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On Balancing Quaternions and Lucas-Balancing Quaternions
Discussiones Mathematicae - General Algebra and Applications, 2021 In this paper we define and study balancing quaternions and Lucas-balancing quaternions. We give the generating functions, matrix generators and Binet formulas for these numbers. Moreover, the well-known properties e.g. Catalan, d’ Ocagne identities have
Bród Dorota
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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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Nature, 1893 PROF. MACFARLANE claims that his “fundamental rules for vectors are based on physical considerations, the principal one of which is that the square of a vector is essentially positive.” His proof is virtually this:—The expression for the kinetic energy (½ mv2) is an essentially positive quantity. It contains one factor ½m evidently positive.
A. Lodge
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On the arithmetic of quaternions [PDF]
Transactions of the American Mathematical Society, 1940 Gordon Pall
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The Discussion on Quaternions [PDF]
Nature, 1893 I HAVE followed with much interest the discussion on quaternions which has with more or less intermission been going on in NATURE for a long time.
Robert S. Ball
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A quaternionic Nullstellensatz [PDF]
Journal of Pure and Applied Algebra, 2021 We prove a Nullstellensatz for the ring of polynomial functions in n non-commuting variables over Hamilton's ring of real quaternions. We also characterize the generalized polynomial identities in n variables which hold over the quaternions, and more generally, over any division algebra.
Elad Paran, Gil Alon
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Communications in Mathematical Physics, 1996 We present the simplest non-abelian version of Seiberg-Witten theory: Quaternionic monopoles. These monopoles are associated with Spin^h(4)-structures on 4-manifolds and form finite-dimensional moduli spaces. On a Kahler surface the quaternionic monopole equations decouple and lead to the projective vortex equation for holomorphic pairs.
Okonek, Christian, Teleman, Andrei
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Higher-Order Jacobsthal–Lucas Quaternions
Axioms, 2022 In this work, we define higher-order Jacobsthal–Lucas quaternions with the help of higher-order Jacobsthal–Lucas numbers. We examine some identities of higher-order Jacobsthal–Lucas quaternions. We introduce their basic definitions and properties.
Mine Uysal, Engin Özkan
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Application of slice regularity to functions of a dual-quaternionic variable
Karpatsʹkì Matematičnì Publìkacìï, 2021 In this paper, we present the algebraic properties of dual quaternions and define a slice regularity of a dual quaternionic function. Since the product of dual quaternions is non-commutative, slice regularity is derived in two ways.
Ji Eun Kim
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