Table of contents

Necessary and sufficient conditions are obtained for stabilization as of the solution of the third mixed problem for the wave equation in the exterior of an infinite closed cylindrical surface in space variables, in the presence of an influx of energy into the region through the boundary (, of arbitrary sign). An asymptotic expansion as is established for the solution. Bibliography: 18 titles.

Let and be holomorphic functions of finite order in a sector , and let and be the distribution functions of their zeros inside this sector. Theorems established in this article permit the assertion that and are equivalent if and differ "little" on the boundary of . In the second part of the article domains bounded by curves of parabola type are considered instead of a sector , and theorems are established which generalize and strengthen Tauberian theorems with a remainder for the distributions of zeros of entire functions and for Stieltjes transforms. Bibliography: 28 titles.

The independence of automorphism groups and lattices of ideals is proved in the class of all semigroups. Bibliography: 12 titles.

The author studies the most typical forms of the connection between the functors and ; the role of the functor and its cardinality properties that arise from this connection, the cardinality and other properties of the functors and , and also of the homology and the cohomology groups of locally compact spaces. Under suitable countability restrictions, the universal coefficient formulas are investigated in situations lacking the usual connection between chains and cochains with different coefficients. The homology of Steenrod-Sitnikov type with locally constant coefficients is treated, as well as a definitive form of the connection between and the Aleksandrov-Čech homology. Bibliography: 41 titles.

Suppose that is a normal operator, the pencil has a discrete and positive spectrum in the domain , and is an operator-valued function that is holomorphic in and small in comparison to (in a certain sense). A theorem is proved on comparison of the spectra of and , i.e., on an estimate of the difference , where () is the distribution function of the spectrum of () in (). This result implies generalizations of theorems of Keldysh on the asymptotic behavior of the spectrum of a polynomial operator pencil. Bibliography: 14 titles.

Let be a connected locally finite vertex-symmetric graph, the number of vertices of at a distance not more than from some fixed vertex. The equivalence of the following assertions is proved: (a) is bounded above by a polynomial. (b) There is an imprimitivity system with finite blocks of on the set of vertices of such that is finitely generated nilpotent-by-finite and the stabilizer of a vertex of in is finite. Thus, in a certain sense, a description is obtained of the connected locally finite vertex-symmetric graphs with polynomial growth. Bibliography. 8 titles.

Let be the tensor algebra of the identity representation of the Lie superalgebras in the series and . The method of Weyl is used to construct a correspondence between the irreducible representations (respectively, the irreducible projective representations) of the symmetric group and the irreducible -(respectively, -) submodules of . The properties of the representations are studied on the basis of this correspondence. A formula is given for the characters on the irreducible -submodules of . Bibliography: 8 titles.

It is proved that among the numbers , where is algebraic, , and is algebraic of degree , there are no fewer than which are algebraically independent over . Bibliography: 17 titles.

A random elliptic operator of positive order is considered, whose coefficients are realizations of a homogeneous random field on given by a dynamical system satisfying an aperiodicity condition indicating the absence of nontrivial periods of the corresponding unitary group. For such an operator, the coincidence of its spectra in and in the Hilbert space of homogeneous random fields is proved. Bibliography: 21 titles.

The authors propose a general effective method for constructing a predicate calculus complete with respect to -general validity in quasi-Hilbert form (i.e. in Hilbert form but using a language extended by finitely many "external metasymbols") on the basis of an arbitrary many-valued logic. For logics in a fairly large class containing many of the logics studied previously, a general effective method is indicated for constructing a predicate calculus of Hilbert type complete with respect to -general validity. The results and methods of the article make it possible to initiate the development of model theory on the basis of an arbitrary finite-valued logic. Bibliography: 25 titles.

The paper studies rings in simple finite-dimensional algebras over a field that are similar to valuation rings in fields. Bibliography: 15 titles.

Under the assumption of a nontrivial shift of the zeros of Dirichlet -series with quadratic character, asymptotic formulas are obtained for the number of lattice points in arbitrary regions on the hyperboloid belonging to given residue classes. A method for applying the results to the study of the distribution of lattice points on general second-order surfaces is outlined. Bibliography: 19 titles.

This article examines germs of holomorphic vector fields for the form

under the assumption that the support of the power series lies either above the bisector of the first quadrant of the integer lattice , or below it. Necessary conditions (imposed on the coefficients of ) are formulated for orbital analytic equivalence of vector fields of the type indicated; these are obtained with the help of approximate calculation of the Écalle-Voronin functional moduli for the analytic classification of germs of holomorphic mappings which are monodromy transformations of the vector fields considered. Bibliography: 18 titles.

The author proves that any -induced flow on a compact solvable homogeneous space is ergodic on a submanifold . For almost any flow the closure of the orbit of the fixed point is the submanifold . Bibliography: 10 titles.