UniversalR-matrix for quantized (super)algebras

For quantum deformations of finite-dimensional contragredient Lie (super)algebras we give an explicit formula for the universalR-matrix. This formula generalizes the analogous formulae for quantized semisimple Lie algebras obtained by M. Rosso, A. N. Kirillov, and N. Reshetikhin, Ya. S. Soibelman, and S. Z. Levendorskii. Our approach is based on careful analysis of quantized rank 1 and 2 (super)algebras, a combinatorial structure of the root systems and algebraic properties ofq-exponential functions. We don't use quantum Weyl group.     

A microeconomic simulation model of reproduction

Translated from Programmnoe Oborudovanie i Voprosy Prinyatiya Reshenii, pp. 152–184, 1989.     

On estimates of the bispectral density of certain models of random processes

Estimates are given for the bispectral densities of stationary random processes. Two models of stationary random processes with discrete time are considered. It is shown that for both models conditions hold under which one can construct a consistent estimate of the bispectral density.Translated fromTeoriya Sluchaínykh Protsessov, Vol. 14, pp. 3–7, 1986.     

Integration of the nonlinear Schroedinger equation with a self-consistent source

It is shown that the nonlinear Schroedinger equation with a self-consistent source admits investigation by the inverse scattering method for the Dirac operator. The conditions are found under which the solutions of the nonlinear Schroedinger equation with a self-consistent source describe the creation and annihilation of solitons.     

Symmetries and conservation laws of Navier-Stokes equations

All the symmetries and conservation laws of Navier-Stokes equations are calculated.     

Behavior of massless feynman integrals near singular points

Nizhnetagil' State Pedagogical Institute. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 80, No. 3, pp. 372–380, September, 1989.