Results 1 to 10 of about 31,418 (283)

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

On Generalized Fibonacci Quaternions and Fibonacci-Narayana Quaternions

Advances in Applied Clifford Algebras, 2013
In this paper, we investigate some properties of generalized Fibonacci quaternions and Fibonacci-Narayana quaternions.Comment: Accepted in Adv. in Appl.
Cristina Flaut, Vitalii S Shpakivskyi
exaly   +3 more sources

Quaternions and matrices of quaternions

Linear Algebra and Its Applications, 1997
The author gives a useful survey on quaternions and matrices of quaternions. He recalls standard facts going back to Rowan Hamilton as well as new results motivated by applications in physical theories. The main research problem presented in the paper is to extend the classical matrix theory from complex to the quaternion matrices.
Fuzhen Zhang
exaly   +4 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

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
openaire   +5 more sources

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

Quaternionic Integrability [PDF]

Journal of Nonlinear Mathematical Physics, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources