Transitive Maps on Topological SpacesSpringer Science and Business Media LLC - Tập 65 - Trang 1293-1318 - 2014
E. Bilokopytov, S. F. Kolyada
In the present paper, we consider the problem of existence of nonequivalent definitions of topological transitivity, which is a classical problem of the topological dynamics. In particular, we use the fact that all available definitions of this kind imply a condition imposed on the dynamical system. The main result of our investigations is the complete classification of these dynamical systems.
Structure of separative dedekind groupsSpringer Science and Business Media LLC - Tập 48 - Trang 1522-1532 - 1996
M. F. Kuzennyi, M. M. Semko
We describe groups such that all their subgroups that do not belong to a certain proper subgroup are normal. We also solve the separate problem of description of such groups with normal non-Abelian subgroups.
Higher-Order Relations for Derivatives of Nonlinear Diffusion SemigroupsSpringer Science and Business Media LLC - Tập 53 - Trang 134-140 - 2001
A. Val. Antonyuk, A. Vik. Antonyuk
We show that a special choice of the Cameron–Martin direction in the characterization of the Wiener measure via the formula of integration by parts leads to a set of natural representations for derivatives of nonlinear diffusion semigroups. In particular, we obtain a final solution of the non-Lipschitz singularities in the Malliavin calculus.
Galilei-invariant higher-order equations of burgers and korteweg-de vries typesSpringer Science and Business Media LLC - Tập 48 - Trang 1799-1814 - 1996
W. I. Fushchych, V. M. Boiko
We describe nonlinear Galilei-invariant higher-order equations of Burgers and Korteweg-de Vries types. We study symmetry properties of these equations and construct new nonlinear extensions for the Galilei algebra AG(1, 1).
Approximation of classes of analytic functions by algebraic polynomials and kolmogorov widthsSpringer Science and Business Media LLC - Tập 48 - Trang 267-282 - 1996
V. S. Romanyuk
We obtain estimates of the best polynomial approximations, uniform in the closure B of Faber domains of the complex plane ℂ, for functions continuous in B and defined by Cauchy-type integrals with densities possessing certain generalized differential properties. We establish estimates exact in order for the Kolmogorov widths of classes of such functions in relevant functional spaces.