16 citations · 43 across the 18 of their papers we have counts for
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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.