16 citations · 31 across the 6 of their papers we have counts for
9 papers
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 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…