Group of quaternion translations of the Dirac-Kähler equation

It is shown that a system of quaternion equations equivalent to the Dirac-Kähler equation is invariant with respect to transformations of field functions inducible by translations in quaternion coordinate space.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 89–92, October, 1989.     

Structural instability during rolling of tungsten in terms of nonlinear thermodynamics

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 47–55, March, 1991.     

Construction of conformal,mappings of biconnected regions

The author's method for conformal mapping of simply connected circular regions of a special form is extended to biconnected regions. Examples are given to show that the solution of the problem for some common biconnected regions may be reduced to examining the corresponding simply connected regions with boundaries along straight lines and circles. The solutions given in this paper are convenient for generating numerical results.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 58, pp. 71–75, 1986.     

Amplitude of Elastic Photon Scattering in Scalar Electrodynamics

In the present paper, the probability of creating pairs of scalar particles in an arbitrary plane electromagnetic wave field is calculated. The amplitude of elastic photon scattering in the field of an arbitrary plane electromagnetic wave is calculated by the method of dispersion relations. Special cases of the plane electromagnetic wave field are examined.     

Integral Method o Reciprocity in the Spectroscopy of Laser Crystals with Impurity Centers

A new method of determining the stimulated emission cross-section spectra from the absorption cross-section spectra, which we call the integral method of reciprocity, is suggested it does not require knowledge of the structure of the impurity-center electron levels. Based on this method, formulas for calculating the radiation lifetime of impurity centers in crystals have been derived. The effectiveness of the integral method of reciprocity was demonstrated in determining the stimulated emission cross sections and radiation lifetime of an ytterbium ion in the laser crystals Yb³⁺:KYW and Yb³⁺:KGW.     

Recurrence of trajectories of systems of linear differential equations with conditionally periodic coefficients

Translated from Matematicheskie Zametki, Vol. 54, No. 1, pp. 52–56, July, 1993.     

Pattern forming precipitation in gels due to coupling of chemical reactions with diffusion

Precipitate-forming chemical reactions have been studied in chemically cross-linked poly(vinyl alcohol) gel medium. One of the reactive components was incorporated into the gel, the other was allowed to diffuse into it. Depending on the experimental conditions the reaction-diffusion process often results in patterns of different type. Experiments performed in tubes and in thin layers were carried out in order to investigate the effects of various factors (cross-linking density, swelling degree as well as the concentrations of the outer and inner electrolytes) on the morphologies of the precipitate patterns. It was found that precipitation occurs not only in the Liesegang bands, but also between bands. Beside Liesegang-type structures, tree-like patterns have been observed, showing a characteristic periodicity in the density profile obtained by digitalized image analyses.