Volume 52, № 10, 2000
On the Scientific, Pedagogic, and Public Activities of Academician Mikhail Alekseevich Lavrent'ev at the Ukrainian Academy of Sciences (1939–1949) (on the 100th Anniversary of the Birth of M. A. Lavrent'ev)
Ukr. Mat. Zh. - 2000. - 52, № 10. - pp. 1312-1321
Ukr. Mat. Zh. - 2000. - 52, № 10. - pp. 1322-1334
We obtain sufficient conditions for the existence of polynomial attractors and polynomial equilibrium.
Ukr. Mat. Zh. - 2000. - 52, № 10. - pp. 1335-1344
We study disjointness classes of extensions of minimal topological transformation semigroups.
Ukr. Mat. Zh. - 2000. - 52, № 10. - pp. 1345-1356
For the difference of nonordinary renewal processes, we find the distribution of the main boundary functionals. For the queuing system D η δ |D ξ κ |1, we determine the distribution of the number of calls in transient and stationary modes.
Ukr. Mat. Zh. - 2000. - 52, № 10. - pp. 1357-1362
We prove a theorem on the strong law of large numbers for martingales. The existence of higher moments is not assumed. From the theorem proved, we deduce numerous well-known results on the strong law of large numbers both for martingales and for sequences of sums of independent random variables.
Ukr. Mat. Zh. - 2000. - 52, № 10. - pp. 1363-1396
A criterion of finite representability of dyadic sets is presented.
Ukr. Mat. Zh. - 2000. - 52, № 10. - pp. 1397-1404
We obtain necessary and sufficient conditions under which the representation of abstract automata in terms of finite groups is consistent with the transition function of an automaton. We obtain sufficient conditions under which the mapping of a free semigroup of an automaton into a group realized by a component of the representation is a homomorphism.
Ukr. Mat. Zh. - 2000. - 52, № 10. - pp. 1405-1414
We describe coefficient multipliers from spaces of the Bergman type to the Hardy spaces.
Numerical Characteristics on the Set of Heteroclinic Points of Morse–Smale Diffeomorphisms on Surfaces
Ukr. Mat. Zh. - 2000. - 52, № 10. - pp. 1415-1420
For Morse–Smale diffeomorphisms on closed surfaces, we investigate the properties of numerical characteristics of heteroclinic trajectories with respect to the local structure of direct product in a small neighborhood of a saddle periodic point.
Ukr. Mat. Zh. - 2000. - 52, № 10. - pp. 1421-1425
We investigate the conjugacy of Morse functions on closed surfaces. By using cellular decompositions of surfaces, we formulate a criterion for the conjugacy of Morse functions. We establish a criterion for the conjugacy of mappings into a circle with nondegenerate critical points.
Ukr. Mat. Zh. - 2000. - 52, № 10. - pp. 1426-1430
We describe a new class of finite groups for which the D π-theorem is true.
Ukr. Mat. Zh. - 2000. - 52, № 10. - pp. 1431-1434
We establish that, for the “majority” of entire functions of finite order, their generalized Phragmén–Lindelöf indicators are identically equal to constants.
Ukr. Mat. Zh. - 2000. - 52, № 10. - pp. 1435-1440
For a certain class of polynomial matrices A(x), we consider transformations S A(x) R(x) with invertible matrices S and R(x), i.e., the so-called semiscalarly equivalent transformations. We indicate necessary and sufficient conditions for this type of equivalence of matrices. We introduce the notion of quasidiagonal equivalence of numerical matrices. We establish the relationship between the semiscalar and quasidiagonal equivalences and the problem of matrix pairs.