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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
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On the Bicomplex Generalized Tribonacci Quaternions
Mathematics, 2019 In this paper, we introduce the bicomplex generalized tribonacci quaternions. Furthermore, Binet’s formula, generating functions, and the summation formula for this type of quaternion are given. Lastly, as an application, we present the determinant
Can Kızılateş +2 more
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Quaternions in Signal and Image Processing: A comprehensive and objective overview
IEEE Signal Processing Magazine, 2023 Quaternions are still largely misunderstood and often considered an “exotic” signal representation without much practical utility despite the fact that they have been around the signal and image processing community for more than 30 years now.
S. Miron +4 more
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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 +2 more
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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
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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 +2 more
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Generalized commutative quaternions of the Fibonacci type
Boletín de la Sociedad Matematica Mexicana, 2021 Quaternions are a four-dimensional hypercomplex number system discovered by Hamilton in 1843 and next intensively applied in mathematics, modern physics, computer graphics and other fields.
A. Szynal-Liana, I. Włoch
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QuatRE: Relation-Aware Quaternions for Knowledge Graph Embeddings [PDF]
The Web Conference, 2020 We propose a simple yet effective embedding model to learn quaternion embeddings for entities and relations in knowledge graphs. Our model aims to enhance correlations between head and tail entities given a relation within the Quaternion space with ...
D. Q. Nguyen +3 more
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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 +1 more
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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 +2 more
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