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Information × Registration Number 0217U000987, 0111U009688 , R & D reports Title Development of topological-algebraic, differential-geometric and numerical methods of investigation the non-linear dynamic systems in applied problems of physics, biology and medicine. popup.stage_title Head Mykytyuk I.V.; Yadzhak M.S., Registration Date 28-03-2017 Organization Pidstryhach Institute of Applied Problems of Mechanics and Mathematics NAS of Ukraine popup.description2 The object of study is nonlinear dynamical systems in applied problems of physics, biology and medicine. The purpose of the work is the construction of new nonlinear mathematical models of complex dynamical systems in physics, biology and medicine and their research by means of modern analytical and numerical methods with using of effective software and hardware. The methods of investigations are methods of topology, algebra, differential geometry; modeling of dynamical systems, numerical methods for solving problems of mathematical physics and the theory of parallel computing. The results and their novelty are the following. Concerning the graph models of discrete systems the method for constructing the current graphs that generate 1-immersions of full graphs into undirected surfaces is developed and some properties of cubic graphs are studied; the non-triviality of the Parton-Piccinni formula for the canonical 8-form on the manifolds with the holonomy group Spin (9) is proved; the differential-geometric structure of the Bargmann type reductions for 2-dimensional differential-difference systems with the triple Lax type linearization is investigated and the Lie-algebraic description of a new class of compatibly bi-Hamiltonian 2-dimensional differential-difference systems is proposed; the necessary and sufficient conditions for the existence of solutions with nonsingular first two components of bilateral matrix equations with three unknowns are found; for studying the physics-technological processes the conditions of the correct solvability of 3-dimensional bilateral boundary problems for the Laplace equations in differential and integral forms in the cases of closed and unclosed boundary surfaces are established; the mechanics-mathematical model for the dynamical analysis of the human gait with the passively controlled exoskeleton is constructed and realized; the high parallel methods and algorithms for processing large amounts of data and performing complex calculations in real time are developed. The obtained results can be used to develop network technology, analysis of protein structures, study of dynamical systems in transport and communications. The results of the work have been applied to the theory of rings of elementary divisors and used in the educational process for training specialists in maintenance and facilities management of the railway transport system. Product Description popup.authors Гентош О.Є. Демидюк М.В. Микитюк І.В. Петричкович В.М. Поліщук О.Д. Яджак М.С. popup.nrat_date 2020-04-02 Close