Results 21 to 30 of about 8,815 (298)
Dual quaternions and dual quaternionic curves [PDF]
Filomat, 2019 After a brief review of the different types of quaternions, we develop a new perspective for dual quaternions with dividing two parts. Due to this new perspective, we will define the isotropic and nonisotropic dual quaternions. Then we will also give the basic algebraic concepts about the dual quaternions. Moreover, we define isotropic dual
Dagdeviren, Ali, Yuce, Salim
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Investigating generalized quaternions with dual-generalized complex numbers [PDF]
Mathematica Bohemica, 2023 We aim to introduce generalized quaternions with dual-generalized complex number coefficients for all real values $\alpha$, $\beta$ and $\mathfrak{p}$.
Nurten Gürses +2 more
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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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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.
Alon, Gil, Paran, Elad
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Dual Quaternions for the Kinematic Description of a Fish–Like Propulsion System
International Journal of Applied Mathematics and Computer Science, 2023 This study discusses the use of quaternions and dual quaternions in the description of artificial fish kinematics. The investigation offered here illustrates quaternion and dual quaternion algebra, as well as its implementation in the software chosen ...
Kitowski Zygmunt +2 more
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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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CoRR, 2022 Quaternion valued neural networks experienced rising popularity and interest from researchers in the last years, whereby the derivatives with respect to quaternions needed for optimization are calculated as the sum of the partial derivatives with respect to the real and imaginary parts.
Johannes Pöppelbaum, Andreas Schwung
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New Properties and Identities for Fibonacci Finite Operator Quaternions
Mathematics, 2022 In this paper, with the help of the finite operators and Fibonacci numbers, we define a new family of quaternions whose components are the Fibonacci finite operator numbers. We also provide some properties of these types of quaternions.
Nazlıhan Terzioğlu +2 more
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Quaternions: A Mathematica Package for Quaternionic Analysis [PDF]
, 2011 This paper describes new issues of theMathematica standard package Quaternions for implementing Hamilton's Quaternion Algebra. This work attempts to endow the original package with the ability to perform operations on symbolic expressions involving quaternion-valued functions.
M. Irene Falcão, Fernando Miranda
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Sextonians and the magic square [PDF]
, 2006 Associated to any complex simple Lie algebra is a non-reductive complex Lie algebra which we call the intermediate Lie algebra. We propose that these algebras can be included in both the magic square and the magic triangle to give an additional row and ...
BRUCE W. WESTBURY, Westbury, Bruce
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