2018
Том 70
№ 11

All Issues

Gerasimenko V. I.

Articles: 7
Anniversaries (Ukrainian)

Myroslav L’vovych Horbachuk (on his 75 th birthday)

Berezansky Yu. M., Gerasimenko V. I., Khruslov E. Ya., Kochubei A. N., Mikhailets V. A., Nizhnik L. P., Samoilenko A. M., Samoilenko Yu. S.

Full text (.pdf)

Ukr. Mat. Zh. - 2013. - 65, № 3. - pp. 451-454

Anniversaries (Ukrainian)

Yurii Ivanovych Samoilenko (on the 80th anniversary of his birthday)

Bakhtin A. K., Gerasimenko V. I., Plaksa S. A., Samoilenko A. M., Sharko V. V., Trohimchuk Yu. Yu, Yacenko V. O., Zelinskii Yu. B.

Full text (.pdf)

Ukr. Mat. Zh. - 2012. - 64, № 4. - pp. 574-576

Article (Ukrainian)

Initial-value problem for the Bogolyubov hierarchy for quantum systems of particles

Gerasimenko V. I., Shtyk V. O.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 9. - pp. 1175–1191

We construct cumulant (semi-invariant) representations for a solution of the initial-value problem for the Bogolyubov hierarchy for quantum systems of particles. In the space of sequences of trace-class operators, we prove a theorem on the existence and uniqueness of a solution. We study the equivalence problem for various representations of a solution in the case of the Maxwell-Boltzmann statistics.

Article (Ukrainian)

Creative Contribution of D. Ya. Petrina to the Development of Contemporary Mathematical Physics

Gerasimenko V. I., Malyshev P. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2004. - 56, № 3. - pp. 293-308

This is a brief survey of the results obtained by Prof. D. Ya. Petrina in various branches of contemporary mathematical physics.

Article (Ukrainian)

Cumulant Representation of Solutions of the BBGKY Hierarchy of Equations

Gerasimenko V. I., Ryabukha T. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2002. - 54, № 10. - pp. 1313-1328

We construct a cumulant representation of solutions of the Cauchy problem for the BBGKY hierarchy of equations and for the dual hierarchy of equations. We define the notion of dual nonequilibrium cluster expansion. We investigate the convergence of the constructed cluster expansions in the corresponding functional spaces.

Article (Ukrainian)

On D. Ya. Petrina's works in contemporary mathematical physics

Gerasimenko V. I., Malyshev P. V., Rebenko A. L.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 4. - pp. 317–328

This is a brief survey of the works of Prof. D. Ya. Petrina in various branches of contemporary mathematical physics.

Article (Ukrainian)

Hydrodynamic potentials method in a region with complex boundary

Gerasimenko V. I., Stashenko M. O.

Full text (.pdf)

Ukr. Mat. Zh. - 1991. - 43, № 5. - pp. 679–684