2019
Том 71
№ 8

All Issues

Kartashov M. V.

Articles: 2
Article (Ukrainian)

General time-dependent bounded perturbation of a strongly continuous semigroup

Kartashov M. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2005. - 57, № 12. - pp. 1625–1632

We consider an evolution family whose generator is formed by a time-dependent bounded perturbation of a strongly continuous semigroup. We do not use the condition of the continuity of a perturbation. We prove a formula for a variation of a parameter and the corresponding generalization of the Dyson-Phillips theorem.

Article (Russian)

Determination of the Spectral Index of Ergodicity of a Birth-and-Death Process

Kartashov M. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2000. - 52, № 7. - pp. 889-897

We obtain a new explicit relation for the calculation of the spectral index of ergodicity of a birth-and-death process with continuous time. The calculation of the index is reduced to the solution of an optimization problem of nonlinear programming that contains the infinitesimal matrix of the process. As an example, we use the proposed method for finding the exact values of the indices of exponential ergodicity for certain Markov queuing systems.