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Information × Registration Number 0220U103928, 0119U101243 , R & D reports Title Development of investigation methods of structures on manifolds associated with groups, algebras and graphs and development it geometric analysis concerning the theory of relativistic fields and particles. popup.stage_title Head Mykytyuk Ihor V., Доктор фізико-математичних наукPelykh Volodymyr O., Доктор фізико-математичних наук Registration Date 30-11-2020 Organization Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine popup.description2 The object of study are structures on manifolds associated with groups, algebras and graphs, matrix functionals, rational approximations, equations of mathematical physics, which describe the motion of elementary particles in flat and curved spaces. The purpose of the work is the creation of new methods for constructing invariant bipoisson structures on the cotangent bundles of homogeneous varieties of compact groups, construction of integrated multidimensional nonlinear dynamical systems, studying homotopy properties of configurational spaces for varieties with edges, finding estimates for the genus, edges, and edges of genera not having their own 2-immersion into the plane, construction and development of differential-geometric and algebraic methods of research, obtaining and approximation of solutions of differential equations with partial derivatives of theoretical physics and astrophysics. In the course of the work, known and new geometric and theoretical-group methods of research of dynamic systems on manifolds, methods of geometric topology, combinatorial analysis of topological theory of graphs, theory of functions and differential equations and differential geometry were used. New classes of homogeneous spaces of compact Lie groups are described, for which the geodetic flow is quite integrable by Liouville, the properties of the canonical 8-form on 16-dimensional manifolds with Spin-9 structure are studied, a rational factorization method is developed for the central expansion of Lie algebra, a new Li-algebraic method for constructing Lax-Sato integral multidimensional non-dispersive systems and their superanalogues has been developed; the homotopy equivalence of the configurational spaces of some manifolds with an edge is proved; the necessary conditions for the existence of its own 2-immersion in a plane for a special class of plane triangulations are determined, the determinant represantation and the properties of generalized Moore-Penrose invers  Product Description popup.authors Andriychuk Mykhaylo I Beshley Vasyl V. Hentosh Oksana Ye. Goyenko Natalya P. Kyrchei Ivan I. Korzhik Vladimir P. Kuchmins' ka Khrystyna Yo. Lozynska Vira Ya Mykytyuk Ihor V. Pelykh Volodymyr О. Petrychkovych Vasyl` M. Petruk Oleh L. Plachta Leonid P. Plyatsko Roman M Symotyuk Mykhaylo M. Sus Olga M. Chernega Iryna V. Shchedryk Volodymyr P. popup.nrat_date 2020-11-30 Close