Volodymyr Koshmanenko

Volodymyr Koshmanenko (Ukrainian: Кошманенко Володимир Дмитрович; born July 28, 1943, Dnipro, Ukraine) — Ukrainian mathematician, Doctor of Science, professor, Leading Researcher of the Institute of Mathematics of the NAS of Ukraine.

Volodymyr Koshmanenko
Born	July 28, 1943
Nationality	Ukrainian
Awards	Yu.O. Mitropol'sky Award by National Academy of Sciences of Ukraine
Scientific career
Fields	Mathematics
Institutions	Institute of Mathematics of the NAS of Ukraine

Volodymyr Koshmanenko is a notable Ukrainian mathematician and a talented researcher. Prof. Koshmanenko has been reading lectures at Taras Shevchenko University, National Pedagogical Dragomanov University and National University of Kyiv-Mohyla Academy. He has over 120 publications and 5 monographs. Volodymyr Koshmanenko promotes creativity in science, incredible performance, healthy lifestyle.

Biography

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 (1970) (the scientific advisor was Prof. Yu. M. Berezansky).

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 Kyïv Mathematical Society
• Member of the editorial board Methods of Functional Analysis and Topology
• Leader of the seminar Complex Conflict Systems: Dynamics, Models, Spectral Analysis at the Institute of Mathematics of the NAS of Ukraine

Awards

2012 — Yu.O. Mitropol'sky Award by National Academy of Sciences of Ukraine.

Research area

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 (spirit) 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, (2018).

• T. Karataieva, V. Koshmanenko, M. Krawczyk, K. Kulakowski, "Mean field model of a game for power" , 15 p. (Feb 2018, arXiv:1802.02860)

• V. Koshmanenko, N. Kharchenko,

Fixed points of complex systems with attractive interaction, MFAT, {\bf 23}, no. 2, 164 - 176, (2017).

• Koshmanenko, V. Spectral Theory for Conflict Dynamical Systems (Ukrainian), Naukova Dumka, Kyiv, 2016, 288p.
• 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, (2016).
• Koshmanenko, V., Karataieva, T., Kharchenko, N., and Verygina, I. Models of the Conflict Redistribution of Vital Resources, SSC (2016).
• Koshmanenko, V. Existence theorems of the omega-limit states for conflict dynamical systems, Methods Funct. Anal. and Top. 20, No. 4, 379-390, (2014).
• 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 (2011).
• Albeverio, S.; Konstantinov, A.; Koshmanenko, V. Remarks on the Inverse Spectral Theory for Singularly Perturbed Operators, Operator Theory: Advance and Appl., 190, 115–122 (2009).
• Albeverio, S.; Koshmanenko, V.; Samoilenko, I. The conflict interaction between two complex systems: Cyclic migration, J. Interdisciplinary Math., 11, No 2, 163–185, (2008).
• Koshmanenko, V. Construction of singular perturbations by the method of rigged Hilbert spaces, Journal of Physics A: Mathematical and General, 38, 4999–5009 (2005).
• V. Koshmanenko, Theorem of conflicts for a pair of probability measures, Math. Methods of Operations Research, 59, 303–313, (2004).