Results 41 to 50 of about 1,636 (288)
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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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.
openaire +2 more sources
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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Dual Attitude Representations and Kinematics for Six-Degree-of-Freedom Spacecraft Dynamics
IEEE Access, 2023 This paper focuses on the development of three newly formed representations of dual attitude and their respective kinematics equations - Dual Classical Rodrigues Parameters, Dual Modified Rodrigues Parameters, Dual Principal Axis and Principal Angle ...
Kyl S. Stanfield, Ahmad Bani Younes
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Immersion and Invariance Adaptive Control for Spacecraft Pose Tracking via Dual Quaternions
Complexity, 2021 This paper addresses the simultaneous attitude and position tracking of a target spacecraft in the presence of general unknown bounded disturbances in the framework of dual quaternions, which provides a concise and integrated description of the coupled ...
Xiaoping Shi, Xuan Peng, Yupeng Gong
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A Novel Distribution for Representation of 6D Pose Uncertainty
Micromachines, 2022 The 6D Pose estimation is a crux in many applications, such as visual perception, autonomous navigation, and spacecraft motion. For robotic grasping, the cluttered and self-occlusion scenarios bring new challenges to the this field.
Lei Zhang, Huiliang Shang, Yandan Lin
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(R2050) Dual Quaternion Matrices and MATLAB Applications
, 2023 There are many studies in the literature on real quaternions and real quaternion matrices. There are few studies in the literature on dual quaternions. Definitions of the matrices of dual quaternions used in this study will be given.
Nalbant, Kemal Gökhan, Yüce, Salim
core
Pediatric Blood &Cancer, EarlyView.ABSTRACT Background Pediatric sarcomas are a heterogeneous group of tumors that contribute disproportionately to cancer mortality in children. Although congenital anomalies are among the strongest known risk factors for childhood cancer, the risk of specific sarcoma subtypes among affected individuals has not yet been thoroughly evaluated. Procedure We
Russ Wolters +17 more
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The Regularity of Functions on Dual Split Quaternions in Clifford Analysis
Abstract and Applied Analysis, 2014 This paper shows some properties of dual split quaternion numbers and expressions of power series in dual split quaternions and provides differential operators in dual split quaternions and a dual split regular function on Ω⊂ℂ2×ℂ2 that has a dual split ...
Ji Eun Kim, Kwang Ho Shon
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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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