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Information × Registration Number 0222U003600, 0116U008182 , R & D reports Title Rings of matrices over certain domains, non-conjugate subalgebras of the Lie algebra of the Poincare group P(1,4), their structure and application to the theory of matrix and differential equations popup.stage_title Head Petrychkovych Vasyl M., д.ф.-м.н.Fedorchuk Vasyl M, д.ф.-м.н. Registration Date 03-05-2022 Organization Institute of Applied Problems of Mechanics and Mathematics named after Ya. S. Pidstryhach of the National Academy of Sciences of Ukraine popup.description2 Conditions of decomposability of complete linear group of matrices over Bezout rings of stable ranges into the product of its subgroups are established. The classical Helmer theorem is generalized. For polynomial matrices, in particular of simple structure and small sizes, the invariants are found and the simpler forms are constructed. Conditions of their semiscalar equivalence are specified and there are applied to the classification problem of collections of numerical matrices. It is established the standard form for matrices over quadratic rings with respect to (z,k)-equivalence. Factorizations in the ring of block triangular matrices over commutative Bezout rings are described. It is developed the methods of solving and investigation of solutions of linear matrix bilateral equations over polynomial and quadratic rings. The structure of solutions of matrix equation of Sylvester type and matrix Diophantine equations are described. The classification of symmetry reductions of the (1+3)-dimensional homogeneous Monge-Ampère equation as well as the classification of symmetry reductions and invariant solutions for the (1+3)-dimensional Euler–Lagrange–Born–Infeld equation and (1+3)-dimensional inhomogeneous Monge-Ampère equation are performed.  Product Description popup.authors Dzhaliuk Nataliia S Ladzoryshyn Nataliia Bohdanivna Romаniv Andrii M. Shavarovsky Bogdan Z. Shchedryk Volodymyr Volodymyr P popup.nrat_date 2022-05-03 Close