Table of contents

This paper investigates surfaces of nonpositive extrinsic curvature in a pseudo- Riemannian space of curvature 1, Kählerian submanifolds of complex projective space , and saddle surfaces in spherical space . It is determined under what conditions a surface is a totally geodesic submanifold. Bibliography: 14 titles.

A finite group is called quasithin if for any 2-local subgroup in and any odd prime . As usual, denotes the -rank of the group . Let denote the set of all known (at the present time) finite non-abelian simple groups. A group is called a -group if each of its proper non-abelian simple sections belongs to . The current state of the classification of finite simple groups points to the importance of studying simple quasithin -groups . The structure of proper subgroups in such groups are investigated in this paper. Moreover, a detailed study is made of the structure of 2-local subgroups in quasithin -groups whose 2-local 3-rank does not exceed 1. As an example of how the results can be applied, we examine the component case of a problem concerning quasithin groups of 2-local 3-rank at most 1. Bibliography: 16 titles.

The well-known results of Steklov, Tamarkin, and Stone on the equiconvergence of Fourier expansions in eigenfunctions and associated functions of differential operators and in a trigonometrical system for arbitrary functions from are carried over to integral operators and to integrodifferential operators of the form

where is a complex number and are linear forms in and (). Bibliography: 23 titles.

In this paper sufficient conditions are found for existence of maximal isolated eigenvalues in the spectrum of the mathematical expectation of a branching diffusion process in an unbounded domain, and limit theorems are proved. Bibliography: 12 titles.

In this paper free categories and functors on them are considered. A generalization of the theorems of Seshadri and Quillen are given, and as a corollary it is proved that every projective functor from a free category over a Dedekind ring is an induced functor. Bibliography: 5 titles.

This paper studies the eigenvalues of a boundary value problem with a weight of variable sign and an oscillating Green's function. Bibliography: 18 titles.

The analogue of a classical theorem of Montessus de Ballore for meromorphic functions given by their Fourier expansion with respect to orthogonal polynomials is proved. Bibliography: 9 titles.

The problem of the motion of an n-dimensional solid body with a fixed point in a gravitational field is considered. More precisely, the integrable case of such motion determined by certain symmetry conditions of the body is considered. These conditions are obtained as a generalization of the conditions for the Lagrange case of the motion of a three-dimensional heavy gyroscope. For the n-dimensional Lagrange case the collection of first integrals presented in the paper is sufficient for complete integrability. The fact that the case considered provides an example of a completely integrable Hamiltonian system with a noncommutative algebra of first integrals is of interest. Bibliography: 7 titles.

The following theorem is proved. Theorem. Let be a finite simple group containing an elementary abelian subgroup of order 9 with , where and for all . Then is isomorphic to the O'Nan-Sims simple group. Bibliography: 10 titles.