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Split Quaternions and Particles in (2+1)-Space [PDF]
, 2014 It is known that quaternions represent rotations in 3D Euclidean and Minkowski spaces. However, product by a quaternion gives rotation in two independent planes at once and to obtain single-plane rotations one has to apply by half-angle quaternions twice
Gogberashvili, Merab
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Hamiltonian Mechanical System with Split Quaternions [PDF]
Universal Journal of Applied Mathematics, 2018 In this article, firstly we study about geometrical applications of split quaternions. Then, we obtain Hamitonian mechanical systems with Split quaternions. Quaternionic and Coquaternionic (split analoque of quaternions) extensions of Hamiltonian mechanics are introduced and are shown as offer a unifying framework for quantum mechanics.
Yormaz, Cansel +2 more
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The Regularity of Functions on Dual Split Quaternions in Clifford Analysis
Abstract and Applied Analysis, 2014 This paper shows some properties of dual split quaternion numbers and expressions of power series in dual split quaternions and provides differential operators in dual split quaternions and a dual split regular function on Ω⊂ℂ2×ℂ2 that has a dual split ...
Ji Eun Kim, Kwang Ho Shon
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Chirality in a quaternionic representation of the genetic code [PDF]
, 2015 A quaternionic representation of the genetic code, previously reported by the authors, is updated in order to incorporate chirality of nucleotide bases and amino acids.
Carlevaro, C. Manuel +2 more
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Quaternionic representation of the genetic code [PDF]
, 2015 A heuristic diagram of the evolution of the standard genetic code is presented. It incorporates, in a way that resembles the energy levels of an atom, the physical notion of broken symmetry and it is consistent with original ideas by Crick on the origin ...
Carlevaro, C. Manuel +2 more
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Some properties of complex quaternion and complex split quaternion matrices [PDF]
Miskolc Mathematical Notes, 2019 The aim of this study is to investigate some properties of complex quaternion and complex split quaternion matrices. To verify this, we use 2x2 complex matrix representation of these quaternions. Moreover, we present a method to find the determinant of complex quaternion and complex split quaternion matrices.
Alagoz, Y., Ozyurt, G.
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ON BÄCKLUND TRANSFORMATIONS WITH SPLIT QUATERNIONS [PDF]
Facta Universitatis, Series: Mathematics and Informatics, 2020 The present paper deals with the introduction of Bäcklund Transformations with split quaternions in Minkowski space. Firstly, we tersely summarized the basic concepts of split quaternion theory and Bishop Frames of non-null curves in Minkowski space.
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On split r-Jacobsthal quaternions
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica, 2020 In this paper we introduce a one-parameter generalization of the split Jacobsthal quaternions, namely the split r-Jacobsthal quaternions. We give a generating function, Binet formula for these numbers. Moreover, we obtain some identities, among others Catalan, Cassini identities and convolution identity for the split r-Jacobsthal quaternions.
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Splitting of differential quaternion algebras
Journal of Algebra, 2023 We study differential splitting fields of quaternion algebras with derivations. A quaternion algebra over a field $k$ is always split by a quadratic extension of $k$. However, a differential quaternion algebra need not be split over any algebraic extension of $k$.
Parul Gupta +2 more
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Journal of Applied Mathematics and Physics, 2019 This paper aims to present, in a unified manner, algebraic techniques for linear equations which are valid on both the algebras of quaternions and split quaternions. This paper, introduces a concept of v-quaternion, studies the problem of v-quaternionic linear equations by means of a complex representation and a real representation of v-quaternion ...
Gang Wang +3 more
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