Results 11 to 20 of about 9,075 (305)

On Balancing Quaternions and Lucas-Balancing Quaternions [PDF]

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   +3 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   +3 more sources

On Pell Quaternions and Pell-Lucas Quaternions [PDF]

Advances in Applied Clifford Algebras, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cimen, Cennet Bolat, Ipek, Ahmet
openaire   +6 more sources

On the Lichtenberg hybrid quaternions [PDF]

Mathematica Moravica
In this study, we define Lichtenberg hybrid quaternions. We give the Binet's formula, the generating functions, exponential generating functions and sum formulas of these quaternions. We find some relations between Jacobsthal hybrid quaternions, Mersenne
Morales Gamaliel
doaj   +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.
Zhang, Fuzhen, Fuzhen Zhang
openaire   +4 more sources

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   +6 more sources

A Unified Approach: Split Quaternions with Quaternion Coefficients and Quaternions with Dual Coefficients

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, Fatih Yılmaz, Mustafa Çalışkan   +2 more
doaj   +2 more sources

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

Obtaining triplet from quaternions [PDF]

, 2021
In this study, we obtain triplets from quaternions. First, we obtain triplets from real quaternions. Then, as an application of this, we obtain dual triplets from the dual quaternions.
Atasoy, Ali, Yaylı, Yusuf
core   +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