Том 70
№ 5

All Issues

Volume 52, № 10, 2000

Anniversaries (Russian)

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)

Mitropolskiy Yu. A.

Full text (.pdf)

Ukr. Mat. Zh. - 2000. - 52, № 10. - pp. 1312-1321

Article (Russian)

Attractors of Ordinary Differential Equations

Voskresenskii E. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2000. - 52, № 10. - pp. 1322-1334

We obtain sufficient conditions for the existence of polynomial attractors and polynomial equilibrium.

Brief Communications (English)

On Some Disjointness Classes of Extensions of Minimal Topological Transformation Semigroups

Gerko A. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2000. - 52, № 10. - pp. 1335-1344

We study disjointness classes of extensions of minimal topological transformation semigroups.

Article (Ukrainian)

Boundary Functionals for the Difference of Nonordinary Renewal Processes with Discrete Time

Kadankov V. F., Yezhov I. I.

↓ Abstract   |   Full text (.pdf)

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.

Article (Russian)

On One Sufficient Condition for the Validity of the Strong Law of Large Numbers for Martingales

Koval V. A.

↓ Abstract   |   Full text (.pdf)

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.

Article (Russian)

Finitely representable dyadic sets

Nazarova L. A., Roiter A. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2000. - 52, № 10. - pp. 1363-1396

A criterion of finite representability of dyadic sets is presented.

Article (Russian)

Representation of Automata by Groups. II

Skobelev V. G.

↓ Abstract   |   Full text (.pdf)

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.

Article (Russian)

On Multipliers from Spaces of the Bergman Type to the Hardy Spaces in a Polydisk

Shamoyan R. F.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2000. - 52, № 10. - pp. 1405-1414

We describe coefficient multipliers from spaces of the Bergman type to the Hardy spaces.

Brief Communications (Ukrainian)

Numerical Characteristics on the Set of Heteroclinic Points of Morse–Smale Diffeomorphisms on Surfaces

Vlasenko I. Yu.

↓ Abstract   |   Full text (.pdf)

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.

Brief Communications (Russian)

Conjugacy of Morse Functions on Surfaces with Values on a Straight Line and Circle

Prishlyak A. O.

↓ Abstract   |   Full text (.pdf)

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.

Brief Communications (Russian)

On Theorems of the Sylow Type for Finite Groups

Tyutyanov V. N.

↓ Abstract   |   Full text (.pdf)

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.

Brief Communications (Ukrainian)

On the Phragmén–Lindelöf Indicator for Random Entire Functions

Filevych P. V.

↓ Abstract   |   Full text (.pdf)

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.

Brief Communications (Ukrainian)

On Semiscalar and Quasidiagonal Equivalences of Matrices

Shavarovskyy B. Z.

↓ Abstract   |   Full text (.pdf)

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.