16 citations · 43 across the 18 of their papers we have counts for
10 papers · 1 filter
Operator Algebras and Their Applications
Vitalii Shpakivskyi
We introduce a new class of commutative associative algebras whose structural constants are linear operators acting in a linear topological space. An analogue of the theory of mono…
Algebras with Variable Operator-Valued Structural Constants and Their Applications
Vitalii Shpakivskyi
We introduce a new class of algebras with variable operator-valued structural constants and develop elements of the theory of monogenic functions in such algebras. Compatibility co…
Algebras with Variable Structural Constants and Their Applications
Vitalii Shpakivskyi
We introduce a new class of algebras with variable structural constants and develop elements of the theory of monogenic functions in such algebras. Compatibility conditions for the…
On h(x)-Fibonacci polynomials in an arbitrary algebra
Cristina Flaut, Vitalii Shpakivskyi, Elena Vlad
In this paper, we introduce h(x)-Fibonacci polynomials in an arbitrary finite-dimensional unitary algebra over a field K (K = R,C), which generalize both h(x)-Fibonacci quaternion…
Some remarks about Fibonacci elements in an arbitrary algebra
Cristina Flaut, Vitalii Shpakivskyi
In this paper, we prove some relations between Fibonacci elements in an arbitrary algebra. Moreover, we define imaginary Fibonacci quaternions and imaginary Fibonacci octonions and…
An efficient method for solving equations in generalized quaternion and octonion algebras
Cristina Flaut, Vitalii Shpakivskyi
Quaternions often appear in wide areas of applied science and engineering such as wireless communications systems, mechanics, etc. It is known that are two types of non-isomorphic…
De Moivre's Formula and Euler's Formula for Octonions
Cristina Flaut, Vitalii Shpakivskyi
In this paper, we generalized De Moivre's formula and Euler's formula to octonions and find the roots of generalized octonions using these formulae.
Real matrix representations for the complex quaternions
Cristina Flaut, Vitalii Shpakivskyi
Starting from known results, due to Y. Tian in [Ti; 00], referring to the real matrix representations of the real quaternions, in this paper we will investigate the left and right…
On Generalized Fibonacci Quaternions and Fibonacci-Narayana Quaternions
Cristina Flaut, Vitalii Shpakivskyi
In this paper, we investigate some properties of generalized Fibonacci quaternions and Fibonacci-Narayana quaternions.
Some identities in algebras obtained by the Cayley-Dickson process
Cristina Flaut, Vitalii Shpakivskyi
In this paper we will prove that the Hall identity is true in all algebras obtained by the Cayley-Dickson process and, in some conditions, the converse is also true.