16 citations · 43 across the 18 of their papers we have counts for
23 papers
Hypercomplex Method for Solving Nonlinear PDEs
Vitalii Shpakivskyi
A hypercomplex method for constructing solutions of a class of nonlinear partial differential equations is developed. A family of two-dimensional commutative associative algebras i…
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…
Representation of Quaternionic -hyperholomorphic Functions
Tetiana Kuzmenko, Vitalii Shpakivskyi
In the algebra of complex quaternions we consider for the first time left- and right--hyperholomorphic functions. We justify the transition in left- and right-$ψ…
Hypercomplex method for solving linear PDEs with constant coefficients
Vitalii Shpakivskyi
In this paper, we propose a procedure for constructing an infinite number of families of solutions of given linear differential equations with partial derivatives with constant coe…
On monogenic functions defined in different commutative algebras
Vitalii Shpakivskyi
A correspondence between a monogenic function in an arbitrary finite-dimensional commutative associative algebra and a finite set of monogenic functions in a special commutative as…
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…
On monogenic mappings of the quaternionic variables
V. S. Shpakivskyi, T. S. Kuzmenko
In the paper [1] we consider a new class, so-called, -monogenic (differentiable in the sense of Gateaux) quaternionic mappings. In the present paper we introduce quaternionic $H…
Integral theorems for monogenic functions in commutative algebras
V. S. Shpakivskyi
Let be an arbitrary -dimensional commutative associative algebra over the field of complex numbers with idempotents. Let with $2\leq…
Monogenic functions in finite-dimensional commutative associative algebras
V. S. Shpakivskyi
Let be an arbitrary -dimensional commutative associative algebra over the field of complex numbers with idempotents. Let with $2\leq…
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…
Curvilinear integral theorems for monogenic functions in commutative associative algebras
Vitalii Shpakivskyi
We consider an arbitrary finite-dimensional commutative associative algebra, , with unit over the field of complex number with idempotents. Let …
Integral theorems for the quaternionic G-monogenic mappings
V. S. Shpakivskyi, T. S. Kuzmenko
In the paper [1] considered a new class of quaternionic mappings, so-called -monogenic mappings. In this paper we prove analogues of classical integral theorems of the holomorph…
On one class of quaternionic mappings
V. S. Shpakivskyi, T. S. Kuzmenko
We consider a new class of quaternionic mappings, associated with the spatial partial differential equations. We describe all mappings from this class using four analytic functions…
Constructive description of monogenic functions in a finite-dimensional commutative associative algebra
Vitalii Shpakivskyi
Let be an arbitrary -dimensional commutative associative algebra over the field of complex numbers with idempotents. Let be elements of $\ma…
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.
Holomorphic functions in generalized Cayley-Dickson algebras
Cristina Flaut, Vitalii Shpakivskyi
In this paper we investigated holomorphic functions (belonging to the kernel of the Dirac operator) in Cayley-Dickson algebras. For this purpose, we study the structure of Cayley-D…
Cauchy theorem for a surface integral in commutative algebras
Sergiy A. Plaksa, Vitalii S. Shpakivskyi
We prove an analogue of the Cauchy integral theorem for hyperholomorphic functions given in three-dimensional domains with non piece-smooth boundaries and taking values in an arbit…
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.