Related papers: A Survey on Dual-Quaternions
An involution is usually defined as a mapping that is its own inverse. In this paper, we study quaternion involutions that have the additional properties of distribution over addition and multiplication. We review formal axioms for such…
Quaternion optimization has attracted significant interest due to its broad applications, including color face recognition, video compression, and signal processing. Despite the growing literature on quadratic and matrix quaternion…
In this study, we introduce the concept of commutative quaternions and commutative quaternion matrices. Firstly, we give some properties of commutative quaternions and their Hamilton matrices. After that we investigate commutative…
The last two decades have seen an explosive growth in the theory and practice of both quantum computing and machine learning. Modern machine learning systems process huge volumes of data and demand massive computational power. As silicon…
This paper proposes a robust dual-quaternion based H-infinity task-space kinematic controller for robot manipulators. To address the manipulator liability to modeling errors, uncertainties, exogenous disturbances, and their influence upon…
In this work, we use the concept of quaternion time and demonstrate that it can be applied for description of four-dimensional space-time intervals. We demonstrate that the quaternion time interval together with the finite speed of light…
Starting with the generalized potentials, currents, field tensors and electromagnetic vector fields of dyons as the complex complex quantities with real and imaginary counter parts as electric and magnetic constituents, we have established…
This paper explores the potential of Lagrangian duality for learning applications that feature complex constraints. Such constraints arise in many science and engineering domains, where the task amounts to learning optimization problems…
Quantum computing is rapidly emerging as a promising technology for solving complex optimization problems that arise in various engineering fields. Therefore, it holds significant promise to transform the computational foundations of power…
The Two-Measure theory (TMT) has been developing since 1998 and has yielded a number of highly interesting results, including those not realized in traditional field theory models. The most important advantage of TMT as an alternative…
Computational imaging has been playing a vital role in the development of natural sciences. Advances in sensory, information, and computer technologies have further extended the scope of influence of imaging, making digital images an…
The paper aims to extend major equations in the electromagnetic and gravitational theories from the flat space into the complex octonion curved space. Maxwell applied simultaneously the quaternion analysis and vector terminology to describe…
Over the past century, a correlation has been an essential mathematical technique utilized in engineering sciences, including practically every signal/image processing field. This paper describes an effective method of calculating the…
Duality transformations are very important in both classical and quantum physics. They allow one to relate two seemingly different formulations of the same physical realm through clever mathematical manipulations, and offer numerous…
Quantum Computing (QC) claims to improve the efficiency of solving complex problems, compared to classical computing. When QC is integrated with Machine Learning (ML), it creates a Quantum Machine Learning (QML) system. This paper aims to…
This article has been written for an educational magazine whose target audience consists of students and teachers of mathematics in universities, colleges and schools. It concerns a notion of duality between rectangles. A proof is given…
Mathematical understanding is built in many ways. Among these, illustration has been a companion and tool for research for as long as research has taken place. We use the term illustration to encompass any way one might bring a mathematical…
The present paper is based upon equations obtained in an earlier paper by the author devoted to a new formulation of quantum electrodynamics. The equations describe the structure of the electron as well as its motion in external fields,…
Quantum computing (QC) has experienced rapid growth in recent years with the advent of robust programming environments, readily accessible software simulators and cloud-based QC hardware platforms, and growing interest in learning how to…
Quaternions often appear in wide areas of applied science and engineering such as wireless communications systems, mechanics, etc. It is known that are two types of non-isomorphic generalized quaternion algebras, namely: the algebra of…