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Information × Registration Number 0219U100268, 0117U002814 , R & D reports Title Research of the properties of differential-algebraic structures associated with some models of mathematical physics popup.stage_title Head Romаniv Andrii M., Кандидат фізико-математичних наук Registration Date 04-02-2019 Organization Instytut pryklаdnykh problem mekhаniky i mаtemаtyky im. Ya.S. Pidstryhаchа NAN Ukrаiny popup.description2  Some arithmetic properties of matrices over the commutative principal ideal domain are investigated, namely: for matrices of small orders and also for arbitrary matrices with some restrictions on the order of the matrices and on their canonical diagonal forms, the relationships between canonical diagonal forms and transforming matrices of two matrices with canonical diagonal forms and transforming matrices of their least common right multiple are established. The stable range of the ring of matrices of the second order over the commutative principal ideal ring is calculated. The necessary and sufficient conditions for the existence of a unified solution of the problem with nonlocal two-point and multi-point conditions for a distinguished variable for equations with partial derivatives over a field of p-adic numbers in the corresponding non-Archived Hilbert function spaces are established. The solution of these problems in the form of a series of physical Hermite polynomials is constructed. The boundary-value problem with the Dirichlet-Neumann conditions for the time variable for a system of weakly-linear hyperbolic equations of high order with constant coefficients is investigated. The conditions for unambiguous solvability of a problem in Sobolev spaces (using the principle of a fixed point) are established. Product Description popup.authors popup.nrat_date 2020-04-02 Close