Separation of variables in kolmogorov's equation. II

This communication continues the investigation begun in [10] of the separation of variables (SV) in Kolmogorov's equation (KE). SV is discussed below with the help of a set of symmetry operators containing a second-order differential operator; a group of KE transformations is constructed with respect to which it is covariant.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 27–32, March, 1979.     

Separation of variables in the nonstationary Schrödinger equation

Separation of variables in the Schrödinger equation is performed by using complete sets of differential operators of symmetry with operators not higher than second order, and all types of electromagnetic field potentials for which separation of variables is possible are listed.     

Integral sets and variable separation in the Klein — Gordon equation

All complete sets of integral operators of definite form and the corresponding electric field potentials, for which the Klein — Gordon equation admits complete variable separation, are enumerated in this paper.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 122–125, November, 1973.     

Separation of variables in the diffusion equation. III

The Separation of variables of type N = 2 is completed, and all complete sets of type N = 1 are constructed for the diffusion equation with a scalar matrix for the leading derivatives.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 48–50, July, 1979.In conclusion, we take this opportunity to thank V. N. Shapovalov for continued interest.     

Magnetic compensation in iron-gadolinium and iron-terbium films

The results of an investigation into the phase composition and various physical properties of iron-gadolinium and iron-terbium films possessing magnetic compensation are presented. The effect of the phase composition on the galvanomagnetic and magnetic properties is noted. An attempt is made to explain the nature of the magnetic compensation observed on first annealing.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 11, pp. 88–92, November, 1971.     

Separation of variables in Kolmogorov's equation. III

We continue the investigation of the complete separation of variables (SV) in an ultraparabolic equation begun in [10, 14]. Here the classes of equivalent characteristics which allow SV are discussed in detail; the solution of the problem of Brownian motion of an oscillator with variable frequency is constructed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 33–35, March, 1979.