On the semiscalar equivalence of 3-by-3 matrices with all different characteristic roots

 

Bogdan Shavarovskii

Department of Algebra, Pidstryhach
Institute for Applied Problems of
Mechanics and Mathematics of
NAS of Ukraine

 

October 15, 2019 at 15:05 in Lecture Room 377

Abstract of talk

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.

Equivalence of matrices over quadratic rings and matrix equations

 

Natalija Ladzoryshyn

Department of Algebra, Pidstryhach
Institute for Applied Problems of
Mechanics and Mathematics of
NAS of Ukraine

 

September 24, 2019 at 15:05 in Lecture Room 377

Abstract of talk

The notation of the (z,k)-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.

Equivalence and factorization of the Kronecker products of polynomial matrices

Volodymyr Zelisko

Department of Algebra and Logic
Faculty of Mechanics and Mathematics
Ivan Franko National University of Lviv

 

April 16, 2019 at 15:05 in Lecture Room 377

Abstract of talk

We consider the problem of equivalence and semiscalar equivalence of the Kronecker products of polynomial matrices and their separation of factors.

The structure of block matrices. I. Factorizations in the rings of the block matrices

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Vasyl’ Petrychkovych

Department of Algebra, Pidstryhach
Institute for Applied Problems of
Mechanics and Mathematics of
NAS of Ukraine

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Nataliia Dzhaliuk

Department of Algebra, Pidstryhach
Institute for Applied Problems of
Mechanics and Mathematics of
NAS of Ukraine

 

March 12, 2019 at 15:05 in Lecture Room 377

Abstract of talk

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.

The arithmetic of solutions of the equation A = BX

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Volodymyr Shchedryk

Department of Algebra, Pidstryhach
Institute for Applied Problems of
Mechanics and Mathematics of
NAS of Ukraine

 

February 26, 2019 at 15:05 in Lecture Room 377

Abstract of talk

We describing the properties of g.c.d. and l.c.m. of matrix equation A = BX solutions over
commutative elementary divisor domain.

Elementary reduction of matrices over rings with almost stable range 1

Bohdan Zabavsky

Department of Algebra and Logic
Faculty of Mechanics and Mathematics
Ivan Franko National University of Lviv

Andriy Romaniv

Department of Algebra, Pidstryhach
Institute for Applied Problems of
Mechanics and Mathematics of
NAS of Ukraine

 

November 27, 2018 at 15:05 in Lecture Room 377

Abstract of talk

In the talk we investigate the elementary reduction of matrices over rings with almost stable range 1.

Classification of Symmetry Reductions for the Eikonal Equation

Vasyl’Fedorchuk

Institute of Mathematics,
Pedagogical University of Kraków, Poland;
Department of Algebra,
Pidstryhach Institute for Applied
Problems of Mechanics and Mathematics
of the NAS of Ukraine

Volodymyr Fedorchuk

Department of Algebra,
Pidstryhach Institute for Applied
Problems of Mechanics and Mathematics
of the NAS of Ukraine

 

November 6, 2018 at 15:05 in Lecture Room 377

 

Abstract of talk

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.

Reduced Triangular Form of Polynomial Matrices and Its Invariants

 

Bogdan Shavarovskii

Department of Algebra, Pidstryhach
Institute for Applied Problems of
Mechanics and Mathematics of
NAS of Ukraine

 

October 16, 2018 at 15:05 in Lecture Room 377

Abstract of talk

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.