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Information × Registration Number 0225U002705, (0120U100496) , R & D reports Title Development and application of topological, differential-geometric, analytical and numerical methods for studying equations of the theory of physical fields and motion of particles in Riemannian spaces popup.stage_title Розвиток та застосування топологічних, диференціально-геометричних, аналітичних і числових методів дослідження рівнянь теорії фізичних полів і руху часток у ріманових просторах Head Korzhyk Volodymyr P., Доктор фізико-математичних наукPelykh Volodymyr O., Доктор фізико-математичних наук Registration Date 31-03-2025 Organization Institute of Applied Problems of Mechanics and Mathematics named after Ya. S. Pidstryhach of the National Academy of Sciences of Ukraine popup.description1 Development of the theory of manifolds of compact groups and algebras, graph theory, algebraic aspects theory of dynamic systems, analytical theory of multidimensional continuos fractions, algebraically-special and asymptotic solutions of field theory equations in Riemann spaces, approximate analytic and numerical solutions of the kinetic equation describing the acceleration particles on shock waves. popup.description2  The aim of the work is to develop the theory of manifolds of compact groups and algebras, graph theory, algebraic aspects of the theory of dynamical systems, the analytical theory of multidimensional continued fractions, algebraically-special and asymptotic solutions of field theory equations in Riemannian spaces, approximate analytical and numerical solutions of the kinetic equation describing the acceleration of particles on shock waves, including: to construct new invariant complete Kähler and Ricci-flat Kähler metrics on cotangent bundles of homogeneous manifolds of compact groups, in particular, symmetric spaces of arbitrary rank and the orbits associated with them of the coadjoint representation of complex Lie algebras, using the method of symplectic reduction and its generalization, the latest results in the geometry of orbits of the coadjoint representation of complex Lie algebras, the theory of groups and Lie algebras, and to investigate them for hyperKählerity; to investigate the algebraic and geometric properties of order 2 Kirk-Livingstone invariants of classical braids and to describe the group structure on coarse braids in a rectangle; to study the structural features of 2-planar graphs and construct all possible 2-planar graphs that have the same skeleton subgraph; to propose a Lie-algebraic description of new classes of Lax-Sato integrable nonlinear dynamical systems on functional manifolds of many independent variables using loop algebras over the Lie algebra of vector fields on an n-dimensional torus and the associated cotangent Lie algebra, their holomorphic generalization and corresponding central extensions; to continue the development of the analytic theory of multidimensional continued fractions, namely: to construct algorithms of the Viskovatov type for the expansion of multiple power series into corresponding multidimensional continued fractions of various types. Product Description popup.authors Beshlei Vasyl' V. Hentosh Oksana Ye. Hoienko Nataliia P. Kyrchei Ivan I. Kuzo Taras V. Kuchminska Khrystyna Y. Matsyuk Roman Ya. Mykytyuk Ihor V. Petruk Oleh L. Plachta Leonid P. Plyatsko Roman М Sus Olha M. Taistra Yurii V. Fenyk Mykola T. popup.nrat_date 2025-03-31 Close