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Inequalities Pertaining to Quaternion Ambiguity Function
The quaternion ambiguity function is an expansion of the standard ambiguity function using quaternion algebra. Various properties such as linearity,...
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Supersymmetry breaking in quaternion space
Kee** in view the advantages of quaternion, an attempt is made to explain supersymmetry breaking in the interacting field in terms of quaternion...
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Exploring Quaternion Neural Network Loss Surfaces
This paper explores the superior performance of quaternion multi-layer perceptron (QMLP) neural networks over real-valued multi-layer perceptron...
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Kinematic equations of Lorentzian magnetic flux tubes based on split quaternion algebra
The aim of the paper is to present a new geometric viewpoint for magnetic flux tubes (MFTs) in the three-dimensional Lorentzian space through split...
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On the Quaternion Transformation and Field Equations in Curved Space-Time
In this paper, we use four-dimensional quaternionic algebra to describe space-time geodesics in curvature form. The transformation relations of a...
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Short Time Quaternion Quadratic Phase Fourier Transform and Its Uncertainty Principles
In this paper, we extend the quadratic phase Fourier transform of a complex valued functions to that of the quaternion-valued functions of two...
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Invariant measures on p-adic Lie groups: the p-adic quaternion algebra and the Haar integral on the p-adic rotation groups
We provide a general expression of the Haar measure—that is, the essentially unique translation-invariant measure—on a p -adic Lie group. We then...
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Some Uncertainty Principles for the Right-Sided Multivariate Continuous Quaternion Wavelet Transform
For the right-sided multivariate continuous quaternion wavelet transform (CQWT), we analyse the concentration of this transform on sets of finite...
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Optimizing Multilayer Perceptrons to Approximate Nonlinear Quaternion Functions
In this contribution, a novel approach to optimize multilayer perceptron artificial neural networks (MLP-ANN) devoted to approximate quaternion...
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Quaternion Regularization of Singularities of Astrodynamics Models Generated by Gravitational Forces (Review)
AbstractThe article presents an analytical review of works devoted to the quaternion regularization of the singularities of differential equations of...
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Least-Squares Solutions of Generalized Sylvester-Type Quaternion Matrix Equations
This paper focuses on finding solutions of generalized Sylvester-type matrix equations over the quaternion skew-field. We express the general...
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Quaternion supersymmetric quantum mechanics and SWKB approximation
A theory of quaternionic supersymmetric quantum mechanics has been developed in terms of quaternion supercharges, superpartner Hamiltonian and energy...
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A Generalised Quaternion and Clifford Algebra Based Mathematical Methodology to Effect Multi-stage Reassembling Transformations in Parallel Robots
A robotic manipulator is a networked assemblage of kinematic pairs, mobile platform(s) and/or tool(s) that generate motion and forces at its...
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Jackson Theorems for the Quaternion Linear Canonical transform
In this paper, we establish Bernstein inequality, Jackson’s direct and inverse theorems for quaternion linear canonical transform using the functions...
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Quaternion Quantum Neural Network for Classification
We propose the quaternionic quantum neural network (QQNN) for pattern recognition based on the formulation of quaternionic qubits and the...
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Wavelet Transform of Dini Lipschitz Functions on the Quaternion Algebra
In this present work, we generalize Titchmarsh’s theorem for the complex- or hypercomplex-valued functions. Firstly, we examine the order of...
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Decomposition for a Quaternion Tensor Triplet with Applications
In this paper, we investigate and discuss in detail the structure and properties of product singular value decomposition for a quaternion tensor...
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Linear Canonical Wavelet Transform in Quaternion Domains
The well-known quaternion algebra is a four-dimensional natural extension of the field of complex numbers and plays a significant role in various...