Invariant interpolation formulas for higher-order derivatives of functions of a vector argument

Interpolation formulas for higher-order derivatives which guarantee the invariance of the results under changes of coordinates are obtained for functions of a vector argument.Translated from Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 25, pp. 22–25, 1987.     

Plant polysaccharides I. Polysaccharides ofLagochilus and their biological activity

Institute of the Chemistry of Plant Substances, Academy of Sciences of the Republic of Uzbekistan, Tashkent, fax (3712) 89 14 75. Translated from Khimiya Prirodnykh Soedinenii, No. 2, pp. 313–314, March–April, 1995. Original article submitted November 7, 1994.     

General-relativistic cosmology with expansion and rotation

A model of an expanding and rotating universe is constructed in the framework of general relativity. The parameters of the model are compared with the fundamental observables and shown to be in good agreement.Kaluzhsk Branch, N. É. Bauman Moscow State Technical University (MGTU). Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 71–77, June, 1993.     

Logarithmic corrections in a quantization rule. The polaron spectrum

A nonlinear integrodifferential equation that arises in polaron theory is considered. The integral nonlinearity is given by a convolution with the Coulomb potential. Radially symmetric solutions are sought. In the semiclassical limit, an equation for the self-consistent potential is found and studied. The potential has a logarithmic singularity at the origin, and also a turning point at 1. The phase shifts at these points are determined. The quantization rule that takes into account the logarithmic corrections gives a simple asymptotic formula for the polaron spectrum. Global semiclassical solutions of the original nonlinear equation are constructed.Moscow Institute of Electronic Engineering; Moscow Power Institute. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 97, No. 1, pp. 78–93, October, 1993.     

On the Causes and Effects of Contaminations during rf Diode Deposition of Cr-Si Alloys

Investigations to the causes and effects of contaminants at the rf diode deposition of CrSi films in a non-heated high vacuum apparatus were carried out comparing an oxygen-free fusion target with an oxygen-containing cermet target. The films of the fusion target contained considerable amounts of oxygen; analogously the oxygen concentration in the films was increased in the case of the cermet target. Moreover, hydrogen was found. The concentration of the contaminants decreased with the sputtering power, however the rate of incorporation increased. For high sputtering rates the contamination process was reproducible and independent of the plant conditioning; the deposited films were depth-homogeneous. The reasons for this behaviour lie in water sources which are activated first of all by the discharge itself. The electrical properties found are explained by the contaminants and the deposition conditions.