Results 21 to 30 of about 31,418 (283)
Unrestricted Tribonacci and Tribonacci–Lucas quaternions [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 We define a generalization of Tribonacci and Tribonacci–Lucas quaternions with arbitrary Tribonacci numbers and Tribonacci–Lucas numbers coefficients, respectively. We get generating functions and Binet's formulas for these quaternions.
Gonca Kızılaslan, Leyla Karabulut
doaj +1 more source
Split Quaternions and Particles in (2+1)-Space [PDF]
, 2014 It is known that quaternions represent rotations in 3D Euclidean and Minkowski spaces. However, product by a quaternion gives rotation in two independent planes at once and to obtain single-plane rotations one has to apply by half-angle quaternions twice
Gogberashvili, Merab
core +3 more sources
On split Narayana and Narayana-Lucas hybrid quaternions [PDF]
Notes on Number Theory and Discrete MathematicsIn this paper, we introduce the novel concepts of split Narayana quaternions and split Narayana-Lucas quaternions within the innovative framework of hybrid numbers.
Pankaj Kumar, Shilpa Kapoor
doaj +1 more source
On complex gaussian jacobsthal and jacobsthal-lucas quaternions
Cumhuriyet Science Journal, 2020 The main aim of this work is to introduce the complex Gaussian Jacobsthal and Jacobsthal-Lucas quaternions and investigate their structures. We obtain the recurrence relations, Binet formulas and generating functions for these quaternions.
Hasan Arslan
doaj +1 more source
The vector algebra war: a historical perspective [PDF]
, 2016 There are a wide variety of different vector formalisms currently utilized in engineering and physics. For example, Gibbs' three-vectors, Minkowski four-vectors, complex spinors in quantum mechanics, quaternions used to describe rigid body rotations and ...
Abbott, Derek +3 more
core +2 more sources
Construction of dual-generalized complex Fibonacci and Lucas quaternions
Karpatsʹkì Matematičnì Publìkacìï, 2022 The aim of this paper is to construct dual-generalized complex Fibonacci and Lucas quaternions. It examines the properties both as dual-generalized complex number and as quaternion. Additionally, general recurrence relations, Binet's formulas, Tagiuri's (
G.Y. Şentürk, N. Gürses, S. Yüce
doaj +1 more source
Advances in Mechanical Engineering, 2017 The robust parameter estimation of unknown space objects is essential to the on-orbit servicing missions. Based on the adaptive filtering techniques along with the dual quaternions modeling methods for pose estimation, this article proposes a dual vector
Xianghao Hou +3 more
doaj +1 more source
Communications in Advanced Mathematical Sciences, 2020 In this paper, dual Jacobsthal quaternions were defined. Also, the relations between dual Jacobsthal quaternions which connected with Jacobsthal and Jacobsthal-Lucas numbers were investigated. Furthermore, Binet's formula, Honsberger identity, D'ocagne'
Fügen Torunbalcı Aydın
doaj +1 more source
On Recursive Hyperbolic Fibonacci Quaternions
Communications in Advanced Mathematical Sciences, 2021 Many quaternions with the coefficients selected from special integer sequences such as Fibonacci and Lucas sequences have been investigated by a great number of researchers.
Ahmet Daşdemir
doaj +1 more source
C. S. Peirce and the Square Root of Minus One: Quaternions and a Complex Approach to Classes of Signs and Categorical Degeneration [PDF]
, 2017 The beginning for C. S. Peirce was the reduction of the traditional categories in a list composed of a fundamental triad: quality, respect and representation.
Venancio, Rafael Duarte Oliveira
core +1 more source