Table of contents

On page 215 of volume 47 (1984) the first author's name should be "Efimova".

In this paper the distribution of prime vectors (i.e., vectors with prime components) in degenerate lattices is investigated, and asymptotic formulas are obtained for the fraction which are valid under certain restrictions on the matrix , where , , and is the number of prime vectors of the degenerate lattice with components not exceeding . The main idea is to reduce the problem to that of solving systems of linear algebraic equations in prime numbers belonging to given arithmetic progressions. An asymptotic formula for the number of solutions of such systems is calculated with the help of a multidimensional variant of the circle method. Bibliography: 12 titles.

For a second-order elliptic equation admitting a weak degeneracy near the boundary, conditions on the geometry of the boundary and on the order of the degeneracy of the equation are given under which every neighborhood of a boundary point where a solution attains an extremum contains a boundary point where the derivative of the solution in an internal direction is necessarily different from zero. Bibliography: 12 titles.

Operator blocks in Banach lattices are studied in this paper. Bibliography: 18 titles.

The level sets of Lyapunov exponents of linearized systems are considered as functions of the linearized Cauchy problem. It is proved that lower semicontinuity is a typical property for these functions. Typicality is understood in the Baire sense: a property is typical if it is possessed by a dense set of points which is a countable intersection of open sets. Bibliography: 11 titles.

In this paper the technique of group action on a tree is used to obtain solutions of the following problems. Suppose that the group is a free construction. 1. Describe the normal subgroups of not containing nonabelian free subgroups. 2. Describe the normal subgroups and of if the mutual commutator subgroup does not contain nonabelian free subgroups. The results are applied to groups obtained by using a sequence of operations of taking HNN-extensions and forming free products with amalgamation. Bibliography: 16 titles.

The purpose of this article is to study generalizations and refinements presented here for the concepts of boundedness and attraction, and to subsequently apply the results to concrete objects. Bibliography: 8 titles.

This article gives a generalization of a theorem of Ryll and Wojtaszczyk on the existence of a sequence of homogeneous polynomials , , in variables with degree for which

where is the sphere in -dimensional complex space. Bibliography: 11 titles.

Let be an ordered Euclidean field (i.e., an ordered field in which the group of nonzero squares coincides with the group of positive elements) and its quadratic extension. Further, let denote the image of the element under the nontrivial automorphism of the extension . We consider the special unitary group of degree over the field , i.e., the subgroup of matrices of the general linear group for which and , where denotes taking conjugate-transpose, i.e., . Defining relations in a certain natural system of generators are found for the group , . Bibliography: 8 titles.

The asymptotic () behavior of solutions of the Cauchy problem is studied for the semilinear parabolic equation

where and as . The existence is established of an infinite collection (a continuum) of distinct self-similar solutions of the form , , where the function satisfies an ordinary differential equation. Conditions for the asymptotic stability of these solutions are established. It is shown that for there exist solutions of the problem whose behavior as is described by approximate self-similar solutions (ap.s.-s.s.'s) which in the case coincide with a family of self-similar solutions of the heat equation , while for and the ap.s.-s.s. has the form

where . Figures: 2. Bibliography: 78 titles.

It is shown that the Zassenhaus algebra over a field of characteristic has, up to equivalence, a unique nontrivial central extension (the modular Virasoro algebra). For the Virasoro algebra we construct a generalized Casimir element. All the irreducible -modules are described. It is shown that there is no simple graded Lie algebra with zero component . Bibliography: 16 titles.

Necessary and sufficient conditions are given for a sequence of numbers to belong to the set of sequences of Fourier coefficients with respect to the Haar system of functions in the space (). Bibliography: 12 titles.

This article deals with the proofs of some multidimensional Tauberian comparison theorems for generalized functions with supports in homogeneous cones, in particular, for measures and functions whose Laplace transforms have nonnegative imaginary parts. "Admissible" generalized functions, which can be regarded as multidimensional analogues of the so-called "R-O" functions of Karamata, serve as comparison functions in these theorems. For circular and n-faced cones a criterion is obtained for admissibility which generalizes the well-known Keldysh Tauberian condition to the multidimensional case. Bibliography: 9 titles.

The basic facts are given in the theory of random elements and random operators acting in Hilbert spaces. Reduction methods are developed for several models for a measurement scheme, including methods for a model with a random operator. Bibliography: 6 titles.

This paper considers the Heins problem and its relation to problems of recovering analytic functions prescribed with an error. Bibliography: 14 titles.