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Number 1, August 1982
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V A Babaĭcev
In this paper the behavior of Iwasawa's μ invariant is studied on the projective space of Zl-extensions of an algebraic number field. The author proves a theorem to the effect that the set of Zl-extensions for which the values of μ are not less than an arbitrary constant forms a linear projective variety.
Bibliography: 9 titles.
V V Batyrev
In this paper a regular classification of smooth Fano 3-folds is given.
Bibliography: 4 titles.
V V Žikov and M M Siražudinov
This paper introduces the concept of G-convergence for nondivergence elliptic operators of second order. It is proved that the class of operators subject to the natural ellipticity inequalities and to a certain "cone" condition (Cordes' condition) is compact in the G-topology.
Bibliography: 14 titles.
N V Krylov
The paper is devoted to the general theory of controlled diffusion processes in a domain of a d-dimensional space in the absence of constraints on the growth of the coefficients at infinity. It turned out that the most suitable object of study is the payoff function in the optimal stopping problem for the controlled process. A theory analogous to the theory of controlled processes in the whole space, with growth constraints on the coefficients, is developed under natural assumptions.
Bibliography: 16 titles.
A I Pavlov
This article investigates the distribution of the first digits (from the left) in the q-nary expansions of numerical sequences and functions (q an integer ≥2).
Bibliography: 13 titles.
A S Rapinčuk
In this paper the class numbers c(f) of quadratic forms f with coefficients in an algebraic number field K are studied by the methods of the theory of algebraic groups. It is shown that if a form f is positive definite, then for any natural number r there exists a quadratic form gr, K-equivalent to f, such that c(gr) is divisible by r. A generalization of this result to semisimple algebraic K-groups of compact type is also obtained.
Bibliography: 21 titles.
Sergei G Tankeev
It is shown that the Q-space of rational cohomology classes of type (r,r) on a simple complex 5-dimensional abelian variety is generated by the classes of intersections of divisors.
Bibliography: 15 titles.
A N Tjurin
In this paper we investigate the geometry of local invariants of a four-dimensional Riemannian manifold and prove that all irreducible components of the curvature tensor can be reconstructed from a local invariant up to proportionality.
O G Harlampovič
In this paper an example is constructed of a solvable group of length 3 with unsolvable word problem that is finitely presented in the class of all groups.
N V Ščerbina
A description is given of the set of those boundary points of a domain of holomorphy which have a neighborhood in which the boundary fibers into analytic curves. For domains with C1-smooth boundary whose closure has a basis of Stein neighborhoods this set coincides with the complement of the Šilov boundary .
Bibliography: 5 titles.
S M Ivaškovič
The author proves that functions holomorphic in a neighborhood of the set , where and are domains in , extend holomorphically to a neighborhood of the set , where is a subdomain of . As a corollary he shows that functions analytic along , where is a curve in , are single-valued in a neighborhood of under certain restrictions to the size of and .
V V Kovtunec
This paper establishes existence theorems for k-snakes, studies their motion under the variation of a parameter, and presents a differential equation satisfied by the snakes. The results contain, as special cases, corresponding properties of constrained polynomials that deviate least from zero.