Results 1 to 10 of about 42,052 (333)

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
doaj   +2 more sources

Pauli–Leonardo quaternions [PDF]

Notes on Number Theory and Discrete Mathematics, 2023
In this study, we define Pauli–Leonardo quaternions by taking the coefficients of the Pauli quaternions as Leonardo numbers. We give the recurrence relation, Binet formula, generating function, exponential generating function, some special equalities ...
Zehra İşbilir, Mahmut Akyiğit, Murat Tosun   +2 more
doaj   +1 more source

Hybrid Quaternions of Leonardo

Trends in Computational and Applied Mathematics, 2022
In this article, we intend to investigate the Leonardo sequence presenting the hybrid Leonardo quaternions. To explore Hybrid Quaternions of Leonardo, the priori, sequence of Leonardo, quaternions and hybrid numbers were presented.
M. C. S. Mangueira, F. R. V. Alves, P. M. M. C. Catarino   +2 more
doaj   +1 more source

Pauli Gaussian Fibonacci and Pauli Gaussian Lucas Quaternions

Mathematics, 2022
We have investigated new Pauli Fibonacci and Pauli Lucas quaternions by taking the components of these quaternions as Gaussian Fibonacci and Gaussian Lucas numbers, respectively. We have calculated some basic identities for these quaternions.
Ayşe Zeynep Azak
doaj   +1 more source

On Dual Quaternions with $k-$Generalized Leonardo Components

Journal of New Theory, 2023
In this paper, we define a one-parameter generalization of Leonardo dual quaternions, namely $k-$generalized Leonardo-like dual quaternions. We introduce the properties of $k$-generalized Leonardo-like dual quaternions, including relations with Leonardo,
Gülsüm Yeliz Saçlı, Çiğdem Zeynep Yılmaz   +1 more
doaj   +1 more source

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, Gülsüm Yeliz Şentürk, Salim Yüce   +2 more
doaj   +1 more source

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, Piskur Paweł, Orłowski Mateusz   +2 more
doaj   +1 more source

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
doaj   +1 more source

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, Can Kızılateş, Wei-Shih Du   +2 more
doaj   +1 more source

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
doaj   +1 more source