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pro vyhledávání: '"Gerasimenko, V."'
Autor:
Gerasimenko, V. I.
The chapter presents some new approaches to describing the collective behavior of complex systems of mathematical biology based on the evolution equations of observables such as open systems. This representation of kinetic evolution has looked to be
Externí odkaz:
http://arxiv.org/abs/2412.09137
Autor:
Gerasimenko, V. I., Gapyak, I. V.
Publikováno v:
In: Modern Problems of Mathematics and its Applications. III. (Eds. V.I. Gerasimenko et al.), Kyiv: IM, 2023, 729-804. ISSN: 1815-2910. The book is dedicated to the 160th anniversary of the birth of academician D. O. Grave
The review presents rigorous results of the theory of fundamental equations of evolution of many-particle systems with collisions and also considers their connection with nonlinear kinetic equations describing the collective behavior of particles in
Externí odkaz:
http://arxiv.org/abs/2308.04143
Autor:
Gerasimenko, V. I., Gapyak, I. V.
Publikováno v:
AIP Advances, 14 125006 (2024)
The article deals with the challenge of the construction of solutions to hierarchies of fundamental evolution equations for many colliding particles. The method of cluster expansions of the groups of operators of the Liouville equations for observabl
Externí odkaz:
http://arxiv.org/abs/2307.02121
Autor:
Gerasimenko, V. I., Gapyak, I. V.
Publikováno v:
J Stat Phys 189, 2 (2022)
The paper develops an approach to the description of the evolution of correlations for many hard spheres based on a hierarchy of evolution equations for the cumulants of the probability distribution function governed by the Liouville equation. It is
Externí odkaz:
http://arxiv.org/abs/2111.13940
Autor:
Gerasimenko, V. I.
Publikováno v:
In: Modern Problems of Mathematics and its Applications. I. (Eds. V.I. Gerasimenko et al.), Kyiv: IM, 2020, 82-112. ISSN: 1815-2910 The book is dedicated to the 100th anniversary of the Institute of Mathematics of NAS of Ukraine
The article provides an overview of some advances in the mathematical understanding of the nature of the kinetic equations of quantum systems of many particles. The fundamental equations of modern mathematical physics are studied, in particular, the
Externí odkaz:
http://arxiv.org/abs/2107.10872
Autor:
Gerasimenko, V. I., Gapyak, I. V.
The possible ways to describe the states of a system of many hard spheres are considered, in particular by means of functions describing correlations of states. It is stated an approach to the description of the evolution based on the dynamics of cor
Externí odkaz:
http://arxiv.org/abs/2012.03001
Autor:
Gerasimenko, V. I., Gapyak, I. V.
Publikováno v:
Reviews in Mathematical Physics, 33 (2021) 2130001 (32 pages)
The article discusses some of the latest advances in the mathematical understanding of the nature of kinetic equations that describe the collective behavior of many-particle systems with collisional dynamics.
Comment: 30 pages. arXiv admin note:
Comment: 30 pages. arXiv admin note:
Externí odkaz:
http://arxiv.org/abs/2001.06786
Autor:
Gerasimenko, V. I.
Publikováno v:
In: Understanding Density Matrices. N.Y.: Nova Science Publ., Inc., pp. 229-250, 2019
In this survey the possible approaches to the description of the evolution of states of quantum many-particle systems by means of the possible modifications of the density operator which kernel known as density matrix are considered. In addition, an
Externí odkaz:
http://arxiv.org/abs/2001.01180
Akademický článek
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Autor:
Gerasimenko, V. I.
Publikováno v:
In: Kinetic Theory, Chapter 5, pp. 71-88. London: InTech, 2018. ISBN: 978-953-51-3802-0
We consider a new approach to the description of the collective behavior of complex systems of mathematical biology based on the evolution equations for observables of such systems. This representation of the kinetic evolution seems, in fact, the dir
Externí odkaz:
http://arxiv.org/abs/1708.04612