Results 31 to 40 of about 1,046 (258)
THE CORRESPONDING CAUCHY - RIEMANN SYSTEM FOR DUAL QUATERNION-VALUED FUNCTIONS
Проблемы анализа, 2018 This paper provides differential operators in dual quaternions and represents the regularity of dual quaternionvalued functions using the dual Cauchy - Riemann system in dual quaternions.
Kim J.E.
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Robust Dual-Color Watermarking Based on Quaternion Singular Value Decomposition
IEEE Access, 2020 This paper proposes a robust dual-color watermarking based on quaternion singular value decomposition (QSVD), which can embed large payloads into color images with low distortion, and can obtain strong robustness to process color image in a holistic ...
Yong Chen +3 more
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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
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Functional Calculus for Dual Quaternions
Advances in Applied Clifford Algebras, 2023 We give a formula for $f(η)$, where $f :\mathbb C \to \mathbb C$ is a continuously differentiable function satisfying $f(\bar z) = \overline{f(z)}$, and $η$ is a dual quaternion. Note this formula is straightforward or well known if $η$ is merely a dual number or a quaternion.
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A dual quaternion algorithm of the Helmert transformation problem
Earth, Planets and Space, 2018 Rigid transformation including rotation and translation can be elegantly represented by a unit dual quaternion. Thus, a non-differential model of the Helmert transformation (3D seven-parameter similarity transformation) is established based on unit dual ...
Huaien Zeng +3 more
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A new proof of the generalized Hamiltonian–Real calculus [PDF]
Royal Society Open Science, 2016 The recently introduced generalized Hamiltonian–Real (GHR) calculus comprises, for the first time, the product and chain rules that makes it a powerful tool for quaternion-based optimization and adaptive signal processing.
Dongpo Xu, Hua Gao, Danilo P. Mandic
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On Rayleigh Quotient Iteration for the Dual Quaternion Hermitian Eigenvalue Problem
MathematicsThe application of eigenvalue theory to dual quaternion Hermitian matrices holds significance in the realm of multi-agent formation control. In this paper, we study the use of Rayleigh quotient iteration (RQI) for solving the right eigenpairs of dual ...
Shan-Qi Duan +2 more
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Dual-Quaternion Fourier Transform
CoRR, 2023 Fourier transform (FT) plays a crucial role in a broad range of applications, from enhancement, restoration and analysis through to security, compression and manipulation. The Fourier transform (FT) is a process that converts a function into a form that describes the frequencies.
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On tertions and dual numbers [PDF]
Notes on Number Theory and Discrete MathematicsIn a previous author's paper [1], the mathematical object called "tertion" was discussed. Some operations over tertions were introduced and their properties were studied. There, it was showed that the complex numbers and quaternions can be represented by
Krassimir T. Atanassov
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IEEE Access, 2020 This paper aims to construct signal sets from quotient rings of the quaternion over a real number field associated with the arithmetic Fuchsian group Γ4g, where g is the genus of the associated surface.
Catia Regina de Oliveira Quilles Queiroz +1 more
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