Mathematics

1997, No. 4

V.E. Voskresenskii

BIRATIONAL GEOMETRY AND ARITHMETIC OF LINEAR ALGEBRAIC GROUPS, II

This article is a continuation of the previous work of the author . In this article the methods of birational geometry are applied to investigation theory of invariants of finite groups of transformations. In chapter IV we study the connections between geometry and arithmetic of an algebraic group.

B.V. Loginov, S.A. Karpova

COMPUTATION OF PERIODICAL SOLUTIONS IN THE PROBLEM ABOUT CAPILLARY-GRAVITY WAVES IN FLOATING FLUID SPATIAL LAYER

Potential of owes of incompressible uid in spatial layer with free upper boundary are investigated. The case of four-dimensional degeneration of linearized operator is studied. At the usage of group analysis methods in bifurcation theory (RZ Mat 1985 11Б1249K, 1989 8Б554, 1978 11Б883K), asymptotics of bifurcating solution families is calculated.

V.G. Mosin

PRIMITIVE IDEALS AND SYMPLECTIC LEAVES OF QUANTUM MATRIXES

It is proved that there exist the bijection between primitive ideals of algebra of regular functions on quantum m × n - matrixes and symplectic leaves of associated Poisson structure.

V.B. Sokolovskii

THE SURFACE LEVI`S LAPLASIAN L_s AND THE INFINITE-DIMENSIONAL PROBLEM WITH A DIRECTIONAL DERIVATIVE

The problem with a directional derivative for the solved about a Levi`s Laplasian equations is considered in the countably dimensional Hilbert space. This consideration is based on the established connection of this problem with a some equation on a boundary surface. This equation contains the so-called surface Levi`s Laplasian, introduced by the author.