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A Unified Approach: Split Quaternions with Quaternion Coefficients and Quaternions with Dual Coefficients [PDF]
Mathematics, 2020 This paper aims to present, in a unified manner, results which are valid on both split quaternions with quaternion coefficients and quaternions with dual coefficients, simultaneously, calling the attention to the main differences between these two ...
Emel Karaca +2 more
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(2 + 1)-Maxwell Equations in Split Quaternions
Physics, 2022 The properties of spinors and vectors in (2 + 2) space of split quaternions are studied. Quaternionic representation of rotations naturally separates two SO(2,1) subgroups of the full group of symmetry of the norms of split quaternions, SO(2,2).
Merab Gogberashvili
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On split quaternion equivalents for Quaternaccis, shortly Split Quaternaccis [PDF]
Open Mathematics, 2021 In this paper, we introduce generalizations of Quaternacci sequences (Quaternaccis), called Split Quaternacci sequences, which arose on a base of split quaternion algebras.
Bajorska-Harapińska Beata +3 more
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Quadratic Equation in Split Quaternions
Axioms, 2022 Split quaternions are noncommutative and contain nontrivial zero divisors. Generally speaking, it is difficult to solve equations in such an algebra. In this paper, by using the roots of any split quaternions and two real nonlinear systems, we derive ...
Wensheng Cao
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Operators induced by certain hypercomplex systems [PDF]
Opuscula Mathematica, 2023 In this paper, we consider a family \(\{ \mathbb{H}_{t}\}_{t\in\mathbb{R}}\) of rings of hypercomplex numbers, indexed by the real numbers, which contain both the quaternions and the split-quaternions. We consider natural Hilbert-space representations \(\
Daniel Alpay, Ilwoo Cho
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On the Split Mersenne and Mersenne-Lucas Hybrid Quaternions
مجلة بغداد للعلوم, 2023 In this communication, introduce the split Mersenne and Mersenne-Lucas hybrid quaternions, also obtaining generating functions and Binet formulas for these hybrid quaternions and investigating some properties among them.
B. Malini Devi, S. Devibala
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Algebraic Techniques for Canonical Forms and Applications in Split Quaternionic Mechanics
Journal of Mathematics, 2023 The algebra of split quaternions is a recently increasing topic in the study of theory and numerical computation in split quaternionic mechanics. This paper, by means of a real representation of a split quaternion matrix, studies the problem of canonical
Tongsong Jiang +4 more
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IEEE Access, 2023 The processing of color images is of great interest, because the human perception of color is a very complex process, still not well understood. In this article, firstly the authors present an analysis of the well-known mathematical methods used to model
Eduardo Bayro-Corrochano +2 more
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Existence of Split Property in Quaternion Algebra Over Composite of Quadratic Fields
Cauchy: Jurnal Matematika Murni dan Aplikasi, 2023 Quaternions are extensions of complex numbers that are four-dimensional objects. Quaternion consists of one real number and three complex numbers, commonly denoted by the standard vectors and .
Muhammad Faldiyan +2 more
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On split Narayana and Narayana-Lucas hybrid quaternions [PDF]
Notes on Number Theory and Discrete MathematicsIn this paper, we introduce the novel concepts of split Narayana quaternions and split Narayana-Lucas quaternions within the innovative framework of hybrid numbers.
Pankaj Kumar, Shilpa Kapoor
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