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Information × Registration Number 0223U002248, 0122U001230 , R & D reports Title Development and application of analytical and numerical methods for the study of non-classical problems in the theory of particle motion and radiation propagation popup.stage_title Head Andriichuk Mykhailo I., Доктор технічних наукPelykh Volodymyr О., Доктор фізико-математичних наук Registration Date 13-02-2023 Organization Institute of Applied Problems of Mechanics and Mathematics named after Ya. S. Pidstryhach of the National Academy of Sciences of Ukraine popup.description2  Symmetric analytic and G-analytic functions of bounded and unbounded types and supersymmetric polynomials in Banach spaces have been studied. Algorithm of Viscovatov expansion of N-multiple power series into N-D and connected continuous fractions was constructed. Development of Appel's hypergeometric function into multidimensional continuous fraction was build. Properties of quaternion MPCEP- and CEPMP-inverse matrices and block-diagonal matrices over rings of principal ideals were studied. Unique solution of the Sylvester-type matrix equation was found, and a symmetric reduction of the (1+3)-D and homogeneous Monge-Ampere equation to algebraic one was established. Family of vertex-edge embeddings of complete graphs of high order was constructed. Conditions for correct solvability of mixed problem with integral conditions have been established. The properties of fundamental solution of the Cauchy problem for ultraparabolic equation of the Kolmogorov type have been established. The time stabilization conditions of the initial-boundary value problem for a linear hyperbolic system of the first order with nonlinear boundary conditions were studied. Expression for the amplification of the flux of the radiation pulse generated in the vicinity of the Kerr black hole was obtained. Analytical method for extracting solutions of Mathieson-Papapetrou equations for describing the motions of the eigencenter of mass of a particle with spin in the Schwarzschild metric has been developed. New Hamiltonian approach has been developed to get solutions to classical Mathieson–Pirani spin equation of motion. The influence of the interstellar magnetic field and the initial inhomogeneities of the stellar emission on the formation of the shape of the remnants of supernovae were investigated. To determine the structure of the interstellar magnetic field at supernova SN1987A, polarization maps were synthesized. Problem of shape restoring of unknown three-dimensional body was solved. Product Description popup.authors Hentosh Oksana Ye. Dron' Vitalij S Kyrchei Ivan Igorovich Korzhik Vladimir P. Kuchmins'ka Khrystyna Yosyphivna Matsyuk Roman Ya. Petrychkovych Vasyl' Mychajlovych Petruk Oleh Leonidovych Pliatsko Roman M. Repetylo Sofia Myroslavivna Savenko Petro Oleksandrovych Savka Ivan Ja. Symotyuk Mykhaylo M. Fedorchuk Vasyl M. Shavarovsky Bogdan Z. Shchedryk Volodymyr P. popup.nrat_date 2023-02-13 Close