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.

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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.

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Session dedicated to the memory of professor Vasyl’ Ivanovych Andriychuk 

 

Session of the Lviv Algebraic Seminar dedicated to the memory of professor 

Vasyl’ Ivanovych Andriychuk 

September 18, 2018 at 15:00 in Lecture Room 377

Program

Photo Gallery

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Семінар присвячений 70-літтю
від дня народження М. Я. Комарницького

shavarovskyj_photo shavarovskyj_photo shavarovskyj_photo
 

29 травня 2018 року, 13:30, аудиторія 377

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On the least common multiple of matrices over
commutative principal ideal domains

shavarovskyj_photo

Andriy Romaniv

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

 

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

Abstract of talk

In the talk it will be shown how to find Smith normal form and transforming matrices of the least common multiply of arbitrary pair of non-singular matrices over a commutative principal ideal domain.

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On Gao’s conjecture related with finite field high order elements

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Roman Popovych

Department of Specialized Computer Systems,
Lviv Polytechnic National University

 

December 5, 2017 at 15:05 in Lecture Room 377

Abstract of talk

The talk will be devoted to the Gao’s conjecture connected with the construction of elements of provable high multiplicative order in general finite fields.

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Semigroups and S-polygons with annihilation conditions

melnyk_photo

Yuriy Ishchuk

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

 

November 21, 2017 at 15:05 in Lecture Room 377

Abstract of talk

The notions of a semi-commutative semigroup and an abelian S-polygon can be introduced by analogy with the notions of semi-commutative, abelian modules and rings.

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Semiscalar equivalence of third order polynomial matrices with only one characteristic root

shavarovskyj_photo

Bogdan Shavarovskii

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

 

November 7, 2017 at 15:05 in Lecture Room 377

Abstract of talk

The canonical forms of polynomial matrices of the third order with only one characteristic root are established.

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