Registration Number
0225U002142,
(0124U000520)
, R & D reports
Title
Complex-algebraic methods in the theory of dynamic systems and their application to radar problems
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Опрацювання методів дослідження
Head
Dilnyi Volodymyr M., Доктор фізико-математичних наук
Registration Date
20-02-2025
Organization
Lviv Polytechnic National University
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The goal is the development of new methods of analysis of mathematical models described by dynamic systems, and their application in physics, in particular, the theory of transmission and signal processing; biology, economics, and chaos theory.
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The first stage of the project implementation involved the development of methods of complex analysis, algebra, and dynamical systems theory, which will be used in subsequent studies of electromagnetic signal identification systems. For Hamiltonian flows of the Lax type in a space dual to the Lie algebra of fractional integro-differential operators, a rational factorization method was developed, which allows obtaining new integrable hierarchies of nonlinear fractional-differential dynamical systems on the Lie algebra of ordinary integro-differential operators and obtaining infinite sequences of their conservation laws. The proposed method is used to construct a new integrable hierarchy of nonlinear fractional-differential systems on the Lie algebra of ordinary integro-differential operators and an infinite sequence of its conservation laws, as well as a new integrable hierarchy of hydrodynamic systems of the Benny type, which is its quasiclassical approximation. Also, new Lebesgue measure-invariant multidimensional Boolean transformations and their ergodicity properties are investigated. The asymptotic properties of entire and analytic functions in the half-plane are investigated. The problem of visualization of multidimensional graphs of functions and integral operators is considered, which is important for convenient presentation of the obtained data.
Product Description
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Andrusiak Ivanna V.
Brodiak Oksana Ya.
Kuchma Mariia I.
Miskiv Volodymyr-Myron V.
Prykarpatskyi Anatolii K.
Filevych Petro V.
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2026-06-23
