and the author of this paper. Under certain assumptions about group-theoretic properties of a system of zero approximation, the results obtained by the method of asymptotic decomposition coincide with the results obtained by the method of normal forms or the Bogolyubov averaging method. We develop a new algorithm of asymptotic decomposition by a part of the variables and its partial case — the algorithm of averaging on a compact Lie group. For the first time, it became possible to consider asymptotic expansions of solutions of differential equations on noncommutative compact groups.     

A Study of Evaporation of Complex Oxide Systems Based on Chromium(III) Oxide

Evaporation of chromium ore and concentrates was studied using high-temperature differential mass-spectrometry. The data obtained, concerning the component vapor pressures in evaporation of complex oxide systems in the range 1700-2100 K, can be used to calculate the evaporation loss in melting and to assess the possibility of utilization of the sublimates formed.     

Optical absorption of hexagonal boron nitride involving nitrogen vacancies and their complexes

The pseudopotential and supercell methods are used to study the optical absorption of graphite-like hexagonal boron nitride involving deep levels of nitrogen vacancies and their clusters. The impurity-induced absorption is shown to be mainly related to electron transitions between the states that are antisymmetric with respect to the horizontal plane. Therefore, this absorption is highly anisotropic and is maximum for light waves polarized normally to the hexagonal axis. The optical absorption and photoconductivity spectra before and after neutron irradiation and thermal treatment are interpreted, and the activation energies for the thermoluminescence and conductivity of nitrogen-depleted boron nitride before and after fast-neutron irradiation and vacuum annealing are found.     

The Ring of Invariants of Three (3 × 3)-Matrices over a Field of Prime Characteristic

We find a minimal system of generators and a homogeneous system of parameters for the algebra of invariants of three matrices of third order over a field of an arbitrary characteristic.     

A method for determining optical constants, dimensions, and concentrations of “soft” absorbing particles in the brightening band region

We investigate the possibilities of creating a method for estimating the optical constants, dimensions, and concentrations of “soft” absorbing particles by applying a theoretical analysis of the angular dependence of the intergrated indicatrix, overall characteristics of light scattering, and absorption on the phase shift and diffraction parameter of particles in the brightening band region. We show that using the investigated optical characteristics, it is possible to determine the unknown parameters of a suspension from experimental data. Institute of Biophysics, Siberian Branch of the Russian Academy of Sciences, Akademgorodok, Krasnoyarsk, 660036, Russia. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 6, pp. 807–812, November–December, 1997.     

Effect of Nitrosodurene on Radical Copolymerization of Styrene with Acrylic Monomers

The effect of nitrosodurene as a source of stable nitroxyl radicals on radical copolymerization of styrene with methyl methacrylate and butyl acrylate was studied.     

Nitration of lignin isolated from spruce wood by mechanical grinding

Summary 1. The nitration of spruce lignin obtained by mechanical grinding has been carried out with nitric acid in an anhydrous medium under heterogeneous and homogeneous conditions. Fractionation of the nitrolignin has been carried out and the elementary and functional composition of the fractions has been determined; the mean semi-empirical formulas of the C₉ structures have been calculated for both fractions. It has been shown that, depending on the nitration conditions, from one to two nitro groups enter the C₆-C₃ structural element of nitrolignin and, with an excess of HNO₃, nitrate groups as well.The fall in the content of OCH₃ groups corresponds to the content of phenolic hydroxyl groups in the initial MGL and can be explained by the demethylation of the guaiacyl structures of the lignin on nitration.Khimiya Prirodnykh Soedinenii, Vol. 2, No. 1, pp. 58–65, 1966