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Bogdan ShavarovskiiDepartment of Algebra, Pidstryhach |
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October 15, 2019 at 15:05 in Lecture Room 377 |
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Some invariants of 3-by-3 polynomial matrices with all different characteristic roots are found. In some cases, the conditions of semiscalar equivalence of such matrices are specified and canonical forms are constructed.
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Natalija LadzoryshynDepartment of Algebra, Pidstryhach |
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September 24, 2019 at 15:05 in Lecture Room 377 |
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-equivalence of matrices over quadratic rings is introduced. The standard forms of matrices and their pairs with respect to this equivalence are established. The conditions of solvability of matrix linear unilateral and bilateral equations over an arbitrary quadratic ring are given and their integer solutions are described. On the basis of constructed standard forms of matrices, we proposed the effective method of solvability of these matrix equations and description of the structure of their solutions. |
Volodymyr ZeliskoDepartment of Algebra and Logic |
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April 16, 2019 at 15:05 in Lecture Room 377 |
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We consider the problem of equivalence and semiscalar equivalence of the Kronecker products of polynomial matrices and their separation of factors.
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Vasyl’ PetrychkovychDepartment of Algebra, Pidstryhach |
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Nataliia DzhaliukDepartment of Algebra, Pidstryhach |
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March 12, 2019 at 15:05 in Lecture Room 377 |
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We investigate equivalences, factorizations, and matrix unilateral and bilateral equations in the rings of the block matrices. In the first part, we consider factorizations of the block matrices, in particular, the block triangular and the block diagonal matrices over integral domains of finitely generated principal ideals. Conditions for existence and uniqueness up to the association of the factorizations in such rings are established.
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Volodymyr ShchedrykDepartment of Algebra, Pidstryhach |
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February 26, 2019 at 15:05 in Lecture Room 377 |
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We describing the properties of g.c.d. and l.c.m. of matrix equation 
solutions over
commutative elementary divisor domain.
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Bohdan ZabavskyDepartment of Algebra and Logic |
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Andriy RomanivDepartment of Algebra, Pidstryhach |
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November 27, 2018 at 15:05 in Lecture Room 377 |
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In the talk we investigate the elementary reduction of matrices over rings with almost stable range 1.
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Vasyl’FedorchukInstitute of Mathematics, |
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Volodymyr FedorchukDepartment of Algebra, |
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November 6, 2018 at 15:05 in Lecture Room 377 |
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In the talk we present the results concerning the relationship between the structural properties of low-dimensional (dim L ≤ 3) nonconjugate subalgebras of the Lie algebra of the Poincare group P(1,4) and the properties of the reduced equations for the eikonal equation. To obtain those results, we have performed the classification of the invariants as well as of the ansatzes for the above mentioned subalgebras. We also present some classes of invariant solutions for the eikonal equation.
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Bogdan ShavarovskiiDepartment of Algebra, Pidstryhach |
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October 16, 2018 at 15:05 in Lecture Room 377 |
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In this report the semiscalar equivalence of polynomial matrices of three-order is
investigated. In particular, the systems of invariants of reduced matrices have been found.