Nonstationary generalized Duru-Kleinert transformation of path integrals for systems of differential equations in one-dimensional space

We obtain new formulas for the transformations of Wiener path integrals corresponding to the parabolic systems of two differential equations with time-dependent coefficients in one-dimensional space. These formulas determine the transformation of the path integrals under a rheonomous-homogeneous-pointwise transformation of integration variables and the path reparameterization transformation. These formulas allow us to obtain an integral relation between the Green's functions of related systems of differential equations. We show how to obtain the generalized Shepp formula from this relation for the path integral under consideration. We derive these new formulas using the properties of random processes under phase transitions and a random change in time.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 109, No. 1, pp. 17–27, October, 1996.     

Infrared reflection spectra in contactless nondestructive measurements of the electron density and mobility in indium phosphide

On the basis of numerical calculations and experimental studies we analyze the possibilities of measuring the electrophysical parameters of indium phosphide by means of infrared reflection spectra at wavelengths ranging from 5 to 200 m. We demonstrate that contactless nondestructive measurements of the electron density in the range 10¹⁶–10²⁰ cm^–3 can be made with a relative error not exceeding 15%, and of mobility with a relative error not exceeding 25%. A nomogram method is presented for rapid conversion of data from infrared reflection spectra into the parameters being measured.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 22–27, January, 1988.     

Calculation of microdosimetric characteristics in electron and gamma-ray irradiated water

The results of a calculation of the characteristics of fluctuations in the absorption of energy of electrons and gamma rays in small sensitive volumes of a material in electronic equilibrium are presented. The calculations were performed by the method developed in [1]. The efficiency and accuracy of the method are demonstrated by comparisons with the experimental results and direct numerical simulation. The experience gained in using the method is analyzed. The main numerical result of this work is a table of coefficients enabling the calculation of the probability of the absorption of energy and the first two moments of the energy absorbed in spherical regions with radii of 1, 2, 4, and 8 m, starting only from the electronic spectrum in these regions, for water absorbers with arbitrary shape and arbitrary electronic or photonic sources with energies up to 1 MeV.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 77–82, February, 1988.     

Problem without initial conditions for some classes of nonlinear parabolic equations

Questions of uniqueness and existence of solutions of the problem without initial conditions for quasilinear parabolic equations of arbitrary order with monotone spatial part, equations of nonstationary filtration type, and operator differential equations of parabolic type are studied. The cases when restrictions are and are not imposed on the behavior of solutions as t– are considered here.Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 14, pp. 3–44, 1989.     

Meta-Hamiltonian groups with elementary commutant of rank 2

This paper is concerned with the structure of periodic meta-Hamiltonian groups with elementary commutant of rank 2 that have complemented Miller Moreno subgroups. It is proved that there exist four types of such groups.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 2, pp. 168–175, February, 1990.The proof of this assertion will be given in another paper of the authors.     

A variational problem in the theory of green potential. I

For a condenser E in an open set D R ^p , p 3, the problem of the minimum of the Green energy in a class of charges, associated with E, is solved.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 4, pp. 494–500, April, 1990.     

Properties of nonlinear waves in dissipative-dispersive media with instability

Wave processes in dissipative-dispersive media with instability described by a fourth-order nonlinear evolution equation are considered. Analytic solutions in the form of solitary and cnoidal waves are obtained. The existence of a critical value of the dispersion coefficient beyond which an initial disturbance (in particular, white noise) is transformed into a structure is demonstrated by numerical modeling.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 130–136, July–August, 1990.     

A numerical analysis of chaotic behaviour in Bianchi IX models

In this paper we investigate the chaotic behaviour of the Bianchi IX cosmological models using techniques developed in the study of dynamical systems and chaotic behaviour. We numerically calculate the Lyapunov exponent, , and show that instead of converging to a constant value, it decreases steadily. We study this effect further by studying the Lyapunov exponent using short-time averages. We show that the usual method of calculating is invalid in the case of a cosmological model.     

Nonlinear properties of surface “screw” instability in symmetric semiconductor plates

For the first time we study the nonlinear properties of the surface screw instability (SSI) when waves are excited at both faces of a plate and the interaction between them must be taken into account. The nature of the SSI development and the stability of surface screw waves against modulation are examined. Diagrams of the regions where the SSI development is soft and explosive as well as the regions of modulated waves are given in the space of parameters characterizing the electro-hole plasma and external fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 30–34, April 1990.