Gerasimenko V. I.
Ukr. Mat. Zh. - 2013. - 65, № 3. - pp. 451-454
Ukr. Mat. Zh. - 2012. - 64, № 4. - pp. 574-576
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.
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.
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.
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.
Ukr. Mat. Zh. - 1991. - 43, № 5. - pp. 679–684