Showing papers in "Journal of Mathematical Sciences in 1976"

Geometry of algebraic varieties

Abstract: The proposed survey is the third in a series of surveys on algebraic geometry [31, 88]. It is made up mainly from the material in Referativnyi Zhurnal \"Matematika\" during 1965-1973 and is devoted to the geometric aspects of the theory of algebraic varieties. After the fundamental papers of Grothendieck, effecting the harmonic connection of the purely geometric ideas of Italian algebraic geometry with the methods of commutative and homologica! algebra, it is difficult to draw a clear boundary between the algebraic and the geometric aspects of algebraic geometry. Our selection, to be sure, is purely conventional: On the one hand we do not include in the survey that material which could serve as a natural continuation of the previous surveys, and on the other hand, space limitations compel us to exclude such important sections of algebraic geometry as the theory of group schemes, algebraic trans formation groups, Abelian varieties, the analytic theory of complex algebraic varieties (we touch upon it only incidently), the theory of automorphic functions, singularities of algebraic varieties, topology of real algebraic varieties.

The existence of a periodic solution in a tide dynamics problem

Abstract: We examine a quasilinear boundary-value problem describing the dynamics of tidal flow in the sea. For small values of ground friction coefficient and under the fulfillment of a certain condition on the function giving the depth of the sea, we prove the existence of a generalized periodic solution. We construct a difference scheme for the numerical solution of the problem being examined and we prove its stability.

Endomorphism rings of modules and lattices of submodules

Abstract: This survey covers material inReferativnyi Zhurnal Matematika and is a continuation of A. V. Mikhalev's survey in Algebra. Topology. Geometry, Vol. 12 (Itogi Nauki i Tekhniki (1974)). Papers on endomorphism rings of modules over associative rings and on lattices of submodules are considered.

Uniform approximations by holomorphic functions

Abstract: This article gives a survey of the study of uniform approximation by holomorphic functions on compact sets in spaces of one or more complex variables during the last two decades.