In 1960, he entered the Department of Physics at Dnipropetrovsk State University and graduated from it in 1966. He attended the lectures of the mathematical content mainly from the third year of study. This leaded him to choice of the mathematical style of thinking. During his post-graduate courses, 1967–1970, he studied the axiomatic approach in quantum field theory. He showed that any Boson scalar quantum field admits the representation and the axiomatic formulation in terms of operator Jacobi matrixes. It was the main result of his PhD thesis . From 1970 up to now he occupied different scientific positions, from junior to leading researcher at the Institute of Mathematics of the NAS of Ukraine in Kyiv. In 1985, he got the Doctor degree in mathematics for the theses "The scattering theory in terms of bilinear functionals" with M.S. Birman, I.Ya. Arefieva, and M.I. Portenko as the main referees. In 1995, he became the professor of Higher Mathematics Department in Kyiv Pedagogical University.
Professional activity
Member of the Academic Council Institute of Mathematics of the NAS of Ukraine
Member
Member of the editorial board
Leader of the seminar at the Institute of Mathematics of the NAS of Ukraine
The research interests of Prof. V. Koshmanenko concern modeling of complex dynamical systems, fractal geometry, functional analysis, operator theory, mathematical physics. He proposed the construction of wave and scattering operators in terms of bilinear functionals, introduced the notion of singular quadratic form and produced the classification of pure singular quadratic forms, developed the self-adjoint extensions approach to the singular perturbation theory in scales of Hilbert spaces, investigated the direct and inverse negative eigenvalues problem under singular perturbations. Volodymyr Koshmanenko developed the original theory of conflict dynamical systems and built a serious new models of complex dynamical systems with repulsive and attractive interaction. He proved the theorem of conflict in terms of probability measures, showed the possibility in fractal setting to reconstruct the lost physical type spectrum under interaction with a source of purely singular continuous spectrum. He introduced a notion of the structural similarity measures and proposed a series models of complex dynamical system with conflict interaction of type conflict triad, fire-water model, society as a mathematical models of conflict system where the invariant fixed points, the limiting cyclic orbits and their attraction basins are investigated.
Main publications
Volodymyr Koshmanenko, Viktoria Voloshyna, The emergence of point spectrum in models of conflict dynamical systems, Ukrainian Math. J., v. 70, 12, 1615-1624,.
T. Karataieva, V. Koshmanenko, M. Krawczyk, K. Kulakowski, "Mean field model of a game for power", 15 p.
V. Koshmanenko, N. Kharchenko,
Fixed points of complex systems with attractive interaction, MFAT,, no. 2, 164 - 176,.
Koshmanenko, V.; Dudkin M. Method of Rigged Spaces in Singular Perturbation Theory of Self-adjoint Operators. Birkhäuser, 2016, 237p.
Koshmanenko V., Verygina I. Dynamical systems of conflict in terms of structural measures. Meth. Funct. Anal. and Top. 22, No 1, 81-93,.
Koshmanenko, V., Karataieva, T., Kharchenko, N., and Verygina, I. Models of the Conflict Redistribution of Vital Resources, SSC.
Koshmanenko, V. Existence theorems of the omega-limit states for conflict dynamical systems, Methods Funct. Anal. and Top. 20, No. 4, 379-390, .
Koshmanenko, V. Singular Quadratic Forms in Perturbation Theory, Kluwer, Dordrecht, 1999.
Koshmanenko, V.; Samoilenko, I. The conflict triad dynamical system. Commun. Nonlinear Sci. Numer. Simul. 16, No. 7, 2917–2935.
Albeverio, S.; Konstantinov, A.; Koshmanenko, V. Remarks on the Inverse Spectral Theory for Singularly Perturbed Operators, Operator Theory: Advance and Appl., 190, 115–122.
Albeverio, S.; Koshmanenko, V.; Samoilenko, I. The conflict interaction between two complex systems: Cyclic migration, J. Interdisciplinary Math., 11, No 2, 163–185,.
