2019
Том 71
№ 8

All Issues

Ibragimov G. I.

Articles: 4
Article (English)

A Pursuit Problem in an Infinite System of Second-Order Differential Equations

Allahabi F., Ibragimov G. I., Kuchkarov A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2013. - 65, № 8. - pp. 1080–1091

We study a pursuit differential game problem for an infinite system of second-order differential equations. The control functions of players, i.e., a pursuer and an evader are subject to integral constraints. The pursuit is completed if z(τ) = \( \dot{z} \) (τ) = 0 at some τ > 0, where z(t) is the state of the system. The pursuer tries to complete the pursuit and the evader tries to avoid this. A sufficient condition is obtained for completing the pursuit in the differential game when the control recourse of the pursuer is greater than the control recourse of the evader. To construct the strategy of the pursuer, we assume that the instantaneous control used by the evader is known to the pursuer.

Article (Russian)

Markov Games with Several Ergodic Classes

Ibragimov G. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2003. - 55, № 6. - pp. 762-778

We consider Markov games of the general form characterized by the property that, for all stationary strategies of players, the set of game states is partitioned into several ergodic sets and a transient set, which may vary depending on the strategies of players. As a criterion, we choose the mean payoff of the first player per unit time. It is proved that the general Markov game with a finite set of states and decisions of both players has a value, and both players have ε-optimal stationary strategies. The correctness of this statement is demonstrated on the well-known Blackwell's example (“Big Match”).

Article (Ukrainian)

Bases of exponentials in the spaces Ep(Dn) on a poly-polygon and the representation of the functions from this class in the form of sums of periodic functions

Ibragimov G. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1990. - 42, № 3. - pp. 324–332

Article (Ukrainian)

Representation of analytic functions of two variables in a product of infinite convex domains by means of Dirichlet series

Ibragimov G. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1987. - 39, № 6. - pp. 711-716