Results 11 to 20 of about 6,678 (298)

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   +4 more sources

On Pell Quaternions and Pell-Lucas Quaternions

Advances in Applied Clifford Algebras, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cimen, Cennet Bolat, Ipek, Ahmet
openaire   +5 more sources

The Neutrosophic Quaternions Numbers [PDF]

Neutrosophic Sets and Systems
This article aims to study the neutrosophic quaternion numbers, where we defined the neutrosophic quaternions numbers and the two equal neutrosophic quaternions numbers, also, the neutrosophic quaternions numbers algebra were introduced by studying ...
Yaser Ahmad Alhasan, Basel Hamdo Alarnous, Iqbal Ahmed Musa   +2 more
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

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   +2 more sources

On Balancing and Lucas-balancing Quaternions [PDF]

, 2021
summary:The aim of this article is to investigate two new classes of quaternions, namely, balancing and Lucas-balancing quaternions that are based on balancing and Lucas-balancing numbers, respectively. Further, some identities including Binet's formulas,
Patel, Bijan Kumar, Ray, Prasanta Kumar
core   +2 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   +5 more sources

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
openaire   +3 more sources

Quaternion Backpropagation

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
openaire   +2 more sources

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
openaire   +2 more sources